The association between higher education and approximate number system acuity.

PubMed

Lindskog, Marcus; Winman, Anders; Juslin, Peter

2014-01-01

Humans are equipped with an approximate number system (ANS) supporting non-symbolic numerosity representation. Studies indicate a relationship between ANS-precision (acuity) and math achievement. Whether the ANS is a prerequisite for learning mathematics or if mathematics education enhances the ANS remains an open question. We investigated the association between higher education and ANS acuity with university students majoring in subjects with varying amounts of mathematics (mathematics, business, and humanities), measured either early (First year) or late (Third year) in their studies. The results suggested a non-significant trend where students taking more mathematics had better ANS acuity and a significant improvement in ANS acuity as a function of study length that was mainly confined to the business students. The results provide partial support for the hypothesis that education in mathematics can enhance the ANS acuity.

Visual Form Perception Can Be a Cognitive Correlate of Lower Level Math Categories for Teenagers.

PubMed

Cui, Jiaxin; Zhang, Yiyun; Cheng, Dazhi; Li, Dawei; Zhou, Xinlin

2017-01-01

Numerous studies have assessed the cognitive correlates of performance in mathematics, but little research has been conducted to systematically examine the relations between visual perception as the starting point of visuospatial processing and typical mathematical performance. In the current study, we recruited 223 seventh graders to perform a visual form perception task (figure matching), numerosity comparison, digit comparison, exact computation, approximate computation, and curriculum-based mathematical achievement tests. Results showed that, after controlling for gender, age, and five general cognitive processes (choice reaction time, visual tracing, mental rotation, spatial working memory, and non-verbal matrices reasoning), visual form perception had unique contributions to numerosity comparison, digit comparison, and exact computation, but had no significant relation with approximate computation or curriculum-based mathematical achievement. These results suggest that visual form perception is an important independent cognitive correlate of lower level math categories, including the approximate number system, digit comparison, and exact computation.

The nonlinear relations of the approximate number system and mathematical language to early mathematics development.

PubMed

Purpura, David J; Logan, Jessica A R

2015-12-01

Both mathematical language and the approximate number system (ANS) have been identified as strong predictors of early mathematics performance. Yet, these relations may be different depending on a child's developmental level. The purpose of this study was to evaluate the relations between these domains across different levels of ability. Participants included 114 children who were assessed in the fall and spring of preschool on a battery of academic and cognitive tasks. Children were 3.12 to 5.26 years old (M = 4.18, SD = .58) and 53.6% were girls. Both mixed-effect and quantile regressions were conducted. The mixed-effect regressions indicated that mathematical language, but not the ANS, nor other cognitive domains, predicted mathematics performance. However, the quantile regression analyses revealed a more nuanced relation among domains. Specifically, it was found that mathematical language and the ANS predicted mathematical performance at different points on the ability continuum. These dual nonlinear relations indicate that different mechanisms may enhance mathematical acquisition dependent on children's developmental abilities. (c) 2015 APA, all rights reserved).

Factors Affecting Minority Students' College Readiness in Mathematics

ERIC Educational Resources Information Center

Houser, Latisha Cheree-Square; An, Shuhua

2015-01-01

This study examined how gender; race/ethnicity; language; socioeconomic status; California Standards Test (CST) scores in mathematics, science, and ELA; and California High School Exit Exam mathematics predict college-ready results on the Early Assessment Program (EAP) in mathematics in urban areas of southern California. Approximately 1,700 high…

A Guided Reinvention of Ring, Integral Domain, and Field

ERIC Educational Resources Information Center

Cook, John Paul

2012-01-01

Abstract algebra enjoys a prestigious position in mathematics and the undergraduate mathematics curriculum. A typical abstract algebra course aims to provide students with a glimpse into the elegance of mathematics by exposing them to structures that form its foundation--it arguably approximates the actual practice of mathematics better than any…

Generating the Patterns of Variation with GeoGebra: The Case of Polynomial Approximations

ERIC Educational Resources Information Center

Attorps, Iiris; Björk, Kjell; Radic, Mirko

2016-01-01

In this paper, we report a teaching experiment regarding the theory of polynomial approximations at the university mathematics teaching in Sweden. The experiment was designed by applying Variation theory and by using the free dynamic mathematics software GeoGebra. The aim of this study was to investigate if the technology-assisted teaching of…

Intuitive Sense of Number Correlates With Math Scores on College-Entrance Examination

PubMed Central

Libertus, Melissa E.; Odic, Darko; Halberda, Justin

2012-01-01

Many educated adults possess exact mathematical abilities in addition to an approximate, intuitive sense of number, often referred to as the Approximate Number System (ANS). Here we investigate the link between ANS precision and mathematics performance in adults by testing participants on an ANS-precision test and collecting their scores on the Scholastic Aptitude Test (SAT), a standardized college-entrance exam in the USA. In two correlational studies, we found that ANS precision correlated with SAT-Quantitative (i.e., mathematics) scores. This relationship remained robust even when controlling for SAT-Verbal scores, suggesting a small but specific relationship between our primitive sense for number and formal mathematical abilities. PMID:23098904

Regularization and Approximation of a Class of Evolution Problems in Applied Mathematics

DTIC Science & Technology

1991-01-01

8217 DT)IG AD-A242 223 FINAL REPORT Nov61991:ti -ll IN IImI 1OV1 Ml99 1 REGULARIZATION AND APPROXIMATION OF A-CLASS OF EVOLUTION -PROBLEMS IN APPLIED...The University of Texas at Austin Austin, TX 78712 91 10 30 050 FINAL REPORT "Regularization and Approximation of a Class of Evolution Problems in...micro-structured parabolic system. A mathematical analysis of the regularized equations-has been developed to support our approach. Supporting

What Is the Long-Run Impact of Learning Mathematics During Preschool?

PubMed

Watts, Tyler W; Duncan, Greg J; Clements, Douglas H; Sarama, Julie

2018-03-01

The current study estimated the causal links between preschool mathematics learning and late elementary school mathematics achievement using variation in treatment assignment to an early mathematics intervention as an instrument for preschool mathematics change. Estimates indicate (n = 410) that a standard deviation of intervention-produced change at age 4 is associated with a 0.24-SD gain in achievement in late elementary school. This impact is approximately half the size of the association produced by correlational models relating later achievement to preschool math change, and is approximately 35% smaller than the effect reported by highly controlled ordinary least squares (OLS) regression models (Claessens et al., 2009; Watts et al., ) using national data sets. Implications for developmental theory and practice are discussed. © 2017 The Authors. Child Development © 2017 Society for Research in Child Development, Inc.

Visual Form Perception Can Be a Cognitive Correlate of Lower Level Math Categories for Teenagers

PubMed Central

Cui, Jiaxin; Zhang, Yiyun; Cheng, Dazhi; Li, Dawei; Zhou, Xinlin

2017-01-01

Numerous studies have assessed the cognitive correlates of performance in mathematics, but little research has been conducted to systematically examine the relations between visual perception as the starting point of visuospatial processing and typical mathematical performance. In the current study, we recruited 223 seventh graders to perform a visual form perception task (figure matching), numerosity comparison, digit comparison, exact computation, approximate computation, and curriculum-based mathematical achievement tests. Results showed that, after controlling for gender, age, and five general cognitive processes (choice reaction time, visual tracing, mental rotation, spatial working memory, and non-verbal matrices reasoning), visual form perception had unique contributions to numerosity comparison, digit comparison, and exact computation, but had no significant relation with approximate computation or curriculum-based mathematical achievement. These results suggest that visual form perception is an important independent cognitive correlate of lower level math categories, including the approximate number system, digit comparison, and exact computation. PMID:28824513

Cosmological applications of Padé approximant

NASA Astrophysics Data System (ADS)

Wei, Hao; Yan, Xiao-Peng; Zhou, Ya-Nan

2014-01-01

As is well known, in mathematics, any function could be approximated by the Padé approximant. The Padé approximant is the best approximation of a function by a rational function of given order. In fact, the Padé approximant often gives better approximation of the function than truncating its Taylor series, and it may still work where the Taylor series does not converge. In the present work, we consider the Padé approximant in two issues. First, we obtain the analytical approximation of the luminosity distance for the flat XCDM model, and find that the relative error is fairly small. Second, we propose several parameterizations for the equation-of-state parameter (EoS) of dark energy based on the Padé approximant. They are well motivated from the mathematical and physical points of view. We confront these EoS parameterizations with the latest observational data, and find that they can work well. In these practices, we show that the Padé approximant could be an useful tool in cosmology, and it deserves further investigation.

Using Representations, Decomposition, and Approximations of Practices to Support Prospective Elementary Mathematics Teachers' Practice of Organizing Discussions

ERIC Educational Resources Information Center

Tyminski, Andrew M.; Zambak, V. Serbay; Drake, Corey; Land, Tonia J.

2014-01-01

This paper examines a series of instructional activities that provide prospective elementary teachers with an opportunity to engage in one of the more difficult practices to learn within mathematics teaching--organizing a mathematical discussion. Within a mathematics methods course, representations and decomposition of practice built from the Five…

Relation between Approximate Number System Acuity and Mathematical Achievement: The Influence of Fluency

PubMed Central

Wang, Li; Sun, Yuhua; Zhou, Xinlin

2016-01-01

Previous studies have observed inconsistent relations between the acuity of the Approximate Number System (ANS) and mathematical achievement. In this paper, we hypothesize that the relation between ANS acuity and mathematical achievement is influenced by fluency; that is, the mathematical achievement test covering a greater expanse of mathematical fluency may better reflect the relation between ANS acuity and mathematics skills. We explored three types of mathematical achievement tests utilized in this study: Subtraction, graded, and semester-final examination. The subtraction test was designed to measure the mathematical fluency. The graded test was more fluency-based than the semester-final examination, but both involved the same mathematical knowledge from the class curriculum. A total of 219 fifth graders from primary schools were asked to perform all three tests, then given a numerosity comparison task, a visual form perception task (figure matching), and a series of other tasks to assess general cognitive processes (mental rotation, non-verbal matrix reasoning, and choice reaction time). The findings were consistent with our expectations. The relation between ANS acuity and mathematical achievement was particularly clearly reflected in the participants’ performance on the visual form perception task, which supports the domain-general explanations for the underlying mechanisms of the relation between ANS acuity and math achievement. PMID:28066291

Mathematically Talented Males and Females and Achievement in the High School Sciences.

ERIC Educational Resources Information Center

Benbow, Camilla Persson; Minor, Lola L.

1986-01-01

Using data on approximately 2,000 students drawn from three talent searches conducted by the Study of Mathematically Precocious Youth, this study investigated the relationship of possible sex differences in science achievement to sex differences in mathematical reasoning ability. (BS)

Differences in the acuity of the Approximate Number System in adults: the effect of mathematical ability.

PubMed

Guillaume, Mathieu; Nys, Julie; Mussolin, Christophe; Content, Alain

2013-11-01

It is largely admitted that processing numerosity relies on an innate Approximate Number System (ANS), and recent research consistently observed a relationship between ANS acuity and mathematical ability in childhood. However, studies assessing this relationship in adults led to contradictory results. In this study, adults with different levels of mathematical expertise performed two tasks on the same pairs of dot collections, based either on numerosity comparison or on cumulative area comparison. Number of dots and cumulative area were congruent in half of the stimuli, and incongruent in the other half. The results showed that adults with higher mathematical ability obtained lower Weber fractions in the numerical condition than participants with lower mathematical ability. Further, adults with lower mathematical ability were more affected by the interference of the continuous dimension in the numerical comparison task, whereas conversely higher-expertise adults showed stronger interference of the numerical dimension in the continuous comparison task. Finally, ANS acuity correlated with arithmetic performance. Taken together, the data suggest that individual differences in ANS acuity subsist in adulthood, and that they are related to mathematical ability. © 2013.

Linking Research and Practice: The NCTM Research Agenda Conference Report

ERIC Educational Resources Information Center

Arbaugh, Fran; Herbel-Eisenmann, Beth; Ramirez, Nora; Knuth, Eric; Kranendonk, Henry; Quander, Judith Reed

2010-01-01

In August 2008, the National Council of Teachers of Mathematics (NCTM) brought together approximately 60 mathematics education researchers and practitioners for a 4-day working conference. During this working conference, the participants analyzed over 350 mathematics education practitioner-generated questions in seven areas: assessment,…

Mathematical formalisms based on approximated kinetic representations for modeling genetic and metabolic pathways.

PubMed

Alves, Rui; Vilaprinyo, Ester; Hernádez-Bermejo, Benito; Sorribas, Albert

2008-01-01

There is a renewed interest in obtaining a systemic understanding of metabolism, gene expression and signal transduction processes, driven by the recent research focus on Systems Biology. From a biotechnological point of view, such a systemic understanding of how a biological system is designed to work can facilitate the rational manipulation of specific pathways in different cell types to achieve specific goals. Due to the intrinsic complexity of biological systems, mathematical models are a central tool for understanding and predicting the integrative behavior of those systems. Particularly, models are essential for a rational development of biotechnological applications and in understanding system's design from an evolutionary point of view. Mathematical models can be obtained using many different strategies. In each case, their utility will depend upon the properties of the mathematical representation and on the possibility of obtaining meaningful parameters from available data. In practice, there are several issues at stake when one has to decide which mathematical model is more appropriate for the study of a given problem. First, one needs a model that can represent the aspects of the system one wishes to study. Second, one must choose a mathematical representation that allows an accurate analysis of the system with respect to different aspects of interest (for example, robustness of the system, dynamical behavior, optimization of the system with respect to some production goal, parameter value determination, etc). Third, before choosing between alternative and equally appropriate mathematical representations for the system, one should compare representations with respect to easiness of automation for model set-up, simulation, and analysis of results. Fourth, one should also consider how to facilitate model transference and re-usability by other researchers and for distinct purposes. Finally, one factor that is important for all four aspects is the regularity in the mathematical structure of the equations because it facilitates computational manipulation. This regularity is a mark of kinetic representations based on approximation theory. The use of approximation theory to derive mathematical representations with regular structure for modeling purposes has a long tradition in science. In most applied fields, such as engineering and physics, those approximations are often required to obtain practical solutions to complex problems. In this paper we review some of the more popular mathematical representations that have been derived using approximation theory and are used for modeling in molecular systems biology. We will focus on formalisms that are theoretically supported by the Taylor Theorem. These include the Power-law formalism, the recently proposed (log)linear and Lin-log formalisms as well as some closely related alternatives. We will analyze the similarities and differences between these formalisms, discuss the advantages and limitations of each representation, and provide a tentative "road map" for their potential utilization for different problems.

Applications of nonlinear systems theory to control design

NASA Technical Reports Server (NTRS)

Hunt, L. R.; Villarreal, Ramiro

1988-01-01

For most applications in the control area, the standard practice is to approximate a nonlinear mathematical model by a linear system. Since the feedback linearizable systems contain linear systems as a subclass, the procedure of approximating a nonlinear system by a feedback linearizable one is examined. Because many physical plants (e.g., aircraft at the NASA Ames Research Center) have mathematical models which are close to feedback linearizable systems, such approximations are certainly justified. Results and techniques are introduced for measuring the gap between the model and its truncated linearizable part. The topic of pure feedback systems is important to the study.

Scale and the evolutionarily based approximate number system: an exploratory study

NASA Astrophysics Data System (ADS)

Delgado, Cesar; Jones, M. Gail; You, Hye Sun; Robertson, Laura; Chesnutt, Katherine; Halberda, Justin

2017-05-01

Crosscutting concepts such as scale, proportion, and quantity are recognised by U.S. science standards as a potential vehicle for students to integrate their scientific and mathematical knowledge; yet, U.S. students and adults trail their international peers in scale and measurement estimation. Culturally based knowledge of scale such as measurement units may be built on evolutionarily-based systems of number such as the approximate number system (ANS), which processes approximate representations of numerical magnitude. ANS is related to mathematical achievement in pre-school and early elementary students, but there is little research on ANS among older students or in science-related areas such as scale. Here, we investigate the relationship between ANS precision in public school U.S. seventh graders and their accuracy estimating the length of standard units of measurement in SI and U.S. customary units. We also explored the relationship between ANS and science and mathematics achievement. Accuracy estimating the metre was positively and significantly related to ANS precision. Mathematics achievement, science achievement, and accuracy estimating other units were not significantly related to ANS. We thus suggest that ANS precision may be related to mathematics understanding beyond arithmetic, beyond the early school years, and to the crosscutting concepts of scale, proportion, and quantity.

FINITE-STATE APPROXIMATIONS TO DENUMERABLE-STATE DYNAMIC PROGRAMS,

DTIC Science & Technology

AIR FORCE OPERATIONS, LOGISTICS), (*INVENTORY CONTROL, DYNAMIC PROGRAMMING), (*DYNAMIC PROGRAMMING, APPROXIMATION(MATHEMATICS)), INVENTORY CONTROL, DECISION MAKING, STOCHASTIC PROCESSES, GAME THEORY, ALGORITHMS, CONVERGENCE

Taking the Guesswork out of Locating Evidence-Based Mathematics Practices for Diverse Learners

ERIC Educational Resources Information Center

Hughes, Elizabeth M.; Powell, Sarah R.; Lembke, Erica S.; Riley-Tillman, T. Chris

2016-01-01

Approximately 5 to 7% of school-age students have a learning disability related to mathematics (Shalev, Auerbach, Manor, & Gross-Tsur, 2000), but the percentage of students who experience mathematics difficulty is much greater. For example, results from the 2015 National Assessment of Educational Progress (NAEP; National Center for Education…

Understanding Mathematics: Some Key Factors

ERIC Educational Resources Information Center

Ali, Asma Amanat; Reid, Norman

2012-01-01

Mathematics is well known as a subject area where there can be problems in terms of understanding as well as retaining positive attitudes. In a large study involving 813 school students (ages approximately 10-12) drawn from two different school systems in Pakistan, the effect of limited working memory capacity on performance in mathematics was…

Integrating Language and Content: Challenges in a Japanese Supplementary School in Victoria

ERIC Educational Resources Information Center

Okumura, Shinji; Obara, Yumi

2017-01-01

The Melbourne International School of Japanese (MISJ) is a supplementary Saturday school which offers Japanese language and mathematics taught in Japanese from kindergarten to senior secondary level. Classes are scheduled on Saturdays from 9am to 3pm and approximately half of the program is dedicated to mathematics. While mathematics education…

Heuristic analogy in Ars Conjectandi: From Archimedes' De Circuli Dimensione to Bernoulli's theorem.

PubMed

Campos, Daniel G

2018-02-01

This article investigates the way in which Jacob Bernoulli proved the main mathematical theorem that undergirds his art of conjecturing-the theorem that founded, historically, the field of mathematical probability. It aims to contribute a perspective into the question of problem-solving methods in mathematics while also contributing to the comprehension of the historical development of mathematical probability. It argues that Bernoulli proved his theorem by a process of mathematical experimentation in which the central heuristic strategy was analogy. In this context, the analogy functioned as an experimental hypothesis. The article expounds, first, Bernoulli's reasoning for proving his theorem, describing it as a process of experimentation in which hypothesis-making is crucial. Next, it investigates the analogy between his reasoning and Archimedes' approximation of the value of π, by clarifying both Archimedes' own experimental approach to the said approximation and its heuristic influence on Bernoulli's problem-solving strategy. The discussion includes some general considerations about analogy as a heuristic technique to make experimental hypotheses in mathematics. Copyright © 2018 Elsevier Ltd. All rights reserved.

Brief non-symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in children

PubMed Central

Spelke, Elizabeth S.

2014-01-01

Recent research reveals a link between individual differences in mathematics achievement and performance on tasks that activate the approximate number system (ANS): a primitive cognitive system shared by diverse animal species and by humans of all ages. Here we used a brief experimental paradigm to test one causal hypothesis suggested by this relationship: activation of the ANS may enhance children's performance of symbolic arithmetic. Over 2 experiments, children who briefly practiced tasks that engaged primitive approximate numerical quantities performed better on subsequent exact, symbolic arithmetic problems than did children given other tasks involving comparison and manipulation of non-numerical magnitudes (brightness and length). The practice effect appeared specific to mathematics, as no differences between groups were observed on a comparable sentence completion task. These results move beyond correlational research and provide evidence that the exercise of non-symbolic numerical processes can enhance children's performance of symbolic mathematics. PMID:24462713

Nuevo enfoque de la ensenanza de las matematicas en el nivel de primaria (A New Approach to the Teaching of Mathematics at the Primary School Level).

ERIC Educational Resources Information Center

Jimenez Lozano, Blanca; And Others

This document is an English-language abstract (approximately 1500 words) of a new approach to the teaching of mathematics in Mexican elementary schools. Three aspects of mathematical reform are discussed: (1) syllabus content; (2) teaching methods; and (3) the question of introducing the pupil to modern mathematics at the earliest possible stage…

From Lobatto Quadrature to the Euler Constant "e"

ERIC Educational Resources Information Center

Khattri, Sanjay Kumar

2010-01-01

Based on the Lobatto quadrature, we develop several new closed form approximations to the mathematical constant "e." For validating effectiveness of our approximations, a comparison of our results to the existing approximations is also presented. Another objective of our work is to inspire students to formulate other better approximations by using…

MATHEMATICAL MODELING OF PESTICIDES IN THE ENVIRONMENT: CURRENT AND FUTURE DEVELOPMENTS

EPA Science Inventory

Transport models, total ecosystem models with aggregated linear approximations, evaluative models, hierarchical models, and influence analysis methods are mathematical techniques that are particularly applicable to the problems encountered when characterizing pesticide chemicals ...

Mathematical models for determining the protected spaces of the vertical lightning rod

NASA Technical Reports Server (NTRS)

Mladenovic, I.; Vorgucic, A.

1991-01-01

Two mathematical models are presented for determining the protected spaces of the vertical lightning-rod. In the first model there was applied the circular approximation. Through the introduction of the modified striking distance in the second improved approximation there was obtained a new model for the protected space of the lightning-rod. The models are of general type, foreseen for the three-dimensional space and they are simply applied on solving the practical problems.

Mathematics Teachers' Views about Teaching as a Profession: Final Results of a Four-Year Longitudinal Study. A Report from the Urban Mathematics Collaborative Documentation Project. Program Report 91-4.

ERIC Educational Resources Information Center

Middleton, James A.; And Others

This paper reports the results of a 4-year longitudinal study of approximately 600 urban mathematics teachers who were surveyed to ascertain their attitudes regarding certain attributes of the profession of mathematics teaching, specifically: the use of the professional organization as a major referent, the belief in service to the public, the…

TEDS-M 2008 User Guide for the International Database. Supplement 4: TEDS-M Released Mathematics and Mathematics Pedagogy Knowledge Assessment Items

ERIC Educational Resources Information Center

Brese, Falk, Ed.

2012-01-01

The goal for selecting the released set of test items was to have approximately 25% of each of the full item sets for mathematics content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK) that would represent the full range of difficulty, content, and item format used in the TEDS-M study. The initial step in the selection was to…

An Evaluation of Elementary School Mathematics Programs Utilizing the Mini-Calculator.

ERIC Educational Resources Information Center

Campbell, Patricia; Virgin, A. E.

The purpose of this study was to compare the achievement, attitudes, and teaching/learning experiences in mathematics programs of two groups of elementary-school students in grades 5 and 6. Approximately 150 students in each of two elementary schools were given as a pretest a standardized mathematics achievement test and a questionnaire regarding…

Matriculation Mathematics, Pure Mathematics - Test Papers. Circular of Information to Secondary Schools.

ERIC Educational Resources Information Center

Victoria Education Dept. (Australia).

This document consists of test questions used in three state high schools teaching the new Matriculation pure mathematics course (approximately grade 12). This material was circulated to all schools teaching this course as a teacher resource. The questions are arranged in 14 papers of varying structure and length. Most questions are of the essay…

A Comparison Study of Student Performance and Study Habits in College Algebra at a Hispanic Serving College

ERIC Educational Resources Information Center

Salinas, Lelia

2011-01-01

Large numbers of students arrive at colleges and universities unprepared, specifically in the area of mathematics. In Texas, approximately 47% of entering freshman students enroll in developmental mathematics. Mathematics is cited in the literature as cornerstone for success in science, and advanced technology. In this study, the extent to which…

The Nature of Feedback Given to Elementary Student Teachers from University Supervisors after Observations of Mathematics Lessons

ERIC Educational Resources Information Center

Schwartz, Catherine; Walkowiak, Temple A.; Poling, Lisa; Richardson, Kerri; Polly, Drew

2018-01-01

This research explores the frequency and nature of mathematics-specific feedback given to elementary student teachers by university supervisors across a collection of post-lesson observation forms. Approximately one-third of the forms (n = 250) analysed from five large universities had no comments related to mathematics. Forms that did have…

What I Wish I Had Learned in School.

ERIC Educational Resources Information Center

Tuttle, Jerome E.

1990-01-01

Discussed are some applications of mathematics involved in actuarial science which may be taught in high school mathematics classes. Described are the importance of approximate solutions, multiple answers, and selling the solution to a problem. (CW)

Approximations of e and ?: An Exploration

ERIC Educational Resources Information Center

Brown, Philip R.

2017-01-01

Fractional approximations of e and p are discovered by searching for repetitions or partial repetitions of digit strings in their expansions in different number bases. The discovery of such fractional approximations is suggested for students and teachers as an entry point into mathematics research.

Near Identifiability of Dynamical Systems

NASA Technical Reports Server (NTRS)

Hadaegh, F. Y.; Bekey, G. A.

1987-01-01

Concepts regarding approximate mathematical models treated rigorously. Paper presents new results in analysis of structural identifiability, equivalence, and near equivalence between mathematical models and physical processes they represent. Helps establish rigorous mathematical basis for concepts related to structural identifiability and equivalence revealing fundamental requirements, tacit assumptions, and sources of error. "Structural identifiability," as used by workers in this field, loosely translates as meaning ability to specify unique mathematical model and set of model parameters that accurately predict behavior of corresponding physical system.

Introduction to Numerical Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schoonover, Joseph A.

2016-06-14

These are slides for a lecture for the Parallel Computing Summer Research Internship at the National Security Education Center. This gives an introduction to numerical methods. Repetitive algorithms are used to obtain approximate solutions to mathematical problems, using sorting, searching, root finding, optimization, interpolation, extrapolation, least squares regresion, Eigenvalue problems, ordinary differential equations, and partial differential equations. Many equations are shown. Discretizations allow us to approximate solutions to mathematical models of physical systems using a repetitive algorithm and introduce errors that can lead to numerical instabilities if we are not careful.

Taking Stock of 40 Years of Research on Mathematical Learning Disability: Methodological Issues and Future Directions

ERIC Educational Resources Information Center

Lewis, Katherine E.; Fisher, Marie B.

2016-01-01

Although approximately 5-8% of students have a mathematical learning disability (MLD), researchers have yet to develop a consensus operational definition. To examine how MLD has been identified and what mathematics topics have been explored, the authors conducted a systematic review of 165 studies on MLD published between 1974 and 2013. To move…

The Effects of Migration to a Blended Self-Paced Format for a Remedial Pre-College Algebra Mathematics Course

ERIC Educational Resources Information Center

Deshler, Jessica; Fuller, Edgar

2016-01-01

Approximately 30% of students entering West Virginia University (WVU) are not ready for college mathematics. The WVU Department of Mathematics has been tasked with remediating these students and has worked over the last decade to find the most efficient way to teach the Pre-College Algebra Workshop; the prerequisite course students must complete…

The prediction of epidemics through mathematical modeling.

PubMed

Schaus, Catherine

2014-01-01

Mathematical models may be resorted to in an endeavor to predict the development of epidemics. The SIR model is one of the applications. Still too approximate, the use of statistics awaits more data in order to come closer to reality.

Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia)

PubMed Central

Mazzocco, Michèle M. M.; Feigenson, Lisa; Halberda, Justin

2015-01-01

Many children have significant mathematical learning disabilities (MLD, or dyscalculia) despite adequate schooling. We hypothesize that MLD partly results from a deficiency in the Approximate Number System (ANS) that supports nonverbal numerical representations across species and throughout development. Here we show that ninth grade students with MLD have significantly poorer ANS precision than students in all other mathematics achievement groups (low-, typically-, and high-achieving), as measured by psychophysical assessments of ANS acuity (w) and of the mappings between ANS representations and number words (cv). This relationship persists even when controlling for domain-general abilities. Furthermore, this ANS precision does not differentiate low- from typically-achieving students, suggesting an ANS deficit that is specific to MLD. PMID:21679173

Hypotetical learning trajectory to anticipate mathematics anxiety in algebra learning based on the perspective of didactical situation theory

NASA Astrophysics Data System (ADS)

Yuliani, R. E.; Suryadi, D.; Dahlan, J. A.

2018-05-01

The objective of this research is to design an alleged teacher learning path or Hypotetical Learning Trajectory (HLT) to anticipate mathematics anxiety of students in learning algebra. HLT loads expected mathematics learning objectives, estimates the level of knowledge and understanding of the students, as well as the selection of mathematical activity in accordance with the learning competencies. This research uses educational design research method. The research steps consist of a preliminary design, experimental and retrospective analysis. Data were gathered from various sources, such as data is written during the research process of test results, documentation, sheet results of students' work, results of interviews, questionnaires, and video recordings. The subjects of the study were 10 junior high school students. Based on the research identified 2 students at the level of high anxiety, 7 people at medium anxiety level and 1 student at low anxiety level. High anxiety levels about 20%, was approximately 70% and approximately 10% lower. These results can be used as an evaluation and reflection for designing materials that can anticipate mathematics anxiety of students learning algebra concepts.

Current problems in applied mathematics and mathematical physics

NASA Astrophysics Data System (ADS)

Samarskii, A. A.

Papers are presented on such topics as mathematical models in immunology, mathematical problems of medical computer tomography, classical orthogonal polynomials depending on a discrete variable, and boundary layer methods for singular perturbation problems in partial derivatives. Consideration is also given to the computer simulation of supernova explosion, nonstationary internal waves in a stratified fluid, the description of turbulent flows by unsteady solutions of the Navier-Stokes equations, and the reduced Galerkin method for external diffraction problems using the spline approximation of fields.

The Story of PI

NASA Technical Reports Server (NTRS)

Apostol, Tom M. (Editor)

1989-01-01

The early history and the uses of the mathematical notation - pi - are presented through both film footage and computer animation in this 'Project Mathematics' series video. Pi comes from the first letter in the Greek word for perimeter. Archimedes, and early Greek mathematician, formulated the equations for the computation of a circle's area using pi and was the first person to seriously approximate pi numerically, although only to a few decimal places. By 1985, pi had been approximated to over one billion decimal places and was found to have no repeating pattern. One use of pi is the application of its approximation calculation as an analytical tool for determining the accuracy of supercomputers and software designs.

Effects of intracerebroventricular administration of beta-amyloid on the dynamics of learning in purebred and mongrel rats.

PubMed

Stepanov, I I; Kuznetsova, N N; Klement'ev, B I; Sapronov, N S

2007-07-01

The effects of intracerebroventricular administration of the beta-amyloid peptide fragment Abeta(25-35) on the dynamics of the acquisition of a conditioned reflex in a Y maze were studied in Wistar and mongrel rats. The dynamics of decreases in the number of errors were assessed using an exponential mathematical model describing the transfer function of a first-order system in response to stepped inputs using non-linear regression analysis. This mathematical model provided a good approximation to the learning dynamics in inbred and mongrel mice. In Wistar rats, beta-amyloid impaired learning, with reduced memory between the first and second training sessions, but without complete blockade of learning. As a result, learning dynamics were no longer approximated by the mathematical model. At the same time, comparison of the number of errors in each training sessions between the control group of Wistar rats and the group given beta-amyloid showed no significant differences (Student's t test). This result demonstrates the advantage of regression analysis based on a mathematical model over the traditionally used statistical methods. In mongrel rats, the effect of beta-amyloid was limited to an a slowing of the process of learning as compared with control mongrel rats, with retention of the approximation by the mathematical model. It is suggested that mongrel animals have some kind of innate, genetically determined protective mechanism against the harmful effects of beta-amyloid.

The Shapes of Tomorrow.

ERIC Educational Resources Information Center

Vermont Univ., Burlington.

This book, written by classroom teachers, introduces the application of secondary school mathematics to space exploration, and is intended to unify science and mathematics. In early chapters geometric concepts are used with general concepts of space and rough approximations of space measurements. Later, these concepts are refined to include the…

Voices of Experience: Understanding the Retention of Veteran Secondary Mathematics Teachers

ERIC Educational Resources Information Center

Whitmore, Diane Marie

2009-01-01

Approximately 50% of teachers leave the profession within five years. A disproportionate number of those who leave are secondary mathematics teachers. Teacher retirements, policy changes, teacher turnover, and teacher requirements contribute to the mass departure from the teaching profession. This phenomenological qualitative study examined…

State and trait effects on individual differences in children's mathematical development.

PubMed

Bailey, Drew H; Watts, Tyler W; Littlefield, Andrew K; Geary, David C

2014-11-01

Substantial longitudinal relations between children's early mathematics achievement and their much later mathematics achievement are firmly established. These findings are seemingly at odds with studies showing that early educational interventions have diminishing effects on children's mathematics achievement across time. We hypothesized that individual differences in children's later mathematical knowledge are more an indicator of stable, underlying characteristics related to mathematics learning throughout development than of direct effects of early mathematical competency on later mathematical competency. We tested this hypothesis in two longitudinal data sets, by simultaneously modeling effects of latent traits (stable characteristics that influence learning across time) and states (e.g., prior knowledge) on children's mathematics achievement over time. Latent trait effects on children's mathematical development were substantially larger than state effects. Approximately 60% of the variance in trait mathematics achievement was accounted for by commonly used control variables, such as working memory, but residual trait effects remained larger than state effects. Implications for research and practice are discussed. © The Author(s) 2014.

State and Trait Effects on Individual Differences in Children's Mathematical Development

PubMed Central

Bailey, Drew H.; Watts, Tyler W.; Littlefield, Andrew K.; Geary, David C.

2015-01-01

Substantial longitudinal relations between children's early mathematics achievement and their much later mathematics achievement are firmly established. These findings are seemingly at odds with studies showing that early educational interventions have diminishing effects on children's mathematics achievement across time. We hypothesized that individual differences in children's later mathematical knowledge are more an indicator of stable, underlying characteristics related to mathematics learning throughout development than of direct effects of early mathematical competency on later mathematical competency. We tested this hypothesis in two longitudinal data sets, by simultaneously modeling effects of latent traits (stable characteristics that influence learning across time) and states (e.g., prior knowledge) on children's mathematics achievement over time. Latent trait effects on children's mathematical development were substantially larger than state effects. Approximately 60% of the variance in trait mathematics achievement was accounted for by commonly used control variables, such as working memory, but residual trait effects remained larger than state effects. Implications for research and practice are discussed. PMID:25231900

New Evidence on Causal Relationship between Approximate Number System (ANS) Acuity and Arithmetic Ability in Elementary-School Students: A Longitudinal Cross-Lagged Analysis.

PubMed

He, Yunfeng; Zhou, Xinlin; Shi, Dexin; Song, Hairong; Zhang, Hui; Shi, Jiannong

2016-01-01

Approximate number system (ANS) acuity and mathematical ability have been found to be closely associated in recent studies. However, whether and how these two measures are causally related still remain less addressed. There are two hypotheses about the possible causal relationship: ANS acuity influences mathematical performances, or access to math education sharpens ANS acuity. Evidences in support of both hypotheses have been reported, but these two hypotheses have never been tested simultaneously. Therefore, questions still remain whether only one-direction or reciprocal causal relationships existed in the association. In this work, we provided a new evidence on the causal relationship between ANS acuity and arithmetic ability. ANS acuity and mathematical ability of elementary-school students were measured sequentially at three time points within one year, and all possible causal directions were evaluated simultaneously using cross-lagged regression analysis. The results show that ANS acuity influences later arithmetic ability while the reverse causal direction was not supported. Our finding adds a strong evidence to the causal association between ANS acuity and mathematical ability, and also has important implications for educational intervention designed to train ANS acuity and thereby promote mathematical ability.

New Evidence on Causal Relationship between Approximate Number System (ANS) Acuity and Arithmetic Ability in Elementary-School Students: A Longitudinal Cross-Lagged Analysis

PubMed Central

He, Yunfeng; Zhou, Xinlin; Shi, Dexin; Song, Hairong; Zhang, Hui; Shi, Jiannong

2016-01-01

Approximate number system (ANS) acuity and mathematical ability have been found to be closely associated in recent studies. However, whether and how these two measures are causally related still remain less addressed. There are two hypotheses about the possible causal relationship: ANS acuity influences mathematical performances, or access to math education sharpens ANS acuity. Evidences in support of both hypotheses have been reported, but these two hypotheses have never been tested simultaneously. Therefore, questions still remain whether only one-direction or reciprocal causal relationships existed in the association. In this work, we provided a new evidence on the causal relationship between ANS acuity and arithmetic ability. ANS acuity and mathematical ability of elementary-school students were measured sequentially at three time points within one year, and all possible causal directions were evaluated simultaneously using cross-lagged regression analysis. The results show that ANS acuity influences later arithmetic ability while the reverse causal direction was not supported. Our finding adds a strong evidence to the causal association between ANS acuity and mathematical ability, and also has important implications for educational intervention designed to train ANS acuity and thereby promote mathematical ability. PMID:27462291

Exposing the Mathematical Wizard: Approximating Trigonometric Functions

ERIC Educational Resources Information Center

Gordon, Sheldon P.

2011-01-01

For almost all students, what happens when they push buttons on their calculators is essentially magic, and the techniques used are seemingly pure wizardry. In this article, the author draws back the curtain to expose some of the mathematics behind computational wizardry and introduces some fundamental ideas that are accessible to precalculus…

Reading Bombelli's x-purgated Algebra.

ERIC Educational Resources Information Center

Arcavi, Abraham; Bruckheimer, Maxim

1991-01-01

Presents the algorithm to approximate square roots as reproduced from the 1579 edition of an algebra book by Rafael Bombelli. The sequence of activities illustrates that the process of understanding an original source of mathematics, first at the algorithmic level and then with respect to its mathematical validity in modern terms, can be an…

Preschoolers' Mathematics Skills and Behavior: Analysis of a National Sample

ERIC Educational Resources Information Center

Dobbs-Oates, Jennifer; Robinson, Chanele

2012-01-01

This study investigated the association between children's mathematical skills and their behavior in the prekindergarten year in a national sample of children attending center-based child care. The sample consisted of approximately 5,400 preschoolers in center-based care from the Early Childhood Longitudinal Study--Birth Cohort. Children's math…

Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia).

PubMed

Mazzocco, Michèle M M; Feigenson, Lisa; Halberda, Justin

2011-01-01

Many children have significant mathematical learning disabilities (MLD, or dyscalculia) despite adequate schooling. The current study hypothesizes that MLD partly results from a deficiency in the Approximate Number System (ANS) that supports nonverbal numerical representations across species and throughout development. In this study of 71 ninth graders, it is shown that students with MLD have significantly poorer ANS precision than students in all other mathematics achievement groups (low, typically, and high achieving), as measured by psychophysical assessments of ANS acuity (w) and of the mappings between ANS representations and number words (cv). This relation persists even when controlling for domain-general abilities. Furthermore, this ANS precision does not differentiate low-achieving from typically achieving students, suggesting an ANS deficit that is specific to MLD. © 2011 The Authors. Child Development © 2011 Society for Research in Child Development, Inc.

Evaluation of the Thermodynamic Consistency of Closure Approximations in Several Models Proposed for the Description of Liquid Crystalline Dynamics

NASA Astrophysics Data System (ADS)

Edwards, Brian J.

2002-05-01

Given the premise that a set of dynamical equations must possess a definite, underlying mathematical structure to ensure local and global thermodynamic stability, as has been well documented, several different models for describing liquid crystalline dynamics are examined with respect to said structure. These models, each derived during the past several years using a specific closure approximation for the fourth moment of the distribution function in Doi's rigid rod theory, are all shown to be inconsistent with this basic mathematical structure. The source of this inconsistency lies in Doi's expressions for the extra stress tensor and temporal evolution of the order parameter, which are rederived herein using a transformation that allows for internal compatibility with the underlying mathematical structure that is present on the distribution function level of description.

Application of the piecewise rational quadratic interpolant to the AUC calculation in the bioavailability study.

PubMed

Akhter, Khalid P; Ahmad, Mahmood; Khan, Shujaat Ali; Ramzan, Munazza; Shafi, Ishrat; Muryam, Burhana; Javed, Zafar; Murtaza, Ghulam

2012-01-01

This study presents an application of the piecewise rational quadratic interpolant to the AUC calculation in the bioavailability study. The objective of this work is to find an area under the plasma concentration-time curve (AUC) for multiple doses of salbutamol sulfate sustained release tablets (Ventolin oral tablets SR 8 mg, GSK, Pakistan) in the group of 24 healthy adults by using computational mathematics techniques. Following the administration of 4 doses of Ventolin tablets 12 hourly to 24 healthy human subjects and bioanalysis of obtained plasma samples, plasma drug concentration-time profile was constructed. The approximated AUC was computed by using computational mathematics techniques such as extended rectangular, extended trapezium and extended Simpson's rule and compared with exact value of AUC calculated by using software - Kinetica to find best computational mathematics method that gives AUC values closest to exact. The exact values of AUC for four consecutive doses of Ventolin oral tablets were 150.58, 157.81, 164.41 and 162.78 ngxh/mL while the closest approximated AUC values were 149.24, 157.33, 164.25 and 162.28 ngxh/mL, respectively, as found by extended rectangular rule. The errors in the approximated values of AUC were negligible. It is concluded that all computational tools approximated values of AUC accurately but the extended rectangular rule gives slightly better approximated values of AUC as compared to extended trapezium and extended Simpson's rules.

The etiology of mathematical self-evaluation and mathematics achievement: understanding the relationship using a cross-lagged twin study from age 9 to 12

PubMed Central

Luo, Yu L.L.; Kovas, Yulia; Haworth, Claire M.A.; Plomin, Robert

2011-01-01

The genetic and environmental origins of individual differences in mathematical self-evaluation over time and its association with later mathematics achievement were investigated in a UK sample of 2138 twin pairs at ages 9 and 12. Self-evaluation indexed how good children think they are at mathematical activities and how much they like those activities. Mathematics achievement was assessed by teachers based on UK National Curriculum standards. At both ages self-evaluation was approximately 40% heritable, with the rest of the variance explained by non-shared environment. The results also suggested moderate reciprocal associations between self-evaluation and mathematics achievement across time, with earlier self-evaluation predicting later performance and earlier performance predicting later self-evaluation. These cross-lagged relationships were genetically rather than environmentally mediated. PMID:22102781

Approximate number sense, symbolic number processing, or number-space mappings: what underlies mathematics achievement?

PubMed

Sasanguie, Delphine; Göbel, Silke M; Moll, Kristina; Smets, Karolien; Reynvoet, Bert

2013-03-01

In this study, the performance of typically developing 6- to 8-year-old children on an approximate number discrimination task, a symbolic comparison task, and a symbolic and nonsymbolic number line estimation task was examined. For the first time, children's performances on these basic cognitive number processing tasks were explicitly contrasted to investigate which of them is the best predictor of their future mathematical abilities. Math achievement was measured with a timed arithmetic test and with a general curriculum-based math test to address the additional question of whether the predictive association between the basic numerical abilities and mathematics achievement is dependent on which math test is used. Results revealed that performance on both mathematics achievement tests was best predicted by how well childrencompared digits. In addition, an association between performance on the symbolic number line estimation task and math achievement scores for the general curriculum-based math test measuring a broader spectrum of skills was found. Together, these results emphasize the importance of learning experiences with symbols for later math abilities. Copyright © 2012 Elsevier Inc. All rights reserved.

EDUCATION ENHANCES THE ACUITY OF THE NON-VERBAL APPROXIMATE NUMBER SYSTEM

PubMed Central

Piazza, Manuela; Pica, Pierre; Izard, Véronique; Spelke, Elizabeth; Dehaene, Stanislas

2015-01-01

All humans share a universal, evolutionarily ancient approximate number system (ANS) that estimates and combines the number of objects in sets with ratio-limited precision. Inter-individual variability in the acuity of the ANS correlates with mathematical achievement, but the causes of this correlation have never been established. We acquired psychophysical measures of ANS acuity in child and adult members of an indigene group in the Amazon, the Mundurucu, who have a very restricted numerical lexicon and highly variable access to mathematical education. By comparing Mundurucu subjects with or without access to schooling, we demonstrate that education significantly enhances the acuity with which sets of concrete objects are estimated. These results speak in favor of an important effect of culture and education on basic number perception. We hypothesize that symbolic and non-symbolic numerical thinking mutually enhance one another over the course of mathematics instruction. PMID:23625879

Reduced linear noise approximation for biochemical reaction networks with time-scale separation: The stochastic tQSSA+

NASA Astrophysics Data System (ADS)

Herath, Narmada; Del Vecchio, Domitilla

2018-03-01

Biochemical reaction networks often involve reactions that take place on different time scales, giving rise to "slow" and "fast" system variables. This property is widely used in the analysis of systems to obtain dynamical models with reduced dimensions. In this paper, we consider stochastic dynamics of biochemical reaction networks modeled using the Linear Noise Approximation (LNA). Under time-scale separation conditions, we obtain a reduced-order LNA that approximates both the slow and fast variables in the system. We mathematically prove that the first and second moments of this reduced-order model converge to those of the full system as the time-scale separation becomes large. These mathematical results, in particular, provide a rigorous justification to the accuracy of LNA models derived using the stochastic total quasi-steady state approximation (tQSSA). Since, in contrast to the stochastic tQSSA, our reduced-order model also provides approximations for the fast variable stochastic properties, we term our method the "stochastic tQSSA+". Finally, we demonstrate the application of our approach on two biochemical network motifs found in gene-regulatory and signal transduction networks.

Investigation of approximate models of experimental temperature characteristics of machines

NASA Astrophysics Data System (ADS)

Parfenov, I. V.; Polyakov, A. N.

2018-05-01

This work is devoted to the investigation of various approaches to the approximation of experimental data and the creation of simulation mathematical models of thermal processes in machines with the aim of finding ways to reduce the time of their field tests and reducing the temperature error of the treatments. The main methods of research which the authors used in this work are: the full-scale thermal testing of machines; realization of various approaches at approximation of experimental temperature characteristics of machine tools by polynomial models; analysis and evaluation of modelling results (model quality) of the temperature characteristics of machines and their derivatives up to the third order in time. As a result of the performed researches, rational methods, type, parameters and complexity of simulation mathematical models of thermal processes in machine tools are proposed.

Individual differences in non-verbal number acuity correlate with maths achievement.

PubMed

Halberda, Justin; Mazzocco, Michèle M M; Feigenson, Lisa

2008-10-02

Human mathematical competence emerges from two representational systems. Competence in some domains of mathematics, such as calculus, relies on symbolic representations that are unique to humans who have undergone explicit teaching. More basic numerical intuitions are supported by an evolutionarily ancient approximate number system that is shared by adults, infants and non-human animals-these groups can all represent the approximate number of items in visual or auditory arrays without verbally counting, and use this capacity to guide everyday behaviour such as foraging. Despite the widespread nature of the approximate number system both across species and across development, it is not known whether some individuals have a more precise non-verbal 'number sense' than others. Furthermore, the extent to which this system interfaces with the formal, symbolic maths abilities that humans acquire by explicit instruction remains unknown. Here we show that there are large individual differences in the non-verbal approximation abilities of 14-year-old children, and that these individual differences in the present correlate with children's past scores on standardized maths achievement tests, extending all the way back to kindergarten. Moreover, this correlation remains significant when controlling for individual differences in other cognitive and performance factors. Our results show that individual differences in achievement in school mathematics are related to individual differences in the acuity of an evolutionarily ancient, unlearned approximate number sense. Further research will determine whether early differences in number sense acuity affect later maths learning, whether maths education enhances number sense acuity, and the extent to which tertiary factors can affect both.

A Review of Mathematical Learning Disabilities in Children with Fragile X Syndrome

ERIC Educational Resources Information Center

Murphy, Melissa M.

2009-01-01

The prevalence rate of mathematical learning disabilities (MLD) among children with fragile X syndrome who do not meet criteria for intellectual and developmental disabilities ([approximately equal to] 50% of female children) exceeds the rate reported in the general population. The purpose of this article is two-fold: (1) to review the findings on…

The Relation between easyCBM and Smarter Balanced Reading and Mathematics Assessments

ERIC Educational Resources Information Center

Alonzo, Julie

2016-01-01

This study investigated the relation between the easyCBM Benchmark Assessments in both mathematics and reading and the Smarter Balanced assessment, widely adopted across the United States. Data for the study were obtained from a convenience sample of approximately 1,000 students per grade in grades 3-8 provided by two school districts in the…

The Monte Carlo Method. Popular Lectures in Mathematics.

ERIC Educational Resources Information Center

Sobol', I. M.

The Monte Carlo Method is a method of approximately solving mathematical and physical problems by the simulation of random quantities. The principal goal of this booklet is to suggest to specialists in all areas that they will encounter problems which can be solved by the Monte Carlo Method. Part I of the booklet discusses the simulation of random…

Post-primary students' images of mathematics: findings from a survey of Irish ordinary level mathematics students

NASA Astrophysics Data System (ADS)

Lane, Ciara; Stynes, Martin; O'Donoghue, John

2016-10-01

A questionnaire survey was carried out as part of a PhD research study to investigate the image of mathematics held by post-primary students in Ireland. The study focused on students in fifth year of post-primary education studying ordinary level mathematics for the Irish Leaving Certificate examination - the final examination for students in second-level or post-primary education. At the time this study was conducted, ordinary level mathematics students constituted approximately 72% of Leaving Certificate students. Students were aged between 15 and 18 years. A definition for 'image of mathematics' was adapted from Lim and Wilson, with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. A questionnaire was composed incorporating 84 fixed-response items chosen from eight pre-established scales by Aiken, Fennema and Sherman, Gourgey and Schoenfeld. This paper focuses on the findings from the questionnaire survey. Students' images of mathematics are compared with regard to gender, type of post-primary school attended and prior mathematical achievement.

Practical aspects and uncertainty analysis of biological effective dose (BED) regarding its three-dimensional calculation in multiphase radiotherapy treatment plans

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kauweloa, Kevin I., E-mail: Kauweloa@livemail.uthscsa.edu; Gutierrez, Alonso N.; Bergamo, Angelo

2014-07-15

Purpose: There is a growing interest in the radiation oncology community to use the biological effective dose (BED) rather than the physical dose (PD) in treatment plan evaluation and optimization due to its stronger correlation with radiobiological effects. Radiotherapy patients may receive treatments involving a single only phase or multiple phases (e.g., primary and boost). Since most treatment planning systems cannot calculate the analytical BED distribution in multiphase treatments, an approximate multiphase BED expression, which is based on the total physical dose distribution, has been used. The purpose of this paper is to reveal the mathematical properties of the approximatemore » BED formulation, relative to the true BED. Methods: The mathematical properties of the approximate multiphase BED equation are analyzed and evaluated. In order to better understand the accuracy of the approximate multiphase BED equation, the true multiphase BED equation was derived and the mathematical differences between the true and approximate multiphase BED equations were determined. The magnitude of its inaccuracies under common clinical circumstances was also studied. All calculations were performed on a voxel-by-voxel basis using the three-dimensional dose matrices. Results: Results showed that the approximate multiphase BED equation is accurate only when the dose-per-fractions (DPFs) in both the first and second phases are equal, which occur when the dose distribution does not significantly change between the phases. In the case of heterogeneous dose distributions, which significantly vary between the phases, there are fewer occurrences of equal DPFs and hence the inaccuracy of the approximate multiphase BED is greater. These characteristics are usually seen in the dose distributions being delivered to organs at risk rather than to targets. Conclusions: The finding of this study indicates that the true multiphase BED equation should be implemented in the treatment planning systems due to the inconsistent accuracy of the approximate multiphase BED equation in most of the clinical situations.« less

Improving Approximate Number Sense Abilities in Preschoolers: PLUS Games

ERIC Educational Resources Information Center

Van Herwegen, Jo; Costa, Hiwet Mariam; Passolunghi, Maria Chiara

2017-01-01

Previous studies in both typically and atypically developing children have shown that approximate number system (ANS) abilities predict formal mathematical knowledge later on in life. The current study investigated whether playing specially designed training games that targets the ANS system using nonsymbolic stimuli only would improve preschool…

A rapid radiative transfer model for reflection of solar radiation

NASA Technical Reports Server (NTRS)

Xiang, X.; Smith, E. A.; Justus, C. G.

1994-01-01

A rapid analytical radiative transfer model for reflection of solar radiation in plane-parallel atmospheres is developed based on the Sobolev approach and the delta function transformation technique. A distinct advantage of this model over alternative two-stream solutions is that in addition to yielding the irradiance components, which turn out to be mathematically equivalent to the delta-Eddington approximation, the radiance field can also be expanded in a mathematically consistent fashion. Tests with the model against a more precise multistream discrete ordinate model over a wide range of input parameters demonstrate that the new approximate method typically produces average radiance differences of less than 5%, with worst average differences of approximately 10%-15%. By the same token, the computational speed of the new model is some tens to thousands times faster than that of the more precise model when its stream resolution is set to generate precise calculations.

Three dimensional thermal pollution models. Volume 1: Review of mathematical formulations. [waste heat discharge from power plants and effects on ecosystems

NASA Technical Reports Server (NTRS)

Lee, S. S.; Sengupta, S.

1978-01-01

A mathematical model package for thermal pollution analyses and prediction is presented. These models, intended as user's manuals, are three dimensional and time dependent using the primitive equation approach. Although they have sufficient generality for application at sites with diverse topographical features; they also present specific instructions regarding data preparation for program execution and sample problems. The mathematical formulation of these models is presented including assumptions, approximations, governing equations, boundary and initial conditions, numerical method of solution, and same results.

An Analysis of College Mathematics Departments' Credit Granting Policies for Students with High School Calculus Experience

ERIC Educational Resources Information Center

Laurent, Theresa A.

2009-01-01

The purpose of this study was to investigate higher education mathematics departments' credit granting policies for students with high school calculus experience. The number of students taking calculus in high school has more than doubled since 1982 (NCES, 2007) and it is estimated that approximately 530,000 students took a calculus course in high…

Use of Intelligent Tutor in Post-Secondary Mathematics Education in the United Arab Emirates

ERIC Educational Resources Information Center

Dani, Anita; Nasser, Ramzi

2016-01-01

The purpose of this paper is to determine potential identifiers of students' academic success in foundation mathematics course from the data logs of the intelligent tutor Assessment for Learning using Knowledge Spaces (ALEKS). A cross-sectional study design was used. A sample of 152 records, which accounts to approximately 60% of the population,…

Aberrant Functional Activation in School Age Children At-Risk for Mathematical Disability: A Functional Imaging Study of Simple Arithmetic Skill

ERIC Educational Resources Information Center

Davis, Nicole; Cannistraci, Christopher J.; Rogers, Baxter P.; Gatenby, J. Christopher; Fuchs, Lynn S.; Anderson, Adam W.; Gore, John C.

2009-01-01

We used functional magnetic resonance imaging (fMRI) to explore the patterns of brain activation associated with different levels of performance in exact and approximate calculation tasks in well-defined cohorts of children with mathematical calculation difficulties (MD) and typically developing controls. Both groups of children activated the same…

Using a Concept-Grounded, Curriculum-Based Measure in Mathematics To Predict Statewide Test Scores for Middle School Students with LD.

ERIC Educational Resources Information Center

Helwig, Robert; Anderson, Lisbeth; Tindal, Gerald

2002-01-01

An 11-item math concept curriculum-based measure (CBM) was administered to 171 eighth grade students. Scores were correlated with scores from a computer adaptive test designed in conjunction with the state to approximate the official statewide mathematics achievement tests. Correlations for general education students and students with learning…

Comparing Future Teachers' Beliefs across Countries: Approximate Measurement Invariance with Bayesian Elastic Constraints for Local Item Dependence and Differential Item Functioning

ERIC Educational Resources Information Center

Braeken, Johan; Blömeke, Sigrid

2016-01-01

Using data from the international Teacher Education and Development Study: Learning to Teach Mathematics (TEDS-M), the measurement equivalence of teachers' beliefs across countries is investigated for the case of "mathematics-as-a fixed-ability". Measurement equivalence is a crucial topic in all international large-scale assessments and…

Individual Differences in Inhibitory Control, Not Non-Verbal Number Acuity, Correlate with Mathematics Achievement

PubMed Central

Gilmore, Camilla; Attridge, Nina; Clayton, Sarah; Cragg, Lucy; Johnson, Samantha; Marlow, Neil; Simms, Victoria; Inglis, Matthew

2013-01-01

Given the well-documented failings in mathematics education in many Western societies, there has been an increased interest in understanding the cognitive underpinnings of mathematical achievement. Recent research has proposed the existence of an Approximate Number System (ANS) which allows individuals to represent and manipulate non-verbal numerical information. Evidence has shown that performance on a measure of the ANS (a dot comparison task) is related to mathematics achievement, which has led researchers to suggest that the ANS plays a critical role in mathematics learning. Here we show that, rather than being driven by the nature of underlying numerical representations, this relationship may in fact be an artefact of the inhibitory control demands of some trials of the dot comparison task. This suggests that recent work basing mathematics assessments and interventions around dot comparison tasks may be inappropriate. PMID:23785521

Symmetric rotating-wave approximation for the generalized single-mode spin-boson system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Albert, Victor V.; Scholes, Gregory D.; Brumer, Paul

2011-10-15

The single-mode spin-boson model exhibits behavior not included in the rotating-wave approximation (RWA) in the ultra and deep-strong coupling regimes, where counter-rotating contributions become important. We introduce a symmetric rotating-wave approximation that treats rotating and counter-rotating terms equally, preserves the invariances of the Hamiltonian with respect to its parameters, and reproduces several qualitative features of the spin-boson spectrum not present in the original rotating-wave approximation both off-resonance and at deep-strong coupling. The symmetric rotating-wave approximation allows for the treatment of certain ultra- and deep-strong coupling regimes with similar accuracy and mathematical simplicity as does the RWA in the weak-coupling regime.more » Additionally, we symmetrize the generalized form of the rotating-wave approximation to obtain the same qualitative correspondence with the addition of improved quantitative agreement with the exact numerical results. The method is readily extended to higher accuracy if needed. Finally, we introduce the two-photon parity operator for the two-photon Rabi Hamiltonian and obtain its generalized symmetric rotating-wave approximation. The existence of this operator reveals a parity symmetry similar to that in the Rabi Hamiltonian as well as another symmetry that is unique to the two-photon case, providing insight into the mathematical structure of the two-photon spectrum, significantly simplifying the numerics, and revealing some interesting dynamical properties.« less

Approximate number and approximate time discrimination each correlate with school math abilities in young children.

PubMed

Odic, Darko; Lisboa, Juan Valle; Eisinger, Robert; Olivera, Magdalena Gonzalez; Maiche, Alejandro; Halberda, Justin

2016-01-01

What is the relationship between our intuitive sense of number (e.g., when estimating how many marbles are in a jar), and our intuitive sense of other quantities, including time (e.g., when estimating how long it has been since we last ate breakfast)? Recent work in cognitive, developmental, comparative psychology, and computational neuroscience has suggested that our representations of approximate number, time, and spatial extent are fundamentally linked and constitute a "generalized magnitude system". But, the shared behavioral and neural signatures between number, time, and space may alternatively be due to similar encoding and decision-making processes, rather than due to shared domain-general representations. In this study, we investigate the relationship between approximate number and time in a large sample of 6-8 year-old children in Uruguay by examining how individual differences in the precision of number and time estimation correlate with school mathematics performance. Over four testing days, each child completed an approximate number discrimination task, an approximate time discrimination task, a digit span task, and a large battery of symbolic math tests. We replicate previous reports showing that symbolic math abilities correlate with approximate number precision and extend those findings by showing that math abilities also correlate with approximate time precision. But, contrary to approximate number and time sharing common representations, we find that each of these dimensions uniquely correlates with formal math: approximate number correlates more strongly with formal math compared to time and continues to correlate with math even when precision in time and individual differences in working memory are controlled for. These results suggest that there are important differences in the mental representations of approximate number and approximate time and further clarify the relationship between quantity representations and mathematics. Copyright © 2015 Elsevier B.V. All rights reserved.

Reliable before-fabrication forecasting of normal and touch mode MEMS capacitive pressure sensor: modeling and simulation

NASA Astrophysics Data System (ADS)

Jindal, Sumit Kumar; Mahajan, Ankush; Raghuwanshi, Sanjeev Kumar

2017-10-01

An analytical model and numerical simulation for the performance of MEMS capacitive pressure sensors in both normal and touch modes is required for expected behavior of the sensor prior to their fabrication. Obtaining such information should be based on a complete analysis of performance parameters such as deflection of diaphragm, change of capacitance when the diaphragm deflects, and sensitivity of the sensor. In the literature, limited work has been carried out on the above-stated issue; moreover, due to approximation factors of polynomials, a tolerance error cannot be overseen. Reliable before-fabrication forecasting requires exact mathematical calculation of the parameters involved. A second-order polynomial equation is calculated mathematically for key performance parameters of both modes. This eliminates the approximation factor, and an exact result can be studied, maintaining high accuracy. The elimination of approximation factors and an approach of exact results are based on a new design parameter (δ) that we propose. The design parameter gives an initial hint to the designers on how the sensor will behave once it is fabricated. The complete work is aided by extensive mathematical detailing of all the parameters involved. Next, we verified our claims using MATLAB® simulation. Since MATLAB® effectively provides the simulation theory for the design approach, more complicated finite element method is not used.

Preschool acuity of the approximate number system correlates with school math ability.

PubMed

Libertus, Melissa E; Feigenson, Lisa; Halberda, Justin

2011-11-01

Previous research shows a correlation between individual differences in people's school math abilities and the accuracy with which they rapidly and nonverbally approximate how many items are in a scene. This finding is surprising because the Approximate Number System (ANS) underlying numerical estimation is shared with infants and with non-human animals who never acquire formal mathematics. However, it remains unclear whether the link between individual differences in math ability and the ANS depends on formal mathematics instruction. Earlier studies demonstrating this link tested participants only after they had received many years of mathematics education, or assessed participants' ANS acuity using tasks that required additional symbolic or arithmetic processing similar to that required in standardized math tests. To ask whether the ANS and math ability are linked early in life, we measured the ANS acuity of 200 3- to 5-year-old children using a task that did not also require symbol use or arithmetic calculation. We also measured children's math ability and vocabulary size prior to the onset of formal math instruction. We found that children's ANS acuity correlated with their math ability, even when age and verbal skills were controlled for. These findings provide evidence for a relationship between the primitive sense of number and math ability starting early in life. 2011 Blackwell Publishing Ltd.

Preschool Acuity of the Approximate Number System Correlates with School Math Ability

PubMed Central

Libertus, Melissa E.; Feigenson, Lisa; Halberda, Justin

2012-01-01

Previous research shows a correlation between individual differences in people’s school math abilities and the accuracy with which they rapidly and nonverbally approximate how many items are in a scene. This finding is surprising because the Approximate Number System (ANS) underlying numerical estimation is shared with infants and non-human animals who never acquire formal mathematics. However, it remains unclear whether the link between individual differences in math ability and the ANS depends on formal mathematics instruction. Earlier studies demonstrating this link tested participants only after they had received many years of mathematics education, or assessed participants’ ANS acuity using tasks that required additional symbolic or arithmetic processing similar to that required in standardized math tests. To ask whether the ANS and math ability are linked early in life, we measured the ANS acuity of 200 3- to 5-year-old children using a task that did not also require symbol use or arithmetic calculation. We also measured children’s math ability and vocabulary size prior to the onset of formal math instruction. We found that children’s ANS acuity correlated with their math ability, even when age and verbal skills were controlled for. These findings provide evidence for a relationship between the primitive sense of number and math ability starting early in life. PMID:22010889

Neurocognitive Predictors of Mathematical Processing in School-Aged Children with Spina Bifida and Their Typically Developing Peers: Attention, Working Memory, and Fine Motor Skills

PubMed Central

Raghubar, Kimberly P.; Barnes, Marcia A.; Dennis, Maureen; Cirino, Paul T.; Taylor, Heather; Landry, Susan

2015-01-01

Objective Math and attention are related in neurobiological and behavioral models of mathematical cognition. This study employed model-driven assessments of attention and math in children with spina bifida myelomeningocele (SBM), who have known math difficulties and specific attentional deficits, to more directly examine putative relations between attention and mathematical processing. The relation of other domain general abilities and math was also investigated. Method Participants were 9.5-year-old children with SBM (N = 44) and typically developing children (N = 50). Participants were administered experimental exact and approximate arithmetic tasks, and standardized measures of math fluency and calculation. Cognitive measures included the Attention Network Test (ANT), and standardized measures of fine motor skills, verbal working memory (WM), and visual-spatial WM. Results Children with SBM performed similarly to peers on exact arithmetic but more poorly on approximate and standardized arithmetic measures. On the ANT, children with SBM differed from controls on orienting attention but not alerting and executive attention. Multiple mediation models showed that: fine motor skills and verbal WM mediated the relation of group to approximate arithmetic; fine motor skills and visual-spatial WM mediated the relation of group to math fluency; and verbal and visual-spatial WM mediated the relation of group to math calculation. Attention was not a significant mediator of the effects of group for any aspect of math in this study. Conclusions Results are discussed with reference to models of attention, WM, and mathematical cognition. PMID:26011113

Neurocognitive predictors of mathematical processing in school-aged children with spina bifida and their typically developing peers: Attention, working memory, and fine motor skills.

PubMed

Raghubar, Kimberly P; Barnes, Marcia A; Dennis, Maureen; Cirino, Paul T; Taylor, Heather; Landry, Susan

2015-11-01

Math and attention are related in neurobiological and behavioral models of mathematical cognition. This study employed model-driven assessments of attention and math in children with spina bifida myelomeningocele (SBM), who have known math difficulties and specific attentional deficits, to more directly examine putative relations between attention and mathematical processing. The relation of other domain general abilities and math was also investigated. Participants were 9.5-year-old children with SBM (n = 44) and typically developing children (n = 50). Participants were administered experimental exact and approximate arithmetic tasks, and standardized measures of math fluency and calculation. Cognitive measures included the Attention Network Test (ANT), and standardized measures of fine motor skills, verbal working memory (WM), and visual-spatial WM. Children with SBM performed similarly to peers on exact arithmetic, but more poorly on approximate and standardized arithmetic measures. On the ANT, children with SBM differed from controls on orienting attention, but not on alerting and executive attention. Multiple mediation models showed that fine motor skills and verbal WM mediated the relation of group to approximate arithmetic; fine motor skills and visual-spatial WM mediated the relation of group to math fluency; and verbal and visual-spatial WM mediated the relation of group to math calculation. Attention was not a significant mediator of the effects of group for any aspect of math in this study. Results are discussed with reference to models of attention, WM, and mathematical cognition. (c) 2015 APA, all rights reserved).

Survey of meshless and generalized finite element methods: A unified approach

NASA Astrophysics Data System (ADS)

Babuška, Ivo; Banerjee, Uday; Osborn, John E.

In the past few years meshless methods for numerically solving partial differential equations have come into the focus of interest, especially in the engineering community. This class of methods was essentially stimulated by difficulties related to mesh generation. Mesh generation is delicate in many situations, for instance, when the domain has complicated geometry; when the mesh changes with time, as in crack propagation, and remeshing is required at each time step; when a Lagrangian formulation is employed, especially with nonlinear PDEs. In addition, the need for flexibility in the selection of approximating functions (e.g., the flexibility to use non-polynomial approximating functions), has played a significant role in the development of meshless methods. There are many recent papers, and two books, on meshless methods; most of them are of an engineering character, without any mathematical analysis.In this paper we address meshless methods and the closely related generalized finite element methods for solving linear elliptic equations, using variational principles. We give a unified mathematical theory with proofs, briefly address implementational aspects, present illustrative numerical examples, and provide a list of references to the current literature.The aim of the paper is to provide a survey of a part of this new field, with emphasis on mathematics. We present proofs of essential theorems because we feel these proofs are essential for the understanding of the mathematical aspects of meshless methods, which has approximation theory as a major ingredient. As always, any new field is stimulated by and related to older ideas. This will be visible in our paper.

Does the Approximate Number System Serve as a Foundation for Symbolic Mathematics?

ERIC Educational Resources Information Center

Szkudlarek, Emily; Brannon, Elizabeth M.

2017-01-01

In this article we first review evidence for the approximate number system (ANS), an evolutionarily ancient and developmentally conservative cognitive mechanism for representing number without language. We then critically review five different lines of support for the proposal that symbolic representations of number build upon the ANS, and discuss…

Mathematical analysis of the boundary-integral based electrostatics estimation approximation for molecular solvation: exact results for spherical inclusions.

PubMed

Bardhan, Jaydeep P; Knepley, Matthew G

2011-09-28

We analyze the mathematically rigorous BIBEE (boundary-integral based electrostatics estimation) approximation of the mixed-dielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to generalized Born models. First, our results suggest a new perspective for analyzing fast electrostatic models: the separation of variables between material properties (the dielectric constants) and geometry (the solute dielectric boundary and charge distribution). Second, we find that the eigenfunctions of the reaction-potential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing charge-charge interactions in molecular binding. Third, a comparison of BIBEE to the recent GBε theory suggests a modified BIBEE model capable of predicting electrostatic solvation free energies to within 4% of a full numerical Poisson calculation. This modified model leads to a projection-framework understanding of BIBEE and suggests opportunities for future improvements. © 2011 American Institute of Physics

Advanced theoretical and experimental studies in automatic control and information systems. [including mathematical programming and game theory

NASA Technical Reports Server (NTRS)

Desoer, C. A.; Polak, E.; Zadeh, L. A.

1974-01-01

A series of research projects is briefly summarized which includes investigations in the following areas: (1) mathematical programming problems for large system and infinite-dimensional spaces, (2) bounded-input bounded-output stability, (3) non-parametric approximations, and (4) differential games. A list of reports and papers which were published over the ten year period of research is included.

The Development of K-8 Progress Monitoring Measures in Mathematics for Use with the 2% and General Education Populations: Kindergarten. Technical Report # 0921

ERIC Educational Resources Information Center

Alonzo, Julie; Tindal, Gerald

2009-01-01

In this technical report, we describe the development and piloting of a series of mathematics progress monitoring measures intended for use with students in kindergarten. These measures, available as part of easyCBM[TM], an online progress monitoring assessment system, were developed in 2008 and administered to approximately 2800 students from…

Mathematical modeling and simulation of the space shuttle imaging radar antennas

NASA Technical Reports Server (NTRS)

Campbell, R. W.; Melick, K. E.; Coffey, E. L., III

1978-01-01

Simulations of space shuttle synthetic aperture radar antennas under the influence of space environmental conditions were carried out at L, C, and X-band. Mathematical difficulties in modeling large, non-planar array antennas are discussed, and an approximate modeling technique is presented. Results for several antenna error conditions are illustrated in far-field profile patterns, earth surface footprint contours, and summary graphs.

A Multifaceted Mathematical Approach for Complex Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alexander, F.; Anitescu, M.; Bell, J.

2012-03-07

Applied mathematics has an important role to play in developing the tools needed for the analysis, simulation, and optimization of complex problems. These efforts require the development of the mathematical foundations for scientific discovery, engineering design, and risk analysis based on a sound integrated approach for the understanding of complex systems. However, maximizing the impact of applied mathematics on these challenges requires a novel perspective on approaching the mathematical enterprise. Previous reports that have surveyed the DOE's research needs in applied mathematics have played a key role in defining research directions with the community. Although these reports have had significantmore » impact, accurately assessing current research needs requires an evaluation of today's challenges against the backdrop of recent advances in applied mathematics and computing. To address these needs, the DOE Applied Mathematics Program sponsored a Workshop for Mathematics for the Analysis, Simulation and Optimization of Complex Systems on September 13-14, 2011. The workshop had approximately 50 participants from both the national labs and academia. The goal of the workshop was to identify new research areas in applied mathematics that will complement and enhance the existing DOE ASCR Applied Mathematics Program efforts that are needed to address problems associated with complex systems. This report describes recommendations from the workshop and subsequent analysis of the workshop findings by the organizing committee.« less

Mathematical model and software for investigation of internal ballistic processes in high-speed projectile installations

NASA Astrophysics Data System (ADS)

Diachkovskii, A. S.; Zykova, A. I.; Ishchenko, A. N.; Kasimov, V. Z.; Rogaev, K. S.; Sidorov, A. D.

2017-11-01

This paper describes a software package that allows to explore the interior ballistics processes occurring in a shot scheme with bulk charges using propellant pasty substances at various loading schemes, etc. As a mathematical model, a model of a polydisperse mixture of non-deformable particles and a carrier gas phase is used in the quasi-one-dimensional approximation. Writing the equations of the mathematical model allows to use it to describe a broad class of interior ballistics processes. Features of the using approach are illustrated by calculating the ignition period for the charge of tubular propellant.

Improving accessibility to mathematical formulas: the Wikipedia Math Accessor

NASA Astrophysics Data System (ADS)

Fuentes Sepúlveda, J.; Ferres, L.

2012-09-01

Mathematics accessibility is an important topic for inclusive education. In this paper, we make Wikipedia's repository of mathematical formulas accessible by providing a natural language description of its more than 420,000 formulas using a well-researched sub-language. We also contribute by targeting Spanish speakers, for whom assistive technologies, particularly domain-specific technologies like the one described here, are scarce. Our focus on the semantics of formulas (rather than their visual appearance) allowed us to generate verbalizations with a precision of approximately 80% of understandable descriptions, as shown in an evaluation with sighted users.

Non-symbolic arithmetic in adults and young children.

PubMed

Barth, Hilary; La Mont, Kristen; Lipton, Jennifer; Dehaene, Stanislas; Kanwisher, Nancy; Spelke, Elizabeth

2006-01-01

Five experiments investigated whether adults and preschool children can perform simple arithmetic calculations on non-symbolic numerosities. Previous research has demonstrated that human adults, human infants, and non-human animals can process numerical quantities through approximate representations of their magnitudes. Here we consider whether these non-symbolic numerical representations might serve as a building block of uniquely human, learned mathematics. Both adults and children with no training in arithmetic successfully performed approximate arithmetic on large sets of elements. Success at these tasks did not depend on non-numerical continuous quantities, modality-specific quantity information, the adoption of alternative non-arithmetic strategies, or learned symbolic arithmetic knowledge. Abstract numerical quantity representations therefore are computationally functional and may provide a foundation for formal mathematics.

On mathematical modelling of aeroelastic problems with finite element method

NASA Astrophysics Data System (ADS)

Sváček, Petr

2018-06-01

This paper is interested in solution of two-dimensional aeroelastic problems. Two mathematical models are compared for a benchmark problem. First, the classical approach of linearized aerodynamical forces is described to determine the aeroelastic instability and the aeroelastic response in terms of frequency and damping coefficient. This approach is compared to the coupled fluid-structure model solved with the aid of finite element method used for approximation of the incompressible Navier-Stokes equations. The finite element approximations are coupled to the non-linear motion equations of a flexibly supported airfoil. Both methods are first compared for the case of small displacement, where the linearized approach can be well adopted. The influence of nonlinearities for the case of post-critical regime is discussed.

David crighton, 1942-2000: a commentary on his career and his influence on aeroacoustic theory

NASA Astrophysics Data System (ADS)

Ffowcs Williams, John E.

David Crighton, a greatly admired figure in fluid mechanics, Head of the Department of Applied Mathematics and Theoretical Physics at Cambridge, and Master of Jesus College, Cambridge, died at the peak of his career. He had made important contributions to the theory of waves generated by unsteady flow. Crighton's work was always characterized by the application of rigorous mathematical approximations to fluid mechanical idealizations of practically relevant problems. At the time of his death, he was certainly the most influential British applied mathematical figure, and his former collaborators and students form a strong school that continues his special style of mathematical application. Rigorous analysis of well-posed aeroacoustical problems was transformed by David Crighton.

Approximate Number Sense, Symbolic Number Processing, or Number-Space Mappings: What Underlies Mathematics Achievement?

ERIC Educational Resources Information Center

Sasanguie, Delphine; Gobel, Silke M.; Moll, Kristina; Smets, Karolien; Reynvoet, Bert

2013-01-01

In this study, the performance of typically developing 6- to 8-year-old children on an approximate number discrimination task, a symbolic comparison task, and a symbolic and nonsymbolic number line estimation task was examined. For the first time, children's performances on these basic cognitive number processing tasks were explicitly contrasted…

Non-Symbolic Arithmetic Abilities and Mathematics Achievement in the First Year of Formal Schooling

ERIC Educational Resources Information Center

Gilmore, Camilla K.; McCarthy, Shannon E.; Spelke, Elizabeth S.

2010-01-01

Children take years to learn symbolic arithmetic. Nevertheless, non-human animals, human adults with no formal education, and human infants represent approximate number in arrays of objects and sequences of events, and they use these capacities to perform approximate addition and subtraction. Do children harness these abilities when they begin to…

Nonlinear functional approximation with networks using adaptive neurons

NASA Technical Reports Server (NTRS)

Tawel, Raoul

1992-01-01

A novel mathematical framework for the rapid learning of nonlinear mappings and topological transformations is presented. It is based on allowing the neuron's parameters to adapt as a function of learning. This fully recurrent adaptive neuron model (ANM) has been successfully applied to complex nonlinear function approximation problems such as the highly degenerate inverse kinematics problem in robotics.

The Nation's Report Card[TM]: Mathematics 2007 Performance of Public School Students in Puerto Rico--Focus on the Content Areas. NCES 2009-451

ERIC Educational Resources Information Center

Dion, G. S.; Kuang, M.; Dresher, A. R.

2008-01-01

In 2007, public school students in Puerto Rico at grades 4 and 8 participated in a Spanish-language version of the National Assessment of Educational Progress (NAEP) in mathematics. A representative sample of approximately 2,800 students from 100 public schools was assessed at each grade. This report contains performance results on NAEP…

The Development of K-8 Progress Monitoring Measures in Mathematics for Use with the 2% and General Education Populations: Grade 1. Technical Report # 0919

ERIC Educational Resources Information Center

Alonzo, Julie; Tindal, Gerald

2009-01-01

In this technical report, we describe the development and piloting of a series of mathematics progress monitoring measures intended for use with students in grade 1. These measures, available as part of easyCBM [TM], an online progress monitoring assessment system, were developed in 2008 and administered to approximately 2800 students from schools…

An Investigation of the Relationship of Achievement Motivation with Achievement in Mathematics for Students in the United States and Japan.

ERIC Educational Resources Information Center

Harnisch, Delwyn L.; Ryan, Katherine E.

A study was made of cross-cultural patterns of achievement motivation in relationship to the mathematics achievement of Japanese and American boys and girls approximately 16 years of age. Sample sizes were 9,582 for the United States subjects (specifically, from Illinois) and 1,700 for the participants from Japan. Data came from performance on the…

Analysis of Student and School Level Variables Related to Mathematics Self-Efficacy Level Based on PISA 2012 Results for China-Shanghai, Turkey, and Greece

ERIC Educational Resources Information Center

Usta, H. Gonca

2016-01-01

This study aims to analyze the student and school level variables that affect students' self-efficacy levels in mathematics in China-Shanghai, Turkey, and Greece based on PISA 2012 results. In line with this purpose, the hierarchical linear regression model (HLM) was employed. The interschool variability is estimated at approximately 17% in…

Non-symbolic approximate arithmetic training improves math performance in preschoolers.

PubMed

Park, Joonkoo; Bermudez, Vanessa; Roberts, Rachel C; Brannon, Elizabeth M

2016-12-01

Math proficiency at early school age is an important predictor of later academic achievement. Thus, an important goal for society should be to improve math readiness in preschool-age children, especially in low-income children who typically arrive in kindergarten with less mathematical competency than their higher income peers. The majority of existing research-based math intervention programs target symbolic verbal number concepts in young children. However, very little attention has been paid to the preverbal intuitive ability to approximately represent numerical quantity, which is hypothesized to be an important foundation for full-fledged mathematical thinking. Here, we tested the hypothesis that repeated engagement of non-symbolic approximate addition and subtraction of large arrays of items results in improved math skills in very young children, an idea that stems from our previous studies in adults. In the current study, 3- to 5-year-olds showed selective improvements in math skills after multiple days of playing a tablet-based non-symbolic approximate arithmetic game compared with children who played a memory game. These findings, collectively with our previous reports, suggest that mental manipulation of approximate numerosities provides an important tool for improving math readiness, even in preschoolers who have yet to master the meaning of number words. Copyright © 2016 Elsevier Inc. All rights reserved.

Approximate number sense correlates with math performance in gifted adolescents.

PubMed

Wang, Jinjing Jenny; Halberda, Justin; Feigenson, Lisa

2017-05-01

Nonhuman animals, human infants, and human adults all share an Approximate Number System (ANS) that allows them to imprecisely represent number without counting. Among humans, people differ in the precision of their ANS representations, and these individual differences have been shown to correlate with symbolic mathematics performance in both children and adults. For example, children with specific math impairment (dyscalculia) have notably poor ANS precision. However, it remains unknown whether ANS precision contributes to individual differences only in populations of people with lower or average mathematical abilities, or whether this link also is present in people who excel in math. Here we tested non-symbolic numerical approximation in 13- to 16-year old gifted children enrolled in a program for talented adolescents (the Center for Talented Youth). We found that in this high achieving population, ANS precision significantly correlated with performance on the symbolic math portion of two common standardized tests (SAT and ACT) that typically are administered to much older students. This relationship was robust even when controlling for age, verbal performance, and reaction times in the approximate number task. These results suggest that the Approximate Number System is linked to symbolic math performance even at the top levels of math performance. Copyright © 2017 Elsevier B.V. All rights reserved.

Non-symbolic approximate arithmetic training improves math performance in preschoolers

PubMed Central

Park, Joonkoo; Bermudez, Vanessa; Roberts, Rachel C.; Brannon, Elizabeth M.

2016-01-01

Math proficiency in early school age is an important predictor of later academic achievement. Thus, an important goal for society should be to improve math readiness in pre-school age children, especially in low-income children who typically arrive in kindergarten with less mathematical competency than their higher-income peers. The majority of existing research-based math intervention programs target symbolic, verbal number concepts in young children. However, very little attention has been paid to the preverbal, intuitive ability to approximately represent numerical quantity, which is hypothesized to be an important foundation for full-fledged mathematical thinking. Here, we test the hypothesis that repeated engagement of non-symbolic approximate addition and subtraction of large array of items results in improved math skills in very young children, an idea that stems from our previous studies in adults. Three to five year-old children showed selective improvements in math skills after multiple days of playing a tablet-based non-symbolic approximate arithmetic game compared to children who played a memory game. These findings, collectively with our previous reports, suggest that mental manipulation of approximate numerosities provides an important tool for improving math readiness, even in preschoolers who have yet to master the meaning of number words. PMID:27596808

Approximate Solutions for a Self-Folding Problem of Carbon Nanotubes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Y Mikata

2006-08-22

This paper treats approximate solutions for a self-folding problem of carbon nanotubes. It has been observed in the molecular dynamics calculations [1] that a carbon nanotube with a large aspect ratio can self-fold due to van der Waals force between the parts of the same carbon nanotube. The main issue in the self-folding problem is to determine the minimum threshold length of the carbon nanotube at which it becomes possible for the carbon nanotube to self-fold due to the van der Waals force. An approximate mathematical model based on the force method is constructed for the self-folding problem of carbonmore » nanotubes, and it is solved exactly as an elastica problem using elliptic functions. Additionally, three other mathematical models are constructed based on the energy method. As a particular example, the lower and upper estimates for the critical threshold (minimum) length are determined based on both methods for the (5,5) armchair carbon nanotube.« less

Gender Representation on Journal Editorial Boards in the Mathematical Sciences.

PubMed

Topaz, Chad M; Sen, Shilad

2016-01-01

We study gender representation on the editorial boards of 435 journals in the mathematical sciences. Women are known to comprise approximately 15% of tenure-stream faculty positions in doctoral-granting mathematical sciences departments in the United States. Compared to this group, we find that 8.9% of the 13067 editorships in our study are held by women. We describe group variations within the editorships by identifying specific journals, subfields, publishers, and countries that significantly exceed or fall short of this average. To enable our study, we develop a semi-automated method for inferring gender that has an estimated accuracy of 97.5%. Our findings provide the first measure of gender distribution on editorial boards in the mathematical sciences, offer insights that suggest future studies in the mathematical sciences, and introduce new methods that enable large-scale studies of gender distribution in other fields.

Gender Representation on Journal Editorial Boards in the Mathematical Sciences

PubMed Central

2016-01-01

We study gender representation on the editorial boards of 435 journals in the mathematical sciences. Women are known to comprise approximately 15% of tenure-stream faculty positions in doctoral-granting mathematical sciences departments in the United States. Compared to this group, we find that 8.9% of the 13067 editorships in our study are held by women. We describe group variations within the editorships by identifying specific journals, subfields, publishers, and countries that significantly exceed or fall short of this average. To enable our study, we develop a semi-automated method for inferring gender that has an estimated accuracy of 97.5%. Our findings provide the first measure of gender distribution on editorial boards in the mathematical sciences, offer insights that suggest future studies in the mathematical sciences, and introduce new methods that enable large-scale studies of gender distribution in other fields. PMID:27536970

GENASIS Mathematics : Object-oriented manifolds, operations, and solvers for large-scale physics simulations

NASA Astrophysics Data System (ADS)

Cardall, Christian Y.; Budiardja, Reuben D.

2018-01-01

The large-scale computer simulation of a system of physical fields governed by partial differential equations requires some means of approximating the mathematical limit of continuity. For example, conservation laws are often treated with a 'finite-volume' approach in which space is partitioned into a large number of small 'cells,' with fluxes through cell faces providing an intuitive discretization modeled on the mathematical definition of the divergence operator. Here we describe and make available Fortran 2003 classes furnishing extensible object-oriented implementations of simple meshes and the evolution of generic conserved currents thereon, along with individual 'unit test' programs and larger example problems demonstrating their use. These classes inaugurate the Mathematics division of our developing astrophysics simulation code GENASIS (Gen eral A strophysical Si mulation S ystem), which will be expanded over time to include additional meshing options, mathematical operations, solver types, and solver variations appropriate for many multiphysics applications.

Phonological awareness and mathematical difficulty: a longitudinal perspective.

PubMed

Jordan, Julie-Ann; Wylie, Judith; Mulhern, Gerry

2010-03-01

The present longitudinal study sought to investigate the impact of poor phonology on children's mathematical status. From a screening sample of 256 five-year-olds, 82 children were identified as either typically achieving (TA; N = 31), having comorbid poor phonology and mathematical difficulties (PDMD; N = 31), or having only poor phonology (phonological difficulty, PD; N = 20). Children were assessed on eight components of informal and formal mathematics achievement at ages 5-7 years. PD children were found to have significant impairments in some, mainly formal, components of mathematics by age 7 compared to TA children. Analysis also revealed that, by age 7, approximately half of the PD children met the criteria for PDMD, while the remainder exhibited less severe deficits in some components of formal mathematics. Children's mathematical performance at age 5, however, did not predict which PD children were more likely to become PDMD at age 7, nor did they differ in terms of phonological awareness at age 5. However, those PD children who later became PDMD had lower scores on verbal and non-verbal tests of general ability.

Early numerical foundations of young children's mathematical development.

PubMed

Chu, Felicia W; vanMarle, Kristy; Geary, David C

2015-04-01

This study focused on the relative contributions of the acuity of the approximate number system (ANS) and knowledge of quantitative symbols to young children's early mathematical learning. At the beginning of preschool, 191 children (Mage=46 months) were administered tasks that assessed ANS acuity and explicit knowledge of the cardinal values represented by number words, and their mathematics achievement was assessed at the end of the school year. Children's executive functions, intelligence, and preliteracy skills and their parents' educational levels were also assessed and served as covariates. Both the ANS and cardinality tasks were significant predictors of end-of-year mathematics achievement with and without control of the covariates. As simultaneous predictors and with control of the covariates, cardinality remained significantly related to mathematics achievement, but ANS acuity did not. Mediation analyses revealed that the relation between ANS acuity and mathematics achievement was fully mediated by cardinality, suggesting that the ANS may facilitate children's explicit understanding of cardinal value and in this way may indirectly influence early mathematical learning. Copyright © 2015 Elsevier Inc. All rights reserved.

ANS acuity and mathematics ability in preschoolers from low-income homes: contributions of inhibitory control.

PubMed

Fuhs, Mary Wagner; McNeil, Nicole M

2013-01-01

Recent findings by Libertus, Feigenson, and Halberda (2011) suggest that there is an association between the acuity of young children's approximate number system (ANS) and their mathematics ability before exposure to instruction in formal schooling. The present study examined the generalizability and validity of these findings in a sample of preschoolers from low-income homes. Children attending Head Start (N = 103) completed measures to assess ANS acuity, mathematics ability, receptive vocabulary, and inhibitory control. Results showed only a weak association between ANS acuity and mathematics ability that was reduced to non-significance when controlling for a direct measure of receptive vocabulary. Results also revealed that inhibitory control plays an important role in the relation between ANS acuity and mathematics ability. Specifically, ANS acuity accounted for significant variance in mathematics ability over and above receptive vocabulary, but only for ANS acuity trials in which surface area conflicted with numerosity. Moreover, this association became non-significant when controlling for inhibitory control. These results suggest that early mathematical experiences prior to formal schooling may influence the strength of the association between ANS acuity and mathematics ability and that inhibitory control may drive that association in young children. © 2012 Blackwell Publishing Ltd.

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

NASA Astrophysics Data System (ADS)

Shadid, J. N.; Smith, T. M.; Cyr, E. C.; Wildey, T. M.; Pawlowski, R. P.

2016-09-01

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts to apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier-Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shadid, J.N., E-mail: jnshadi@sandia.gov; Department of Mathematics and Statistics, University of New Mexico; Smith, T.M.

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts tomore » apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.« less

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shadid, J. N.; Smith, T. M.; Cyr, E. C.

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. The understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In our study we report on initial efforts to apply integrated adjoint-basedmore » computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. We present the initial results that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.« less

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

DOE PAGES

Shadid, J. N.; Smith, T. M.; Cyr, E. C.; ...

2016-05-20

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. The understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In our study we report on initial efforts to apply integrated adjoint-basedmore » computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. We present the initial results that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.« less

The Effects of Computer Assisted Instruction Materials on Approximate Number Skills of Students with Dyscalculia

ERIC Educational Resources Information Center

Mutlu, Yilmaz; Akgün, Levent

2017-01-01

The aim of this study is to examine the effects of computer assisted instruction materials on approximate number skills of students with mathematics learning difficulties. The study was carried out with pretest-posttest quasi experimental method with a single subject. The participants of the study consist of a girl and two boys who attend 3rd…

Using the History of Mathematics as a Starting Point for Investigations: Some Examples on Approximations

ERIC Educational Resources Information Center

Lopez-Real, Francis

2004-01-01

This paper discusses an investigative approach to problems concerned with approximations. Two problems are analysed in detail and both are inspired by their historical origins. The first examines an ancient Chinese formula for calculating the area of a segment. The second looks at Durer's construction for the trisection of an angle. It is argued…

Approximating the Practice of Mathematics Teaching: What Learning Can Web-Based, Multimedia Storyboarding Software Enable?

ERIC Educational Resources Information Center

Herbst, Patricio; Chieu, Vu-Minh; Rougée, Annick

2014-01-01

This paper builds on Grossman's notion of approximations of practice as scaled-down opportunities for preservice teachers to learn to teach by doing. The authors propose the use of media rich, collaborative web-authoring tools for preservice teachers to create, complete, or edit scenarios in which they practice particular activities of teaching,…

Understanding the Mapping between Numerical Approximation and Number Words: Evidence from Williams Syndrome and Typical Development

ERIC Educational Resources Information Center

Libertus, Melissa E.; Feigenson, Lisa; Halberda, Justin; Landau, Barbara

2014-01-01

All numerate humans have access to two systems of number representation: an exact system that is argued to be based on language and that supports formal mathematics, and an Approximate Number System (ANS) that is present at birth and appears independent of language. Here we examine the interaction between these two systems by comparing the…

Mathematics anxiety in secondary students in England.

PubMed

Chinn, Steve

2009-02-01

Whatever the changes that are made to the mathematics curriculum in England, there will always remain a problem with mathematics anxiety. Maths anxiety is rarely facilitative. This study examined aspects of mathematics in secondary schools and how students rated them as sources of anxiety. Over 2000 students in independent and mainstream schools in England completed a 20-item questionnaire designed to investigate maths anxiety levels. The same questionnaire was given to over 440 dyslexic males in specialist schools within the same age range. The results showed that examinations and tests create high levels of anxiety in approximately 4% of students. The results suggest that certain aspects and topics in the maths curriculum, such as long division, cause similar levels of anxiety for students in all year groups in secondary schools.

A Mathematical Evaluation of the Core Conductor Model

PubMed Central

Clark, John; Plonsey, Robert

1966-01-01

This paper is a mathematical evaluation of the core conductor model where its three dimensionality is taken into account. The problem considered is that of a single, active, unmyelinated nerve fiber situated in an extensive, homogeneous, conducting medium. Expressions for the various core conductor parameters have been derived in a mathematically rigorous manner according to the principles of electromagnetic theory. The purpose of employing mathematical rigor in this study is to bring to light the inherent assumptions of the one dimensional core conductor model, providing a method of evaluating the accuracy of this linear model. Based on the use of synthetic squid axon data, the conclusion of this study is that the linear core conductor model is a good approximation for internal but not external parameters. PMID:5903155

Structural optimization: Status and promise

NASA Astrophysics Data System (ADS)

Kamat, Manohar P.

Chapters contained in this book include fundamental concepts of optimum design, mathematical programming methods for constrained optimization, function approximations, approximate reanalysis methods, dual mathematical programming methods for constrained optimization, a generalized optimality criteria method, and a tutorial and survey of multicriteria optimization in engineering. Also included are chapters on the compromise decision support problem and the adaptive linear programming algorithm, sensitivity analyses of discrete and distributed systems, the design sensitivity analysis of nonlinear structures, optimization by decomposition, mixed elements in shape sensitivity analysis of structures based on local criteria, and optimization of stiffened cylindrical shells subjected to destabilizing loads. Other chapters are on applications to fixed-wing aircraft and spacecraft, integrated optimum structural and control design, modeling concurrency in the design of composite structures, and tools for structural optimization. (No individual items are abstracted in this volume)

Using Wavelet Bases to Separate Scales in Quantum Field Theory

NASA Astrophysics Data System (ADS)

Michlin, Tracie L.

This thesis investigates the use of Daubechies wavelets to separate scales in local quantum field theory. Field theories have an infinite number of degrees of freedom on all distance scales. Quantum field theories are believed to describe the physics of subatomic particles. These theories have no known mathematically convergent approximation methods. Daubechies wavelet bases can be used separate degrees of freedom on different distance scales. Volume and resolution truncations lead to mathematically well-defined truncated theories that can be treated using established methods. This work demonstrates that flow equation methods can be used to block diagonalize truncated field theoretic Hamiltonians by scale. This eliminates the fine scale degrees of freedom. This may lead to approximation methods and provide an understanding of how to formulate well-defined fine resolution limits.

The contribution of parent-child numeracy activities to young Chinese children's mathematical ability.

PubMed

Huang, Qi; Zhang, Xiao; Liu, Yingyi; Yang, Wen; Song, Zhanmei

2017-09-01

A growing body of recent research has shown that parent-child mathematical activities have a strong effect on children's mathematical learning. However, this research was conducted predominantly in Western societies and focused mainly on mothers' involvement in such activities. This study aimed to examine both mother-child and father-child numeracy activities in Hong Kong Chinese families and both parents' unique roles in predicting young Chinese children's mathematics ability. A sample of 104 Hong Kong Chinese children aged approximately 5 years and their mothers and fathers participated in this study. Mothers and fathers independently reported the frequency of their own numeracy activities with their children. Children were assessed individually using two measures of mathematical ability. Hierarchical regression models were used to investigate the contribution of parent-child numeracy activities to children's mathematical ability. Mothers' participation in number skill activities and fathers' participation in number game and application activities significantly predicted their children's mathematical performance even after controlling for background variables and children's language ability. This study extends previous research with a sample of Chinese kindergarten children and shows that parent-child numeracy activities are related to young children's mathematical ability. The findings highlight the important roles that mothers and fathers play in their young children's mathematical learning. © 2017 The British Psychological Society.

Mathematical description of drug-target interactions: application to biologics that bind to targets with two binding sites.

PubMed

Gibiansky, Leonid; Gibiansky, Ekaterina

2018-02-01

The emerging discipline of mathematical pharmacology occupies the space between advanced pharmacometrics and systems biology. A characteristic feature of the approach is application of advance mathematical methods to study the behavior of biological systems as described by mathematical (most often differential) equations. One of the early application of mathematical pharmacology (that was not called this name at the time) was formulation and investigation of the target-mediated drug disposition (TMDD) model and its approximations. The model was shown to be remarkably successful, not only in describing the observed data for drug-target interactions, but also in advancing the qualitative and quantitative understanding of those interactions and their role in pharmacokinetic and pharmacodynamic properties of biologics. The TMDD model in its original formulation describes the interaction of the drug that has one binding site with the target that also has only one binding site. Following the framework developed earlier for drugs with one-to-one binding, this work aims to describe a rigorous approach for working with similar systems and to apply it to drugs that bind to targets with two binding sites. The quasi-steady-state, quasi-equilibrium, irreversible binding, and Michaelis-Menten approximations of the model are also derived. These equations can be used, in particular, to predict concentrations of the partially bound target (RC). This could be clinically important if RC remains active and has slow internalization rate. In this case, introduction of the drug aimed to suppress target activity may lead to the opposite effect due to RC accumulation.

Longitudinal study of low and high achievers in early mathematics.

PubMed

Navarro, Jose I; Aguilar, Manuel; Marchena, Esperanza; Ruiz, Gonzalo; Menacho, Inmaculada; Van Luit, Johannes E H

2012-03-01

Longitudinal studies allow us to identify, which specific maths skills are weak in young children, and whether there is a continuing weakness in these areas throughout their school years. This 2-year study investigated whether certain socio-demographic variables affect early mathematical competency in children aged 5-7 years. A randomly selected sample of 127 students (64 female; 63 male) participated. At the start of the study, the students were approximately 5 years old (M= 5.2; SD= 0.28; range = 4.5-5.8). The students were assessed using the Early Numeracy Test and then allocated to a high (n= 26), middle (n= 76), or low (n= 25) achievers group. The same children were assessed again with the Early Numeracy Test at 6 and 7 years old, respectively. Eight socio-demographic characteristics were also evaluated: family model, education of the parent(s), job of the parent(s), number of family members, birth order, number of computers at home, frequency of teacher visits, and hours watching television. Early Numeracy Test scores were more consistent for the high-achievers group than for the low-achievers group. Approximately 5.5% of low achievers obtained low scores throughout the study. A link between specific socio-demographic characteristics and early achievement in mathematics was only found for number of computers at home. The level of mathematical ability among students aged 5-7 years remains relatively stable regardless of the initial level of achievement. However, early screening for mathematics learning disabilities could be useful in helping low-achieving students overcome learning obstacles. ©2011 The British Psychological Society.

Mathematical aspects of finite element methods for incompressible viscous flows

NASA Technical Reports Server (NTRS)

Gunzburger, M. D.

1986-01-01

Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.

Simplified mathematics for customized refractive surgery.

PubMed

Preussner, Paul Rolf; Wahl, Jochen

2003-03-01

To describe a simple mathematical approach to customized corneal refractive surgery or customized intraocular lens (IOL) design that allows "hypervision" and to investigate the accuracy limits. University eye hospital, Mainz, Germany. Corneal shape and at least 1 IOL surface are approximated by the well-known Cartesian conic section curves (ellipsoid, paraboloid, or hyperboloid). They are characterized by only 2 parameters, the vertex radius and the numerical eccentricity. Residual refraction errors for this approximation are calculated by numerical ray tracing. These errors can be displayed as a 2-dimensional refraction map across the pupil or by blurring the image of a Landolt ring superimposed on the retinal receptor grid, giving an overall impression of the visual outcome. If the eye is made emmetropic for paraxial rays and if the numerical eccentricities of the cornea and lens are appropriately fitted to each other, the residual refractive errors are small enough to allow hypervision. Visual acuity of at least 2.0 (20/10) appears to be possible, particularly for mesopic pupil diameters. However, customized optics may have limited application due to their sensitivity to misalignment errors such as decentrations or rotations. The mathematical approach described by Descartes 350 years ago is adequate to calculate hypervision optics for the human eye. The availability of suitable mathematical tools should, however, not be viewed with too much optimism as long as the accuracy of the implementation in surgical procedures is limited.

Approximating a nonlinear advanced-delayed equation from acoustics

NASA Astrophysics Data System (ADS)

Teodoro, M. Filomena

2016-10-01

We approximate the solution of a particular non-linear mixed type functional differential equation from physiology, the mucosal wave model of the vocal oscillation during phonation. The mathematical equation models a superficial wave propagating through the tissues. The numerical scheme is adapted from the work presented in [1, 2, 3], using homotopy analysis method (HAM) to solve the non linear mixed type equation under study.

Mathematical, Constitutive and Numerical Modelling of Catastrophic Landslides and Related Phenomena

NASA Astrophysics Data System (ADS)

Pastor, M.; Fernández Merodo, J. A.; Herreros, M. I.; Mira, P.; González, E.; Haddad, B.; Quecedo, M.; Tonni, L.; Drempetic, V.

2008-02-01

Mathematical and numerical models are a fundamental tool for predicting the behaviour of geostructures and their interaction with the environment. The term “mathematical model” refers to a mathematical description of the more relevant physical phenomena which take place in the problem being analyzed. It is indeed a wide area including models ranging from the very simple ones for which analytical solutions can be obtained to those more complicated requiring the use of numerical approximations such as the finite element method. During the last decades, mathematical, constitutive and numerical models have been very much improved and today their use is widespread both in industry and in research. One special case is that of fast catastrophic landslides, for which simplified methods are not able to provide accurate solutions in many occasions. Moreover, many finite element codes cannot be applied for propagation of the mobilized mass. The purpose of this work is to present an overview of the different alternative mathematical and numerical models which can be applied to both the initiation and propagation mechanisms of fast catastrophic landslides and other related problems such as waves caused by landslides.

Vistas in applied mathematics: Numerical analysis, atmospheric sciences, immunology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balakrishnan, A.V.; Dorodnitsyn, A.A.; Lions, J.L.

1986-01-01

Advances in the theory and application of numerical modeling techniques are discussed in papers contributed, primarily by Soviet scientists, on the occasion of the 60th birthday of Gurii I. Marchuk. Topics examined include splitting techniques for computations of industrial flows, the mathematical foundations of the k-epsilon turbulence model, splitting methods for the solution of the incompressible Navier-Stokes equations, the approximation of inhomogeneous hyperbolic boundary-value problems, multigrid methods, and the finite-element approximation of minimal surfaces. Consideration is given to dynamic modeling of moist atmospheres, satellite observations of the earth radiation budget and the problem of energy-active ocean regions, a numerical modelmore » of the biosphere for use with GCMs, and large-scale modeling of ocean circulation. Also included are several papers on modeling problems in immunology.« less

[Dyscalculia].

PubMed

Räsänen, Pekka

2012-01-01

The information society has raised the value of numeracy. This is a challenge to schools and societies, because individual differences are large already in basic number sense and calculation skills. Approximately 5-7 % of school children have extensive difficulties to keep with the speed of curricular demands, i.e. one child in every classroom. These children often have difficulties in other areas of learning too, but disorders in learning can also manifest only in mathematics. Undiagnosed and untreated mathematical disorders become a lifelong handicap creating a barrier to vocational education. They also hinder independent management of mathematical activities of daily living. Low numeracy is a measurable social problem. Intensive and early special education or neuropsychological rehabilitation can diminish the negative effects of the disorders.

Communication: Analytic continuation of the virial series through the critical point using parametric approximants.

PubMed

Barlow, Nathaniel S; Schultz, Andrew J; Weinstein, Steven J; Kofke, David A

2015-08-21

The mathematical structure imposed by the thermodynamic critical point motivates an approximant that synthesizes two theoretically sound equations of state: the parametric and the virial. The former is constructed to describe the critical region, incorporating all scaling laws; the latter is an expansion about zero density, developed from molecular considerations. The approximant is shown to yield an equation of state capable of accurately describing properties over a large portion of the thermodynamic parameter space, far greater than that covered by each treatment alone.

Theoretical Foundations of Study of Cartography

NASA Astrophysics Data System (ADS)

Talhofer, Václav; Hošková-Mayerová, Šárka

2018-05-01

Cartography and geoinformatics are technical-based fields which deal with modelling and visualization of landscape in the form of a map. The theoretical foundation is necessary to obtain during study of cartography and geoinformatics based mainly on mathematics. For the given subjects, mathematics is necessary for understanding of many procedures that are connected to modelling of the Earth as a celestial body, to ways of its projection into a plane, to methods and procedures of modelling of landscape and phenomena in society and visualization of these models in the form of electronic as well as classic paper maps. Not only general mathematics, but also its extension of differential geometry of curves and surfaces, ways of approximation of lines and surfaces of functional surfaces, mathematical statistics and multi-criterial analyses seem to be suitable and necessary. Underestimation of the significance of mathematical education in cartography and geoinformatics is inappropriate and lowers competence of cartographers and professionals in geographic information science and technology to solve problems.

On the Approximation of Generalized Lipschitz Function by Euler Means of Conjugate Series of Fourier Series

PubMed Central

Kushwaha, Jitendra Kumar

2013-01-01

Approximation theory is a very important field which has various applications in pure and applied mathematics. The present study deals with a new theorem on the approximation of functions of Lipschitz class by using Euler's mean of conjugate series of Fourier series. In this paper, the degree of approximation by using Euler's means of conjugate of functions belonging to Lip (ξ(t), p) class has been obtained. Lipα and Lip (α, p) classes are the particular cases of Lip (ξ(t), p) class. The main result of this paper generalizes some well-known results in this direction. PMID:24379744

A mathematical model of neuro-fuzzy approximation in image classification

NASA Astrophysics Data System (ADS)

Gopalan, Sasi; Pinto, Linu; Sheela, C.; Arun Kumar M., N.

2016-06-01

Image digitization and explosion of World Wide Web has made traditional search for image, an inefficient method for retrieval of required grassland image data from large database. For a given input query image Content-Based Image Retrieval (CBIR) system retrieves the similar images from a large database. Advances in technology has increased the use of grassland image data in diverse areas such has agriculture, art galleries, education, industry etc. In all the above mentioned diverse areas it is necessary to retrieve grassland image data efficiently from a large database to perform an assigned task and to make a suitable decision. A CBIR system based on grassland image properties and it uses the aid of a feed-forward back propagation neural network for an effective image retrieval is proposed in this paper. Fuzzy Memberships plays an important role in the input space of the proposed system which leads to a combined neural fuzzy approximation in image classification. The CBIR system with mathematical model in the proposed work gives more clarity about fuzzy-neuro approximation and the convergence of the image features in a grassland image.

A mathematical study of a random process proposed as an atmospheric turbulence model

NASA Technical Reports Server (NTRS)

Sidwell, K.

1977-01-01

A random process is formed by the product of a local Gaussian process and a random amplitude process, and the sum of that product with an independent mean value process. The mathematical properties of the resulting process are developed, including the first and second order properties and the characteristic function of general order. An approximate method for the analysis of the response of linear dynamic systems to the process is developed. The transition properties of the process are also examined.

Stability Analysis of Finite Difference Approximations to Hyperbolic Systems,and Problems in Applied and Computational Matrix and Operator Theory

DTIC Science & Technology

1990-12-07

Fundaqao Calouste Gulbenkian, Instituto Gulbenkian de Ci~ncia, Centro de C6lculo Cientifico , Coimbra, 1973. 28, Dirac, P. A. M., Spinors in Hilbert Space...Office of Scientific Research grants 1965 Mathematical Association of America Editorial Prize for the article entitled: "Linear Transformations on...matrices" 1966 L.R. Ford Memorial Prize awarded by the Mathematical Association of America for the article , "Permanents" 1989 Outstanding Computer

The research of statistical properties of colorimetric features of screens with a three-component color formation principle

NASA Astrophysics Data System (ADS)

Zharinov, I. O.; Zharinov, O. O.

2017-12-01

The problem of the research is concerned with quantitative analysis of influence of technological variation of the screen color profile parameters on chromaticity coordinates of the displayed image. Some mathematical expressions which approximate the two-dimensional distribution of chromaticity coordinates of an image, which is displayed on the screen with a three-component color formation principle were proposed. Proposed mathematical expressions show the way to development of correction techniques to improve reproducibility of the colorimetric features of displays.

Numerical simulation of injection process of warm carbon dioxide into layer saturated with methane and its hydrate

NASA Astrophysics Data System (ADS)

Khasanov, M. K.; Stolpovsky, M. V.; Gimaltdinov, I. K.

2018-05-01

In this article, in a flat-one-dimensional approximation, a mathematical model is presented for injecting warm carbon dioxide into a methane hydrate formation of finite length. It is established that the model of formation of hydrate of carbon dioxide in the absence of an area saturated with methane and water, under certain parameters, leads to thermodynamic contradiction. The mathematical model of carbon dioxide injection with formation of the region saturated with methane and water is constructed.

Error analysis for spectral approximation of the Korteweg-De Vries equation

NASA Technical Reports Server (NTRS)

Maday, Y.; recent years.

1987-01-01

The conservation and convergence properties of spectral Fourier methods for the numerical approximation of the Korteweg-de Vries equation are analyzed. It is proved that the (aliased) collocation pseudospectral method enjoys the same convergence properties as the spectral Galerkin method, which is less effective from the computational point of view. This result provides a precise mathematical answer to a question raised by several authors in recent years.

Flexible Approximation Model Approach for Bi-Level Integrated System Synthesis

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, Jaroslaw; Kim, Hongman; Ragon, Scott; Soremekun, Grant; Malone, Brett

2004-01-01

Bi-Level Integrated System Synthesis (BLISS) is an approach that allows design problems to be naturally decomposed into a set of subsystem optimizations and a single system optimization. In the BLISS approach, approximate mathematical models are used to transfer information from the subsystem optimizations to the system optimization. Accurate approximation models are therefore critical to the success of the BLISS procedure. In this paper, new capabilities that are being developed to generate accurate approximation models for BLISS procedure will be described. The benefits of using flexible approximation models such as Kriging will be demonstrated in terms of convergence characteristics and computational cost. An approach of dealing with cases where subsystem optimization cannot find a feasible design will be investigated by using the new flexible approximation models for the violated local constraints.

A family of approximate solutions and explicit error estimates for the nonlinear stationary Navier-Stokes problem

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.; Karel, S.

1975-01-01

An algorithm for solving the nonlinear stationary Navier-Stokes problem is developed. Explicit error estimates are given. This mathematical technique is potentially adaptable to the separation problem.

Analysis of anatomic variability in children with low mathematical skills

NASA Astrophysics Data System (ADS)

Han, Zhaoying; Fuchs, Lynn; Davis, Nikki; Cannistraci, Christopher J.; Anderson, Adam W.; Gore, John C.; Dawant, Benoit M.

2008-03-01

Mathematical difficulty affects approximately 5-9% of the population. Studies on individuals with dyscalculia, a neurologically based math disorder, provide important insight into the neural correlates of mathematical ability. For example, cognitive theories, neuropsychological studies, and functional neuroimaging studies in individuals with dyscalculia suggest that the bilateral parietal lobes and intraparietal sulcus are central to mathematical performance. The purpose of the present study was to investigate morphological differences in a group of third grade children with poor math skills. We compare population averages of children with low math skill (MD) to gender and age matched controls with average math ability. Anatomical data were gathered with high resolution MRI and four different population averaging methods were used to study the effect of the normalization technique on the results. Statistical results based on the deformation fields between the two groups show anatomical differences in the bilateral parietal lobes, right frontal lobe, and left occipital/parietal lobe.

The mathematical properties of the quasi-chemical model for microorganism growth-death kinetics in foods.

PubMed

Ross, E W; Taub, I A; Doona, C J; Feeherry, F E; Kustin, K

2005-03-15

Knowledge of the mathematical properties of the quasi-chemical model [Taub, Feeherry, Ross, Kustin, Doona, 2003. A quasi-chemical kinetics model for the growth and death of Staphylococcus aureus in intermediate moisture bread. J. Food Sci. 68 (8), 2530-2537], which is used to characterize and predict microbial growth-death kinetics in foods, is important for its applications in predictive microbiology. The model consists of a system of four ordinary differential equations (ODEs), which govern the temporal dependence of the bacterial life cycle (the lag, exponential growth, stationary, and death phases, respectively). The ODE system derives from a hypothetical four-step reaction scheme that postulates the activity of a critical intermediate as an antagonist to growth (perhaps through a quorum sensing biomechanism). The general behavior of the solutions to the ODEs is illustrated by several examples. In instances when explicit mathematical solutions to these ODEs are not obtainable, mathematical approximations are used to find solutions that are helpful in evaluating growth in the early stages and again near the end of the process. Useful solutions for the ODE system are also obtained in the case where the rate of antagonist formation is small. The examples and the approximate solutions provide guidance in the parameter estimation that must be done when fitting the model to data. The general behavior of the solutions is illustrated by examples, and the MATLAB programs with worked examples are included in the appendices for use by predictive microbiologists for data collected independently.

Mathematical Simulation of Perturbations of Attack Angle of Asymmetric Nanosatellite Passing through Resonance

NASA Astrophysics Data System (ADS)

Lyubimov, V. V.; Kurkina, E. V.

2018-05-01

The authors consider the problem of a dynamic system passing through a low-order resonance, describing an uncontrolled atmospheric descent of an asymmetric nanosatellite in the Earth's atmosphere. The authors perform mathematical and numerical modeling of the motion of the nanosatellite with a small mass-aerodynamic asymmetry relative to the center of mass. The aim of the study is to obtain new reliable approximate analytical estimates of perturbations of the angle of attack of a nanosatellite passing through resonance at angles of attack of not more than 0.5π. By using the stationary phase method, the authors were able to investigate a discontinuous perturbation in the angle of attack of a nanosatellite passing through a resonance with two different nanosatellite designs. Comparison of the results of the numerical modeling and new approximate analytical estimates of the perturbation of the angle of attack confirms the reliability of the said estimates.

The Torsion of Members Having Sections Common in Aircraft Construction

NASA Technical Reports Server (NTRS)

Trayer, George W; March, H W

1930-01-01

Within recent years a great variety of approximate torsion formulas and drafting-room processes have been advocated. In some of these, especially where mathematical considerations are involved, the results are extremely complex and are not generally intelligible to engineers. The principal object of this investigation was to determine by experiment and theoretical investigation how accurate the more common of these formulas are and on what assumptions they are founded and, if none of the proposed methods proved to be reasonable accurate in practice, to produce simple, practical formulas from reasonably correct assumptions, backed by experiment. A second object was to collect in readily accessible form the most useful of known results for the more common sections. Formulas for all the important solid sections that have yielded to mathematical treatment are listed. Then follows a discussion of the torsion of tubular rods with formulas both rigorous and approximate.

Cognitive mechanisms underlying third graders' arithmetic skills: Expanding the pathways to mathematics model.

PubMed

Träff, Ulf; Olsson, Linda; Skagerlund, Kenny; Östergren, Rickard

2018-03-01

A modified pathways to mathematics model was used to examine the cognitive mechanisms underlying arithmetic skills in third graders. A total of 269 children were assessed on tasks tapping the four pathways and arithmetic skills. A path analysis showed that symbolic number processing was directly supported by the linguistic and approximate quantitative pathways. The direct contribution from the four pathways to arithmetic proficiency varied; the linguistic pathway supported single-digit arithmetic and word problem solving, whereas the approximate quantitative pathway supported only multi-digit calculation. The spatial processing and verbal working memory pathways supported only arithmetic word problem solving. The notion of hierarchical levels of arithmetic was supported by the results, and the different levels were supported by different constellations of pathways. However, the strongest support to the hierarchical levels of arithmetic were provided by the proximal arithmetic skills. Copyright © 2017 Elsevier Inc. All rights reserved.

Thermodynamic Modeling and Optimization of the Copper Flash Converting Process Using the Equilibrium Constant Method

NASA Astrophysics Data System (ADS)

Li, Ming-zhou; Zhou, Jie-min; Tong, Chang-ren; Zhang, Wen-hai; Chen, Zhuo; Wang, Jin-liang

2018-05-01

Based on the principle of multiphase equilibrium, a mathematical model of the copper flash converting process was established by the equilibrium constant method, and a computational system was developed with the use of MetCal software platform. The mathematical model was validated by comparing simulated outputs, industrial data, and published data. To obtain high-quality blister copper, a low copper content in slag, and increased impurity removal rate, the model was then applied to investigate the effects of the operational parameters [oxygen/feed ratio (R OF), flux rate (R F), and converting temperature (T)] on the product weights, compositions, and the distribution behaviors of impurity elements. The optimized results showed that R OF, R F, and T should be controlled at approximately 156 Nm3/t, within 3.0 pct, and at approximately 1523 K (1250 °C), respectively.

Exact PDF equations and closure approximations for advective-reactive transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Venturi, D.; Tartakovsky, Daniel M.; Tartakovsky, Alexandre M.

2013-06-01

Mathematical models of advection–reaction phenomena rely on advective flow velocity and (bio) chemical reaction rates that are notoriously random. By using functional integral methods, we derive exact evolution equations for the probability density function (PDF) of the state variables of the advection–reaction system in the presence of random transport velocity and random reaction rates with rather arbitrary distributions. These PDF equations are solved analytically for transport with deterministic flow velocity and a linear reaction rate represented mathematically by a heterog eneous and strongly-correlated random field. Our analytical solution is then used to investigate the accuracy and robustness of the recentlymore » proposed large-eddy diffusivity (LED) closure approximation [1]. We find that the solution to the LED-based PDF equation, which is exact for uncorrelated reaction rates, is accurate even in the presence of strong correlations and it provides an upper bound of predictive uncertainty.« less

A National Symposium on Best Practices for Student Achievement in Science, Mathematics, Engineering, and Technology in Two-Year Hispanic-Serving Institutions (HSIs) (Avondale, Arizona, April 27-28, 2001).

ERIC Educational Resources Information Center

Estrella Mountain Community Coll., Avondale, AZ.

Approximately 130 community colleges in the U.S. are designated as Hispanic Serving Institutions (HSIs). The Census Bureau predicts that there will be approximately 21 million Hispanic residents in the U.S. by 2025. A total of 55% of Hispanic students seeking undergraduate degrees are enrolled in community colleges. Therefore, it is critical that…

Quantum Chemistry in Great Britain: Developing a Mathematical Framework for Quantum Chemistry

NASA Astrophysics Data System (ADS)

Simões, Ana; Gavroglu, Kostas

By 1935 quantum chemistry was already delineated as a distinct sub-discipline due to the contributions of Fritz London, Walter Heitler, Friedrich Hund, Erich Hückel, Robert Mulliken, Linus Pauling, John van Vleck and John Slater. These people are credited with showing that the application of quantum mechanics to the solution of chemical problems was, indeed, possible, especially so after the introduction of a number of new concepts and the adoption of certain approximation methods. And though a number of chemists had started talking of the formation of theoretical or, even, mathematical chemistry, a fully developed mathematical framework of quantum chemistry was still wanting. The work of three persons in particular-of John E. Lennard-Jones, Douglas R. Hartree, and Charles Alfred Coulson-has been absolutely crucial in the development of such a framework. In this paper we shall discuss the work of these three researchers who started their careers in the Cambridge tradition of mathematical physics and who at some point of their careers all became professors of applied mathematics. We shall argue that their work consisted of decisive contributions to the development of such a mathematical framework for quantum chemistry.

Modeling eBook acceptance: A study on mathematics teachers

NASA Astrophysics Data System (ADS)

Jalal, Azlin Abd; Ayub, Ahmad Fauzi Mohd; Tarmizi, Rohani Ahmad

2014-12-01

The integration and effectiveness of eBook utilization in Mathematics teaching and learning greatly relied upon the teachers, hence the need to understand their perceptions and beliefs. The eBook, an individual laptop completed with digitized textbook sofwares, were provided for each students in line with the concept of 1 student:1 laptop. This study focuses on predicting a model on the acceptance of the eBook among Mathematics teachers. Data was collected from 304 mathematics teachers in selected schools using a survey questionnaire. The selection were based on the proportionate stratified sampling. Structural Equation Modeling (SEM) were employed where the model was tested and evaluated and was found to have a good fit. The variance explained for the teachers' attitude towards eBook is approximately 69.1% where perceived usefulness appeared to be a stronger determinant compared to perceived ease of use. This study concluded that the attitude of mathematics teachers towards eBook depends largely on the perception of how useful the eBook is on improving their teaching performance, implying that teachers should be kept updated with the latest mathematical application and sofwares to use with the eBook to ensure positive attitude towards using it in class.

Mathematics and Science Learning Opportunities in Preschool Classrooms

PubMed Central

Piasta, Shayne B.; Pelatti, Christina Yeager; Miller, Heather Lynnine

2014-01-01

Research findings The present study observed and coded instruction in 65 preschool classrooms to examine (a) overall amounts and (b) types of mathematics and science learning opportunities experienced by preschool children as well as (c) the extent to which these opportunities were associated with classroom and program characteristics. Results indicated that children were afforded an average of 24 and 26 minutes of mathematics and science learning opportunities, respectively, corresponding to spending approximately 25% of total instructional time in each domain. Considerable variability existed, however, in the amounts and types of mathematics and science opportunities provided to children in their classrooms; to some extent, this variability was associated with teachers’ years of experience, teachers’ levels of education, and the socioeconomic status of children served in the program. Practice/policy Although results suggest greater integration of mathematics and science in preschool classrooms than previously established, there was considerable diversity in the amounts and types of learning opportunities provided in preschool classrooms. Affording mathematics and science experiences to all preschool children, as outlined in professional and state standards, may require additional professional development aimed at increasing preschool teachers’ understanding and implementation of learning opportunities in these two domains in their classrooms. PMID:25489205

Student and high-school characteristics related to completing a science, technology, engineering or mathematics (STEM) major in college

NASA Astrophysics Data System (ADS)

LeBeau, Brandon; Harwell, Michael; Monson, Debra; Dupuis, Danielle; Medhanie, Amanuel; Post, Thomas R.

2012-04-01

Background: The importance of increasing the number of US college students completing degrees in science, technology, engineering or mathematics (STEM) has prompted calls for research to provide a better understanding of factors related to student participation in these majors, including the impact of a student's high-school mathematics curriculum. Purpose: This study examines the relationship between various student and high-school characteristics and completion of a STEM major in college. Of specific interest is the influence of a student's high-school mathematics curriculum on the completion of a STEM major in college. Sample: The sample consisted of approximately 3500 students from 229 high schools. Students were predominantly Caucasian (80%), with slightly more males than females (52% vs 48%). Design and method: A quasi-experimental design with archival data was used for students who enrolled in, and graduated from, a post-secondary institution in the upper Midwest. To be included in the sample, students needed to have completed at least three years of high-school mathematics. A generalized linear mixed model was used with students nested within high schools. The data were cross-sectional. Results: High-school predictors were not found to have a significant impact on the completion of a STEM major. Significant student-level predictors included ACT mathematics score, gender and high-school mathematics GPA. Conclusions: The results provide evidence that on average students are equally prepared for the rigorous mathematics coursework regardless of the high-school mathematics curriculum they completed.

An operator calculus for surface and volume modeling

NASA Technical Reports Server (NTRS)

Gordon, W. J.

1984-01-01

The mathematical techniques which form the foundation for most of the surface and volume modeling techniques used in practice are briefly described. An outline of what may be termed an operator calculus for the approximation and interpolation of functions of more than one independent variable is presented. By considering the linear operators associated with bivariate and multivariate interpolation/approximation schemes, it is shown how they can be compounded by operator multiplication and Boolean addition to obtain a distributive lattice of approximation operators. It is then demonstrated via specific examples how this operator calculus leads to practical techniques for sculptured surface and volume modeling.

The Function sin x/x.

ERIC Educational Resources Information Center

Gearhart, William B.; Shultz, Harris S.

1990-01-01

Presents some examples from geometry: area of a circle; centroid of a sector; Buffon's needle problem; and expression for pi. Describes several roles of the trigonometric function in mathematics and applications, including Fourier analysis, spectral theory, approximation theory, and numerical analysis. (YP)

Use of altimetry data in a sampling-function approach to the geoid

NASA Technical Reports Server (NTRS)

Lundquist, C. A.; Giacaglia, G. E. O.

1972-01-01

Problems associated with using an altimetry sampling function approach to the geoid are examined. They include: (1) conventent mathematical representation of short-wavelength (eventually approximately 1 deg) features of the geoid or geopotential, (2) utilization of detailed data from only part of the globe (i.e., the oceans) (3) application of appropriate formalism to relate the sea-level equipotential below the atmospheric mass to the external potential above the atmosphere, (4) mathematical applicability of an adopted geopotential representation on the surface of the physical geoid.

On laminar and turbulent friction

NASA Technical Reports Server (NTRS)

Von Karman, TH

1946-01-01

Report deals, first with the theory of the laminar friction flow, where the basic concepts of Prandtl's boundary layer theory are represented from mathematical and physical points of view, and a method is indicated by means of which even more complicated cases can be treated with simple mathematical means, at least approximately. An attempt is also made to secure a basis for the computation of the turbulent friction by means of formulas through which the empirical laws of the turbulent pipe resistance can be applied to other problems on friction drag. (author)

Molecular modeling: An open invitation for applied mathematics

NASA Astrophysics Data System (ADS)

Mezey, Paul G.

2013-10-01

Molecular modeling methods provide a very wide range of challenges for innovative mathematical and computational techniques, where often high dimensionality, large sets of data, and complicated interrelations imply a multitude of iterative approximations. The physical and chemical basis of these methodologies involves quantum mechanics with several non-intuitive aspects, where classical interpretation and classical analogies are often misleading or outright wrong. Hence, instead of the everyday, common sense approaches which work so well in engineering, in molecular modeling one often needs to rely on rather abstract mathematical constraints and conditions, again emphasizing the high level of reliance on applied mathematics. Yet, the interdisciplinary aspects of the field of molecular modeling also generates some inertia and perhaps too conservative reliance on tried and tested methodologies, that is at least partially caused by the less than up-to-date involvement in the newest developments in applied mathematics. It is expected that as more applied mathematicians take up the challenge of employing the latest advances of their field in molecular modeling, important breakthroughs may follow. In this presentation some of the current challenges of molecular modeling are discussed.

Fuzzy Logic for Incidence Geometry

PubMed Central

2016-01-01

The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects “as if they were points.” Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid's first postulate. Fuzzy equivalence relation “extended lines sameness” is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy “degree of indiscernibility” and “discernibility measure” of extended points. PMID:27689133

Approximate approach for optimization space flights with a low thrust on the basis of sufficient optimality conditions

NASA Astrophysics Data System (ADS)

Salmin, Vadim V.

2017-01-01

Flight mechanics with a low-thrust is a new chapter of mechanics of space flight, considered plurality of all problems trajectory optimization and movement control laws and the design parameters of spacecraft. Thus tasks associated with taking into account the additional factors in mathematical models of the motion of spacecraft becomes increasingly important, as well as additional restrictions on the possibilities of the thrust vector control. The complication of the mathematical models of controlled motion leads to difficulties in solving optimization problems. Author proposed methods of finding approximate optimal control and evaluating their optimality based on analytical solutions. These methods are based on the principle of extending the class of admissible states and controls and sufficient conditions for the absolute minimum. Developed procedures of the estimation enabling to determine how close to the optimal founded solution, and indicate ways to improve them. Authors describes procedures of estimate for approximately optimal control laws for space flight mechanics problems, in particular for optimization flight low-thrust between the circular non-coplanar orbits, optimization the control angle and trajectory movement of the spacecraft during interorbital flights, optimization flights with low-thrust between arbitrary elliptical orbits Earth satellites.

Approximate method for calculating convective heat flux on the surface of bodies of simple geometric shapes

NASA Astrophysics Data System (ADS)

Kuzenov, V. V.; Ryzhkov, S. V.

2017-02-01

The paper formulated engineering and physical mathematical model for aerothermodynamics hypersonic flight vehicle (HFV) in laminar and turbulent boundary layers (model designed for an approximate estimate of the convective heat flow in the range of speeds M = 6-28, and height H = 20-80 km). 2D versions of calculations of convective heat flows for bodies of simple geometric forms (individual elements of the design HFV) are presented.

Generating the patterns of variation with GeoGebra: the case of polynomial approximations

NASA Astrophysics Data System (ADS)

Attorps, Iiris; Björk, Kjell; Radic, Mirko

2016-01-01

In this paper, we report a teaching experiment regarding the theory of polynomial approximations at the university mathematics teaching in Sweden. The experiment was designed by applying Variation theory and by using the free dynamic mathematics software GeoGebra. The aim of this study was to investigate if the technology-assisted teaching of Taylor polynomials compared with traditional way of work at the university level can support the teaching and learning of mathematical concepts and ideas. An engineering student group (n = 19) was taught Taylor polynomials with the assistance of GeoGebra while a control group (n = 18) was taught in a traditional way. The data were gathered by video recording of the lectures, by doing a post-test concerning Taylor polynomials in both groups and by giving one question regarding Taylor polynomials at the final exam for the course in Real Analysis in one variable. In the analysis of the lectures, we found Variation theory combined with GeoGebra to be a potentially powerful tool for revealing some critical aspects of Taylor Polynomials. Furthermore, the research results indicated that applying Variation theory, when planning the technology-assisted teaching, supported and enriched students' learning opportunities in the study group compared with the control group.

A consistent modelling methodology for secondary settling tanks in wastewater treatment.

PubMed

Bürger, Raimund; Diehl, Stefan; Nopens, Ingmar

2011-03-01

The aim of this contribution is partly to build consensus on a consistent modelling methodology (CMM) of complex real processes in wastewater treatment by combining classical concepts with results from applied mathematics, and partly to apply it to the clarification-thickening process in the secondary settling tank. In the CMM, the real process should be approximated by a mathematical model (process model; ordinary or partial differential equation (ODE or PDE)), which in turn is approximated by a simulation model (numerical method) implemented on a computer. These steps have often not been carried out in a correct way. The secondary settling tank was chosen as a case since this is one of the most complex processes in a wastewater treatment plant and simulation models developed decades ago have no guarantee of satisfying fundamental mathematical and physical properties. Nevertheless, such methods are still used in commercial tools to date. This particularly becomes of interest as the state-of-the-art practice is moving towards plant-wide modelling. Then all submodels interact and errors propagate through the model and severely hamper any calibration effort and, hence, the predictive purpose of the model. The CMM is described by applying it first to a simple conversion process in the biological reactor yielding an ODE solver, and then to the solid-liquid separation in the secondary settling tank, yielding a PDE solver. Time has come to incorporate established mathematical techniques into environmental engineering, and wastewater treatment modelling in particular, and to use proven reliable and consistent simulation models. Copyright © 2011 Elsevier Ltd. All rights reserved.

Approximate Model of Zone Sedimentation

NASA Astrophysics Data System (ADS)

Dzianik, František

2011-12-01

The process of zone sedimentation is affected by many factors that are not possible to express analytically. For this reason, the zone settling is evaluated in practice experimentally or by application of an empirical mathematical description of the process. The paper presents the development of approximate model of zone settling, i.e. the general function which should properly approximate the behaviour of the settling process within its entire range and at the various conditions. Furthermore, the specification of the model parameters by the regression analysis of settling test results is shown. The suitability of the model is reviewed by graphical dependencies and by statistical coefficients of correlation. The approximate model could by also useful on the simplification of process design of continual settling tanks and thickeners.

Analytical approximation of the InGaZnO thin-film transistors surface potential

NASA Astrophysics Data System (ADS)

Colalongo, Luigi

2016-10-01

Surface-potential-based mathematical models are among the most accurate and physically based compact models of thin-film transistors, and in turn of indium gallium zinc oxide TFTs, available today. However, the need of iterative computations of the surface potential limits their computational efficiency and diffusion in CAD applications. The existing closed-form approximations of the surface potential are based on regional approximations and empirical smoothing functions that could result not accurate enough in particular to model transconductances and transcapacitances. In this work we present an extremely accurate (in the range of nV) and computationally efficient non-iterative approximation of the surface potential that can serve as a basis for advanced surface-potential-based indium gallium zinc oxide TFTs models.

A study of school mathematics curriculum enacted by competent teachers in Singapore secondary schools

NASA Astrophysics Data System (ADS)

Kaur, Berinderjeet; Tay, Eng Guan; Toh, Tin Lam; Leong, Yew Hoong; Lee, Ngan Hoe

2018-03-01

A study of school mathematics curriculum enacted by competent teachers in Singapore secondary schools is a programmatic research project at the National Institute of Education (NIE) funded by the Ministry of Education (MOE) in Singapore through the Office of Education Research (OER) at NIE. The main goal of the project is to collect a set of data that would be used by two studies to research the enacted secondary school mathematics curriculum. The project aims to examine how competent experienced secondary school teachers implement the designated curriculum prescribed by the MOE in the 2013 revision of curriculum. It does this firstly by examining the video recordings of the classroom instruction and interactions between secondary school mathematics teachers and their students, as it is these interactions that fundamentally determine the nature of the actual mathematics learning and teaching that take place in the classroom. It also examines content through the instructional materials used—their preparation, use in classroom and as homework. The project comprises a video segment and a survey segment. Approximately 630 secondary mathematics teachers and 600 students are participating in the project. The data collection for the video segment of the project is guided by the renowned complementary accounts methodology while the survey segment adopts a self-report questionnaire approach. The findings of the project will serve several purposes. They will provide timely feedback to mathematics specialists in the MOE, inform pre-service and professional development programmes for mathematics teachers at the NIE and contribute towards articulation of "Mathematics pedagogy in Singapore secondary schools" that is evidence based.

Which Instructional Practices Most Help First Grade Students with and without Mathematics Difficulties?

PubMed

Morgan, Paul L; Farkas, George; Maczuga, Steve

2015-06-01

We used population-based, longitudinal data to investigate the relation between mathematics instructional practices used by 1 st grade teachers in the U.S. and the mathematics achievement of their students. Factor analysis identified four types of instructional activities (i.e., teacher-directed, student-centered, manipulatives/calculators, movement/music) and eight types of specific skills taught (e.g., adding two-digit numbers). First-grade students were then classified into five groups on the basis of their fall and/or spring of kindergarten mathematics achievement-three groups with mathematics difficulties (MD) and two without MD. Regression analysis indicated that a higher percentage of MD students in 1 st grade classrooms was associated with greater use by teachers of manipulatives/calculators and movement/music to teach mathematics. Yet follow-up analysis for each of the MD and non-MD groups indicated that only teacher-directed instruction was significantly associated with the achievement of students with MD (covariate-adjusted ES s = .05-.07). The largest predicted effect for a specific instructional practice was for routine practice and drill. In contrast, for both groups of non-MD students, teacher-directed and student-centered instruction had approximately equal, statistically significant positive predicted effects (covariate-adjusted ES s = .03-.04). First-grade teachers in the U.S. may need to increase their use of teacher-directed instruction if they are to raise the mathematics achievement of students with MD.

Formulation and Testing of a Novel River Nitrification Model

EPA Science Inventory

The nitrification process in many riverwater quality models has been approximated by a simple first order dependency on the water column ammonia concentration, while the benthic contribution has routinely been neglected. In this study a mathematical framework was developed for se...

Multidisciplinary design optimization - An emerging new engineering discipline

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, Jaroslaw

1993-01-01

A definition of the multidisciplinary design optimization (MDO) is introduced, and functionality and relationship of the MDO conceptual components are examined. The latter include design-oriented analysis, approximation concepts, mathematical system modeling, design space search, an optimization procedure, and a humane interface.

Least Squares Procedures.

ERIC Educational Resources Information Center

Hester, Yvette

Least squares methods are sophisticated mathematical curve fitting procedures used in all classical parametric methods. The linear least squares approximation is most often associated with finding the "line of best fit" or the regression line. Since all statistical analyses are correlational and all classical parametric methods are least…

Animating Preservice Teachers' Noticing

ERIC Educational Resources Information Center

de Araujo, Zandra; Amador, Julie; Estapa, Anne; Weston, Tracy; Aming-Attai, Rachael; Kosko, Karl W.

2015-01-01

The incorporation of animation in mathematics teacher education courses is one method for transforming practices and promoting practice-based education. Animation can be used as an approximation of practice that engages preservice teachers (PSTs) in creating classroom scenes in which they select characters, regulate movement, and construct…

SSMILES.

ERIC Educational Resources Information Center

Sunal, Dennis W., Ed.; Tracy, Dyanne M., Ed.

1993-01-01

Describes an activity in which the students utilize the mathematics concepts of ratio, proportion, and data tabulation to examine the relationship between air pressure, temperature, and humidity. Students learn to approximate partial pressure by using humidity and temperature readings and by interpolating from the vapor pressure-temperature table.…

A new mathematical model and control of a three-phase AC-DC voltage source converter

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blasko, V.; Kaura, V.

1997-01-01

A new mathematical model of the power circuit of a three-phase voltage source converter (VSC) was developed in the stationary and synchronous reference frames. The mathematical model was then used to analyze and synthesize the voltage and current control loops for the VSC. Analytical expressions were derived for calculating the gains and time constants of the current and voltage regulators. The mathematical model was used to control a 140-kW regenerative VSC. The synchronous reference frame model was used to define feedforward signals in the current regulators to eliminate the cross coupling between the d and q phases. It allowed themore » reduction of the current control loop to first-order plants and improved their tracking capability. The bandwidths of the current and voltage-control loops were found to be approximately 20 and 60 times (respectively) smaller than the sampling frequency. All control algorithms were implemented in a digital-signal processor. All results of the analysis were experimentally verified.« less

Geometric model of pseudo-distance measurement in satellite location systems

NASA Astrophysics Data System (ADS)

Panchuk, K. L.; Lyashkov, A. A.; Lyubchinov, E. V.

2018-04-01

The existing mathematical model of pseudo-distance measurement in satellite location systems does not provide a precise solution of the problem, but rather an approximate one. The existence of such inaccuracy, as well as bias in measurement of distance from satellite to receiver, results in inaccuracy level of several meters. Thereupon, relevance of refinement of the current mathematical model becomes obvious. The solution of the system of quadratic equations used in the current mathematical model is based on linearization. The objective of the paper is refinement of current mathematical model and derivation of analytical solution of the system of equations on its basis. In order to attain the objective, geometric analysis is performed; geometric interpretation of the equations is given. As a result, an equivalent system of equations, which allows analytical solution, is derived. An example of analytical solution implementation is presented. Application of analytical solution algorithm to the problem of pseudo-distance measurement in satellite location systems allows to improve the accuracy such measurements.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

PubMed

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM

PubMed Central

Singh, Brajesh K.; Srivastava, Vineet K.

2015-01-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations. PMID:26064639

ACCESS 1: Approximation Concepts Code for Efficient Structural Synthesis program documentation and user's guide

NASA Technical Reports Server (NTRS)

Miura, H.; Schmit, L. A., Jr.

1976-01-01

The program documentation and user's guide for the ACCESS-1 computer program is presented. ACCESS-1 is a research oriented program which implements a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and general mathematical programming algorithms are applied in the design optimization procedure. Implementation of the computer program, preparation of input data and basic program structure are described, and three illustrative examples are given.

Arbitrary-level hanging nodes for adaptive hphp-FEM approximations in 3D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pavel Kus; Pavel Solin; David Andrs

2014-11-01

In this paper we discuss constrained approximation with arbitrary-level hanging nodes in adaptive higher-order finite element methods (hphp-FEM) for three-dimensional problems. This technique enables using highly irregular meshes, and it greatly simplifies the design of adaptive algorithms as it prevents refinements from propagating recursively through the finite element mesh. The technique makes it possible to design efficient adaptive algorithms for purely hexahedral meshes. We present a detailed mathematical description of the method and illustrate it with numerical examples.

Foundations of mathematics and literacy: The role of executive functioning components.

PubMed

Purpura, David J; Schmitt, Sara A; Ganley, Colleen M

2017-01-01

The current study investigated the relations between the three cognitive processes that comprise executive functioning (EF)-response inhibition, working memory, and cognitive flexibility-and individual components of mathematics and literacy skills in preschool children. Participants were 125 preschool children ranging in age from 3.12 to 5.26years (M=4.17years, SD=0.58). Approximately 53.2% were female, and the sample was predominantly Caucasian (69.8%). Results suggest that the components of EF may be differentially related to the specific components of early mathematics and literacy. For mathematics, response inhibition was broadly related to most components. Working memory was related to more advanced mathematics skills that involve comparison or combination of numbers and quantities. Cognitive flexibility was related to more conceptual or abstract mathematics skills. For early literacy, response inhibition and cognitive flexibility were related to print knowledge, and working memory was related only to phonological awareness. None of the EF components was related to vocabulary. These findings provide initial evidence for better understanding the ways in which EF components and academic skills are related and measured. Furthermore, the findings provide a foundation for further study of the components of each domain using a broader and more diverse array of measures. Copyright © 2016 Elsevier Inc. All rights reserved.

Solving the infeasible trust-region problem using approximations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Renaud, John E.; Perez, Victor M.; Eldred, Michael Scott

2004-07-01

The use of optimization in engineering design has fueled the development of algorithms for specific engineering needs. When the simulations are expensive to evaluate or the outputs present some noise, the direct use of nonlinear optimizers is not advisable, since the optimization process will be expensive and may result in premature convergence. The use of approximations for both cases is an alternative investigated by many researchers including the authors. When approximations are present, a model management is required for proper convergence of the algorithm. In nonlinear programming, the use of trust-regions for globalization of a local algorithm has been provenmore » effective. The same approach has been used to manage the local move limits in sequential approximate optimization frameworks as in Alexandrov et al., Giunta and Eldred, Perez et al. , Rodriguez et al., etc. The experience in the mathematical community has shown that more effective algorithms can be obtained by the specific inclusion of the constraints (SQP type of algorithms) rather than by using a penalty function as in the augmented Lagrangian formulation. The presence of explicit constraints in the local problem bounded by the trust region, however, may have no feasible solution. In order to remedy this problem the mathematical community has developed different versions of a composite steps approach. This approach consists of a normal step to reduce the amount of constraint violation and a tangential step to minimize the objective function maintaining the level of constraint violation attained at the normal step. Two of the authors have developed a different approach for a sequential approximate optimization framework using homotopy ideas to relax the constraints. This algorithm called interior-point trust-region sequential approximate optimization (IPTRSAO) presents some similarities to the two normal-tangential steps algorithms. In this paper, a description of the similarities is presented and an expansion of the two steps algorithm is presented for the case of approximations.« less

Derivation and computation of discrete-delay and continuous-delay SDEs in mathematical biology.

PubMed

Allen, Edward J

2014-06-01

Stochastic versions of several discrete-delay and continuous-delay differential equations, useful in mathematical biology, are derived from basic principles carefully taking into account the demographic, environmental, or physiological randomness in the dynamic processes. In particular, stochastic delay differential equation (SDDE) models are derived and studied for Nicholson's blowflies equation, Hutchinson's equation, an SIS epidemic model with delay, bacteria/phage dynamics, and glucose/insulin levels. Computational methods for approximating the SDDE models are described. Comparisons between computational solutions of the SDDEs and independently formulated Monte Carlo calculations support the accuracy of the derivations and of the computational methods.

Effect of design selection on response surface performance

NASA Technical Reports Server (NTRS)

Carpenter, William C.

1993-01-01

The mathematical formulation of the engineering optimization problem is given. Evaluation of the objective function and constraint equations can be very expensive in a computational sense. Thus, it is desirable to use as few evaluations as possible in obtaining its solution. In solving the equation, one approach is to develop approximations to the objective function and/or restraint equations and then to solve the equation using the approximations in place of the original functions. These approximations are referred to as response surfaces. The desirability of using response surfaces depends upon the number of functional evaluations required to build the response surfaces compared to the number required in the direct solution of the equation without approximations. The present study is concerned with evaluating the performance of response surfaces so that a decision can be made as to their effectiveness in optimization applications. In particular, this study focuses on how the quality of approximations is effected by design selection. Polynomial approximations and neural net approximations are considered.

Mathematical and Computational Aspects Related to Soil Modeling and Simulation

DTIC Science & Technology

2017-09-26

and simulation challenges at the interface of applied math (homogenization, handling of discontinuous behavior, discrete vs. continuum representations...applied math tools need to be established and used to figure out how to impose compatible boundary conditions, how to better approximate the gradient

Computer Based Screening Dyscalculia: Cognitive and Neuropsychological Correlates

ERIC Educational Resources Information Center

Cangoz, Banu; Altun, Arif; Olkun, Sinan; Kacar, Funda

2013-01-01

Mathematical skills are becoming increasingly critical for achieving academic and professional success. Developmental dyscalculia (DD) is a childhood-onset disorder characterized by the presence of abnormalities in the acquisition of arithmetic skills affecting approximately 5% of school age children. Diagnosing students with possible dyscalculia…

Angular Distribution of Ly(alpha) Resonant Photons Emergent from Optically Thick Medium

DTIC Science & Technology

2012-02-26

cosmology : theory - intergalactic medium - radiation transfer - scattering 1Division of Applied Mathematics, Brown University, Providence, RI 02912, USA...It definitely cannot be described by the Eddington approximation. The evolution of the angular distribution of resonant photons is not trivial. We

Finite fringe hologram

NASA Technical Reports Server (NTRS)

Heflinger, L. O.

1970-01-01

In holographic interferometry a small movement of apparatus between exposures causes the background of the reconstructed scene to be covered with interference fringes approximately parallel to each other. The three-dimensional quality of the holographic image is allowable since a mathematical model will give the location of the fringes.

Basic math in monkeys and college students.

PubMed

Cantlon, Jessica F; Brannon, Elizabeth M

2007-12-01

Adult humans possess a sophisticated repertoire of mathematical faculties. Many of these capacities are rooted in symbolic language and are therefore unlikely to be shared with nonhuman animals. However, a subset of these skills is shared with other animals, and this set is considered a cognitive vestige of our common evolutionary history. Current evidence indicates that humans and nonhuman animals share a core set of abilities for representing and comparing approximate numerosities nonverbally; however, it remains unclear whether nonhuman animals can perform approximate mental arithmetic. Here we show that monkeys can mentally add the numerical values of two sets of objects and choose a visual array that roughly corresponds to the arithmetic sum of these two sets. Furthermore, monkeys' performance during these calculations adheres to the same pattern as humans tested on the same nonverbal addition task. Our data demonstrate that nonverbal arithmetic is not unique to humans but is instead part of an evolutionarily primitive system for mathematical thinking shared by monkeys.

Impact of High Mathematics Education on the Number Sense

PubMed Central

Castronovo, Julie; Göbel, Silke M.

2012-01-01

In adult number processing two mechanisms are commonly used: approximate estimation of quantity and exact calculation. While the former relies on the approximate number sense (ANS) which we share with animals and preverbal infants, the latter has been proposed to rely on an exact number system (ENS) which develops later in life following the acquisition of symbolic number knowledge. The current study investigated the influence of high level math education on the ANS and the ENS. Our results showed that the precision of non-symbolic quantity representation was not significantly altered by high level math education. However, performance in a symbolic number comparison task as well as the ability to map accurately between symbolic and non-symbolic quantities was significantly better the higher mathematics achievement. Our findings suggest that high level math education in adults shows little influence on their ANS, but it seems to be associated with a better anchored ENS and better mapping abilities between ENS and ANS. PMID:22558077

Number Processing and Heterogeneity of Developmental Dyscalculia: Subtypes With Different Cognitive Profiles and Deficits.

PubMed

Skagerlund, Kenny; Träff, Ulf

2016-01-01

This study investigated if developmental dyscalculia (DD) in children with different profiles of mathematical deficits has the same or different cognitive origins. The defective approximate number system hypothesis and the access deficit hypothesis were tested using two different groups of children with DD (11-13 years old): a group with arithmetic fact dyscalculia (AFD) and a group with general dyscalculia (GD). Several different aspects of number magnitude processing were assessed in these two groups and compared with age-matched typically achieving children. The GD group displayed weaknesses with both symbolic and nonsymbolic number processing, whereas the AFD group displayed problems only with symbolic number processing. These findings provide evidence that the origins of DD in children with different profiles of mathematical problems diverge. Children with GD have impairment in the innate approximate number system, whereas children with AFD suffer from an access deficit. These findings have implications for researchers' selection procedures when studying dyscalculia, and also for practitioners in the educational setting. © Hammill Institute on Disabilities 2014.

Impact of high mathematics education on the number sense.

PubMed

Castronovo, Julie; Göbel, Silke M

2012-01-01

In adult number processing two mechanisms are commonly used: approximate estimation of quantity and exact calculation. While the former relies on the approximate number sense (ANS) which we share with animals and preverbal infants, the latter has been proposed to rely on an exact number system (ENS) which develops later in life following the acquisition of symbolic number knowledge. The current study investigated the influence of high level math education on the ANS and the ENS. Our results showed that the precision of non-symbolic quantity representation was not significantly altered by high level math education. However, performance in a symbolic number comparison task as well as the ability to map accurately between symbolic and non-symbolic quantities was significantly better the higher mathematics achievement. Our findings suggest that high level math education in adults shows little influence on their ANS, but it seems to be associated with a better anchored ENS and better mapping abilities between ENS and ANS.

Mimetic finite difference method

NASA Astrophysics Data System (ADS)

Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail

2014-01-01

The mimetic finite difference (MFD) method mimics fundamental properties of mathematical and physical systems including conservation laws, symmetry and positivity of solutions, duality and self-adjointness of differential operators, and exact mathematical identities of the vector and tensor calculus. This article is the first comprehensive review of the 50-year long history of the mimetic methodology and describes in a systematic way the major mimetic ideas and their relevance to academic and real-life problems. The supporting applications include diffusion, electromagnetics, fluid flow, and Lagrangian hydrodynamics problems. The article provides enough details to build various discrete operators on unstructured polygonal and polyhedral meshes and summarizes the major convergence results for the mimetic approximations. Most of these theoretical results, which are presented here as lemmas, propositions and theorems, are either original or an extension of existing results to a more general formulation using polyhedral meshes. Finally, flexibility and extensibility of the mimetic methodology are shown by deriving higher-order approximations, enforcing discrete maximum principles for diffusion problems, and ensuring the numerical stability for saddle-point systems.

Novel method for edge detection of retinal vessels based on the model of the retinal vascular network and mathematical morphology

NASA Astrophysics Data System (ADS)

Xu, Lei; Zheng, Xiaoxiang; Zhang, Hengyi; Yu, Yajun

1998-09-01

Accurate edge detection of retinal vessels is a prerequisite for quantitative analysis of subtle morphological changes of retinal vessels under different pathological conditions. A novel method for edge detection of retinal vessels is presented in this paper. Methods: (1) Wavelet-based image preprocessing. (2) The signed edge detection algorithm and mathematical morphological operation are applied to get the approximate regions that contain retinal vessels. (3) By convolving the preprocessed image with a LoG operator only on the detected approximate regions of retinal vessels, followed by edges refining, clear edge maps of the retinal vessels are fast obtained. Results: A detailed performance evaluation together with the existing techniques is given to demonstrate the strong features of our method. Conclusions: True edge locations of retinal vessels can be fast detected with continuous structures of retinal vessels, less non- vessel segments left and insensitivity to noise. The method is also suitable for other application fields such as road edge detection.

An Event to Encourage High School Students to Pursue College Degrees in Physics and Math

NASA Astrophysics Data System (ADS)

Bukiet, Bruce; Thomas, Gordon

2003-04-01

We discuss a Math and Physics Day for high school students and teachers, with hands-on activities and seminars involving mathematics and physics. Participants also learn about careers for those who go on to major in physics and mathematics in college. The New York State Section of the APS has provided generous support for this workshop through its Outreach grant program. Approximately a dozen high schools and 100 students attend each year. The program, which runs from 9:15 AM until 2:15 PM, includes an introduction to undergraduate degree programs in Mathematics, Statistics, Optics, Actuarial Science and Applied Physics, a group physics experiment/contest, brief talks over lunch by speakers from industry who have degrees in Math or Physics, and an afternoon seminar. Teachers earn Professional Development credit.

An experimental and theoretical evaluation of increased thermal diffusivity phase change devices

NASA Technical Reports Server (NTRS)

White, S. P.; Golden, J. O.; Stermole, F. J.

1972-01-01

This study was to experimentally evaluate and mathematically model the performance of phase change thermal control devices containing high thermal conductivity metal matrices. Three aluminum honeycomb filters were evaluated at five different heat flux levels using n-oct-adecane as the test material. The system was mathematically modeled by approximating the partial differential equations with a three-dimensional implicit alternating direction technique. The mathematical model predicts the system quite well. All of the phase change times are predicted. The heating of solid phase is predicted exactly while there is some variation between theoretical and experimental results in the liquid phase. This variation in the liquid phase could be accounted for by the fact that there are some heat losses in the cell and there could be some convection in the experimental system.

Dual methods and approximation concepts in structural synthesis

NASA Technical Reports Server (NTRS)

Fleury, C.; Schmit, L. A., Jr.

1980-01-01

Approximation concepts and dual method algorithms are combined to create a method for minimum weight design of structural systems. Approximation concepts convert the basic mathematical programming statement of the structural synthesis problem into a sequence of explicit primal problems of separable form. These problems are solved by constructing explicit dual functions, which are maximized subject to nonnegativity constraints on the dual variables. It is shown that the joining together of approximation concepts and dual methods can be viewed as a generalized optimality criteria approach. The dual method is successfully extended to deal with pure discrete and mixed continuous-discrete design variable problems. The power of the method presented is illustrated with numerical results for example problems, including a metallic swept wing and a thin delta wing with fiber composite skins.

Influence of scattering processes on electron quantum states in nanowires

PubMed Central

Galenchik, Vadim; Borzdov, Andrei; Borzdov, Vladimir; Komarov, Fadei

2007-01-01

In the framework of quantum perturbation theory the self-consistent method of calculation of electron scattering rates in nanowires with the one-dimensional electron gas in the quantum limit is worked out. The developed method allows both the collisional broadening and the quantum correlations between scattering events to be taken into account. It is an alternativeper seto the Fock approximation for the self-energy approach based on Green’s function formalism. However this approach is free of mathematical difficulties typical to the Fock approximation. Moreover, the developed method is simpler than the Fock approximation from the computational point of view. Using the approximation of stable one-particle quantum states it is proved that the electron scattering processes determine the dependence of electron energy versus its wave vector.

The Approximate Number System and its Relation to Early Math Achievement: Evidence from the Preschool Years

PubMed Central

Bonny, Justin W.; Lourenco, Stella F.

2012-01-01

Humans rely on two main systems of quantification - one is non-symbolic and involves approximate number representations (known as the approximate number system or ANS), the other is symbolic and allows for exact calculations of number. Despite the pervasiveness of the ANS across development, recent studies with adolescents and school-aged children point to individual differences in the precision of these representations, which, importantly, have been shown to relate to symbolic math competence, even after controlling for general aspects of intelligence. Such findings suggest that the ANS, which humans share with nonhuman animals, interfaces specifically with a uniquely human system of formal mathematics. Other findings, however, point to a less straightforward picture, leaving open questions about the nature and ontogenetic origins of the relation between these two systems. Testing children across the preschool period, we found that ANS precision correlated with early math achievement, but, critically, that this relation was non-linear. More specifically, the correlation between ANS precision and math competence was stronger for children with lower math scores than for children with higher math scores. Taken together, our findings suggest that early-developing connections between the ANS and mathematics may be fundamentally discontinuous. Possible mechanisms underlying such non-linearity are discussed. PMID:23201156

The approximate number system and its relation to early math achievement: evidence from the preschool years.

PubMed

Bonny, Justin W; Lourenco, Stella F

2013-03-01

Humans rely on two main systems of quantification; one is nonsymbolic and involves approximate number representations (known as the approximate number system or ANS), and the other is symbolic and allows for exact calculations of number. Despite the pervasiveness of the ANS across development, recent studies with adolescents and school-aged children point to individual differences in the precision of these representations that, importantly, have been shown to relate to symbolic math competence even after controlling for general aspects of intelligence. Such findings suggest that the ANS, which humans share with nonhuman animals, interfaces specifically with a uniquely human system of formal mathematics. Other findings, however, point to a less straightforward picture, leaving open questions about the nature and ontogenetic origins of the relation between these two systems. Testing children across the preschool period, we found that ANS precision correlated with early math achievement but, critically, that this relation was nonlinear. More specifically, the correlation between ANS precision and math competence was stronger for children with lower math scores than for children with higher math scores. Taken together, our findings suggest that early-developing connections between the ANS and mathematics may be fundamentally discontinuous. Possible mechanisms underlying such nonlinearity are discussed. Copyright © 2012 Elsevier Inc. All rights reserved.

Quiet Quincy Quarter. Teacher's Guide [and] Student Materials.

ERIC Educational Resources Information Center

Zishka, Phyllis

This document suggests learning activities, teaching methods, objectives, and evaluation measures for a second grade consumer education unit on quarters. The unit, which requires approximately six hours of class time, reinforces basic social studies and mathematics skills including following sequences of numbers, distinguishing left from right,…

Assessing the Benefits of U.S. Customs and Border Protection Regulatory Actions to Reduce Terrorism Risks

DTIC Science & Technology

2012-01-01

conceptual, mathematical , etc.  More formally, models are approximations, representations, or idealizations of selected aspects of the structure...essential – Actuarial estimates inadequate – limited data, great heterogeneity over time & location, conditions change so present & future may not be

Basic Skills Applications in Occupational Investigation.

ERIC Educational Resources Information Center

Hendrix, Mary

This guide contains 50 lesson plans for learning activities that incorporate basic skills into content areas of career education, mathematics, science, social studies, communications, and productive work habits. Each lesson consists of a purpose, basic skills applications, approximate time required, materials needed, things for the teacher to do…

CAI: Overcoming Attitude Barriers.

ERIC Educational Resources Information Center

Netusil, Anton J.; Kockler, Lois H.

During each of two school quarters, approximately 60 college students enrolled in a mathematics course were randomly assigned to an experimental group or a control group. The control group received instruction by the lecture method only; the experimental group received the same instruction, except that six computer-assisted instruction (CAI) units…

SOLUTIONS APPROXIMATING SOLUTE TRANSPORT IN A LEAKY AQUIFER RECEIVING WASTEWATER INJECTION

EPA Science Inventory

A mathematical model amenable to analytical solution techniques is developed for the investigation of contaminant transport from an injection well into a leaky aquifer system, which comprises a pumped and an unpumped aquifer connected to each other by an aquitard. A steady state ...

Factors influencing undergraduates' self-evaluation of numerical competence

NASA Astrophysics Data System (ADS)

Tariq, Vicki N.; Durrani, Naureen

2012-04-01

This empirical study explores factors influencing undergraduates' self-evaluation of their numerical competence, using data from an online survey completed by 566 undergraduates from a diversity of academic disciplines, across all four faculties at a post-1992 UK university. Analysis of the data, which included correlation and multiple regression analyses, revealed that undergraduates exhibiting greater confidence in their mathematical and numeracy skills, as evidenced by their higher self-evaluation scores and their higher scores on the confidence sub-scale contributing to the measurement of attitude, possess more cohesive, rather than fragmented, conceptions of mathematics, and display more positive attitudes towards mathematics/numeracy. They also exhibit lower levels of mathematics anxiety. Students exhibiting greater confidence also tended to be those who were relatively young (i.e. 18-29 years), whose degree programmes provided them with opportunities to practise and further develop their numeracy skills, and who possessed higher pre-university mathematics qualifications. The multiple regression analysis revealed two positive predictors (overall attitude towards mathematics/numeracy and possession of a higher pre-university mathematics qualification) and five negative predictors (mathematics anxiety, lack of opportunity to practise/develop numeracy skills, being a more mature student, being enrolled in Health and Social Care compared with Science and Technology, and possessing no formal mathematics/numeracy qualification compared with a General Certificate of Secondary Education or equivalent qualification) accounted for approximately 64% of the variation in students' perceptions of their numerical competence. Although the results initially suggested that male students were significantly more confident than females, one compounding variable was almost certainly the students' highest pre-university mathematics or numeracy qualification, since a higher percentage of males (24%) compared to females (15%) possessed an Advanced Subsidiary or A2 qualification (or equivalent) in mathematics. Of particular concern is the fact that undergraduates based in Health and Social Care expressed significantly less confidence in their numeracy skills than students from any of the other three faculties.

Mathematical model to compare the relative tensile strength of the cornea after PRK, LASIK, and small incision lenticule extraction.

PubMed

Reinstein, Dan Z; Archer, Timothy J; Randleman, J Bradley

2013-07-01

To develop a mathematical model to estimate the relative differences in postoperative stromal tensile strength following photorefractive keratectomy (PRK), LASIK, and small incision lenticule extraction (SMILE). Using previously published data where in vitro corneal stromal tensile strength was determined as a function of depth, a mathematical model was built to calculate the relative remaining tensile strength by fitting the data with a fourth order polynomial function yielding a high correlation coefficient (R(2) = 0.930). Calculating the area under this function provided a measure of total stromal tensile strength (TTS), based only on the residual stromal layer for PRK or LASIK and the residual stromal layers above and below the lenticule interface for SMILE. Postoperative TTS was greatest after SMILE, followed by PRK, then LASIK; for example, in a 550-μm cornea after 100-μm tissue removal, postoperative TTS was 75% for SMILE (130-μm cap), 68% for PRK, and 54% for LASIK (110-μm flap). The postoperative TTS decreased for thinner corneal pachymetry for all treatment types. In LASIK, the postoperative TTS decreased with increasing flap thickness by 0.22%/μm, but increased by 0.08%/μm for greater cap thickness in SMILE. The model predicted that SMILE lenticule thickness could be approximately 100 μm greater than the LASIK ablation depth and still have equivalent corneal strength (equivalent to approximately 7.75 diopters). This mathematical model predicts that the postoperative TTS is considerably higher after SMILE than both PRK and LASIK, as expected given that the strongest anterior lamellae remain intact. Consequently, SMILE should be able to correct higher levels of myopia. Copyright 2013, SLACK Incorporated.

An Approach for a Mathematical Description of Human Root Canals by Means of Elementary Parameters.

PubMed

Dannemann, Martin; Kucher, Michael; Kirsch, Jasmin; Binkowski, Alexander; Modler, Niels; Hannig, Christian; Weber, Marie-Theres

2017-04-01

Root canal geometry is an important factor for instrumentation and preparation of the canals. Curvature, length, shape, and ramifications need to be evaluated in advance to enhance the success of the treatment. Therefore, the present study aimed to design and realize a method for analyzing the geometric characteristics of human root canals. Two extracted human lower molars were radiographed in the occlusal direction using micro-computed tomographic imaging. The 3-dimensional geometry of the root canals, calculated by a self-implemented image evaluation algorithm, was described by 3 different mathematical models: the elliptical model, the 1-circle model, and the 3-circle model. The different applied mathematical models obtained similar geometric properties depending on the parametric model used. Considering more complex root canals, the differences of the results increase because of the different adaptability and the better approximation of the geometry. With the presented approach, it is possible to estimate and compare the geometry of natural root canals. Therefore, the deviation of the canal can be assessed, which is important for the choice of taper of root canal instruments. Root canals with a nearly elliptical cross section are reasonably approximated by the elliptical model, whereas the 3-circle model obtains a good agreement for curved shapes. Copyright © 2017 American Association of Endodontists. Published by Elsevier Inc. All rights reserved.

Which Instructional Practices Most Help First Grade Students with and without Mathematics Difficulties?

PubMed Central

Morgan, Paul L.; Farkas, George; Maczuga, Steve

2015-01-01

We used population-based, longitudinal data to investigate the relation between mathematics instructional practices used by 1st grade teachers in the U.S. and the mathematics achievement of their students. Factor analysis identified four types of instructional activities (i.e., teacher-directed, student-centered, manipulatives/calculators, movement/music) and eight types of specific skills taught (e.g., adding two-digit numbers). First-grade students were then classified into five groups on the basis of their fall and/or spring of kindergarten mathematics achievement—three groups with mathematics difficulties (MD) and two without MD. Regression analysis indicated that a higher percentage of MD students in 1st grade classrooms was associated with greater use by teachers of manipulatives/calculators and movement/music to teach mathematics. Yet follow-up analysis for each of the MD and non-MD groups indicated that only teacher-directed instruction was significantly associated with the achievement of students with MD (covariate-adjusted ESs = .05–.07). The largest predicted effect for a specific instructional practice was for routine practice and drill. In contrast, for both groups of non-MD students, teacher-directed and student-centered instruction had approximately equal, statistically significant positive predicted effects (covariate-adjusted ESs = .03–.04). First-grade teachers in the U.S. may need to increase their use of teacher-directed instruction if they are to raise the mathematics achievement of students with MD. PMID:26180268

Igniting Creativity and Planning for Your Gifted Students.

ERIC Educational Resources Information Center

Russell, Don W., Ed.

The collection of instructional plans is designed to offer samples of strategies and ideas to teachers involved with gifted students. Approximately 30 plans are presented for the following areas (sample subtopics in science (atomic fusion), social studies (mores and folkways), mathematics (spatial relations), health and physiology, philosophy, and…

Is It Counting, or Is It Adding?

ERIC Educational Resources Information Center

Eisenhardt, Sara; Fisher, Molly H.; Thomas, Jonathan; Schack, Edna O.; Tassell, Janet; Yoder, Margaret

2014-01-01

The Common Core State Standards for Mathematics (CCSSI 2010) expect second grade students to "fluently add and subtract within 20 using mental strategies" (2.OA.B.2). Most children begin with number word sequences and counting approximations and then develop greater skill with counting. But do all teachers really understand how this…

Alternative Analysis of the Michaelis-Menten Equations

ERIC Educational Resources Information Center

Krogstad, Harald E.; Dawed, Mohammed Yiha; Tegegne, Tadele Tesfa

2011-01-01

Courses in mathematical modelling are always in need of simple, illustrative examples. The Michaelis-Menten reaction kinetics equations have been considered to be a basic example of scaling and singular perturbation. However, the leading order approximations do not easily show the expected behaviour, and this note proposes a different perturbation…

Copernican Mathematics: Calculating Periods and Distances of the Planets

ERIC Educational Resources Information Center

Rosenkrantz, Kurt J.

2004-01-01

The heliocentric, or Sun-centered model, one of the most important revolutions in scientific thinking, allowed Nicholas Copernicus to calculate the periods, relative distances, and approximate orbital shapes of all the known planets, thereby paving the way for Kepler's laws and Newton's formation of gravitation. Recreating Copernicus's…

The Achievement of Indigenous Students in Guatemalan Primary Schools

ERIC Educational Resources Information Center

McEwan, Patrick J.; Trowbridge, Marisol

2007-01-01

This paper analyses the difference in academic achievement between indigenous and nonindigenous children that attend rural primary schools in Guatemala. The gap ranges between 0.8 and 1 standard deviation in Spanish, and approximately half that in Mathematics. A decomposition procedure suggests that a relatively small portion of the achievement…

Metaheuristic optimisation methods for approximate solving of singular boundary value problems

NASA Astrophysics Data System (ADS)

Sadollah, Ali; Yadav, Neha; Gao, Kaizhou; Su, Rong

2017-07-01

This paper presents a novel approximation technique based on metaheuristics and weighted residual function (WRF) for tackling singular boundary value problems (BVPs) arising in engineering and science. With the aid of certain fundamental concepts of mathematics, Fourier series expansion, and metaheuristic optimisation algorithms, singular BVPs can be approximated as an optimisation problem with boundary conditions as constraints. The target is to minimise the WRF (i.e. error function) constructed in approximation of BVPs. The scheme involves generational distance metric for quality evaluation of the approximate solutions against exact solutions (i.e. error evaluator metric). Four test problems including two linear and two non-linear singular BVPs are considered in this paper to check the efficiency and accuracy of the proposed algorithm. The optimisation task is performed using three different optimisers including the particle swarm optimisation, the water cycle algorithm, and the harmony search algorithm. Optimisation results obtained show that the suggested technique can be successfully applied for approximate solving of singular BVPs.

Numerical scheme approximating solution and parameters in a beam equation

NASA Astrophysics Data System (ADS)

Ferdinand, Robert R.

2003-12-01

We present a mathematical model which describes vibration in a metallic beam about its equilibrium position. This model takes the form of a nonlinear second-order (in time) and fourth-order (in space) partial differential equation with boundary and initial conditions. A finite-element Galerkin approximation scheme is used to estimate model solution. Infinite-dimensional model parameters are then estimated numerically using an inverse method procedure which involves the minimization of a least-squares cost functional. Numerical results are presented and future work to be done is discussed.

Wave refraction diagrams for the Baltimore Canyon region of the mid-Atlantic continental shelf computed by using three bottom topography approximation techniques

NASA Technical Reports Server (NTRS)

Poole, L. R.

1976-01-01

The Langley Research Center and Virginia Institute of Marine Science wave refraction computer model was applied to the Baltimore Canyon region of the mid-Atlantic continental shelf. Wave refraction diagrams for a wide range of normally expected wave periods and directions were computed by using three bottom topography approximation techniques: quadratic least squares, cubic least squares, and constrained bicubic interpolation. Mathematical or physical interpretation of certain features appearing in the computed diagrams is discussed.

Strong solutions and instability for the fitness gradient system in evolutionary games between two populations

NASA Astrophysics Data System (ADS)

Xu, Qiuju; Belmonte, Andrew; deForest, Russ; Liu, Chun; Tan, Zhong

2017-04-01

In this paper, we study a fitness gradient system for two populations interacting via a symmetric game. The population dynamics are governed by a conservation law, with a spatial migration flux determined by the fitness. By applying the Galerkin method, we establish the existence, regularity and uniqueness of global solutions to an approximate system, which retains most of the interesting mathematical properties of the original fitness gradient system. Furthermore, we show that a Turing instability occurs for equilibrium states of the fitness gradient system, and its approximations.

Gaussian-Beam/Physical-Optics Design Of Beam Waveguide

NASA Technical Reports Server (NTRS)

Veruttipong, Watt; Chen, Jacqueline C.; Bathker, Dan A.

1993-01-01

In iterative method of designing wideband beam-waveguide feed for paraboloidal-reflector antenna, Gaussian-beam approximation alternated with more nearly exact physical-optics analysis of diffraction. Includes curved and straight reflectors guiding radiation from feed horn to subreflector. For iterative design calculations, curved mirrors mathematically modeled as thin lenses. Each distance Li is combined length of two straight-line segments intersecting at one of flat mirrors. Method useful for designing beam-waveguide reflectors or mirrors required to have diameters approximately less than 30 wavelengths at one or more intended operating frequencies.

Approximate solutions to Mathieu's equation

NASA Astrophysics Data System (ADS)

Wilkinson, Samuel A.; Vogt, Nicolas; Golubev, Dmitry S.; Cole, Jared H.

2018-06-01

Mathieu's equation has many applications throughout theoretical physics. It is especially important to the theory of Josephson junctions, where it is equivalent to Schrödinger's equation. Mathieu's equation can be easily solved numerically, however there exists no closed-form analytic solution. Here we collect various approximations which appear throughout the physics and mathematics literature and examine their accuracy and regimes of applicability. Particular attention is paid to quantities relevant to the physics of Josephson junctions, but the arguments and notation are kept general so as to be of use to the broader physics community.

Reaction-Diffusion-Delay Model for EPO/TNF-α Interaction in articular cartilage lesion abatement

PubMed Central

2012-01-01

Background Injuries to articular cartilage result in the development of lesions that form on the surface of the cartilage. Such lesions are associated with articular cartilage degeneration and osteoarthritis. The typical injury response often causes collateral damage, primarily an effect of inflammation, which results in the spread of lesions beyond the region where the initial injury occurs. Results and discussion We present a minimal mathematical model based on known mechanisms to investigate the spread and abatement of such lesions. The first case corresponds to the parameter values listed in Table 1, while the second case has parameter values as in Table 2. In particular we represent the "balancing act" between pro-inflammatory and anti-inflammatory cytokines that is hypothesized to be a principal mechanism in the expansion properties of cartilage damage during the typical injury response. We present preliminary results of in vitro studies that confirm the anti-inflammatory activities of the cytokine erythropoietin (EPO). We assume that the diffusion of cytokines determine the spatial behavior of injury response and lesion expansion so that a reaction diffusion system involving chemical species and chondrocyte cell state population densities is a natural way to represent cartilage injury response. We present computational results using the mathematical model showing that our representation is successful in capturing much of the interesting spatial behavior of injury associated lesion development and abatement in articular cartilage. Further, we discuss the use of this model to study the possibility of using EPO as a therapy for reducing the amount of inflammation induced collateral damage to cartilage during the typical injury response. Table 1 Model Parameter Values for Results in Figure 5 Table of Parameter Values Corresponding to Simulations in Figure 5 Parameter Value Units Reason D R 0.1 c m 2 day Determined from [13] D M 0.05 c m 2 day Determined from [13] D F 0.05 c m 2 day Determined from [13] D P 0.005 c m 2 day Determined from [13] δ R 0.01 1 day Approximated δ M 0.6 1 day Approximated δ F 0.6 1 day Approximated δ P 0.0087 1 day Approximated δ U 0.0001 1 day Approximated σ R 0.0001 micromolar ⋅ c m 2 day ⋅ cells Approximated σ M 0.00001 micromolar ⋅ c m 2 day ⋅ cells Approximated σ F 0.0001 micromolar ⋅ c m 2 day ⋅ cells Approximated σ P 0 micromolar ⋅ c m 2 day ⋅ cells Case with no anti-inflammatory response Λ 10 micromolar Approximated λ R 10 micromolar Approximated λ M 10 micromolar Approximated λ F 10 micromolar Approximated λ P 10 micromolar Approximated α 0 1 day Case with no anti-inflammatory response β 1 100 1 day Approximated Β 2 50 1 day Approximated γ 10 1 day Approximated ν 0.5 1 day Approximated μ S A 1 1 day Approximated μ D N 0.5 1 day Approximated τ 1 0.5 days Taken from [5] τ 2 1 days Taken from [5] Table 2 Model Parameter Values for Results in Figure 6 Table of Parameter Values Corresponding to Simulations in Figure 6 Parameter Value Units Reason D R 0.1 c m 2 day Determined from [13] D M 0.05 c m 2 day Determined from [13] D F 0.05 c m 2 day Determined from [13] DP 0.005 c m 2 day Determined from [13] δ R 0.01 1 day Approximated δ M 0.6 1 day Approximated δ F 0.6 1 day Approximated δ P 0.0087 1 day Approximated δ U 0.0001 1 day Approximated σ R 0.0001 micromolar ⋅ c m 2 day ⋅ cells Approximated σ M 0.00001 micromolar ⋅ c m 2 day ⋅ cells Approximated σ F 0.0001 micromolar ⋅ c m 2 day ⋅ cells Approximated σ P 0.001 micromolar ⋅ c m 2 day ⋅ cells Approximated Λ 10 micromolar Approximated λ R 10 micromolar Approximated λ M 10 micromolar Approximated λ F 10 micromolar Approximated λ P 10 micromolar Approximated α 10 1 day Approximated β 1 100 1 day Approximated β 2 50 1 day Approximated γ 10 1 day Approximated ν 0.5 1 day Approximated μ S A 1 1 day Approximated μ D N 0.5 1 day Approximated τ 1 0.5 days Taken from [5] τ 2 1 days Taken from [5] Conclusions The mathematical model presented herein suggests that not only are anti-inflammatory cy-tokines, such as EPO necessary to prevent chondrocytes signaled by pro-inflammatory cytokines from entering apoptosis, they may also influence how chondrocytes respond to signaling by pro-inflammatory cytokines. Reviewers This paper has been reviewed by Yang Kuang, James Faeder and Anna Marciniak-Czochra. PMID:22353555

Microwave Brightness Of Land Surfaces From Outer Space

NASA Technical Reports Server (NTRS)

Kerr, Yann H.; Njoku, Eni G.

1991-01-01

Mathematical model approximates microwave radiation emitted by land surfaces traveling to microwave radiometer in outer space. Applied to measurements made by Scanning Multichannel Microwave Radiometer (SMMR). Developed for interpretation of microwave imagery of Earth to obtain distributions of various chemical, physical, and biological characteristics across its surface. Intended primarily for use in mapping moisture content of soil and fraction of Earth covered by vegetation. Advanced Very-High-Resolution Radiometer (AVHRR), provides additional information on vegetative cover, thereby making possible retrieval of soil-moisture values from SMMR measurements. Possible to monitor changes of land surface during intervals of 5 to 10 years, providing significant data for mathematical models of evolution of climate.

Compressed modes for variational problems in mathematics and physics

PubMed Central

Ozoliņš, Vidvuds; Lai, Rongjie; Caflisch, Russel; Osher, Stanley

2013-01-01

This article describes a general formalism for obtaining spatially localized (“sparse”) solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems, such as the important case of Schrödinger’s equation in quantum mechanics. Sparsity is achieved by adding an regularization term to the variational principle, which is shown to yield solutions with compact support (“compressed modes”). Linear combinations of these modes approximate the eigenvalue spectrum and eigenfunctions in a systematically improvable manner, and the localization properties of compressed modes make them an attractive choice for use with efficient numerical algorithms that scale linearly with the problem size. PMID:24170861

Compressed modes for variational problems in mathematics and physics.

PubMed

Ozolins, Vidvuds; Lai, Rongjie; Caflisch, Russel; Osher, Stanley

2013-11-12

This article describes a general formalism for obtaining spatially localized ("sparse") solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems, such as the important case of Schrödinger's equation in quantum mechanics. Sparsity is achieved by adding an regularization term to the variational principle, which is shown to yield solutions with compact support ("compressed modes"). Linear combinations of these modes approximate the eigenvalue spectrum and eigenfunctions in a systematically improvable manner, and the localization properties of compressed modes make them an attractive choice for use with efficient numerical algorithms that scale linearly with the problem size.

Kinetic modeling of plant metabolism and its predictive power: peppermint essential oil biosynthesis as an example.

PubMed

Lange, Bernd Markus; Rios-Estepa, Rigoberto

2014-01-01

The integration of mathematical modeling with analytical experimentation in an iterative fashion is a powerful approach to advance our understanding of the architecture and regulation of metabolic networks. Ultimately, such knowledge is highly valuable to support efforts aimed at modulating flux through target pathways by molecular breeding and/or metabolic engineering. In this article we describe a kinetic mathematical model of peppermint essential oil biosynthesis, a pathway that has been studied extensively for more than two decades. Modeling assumptions and approximations are described in detail. We provide step-by-step instructions on how to run simulations of dynamic changes in pathway metabolites concentrations.

Influence of Hall Current and Viscous Dissipation on Pressure Driven Flow of Pseudoplastic Fluid with Heat Generation: A Mathematical Study.

PubMed

Noreen, Saima; Qasim, Muhammad

2015-01-01

In this paper, we study the influence of heat sink (or source) on the peristaltic motion of pseudoplastic fluid in the presence of Hall current, where channel walls are non-conducting in nature. Flow analysis has been carried out under the approximations of a low Reynolds number and long wavelength. Coupled equations are solved using shooting method for numerical solution for the axial velocity function, temperature and pressure gradient distributions. We analyze the influence of various interesting parameters on flow quantities. The present study can be considered as a mathematical presentation of the dynamics of physiological organs with stones.

New verifiable stationarity concepts for a class of mathematical programs with disjunctive constraints.

PubMed

Benko, Matúš; Gfrerer, Helmut

2018-01-01

In this paper, we consider a sufficiently broad class of non-linear mathematical programs with disjunctive constraints, which, e.g. include mathematical programs with complemetarity/vanishing constraints. We present an extension of the concept of [Formula: see text]-stationarity which can be easily combined with the well-known notion of M-stationarity to obtain the stronger property of so-called [Formula: see text]-stationarity. We show how the property of [Formula: see text]-stationarity (and thus also of M-stationarity) can be efficiently verified for the considered problem class by computing [Formula: see text]-stationary solutions of a certain quadratic program. We consider further the situation that the point which is to be tested for [Formula: see text]-stationarity, is not known exactly, but is approximated by some convergent sequence, as it is usually the case when applying some numerical method.

Links Between the Intuitive Sense of Number and Formal Mathematics Ability.

PubMed

Feigenson, Lisa; Libertus, Melissa E; Halberda, Justin

2013-06-01

Humans share with other animals a system for thinking about numbers in an imprecise and intuitive way. The Approximate Number System (ANS) that underlies this thinking is present throughout the lifespan, is entirely nonverbal, and supports basic numerical computations like comparing, adding, and subtracting quantities. Humans, unlike other animals, also have a system for representing exact numbers. This linguistically mediated system is slowly mastered over the course of many years and provides the basis for most of our formal mathematical thought. A growing body of evidence suggests that the nonverbal ANS and the culturally invented system of exact numbers are fundamentally linked. In this article, we review evidence for this relationship, describing how group and individual differences in the ANS correlate with and even predict formal math ability. In this way, we illustrate how a system of ancient core knowledge may serve as a foundation for more complex mathematical thought.

Early Foundations for Mathematics Learning and Their Relations to Learning Disabilities.

PubMed

Geary, David C

2013-02-01

Children's quantitative competencies upon entry into school can have lifelong consequences. Children who start behind generally stay behind, and mathematical skills at school completion influence employment prospects and wages in adulthood. I review the current debate over whether early quantitative learning is supported by (a) an inherent system for representing approximate magnitudes, (b) an attentional-control system that enables explicit processing of quantitative symbols, such as Arabic numerals, or (c) the logical problem-solving abilities that facilitate learning of the relations among numerals. Studies of children with mathematical learning disabilities and difficulties have suggested that each of these competencies may be involved, but to different degrees and at different points in the learning process. Clarifying how and when these competencies facilitate early quantitative learning and developing interventions to address their impact on children have the potential to yield substantial benefits for individuals and for society.

Two-dimensional coupled mathematical modeling of fluvial processes with intense sediment transport and rapid bed evolution

NASA Astrophysics Data System (ADS)

Yue, Zhiyuan; Cao, Zhixian; Li, Xin; Che, Tao

2008-09-01

Alluvial rivers may experience intense sediment transport and rapid bed evolution under a high flow regime, for which traditional decoupled mathematical river models based on simplified conservation equations are not applicable. A two-dimensional coupled mathematical model is presented, which is generally applicable to the fluvial processes with either intense or weak sediment transport. The governing equations of the model comprise the complete shallow water hydrodynamic equations closed with Manning roughness for boundary resistance and empirical relationships for sediment exchange with the erodible bed. The second-order Total-Variation-Diminishing version of the Weighted-Average-Flux method, along with the HLLC approximate Riemann Solver, is adapted to solve the governing equations, which can properly resolve shock waves and contact discontinuities. The model is applied to the pilot study of the flooding due to a sudden outburst of a real glacial-lake.

Linear Water Waves

NASA Astrophysics Data System (ADS)

Kuznetsov, N.; Maz'ya, V.; Vainberg, B.

2002-08-01

This book gives a self-contained and up-to-date account of mathematical results in the linear theory of water waves. The study of waves has many applications, including the prediction of behavior of floating bodies (ships, submarines, tension-leg platforms etc.), the calculation of wave-making resistance in naval architecture, and the description of wave patterns over bottom topography in geophysical hydrodynamics. The first section deals with time-harmonic waves. Three linear boundary value problems serve as the approximate mathematical models for these types of water waves. The next section uses a plethora of mathematical techniques in the investigation of these three problems. The techniques used in the book include integral equations based on Green's functions, various inequalities between the kinetic and potential energy and integral identities which are indispensable for proving the uniqueness theorems. The so-called inverse procedure is applied to constructing examples of non-uniqueness, usually referred to as 'trapped nodes.'

Cross-validating a bidimensional mathematics anxiety scale.

PubMed

Haiyan Bai

2011-03-01

The psychometric properties of a 14-item bidimensional Mathematics Anxiety Scale-Revised (MAS-R) were empirically cross-validated with two independent samples consisting of 647 secondary school students. An exploratory factor analysis on the scale yielded strong construct validity with a clear two-factor structure. The results from a confirmatory factor analysis indicated an excellent model-fit (χ(2) = 98.32, df = 62; normed fit index = .92, comparative fit index = .97; root mean square error of approximation = .04). The internal consistency (.85), test-retest reliability (.71), interfactor correlation (.26, p < .001), and positive discrimination power indicated that MAS-R is a psychometrically reliable and valid instrument for measuring mathematics anxiety. Math anxiety, as measured by MAS-R, correlated negatively with student achievement scores (r = -.38), suggesting that MAS-R may be a useful tool for classroom teachers and other educational personnel tasked with identifying students at risk of reduced math achievement because of anxiety.

On the connection between multigrid and cyclic reduction

NASA Technical Reports Server (NTRS)

Merriam, M. L.

1984-01-01

A technique is shown whereby it is possible to relate a particular multigrid process to cyclic reduction using purely mathematical arguments. This technique suggest methods for solving Poisson's equation in 1-, 2-, or 3-dimensions with Dirichlet or Neumann boundary conditions. In one dimension the method is exact and, in fact, reduces to cyclic reduction. This provides a valuable reference point for understanding multigrid techniques. The particular multigrid process analyzed is referred to here as Approximate Cyclic Reduction (ACR) and is one of a class known as Multigrid Reduction methods in the literature. It involves one approximation with a known error term. It is possible to relate the error term in this approximation with certain eigenvector components of the error. These are sharply reduced in amplitude by classical relaxation techniques. The approximation can thus be made a very good one.

Time allocated to mathematics in post-primary schools in Ireland: are we in double trouble?

NASA Astrophysics Data System (ADS)

O'Meara, Niamh; Prendergast, Mark

2018-05-01

Mathematics educators and legislators worldwide have begun placing a greater emphasis on teaching mathematics for understanding and through the use of real-life applications. Revised curricula have led to the time allocated to mathematics in effected countries being scrutinised. This has resulted in policy-makers and educationalists worldwide calling for the inclusion of double class periods on the mathematics timetable. Research from the United States suggests that the introduction of double or block periods allow for the objectives of revised curricula to be realized. The aim of this study, which is set in the school context, is first to ascertain if schools in Ireland are scheduling double periods for mathematics at both lower post-primary level (Junior Cycle) and upper post-primary level (Senior Cycle). It also seeks to determine if there is a link between teachers' levels of satisfaction with the time allocated to mathematics and the provision of double periods and to get insights from teachers in relation to their opinions on what can be achieved through the introduction of such classes. Questionnaires were sent to 400 post-primary schools (approximately 1600 teachers) which were selected using stratified sampling techniques. It was found that 8.7% of mathematics teachers reported the provision of double periods at Junior Cycle while 55% reported that double periods were included on their timetable at Senior Cycle. The study also identified a link between teachers' levels of satisfaction with the time allocated to mathematics and the provision of double periods. Finally, teachers felt that double periods allowed for new teaching methodologies, which were promoted by the revised curricula, to be implemented and teaching for understanding was also more feasible. In essence, it was found that double periods have an influence on the mathematical experience of post-primary students as well as the teaching approaches employed.

Spline approximation, Part 1: Basic methodology

NASA Astrophysics Data System (ADS)

Ezhov, Nikolaj; Neitzel, Frank; Petrovic, Svetozar

2018-04-01

In engineering geodesy point clouds derived from terrestrial laser scanning or from photogrammetric approaches are almost never used as final results. For further processing and analysis a curve or surface approximation with a continuous mathematical function is required. In this paper the approximation of 2D curves by means of splines is treated. Splines offer quite flexible and elegant solutions for interpolation or approximation of "irregularly" distributed data. Depending on the problem they can be expressed as a function or as a set of equations that depend on some parameter. Many different types of splines can be used for spline approximation and all of them have certain advantages and disadvantages depending on the approximation problem. In a series of three articles spline approximation is presented from a geodetic point of view. In this paper (Part 1) the basic methodology of spline approximation is demonstrated using splines constructed from ordinary polynomials and splines constructed from truncated polynomials. In the forthcoming Part 2 the notion of B-spline will be explained in a unique way, namely by using the concept of convex combinations. The numerical stability of all spline approximation approaches as well as the utilization of splines for deformation detection will be investigated on numerical examples in Part 3.

Risk approximation in decision making: approximative numeric abilities predict advantageous decisions under objective risk.

PubMed

Mueller, Silke M; Schiebener, Johannes; Delazer, Margarete; Brand, Matthias

2018-01-22

Many decision situations in everyday life involve mathematical considerations. In decisions under objective risk, i.e., when explicit numeric information is available, executive functions and abilities to handle exact numbers and ratios are predictors of objectively advantageous choices. Although still debated, exact numeric abilities, e.g., normative calculation skills, are assumed to be related to approximate number processing skills. The current study investigates the effects of approximative numeric abilities on decision making under objective risk. Participants (N = 153) performed a paradigm measuring number-comparison, quantity-estimation, risk-estimation, and decision-making skills on the basis of rapid dot comparisons. Additionally, a risky decision-making task with exact numeric information was administered, as well as tasks measuring executive functions and exact numeric abilities, e.g., mental calculation and ratio processing skills, were conducted. Approximative numeric abilities significantly predicted advantageous decision making, even beyond the effects of executive functions and exact numeric skills. Especially being able to make accurate risk estimations seemed to contribute to superior choices. We recommend approximation skills and approximate number processing to be subject of future investigations on decision making under risk.

Scale and the Evolutionarily Based Approximate Number System: An Exploratory Study

ERIC Educational Resources Information Center

Delgado, Cesar; Jones, M. Gail; You, Hye Sun; Robertson, Laura; Chesnutt, Katherine; Halberda, Justin

2017-01-01

Crosscutting concepts such as "scale, proportion, and quantity" are recognised by U.S. science standards as a potential vehicle for students to integrate their scientific and mathematical knowledge; yet, U.S. students and adults trail their international peers in scale and measurement estimation. Culturally based knowledge of scale such…

Strategies for Reducing Math Anxiety. Information Capsule. Volume 1102

ERIC Educational Resources Information Center

Blazer, Christie

2011-01-01

Approximately 93 percent of Americans indicate that they experience some level of math anxiety. Math anxiety is defined as negative emotions that interfere with the solving of mathematical problems. Studies have found that some students who perform poorly on math assessments actually have a full understanding of the concepts being tested; however,…

Bolden Visit Davis Elementary

NASA Image and Video Library

2009-09-10

NASA Administrator Charles F. Bolden speaks to students during a visit to Davis Elementary School, Friday, Sept. 11, 2009, in Washington. Bolden spent time with approximately 120 students in third, fourth and fifth grade talking about science, technology, mathematics and engineering as part of the National Day of Service and Remembrance. Photo Credit: (NASA/Paul E. Alers)

Functional DNA: Teaching Infinite Series through Genetic Analogy

ERIC Educational Resources Information Center

Kowalski, R. Travis

2011-01-01

This article presents an extended analogy that connects infinite sequences and series to the science of genetics, by identifying power series as "DNA for a function." This analogy allows standard topics such as convergence tests or Taylor approximations to be recast in a "forensic" light as mathematical analogs of genetic concepts such as DNA…

The End of the Flynn Effect?

ERIC Educational Resources Information Center

Sundet, Jon Martin; Barlaug, Dag G.; Torjussen, Tore M.

2004-01-01

The present paper reports secular trends in the mean scores of a language, mathematics, and a Raven-like test together with a combined general ability (GA) score among Norwegian (male) conscripts tested from the mid 1950s to 2002 (birth cohorts approximately equal to 1935-1984). Secular gains in standing height (indicating improved nutrition and…

How Do Volcanoes Affect Human Life? Integrated Unit.

ERIC Educational Resources Information Center

Dayton, Rebecca; Edwards, Carrie; Sisler, Michelle

This packet contains a unit on teaching about volcanoes. The following question is addressed: How do volcanoes affect human life? The unit covers approximately three weeks of instruction and strives to present volcanoes in an holistic form. The five subject areas of art, language arts, mathematics, science, and social studies are integrated into…

An Analysis of Grade 4 Teachers' Mathematical Instructional Strategies

ERIC Educational Resources Information Center

Wilson-Patrick, Dedra

2016-01-01

The standardized math test scores of approximately 48 African American and Hispanic students from 4 different classes at a rural Title I elementary school located in the southern United States decreased by 10 points on the Palmetto Assessment of State Standards Test. For this qualitative case study, purposive sampling was used to recruit four…

Numerical Integration with GeoGebra in High School

ERIC Educational Resources Information Center

Herceg, Dorde; Herceg, Dragoslav

2010-01-01

The concept of definite integral is almost always introduced as the Riemann integral, which is defined in terms of the Riemann sum, and its geometric interpretation. This definition is hard to understand for high school students. With the aid of mathematical software for visualisation and computation of approximate integrals, the notion of…

Teachers See What Ability Scores Cannot: Predicting Student Performance with Challenging Mathematics

ERIC Educational Resources Information Center

Foreman, Jennifer L.; Gubbins, E. Jean

2015-01-01

Teacher nominations of students are commonly used in gifted and talented identification systems to supplement psychometric measures of reasoning ability. In this study, second grade teachers were requested to nominate approximately one fourth of their students as having high learning potential in the year prior to the students' participation in a…

Understanding quantum phenomena without solving the Schrödinger equation: the case of the finite square well

NASA Astrophysics Data System (ADS)

Barsan, Victor

2015-11-01

An approximate formula for the energy levels of the bound states of a particle in a finite square well are obtained, without using the Schrödinger equation. The physics and mathematics involved in this approach are accessible to a gifted high school student.

An Improved Mathematical Scheme for LTE-Advanced Coexistence with FM Broadcasting Service

PubMed Central

Al-hetar, Abdulaziz M.

2016-01-01

Power spectral density (PSD) overlapping analysis is considered the surest approach to evaluate feasibility of compatibility between wireless communication systems. In this paper, a new closed-form for the Interference Signal Power Attenuation (ISPA) is mathematically derived to evaluate interference caused from Orthogonal Frequency Division Multiplexing (OFDM)-based Long Term Evolution (LTE)-Advanced into Frequency Modulation (FM) broadcasting service. In this scheme, ISPA loss due to PSD overlapping of both OFDM-based LTE-Advanced and FM broadcasting service is computed. The proposed model can estimate power attenuation loss more precisely than the Advanced Minimum Coupling Loss (A-MCL) and approximate-ISPA methods. Numerical results demonstrate that the interference power is less than that obtained using the A-MCL and approximate ISPA methods by 2.8 and 1.5 dB at the co-channel and by 5.2 and 2.2 dB at the adjacent channel with null guard band, respectively. The outperformance of this scheme over the other methods leads to more diminishing in the required physical distance between the two systems which ultimately supports efficient use of the radio frequency spectrum. PMID:27855216

An Improved Mathematical Scheme for LTE-Advanced Coexistence with FM Broadcasting Service.

PubMed

Shamsan, Zaid Ahmed; Al-Hetar, Abdulaziz M

2016-01-01

Power spectral density (PSD) overlapping analysis is considered the surest approach to evaluate feasibility of compatibility between wireless communication systems. In this paper, a new closed-form for the Interference Signal Power Attenuation (ISPA) is mathematically derived to evaluate interference caused from Orthogonal Frequency Division Multiplexing (OFDM)-based Long Term Evolution (LTE)-Advanced into Frequency Modulation (FM) broadcasting service. In this scheme, ISPA loss due to PSD overlapping of both OFDM-based LTE-Advanced and FM broadcasting service is computed. The proposed model can estimate power attenuation loss more precisely than the Advanced Minimum Coupling Loss (A-MCL) and approximate-ISPA methods. Numerical results demonstrate that the interference power is less than that obtained using the A-MCL and approximate ISPA methods by 2.8 and 1.5 dB at the co-channel and by 5.2 and 2.2 dB at the adjacent channel with null guard band, respectively. The outperformance of this scheme over the other methods leads to more diminishing in the required physical distance between the two systems which ultimately supports efficient use of the radio frequency spectrum.

An unsteady lifting surface method for single rotation propellers

NASA Technical Reports Server (NTRS)

Williams, Marc H.

1990-01-01

The mathematical formulation of a lifting surface method for evaluating the steady and unsteady loads induced on single rotation propellers by blade vibration and inflow distortion is described. The scheme is based on 3-D linearized compressible aerodynamics and presumes that all disturbances are simple harmonic in time. This approximation leads to a direct linear integral relation between the normal velocity on the blade (which is determined from the blade geometry and motion) and the distribution of pressure difference across the blade. This linear relation is discretized by breaking the blade up into subareas (panels) on which the pressure difference is treated as approximately constant, and constraining the normal velocity at one (control) point on each panel. The piece-wise constant loads can then be determined by Gaussian elimination. The resulting blade loads can be used in performance, stability and forced response predictions for the rotor. Mathematical and numerical aspects of the method are examined. A selection of results obtained from the method is presented. The appendices include various details of the derivation that were felt to be secondary to the main development in Section 1.

Modeling for intra-body communication with bone effect.

PubMed

Pun, S H; Gao, Y M; Mak, P U; Du, M; Vai, M I

2009-01-01

Intra-body communication (IBC) is a new, different "wireless" communication technique based on the human tissue. This short range "wireless" communication technology provides an alternative solution to wearable sensors, home health system, telemedicine and implanted devices. The development of the IBC enables the possibilities of providing less complexity and convenient communication methodologies for these devices. By regarding human tissue as communication channel, IBC making use of the conductivities properties of human tissue to send electrical signal from transmitter to receiver. In this paper, the authors proposed a new mathematical model for galvanic coupling type IBC based on a human limb. Starting from the electromagnetic theory, the authors treat human tissue as volume conductor, which is in analogous with the bioelectric phenomena analysis. In order to explain the mechanism of galvanic coupling type technique of IBC, applying the quasi-static approximation, the governing equation can be reduced to Laplace Equation. Finally, the analytical model is evaluated with on-body measurement for testing its performance. The comparison result shows that the developed mathematical model can provide good approximation for galvanic coupling type IBC on human limb under low operating frequencies.

Mathematical treatment of isotopologue and isotopomer speciation and fractionation in biochemical kinetics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maggi, F.M.; Riley, W.J.

2009-11-01

We present a mathematical treatment of the kinetic equations that describe isotopologue and isotopomer speciation and fractionation during enzyme-catalyzed biochemical reactions. These equations, presented here with the name GEBIK (general equations for biochemical isotope kinetics) and GEBIF (general equations for biochemical isotope fractionation), take into account microbial biomass and enzyme dynamics, reaction stoichiometry, isotope substitution number, and isotope location within each isotopologue and isotopomer. In addition to solving the complete GEBIK and GEBIF, we also present and discuss two approximations to the full solutions under the assumption of biomass-free and enzyme steady-state, and under the quasi-steady-state assumption as applied tomore » the complexation rate. The complete and approximate approaches are applied to observations of biological denitrification in soils. Our analysis highlights that the full GEBIK and GEBIF provide a more accurate description of concentrations and isotopic compositions of substrates and products throughout the reaction than do the approximate forms. We demonstrate that the isotopic effects of a biochemical reaction depend, in the most general case, on substrate and complex concentrations and, therefore, the fractionation factor is a function of time. We also demonstrate that inverse isotopic effects can occur for values of the fractionation factor smaller than 1, and that reactions that do not discriminate isotopes do not necessarily imply a fractionation factor equal to 1.« less

Numerical Activities and Information Learned at Home Link to the Exact Numeracy Skills in 5–6 Years-Old Children

PubMed Central

Benavides-Varela, Silvia; Butterworth, Brian; Burgio, Francesca; Arcara, Giorgio; Lucangeli, Daniela; Semenza, Carlo

2016-01-01

It is currently accepted that certain activities within the family environment contribute to develop early numerical skills before schooling. However, it is unknown whether this early experience influences both the exact and the approximate representation of numbers, and if so, which is more important for numerical tasks. In the present study the mathematical performance of 110 children (mean age 5 years 11 months) was evaluated using a battery that included tests of approximate and exact numerical abilities, as well as everyday numerical problems. Moreover, children were assessed on their knowledge of number information learned at home. The parents of the participants provided information regarding daily activities of the children and socio-demographic characteristics of the family. The results showed that the amount of numerical information learned at home was a significant predictor of participants' performance on everyday numerical problems and exact number representations, even after taking account of age, memory span and socio-economic and educational status of the family. We also found that particular activities, such as board games, correlate with the children's counting skills, which are foundational for arithmetic. Crucially, tests relying on approximate representations were not predicted by the numerical knowledge acquired at home. The present research supports claims about the importance and nature of home experiences in the child's acquisition of mathematics. PMID:26903902

The approximate number system and domain-general abilities as predictors of math ability in children with normal hearing and hearing loss.

PubMed

Bull, Rebecca; Marschark, Marc; Nordmann, Emily; Sapere, Patricia; Skene, Wendy A

2018-06-01

Many children with hearing loss (CHL) show a delay in mathematical achievement compared to children with normal hearing (CNH). This study examined whether there are differences in acuity of the approximate number system (ANS) between CHL and CNH, and whether ANS acuity is related to math achievement. Working memory (WM), short-term memory (STM), and inhibition were considered as mediators of any relationship between ANS acuity and math achievement. Seventy-five CHL were compared with 75 age- and gender-matched CNH. ANS acuity, mathematical reasoning, WM, and STM of CHL were significantly poorer compared to CNH. Group differences in math ability were no longer significant when ANS acuity, WM, or STM was controlled. For CNH, WM and STM fully mediated the relationship of ANS acuity to math ability; for CHL, WM and STM only partially mediated this relationship. ANS acuity, WM, and STM are significant contributors to hearing status differences in math achievement, and to individual differences within the group of CHL. Statement of contribution What is already known on this subject? Children with hearing loss often perform poorly on measures of math achievement, although there have been few studies focusing on basic numerical cognition in these children. In typically developing children, the approximate number system predicts math skills concurrently and longitudinally, although there have been some contradictory findings. Recent studies suggest that domain-general skills, such as inhibition, may account for the relationship found between the approximate number system and math achievement. What does this study adds? This is the first robust examination of the approximate number system in children with hearing loss, and the findings suggest poorer acuity of the approximate number system in these children compared to hearing children. The study addresses recent issues regarding the contradictory findings of the relationship of the approximate number system to math ability by examining how this relationship varies across children with normal hearing and hearing loss, and by examining whether this relationship is mediated by domain-general skills (working memory, short-term memory, and inhibition). © 2017 The British Psychological Society.

Quantitative model of transport-aperture coordination during reach-to-grasp movements.

PubMed

Rand, Miya K; Shimansky, Y P; Hossain, Abul B M I; Stelmach, George E

2008-06-01

It has been found in our previous studies that the initiation of aperture closure during reach-to-grasp movements occurs when the hand distance to target crosses a threshold that is a function of peak aperture amplitude, hand velocity, and hand acceleration. Thus, a stable relationship between those four movement parameters is observed at the moment of aperture closure initiation. Based on the concept of optimal control of movements (Naslin 1969) and its application for reach-to-grasp movement regulation (Hoff and Arbib 1993), it was hypothesized that the mathematical equation expressing that relationship can be generalized to describe coordination between hand transport and finger aperture during the entire reach-to-grasp movement by adding aperture velocity and acceleration to the above four movement parameters. The present study examines whether this hypothesis is supported by the data obtained in experiments in which young adults performed reach-to-grasp movements in eight combinations of two reach-amplitude conditions and four movement-speed conditions. It was found that linear approximation of the mathematical model described the relationship among the six movement parameters for the entire aperture-closure phase with very high precision for each condition, thus supporting the hypothesis for that phase. Testing whether one mathematical model could approximate the data across all the experimental conditions revealed that it was possible to achieve the same high level of data-fitting precision only by including in the model two additional, condition-encoding parameters and using a nonlinear, artificial neural network-based approximator with two hidden layers comprising three and two neurons, respectively. This result indicates that transport-aperture coordination, as a specific relationship between the parameters of hand transport and finger aperture, significantly depends on the condition-encoding variables. The data from the aperture-opening phase also fit a linear model, whose coefficients were substantially different from those identified for the aperture-closure phase. This result supports the above hypothesis for the aperture-opening phase, and consequently, for the entire reach-to-grasp movement. However, the fitting precision was considerably lower than that for the aperture-closure phase, indicating significant trial-to-trial variability of transport-aperture coordination during the aperture-opening phase. Implications for understanding the neural mechanisms employed by the CNS for controlling reach-to-grasp movements and utilization of the mathematical model of transport-aperture coordination for data analysis are discussed.

Boundary curves of individual items in the distribution of total depressive symptom scores approximate an exponential pattern in a general population.

PubMed

Tomitaka, Shinichiro; Kawasaki, Yohei; Ide, Kazuki; Akutagawa, Maiko; Yamada, Hiroshi; Furukawa, Toshiaki A; Ono, Yutaka

2016-01-01

Previously, we proposed a model for ordinal scale scoring in which individual thresholds for each item constitute a distribution by each item. This lead us to hypothesize that the boundary curves of each depressive symptom score in the distribution of total depressive symptom scores follow a common mathematical model, which is expressed as the product of the frequency of the total depressive symptom scores and the probability of the cumulative distribution function of each item threshold. To verify this hypothesis, we investigated the boundary curves of the distribution of total depressive symptom scores in a general population. Data collected from 21,040 subjects who had completed the Center for Epidemiologic Studies Depression Scale (CES-D) questionnaire as part of a national Japanese survey were analyzed. The CES-D consists of 20 items (16 negative items and four positive items). The boundary curves of adjacent item scores in the distribution of total depressive symptom scores for the 16 negative items were analyzed using log-normal scales and curve fitting. The boundary curves of adjacent item scores for a given symptom approximated a common linear pattern on a log normal scale. Curve fitting showed that an exponential fit had a markedly higher coefficient of determination than either linear or quadratic fits. With negative affect items, the gap between the total score curve and boundary curve continuously increased with increasing total depressive symptom scores on a log-normal scale, whereas the boundary curves of positive affect items, which are not considered manifest variables of the latent trait, did not exhibit such increases in this gap. The results of the present study support the hypothesis that the boundary curves of each depressive symptom score in the distribution of total depressive symptom scores commonly follow the predicted mathematical model, which was verified to approximate an exponential mathematical pattern.

Boundary curves of individual items in the distribution of total depressive symptom scores approximate an exponential pattern in a general population

PubMed Central

Kawasaki, Yohei; Akutagawa, Maiko; Yamada, Hiroshi; Furukawa, Toshiaki A.; Ono, Yutaka

2016-01-01

Background Previously, we proposed a model for ordinal scale scoring in which individual thresholds for each item constitute a distribution by each item. This lead us to hypothesize that the boundary curves of each depressive symptom score in the distribution of total depressive symptom scores follow a common mathematical model, which is expressed as the product of the frequency of the total depressive symptom scores and the probability of the cumulative distribution function of each item threshold. To verify this hypothesis, we investigated the boundary curves of the distribution of total depressive symptom scores in a general population. Methods Data collected from 21,040 subjects who had completed the Center for Epidemiologic Studies Depression Scale (CES-D) questionnaire as part of a national Japanese survey were analyzed. The CES-D consists of 20 items (16 negative items and four positive items). The boundary curves of adjacent item scores in the distribution of total depressive symptom scores for the 16 negative items were analyzed using log-normal scales and curve fitting. Results The boundary curves of adjacent item scores for a given symptom approximated a common linear pattern on a log normal scale. Curve fitting showed that an exponential fit had a markedly higher coefficient of determination than either linear or quadratic fits. With negative affect items, the gap between the total score curve and boundary curve continuously increased with increasing total depressive symptom scores on a log-normal scale, whereas the boundary curves of positive affect items, which are not considered manifest variables of the latent trait, did not exhibit such increases in this gap. Discussion The results of the present study support the hypothesis that the boundary curves of each depressive symptom score in the distribution of total depressive symptom scores commonly follow the predicted mathematical model, which was verified to approximate an exponential mathematical pattern. PMID:27761346

Nonlinear programming extensions to rational function approximation methods for unsteady aerodynamic forces

NASA Technical Reports Server (NTRS)

Tiffany, Sherwood H.; Adams, William M., Jr.

1988-01-01

The approximation of unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft are discussed. Two methods of formulating these approximations are extended to include the same flexibility in constraining the approximations and the same methodology in optimizing nonlinear parameters as another currently used extended least-squares method. Optimal selection of nonlinear parameters is made in each of the three methods by use of the same nonlinear, nongradient optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is lower order than that required when no optimization of the nonlinear terms is performed. The free linear parameters are determined using the least-squares matrix techniques of a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from different approaches are described and results are presented that show comparative evaluations from application of each of the extended methods to a numerical example.

Asymptotic solution of the diffusion equation in slender impermeable tubes of revolution. I. The leading-term approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Traytak, Sergey D., E-mail: sergtray@mail.ru; Le STUDIUM; Semenov Institute of Chemical Physics RAS, 4 Kosygina St., 117977 Moscow

The anisotropic 3D equation describing the pointlike particles diffusion in slender impermeable tubes of revolution with cross section smoothly depending on the longitudinal coordinate is the object of our study. We use singular perturbations approach to find the rigorous asymptotic expression for the local particles concentration as an expansion in the ratio of the characteristic transversal and longitudinal diffusion relaxation times. The corresponding leading-term approximation is a generalization of well-known Fick-Jacobs approximation. This result allowed us to delineate the conditions on temporal and spatial scales under which the Fick-Jacobs approximation is valid. A striking analogy between solution of our problemmore » and the method of inner-outer expansions for low Knudsen numbers gas kinetic theory is established. With the aid of this analogy we clarify the physical and mathematical meaning of the obtained results.« less

Electromagnetic fields radiated from a lightning return stroke - Application of an exact solution to Maxwell's equations

NASA Technical Reports Server (NTRS)

Le Vine, D. M.; Meneghini, R.

1978-01-01

A solution is presented for the electromagnetic fields radiated by an arbitrarily oriented current filament over a conducting ground plane in the case where the current propagates along the filament at the speed of light, and this solution is interpreted in terms of radiation from lightning return strokes. The solution is exact in the fullest sense; no mathematical approximations are made, and the governing differential equations and boundary conditions are satisfied. The solution has the additional attribute of being specified in closed form in terms of elementary functions. This solution is discussed from the point of view of deducing lightning current wave forms from measurements of the electromagnetic fields and understanding the effects of channel tortuosity on the radiated fields. In addition, it is compared with two approximate solutions, the traditional moment approximation and the Fraunhofer approximation, and a set of criteria describing their applicability are presented and interpreted.

Comparison of two methods of numerical tracking of the soil contamination dynamics during a leak from a pipeline

NASA Astrophysics Data System (ADS)

Kosterina, E. A.

2018-01-01

The situation of leakage of a polluting liquid from a longitudinal crack of the pipeline lying on the ground surface is considered. The two-dimensional nonstationary mathematical model is based on the mass balance equation in terms of pressure, which is satisfied in a domain with an unknown moving boundary. This area corresponds to the area of contaminated zone. A function characterizing the region of action of the equation is introduced, which makes it possible to obtain the formulation of the problem in a fixed domain. Two types of finite-difference approximation of the problem statement are proposed. They differ by approximation of the convective term. Counter-current approximation and approximation along characteristics are used. The results of computational experiments, which are in favor of using the method of characteristics, are presented. The methods application is illustrated by an example of spread of oil pollution.

The ambivalent effect of lattice structure on a spatial game

NASA Astrophysics Data System (ADS)

Zhang, Hui; Gao, Meng; Li, Zizhen; Maa, Zhihui; Wang, Hailong

2011-06-01

The evolution of cooperation is studied in lattice-structured populations, in which each individual who adopts one of the following strategies ‘always defect' (ALLD), ‘tit-for-tat' (TFT), and ‘always cooperate' (ALLC) plays the repeated Prisoner's Dilemma game with its neighbors according to an asynchronous update rule. Computer simulations are applied to analyse the dynamics depending on major parameters. Mathematical analyses based on invasion probability analysis, mean-field approximation, as well as pair approximation are also used. We find that the lattice structure promotes the evolution of cooperation compared with a non-spatial population, this is also confirmed by invasion probability analysis in one dimension. Meanwhile, it also inhibits the evolution of cooperation due to the advantage of being spiteful, which indicates the key role of specific life-history assumptions. Mean-field approximation fails to predict the outcome of computer simulations. Pair approximation is accurate in two dimensions but fails in one dimension.

A comparison of the reduced and approximate systems for the time dependent computation of the polar wind and multiconstituent stellar winds

NASA Technical Reports Server (NTRS)

Browning, G. L.; Holzer, T. E.

1992-01-01

The paper derives the 'reduced' system of equations commonly used to describe the time evolution of the polar wind and multiconstituent stellar winds from the equations for a multispecies plasma with known temperature profiles by assuming that the electron thermal speed approaches infinity. The reduced system is proved to have unbounded growth near the sonic point of the protons for many of the standard parameter cases. For the same parameter cases, the unmodified system exhibits growth in some of the Fourier modes, but this growth is bounded. An alternate system (the 'approximate' system) in which the electron thermal speed is slowed down is introduced. The approximate system retains the mathematical behavior of the unmodified system and can be shown to accurately describe the smooth solutions of the unmodified system. Other advantages of the approximate system over the reduced system are discussed.

Hierarchical hybrid control of manipulators: Artificial intelligence in large scale integrated circuits

NASA Technical Reports Server (NTRS)

Greene, P. H.

1972-01-01

Both in practical engineering and in control of muscular systems, low level subsystems automatically provide crude approximations to the proper response. Through low level tuning of these approximations, the proper response variant can emerge from standardized high level commands. Such systems are expressly suited to emerging large scale integrated circuit technology. A computer, using symbolic descriptions of subsystem responses, can select and shape responses of low level digital or analog microcircuits. A mathematical theory that reveals significant informational units in this style of control and software for realizing such information structures are formulated.

The KP Approximation Under a Weak Coriolis Forcing

NASA Astrophysics Data System (ADS)

Melinand, Benjamin

2018-02-01

In this paper, we study the asymptotic behavior of weakly transverse water-waves under a weak Coriolis forcing in the long wave regime. We derive the Boussinesq-Coriolis equations in this setting and we provide a rigorous justification of this model. Then, from these equations, we derive two other asymptotic models. When the Coriolis forcing is weak, we fully justify the rotation-modified Kadomtsev-Petviashvili equation (also called Grimshaw-Melville equation). When the Coriolis forcing is very weak, we rigorously justify the Kadomtsev-Petviashvili equation. This work provides the first mathematical justification of the KP approximation under a Coriolis forcing.

Optimal solutions for a bio mathematical model for the evolution of smoking habit

NASA Astrophysics Data System (ADS)

Sikander, Waseem; Khan, Umar; Ahmed, Naveed; Mohyud-Din, Syed Tauseef

In this study, we apply Variation of Parameter Method (VPM) coupled with an auxiliary parameter to obtain the approximate solutions for the epidemic model for the evolution of smoking habit in a constant population. Convergence of the developed algorithm, namely VPM with an auxiliary parameter is studied. Furthermore, a simple way is considered for obtaining an optimal value of auxiliary parameter via minimizing the total residual error over the domain of problem. Comparison of the obtained results with standard VPM shows that an auxiliary parameter is very feasible and reliable in controlling the convergence of approximate solutions.

An experiment-based comparative study of fuzzy logic control

NASA Technical Reports Server (NTRS)

Berenji, Hamid R.; Chen, Yung-Yaw; Lee, Chuen-Chein; Murugesan, S.; Jang, Jyh-Shing

1989-01-01

An approach is presented to the control of a dynamic physical system through the use of approximate reasoning. The approach has been implemented in a program named POLE, and the authors have successfully built a prototype hardware system to solve the cartpole balancing problem in real-time. The approach provides a complementary alternative to the conventional analytical control methodology and is of substantial use when a precise mathematical model of the process being controlled is not available. A set of criteria for comparing controllers based on approximate reasoning and those based on conventional control schemes is furnished.

The role of language in mathematical development: evidence from children with specific language impairments.

PubMed

Donlan, Chris; Cowan, Richard; Newton, Elizabeth J; Lloyd, Delyth

2007-04-01

A sample (n=48) of eight-year-olds with specific language impairments is compared with age-matched (n=55) and language matched controls (n=55) on a range of tasks designed to test the interdependence of language and mathematical development. Performance across tasks varies substantially in the SLI group, showing profound deficits in production of the count word sequence and basic calculation and significant deficits in understanding of the place-value principle in Hindu-Arabic notation. Only in understanding of arithmetic principles does SLI performance approximate that of age-matched-controls, indicating that principled understanding can develop even where number sequence production and other aspects of number processing are severely compromised.

Bayesian classification theory

NASA Technical Reports Server (NTRS)

Hanson, Robin; Stutz, John; Cheeseman, Peter

1991-01-01

The task of inferring a set of classes and class descriptions most likely to explain a given data set can be placed on a firm theoretical foundation using Bayesian statistics. Within this framework and using various mathematical and algorithmic approximations, the AutoClass system searches for the most probable classifications, automatically choosing the number of classes and complexity of class descriptions. A simpler version of AutoClass has been applied to many large real data sets, has discovered new independently-verified phenomena, and has been released as a robust software package. Recent extensions allow attributes to be selectively correlated within particular classes, and allow classes to inherit or share model parameters though a class hierarchy. We summarize the mathematical foundations of AutoClass.

Rational-Spline Subroutines

NASA Technical Reports Server (NTRS)

Schiess, James R.; Kerr, Patricia A.; Smith, Olivia C.

1988-01-01

Smooth curves drawn among plotted data easily. Rational-Spline Approximation with Automatic Tension Adjustment algorithm leads to flexible, smooth representation of experimental data. "Tension" denotes mathematical analog of mechanical tension in spline or other mechanical curve-fitting tool, and "spline" as denotes mathematical generalization of tool. Program differs from usual spline under tension, allows user to specify different values of tension between adjacent pairs of knots rather than constant tension over entire range of data. Subroutines use automatic adjustment scheme that varies tension parameter for each interval until maximum deviation of spline from line joining knots less than or equal to amount specified by user. Procedure frees user from drudgery of adjusting individual tension parameters while still giving control over local behavior of spline.

ɛ-connectedness, finite approximations, shape theory and coarse graining in hyperspaces

NASA Astrophysics Data System (ADS)

Alonso-Morón, Manuel; Cuchillo-Ibanez, Eduardo; Luzón, Ana

2008-12-01

We use upper semifinite hyperspaces of compacta to describe ε-connectedness and to compute homology from finite approximations. We find a new connection between ε-connectedness and the so-called Shape Theory. We construct a geodesically complete R-tree, by means of ε-components at different resolutions, whose behavior at infinite captures the topological structure of the space of components of a given compact metric space. We also construct inverse sequences of finite spaces using internal finite approximations of compact metric spaces. These sequences can be converted into inverse sequences of polyhedra and simplicial maps by means of what we call the Alexandroff-McCord correspondence. This correspondence allows us to relate upper semifinite hyperspaces of finite approximation with the Vietoris-Rips complexes of such approximations at different resolutions. Two motivating examples are included in the introduction. We propose this procedure as a different mathematical foundation for problems on data analysis. This process is intrinsically related to the methodology of shape theory. This paper reinforces Robins’s idea of using methods from shape theory to compute homology from finite approximations.

Adaptive control using neural networks and approximate models.

PubMed

Narendra, K S; Mukhopadhyay, S

1997-01-01

The NARMA model is an exact representation of the input-output behavior of finite-dimensional nonlinear discrete-time dynamical systems in a neighborhood of the equilibrium state. However, it is not convenient for purposes of adaptive control using neural networks due to its nonlinear dependence on the control input. Hence, quite often, approximate methods are used for realizing the neural controllers to overcome computational complexity. In this paper, we introduce two classes of models which are approximations to the NARMA model, and which are linear in the control input. The latter fact substantially simplifies both the theoretical analysis as well as the practical implementation of the controller. Extensive simulation studies have shown that the neural controllers designed using the proposed approximate models perform very well, and in many cases even better than an approximate controller designed using the exact NARMA model. In view of their mathematical tractability as well as their success in simulation studies, a case is made in this paper that such approximate input-output models warrant a detailed study in their own right.

Gifted Students and the Adults Who Provide for Them: Lessons Learned from Terrorism

ERIC Educational Resources Information Center

Cross, Tracy L.

2002-01-01

Every fall, approximately 300 gifted adolescents descend on the Ball State University campus to attend the Indiana Academy for Science, Mathematics, and Humanities (the Academy). The Academy is a state-funded residential school for academically gifted junior and senior high school aged students. It draws its students from across the state,…

A Middle-School Classroom Inquiry: Estimating the Height of a Tree

ERIC Educational Resources Information Center

Watson, Jane; Brown, Natalie; Wright, Suzie; Skalicky, Jane

2011-01-01

There is an old saying that "there is more than one way to skin a cat." Such is the case with finding the height of tall objects, a task that people have been approximating for centuries. Following an article in the "Australian Primary Mathematics Classroom" (APMC) with methods appropriate for primary students (Brown, Watson,…

Functional Brain Organization for Number Processing in Pre-Verbal Infants

ERIC Educational Resources Information Center

Edwards, Laura A.; Wagner, Jennifer B.; Simon, Charline E.; Hyde, Daniel C.

2016-01-01

Humans are born with the ability to mentally represent the approximate numerosity of a set of objects, but little is known about the brain systems that sub-serve this ability early in life and their relation to the brain systems underlying symbolic number and mathematics later in development. Here we investigate processing of numerical magnitudes…

New Utrecht High School Project IMPACT. O.E.E. Evaluation Report, 1982-1983.

ERIC Educational Resources Information Center

Bulkin, Elly; Sica, Michael

Project IMPACT, a magnet program in its third and final year of funding, provided instruction in ESL and Italian language skills, as well as bilingual instruction in mathematics, social studies and typing to approximately 200 students of limited English proficiency in a Brooklyn, New York, high school. Nearly all program students were born in…

Secondary School Science Predictors of Academic Performance in University Bioscience Subjects

ERIC Educational Resources Information Center

Green, Rod; Brown, Elizabeth; Ward, Alex

2009-01-01

In 2009 the Faculty of Health Sciences at La Trobe University in Melbourne, Australia is introducing a common first year for 11 different undergraduate courses in the faculty. Current prerequisite science entry requirements vary with course and range from none to at least two science or mathematics subjects and from [approximately]50 to 99 in…

Random function theory revisited - Exact solutions versus the first order smoothing conjecture

NASA Technical Reports Server (NTRS)

Lerche, I.; Parker, E. N.

1975-01-01

We remark again that the mathematical conjecture known as first order smoothing or the quasi-linear approximation does not give the correct dependence on correlation length (time) in many cases, although it gives the correct limit as the correlation length (time) goes to zero. In this sense, then, the method is unreliable.

Number Processing and Heterogeneity of Developmental Dyscalculia: Subtypes with Different Cognitive Profiles and Deficits

ERIC Educational Resources Information Center

Skagerlund, Kenny; Träff, Ulf

2016-01-01

This study investigated if developmental dyscalculia (DD) in children with different profiles of mathematical deficits has the same or different cognitive origins. The defective approximate number system hypothesis and the access deficit hypothesis were tested using two different groups of children with DD (11-13 years old): a group with…

The Contribution of General Cognitive Abilities and Approximate Number System to Early Mathematics

ERIC Educational Resources Information Center

Passolunghi, Maria Chiara; Cargnelutti, Elisa; Pastore, Massimiliano

2014-01-01

Background: Math learning is a complex process that entails a wide range of cognitive abilities to be fulfilled. There is sufficient evidence that both general and specific cognitive skills assume a fundamental role, despite the absence of shared consensus about the relative extent of their involvement. Moreover, regarding general abilities, there…

William H. Taft High School Project HOLA 1983-1984. O.E.A. Evaluation Report.

ERIC Educational Resources Information Center

New York City Board of Education, Brooklyn, NY. Office of Educational Evaluation.

This report evaluates Project HOLA, in its first year of funding, which provides instruction in English as a second language, Spanish language skills, and bilingual instruction in mathematics, science, and social studies to approximately 230 students in a high school in Bronx, New York. The report examines the project's long- and short-range…

Development of a Conference Planning Model Using Integrated Database, Word Processing, and Spreadsheet Software.

ERIC Educational Resources Information Center

Stevens, William E.

This report presents a model for conducting a statewide conference for the approximately 900 members of the South Carolina Council of Teachers of Mathematics (SCCTM) using the AppleWorks integrated software as the basis of the implementation plan. The first and second chapters provide background information on the conference and the…

The Relationship between Non-Verbal Systems of Number and Counting Development: A Neural Signatures Approach

ERIC Educational Resources Information Center

Hyde, Daniel C.; Simon, Charline E.; Berteletti, Ilaria; Mou, Yi

2017-01-01

Two non-verbal cognitive systems, an approximate number system (ANS) for extracting the numerosity of a set and a parallel individuation (PI) system for distinguishing between individual items, are hypothesized to be foundational to symbolic number and mathematics abilities. However, the exact role of each remains unclear and highly debated. Here…

Effects of Administrator Performance on Student Performance in the Trial State Assessment.

ERIC Educational Resources Information Center

McLaughlin, Donald H.

In 1990 the scope of the National Assessment of Educational Progress (NAEP) was broadened by adding the Trial State Assessment (TSA), in which approximately 2,500 eighth graders in 100 schools in 40 states and U.S. territories participated in the mathematics assessment. A major step was training local test administrators to administer the TSA…

A Demonstration of Techniques in the Identification, Diagnosis, and Treatment of Children with Learning Disabilities. Final Report.

ERIC Educational Resources Information Center

Skokie School District 68, IL.

A Chicago suburban public school with approximately 450 children per grade level demonstrated a system-wide program for identification, diagnosis, and educational treatment of children with learning disabilities in grades 2 through 6. Children were judged to underachieve when achievement measures in language or mathematics fell more than 10% below…

PBS TeacherLine National Survey of Teacher Professional Development, 2005-2006

ERIC Educational Resources Information Center

Hezel Associates (NJ1), 2007

2007-01-01

PBS TeacherLine, an initiative funded under the U.S. Department of Education's Ready To Teach program, is designed to provide high-quality online professional development for K-12 teachers. Through the first five-year grant cycle, ending in 2005, PBS TeacherLine produced approximately 100 online facilitated courses in reading, mathematics,…

A Simulation Algorithm to Approximate the Area of Mapped Forest Inventory Plots

Treesearch

William A. Bechtold; Naser E. Heravi; Matthew E. Kinkenon

2003-01-01

Calculating the area of polygons associated with mapped forest inventory plots can be mathematically cumbersome, especially when computing change between inventories. We developed a simulation technique that utilizes a computer-generated dot grid and geometry to estimate the area of mapped polygons within any size circle. The technique also yields a matrix of change in...

ACCESS 3. Approximation concepts code for efficient structural synthesis: User's guide

NASA Technical Reports Server (NTRS)

Fleury, C.; Schmit, L. A., Jr.

1980-01-01

A user's guide is presented for ACCESS-3, a research oriented program which combines dual methods and a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and dual algorithms of mathematical programming are applied in the design optimization procedure. This program retains all of the ACCESS-2 capabilities and the data preparation formats are fully compatible. Four distinct optimizer options were added: interior point penalty function method (NEWSUMT); second order primal projection method (PRIMAL2); second order Newton-type dual method (DUAL2); and first order gradient projection-type dual method (DUAL1). A pure discrete and mixed continuous-discrete design variable capability, and zero order approximation of the stress constraints are also included.

Physiological time-series analysis: what does regularity quantify?

NASA Technical Reports Server (NTRS)

Pincus, S. M.; Goldberger, A. L.

1994-01-01

Approximate entropy (ApEn) is a recently developed statistic quantifying regularity and complexity that appears to have potential application to a wide variety of physiological and clinical time-series data. The focus here is to provide a better understanding of ApEn to facilitate its proper utilization, application, and interpretation. After giving the formal mathematical description of ApEn, we provide a multistep description of the algorithm as applied to two contrasting clinical heart rate data sets. We discuss algorithm implementation and interpretation and introduce a general mathematical hypothesis of the dynamics of a wide class of diseases, indicating the utility of ApEn to test this hypothesis. We indicate the relationship of ApEn to variability measures, the Fourier spectrum, and algorithms motivated by study of chaotic dynamics. We discuss further mathematical properties of ApEn, including the choice of input parameters, statistical issues, and modeling considerations, and we conclude with a section on caveats to ensure correct ApEn utilization.

Mathematical simulation of convective-radiative heat transfer in a ventilated rectangular cavity with consideration of internal mass transfer

NASA Astrophysics Data System (ADS)

Sheremet, M. A.; Shishkin, N. I.

2012-07-01

Mathematical simulation of the nonstationary regimes of heat-and-mass transfer in a ventilated rectangular cavity with heat-conducting walls of finite thickness in the presence of a heat-generating element of constant temperature has been carried out with account for the radiative heat transfer in the Rosseland approximation. As mechanisms of energy transfer in this cavity, the combined convection and the thermal radiation in the gas space of the cavity and the heat conduction in the elements of its fencing solid shell were considered. The mathematical model formulated in the dimensionless stream function-vorticity vector-temperature-concentration variables was realized numerically with the use of the finite-difference method. The streamline, temperature-field, and concentration distributions reflecting the influence of the Rayleigh number (Ra = 104, 105, 106), the nonstationarity (0 < τ ≤ 1000), and the optical thickness of the medium (τλ = 50, 100, 200) on the regimes of the gas flow and the heat-and-mass transfer in the cavity have been obtained.

Robust all-source positioning of UAVs based on belief propagation

NASA Astrophysics Data System (ADS)

Chen, Xi; Gao, Wenyun; Wang, Jiabo

2013-12-01

For unmanned air vehicles (UAVs) to survive hostile operational environments, it is always preferable to utilize all wireless positioning sources available to fuse a robust position. While belief propagation is a well-established method for all source data fusion, it is not an easy job to handle all the mathematics therein. In this work, a comprehensive mathematical framework for belief propagation-based all-source positioning of UAVs is developed, taking wireless sources including Global Navigation Satellite Systems (GNSS) space vehicles, peer UAVs, ground control stations, and signal of opportunities. Based on the mathematical framework, a positioning algorithm named Belief propagation-based Opportunistic Positioning of UAVs (BOPU) is proposed, with an unscented particle filter for Bayesian approximation. The robustness of the proposed BOPU is evaluated by a fictitious scenario that a group of formation flying UAVs encounter GNSS countermeasures en route. Four different configurations of measurements availability are simulated. The results show that the performance of BOPU varies only slightly with different measurements availability.

The research of 4th grade mathematical curriculum electronic picture book construction and development in integrating indigenous culture

NASA Astrophysics Data System (ADS)

Chen, Yen Ting; Hsin Wang, Juei

2017-02-01

This research aimed at integrating Seediq culture and mathematical course design for fourth-grade elementary school, and then transforming this mathematical course into an electronic picture book. During the process of electronic book development, the researchers collected videos of six participants engaged in discussion, reflection minutes after the meeting written by the attendants, the researchers' observation and review journals, and conversations with the participants. Then, researchers utilized Content Analysis to explore, try, review and retry steps of electronic book making process. The main findings: There are four periods of electronic book making process, research occurrence period, curriculum design period, electronic book transformation period, and result evaluation period. The picture book included the White Stone Legend born from Seediq seniors, historical battle for hunting field between tribes, and concepts of approximation, angle, triangle, and quadrangle features. At last, with the research result, this article presents the corroboration of related works, and then proposes suggestions of electronic book teaching and follow-up studies.

DNN-state identification of 2D distributed parameter systems

NASA Astrophysics Data System (ADS)

Chairez, I.; Fuentes, R.; Poznyak, A.; Poznyak, T.; Escudero, M.; Viana, L.

2012-02-01

There are many examples in science and engineering which are reduced to a set of partial differential equations (PDEs) through a process of mathematical modelling. Nevertheless there exist many sources of uncertainties around the aforementioned mathematical representation. Moreover, to find exact solutions of those PDEs is not a trivial task especially if the PDE is described in two or more dimensions. It is well known that neural networks can approximate a large set of continuous functions defined on a compact set to an arbitrary accuracy. In this article, a strategy based on the differential neural network (DNN) for the non-parametric identification of a mathematical model described by a class of two-dimensional (2D) PDEs is proposed. The adaptive laws for weights ensure the 'practical stability' of the DNN-trajectories to the parabolic 2D-PDE states. To verify the qualitative behaviour of the suggested methodology, here a non-parametric modelling problem for a distributed parameter plant is analysed.

Optimal policies of non-cross-resistant chemotherapy on Goldie and Coldman's cancer model.

PubMed

Chen, Jeng-Huei; Kuo, Ya-Hui; Luh, Hsing Paul

2013-10-01

Mathematical models can be used to study the chemotherapy on tumor cells. Especially, in 1979, Goldie and Coldman proposed the first mathematical model to relate the drug sensitivity of tumors to their mutation rates. Many scientists have since referred to this pioneering work because of its simplicity and elegance. Its original idea has also been extended and further investigated in massive follow-up studies of cancer modeling and optimal treatment. Goldie and Coldman, together with Guaduskas, later used their model to explain why an alternating non-cross-resistant chemotherapy is optimal with a simulation approach. Subsequently in 1983, Goldie and Coldman proposed an extended stochastic based model and provided a rigorous mathematical proof to their earlier simulation work when the extended model is approximated by its quasi-approximation. However, Goldie and Coldman's analytic study of optimal treatments majorly focused on a process with symmetrical parameter settings, and presented few theoretical results for asymmetrical settings. In this paper, we recast and restate Goldie, Coldman, and Guaduskas' model as a multi-stage optimization problem. Under an asymmetrical assumption, the conditions under which a treatment policy can be optimal are derived. The proposed framework enables us to consider some optimal policies on the model analytically. In addition, Goldie, Coldman and Guaduskas' work with symmetrical settings can be treated as a special case of our framework. Based on the derived conditions, this study provides an alternative proof to Goldie and Coldman's work. In addition to the theoretical derivation, numerical results are included to justify the correctness of our work. Copyright © 2013 Elsevier Inc. All rights reserved.

A mathematical approach for evaluating Markov models in continuous time without discrete-event simulation.

PubMed

van Rosmalen, Joost; Toy, Mehlika; O'Mahony, James F

2013-08-01

Markov models are a simple and powerful tool for analyzing the health and economic effects of health care interventions. These models are usually evaluated in discrete time using cohort analysis. The use of discrete time assumes that changes in health states occur only at the end of a cycle period. Discrete-time Markov models only approximate the process of disease progression, as clinical events typically occur in continuous time. The approximation can yield biased cost-effectiveness estimates for Markov models with long cycle periods and if no half-cycle correction is made. The purpose of this article is to present an overview of methods for evaluating Markov models in continuous time. These methods use mathematical results from stochastic process theory and control theory. The methods are illustrated using an applied example on the cost-effectiveness of antiviral therapy for chronic hepatitis B. The main result is a mathematical solution for the expected time spent in each state in a continuous-time Markov model. It is shown how this solution can account for age-dependent transition rates and discounting of costs and health effects, and how the concept of tunnel states can be used to account for transition rates that depend on the time spent in a state. The applied example shows that the continuous-time model yields more accurate results than the discrete-time model but does not require much computation time and is easily implemented. In conclusion, continuous-time Markov models are a feasible alternative to cohort analysis and can offer several theoretical and practical advantages.

Asymptotic tracking and disturbance rejection of the blood glucose regulation system.

PubMed

Ashley, Brandon; Liu, Weijiu

2017-07-01

Type 1 diabetes patients need external insulin to maintain blood glucose within a narrow range from 65 to 108 mg/dl (3.6 to 6.0 mmol/l). A mathematical model for the blood glucose regulation is required for integrating a glucose monitoring system into insulin pump technology to form a closed-loop insulin delivery system on the feedback of the blood glucose, the so-called "artificial pancreas". The objective of this paper is to treat the exogenous glucose from food as a glucose disturbance and then develop a closed-loop feedback and feedforward control system for the blood glucose regulation system subject to the exogenous glucose disturbance. For this, a mathematical model for the glucose disturbance is proposed on the basis of experimental data, and then incorporated into an existing blood glucose regulation model. Because all the eigenvalues of the disturbance model have zero real parts, the center manifold theory is used to establish blood glucose regulator equations. We then use their solutions to synthesize a required feedback and feedforward controller to reject the disturbance and asymptotically track a constant glucose reference of 90  mg/dl. Since the regulator equations are nonlinear partial differential equations and usually impossible to solve analytically, a linear approximation solution is obtained. Our numerical simulations show that, under the linear approximate feedback and feedforward controller, the blood glucose asymptotically tracks its desired level of 90 mg/dl approximately. Copyright © 2017 Elsevier Inc. All rights reserved.

Epidemics Modelings: Some New Challenges

NASA Astrophysics Data System (ADS)

Boatto, Stefanella; Khouri, Renata Stella; Solerman, Lucas; Codeço, Claudia; Bonnet, Catherine

2010-09-01

Epidemics modeling has been particularly growing in the past years. In epidemics studies, mathematical modeling is used in particular to reach a better understanding of some neglected diseases (dengue, malaria, …) and of new emerging ones (SARS, influenza A,….) of big agglomerates. Such studies offer new challenges both from the modeling point of view (searching for simple models which capture the main characteristics of the disease spreading), data analysis and mathematical complexity. We are facing often with complex networks especially when modeling the city dynamics. Such networks can be static (in first approximation) and homogeneous, static and not homogeneous and/or not static (when taking into account the city structure, micro-climates, people circulation, etc.). The objective being studying epidemics dynamics and being able to predict its spreading.

Autoclass: An automatic classification system

NASA Technical Reports Server (NTRS)

Stutz, John; Cheeseman, Peter; Hanson, Robin

1991-01-01

The task of inferring a set of classes and class descriptions most likely to explain a given data set can be placed on a firm theoretical foundation using Bayesian statistics. Within this framework, and using various mathematical and algorithmic approximations, the AutoClass System searches for the most probable classifications, automatically choosing the number of classes and complexity of class descriptions. A simpler version of AutoClass has been applied to many large real data sets, has discovered new independently-verified phenomena, and has been released as a robust software package. Recent extensions allow attributes to be selectively correlated within particular classes, and allow classes to inherit, or share, model parameters through a class hierarchy. The mathematical foundations of AutoClass are summarized.

A new mathematical solution for predicting char activation reactions

USGS Publications Warehouse

Rafsanjani, H.H.; Jamshidi, E.; Rostam-Abadi, M.

2002-01-01

The differential conservation equations that describe typical gas-solid reactions, such as activation of coal chars, yield a set of coupled second-order partial differential equations. The solution of these coupled equations by exact analytical methods is impossible. In addition, an approximate or exact solution only provides predictions for either reaction- or diffusion-controlling cases. A new mathematical solution, the quantize method (QM), was applied to predict the gasification rates of coal char when both chemical reaction and diffusion through the porous char are present. Carbon conversion rates predicted by the QM were in closer agreement with the experimental data than those predicted by the random pore model and the simple particle model. ?? 2002 Elsevier Science Ltd. All rights reserved.

Extension of transonic flow computational concepts in the analysis of cavitated bearings

NASA Technical Reports Server (NTRS)

Vijayaraghavan, D.; Keith, T. G., Jr.; Brewe, D. E.

1990-01-01

An analogy between the mathematical modeling of transonic potential flow and the flow in a cavitating bearing is described. Based on the similarities, characteristics of the cavitated region and jump conditions across the film reformation and rupture fronts are developed using the method of weak solutions. The mathematical analogy is extended by utilizing a few computational concepts of transonic flow to numerically model the cavitating bearing. Methods of shock fitting and shock capturing are discussed. Various procedures used in transonic flow computations are adapted to bearing cavitation applications, for example, type differencing, grid transformation, an approximate factorization technique, and Newton's iteration method. These concepts have proved to be successful and have vastly improved the efficiency of numerical modeling of cavitated bearings.

Hpm of Estrogen Model on the Dynamics of Breast Cancer

NASA Astrophysics Data System (ADS)

Govindarajan, A.; Balamuralitharan, S.; Sundaresan, T.

2018-04-01

We enhance a deterministic mathematical model involving universal dynamics on breast cancer with immune response. This is population model so includes Normal cells class, Tumor cells, Immune cells and Estrogen. The eects regarding Estrogen are below incorporated in the model. The effects show to that amount the arrival of greater Estrogen increases the danger over growing breast cancer. Furthermore, approximate solution regarding nonlinear differential equations is arrived by Homotopy Perturbation Method (HPM). Hes HPM is good and correct technique after solve nonlinear differential equation directly. Approximate solution learnt with the support of that method is suitable same as like the actual results in accordance with this models.

Mollier-I, S-Diagrams for Combustion Gases in Data Processing

NASA Technical Reports Server (NTRS)

Zacharias, F.

1982-01-01

In order to have all the thermal and caloric states of combustion gases accessible in a computer, closed mathematical approximation equations were established for the real factors, the enthalpy and the entropy of a real combustion gas. The equations approximate the various effects of molecular forces real gas influence and dissociation - at temperatures of 200 K to 6,000 K, pressures of 0.001 to 1,000 bar, and in the range from stoichiometric composition to air. A system of subprograms is listed in FORTRAN, by means of which thermodynamic calculations can be carried out in the same manner as with Mollier I,S diagrams.

The transference of heat from a hot plate to an air stream

NASA Technical Reports Server (NTRS)

Elias, Franz

1931-01-01

The object of the present study was to define experimentally the field of temperature and velocity in a heated flat plate when exposed to an air stream whose direction is parallel to it, then calculate therefrom the heat transference and the friction past the flat plate, and lastly, compare the test data with the mathematical theory. To ensure comparable results, we were to actually obtain or else approximate: a) two-dimensional flow; b) constant plate temperature in the direction of the stream. To approximate the flow in two dimensions, we chose a relatively wide plate and measured the velocity and temperature in the median plane.

A method for digital image registration using a mathematical programming technique

NASA Technical Reports Server (NTRS)

Yao, S. S.

1973-01-01

A new algorithm based on a nonlinear programming technique to correct the geometrical distortions of one digital image with respect to another is discussed. This algorithm promises to be superior to existing ones in that it is capable of treating localized differential scaling, translational and rotational errors over the whole image plane. A series of piece-wise 'rubber-sheet' approximations are used, constrained in such a manner that a smooth approximation over the entire image can be obtained. The theoretical derivation is included. The result of using the algorithm to register four channel S065 Apollo IX digitized photography over Imperial Valley, California, is discussed in detail.

The diffusion approximation. An application to radiative transfer in clouds

NASA Technical Reports Server (NTRS)

Arduini, R. F.; Barkstrom, B. R.

1976-01-01

It is shown how the radiative transfer equation reduces to the diffusion equation. To keep the mathematics as simple as possible, the approximation is applied to a cylindrical cloud of radius R and height h. The diffusion equation separates in cylindrical coordinates and, in a sample calculation, the solution is evaluated for a range of cloud radii with cloud heights of 0.5 km and 1.0 km. The simplicity of the method and the speed with which solutions are obtained give it potential as a tool with which to study the effects of finite-sized clouds on the albedo of the earth-atmosphere system.

A lattice model for data display

NASA Technical Reports Server (NTRS)

Hibbard, William L.; Dyer, Charles R.; Paul, Brian E.

1994-01-01

In order to develop a foundation for visualization, we develop lattice models for data objects and displays that focus on the fact that data objects are approximations to mathematical objects and real displays are approximations to ideal displays. These lattice models give us a way to quantize the information content of data and displays and to define conditions on the visualization mappings from data to displays. Mappings satisfy these conditions if and only if they are lattice isomorphisms. We show how to apply this result to scientific data and display models, and discuss how it might be applied to recursively defined data types appropriate for complex information processing.

Hamilton-Jacobi-Bellman equations and approximate dynamic programming on time scales.

PubMed

Seiffertt, John; Sanyal, Suman; Wunsch, Donald C

2008-08-01

The time scales calculus is a key emerging area of mathematics due to its potential use in a wide variety of multidisciplinary applications. We extend this calculus to approximate dynamic programming (ADP). The core backward induction algorithm of dynamic programming is extended from its traditional discrete case to all isolated time scales. Hamilton-Jacobi-Bellman equations, the solution of which is the fundamental problem in the field of dynamic programming, are motivated and proven on time scales. By drawing together the calculus of time scales and the applied area of stochastic control via ADP, we have connected two major fields of research.

A Historical Note on the Proof of the Area of a Circle

ERIC Educational Resources Information Center

Wilamowsky, Yonah; Epstein, Sheldon; Dickman, Bernard

2011-01-01

Proofs that the area of a circle is nr[superscript 2] can be found in mathematical literature dating as far back as the time of the Greeks. The early proofs, e.g. Archimedes, involved dividing the circle into wedges and then fitting the wedges together in a way to approximate a rectangle. Later more sophisticated proofs relied on arguments…

NASA Tech Briefs Index, 1978. [bibliography

NASA Technical Reports Server (NTRS)

1978-01-01

Approximately 601 announcements of new technology derived from the research and development activities of the National Aeronautics and Space Administration are presented. Emphasis is placed on information considered likely to be transferrable across industrial, regional, or disciplinary lines. Subject matter covered includes: electronic components and circuits; electron systems; physical sciences; materials; life sciences; mechanics; machinery; fabrication technology; and mathematics and information sciences.

A Quantitative Study Examining the Differences in Motivation and Achievement between Traditional versus Team-Based Learning

ERIC Educational Resources Information Center

Ku, James Yu-Fan

2016-01-01

Obtaining a degree from a community college could be the opportunity for students to advance their education or career. Nevertheless, nearly two-thirds of first-time community college students in the U.S. were required to take developmental mathematics courses. The problem was that approximately three-fourth of those students did not successfully…

Control by model error estimation

NASA Technical Reports Server (NTRS)

Likins, P. W.; Skelton, R. E.

1976-01-01

Modern control theory relies upon the fidelity of the mathematical model of the system. Truncated modes, external disturbances, and parameter errors in linear system models are corrected by augmenting to the original system of equations an 'error system' which is designed to approximate the effects of such model errors. A Chebyshev error system is developed for application to the Large Space Telescope (LST).

Free Radical Addition Polymerization Kinetics without Steady-State Approximations: A Numerical Analysis for the Polymer, Physical, or Advanced Organic Chemistry Course

ERIC Educational Resources Information Center

Iler, H. Darrell; Brown, Amber; Landis, Amanda; Schimke, Greg; Peters, George

2014-01-01

A numerical analysis of the free radical addition polymerization system is described that provides those teaching polymer, physical, or advanced organic chemistry courses the opportunity to introduce students to numerical methods in the context of a simple but mathematically stiff chemical kinetic system. Numerical analysis can lead students to an…

L1-Based Approximations of PDEs and Applications

DTIC Science & Technology

2012-09-05

the analysis of the Navier-Stokes equations. The early versions of artificial vis- cosities being overly dissipative, the interest for these technique ...Guermond, and B. Popov. Stability analysis of explicit en- tropy viscosity methods for non-linear scalar conservation equations. Math. Comp., 2012... methods for solv- ing mathematical models of nonlinear phenomena such as nonlinear conservation laws, surface/image/data reconstruction problems

Seward Park High School Project Superemos, 1982-1983. O.E.E. Evaluation Report.

ERIC Educational Resources Information Center

Velazquez, Clara; Schulman, Robert

Project Superemos, in its final year of a two-year funding cycle, provided instruction in English as a Second Language (ESL) and native language skills, as well as bilingual instruction in mathematics, science, and social studies, to approximately 125 Spanish speaking students of limited English proficiency (LEP) in grades 9 and 10. The project's…

Feedback in Software and a Desktop Manufacturing Context for Learning Estimation Strategies in Middle School

ERIC Educational Resources Information Center

Malcolm, Peter

2013-01-01

The ability and to make good estimates is essential, as is the ability to assess the reasonableness of estimates. These abilities are becoming increasingly important as digital technologies transform the ways in which people work. To estimate is to provide an approximation to a problem that is mathematical in nature, and the ability to estimate is…

Copper nanoparticles impinging on a curved channel with compliant walls and peristalsis

NASA Astrophysics Data System (ADS)

Akbar, Noreen Sher; Maraj, E. N.; Butt, Adil Wahid

2014-08-01

In the present article peristaltic transport of copper nanofluids in a curved channel with compliant walls is analytically studied. The mathematical analysis is carried out under the low Reynolds number and long wavelenght approximation. The exact solutions are computed for fluid velocity and temperature profile. The effect of meaningful parameters are shown graphically in the last section.

The Chem-Math Project: Enhancing Success in General Chemistry through the Integration of Mathematics, Problem-Solving and Conceptual Understanding. An Action-Research Study

ERIC Educational Resources Information Center

Kilner, William Cary

2014-01-01

Freshmen with declared life-science majors typically matriculate with a determination to succeed. However, inadequately-prepared students are easily overwhelmed and at risk of abandoning their aspirations for a STEM career. The investigator designed and taught weekly recitations for approximately 850 students during a five-year span, and…

AP® STEM Participation and Postsecondary STEM Outcomes: Focus on Underrepresented Minority, First-Generation, and Female Students

ERIC Educational Resources Information Center

Smith, Kara; Jagesic, Sanja; Wyatt, Jeff; Ewing, Maureen

2018-01-01

Projections by the President's Council of Advisors on Science and Technology (2012) point to a need for approximately one million more Science Technology Engineering and Mathematics (STEM) professionals than the U.S. will be able to produce considering the current rate of STEM postsecondary degree completions (Executive Office of the President of…

Students' Experiences of the Implementation of an Interactive Learning System in Their Eighth Grade Mathematics Classes: An Exploratory Study.

ERIC Educational Resources Information Center

FitzPatrick, Sarah B.

During the last decade, United States K-12 schools have approximately tripled their spending on increasingly powerful computers, and have expanded network access and novel computer applications. The number of questions being asked by educators, policymakers, and the general public about the extent to which students are using these educational…

Bolden Visit Davis Elementary

NASA Image and Video Library

2009-09-10

NASA Administrator Charles F. Bolden reads a passage from the book "Can You Fly High Wright Brothers?" while visiting with students at Davis Elementary School, Friday, Sept. 11, 2009, in Washington. Bolden spent time with approximately 120 students in third, fourth and fifth grade talking about science, technology, mathematics and engineering as part of the National Day of Service and Remembrance. Photo Credit: (NASA/Paul E. Alers)

An Exploratory Study of the Implementation of an Interactive Learning System in Two Eighth Grade Mathematics Classes.

ERIC Educational Resources Information Center

FitzPatrick, Sarah B.; Faux, Russell

During the last decade, U.S. K-12 schools have approximately tripled their spending on increasingly powerful computers, expanded network access, and novel computer applications. The number of questions being asked by educators, policymakers, and the general public about the extent to which these technologies are being used in classrooms, for what…

Wisconsin Title I Migrant Education. Section 143 Project: Development of an Item Bank. Summary Report.

ERIC Educational Resources Information Center

Brown, Frank N.; And Others

The successful Wisconsin Title 1 project item bank offers a valid, flexible, and efficient means of providing migrant student tests in reading and mathematics tailored to instructor curricula. The item bank system consists of nine PASCAL computer programs which maintain, search, and select from approximately 1,000 test items stored on floppy disks…

A simulation model of the oxygen alveolo-capillary exchange in normal and pathological conditions.

PubMed

Brighenti, Chiara; Gnudi, Gianni; Avanzolini, Guido

2003-05-01

This paper presents a mathematical model of the oxygen alveolo-capillary exchange to provide the capillary oxygen partial pressure profile in normal and pathological conditions. In fact, a thickening of the blood-gas barrier, heavy exercise or a low oxygen partial pressure (PO2) in the alveolar space can reduce the O2 alveolo-capillary exchange. Since the reversible binding between haemoglobin and oxygen makes it impossible to determine the closed form for the mathematical description of the PO2 profile along the pulmonary capillaries, an approximate analytical solution of the capillary PO2 profile is proposed. Simulation results are compared with the capillary PO2 profile obtained by numerical integration and by a piecewise linear interpolation of the oxyhaemoglobin dissociation curve. Finally, the proposed model is evaluated in a large range of physiopathological diffusive conditions. The good fit to numerical solutions in all experimental conditions seems to represent a substantial improvement with respect to the approach based on a linear approximation of the oxyhaemoglobin dissociation curve, and makes this model a candidate to be incorporated into the integrated descriptions of the entire respiratory system, where the datum of primary interest is the value of end capillary PO2.

Numerical methods for stochastic differential equations

NASA Astrophysics Data System (ADS)

Kloeden, Peter; Platen, Eckhard

1991-06-01

The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations due to the peculiarities of stochastic calculus. This book provides an introduction to stochastic calculus and stochastic differential equations, both theory and applications. The main emphasise is placed on the numerical methods needed to solve such equations. It assumes an undergraduate background in mathematical methods typical of engineers and physicists, through many chapters begin with a descriptive summary which may be accessible to others who only require numerical recipes. To help the reader develop an intuitive understanding of the underlying mathematicals and hand-on numerical skills exercises and over 100 PC Exercises (PC-personal computer) are included. The stochastic Taylor expansion provides the key tool for the systematic derivation and investigation of discrete time numerical methods for stochastic differential equations. The book presents many new results on higher order methods for strong sample path approximations and for weak functional approximations, including implicit, predictor-corrector, extrapolation and variance-reduction methods. Besides serving as a basic text on such methods. the book offers the reader ready access to a large number of potential research problems in a field that is just beginning to expand rapidly and is widely applicable.

Fostering Formal Commutativity Knowledge with Approximate Arithmetic

PubMed Central

Hansen, Sonja Maria; Haider, Hilde; Eichler, Alexandra; Godau, Claudia; Frensch, Peter A.; Gaschler, Robert

2015-01-01

How can we enhance the understanding of abstract mathematical principles in elementary school? Different studies found out that nonsymbolic estimation could foster subsequent exact number processing and simple arithmetic. Taking the commutativity principle as a test case, we investigated if the approximate calculation of symbolic commutative quantities can also alter the access to procedural and conceptual knowledge of a more abstract arithmetic principle. Experiment 1 tested first graders who had not been instructed about commutativity in school yet. Approximate calculation with symbolic quantities positively influenced the use of commutativity-based shortcuts in formal arithmetic. We replicated this finding with older first graders (Experiment 2) and third graders (Experiment 3). Despite the positive effect of approximation on the spontaneous application of commutativity-based shortcuts in arithmetic problems, we found no comparable impact on the application of conceptual knowledge of the commutativity principle. Overall, our results show that the usage of a specific arithmetic principle can benefit from approximation. However, the findings also suggest that the correct use of certain procedures does not always imply conceptual understanding. Rather, the conceptual understanding of commutativity seems to lag behind procedural proficiency during elementary school. PMID:26560311

LinguisticBelief: a java application for linguistic evaluation using belief, fuzzy sets, and approximate reasoning.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Darby, John L.

LinguisticBelief is a Java computer code that evaluates combinations of linguistic variables using an approximate reasoning rule base. Each variable is comprised of fuzzy sets, and a rule base describes the reasoning on combinations of variables fuzzy sets. Uncertainty is considered and propagated through the rule base using the belief/plausibility measure. The mathematics of fuzzy sets, approximate reasoning, and belief/ plausibility are complex. Without an automated tool, this complexity precludes their application to all but the simplest of problems. LinguisticBelief automates the use of these techniques, allowing complex problems to be evaluated easily. LinguisticBelief can be used free of chargemore » on any Windows XP machine. This report documents the use and structure of the LinguisticBelief code, and the deployment package for installation client machines.« less

The passage of an infinite swept airfoil through an oblique gust. [approximate solution for aerodynamic response

NASA Technical Reports Server (NTRS)

Adamczyk, J. L.

1974-01-01

An approximate solution is reported for the unsteady aerodynamic response of an infinite swept wing encountering a vertical oblique gust in a compressible stream. The approximate expressions are of closed form and do not require excessive computer storage or computation time, and further, they are in good agreement with the results of exact theory. This analysis is used to predict the unsteady aerodynamic response of a helicopter rotor blade encountering the trailing vortex from a previous blade. Significant effects of three dimensionality and compressibility are evident in the results obtained. In addition, an approximate solution for the unsteady aerodynamic forces associated with the pitching or plunging motion of a two dimensional airfoil in a subsonic stream is presented. The mathematical form of this solution approaches the incompressible solution as the Mach number vanishes, the linear transonic solution as the Mach number approaches one, and the solution predicted by piston theory as the reduced frequency becomes large.

Theoretical simulation of solar spectra in the middle ultraviolet and visible for atmospheric trace constituent measurements

NASA Technical Reports Server (NTRS)

Goldman, A.

1978-01-01

Two balloon flights reaching float altitudes of approximately 30 and 40 km respectively, were used to obtain scans of the ultraviolet and visible solar spectra. Both flights covered the UV (2800-3500A) at approximately 0.3A resolution and the visible at approximately 0.6A. Numerous scans were obtained during ascent and from float for both flights. All spectral scans obtained at float, from high sun to low sun, were calibrated in wavelength by using several standard solar spectra for line position references. Comparisons of low sun scans and high sun scans show significant atmospheric continuum extinction and have the potential of being used to identify atmospheric lines superimposed on the attenuated solar spectrum. The resolution was mathematically degraded to approximately 5A to better see the broad band atmospheric extinction. This low resolution is also appropriate for the available low resolution absorption coefficients of NO2 and O3, allowing the identification of NO2 and O3 features on the sunset spectra.

Polynomial approximation of functions of matrices and its application to the solution of a general system of linear equations

NASA Technical Reports Server (NTRS)

Tal-Ezer, Hillel

1987-01-01

During the process of solving a mathematical model numerically, there is often a need to operate on a vector v by an operator which can be expressed as f(A) while A is NxN matrix (ex: exp(A), sin(A), A sup -1). Except for very simple matrices, it is impractical to construct the matrix f(A) explicitly. Usually an approximation to it is used. In the present research, an algorithm is developed which uses a polynomial approximation to f(A). It is reduced to a problem of approximating f(z) by a polynomial in z while z belongs to the domain D in the complex plane which includes all the eigenvalues of A. This problem of approximation is approached by interpolating the function f(z) in a certain set of points which is known to have some maximal properties. The approximation thus achieved is almost best. Implementing the algorithm to some practical problem is described. Since a solution to a linear system Ax = b is x= A sup -1 b, an iterative solution to it can be regarded as a polynomial approximation to f(A) = A sup -1. Implementing the algorithm in this case is also described.

Li-SF(6) Combustion in Stored Chemical Energy Propulsion Systems

DTIC Science & Technology

1990-07-01

S 3. STRUCTURE OF SF6 3ETS IN MOLTEN LI ........... ................. 8 3.1 Mathematical Model ...ill - ABSTRACT Appropriate thermodynamic models and thermo-chemical data for multicompo- nents and immiscible phases have been Incorporated into a code...by a simplified integral model which was improved9 by the use of the local homogeneous flow approximation, equilibrium combustion model and Kc-C-g

WWC Quick Review of the Report "Middle School Mathematics Professional Development Impact Study: Findings after the First Year of Implementation"

ERIC Educational Resources Information Center

What Works Clearinghouse, 2010

2010-01-01

The study examined whether 7th-graders' knowledge of rational numbers improved when the students' math teachers participated in related professional development activities. The study analyzed data on about 4,500 students and 200 teachers from approximately 80 schools in 12 districts during the 2007-08 academic year. The study found that students…

Physico-chemical study of some areas of fundamental significance to biophysics. Final report, 1974--1977

DOE Office of Scientific and Technical Information (OSTI.GOV)

McGlynn, S.P.

1977-08-18

The comprehensive report includes a complete list of publications resulting from the work and a review of studies made in the vacuum ultraviolet, photoelectron spectroscopy, excited states and electron structure of inorganic salts, a model for polar molecules, application of abstract mathematics to the genetic code, the orbital approximation in which orbital properties are related to state properties. (JSR)

Atomic Schroedinger cat-like states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Enriquez-Flores, Marco; Rosas-Ortiz, Oscar; Departamento de Fisica, Cinvestav, A.P. 14-740, Mexico D.F. 07000

2010-10-11

After a short overview of the basic mathematical structure of quantum mechanics we analyze the Schroedinger's antinomic example of a living and dead cat mixed in equal parts. Superpositions of Glauber kets are shown to approximate such macroscopic states. Then, two-level atomic states are used to construct mesoscopic kittens as appropriate linear combinations of angular momentum eigenkets for j = 1/2. Some general comments close the present contribution.

Functional Magnetic Resonance Imaging Study of Piaget's Conservation-of-Number Task in Preschool and School-Age Children: A Neo-Piagetian Approach

ERIC Educational Resources Information Center

Houde, Olivier; Pineau, Arlette; Leroux, Gaelle; Poirel, Nicolas; Perchey, Guy; Lanoe, Celine; Lubin, Amelie; Turbelin, Marie-Renee; Rossi, Sandrine; Simon, Gregory; Delcroix, Nicolas; Lamberton, Franck; Vigneau, Mathieu; Wisniewski, Gabriel; Vicet, Jean-Rene; Mazoyer, Bernard

2011-01-01

Jean Piaget's theory is a central reference point in the study of logico-mathematical development in children. One of the most famous Piagetian tasks is number conservation. Failures and successes in this task reveal two fundamental stages in children's thinking and judgment, shifting at approximately 7 years of age from visuospatial intuition to…

Mathematical and Pedagogical Perspectives on Warranting: Approximating the Root of 18

ERIC Educational Resources Information Center

Cooper, Jason; Pinto, Alon

2017-01-01

"The root of 18 is closer to 4 than it is to 5 because 18 is closer to 16 than it is to 25". Is this statement, voiced in an 8th grade class, valid? We suggest hypothetical arguments upon which this statement might be based, and analyze them from two complementary perspectives--epistemic and pedagogical--drawing on Toulmin's notion of…

Mathematical Modeling of the Heat Transfer and Conditions of Ignition of a Turbulent Flow of a Reactive Gas

NASA Astrophysics Data System (ADS)

Matvienko, O. V.

2016-01-01

Results of investigations into the heat transfer and conditions of ignition of a turbulent flow of a chemically reactive gas have been presented. Approximation formulas have been obtained for determining the critical conditions of ignition of the turbulent flow, the length of the preflame zone, and the criterion of heat transfer in subcritical and supercritical reaction regimes.

A Numerical Study on Microwave Coagulation Therapy

DTIC Science & Technology

2013-01-01

hepatocellular carcinoma (small size liver tumor). Through extensive numerical simulations, we reveal the mathematical relationships between some critical parameters in the therapy, including input power, frequency, temperature, and regions of impact. It is shown that these relationships can be approximated using simple polynomial functions. Compared to solutions of partial differential equations, these functions are significantly easier to compute and simpler to analyze for engineering design and clinical

New Jersey Statewide Minimum Standards: Results from the Program's Second Year. Occasional Papers in Education.

ERIC Educational Resources Information Center

Koffler, Stephen L.

Results of the second year of the New Jersey Minimum Basic Skills Tests in reading and mathematics, mandated by the New Jersey Public School Education Act of 1975, are summarized. Approximately 397,000 students in grades three, six, nine, and eleven were tested. Results of the tests showed that a smaller percentage of sixth-grade students met…

UNFINISHED JOURNEY Project. Quarterly report, September 1994--December 1994

DOE Office of Scientific and Technical Information (OSTI.GOV)

NONE

1998-02-01

In September, 1994, the U.S. Department of Energy (Nevada Operations Office) made a $199,708 grant (through the Mathematics, Science, and Technology Education Program), to the UNFINISHED JOURNEY Project. The Project began in April, 1994, to develop and implement an innovative model of student outreach by San Jose State University (SJSU) to underserved, underrepresented student populations of the East Side Union High School District (ESUHSD). The Project was formed by a consortium involving SJSU, ESUHSD, some 20 private sector organizations (foundations/corporations), numerous local community/professional organizations, and approximately 100 private funders. This proposal to the U.S. Department of Energy was to havemore » the Department join this unique partnership to focus University outreach to underserved student populations to pursue careers in mathematics, science, and technology.« less

Model for growth of fractal solid state surface and possibility of its verification by means of atomic force microscopy

NASA Astrophysics Data System (ADS)

Kulikov, D. A.; Potapov, A. A.; Rassadin, A. E.; Stepanov, A. V.

2017-10-01

In the paper, methods of verification of models for growth of solid state surface by means of atomic force microscopy are suggested. Simulation of growth of fractals with cylindrical generatrix on the solid state surface is presented. Our mathematical model of this process is based on generalization of the Kardar-Parisi-Zhang equation. Corner stones of this generalization are both conjecture of anisotropy of growth of the surface and approximation of small angles. The method of characteristics has been applied to solve the Kardar-Parisi-Zhang equation. Its solution should be considered up to the gradient catastrophe. The difficulty of nondifferentiability of fractal initial generatrix has been overcome by transition from a mathematical fractal to a physical one.

An improved version of the consequence analysis model for chemical emergencies, ESCAPE

NASA Astrophysics Data System (ADS)

Kukkonen, J.; Nikmo, J.; Riikonen, K.

2017-02-01

We present a refined version of a mathematical model called ESCAPE, "Expert System for Consequence Analysis and Preparing for Emergencies". The model has been designed for evaluating the releases of toxic and flammable gases into the atmosphere, their atmospheric dispersion and the effects on humans and the environment. We describe (i) the mathematical treatments of this model, (ii) a verification and evaluation of the model against selected experimental field data, and (iii) a new operational implementation of the model. The new mathematical treatments include state-of-the-art atmospheric vertical profiles and new submodels for dense gas and passive atmospheric dispersion. The model performance was first successfully verified using the data of the Thorney Island campaign, and then evaluated against the Desert Tortoise campaign. For the latter campaign, the geometric mean bias was 1.72 (this corresponds to an underprediction of approximately 70%) and 0.71 (overprediction of approximately 30%) for the concentration and the plume half-width, respectively. The geometric variance was <1.5 (this corresponds to an agreement that is better than a factor of two). These values can be considered to indicate a good agreement of predictions and data, in comparison to values evaluated for a range of other similar models. The model has also been adapted to be able to automatically use the real time predictions and forecasts of the numerical weather prediction model HIRLAM, "HIgh Resolution Limited Area Model". The operational implementation of the ESCAPE modelling system can be accessed anywhere using internet browsers, on laptop computers, tablets and mobile phones. The predicted results can be post-processed using geographic information systems. The model has already proved to be a useful tool of assessment for the needs of emergency response authorities in contingency planning.

Increasing the Number of Canadian Indigenous Students in STEM at the University of Regina, Saskatchewan, Canada

NASA Astrophysics Data System (ADS)

St-Jacques, J. M.; McGee, S.; Janze, R.; Longman, M.; Pete, S.; Starblanket, N.

2016-12-01

Canadian Indigenous people are an extremely poorly represented group in STEM today due to major barriers in obtaining a high school and then a university education. Approximately 10% of the undergraduate student population out of a total 12,600 students at the University of Regina, Regina, Saskatchewan, is First Nations, Métis or Inuit. The university is located in a catchment region where 30% of the population is First Nations or Métis. Approximately 100 students majoring in the sciences, mathematics and engineering have self-declared themselves to be Indigenous. For the past two years, we have been running a pilot project, the Initiative to Support and Increase the Number of Indigenous Students in the Sciences, Mathematics and Engineering at the Aboriginal Student Centre, with financial support from the Deans of Science and Engineering. We provide student networking lunches, Indigenous scientist and engineer speakers and mentors and supplemental tutoring. Our program is actively supported and guided by Elder Noel Starblanket, former president of the National Indian Brotherhood (now the Assembly of First Nations). Our students are greatly interested in the health and environmental sciences (particularly water quality), with a sprinkling of physics, mathematics and engineering majors. Our students have gone on to graduate work with prestigious scholarships and a paid internship in engineering. We report here on various lessons learned: the involvement of elders is key, as is the acceptance of non-traditional academic paths, and any STEM support program must respect Indigenous culture. There is great interest in science and engineering on the part of these students, if scientists and engineers are willing to listen and learn to talk with these students on their own terms.

The Symbol Grounding Problem Revisited: A Thorough Evaluation of the ANS Mapping Account and the Proposal of an Alternative Account Based on Symbol–Symbol Associations

PubMed Central

Reynvoet, Bert; Sasanguie, Delphine

2016-01-01

Recently, a lot of studies in the domain of numerical cognition have been published demonstrating a robust association between numerical symbol processing and individual differences in mathematics achievement. Because numerical symbols are so important for mathematics achievement, many researchers want to provide an answer on the ‘symbol grounding problem,’ i.e., how does a symbol acquires its numerical meaning? The most popular account, the approximate number system (ANS) mapping account, assumes that a symbol acquires its numerical meaning by being mapped on a non-verbal and ANS. Here, we critically evaluate four arguments that are supposed to support this account, i.e., (1) there is an evolutionary system for approximate number processing, (2) non-symbolic and symbolic number processing show the same behavioral effects, (3) non-symbolic and symbolic numbers activate the same brain regions which are also involved in more advanced calculation and (4) non-symbolic comparison is related to the performance on symbolic mathematics achievement tasks. Based on this evaluation, we conclude that all of these arguments and consequently also the mapping account are questionable. Next we explored less popular alternative, where small numerical symbols are initially mapped on a precise representation and then, in combination with increasing knowledge of the counting list result in an independent and exact symbolic system based on order relations between symbols. We evaluate this account by reviewing evidence on order judgment tasks following the same four arguments. Although further research is necessary, the available evidence so far suggests that this symbol–symbol association account should be considered as a worthy alternative of how symbols acquire their meaning. PMID:27790179

Approximate analysis of the formation of a buoyant solid sphere in a supercooled melt

DOE Office of Scientific and Technical Information (OSTI.GOV)

Solomon, A.D.; Wilson, D.G.; Alexiades, V.

1986-03-01

A mathematical model is presented for the idealized formation and development of a buoyant sphere solidifying in an infinite pool of supercooled liquid. The solid and liquid are of the same pure material and the solid is less dense than the liquid. Initially the liquid is at a uniform temperature that is below its equilibrium freezing temperature, T/sub cr/, but above the so called hypercooled temperature, T/sub cr/ - H/c/sub L/. Here H and c/sub L/ are the latent heat of solidification and the specific heat of the liquid, respectively. An approximate solution is derived based on the Megerlin approximationmore » method. 11 refs.« less

Multivariate approximation methods and applications to geophysics and geodesy

NASA Technical Reports Server (NTRS)

Munteanu, M. J.

1979-01-01

The first report in a series is presented which is intended to be written by the author with the purpose of treating a class of approximation methods of functions in one and several variables and ways of applying them to geophysics and geodesy. The first report is divided in three parts and is devoted to the presentation of the mathematical theory and formulas. Various optimal ways of representing functions in one and several variables and the associated error when information is had about the function such as satellite data of different kinds are discussed. The framework chosen is Hilbert spaces. Experiments were performed on satellite altimeter data and on satellite to satellite tracking data.

On the control of spin-boson systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boscain, Ugo, E-mail: ugo.boscain@polytechnique.edu; Mason, Paolo, E-mail: Paolo.Mason@l2s.centralesupelec.fr; Panati, Gianluca, E-mail: panati@mat.uniroma1.it

2015-09-15

In this paper, we study the so-called spin-boson system, namely, a two-level system in interaction with a distinguished mode of a quantized bosonic field. We give a brief description of the controlled Rabi and Jaynes–Cummings models and we discuss their appearance in the mathematics and physics literature. We then study the controllability of the Rabi model when the control is an external field acting on the bosonic part. Applying geometric control techniques to the Galerkin approximation and using perturbation theory to guarantee non-resonance of the spectrum of the drift operator, we prove approximate controllability of the system, for almost everymore » value of the interaction parameter.« less

Approximate analytical modeling of leptospirosis infection

NASA Astrophysics Data System (ADS)

Ismail, Nur Atikah; Azmi, Amirah; Yusof, Fauzi Mohamed; Ismail, Ahmad Izani

2017-11-01

Leptospirosis is an infectious disease carried by rodents which can cause death in humans. The disease spreads directly through contact with feces, urine or through bites of infected rodents and indirectly via water contaminated with urine and droppings from them. Significant increase in the number of leptospirosis cases in Malaysia caused by the recent severe floods were recorded during heavy rainfall season. Therefore, to understand the dynamics of leptospirosis infection, a mathematical model based on fractional differential equations have been developed and analyzed. In this paper an approximate analytical method, the multi-step Laplace Adomian decomposition method, has been used to conduct numerical simulations so as to gain insight on the spread of leptospirosis infection.

Noise elimination algorithm for modal analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bao, X. X., E-mail: baoxingxian@upc.edu.cn; Li, C. L.; Xiong, C. B.

2015-07-27

Modal analysis is an ongoing interdisciplinary physical issue. Modal parameters estimation is applied to determine the dynamic characteristics of structures under vibration excitation. Modal analysis is more challenging for the measured vibration response signals are contaminated with noise. This study develops a mathematical algorithm of structured low rank approximation combined with the complex exponential method to estimate the modal parameters. Physical experiments using a steel cantilever beam with ten accelerometers mounted, excited by an impulse load, demonstrate that this method can significantly eliminate noise from measured signals and accurately identify the modal frequencies and damping ratios. This study provides amore » fundamental mechanism of noise elimination using structured low rank approximation in physical fields.« less

Analysis of the dynamic response of a supersonic inlet to flow-field perturbations upstream of the normal shock

NASA Technical Reports Server (NTRS)

Cole, G. L.; Willoh, R. G.

1975-01-01

A linearized mathematical analysis is presented for determining the response of normal shock position and subsonic duct pressures to flow-field perturbations upstream of the normal shock in mixed-compression supersonic inlets. The inlet duct cross-sectional area variation is approximated by constant-area sections; this approximation results in one-dimensional wave equations. A movable normal shock separates the supersonic and subsonic flow regions, and a choked exit is assumed for the inlet exit condition. The analysis leads to a closed-form matrix solution for the shock position and pressure transfer functions. Analytical frequency response results are compared with experimental data and a method of characteristics solution.

Slow Invariant Manifolds in Chemically Reactive Systems

NASA Astrophysics Data System (ADS)

Paolucci, Samuel; Powers, Joseph M.

2006-11-01

The scientific design of practical gas phase combustion devices has come to rely on the use of mathematical models which include detailed chemical kinetics. Such models intrinsically admit a wide range of scales which renders their accurate numerical approximation difficult. Over the past decade, rational strategies, such as Intrinsic Low Dimensional Manifolds (ILDM) or Computational Singular Perturbations (CSP), for equilibrating fast time scale events have been successfully developed, though their computation can be challenging and their accuracy in most cases uncertain. Both are approximations to the preferable slow invariant manifold which best describes how the system evolves in the long time limit. Strategies for computing the slow invariant manifold are examined, and results are presented for practical combustion systems.

A mathematical model for simulating noise suppression of lined ejectors

NASA Technical Reports Server (NTRS)

Watson, Willie R.

1994-01-01

A mathematical model containing the essential features embodied in the noise suppression of lined ejectors is presented. Although some simplification of the physics is necessary to render the model mathematically tractable, the current model is the most versatile and technologically advanced at the current time. A system of linearized equations and the boundary conditions governing the sound field are derived starting from the equations of fluid dynamics. A nonreflecting boundary condition is developed. In view of the complex nature of the equations, a parametric study requires the use of numerical techniques and modern computers. A finite element algorithm that solves the differential equations coupled with the boundary condition is then introduced. The numerical method results in a matrix equation with several hundred thousand degrees of freedom that is solved efficiently on a supercomputer. The model is validated by comparing results either with exact solutions or with approximate solutions from other works. In each case, excellent correlations are obtained. The usefulness of the model as an optimization tool and the importance of variable impedance liners as a mechanism for achieving broadband suppression within a lined ejector are demonstrated.

[Study on balance group in steady-state extraction process of Chinese medicine and experimental verification to Houttuynia cordata].

PubMed

Liu, Wenlong; Zhang, Xili; He, Fuyuan; Zhang, Ping; Wang, Haiqin; Wu, Dezhi; Chen, Zuohong

2011-11-01

To establish and experimental verification the mathematical model of the balance groups that is the steady-state of traditional Chinese medicine in extraction. Using the entropy and genetic principles of statistics, and taking the coefficient of variation of GC fingerprint which is the naphtha of the Houttuynia cordata between strains in the same GAP place as a pivot to establish and verify the mathematical model was established of the balance groups that is the steady-state of traditional Chinese medicine in extraction. A mathematical model that is suitable for the balance groups of the steady-state of traditional Chinese medicine and preparation in extraction, and the balance groups which is 29 683 strains (approximately 118.7 kg) were gained with the same origin of H. cordata as the model drug. Under the GAP of quality control model, controlling the stability of the quality through further using the Hardy-Weinberg balance groups of the H. cordata between strains, the new theory and experiment foundation is established for the steady-state of traditional Chinese medicine in extraction and quality control.

The effects of home computer access and social capital on mathematics and science achievement among Asian-American high school students in the NELS:88 data set

NASA Astrophysics Data System (ADS)

Quigley, Mark Declan

The purpose of this researcher was to examine specific environmental, educational, and demographic factors and their influence on mathematics and science achievement. In particular, the researcher ascertained the interconnections of home computer access and social capital, with Asian American students and the effect on mathematics and science achievement. Coleman's theory on social capital and parental influence was used as a basis for the analysis of data. Subjects for this study were the base year students from the National Education Longitudinal Study of 1988 (NELS:88) and the subsequent follow-up survey data in 1990, 1992, and 1994. The approximate sample size for this study is 640 ethnic Asians from the NELS:88 database. The analysis was a longitudinal study based on the Student and Parent Base Year responses and the Second Follow-up survey of 1992, when the subjects were in 12th grade. Achievement test results from the NELS:88 data were used to measure achievement in mathematics and science. The NELS:88 test battery was developed to measure both individual status and a student's growth in a number of achievement areas. The subject's responses were analyzed by principal components factor analysis, weights, effect sizes, hierarchial regression analysis, and PLSPath Analysis. The results of this study were that prior ability in mathematics and science is a major influence in the student's educational achievement. Findings from the study support the view that home computer access has a negative direct effect on mathematics and science achievement for both Asian American males and females. None of the social capital factors in the study had either a negative or positive direct effect on mathematics and science achievement although some indirect effects were found. Suggestions were made toward increasing parental involvement in their children's academic endeavors. Computer access in the home should be considered related to television viewing and should be closely monitored by the parents to promote educational uses.

An HP Adaptive Discontinuous Galerkin Method for Hyperbolic Conservation Laws. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Bey, Kim S.

1994-01-01

This dissertation addresses various issues for model classes of hyperbolic conservation laws. The basic approach developed in this work employs a new family of adaptive, hp-version, finite element methods based on a special discontinuous Galerkin formulation for hyperbolic problems. The discontinuous Galerkin formulation admits high-order local approximations on domains of quite general geometry, while providing a natural framework for finite element approximations and for theoretical developments. The use of hp-versions of the finite element method makes possible exponentially convergent schemes with very high accuracies in certain cases; the use of adaptive hp-schemes allows h-refinement in regions of low regularity and p-enrichment to deliver high accuracy, while keeping problem sizes manageable and dramatically smaller than many conventional approaches. The use of discontinuous Galerkin methods is uncommon in applications, but the methods rest on a reasonable mathematical basis for low-order cases and has local approximation features that can be exploited to produce very efficient schemes, especially in a parallel, multiprocessor environment. The place of this work is to first and primarily focus on a model class of linear hyperbolic conservation laws for which concrete mathematical results, methodologies, error estimates, convergence criteria, and parallel adaptive strategies can be developed, and to then briefly explore some extensions to more general cases. Next, we provide preliminaries to the study and a review of some aspects of the theory of hyperbolic conservation laws. We also provide a review of relevant literature on this subject and on the numerical analysis of these types of problems.

The Dropout Learning Algorithm

PubMed Central

Baldi, Pierre; Sadowski, Peter

2014-01-01

Dropout is a recently introduced algorithm for training neural network by randomly dropping units during training to prevent their co-adaptation. A mathematical analysis of some of the static and dynamic properties of dropout is provided using Bernoulli gating variables, general enough to accommodate dropout on units or connections, and with variable rates. The framework allows a complete analysis of the ensemble averaging properties of dropout in linear networks, which is useful to understand the non-linear case. The ensemble averaging properties of dropout in non-linear logistic networks result from three fundamental equations: (1) the approximation of the expectations of logistic functions by normalized geometric means, for which bounds and estimates are derived; (2) the algebraic equality between normalized geometric means of logistic functions with the logistic of the means, which mathematically characterizes logistic functions; and (3) the linearity of the means with respect to sums, as well as products of independent variables. The results are also extended to other classes of transfer functions, including rectified linear functions. Approximation errors tend to cancel each other and do not accumulate. Dropout can also be connected to stochastic neurons and used to predict firing rates, and to backpropagation by viewing the backward propagation as ensemble averaging in a dropout linear network. Moreover, the convergence properties of dropout can be understood in terms of stochastic gradient descent. Finally, for the regularization properties of dropout, the expectation of the dropout gradient is the gradient of the corresponding approximation ensemble, regularized by an adaptive weight decay term with a propensity for self-consistent variance minimization and sparse representations. PMID:24771879

Approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays: a robust stability problem.

PubMed

Pandiselvi, S; Raja, R; Cao, Jinde; Rajchakit, G; Ahmad, Bashir

2018-01-01

This work predominantly labels the problem of approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays. Here we design a linear estimator in such a way that the absorption of mRNA and protein can be approximated via known measurement outputs. By utilizing a Lyapunov-Krasovskii functional and some stochastic analysis execution, we obtain the stability formula of the estimation error systems in the structure of linear matrix inequalities under which the estimation error dynamics is robustly exponentially stable. Further, the obtained conditions (in the form of LMIs) can be effortlessly solved by some available software packages. Moreover, the specific expression of the desired estimator is also shown in the main section. Finally, two mathematical illustrative examples are accorded to show the advantage of the proposed conceptual results.

Quantifying the effect of finite spectral bandwidth on extinction coefficient of species in laser absorption spectroscopy

NASA Astrophysics Data System (ADS)

Singh, Manjeet; Singh, Jaswant; Singh, Baljit; Ghanshyam, C.

2016-11-01

The aim of this study is to quantify the finite spectral bandwidth effect on laser absorption spectroscopy for a wide-band laser source. Experimental analysis reveals that the extinction coefficient of an analyte is affected by the bandwidth of the spectral source, which may result in the erroneous conclusions. An approximate mathematical model has been developed for optical intensities having Gaussian line shape, which includes the impact of source's spectral bandwidth in the equation for spectroscopic absorption. This is done by introducing a suitable first order and second order bandwidth approximation in the Beer-Lambert law equation for finite bandwidth case. The derived expressions were validated using spectroscopic analysis with higher SBW on a test sample, Rhodamine B. The concentrations calculated using proposed approximation, were in significant agreement with the true values when compared with those calculated with conventional approach.

Enhancing dendritic cell immunotherapy for melanoma using a simple mathematical model.

PubMed

Castillo-Montiel, E; Chimal-Eguía, J C; Tello, J Ignacio; Piñon-Zaráte, G; Herrera-Enríquez, M; Castell-Rodríguez, A E

2015-06-09

The immunotherapy using dendritic cells (DCs) against different varieties of cancer is an approach that has been previously explored which induces a specific immune response. This work presents a mathematical model of DCs immunotherapy for melanoma in mice based on work by Experimental Immunotherapy Laboratory of the Medicine Faculty in the Universidad Autonoma de Mexico (UNAM). The model is a five delay differential equation (DDEs) which represents a simplified view of the immunotherapy mechanisms. The mathematical model takes into account the interactions between tumor cells, dendritic cells, naive cytotoxic T lymphocytes cells (inactivated cytotoxic cells), effector cells (cytotoxic T activated cytotoxic cells) and transforming growth factor β cytokine (T G F-β). The model is validated comparing the computer simulation results with biological trial results of the immunotherapy developed by the research group of UNAM. The results of the growth of tumor cells obtained by the control immunotherapy simulation show a similar amount of tumor cell population than the biological data of the control immunotherapy. Moreover, comparing the increase of tumor cells obtained from the immunotherapy simulation and the biological data of the immunotherapy applied by the UNAM researchers obtained errors of approximately 10 %. This allowed us to use the model as a framework to test hypothetical treatments. The numerical simulations suggest that by using more doses of DCs and changing the infusion time, the tumor growth decays compared with the current immunotherapy. In addition, a local sensitivity analysis is performed; the results show that the delay in time " τ", the maximal growth rate of tumor "r" and the maximal efficiency of tumor cytotoxic cells rate "aT" are the most sensitive model parameters. By using this mathematical model it is possible to simulate the growth of the tumor cells with or without immunotherapy using the infusion protocol of the UNAM researchers, to obtain a good approximation of the biological trials data. It is worth mentioning that by manipulating the different parameters of the model the effectiveness of the immunotherapy may increase. This last suggests that different protocols could be implemented by the Immunotherapy Laboratory of UNAM in order to improve their results.

Introduction to the Theory of Atmospheric Radiative Transfer

NASA Technical Reports Server (NTRS)

Buglia, J. J.

1986-01-01

The fundamental physical and mathematical principles governing the transmission of radiation through the atmosphere are presented, with emphasis on the scattering of visible and near-IR radiation. The classical two-stream, thin-atmosphere, and Eddington approximations, along with some of their offspring, are developed in detail, along with the discrete ordinates method of Chandrasekhar. The adding and doubling methods are discussed from basic principles, and references for further reading are suggested.

Defense AT&L. Volume 44, Number 4

DTIC Science & Technology

2015-08-01

experiment that seemed to make a lot of people nervous. Some of the nervousness stemmed from concerns that I was putting the PMs in an awkward...relation with decreasing numbers of graduates with science, technology, engineering and mathematics ( STEM ) degrees. And, while all this happened...is developing people with backgrounds in STEM . Approximately 45 percent of the federal government’s scientists and engineers work in the DoD, which

Models of determining deformations

NASA Astrophysics Data System (ADS)

Gladilin, V. N.

2016-12-01

In recent years, a lot of functions designed to determine deformation values that occur mostly as a result of settlement of structures and industrial equipment. Some authors suggest such advanced mathematical functions approximating deformations as general methods for the determination of deformations. The article describes models of deformations as physical processes. When comparing static, cinematic and dynamic models, it was found that the dynamic model reflects the deformation of structures and industrial equipment most reliably.

Engage to Excel: Producing One Million Additional College Graduates with Degrees in Science, Technology, Engineering, and Mathematics. Report to the President

ERIC Educational Resources Information Center

Olson, Steve; Riordan, Donna Gerardi

2012-01-01

Economic projections point to a need for approximately 1 million more STEM professionals than the U.S. will produce at the current rate over the next decade if the country is to retain its historical preeminence in science and technology. To meet this goal, the United States will need to increase the number of students who receive undergraduate…

Attitude dynamics and control of spacecraft with a partially filled liquid tank and flexible panels

NASA Astrophysics Data System (ADS)

Liu, Feng; Yue, Baozeng; Zhao, Liangyu

2018-02-01

A liquid-filled flexible spacecraft is essentially a time-variant fully-coupled system, whose dynamics characteristics are closely associated with its motion features. This paper focuses on the mathematical modelling and attitude control of the spacecraft coupled with fuel sloshing dynamics and flexible solar panels vibration. The slosh motion is represented by a spherical pendulum, whose motion description method is improved by using split variable operation. Benefiting from this improvement, the nonlinear lateral sloshing and the rotary sloshing as well as the rigid motion of a liquid respect to the spacecraft can be approximately described. The assumed modes discretization method has been adopted to approximate the elastic displacements of the attached panels, and the coupled dynamics is derived by using the Lagrangian formulation. A variable substitution method is proposed to obtain the apparently-uncoupled mathematical model of the rigid-flexible-liquid spacecraft. After linearization, this model can be directly used for designing Lyapunov output-feedback attitude controller (OFAC). With only torque actuators, and attitude and rate sensors installed, this kind of attitude controller, as simulation results show, is capable of not only bringing the spacecraft to the desired orientation, but also suppressing the effect of flex and slosh on the attitude motion of the spacecraft.

INTERACTION OF LASER RADIATION WITH MATTER. LASER PLASMA: Mathematical simulation of the spectrum of a nonequilibrium laser plasma

NASA Astrophysics Data System (ADS)

Mazhukin, V. I.; Nikiforov, M. G.; Fievet, Christian

2006-02-01

A method is proposed for calculating the spectrum of a nonequilibrium plasma, which is based on a nonequilibrium collision—radiation model including all common line broadening mechanisms (natural, pressure, Doppler, and quadratic Stark effect broadening) and supplemented with the energy balance equations for electrons and ions. The nonequilibrium populations of the ground and excited states of neutral atoms and ions for an arbitrary instant of time are found by solving kinetic equations. The shape of each spectral line is determined by its central core calculated in the collision approximation up to the frequency boundary of its applicability, where the central core is 'joined' with the line wings calculated in the quasi-static approximation. The validity of this theoretical model is confirmed by simulations of a number of experimental studies of emission spectra under the conditions of a local thermodynamic equilibrium. It is shown that the calculated and experimental data obtained for the ground-state lines of the first carbon ion and neutral helium and argon atoms are in good agreement. The nonequilibrium spectrum of the optical breakdown in argon is calculated. Mathematical simulations showed that the intensities of nonequilibrium line spectra can be noticeably (by several times) lower than those of equilibrium spectra.

Shaping the micromechanical behavior of multi-phase composites for bone tissue engineering.

PubMed

Ranganathan, Shivakumar I; Yoon, Diana M; Henslee, Allan M; Nair, Manitha B; Smid, Christine; Kasper, F Kurtis; Tasciotti, Ennio; Mikos, Antonios G; Decuzzi, Paolo; Ferrari, Mauro

2010-09-01

Mechanical stiffness is a fundamental parameter in the rational design of composites for bone tissue engineering in that it affects both the mechanical stability and the osteo-regeneration process at the fracture site. A mathematical model is presented for predicting the effective Young's modulus (E) and shear modulus (G) of a multi-phase biocomposite as a function of the geometry, material properties and volume concentration of each individual phase. It is demonstrated that the shape of the reinforcing particles may dramatically affect the mechanical stiffness: E and G can be maximized by employing particles with large geometrical anisotropy, such as thin platelet-like or long fibrillar-like particles. For a porous poly(propylene fumarate) (60% porosity) scaffold reinforced with silicon particles (10% volume concentration) the Young's (shear) modulus could be increased by more than 10 times by just using thin platelet-like as opposed to classical spherical particles, achieving an effective modulus E approximately 8 GPa (G approximately 3.5 GPa). The mathematical model proposed provides results in good agreement with several experimental test cases and could help in identifying the proper formulation of bone scaffolds, reducing the development time and guiding the experimental testing. 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

WKB analysis of relativistic Stern–Gerlach measurements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Palmer, Matthew C., E-mail: m.palmer@physics.usyd.edu.au; Takahashi, Maki, E-mail: m.takahashi@physics.usyd.edu.au; Westman, Hans F., E-mail: hwestman74@gmail.com

2013-09-15

Spin is an important quantum degree of freedom in relativistic quantum information theory. This paper provides a first-principles derivation of the observable corresponding to a Stern–Gerlach measurement with relativistic particle velocity. The specific mathematical form of the Stern–Gerlach operator is established using the transformation properties of the electromagnetic field. To confirm that this is indeed the correct operator we provide a detailed analysis of the Stern–Gerlach measurement process. We do this by applying a WKB approximation to the minimally coupled Dirac equation describing an interaction between a massive fermion and an electromagnetic field. Making use of the superposition principle wemore » show that the +1 and −1 spin eigenstates of the proposed spin operator are split into separate packets due to the inhomogeneity of the Stern–Gerlach magnetic field. The operator we obtain is dependent on the momentum between particle and Stern–Gerlach apparatus, and is mathematically distinct from two other commonly used operators. The consequences for quantum tomography are considered. -- Highlights: •Derivation of the spin observable for a relativistic Stern–Gerlach measurement. •Relativistic model of spin measurement using WKB approximation of Dirac equation. •The derived spin operator is distinct from two other commonly used operators. •Consequences for quantum tomography are considered.« less

Fadeout in an early mathematics intervention: Constraining content or preexisting differences?

PubMed

Bailey, Drew H; Nguyen, Tutrang; Jenkins, Jade Marcus; Domina, Thurston; Clements, Douglas H; Sarama, Julie S

2016-09-01

A robust finding across research on early childhood educational interventions is that the treatment effect diminishes over time, with children not receiving the intervention eventually catching up to children who did. One popular explanation for fadeout of early mathematics interventions is that elementary school teachers may not teach the kind of advanced content that children are prepared for after receiving the intervention, so lower-achieving children in the control groups of early mathematics interventions catch up to the higher-achieving children in the treatment groups. An alternative explanation is that persistent individual differences in children's long-term mathematical development result more from relatively stable preexisting differences in their skills and environments than from the direct effects of previous knowledge on later knowledge. We tested these 2 hypotheses using data from an effective preschool mathematics intervention previously known to show a diminishing treatment effect over time. We compared the intervention group to a matched subset of the control group with a similar mean and variance of scores at the end of treatment. We then tested the relative contributions of factors that similarly constrain learning in children from treatment and control groups with the same level of posttreatment achievement and preexisting differences between these 2 groups to the fadeout of the treatment effect over time. We found approximately 72% of the fadeout effect to be attributable to preexisting differences between children in treatment and control groups with the same level of achievement at posttest. These differences were fully statistically attenuated by children's prior academic achievement. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Fadeout in an Early Mathematics Intervention: Constraining Content or Pre-existing Differences?

PubMed Central

Bailey, Drew H.; Nguyen, Tutrang; Jenkins, Jade Marcus; Domina, Thurston; Clements, Douglas H.; Sarama, Julie S.

2016-01-01

A robust finding across research on early childhood educational interventions is that the treatment effect diminishes over time, with children not receiving the intervention eventually catching up to children who did. One popular explanation for fadeout of early mathematics interventions is that elementary school teachers may not teach the kind of advanced content that children are prepared for after receiving the intervention, so lower-achieving children in the control groups of early mathematics interventions catch up to the higher-achieving children in the treatment groups. An alternative explanation is that persistent individual differences in children’s long-term mathematical development result more from relatively stable pre-existing differences in their skills and environments than from the direct effects of previous knowledge on later knowledge. We tested these two hypotheses using data from an effective preschool mathematics intervention previously known to show a diminishing treatment effect over time. We compared the intervention group to a matched subset of the control group with a similar mean and variance of scores at the end of treatment. We then tested the relative contributions of factors that similarly constrain learning in children from treatment and control groups with the same level of post-treatment achievement and pre-existing differences between these two groups to the fadeout of the treatment effect over time. We found approximately 72% of the fadeout effect to be attributable to pre-existing differences between children in treatment and control groups with the same level of achievement at post-test. These differences were fully statistically attenuated by children’s prior academic achievement. PMID:27505700

Sparse approximation problem: how rapid simulated annealing succeeds and fails

NASA Astrophysics Data System (ADS)

Obuchi, Tomoyuki; Kabashima, Yoshiyuki

2016-03-01

Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an overcomplete basis is termed the sparse approximation. In this paper, we apply simulated annealing, a metaheuristic algorithm for general optimization problems, to sparse approximation in the situation where the given data have a planted sparse representation and noise is present. The result in the noiseless case shows that our simulated annealing works well in a reasonable parameter region: the planted solution is found fairly rapidly. This is true even in the case where a common relaxation of the sparse approximation problem, the G-relaxation, is ineffective. On the other hand, when the dimensionality of the data is close to the number of non-zero components, another metastable state emerges, and our algorithm fails to find the planted solution. This phenomenon is associated with a first-order phase transition. In the case of very strong noise, it is no longer meaningful to search for the planted solution. In this situation, our algorithm determines a solution with close-to-minimum distortion fairly quickly.

Approximate spatial reasoning

NASA Technical Reports Server (NTRS)

Dutta, Soumitra

1988-01-01

Much of human reasoning is approximate in nature. Formal models of reasoning traditionally try to be precise and reject the fuzziness of concepts in natural use and replace them with non-fuzzy scientific explicata by a process of precisiation. As an alternate to this approach, it has been suggested that rather than regard human reasoning processes as themselves approximating to some more refined and exact logical process that can be carried out with mathematical precision, the essence and power of human reasoning is in its capability to grasp and use inexact concepts directly. This view is supported by the widespread fuzziness of simple everyday terms (e.g., near tall) and the complexity of ordinary tasks (e.g., cleaning a room). Spatial reasoning is an area where humans consistently reason approximately with demonstrably good results. Consider the case of crossing a traffic intersection. We have only an approximate idea of the locations and speeds of various obstacles (e.g., persons and vehicles), but we nevertheless manage to cross such traffic intersections without any harm. The details of our mental processes which enable us to carry out such intricate tasks in such apparently simple manner are not well understood. However, it is that we try to incorporate such approximate reasoning techniques in our computer systems. Approximate spatial reasoning is very important for intelligent mobile agents (e.g., robots), specially for those operating in uncertain or unknown or dynamic domains.

Using confirmatory factor analysis to validate the Chamberlin affective instrument for mathematical problem solving with academically advanced students.

PubMed

Chamberlin, Scott A; Moore, Alan D; Parks, Kelly

2017-09-01

Student affect plays a considerable role in mathematical problem solving performance, yet is rarely formally assessed. In this manuscript, an instrument and its properties are discussed to enable educational psychologists the opportunity to assess student affect. The study was conducted to norm the CAIMPS (instrument) with gifted students. In so doing, educational psychologists are informed of the process and the instrument's properties. The sample was comprised of 160 middle-grade (7 and 8) students, identified as gifted, in the United States. After completing one of four model-eliciting activities (MEAs), all participants completed the CAIMPS (Chamberlin Affective Instrument for Mathematical Problem Solving). Data were analysed using confirmatory factor analysis to ascertain the number of factors in the instrument. The normed fit index (0.6939), non-normed fit index (0.8072), and root mean square error approximation (.076) were at or near the acceptable levels. Alpha levels for factors were also robust (.637-.923). Data suggest that the instrument was a good fit for use with mathematics students in middle grades when solving problems. Perhaps the most impressive characteristic of the instrument was that the four factors (AVI: anxiety, value, and interest), SS (self-efficacy and self-esteem), ASP (aspiration), and ANX (anxiety) did not correlate highly with one another, which defies previous hypotheses in educational psychology. © 2017 The British Psychological Society.

The Intercomparison of 3D Radiation Codes (I3RC): Showcasing Mathematical and Computational Physics in a Critical Atmospheric Application

NASA Astrophysics Data System (ADS)

Davis, A. B.; Cahalan, R. F.

2001-05-01

The Intercomparison of 3D Radiation Codes (I3RC) is an on-going initiative involving an international group of over 30 researchers engaged in the numerical modeling of three-dimensional radiative transfer as applied to clouds. Because of their strong variability and extreme opacity, clouds are indeed a major source of uncertainty in the Earth's local radiation budget (at GCM grid scales). Also 3D effects (at satellite pixel scales) invalidate the standard plane-parallel assumption made in the routine of cloud-property remote sensing at NASA and NOAA. Accordingly, the test-cases used in I3RC are based on inputs and outputs which relate to cloud effects in atmospheric heating rates and in real-world remote sensing geometries. The main objectives of I3RC are to (1) enable participants to improve their models, (2) publish results as a community, (3) archive source code, and (4) educate. We will survey the status of I3RC and its plans for the near future with a special emphasis on the mathematical models and computational approaches. We will also describe some of the prime applications of I3RC's efforts in climate models, cloud-resolving models, and remote-sensing observations of clouds, or that of the surface in their presence. In all these application areas, computational efficiency is the main concern and not accuracy. One of I3RC's main goals is to document the performance of as wide a variety as possible of three-dimensional radiative transfer models for a small but representative number of ``cases.'' However, it is dominated by modelers working at the level of linear transport theory (i.e., they solve the radiative transfer equation) and an overwhelming majority of these participants use slow-but-robust Monte Carlo techniques. This means that only a small portion of the efficiency vs. accuracy vs. flexibility domain is currently populated by I3RC participants. To balance this natural clustering the present authors have organized a systematic outreach towards modelers that have used approximate methods in radiation transport. In this context, different, presumably simpler, equations (such as diffusion) are used in order to make a significant gain on the efficiency axis. We will describe in some detail the most promising approaches to approximate 3D radiative transfer in clouds. Somewhat paradoxically, and in spite of its importance in the above-mentioned applications, approximate radiative transfer modeling lags significantly behind its exact counterpart because the required mathematical and computational culture is essentially alien to the native atmospheric radiation community. I3RC is receiving enough funding from NASA/HQ and DOE/ARM for its essential operations out of NASA/GSFC. However, this does not cover the time and effort of any of the participants; so only existing models were entered. At present, none of inherently approximate methods are represented, only severe truncations of some exact methods. We therefore welcome the Math/Geo initiative at NSF which should enable the proper consortia of experts in atmospheric radiation and in applied mathematics to fill an important niche.

Quantum entanglement of a harmonic oscillator with an electromagnetic field.

PubMed

Makarov, Dmitry N

2018-05-29

At present, there are many methods for obtaining quantum entanglement of particles with an electromagnetic field. Most methods have a low probability of quantum entanglement and not an exact theoretical apparatus based on an approximate solution of the Schrodinger equation. There is a need for new methods for obtaining quantum-entangled particles and mathematically accurate studies of such methods. In this paper, a quantum harmonic oscillator (for example, an electron in a magnetic field) interacting with a quantized electromagnetic field is considered. Based on the exact solution of the Schrodinger equation for this system, it is shown that for certain parameters there can be a large quantum entanglement between the electron and the electromagnetic field. Quantum entanglement is analyzed on the basis of a mathematically exact expression for the Schmidt modes and the Von Neumann entropy.

A model of yeast glycolysis based on a consistent kinetic characterisation of all its enzymes

PubMed Central

Smallbone, Kieran; Messiha, Hanan L.; Carroll, Kathleen M.; Winder, Catherine L.; Malys, Naglis; Dunn, Warwick B.; Murabito, Ettore; Swainston, Neil; Dada, Joseph O.; Khan, Farid; Pir, Pınar; Simeonidis, Evangelos; Spasić, Irena; Wishart, Jill; Weichart, Dieter; Hayes, Neil W.; Jameson, Daniel; Broomhead, David S.; Oliver, Stephen G.; Gaskell, Simon J.; McCarthy, John E.G.; Paton, Norman W.; Westerhoff, Hans V.; Kell, Douglas B.; Mendes, Pedro

2013-01-01

We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a “cycle of knowledge” strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought. PMID:23831062

Induced Eddy Currents in Simple Conductive Geometries: Mathematical Formalism Describes the Excitation of Electrical Eddy Currents in a Time-Varying Magnetic Field

DOE PAGES

Nagel, James R.

2017-12-22

In this paper, a complete mathematical formalism is introduced to describe the excitation of electrical eddy currents due to a time-varying magnetic field. The process works by applying a quasistatic approximation to Ampere's law and then segregating the magnetic field into impressed and induced terms. The result is a nonhomogeneous vector Helmholtz equation that can be analytically solved for many practical geometries. Four demonstration cases are then solved under a constant excitation field over all space—an infinite slab in one dimension, a longitudinal cylinder in two dimensions, a transverse cylinder in two dimensions, and a sphere in three dimensions. Numericalmore » simulations are also performed in parallel with analytic computations, all of which verify the accuracy of the derived expressions.« less

Combinatorial vector fields and the valley structure of fitness landscapes.

PubMed

Stadler, Bärbel M R; Stadler, Peter F

2010-12-01

Adaptive (downhill) walks are a computationally convenient way of analyzing the geometric structure of fitness landscapes. Their inherently stochastic nature has limited their mathematical analysis, however. Here we develop a framework that interprets adaptive walks as deterministic trajectories in combinatorial vector fields and in return associate these combinatorial vector fields with weights that measure their steepness across the landscape. We show that the combinatorial vector fields and their weights have a product structure that is governed by the neutrality of the landscape. This product structure makes practical computations feasible. The framework presented here also provides an alternative, and mathematically more convenient, way of defining notions of valleys, saddle points, and barriers in landscape. As an application, we propose a refined approximation for transition rates between macrostates that are associated with the valleys of the landscape.

Using Mathematical Transmission Modelling to Investigate Drivers of Respiratory Syncytial Virus Seasonality in Children in the Philippines

PubMed Central

Paynter, Stuart; Yakob, Laith; Simões, Eric A. F.; Lucero, Marilla G.; Tallo, Veronica; Nohynek, Hanna; Ware, Robert S.; Weinstein, Philip; Williams, Gail; Sly, Peter D.

2014-01-01

We used a mathematical transmission model to estimate when ecological drivers of respiratory syncytial virus (RSV) transmissibility would need to act in order to produce the observed seasonality of RSV in the Philippines. We estimated that a seasonal peak in transmissibility would need to occur approximately 51 days prior to the observed peak in RSV cases (range 49 to 67 days). We then compared this estimated seasonal pattern of transmissibility to the seasonal patterns of possible ecological drivers of transmissibility: rainfall, humidity and temperature patterns, nutritional status, and school holidays. The timing of the seasonal patterns of nutritional status and rainfall were both consistent with the estimated seasonal pattern of transmissibility and these are both plausible drivers of the seasonality of RSV in this setting. PMID:24587222

Mathematical modeling of synthetic unit hydrograph case study: Citarum watershed

NASA Astrophysics Data System (ADS)

Islahuddin, Muhammad; Sukrainingtyas, Adiska L. A.; Kusuma, M. Syahril B.; Soewono, Edy

2015-09-01

Deriving unit hydrograph is very important in analyzing watershed's hydrologic response of a rainfall event. In most cases, hourly measures of stream flow data needed in deriving unit hydrograph are not always available. Hence, one needs to develop methods for deriving unit hydrograph for ungagged watershed. Methods that have evolved are based on theoretical or empirical formulas relating hydrograph peak discharge and timing to watershed characteristics. These are usually referred to Synthetic Unit Hydrograph. In this paper, a gamma probability density function and its variant are used as mathematical approximations of a unit hydrograph for Citarum Watershed. The model is adjusted with real field condition by translation and scaling. Optimal parameters are determined by using Particle Swarm Optimization method with weighted objective function. With these models, a synthetic unit hydrograph can be developed and hydrologic parameters can be well predicted.

Mathematical model of the current density for the 30-cm engineering model thruster

NASA Technical Reports Server (NTRS)

Cuffel, R. F.

1975-01-01

Mathematical models are presented for both the singly and doubly charged ion current densities downstream of the 30-cm engineering model thruster with 0.5% compensated dished grids. These models are based on the experimental measurements of Vahrenkamp at a 2-amp ion beam operating condition. The cylindrically symmetric beam of constant velocity ions is modeled with continuous radial source and focusing functions across 'plane' grids with similar angular distribution functions. A computer program is used to evaluate the double integral for current densities in the near field and to obtain a far field approximation beyond 10 grid radii. The utility of the model is demonstrated for (1) calculating the directed thrust and (2) determining the impingement levels on various spacecraft surfaces from a two-axis gimballed, 2 x 3 thruster array.

Induced Eddy Currents in Simple Conductive Geometries: Mathematical Formalism Describes the Excitation of Electrical Eddy Currents in a Time-Varying Magnetic Field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nagel, James R.

In this paper, a complete mathematical formalism is introduced to describe the excitation of electrical eddy currents due to a time-varying magnetic field. The process works by applying a quasistatic approximation to Ampere's law and then segregating the magnetic field into impressed and induced terms. The result is a nonhomogeneous vector Helmholtz equation that can be analytically solved for many practical geometries. Four demonstration cases are then solved under a constant excitation field over all space—an infinite slab in one dimension, a longitudinal cylinder in two dimensions, a transverse cylinder in two dimensions, and a sphere in three dimensions. Numericalmore » simulations are also performed in parallel with analytic computations, all of which verify the accuracy of the derived expressions.« less

Analytical approximations to the dynamics of an array of coupled DC SQUIDs

NASA Astrophysics Data System (ADS)

Berggren, Susan; Palacios, Antonio

2014-04-01

Coupled dynamical systems that operate near the onset of a bifurcation can lead, under certain conditions, to strong signal amplification effects. Over the past years we have studied this generic feature on a wide range of systems, including: magnetic and electric fields sensors, gyroscopic devices, and arrays of loops of superconducting quantum interference devices, also known as SQUIDs. In this work, we consider an array of SQUID loops connected in series as a case study to derive asymptotic analytical approximations to the exact solutions through perturbation analysis. Two approaches are considered. First, a straightforward expansion in which the non-linear parameter related to the inductance of the DC SQUID is treated as the small perturbation parameter. Second, a more accurate procedure that considers the SQUID phase dynamics as non-uniform motion on a circle. This second procedure is readily extended to the series array and it could serve as a mathematical framework to find approximate solutions to related complex systems with high-dimensionality. To the best of our knowledge, an approximate analytical solutions to an array of SQUIDs has not been reported yet in the literature.

Neural Network and Regression Approximations in High Speed Civil Transport Aircraft Design Optimization

NASA Technical Reports Server (NTRS)

Patniak, Surya N.; Guptill, James D.; Hopkins, Dale A.; Lavelle, Thomas M.

1998-01-01

Nonlinear mathematical-programming-based design optimization can be an elegant method. However, the calculations required to generate the merit function, constraints, and their gradients, which are frequently required, can make the process computational intensive. The computational burden can be greatly reduced by using approximating analyzers derived from an original analyzer utilizing neural networks and linear regression methods. The experience gained from using both of these approximation methods in the design optimization of a high speed civil transport aircraft is the subject of this paper. The Langley Research Center's Flight Optimization System was selected for the aircraft analysis. This software was exercised to generate a set of training data with which a neural network and a regression method were trained, thereby producing the two approximating analyzers. The derived analyzers were coupled to the Lewis Research Center's CometBoards test bed to provide the optimization capability. With the combined software, both approximation methods were examined for use in aircraft design optimization, and both performed satisfactorily. The CPU time for solution of the problem, which had been measured in hours, was reduced to minutes with the neural network approximation and to seconds with the regression method. Instability encountered in the aircraft analysis software at certain design points was also eliminated. On the other hand, there were costs and difficulties associated with training the approximating analyzers. The CPU time required to generate the input-output pairs and to train the approximating analyzers was seven times that required for solution of the problem.

Predicting synchrony in heterogeneous pulse coupled oscillators

NASA Astrophysics Data System (ADS)

Talathi, Sachin S.; Hwang, Dong-Uk; Miliotis, Abraham; Carney, Paul R.; Ditto, William L.

2009-08-01

Pulse coupled oscillators (PCOs) represent an ubiquitous model for a number of physical and biological systems. Phase response curves (PRCs) provide a general mathematical framework to analyze patterns of synchrony generated within these models. A general theoretical approach to account for the nonlinear contributions from higher-order PRCs in the generation of synchronous patterns by the PCOs is still lacking. Here, by considering a prototypical example of a PCO network, i.e., two synaptically coupled neurons, we present a general theory that extends beyond the weak-coupling approximation, to account for higher-order PRC corrections in the derivation of an approximate discrete map, the stable fixed point of which can predict the domain of 1:1 phase locked synchronous states generated by the PCO network.

The effect of the earth's rotation on ground water motion.

PubMed

Loáiciga, Hugo A

2007-01-01

The average pore velocity of ground water according to Darcy's law is a function of the fluid pressure gradient and the gravitational force (per unit volume of ground water) and of aquifer properties. There is also an acceleration exerted on ground water that arises from the Earth's rotation. The magnitude and direction of this rotation-induced force are determined in exact mathematical form in this article. It is calculated that the gravitational force is at least 300 times larger than the largest rotation-induced force anywhere on Earth, the latter force being maximal along the equator and approximately equal to 34 N/m(3) there. This compares with a gravitational force of approximately 10(4) N/m(3).

On approximation of non-Newtonian fluid flow by the finite element method

NASA Astrophysics Data System (ADS)

Svácek, Petr

2008-08-01

In this paper the problem of numerical approximation of non-Newtonian fluid flow with free surface is considered. Namely, the flow of fresh concrete is addressed. Industrial mixtures often behaves like non-Newtonian fluids exhibiting a yield stress that needs to be overcome for the flow to take place, cf. [R.B. Bird, R.C. Armstrong, O. Hassager, Dynamics of Polymeric Liquids, vol. 1, Fluid Mechanics, Wiley, New York, 1987; R.P. Chhabra, J.F. Richardson, Non-Newtonian Flow in the Process Industries, Butterworth-Heinemann, London, 1999]. The main interest is paid to the mathematical formulation of the problem and to discretization with the aid of finite element method. The described numerical procedure is applied onto the solution of several problems.

Direct and inverse problems of studying the properties of multilayer nanostructures based on a two-dimensional model of X-ray reflection and scattering

NASA Astrophysics Data System (ADS)

Khachaturov, R. V.

2014-06-01

A mathematical model of X-ray reflection and scattering by multilayered nanostructures in the quasi-optical approximation is proposed. X-ray propagation and the electric field distribution inside the multilayered structure are considered with allowance for refraction, which is taken into account via the second derivative with respect to the depth of the structure. This model is used to demonstrate the possibility of solving inverse problems in order to determine the characteristics of irregularities not only over the depth (as in the one-dimensional problem) but also over the length of the structure. An approximate combinatorial method for system decomposition and composition is proposed for solving the inverse problems.

Teacher Enhancement and Preparation Programs

NASA Technical Reports Server (NTRS)

1995-01-01

These two programs provide opportunities for K-12 teachers of mathematics, science, and technology to spend two weeks at a NASA center learning about aeronautics and space. Participants are selected by peer review from a contracting agent that assists NASA in administering the program. Each teacher receives a stipend that covers the cost of travel, housing, meals, and graduate credit. NEWMAST provides for approximately 100 secondary teachers, and NEWTEST is a program designed to meet the needs of approximately 125 elementary teachers each summer. Teachers are provided with a wide variety of experiences including research laboratory observations, presentations, and 'shadowships'. Individual and team projects are used to enhance the participants knowledge of space and aeronautics and to motivate the teachers to incorporate the summer workshop activities into their classrooms.

Prediction of the Main Engine Power of a New Container Ship at the Preliminary Design Stage

NASA Astrophysics Data System (ADS)

Cepowski, Tomasz

2017-06-01

The paper presents mathematical relationships that allow us to forecast the estimated main engine power of new container ships, based on data concerning vessels built in 2005-2015. The presented approximations allow us to estimate the engine power based on the length between perpendiculars and the number of containers the ship will carry. The approximations were developed using simple linear regression and multivariate linear regression analysis. The presented relations have practical application for estimation of container ship engine power needed in preliminary parametric design of the ship. It follows from the above that the use of multiple linear regression to predict the main engine power of a container ship brings more accurate solutions than simple linear regression.

Ispitivanje predznanja djece prilikom upisa u prvi razred osnovne skole (Testing the Level of Knowledge of Children on Enrollment in the first Grade of Primary School).

ERIC Educational Resources Information Center

Kustreba, T.

1969-01-01

This document is an English-language abstract (approximately 1,500 words) of an analysis of tests given to newly enrolled first graders in Zagreb public schools. The analysis of the results of the investigation are presented into three sections: reading, mathematics, and social studies. The aim of the examination in the rudiments of literacy was…

Torsion Tests of 24S-T Aluminum-alloy Noncircular Bar and Tubing

NASA Technical Reports Server (NTRS)

Moore, R L; Paul, D A

1943-01-01

Tests of 24S-T aluminum alloy have been made to determine the yield and ultimate strengths in torsion of noncircular bar and tubing. An approximate basis for predicting these torsional strength characteristics has been indicated. The results show that the torsional stiffness and maximum shearing stresses within the elastic range may be computed quite closely by means of existing formulas based on mathematical analysis and the membrane analogy.

Design of a Linear Gaussian Control Law for an Adaptive Optics System

DTIC Science & Technology

1990-12-01

3-7 3.4. X-Axis Slice of Actuator :#49 Influence Function .. .. .... ...... ...... 3-9 3.5. Approximate Influence Function for Actuator #49... influence function is a mathematical representation of the effect of a single ac- tuator voltage on the local mirror shape. Usually, the influence ... function is nonzero only in the vicinity of the actuator: the influence function of an actualor has a limited spa- tial domain. Several factors affect the

Mathematical Aspects of Finite Element Methods for Incompressible Viscous Flows.

DTIC Science & Technology

1986-09-01

respectively. Here h is a parameter which is usually related to the size of the grid associated with the finite element partitioning of Q. Then one... grid and of not at least performing serious mesh refinement studies. It also points out the usefulness of rigorous results concerning the stability...overconstrained the .1% approximate velocity field. However, by employing different grids for the ’z pressure and velocity fields, the linear-constant

Inferring interactions in complex microbial communities from nucleotide sequence data and environmental parameters

PubMed Central

Shang, Yu; Sikorski, Johannes; Bonkowski, Michael; Fiore-Donno, Anna-Maria; Kandeler, Ellen; Marhan, Sven; Boeddinghaus, Runa S.; Solly, Emily F.; Schrumpf, Marion; Schöning, Ingo; Wubet, Tesfaye; Buscot, Francois; Overmann, Jörg

2017-01-01

Interactions occur between two or more organisms affecting each other. Interactions are decisive for the ecology of the organisms. Without direct experimental evidence the analysis of interactions is difficult. Correlation analyses that are based on co-occurrences are often used to approximate interaction. Here, we present a new mathematical model to estimate the interaction strengths between taxa, based on changes in their relative abundances across environmental gradients. PMID:28288199

Mathematical justification of a viscoelastic elliptic membrane problem

NASA Astrophysics Data System (ADS)

Castiñeira, Gonzalo; Rodríguez-Arós, Ángel

2017-12-01

We consider a family of linearly viscoelastic elliptic shells, and we use asymptotic analysis to justify that what we have identified as the two-dimensional viscoelastic elliptic membrane problem is an accurate approximation when the thickness of the shell tends to zero. Most noticeable is that the limit problem includes a long-term memory that takes into account the previous history of deformations. We provide convergence results which justify our asymptotic approach.

Monte Carlo Calculations of the Properties of Solid Nitromethane

DTIC Science & Technology

1991-09-01

a pressure of 6.0 GPa (Cromer, Ryan, and Schiferl 1985). The neutron spectroscopy was instrumental in allowing an accurate mathematical description...rotation of the methyl group is only slightly hindered (Cromer, Ryan, and Schiferl 1985). At 3.5 GPa, the x-ray diffraction data inferred that the... Schiferl (1985). We found that below 3.5 GPa, the classical barrier height for rotation was approximately room temperature, consi.tent with a weakly

Linearized Alternating Direction Method of Multipliers for Constrained Nonconvex Regularized Optimization

DTIC Science & Technology

2016-11-22

structure of the graph, we replace the ℓ1- norm by the nonconvex Capped -ℓ1 norm , and obtain the Generalized Capped -ℓ1 regularized logistic regression...X. M. Yuan. Linearized augmented lagrangian and alternating direction methods for nuclear norm minimization. Mathematics of Computation, 82(281):301...better approximations of ℓ0- norm theoretically and computationally beyond ℓ1- norm , for example, the compressive sensing (Xiao et al., 2011). The

JPRS Report, Science & Technology USSR: Physics & Mathematics

DTIC Science & Technology

1991-03-07

field B < mw 2 / e (mw - mass of gauge W- boson ) does not invalidate this approximation inasmuch as the respective momentum integrals remain...model (sin29w = Vi where 0W - angle of W- boson momentum) indicate that, in an ultras- trong magnetic field, photon fusion produces more elec- tron... boson field throughout the 8^8* range. This study was made within the scope of Project N 344 in the Government Program "High-Temperature

Development of an acoustical-mathematical model of a human heart for a fast diagnosis of preinfarction angina by pulse

NASA Astrophysics Data System (ADS)

Glotov, V. P.; Vadov, R. A.; Kolobaev, P. A.

2004-09-01

An approximate model for nonlinear self-induced vibrations of a myocardium pump which involves in situ experiments on evaluation of the resonance, Q-factor, and elastic parameters of a cardiac circuit (cavity) in the frequency range of 0.1 15 Hz is presented. A concept of a fast diagnosis of human preinfarction angina by the pulse at the wrist is proposed.

Mathematical modeling of damage in unidirectional composites

NASA Technical Reports Server (NTRS)

Goree, J. G.; Dharani, L. R.; Jones, W. F.

1981-01-01

A review of some approximate analytical models for damaged, fiber reinforced composite materials is presented. Using the classical shear lag stress displacement assumption, solutions are presented for a unidirectional laminate containing a notch, a rectangular cut-out, and a circular hole. The models account for longitudinal matrix yielding and splitting as well as transverse matrix yielding and fiber breakage. The constraining influence of a cover sheet on the unidirectional laminate is also modeled.

Discrete Applied Mathematics

DTIC Science & Technology

1993-05-31

program. In paper [28], we give a brief and elementary proof of a result of Hoffman [1952) about approximate solutions to systems, of linear inequalities...UCLA, Vestvood, CA, February 1993. " Linear Problems: Formulation and Solution," International Linear Algebra Society, Pensacola, FL, May 1993. Denise S...thresAold If there is a number h and a linear k-separator w assigning a real number to each vertex so that for any subset S of vertices, the sum of w

Radiation Diffusion:. AN Overview of Physical and Numerical Concepts

NASA Astrophysics Data System (ADS)

Graziani, Frank

2005-12-01

An overview of the physical and mathematical foundations of radiation transport is given. Emphasis is placed on how the diffusion approximation and its transport corrections arise. An overview of the numerical handling of radiation diffusion coupled to matter is also given. Discussions center on partial temperature and grey methods with comments concerning fully implicit methods. In addition finite difference, finite element and Pert representations of the div-grad operator is also discussed

Melanoma Cell Colony Expansion Parameters Revealed by Approximate Bayesian Computation

PubMed Central

Vo, Brenda N.; Drovandi, Christopher C.; Pettitt, Anthony N.; Pettet, Graeme J.

2015-01-01

In vitro studies and mathematical models are now being widely used to study the underlying mechanisms driving the expansion of cell colonies. This can improve our understanding of cancer formation and progression. Although much progress has been made in terms of developing and analysing mathematical models, far less progress has been made in terms of understanding how to estimate model parameters using experimental in vitro image-based data. To address this issue, a new approximate Bayesian computation (ABC) algorithm is proposed to estimate key parameters governing the expansion of melanoma cell (MM127) colonies, including cell diffusivity, D, cell proliferation rate, λ, and cell-to-cell adhesion, q, in two experimental scenarios, namely with and without a chemical treatment to suppress cell proliferation. Even when little prior biological knowledge about the parameters is assumed, all parameters are precisely inferred with a small posterior coefficient of variation, approximately 2–12%. The ABC analyses reveal that the posterior distributions of D and q depend on the experimental elapsed time, whereas the posterior distribution of λ does not. The posterior mean values of D and q are in the ranges 226–268 µm2h−1, 311–351 µm2h−1 and 0.23–0.39, 0.32–0.61 for the experimental periods of 0–24 h and 24–48 h, respectively. Furthermore, we found that the posterior distribution of q also depends on the initial cell density, whereas the posterior distributions of D and λ do not. The ABC approach also enables information from the two experiments to be combined, resulting in greater precision for all estimates of D and λ. PMID:26642072

Systematic investigation of non-Boussinesq effects in variable-density groundwater flow simulations.

PubMed

Guevara Morel, Carlos R; van Reeuwijk, Maarten; Graf, Thomas

2015-12-01

The validity of three mathematical models describing variable-density groundwater flow is systematically evaluated: (i) a model which invokes the Oberbeck-Boussinesq approximation (OB approximation), (ii) a model of intermediate complexity (NOB1) and (iii) a model which solves the full set of equations (NOB2). The NOB1 and NOB2 descriptions have been added to the HydroGeoSphere (HGS) model, which originally contained an implementation of the OB description. We define the Boussinesq parameter ερ=βω Δω where βω is the solutal expansivity and Δω is the characteristic difference in solute mass fraction. The Boussinesq parameter ερ is used to systematically investigate three flow scenarios covering a range of free and mixed convection problems: 1) the low Rayleigh number Elder problem (Van Reeuwijk et al., 2009), 2) a convective fingering problem (Xie et al., 2011) and 3) a mixed convective problem (Schincariol et al., 1994). Results indicate that small density differences (ερ≤ 0.05) produce no apparent changes in the total solute mass in the system, plume penetration depth, center of mass and mass flux independent of the mathematical model used. Deviations between OB, NOB1 and NOB2 occur for large density differences (ερ>0.12), where lower description levels will underestimate the vertical plume position and overestimate mass flux. Based on the cases considered here, we suggest the following guidelines for saline convection: the OB approximation is valid for cases with ερ<0.05, and the full NOB set of equations needs to be used for cases with ερ>0.10. Whether NOB effects are important in the intermediate region differ from case to case. Copyright © 2015 Elsevier B.V. All rights reserved.

Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arampatzis, Giorgos, E-mail: garab@math.uoc.gr; Katsoulakis, Markos A., E-mail: markos@math.umass.edu; Plechac, Petr, E-mail: plechac@math.udel.edu

2012-10-01

We present a mathematical framework for constructing and analyzing parallel algorithms for lattice kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in spatially distributed, non-equilibrium physiochemical processes with complex chemistry and transport micro-mechanisms. Rather than focusing on constructing exactly the stochastic trajectories, our approach relies on approximating the evolution of observables, such as density, coverage, correlations and so on. More specifically, we develop a spatial domain decomposition of the Markov operator (generator) that describes the evolution of all observables according to the kinetic Monte Carlo algorithm. This domain decompositionmore » corresponds to a decomposition of the Markov generator into a hierarchy of operators and can be tailored to specific hierarchical parallel architectures such as multi-core processors or clusters of Graphical Processing Units (GPUs). Based on this operator decomposition, we formulate parallel Fractional step kinetic Monte Carlo algorithms by employing the Trotter Theorem and its randomized variants; these schemes, (a) are partially asynchronous on each fractional step time-window, and (b) are characterized by their communication schedule between processors. The proposed mathematical framework allows us to rigorously justify the numerical and statistical consistency of the proposed algorithms, showing the convergence of our approximating schemes to the original serial KMC. The approach also provides a systematic evaluation of different processor communicating schedules. We carry out a detailed benchmarking of the parallel KMC schemes using available exact solutions, for example, in Ising-type systems and we demonstrate the capabilities of the method to simulate complex spatially distributed reactions at very large scales on GPUs. Finally, we discuss work load balancing between processors and propose a re-balancing scheme based on probabilistic mass transport methods.« less

Quantification of ETS exposure in hospitality workers who have never smoked

PubMed Central

2010-01-01

Background Environmental Tobacco Smoke (ETS) was classified as human carcinogen (K1) by the German Research Council in 1998. According to epidemiological studies, the relative risk especially for lung cancer might be twice as high in persons who have never smoked but who are in the highest exposure category, for example hospitality workers. In order to implement these results in the German regulations on occupational illnesses, a valid method is needed to retrospectively assess the cumulative ETS exposure in the hospitality environment. Methods A literature-based review was carried out to locate a method that can be used for the German hospitality sector. Studies assessing ETS exposure using biological markers (for example urinary cotinine, DNA adducts) or questionnaires were excluded. Biological markers are not considered relevant as they assess exposure only over the last hours, weeks or months. Self-reported exposure based on questionnaires also does not seem adequate for medico-legal purposes. Therefore, retrospective exposure assessment should be based on mathematical models to approximate past exposure. Results For this purpose a validated model developed by Repace and Lowrey was considered appropriate. It offers the possibility of retrospectively assessing exposure with existing parameters (such as environmental dimensions, average number of smokers, ventilation characteristics and duration of exposure). The relative risk of lung cancer can then be estimated based on the individual cumulative exposure of the worker. Conclusion In conclusion, having adapted it to the German hospitality sector, an existing mathematical model appears to be capable of approximating the cumulative exposure. However, the level of uncertainty of these approximations has to be taken into account, especially for diseases with a long latency period such as lung cancer. PMID:20704719

Quantification of ETS exposure in hospitality workers who have never smoked.

PubMed

Kolb, Stefanie; Brückner, Ulrike; Nowak, Dennis; Radon, Katja

2010-08-12

Environmental Tobacco Smoke (ETS) was classified as human carcinogen (K1) by the German Research Council in 1998. According to epidemiological studies, the relative risk especially for lung cancer might be twice as high in persons who have never smoked but who are in the highest exposure category, for example hospitality workers. In order to implement these results in the German regulations on occupational illnesses, a valid method is needed to retrospectively assess the cumulative ETS exposure in the hospitality environment. A literature-based review was carried out to locate a method that can be used for the German hospitality sector. Studies assessing ETS exposure using biological markers (for example urinary cotinine, DNA adducts) or questionnaires were excluded. Biological markers are not considered relevant as they assess exposure only over the last hours, weeks or months. Self-reported exposure based on questionnaires also does not seem adequate for medico-legal purposes. Therefore, retrospective exposure assessment should be based on mathematical models to approximate past exposure. For this purpose a validated model developed by Repace and Lowrey was considered appropriate. It offers the possibility of retrospectively assessing exposure with existing parameters (such as environmental dimensions, average number of smokers, ventilation characteristics and duration of exposure). The relative risk of lung cancer can then be estimated based on the individual cumulative exposure of the worker. In conclusion, having adapted it to the German hospitality sector, an existing mathematical model appears to be capable of approximating the cumulative exposure. However, the level of uncertainty of these approximations has to be taken into account, especially for diseases with a long latency period such as lung cancer.

Fluid reasoning predicts future mathematics among children and adolescents

PubMed Central

Green, Chloe T.; Bunge, Silvia A.; Chiongbian, Victoria Briones; Barrow, Maia; Ferrer, Emilio

2017-01-01

The aim of this longitudinal study was to determine whether fluid reasoning (FR) plays a significant role in the acquisition of mathematics skills, above and beyond the effects of other cognitive and numerical abilities. Using a longitudinal cohort sequential design, we examined how FR measured at three assessment occasions, spaced approximately 1.5 years apart, predicted math outcomes for a group of 69 participants between ages 6 and 21 across all three assessment occasions. We used structural equation modeling (SEM) to examine the direct and indirect relations between children's prior cognitive abilities and their future math achievement. A model including age, FR, vocabulary, and spatial skills accounted for 90% of the variance in future math achievement. In this model, FR was the only significant predictor of future math achievement; neither age, vocabulary, nor spatial skills were significant predictors. Thus, FR was the only predictor of future math achievement across a wide age range that spanned primary and secondary school. These findings build on Cattell's conceptualization of FR (Cattell, 1987) as a scaffold for learning, showing that this domain-general ability supports the acquisition of rudimentary math skills as well as the ability to solve more complex mathematical problems. PMID:28152390

Quantum dots as contrast agents for endoscopy: mathematical modeling and experimental validation of the optimal excitation wavelength

NASA Astrophysics Data System (ADS)

Roy, Mathieu; DaCosta, Ralph S.; Weersink, Robert; Netchev, George; Davidson, Sean R. H.; Chan, Warren; Wilson, Brian C.

2007-02-01

Our group is investigating the use of ZnS-capped CdSe quantum dot (QD) bioconjugates combined with fluorescence endoscopy for improved early cancer detection in the esophagus, colon and lung. A major challenge in using fluorescent contrast agents in vivo is to extract the relevant signal from the tissue autofluorescence (AF). Our studies are aimed at maximizing the QD signal to AF background ratio (SBR) to facilitate detection. This work quantitatively evaluates the effect of the excitation wavelength on the SBR, using both experimental measurements and mathematical modeling. Experimental SBR measurements were done by imaging QD solutions placed onto (surface) or embedded in (sub-surface) ex vivo murine tissue samples (brain, kidney, liver, lung), using a polymethylmethacrylate (PMMA) microchannel phantom. The results suggest that the maximum contrast is reached when the excitation wavelength is set at 400+/-20 μm for the surface configuration. For the sub-surface configuration, the optimal excitation wavelength varies with the tissue type and QD emission wavelengths. Our mathematical model, based on an approximation to the diffusion equation, successfully predicts the optimal excitation wavelength for the surface configuration, but needs further modifications to be accurate in the sub-surface configuration.

Dose conversion coefficients based on the Chinese mathematical phantom and MCNP code for external photon irradiation.

PubMed

Qiu, Rui; Li, Junli; Zhang, Zhan; Liu, Liye; Bi, Lei; Ren, Li

2009-02-01

A set of conversion coefficients from kerma free-in-air to the organ-absorbed dose are presented for external monoenergetic photon beams from 10 keV to 10 MeV based on the Chinese mathematical phantom, a whole-body mathematical phantom model. The model was developed based on the methods of the Oak Ridge National Laboratory mathematical phantom series and data from the Chinese Reference Man and the Reference Asian Man. This work is carried out to obtain the conversion coefficients based on this model, which represents the characteristics of the Chinese population, as the anatomical parameters of the Chinese are different from those of Caucasians. Monte Carlo simulation with MCNP code is carried out to calculate the organ dose conversion coefficients. Before the calculation, the effects from the physics model and tally type are investigated, considering both the calculation efficiency and precision. In the calculation irradiation conditions include anterior-posterior, posterior-anterior, right lateral, left lateral, rotational and isotropic geometries. Conversion coefficients from this study are compared with those recommended in the Publication 74 of International Commission on Radiological Protection (ICRP74) since both the sets of data are calculated with mathematical phantoms. Overall, consistency between the two sets of data is observed and the difference for more than 60% of the data is below 10%. However, significant deviations are also found, mainly for the superficial organs (up to 65.9%) and bone surface (up to 66%). The big difference of the dose conversion coefficients for the superficial organs at high photon energy could be ascribed to kerma approximation for the data in ICRP74. Both anatomical variations between races and the calculation method contribute to the difference of the data for bone surface.

Numerical cognition is resilient to dramatic changes in early sensory experience.

PubMed

Kanjlia, Shipra; Feigenson, Lisa; Bedny, Marina

2018-06-20

Humans and non-human animals can approximate large visual quantities without counting. The approximate number representations underlying this ability are noisy, with the amount of noise proportional to the quantity being represented. Numerate humans also have access to a separate system for representing exact quantities using number symbols and words; it is this second, exact system that supports most of formal mathematics. Although numerical approximation abilities and symbolic number abilities are distinct in representational format and in their phylogenetic and ontogenetic histories, they appear to be linked throughout development--individuals who can more precisely discriminate quantities without counting are better at math. The origins of this relationship are debated. On the one hand, symbolic number abilities may be directly linked to, perhaps even rooted in, numerical approximation abilities. On the other hand, the relationship between the two systems may simply reflect their independent relationships with visual abilities. To test this possibility, we asked whether approximate number and symbolic math abilities are linked in congenitally blind individuals who have never experienced visual sets or used visual strategies to learn math. Congenitally blind and blind-folded sighted participants completed an auditory numerical approximation task, as well as a symbolic arithmetic task and non-math control tasks. We found that the precision of approximate number representations was identical across congenitally blind and sighted groups, suggesting that the development of the Approximate Number System (ANS) does not depend on visual experience. Crucially, the relationship between numerical approximation and symbolic math abilities is preserved in congenitally blind individuals. These data support the idea that the Approximate Number System and symbolic number abilities are intrinsically linked, rather than indirectly linked through visual abilities. Copyright © 2018. Published by Elsevier B.V.

Mathematical model of microbicidal flow dynamics and optimization of rheological properties for intra-vaginal drug delivery: Role of tissue mechanics and fluid rheology.

PubMed

Anwar, Md Rajib; Camarda, Kyle V; Kieweg, Sarah L

2015-06-25

Topically applied microbicide gels can provide a self-administered and effective strategy to prevent sexually transmitted infections (STIs). We have investigated the interplay between vaginal tissue elasticity and the yield-stress of non-Newtonian fluids during microbicide deployment. We have developed a mathematical model of tissue deformation driven spreading of microbicidal gels based on thin film lubrication approximation and demonstrated the effect of tissue elasticity and fluid yield-stress on the spreading dynamics. Our results show that both elasticity of tissue and yield-stress rheology of gel are strong determinants of the coating behavior. An optimization framework has been demonstrated which leverages the flow dynamics of yield-stress fluid during deployment to maximize retention while reaching target coating length for a given tissue elasticity. Copyright © 2015 Elsevier Ltd. All rights reserved.

Functional Concept of a Multipurpose Actuator: Design and Analysis

NASA Astrophysics Data System (ADS)

Krivka, Vladimir

2018-05-01

The principles of operation (dynamic characteristics) of electromagnetic devices are discussed using a threephase multifunctional actuator as an example, whose major limitations are associated with the magnetic field nonlinearity and control over the magnetic forces affecting the moving element. The investigation is carried out using the methods of physico-mathematical modeling and a full-scale experiment. A physico-mathematical model is proposed, which is based on acceptable approximations and simplifications, the replacement of a nonlinear (but periodic) magnetic field in a quasi-stationary state by a harmonic magnetic field being the most important among them. The magnetic permeability in every cell of the discretization grid is assumed to be constant and corresponds to the local magnetic flux density. The features and characteristics obtained through this modeling are quite consistent with the observed behavior and measured values. It is shown that the dependence of friction coefficient on its velocity exhibits a hysteresis.

A model for precalculus students to determine the resonance frequency of a trumpet mouthpiece

NASA Astrophysics Data System (ADS)

Chapman, Robert C.

2004-05-01

The trumpet mouthpiece as a Helmholtz resonator is used to show precalculus students a mathematical model for determining the approximate resonance frequency of the mouthpiece. The mathematics is limited to algebra and trigonometry. Using a system of mouthpieces that have interchangeable cups and backbores, students are introduced to the acoustics of this resonator. By gathering data on 51 different configurations of mouthpieces, the author modifies the existing Helmholtz resonator equation to account for both cup volumes and backbore configurations. Students then use this model for frequency predictions. Included are how to measure the different physical attributes of a trumpet mouthpiece at minimal cost. This includes methods for measuring cup volume, backbore volume, backbore length, throat area, etc. A portion of this phase is de-signed for students to become acquainted with some of the vocabulary of acoustics and the physics of sound.

Integration of the Rotation of an Earth-like Body as a Perturbed Spherical Rotor

NASA Astrophysics Data System (ADS)

Ferrer, Sebastián; Lara, Martin

2010-05-01

For rigid bodies close to a sphere, we propose an analytical solution that is free from elliptic integrals and functions, and can be fundamental for application to perturbed problems. After reordering the Hamiltonian as a perturbed spherical rotor, the Lie-series solution is generated up to an arbitrary order. Using the inertia parameters of different solar system bodies, the comparison of the approximate series solution with the exact analytical one shows that the precision reached with relatively low orders is at the same level of the observational accuracy for the Earth and Mars. Thus, for instance, the periodic errors of the mathematical solution are confined to the microarcsecond level with a simple second-order truncation for the Earth. On the contrary, higher orders are required for the mathematical solution to reach a precision at the expected level of accuracy of proposed new theories for the rotational dynamics of the Moon.

Conservation laws with coinciding smooth solutions but different conserved variables

NASA Astrophysics Data System (ADS)

Colombo, Rinaldo M.; Guerra, Graziano

2018-04-01

Consider two hyperbolic systems of conservation laws in one space dimension with the same eigenvalues and (right) eigenvectors. We prove that solutions to Cauchy problems with the same initial data differ at third order in the total variation of the initial datum. As a first application, relying on the classical Glimm-Lax result (Glimm and Lax in Decay of solutions of systems of nonlinear hyperbolic conservation laws. Memoirs of the American Mathematical Society, No. 101. American Mathematical Society, Providence, 1970), we obtain estimates improving those in Saint-Raymond (Arch Ration Mech Anal 155(3):171-199, 2000) on the distance between solutions to the isentropic and non-isentropic inviscid compressible Euler equations, under general equations of state. Further applications are to the general scalar case, where rather precise estimates are obtained, to an approximation by Di Perna of the p-system and to a traffic model.

Collaborative, Sequential and Isolated Decisions in Design

NASA Technical Reports Server (NTRS)

Lewis, Kemper; Mistree, Farrokh

1997-01-01

The Massachusetts Institute of Technology (MIT) Commission on Industrial Productivity, in their report Made in America, found that six recurring weaknesses were hampering American manufacturing industries. The two weaknesses most relevant to product development were 1) technological weakness in development and production, and 2) failures in cooperation. The remedies to these weaknesses are considered the essential twin pillars of CE: 1) improved development process, and 2) closer cooperation. In the MIT report, it is recognized that total cooperation among teams in a CE environment is rare in American industry, while the majority of the design research in mathematically modeling CE has assumed total cooperation. In this paper, we present mathematical constructs, based on game theoretic principles, to model degrees of collaboration characterized by approximate cooperation, sequential decision making and isolation. The design of a pressure vessel and a passenger aircraft are included as illustrative examples.

A mathematical model describes the malignant transformation of low grade gliomas: Prognostic implications.

PubMed

Bogdańska, Magdalena U; Bodnar, Marek; Piotrowska, Monika J; Murek, Michael; Schucht, Philippe; Beck, Jürgen; Martínez-González, Alicia; Pérez-García, Víctor M

2017-01-01

Gliomas are the most frequent type of primary brain tumours. Low grade gliomas (LGGs, WHO grade II gliomas) may grow very slowly for the long periods of time, however they inevitably cause death due to the phenomenon known as the malignant transformation. This refers to the transition of LGGs to more aggressive forms of high grade gliomas (HGGs, WHO grade III and IV gliomas). In this paper we propose a mathematical model describing the spatio-temporal transition of LGGs into HGGs. Our modelling approach is based on two cellular populations with transitions between them being driven by the tumour microenvironment transformation occurring when the tumour cell density grows beyond a critical level. We show that the proposed model describes real patient data well. We discuss the relationship between patient prognosis and model parameters. We approximate tumour radius and velocity before malignant transformation as well as estimate the onset of this process.

The YAV-8B simulation and modeling. Volume 2: Program listing

NASA Technical Reports Server (NTRS)

1983-01-01

Detailed mathematical models of varying complexity representative of the YAV-8B aircraft are defined and documented. These models are used in parameter estimation and in linear analysis computer programs while investigating YAV-8B aircraft handling qualities. Both a six degree of freedom nonlinear model and a linearized three degree of freedom longitudinal and lateral directional model were developed. The nonlinear model is based on the mathematical model used on the MCAIR YAV-8B manned flight simulator. This simulator model has undergone periodic updating based on the results of approximately 360 YAV-8B flights and 8000 hours of wind tunnel testing. Qualified YAV-8B flight test pilots have commented that the handling qualities characteristics of the simulator are quite representative of the real aircraft. These comments are validated herein by comparing data from both static and dynamic flight test maneuvers to the same obtained using the nonlinear program.

Modeling Selection and Extinction Mechanisms of Biological Systems

NASA Astrophysics Data System (ADS)

Amirjanov, Adil

In this paper, the behavior of a genetic algorithm is modeled to enhance its applicability as a modeling tool of biological systems. A new description model for selection mechanism is introduced which operates on a portion of individuals of population. The extinction and recolonization mechanism is modeled, and solving the dynamics analytically shows that the genetic drift in the population with extinction/recolonization is doubled. The mathematical analysis of the interaction between selection and extinction/recolonization processes is carried out to assess the dynamics of motion of the macroscopic statistical properties of population. Computer simulations confirm that the theoretical predictions of described models are in good approximations. A mathematical model of GA dynamics was also examined, which describes the anti-predator vigilance in an animal group with respect to a known analytical solution of the problem, and showed a good agreement between them to find the evolutionarily stable strategies.

Polarization independent thermally tunable erbium-doped fiber amplifier gain equalizer using a cascaded Mach-Zehnder coupler.

PubMed

Sahu, P P

2008-02-10

A thermally tunable erbium-doped fiber amplifier (EDFA) gain equalizer filter based on compact point symmetric cascaded Mach-Zehnder (CMZ) coupler is presented with its mathematical model and is found to be polarization dependent due to stress anisotropy caused by local heating for thermo-optic phase change from its mathematical analysis. A thermo-optic delay line structure with a stress releasing groove is proposed and designed for the reduction of polarization dependent characteristics of the high index contrast point symmetric delay line structure of the device. It is found from thermal analysis by using an implicit finite difference method that temperature gradients of the proposed structure, which mainly causes the release of stress anisotropy, is approximately nine times more than that of the conventional structure. It is also seen that the EDFA gain equalized spectrum by using the point symmetric CMZ device based on the proposed structure is almost polarization independent.

[Mathematic concept model of accumulation of functional disorders associated with environmental factors].

PubMed

Zaĭtseva, N V; Trusov, P V; Kir'ianov, D A

2012-01-01

The mathematic concept model presented describes accumulation of functional disorders associated with environmental factors, plays predictive role and is designed for assessments of possible effects caused by heterogenous factors with variable exposures. Considering exposure changes with self-restoration process opens prospects of using the model to evaluate, analyse and manage occupational risks. To develop current theoretic approaches, the authors suggested a model considering age-related body peculiarities, systemic interactions of organs, including neuro-humoral regulation, accumulation of functional disorders due to external factors, rehabilitation of functions during treatment. General objective setting covers defining over a hundred unknow coefficients that characterize speed of various processes within the body. To solve this problem, the authors used iteration approach, successive identification, that starts from the certain primary approximation of the model parameters and processes subsequent updating on the basis of new theoretic and empirical knowledge.

The effect of gas and fluid flows on nonlinear lateral vibrations of rotating drill strings

NASA Astrophysics Data System (ADS)

Khajiyeva, Lelya; Kudaibergenov, Askar; Kudaibergenov, Askat

2018-06-01

In this work we develop nonlinear mathematical models describing coupled lateral vibrations of a rotating drill string under the effect of external supersonic gas and internal fluid flows. An axial compressive load and a torque also affect the drill string. The mathematical models are derived by the use of Novozhilov's nonlinear theory of elasticity with implementation of Hamilton's variation principle. Expressions for the gas flow pressure are determined according to the piston theory. The fluid flow is considered as added mass inside the curved tube of the drill string. Using an algorithm developed in the Mathematica computation program on the basis of the Galerkin approach and the stiffness switching method the numerical solution of the obtained approximate differential equations is found. Influences of the external loads, drill string angular speed of rotation, parameters of the gas and fluid flows on the drill string vibrations are shown.

A variable-order laminated plate theory based on the variational-asymptotical method

NASA Technical Reports Server (NTRS)

Lee, Bok W.; Sutyrin, Vladislav G.; Hodges, Dewey H.

1993-01-01

The variational-asymptotical method is a mathematical technique by which the three-dimensional analysis of laminated plate deformation can be split into a linear, one-dimensional, through-the-thickness analysis and a nonlinear, two-dimensional, plate analysis. The elastic constants used in the plate analysis are obtained from the through-the-thickness analysis, along with approximate, closed-form three-dimensional distributions of displacement, strain, and stress. In this paper, a theory based on this technique is developed which is capable of approximating three-dimensional elasticity to any accuracy desired. The asymptotical method allows for the approximation of the through-the-thickness behavior in terms of the eigenfunctions of a certain Sturm-Liouville problem associated with the thickness coordinate. These eigenfunctions contain all the necessary information about the nonhomogeneities along the thickness coordinate of the plate and thus possess the appropriate discontinuities in the derivatives of displacement. The theory is presented in this paper along with numerical results for the eigenfunctions of various laminated plates.

Bridging the gap between the Babinet principle and the physical optics approximation: Vectorial problem

NASA Astrophysics Data System (ADS)

Kubické, Gildas; Bourlier, Christophe; Delahaye, Morgane; Corbel, Charlotte; Pinel, Nicolas; Pouliguen, Philippe

2013-09-01

For a three-dimensional problem and by assuming perfectly electric conducting objects, this paper shows that the Babinet principle (BP) can be derived from the physical optics (PO) approximation. Indeed, following the same idea as Ufimtsev, from the PO approximation and in the far-field zone, the field scattered by an object can be split up into a field which mainly contributes around the specular direction (illuminated zone) and a field which mainly contributes around the forward direction (shadowed zone), which is strongly related to the scattered field obtained from the BP. The only difference resides in the integration surface. We show mathematically that the involved integral does not depend on the shape of the object but only on its contour. Simulations are provided to illustrate the link between BP and PO. The main gain of this work is that it provides a more complete physical insight into the connection between PO and BP.

Characterizing traveling-wave collisions in granular chains starting from integrable limits: the case of the Korteweg-de Vries equation and the Toda lattice.

PubMed

Shen, Y; Kevrekidis, P G; Sen, S; Hoffman, A

2014-08-01

Our aim in the present work is to develop approximations for the collisional dynamics of traveling waves in the context of granular chains in the presence of precompression. To that effect, we aim to quantify approximations of the relevant Hertzian FPU-type lattice through both the Korteweg-de Vries (KdV) equation and the Toda lattice. Using the availability in such settings of both one-soliton and two-soliton solutions in explicit analytical form, we initialize such coherent structures in the granular chain and observe the proximity of the resulting evolution to the underlying integrable (KdV or Toda) model. While the KdV offers the possibility to accurately capture collisions of solitary waves propagating in the same direction, the Toda lattice enables capturing both copropagating and counterpropagating soliton collisions. The error in the approximation is quantified numerically and connections to bounds established in the mathematical literature are also given.

Spectrophotovoltaic orbital power generation

NASA Technical Reports Server (NTRS)

Knowles, G.; Carroll, J.

1983-01-01

A subscale model of a photovoltaic power system employing spectral splitting and 1000:1 concentration was fabricated and tested. The 10-in. aperture model demonstrated 15.5% efficiency with 86% of the energy produced by a GaAs solar cell and 14% of the energy produced by an Si cell. The calculated efficiency of the system using the same solar cells, but having perfect optics, would be approximately 20%. The model design, component measurements, test results, and mathematical model are presented.

Discrete maximum principle for the P1 - P0 weak Galerkin finite element approximations

NASA Astrophysics Data System (ADS)

Wang, Junping; Ye, Xiu; Zhai, Qilong; Zhang, Ran

2018-06-01

This paper presents two discrete maximum principles (DMP) for the numerical solution of second order elliptic equations arising from the weak Galerkin finite element method. The results are established by assuming an h-acute angle condition for the underlying finite element triangulations. The mathematical theory is based on the well-known De Giorgi technique adapted in the finite element context. Some numerical results are reported to validate the theory of DMP.

Discrete Tchebycheff orthonormal polynomials and applications

NASA Technical Reports Server (NTRS)

Lear, W. M.

1980-01-01

Discrete Tchebycheff orthonormal polynomials offer a convenient way to make least squares polynomial fits of uniformly spaced discrete data. Computer programs to do so are simple and fast, and appear to be less affected by computer roundoff error, for the higher order fits, than conventional least squares programs. They are useful for any application of polynomial least squares fits: approximation of mathematical functions, noise analysis of radar data, and real time smoothing of noisy data, to name a few.

Development of a Mathematical Code to Predict Thermal Degradation of Fuel and Deposit Formation in a Fuel System

DTIC Science & Technology

1990-09-01

and D, as the finite difference approximation to the x- derivatives and the r-derivatives, respectively. Then, using the Crank-Nicholson scheme, we can...Frankenfeld, 1978). Deposits formed under these conditions differ in composition from those formed in the pres- ence of oxygen. Furthermore, in deoxygenated...characteristics were in many significant respects quite different than Marteney’s data. Thus, there are still some unanswered questions regarding the exact

Structural tailoring of engine blades (STAEBL)

NASA Technical Reports Server (NTRS)

Platt, C. E.; Pratt, T. K.; Brown, K. W.

1982-01-01

A mathematical optimization procedure was developed for the structural tailoring of engine blades and was used to structurally tailor two engine fan blades constructed of composite materials without midspan shrouds. The first was a solid blade made from superhybrid composites, and the second was a hollow blade with metal matrix composite inlays. Three major computerized functions were needed to complete the procedure: approximate analysis with the established input variables, optimization of an objective function, and refined analysis for design verification.

Comments on numerical solution of boundary value problems of the Laplace equation and calculation of eigenvalues by the grid method

NASA Technical Reports Server (NTRS)

Lyusternik, L. A.

1980-01-01

The mathematics involved in numerically solving for the plane boundary value of the Laplace equation by the grid method is developed. The approximate solution of a boundary value problem for the domain of the Laplace equation by the grid method consists of finding u at the grid corner which satisfies the equation at the internal corners (u=Du) and certain boundary value conditions at the boundary corners.

A Nonlinear differential equation model of Asthma effect of environmental pollution using LHAM

NASA Astrophysics Data System (ADS)

Joseph, G. Arul; Balamuralitharan, S.

2018-04-01

In this paper, we investigated a nonlinear differential equation mathematical model to study the spread of asthma in the environmental pollutants from industry and mainly from tobacco smoke from smokers in different type of population. Smoking is the main cause to spread Asthma in the environment. Numerical simulation is also discussed. Finally by using Liao’s Homotopy analysis Method (LHAM), we found that the approximate analytical solution of Asthmatic disease in the environmental.

A minimalist approach to conceptualization of time in quantum theory

NASA Astrophysics Data System (ADS)

Kitada, Hitoshi; Jeknić-Dugić, Jasmina; Arsenijević, Momir; Dugić, Miroljub

2016-12-01

Ever since Schrödinger, Time in quantum theory is postulated Newtonian for every reference frame. With the help of certain known mathematical results, we show that the concept of the so-called Local Time allows avoiding the postulate. In effect, time appears as neither fundamental nor universal on the quantum-mechanical level while being consistently attributable to every, at least approximately, closed quantum system as well as to every of its (conservative or not) subsystems.

Gas Diffusion in Fluids Containing Bubbles

NASA Technical Reports Server (NTRS)

Zak, M.; Weinberg, M. C.

1982-01-01

Mathematical model describes movement of gases in fluid containing many bubbles. Model makes it possible to predict growth and shrink age of bubbles as function of time. New model overcomes complexities involved in analysis of varying conditions by making two simplifying assumptions. It treats bubbles as point sources, and it employs approximate expression for gas concentration gradient at liquid/bubble interface. In particular, it is expected to help in developing processes for production of high-quality optical glasses in space.

Foundations of children's numerical and mathematical skills: the roles of symbolic and nonsymbolic representations of numerical magnitude.

PubMed

Lyons, Ian M; Ansari, Daniel

2015-01-01

Numerical and mathematical skills are critical predictors of academic success. The last three decades have seen a substantial growth in our understanding of how the human mind and brain represent and process numbers. In particular, research has shown that we share with animals the ability to represent numerical magnitude (the total number of items in a set) and that preverbal infants can process numerical magnitude. Further research has shown that similar processing signatures characterize numerical magnitude processing across species and developmental time. These findings suggest that an approximate system for nonsymbolic (e.g., dot arrays) numerical magnitude representation serves as the basis for the acquisition of cultural, symbolic (e.g., Arabic numerals) representations of numerical magnitude. This chapter explores this hypothesis by reviewing studies that have examined the relation between individual differences in nonsymbolic numerical magnitude processing and symbolic math abilities (e.g., arithmetic). Furthermore, we examine the extent to which the available literature provides strong evidence for a link between symbolic and nonsymbolic representations of numerical magnitude at the behavioral and neural levels of analysis. We conclude that claims that symbolic number abilities are grounded in the approximate system for the nonsymbolic representation of numerical magnitude are not strongly supported by the available evidence. Alternative models and future research directions are discussed. © 2015 Elsevier Inc. All rights reserved.

Evolvable mathematical models: A new artificial Intelligence paradigm

NASA Astrophysics Data System (ADS)

Grouchy, Paul

We develop a novel Artificial Intelligence paradigm to generate autonomously artificial agents as mathematical models of behaviour. Agent/environment inputs are mapped to agent outputs via equation trees which are evolved in a manner similar to Symbolic Regression in Genetic Programming. Equations are comprised of only the four basic mathematical operators, addition, subtraction, multiplication and division, as well as input and output variables and constants. From these operations, equations can be constructed that approximate any analytic function. These Evolvable Mathematical Models (EMMs) are tested and compared to their Artificial Neural Network (ANN) counterparts on two benchmarking tasks: the double-pole balancing without velocity information benchmark and the challenging discrete Double-T Maze experiments with homing. The results from these experiments show that EMMs are capable of solving tasks typically solved by ANNs, and that they have the ability to produce agents that demonstrate learning behaviours. To further explore the capabilities of EMMs, as well as to investigate the evolutionary origins of communication, we develop NoiseWorld, an Artificial Life simulation in which interagent communication emerges and evolves from initially noncommunicating EMM-based agents. Agents develop the capability to transmit their x and y position information over a one-dimensional channel via a complex, dialogue-based communication scheme. These evolved communication schemes are analyzed and their evolutionary trajectories examined, yielding significant insight into the emergence and subsequent evolution of cooperative communication. Evolved agents from NoiseWorld are successfully transferred onto physical robots, demonstrating the transferability of EMM-based AIs from simulation into physical reality.

Nonsymbolic number and cumulative area representations contribute shared and unique variance to symbolic math competence

PubMed Central

Lourenco, Stella F.; Bonny, Justin W.; Fernandez, Edmund P.; Rao, Sonia

2012-01-01

Humans and nonhuman animals share the capacity to estimate, without counting, the number of objects in a set by relying on an approximate number system (ANS). Only humans, however, learn the concepts and operations of symbolic mathematics. Despite vast differences between these two systems of quantification, neural and behavioral findings suggest functional connections. Another line of research suggests that the ANS is part of a larger, more general system of magnitude representation. Reports of cognitive interactions and common neural coding for number and other magnitudes such as spatial extent led us to ask whether, and how, nonnumerical magnitude interfaces with mathematical competence. On two magnitude comparison tasks, college students estimated (without counting or explicit calculation) which of two arrays was greater in number or cumulative area. They also completed a battery of standardized math tests. Individual differences in both number and cumulative area precision (measured by accuracy on the magnitude comparison tasks) correlated with interindividual variability in math competence, particularly advanced arithmetic and geometry, even after accounting for general aspects of intelligence. Moreover, analyses revealed that whereas number precision contributed unique variance to advanced arithmetic, cumulative area precision contributed unique variance to geometry. Taken together, these results provide evidence for shared and unique contributions of nonsymbolic number and cumulative area representations to formally taught mathematics. More broadly, they suggest that uniquely human branches of mathematics interface with an evolutionarily primitive general magnitude system, which includes partially overlapping representations of numerical and nonnumerical magnitude. PMID:23091023

A computer model for the 30S ribosome subunit.

PubMed Central

Kuntz, I D; Crippen, G M

1980-01-01

We describe a computer-generated model for the locations of the 21 proteins of the 30S subunit of the E. coli ribosome. The model uses a new method of incorporating experimental measurements based on a mathematical technique called distance geometry. In this paper, we use data from two sources: immunoelectron microscopy and neutron-scattering studies. The data are generally self-consistent and lead to a set of relatively well-defined structures in which individual protein coordinates differ by approximately 20 A from one structure to another. Two important features of this calculation are the use of extended proteins rather than just the centers of mass, and the ability to confine the protein locations within an arbitrary boundary surface so that only solutions with an approximate 30S "shape" are permitted. PMID:7020786

The concentration of the mitochondrial pyruvate carrier in rat liver and heart mitochondria determined with alpha-cyano-beta-(1-phenylindol-3-yl)acrylate.

PubMed Central

Shearman, M S; Halestrap, A P

1984-01-01

alpha-Cyano-beta-(1-phenylindol-3-yl)acrylate inhibited pyruvate transport into both liver and heart mitochondria approximately linearly with respect to its concentration until 65% inhibition was achieved. The extent of inhibition was dependent on the mitochondrial protein concentration. By extrapolation of plots of inhibition versus inhibitor concentration to total inhibition, or by mathematical analysis of the plots, the concentration of pyruvate transporter molecules per mg of protein was calculated to be approximately 100 pmol/mg for both heart and liver mitochondria, and the Ki about 7 nM. The data also suggest that pyruvate transport is rate-limiting for pyruvate oxidation by heart mitochondria in State 3, but not by liver mitochondria. PMID:6508736

A review of the matrix-exponential formalism in radiative transfer

NASA Astrophysics Data System (ADS)

Efremenko, Dmitry S.; Molina García, Víctor; Gimeno García, Sebastián; Doicu, Adrian

2017-07-01

This paper outlines the matrix exponential description of radiative transfer. The eigendecomposition method which serves as a basis for computing the matrix exponential and for representing the solution in a discrete ordinate setting is considered. The mathematical equivalence of the discrete ordinate method, the matrix operator method, and the matrix Riccati equations method is proved rigorously by means of the matrix exponential formalism. For optically thin layers, approximate solution methods relying on the Padé and Taylor series approximations to the matrix exponential, as well as on the matrix Riccati equations, are presented. For optically thick layers, the asymptotic theory with higher-order corrections is derived, and parameterizations of the asymptotic functions and constants for a water-cloud model with a Gamma size distribution are obtained.

Inelastic behavior of structural components

NASA Technical Reports Server (NTRS)

Hussain, N.; Khozeimeh, K.; Toridis, T. G.

1980-01-01

A more accurate procedure was developed for the determination of the inelastic behavior of structural components. The actual stress-strain curve for the mathematical of the structure was utilized to generate the force-deformation relationships for the structural elements, rather than using simplified models such as elastic-plastic, bilinear and trilinear approximations. relationships were generated for beam elements with various types of cross sections. In the generational of these curves, stress or load reversals, kinematic hardening and hysteretic behavior were taken into account. Intersections between loading and unloading branches were determined through an iterative process. Using the inelastic properties obtained, the plastic static response of some simple structural systems composed of beam elements was computed. Results were compared with known solutions, indicating a considerable improvement over response predictions obtained by means of simplified approximations used in previous investigations.

Qualitative methods in quantum theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Migdal, A.B.

The author feels that the solution of most problems in theoretical physics begins with the application of qualitative methods - dimensional estimates and estimates made from simple models, the investigation of limiting cases, the use of the analytic properties of physical quantities, etc. This book proceeds in this spirit, rather than in a formal, mathematical way with no traces of the sweat involved in the original work left to show. The chapters are entitled Dimensional and model approximations, Various types of perturbation theory, The quasi-classical approximation, Analytic properties of physical quantities, Methods in the many-body problem, and Qualitative methods inmore » quantum field theory. Each chapter begins with a detailed introduction, in which the physical meaning of the results obtained in that chapter is explained in a simple way. 61 figures. (RWR)« less

Numerical Analysis of an Impinging Jet Reactor for the CVD and Gas-Phase Nucleation of Titania

NASA Technical Reports Server (NTRS)

Gokoglu, Suleyman A.; Stewart, Gregory D.; Collins, Joshua; Rosner, Daniel E.

1994-01-01

We model a cold-wall atmospheric pressure impinging jet reactor to study the CVD and gas-phase nucleation of TiO2 from a titanium tetra-iso-propoxide (TTIP)/oxygen dilute source gas mixture in nitrogen. The mathematical model uses the computational code FIDAP and complements our recent asymptotic theory for high activation energy gas-phase reactions in thin chemically reacting sublayers. The numerical predictions highlight deviations from ideality in various regions inside the experimental reactor. Model predictions of deposition rates and the onset of gas-phase nucleation compare favorably with experiments. Although variable property effects on deposition rates are not significant (approximately 11 percent at 1000 K), the reduction rates due to Soret transport is substantial (approximately 75 percent at 1000 K).

Operating room scheduling using hybrid clustering priority rule and genetic algorithm

NASA Astrophysics Data System (ADS)

Santoso, Linda Wahyuni; Sinawan, Aisyah Ashrinawati; Wijaya, Andi Rahadiyan; Sudiarso, Andi; Masruroh, Nur Aini; Herliansyah, Muhammad Kusumawan

2017-11-01

Operating room is a bottleneck resource in most hospitals so that operating room scheduling system will influence the whole performance of the hospitals. This research develops a mathematical model of operating room scheduling for elective patients which considers patient priority with limit number of surgeons, operating rooms, and nurse team. Clustering analysis was conducted to the data of surgery durations using hierarchical and non-hierarchical methods. The priority rule of each resulting cluster was determined using Shortest Processing Time method. Genetic Algorithm was used to generate daily operating room schedule which resulted in the lowest values of patient waiting time and nurse overtime. The computational results show that this proposed model reduced patient waiting time by approximately 32.22% and nurse overtime by approximately 32.74% when compared to actual schedule.

Bounds on stochastic chemical kinetic systems at steady state

NASA Astrophysics Data System (ADS)

Dowdy, Garrett R.; Barton, Paul I.

2018-02-01

The method of moments has been proposed as a potential means to reduce the dimensionality of the chemical master equation (CME) appearing in stochastic chemical kinetics. However, attempts to apply the method of moments to the CME usually result in the so-called closure problem. Several authors have proposed moment closure schemes, which allow them to obtain approximations of quantities of interest, such as the mean molecular count for each species. However, these approximations have the dissatisfying feature that they come with no error bounds. This paper presents a fundamentally different approach to the closure problem in stochastic chemical kinetics. Instead of making an approximation to compute a single number for the quantity of interest, we calculate mathematically rigorous bounds on this quantity by solving semidefinite programs. These bounds provide a check on the validity of the moment closure approximations and are in some cases so tight that they effectively provide the desired quantity. In this paper, the bounded quantities of interest are the mean molecular count for each species, the variance in this count, and the probability that the count lies in an arbitrary interval. At present, we consider only steady-state probability distributions, intending to discuss the dynamic problem in a future publication.

Approximate Algorithms for Computing Spatial Distance Histograms with Accuracy Guarantees

PubMed Central

Grupcev, Vladimir; Yuan, Yongke; Tu, Yi-Cheng; Huang, Jin; Chen, Shaoping; Pandit, Sagar; Weng, Michael

2014-01-01

Particle simulation has become an important research tool in many scientific and engineering fields. Data generated by such simulations impose great challenges to database storage and query processing. One of the queries against particle simulation data, the spatial distance histogram (SDH) query, is the building block of many high-level analytics, and requires quadratic time to compute using a straightforward algorithm. Previous work has developed efficient algorithms that compute exact SDHs. While beating the naive solution, such algorithms are still not practical in processing SDH queries against large-scale simulation data. In this paper, we take a different path to tackle this problem by focusing on approximate algorithms with provable error bounds. We first present a solution derived from the aforementioned exact SDH algorithm, and this solution has running time that is unrelated to the system size N. We also develop a mathematical model to analyze the mechanism that leads to errors in the basic approximate algorithm. Our model provides insights on how the algorithm can be improved to achieve higher accuracy and efficiency. Such insights give rise to a new approximate algorithm with improved time/accuracy tradeoff. Experimental results confirm our analysis. PMID:24693210

The 6th International Conference on Computer Science and Computational Mathematics (ICCSCM 2017)

NASA Astrophysics Data System (ADS)

2017-09-01

The ICCSCM 2017 (The 6th International Conference on Computer Science and Computational Mathematics) has aimed to provide a platform to discuss computer science and mathematics related issues including Algebraic Geometry, Algebraic Topology, Approximation Theory, Calculus of Variations, Category Theory; Homological Algebra, Coding Theory, Combinatorics, Control Theory, Cryptology, Geometry, Difference and Functional Equations, Discrete Mathematics, Dynamical Systems and Ergodic Theory, Field Theory and Polynomials, Fluid Mechanics and Solid Mechanics, Fourier Analysis, Functional Analysis, Functions of a Complex Variable, Fuzzy Mathematics, Game Theory, General Algebraic Systems, Graph Theory, Group Theory and Generalizations, Image Processing, Signal Processing and Tomography, Information Fusion, Integral Equations, Lattices, Algebraic Structures, Linear and Multilinear Algebra; Matrix Theory, Mathematical Biology and Other Natural Sciences, Mathematical Economics and Financial Mathematics, Mathematical Physics, Measure Theory and Integration, Neutrosophic Mathematics, Number Theory, Numerical Analysis, Operations Research, Optimization, Operator Theory, Ordinary and Partial Differential Equations, Potential Theory, Real Functions, Rings and Algebras, Statistical Mechanics, Structure Of Matter, Topological Groups, Wavelets and Wavelet Transforms, 3G/4G Network Evolutions, Ad-Hoc, Mobile, Wireless Networks and Mobile Computing, Agent Computing & Multi-Agents Systems, All topics related Image/Signal Processing, Any topics related Computer Networks, Any topics related ISO SC-27 and SC- 17 standards, Any topics related PKI(Public Key Intrastructures), Artifial Intelligences(A.I.) & Pattern/Image Recognitions, Authentication/Authorization Issues, Biometric authentication and algorithms, CDMA/GSM Communication Protocols, Combinatorics, Graph Theory, and Analysis of Algorithms, Cryptography and Foundation of Computer Security, Data Base(D.B.) Management & Information Retrievals, Data Mining, Web Image Mining, & Applications, Defining Spectrum Rights and Open Spectrum Solutions, E-Comerce, Ubiquitous, RFID, Applications, Fingerprint/Hand/Biometrics Recognitions and Technologies, Foundations of High-performance Computing, IC-card Security, OTP, and Key Management Issues, IDS/Firewall, Anti-Spam mail, Anti-virus issues, Mobile Computing for E-Commerce, Network Security Applications, Neural Networks and Biomedical Simulations, Quality of Services and Communication Protocols, Quantum Computing, Coding, and Error Controls, Satellite and Optical Communication Systems, Theory of Parallel Processing and Distributed Computing, Virtual Visions, 3-D Object Retrievals, & Virtual Simulations, Wireless Access Security, etc. The success of ICCSCM 2017 is reflected in the received papers from authors around the world from several countries which allows a highly multinational and multicultural idea and experience exchange. The accepted papers of ICCSCM 2017 are published in this Book. Please check http://www.iccscm.com for further news. A conference such as ICCSCM 2017 can only become successful using a team effort, so herewith we want to thank the International Technical Committee and the Reviewers for their efforts in the review process as well as their valuable advices. We are thankful to all those who contributed to the success of ICCSCM 2017. The Secretary

Explicit solutions of a gravity-induced film flow along a convectively heated vertical wall.

PubMed

Raees, Ammarah; Xu, Hang

2013-01-01

The gravity-driven film flow has been analyzed along a vertical wall subjected to a convective boundary condition. The Boussinesq approximation is applied to simplify the buoyancy term, and similarity transformations are used on the mathematical model of the problem under consideration, to obtain a set of coupled ordinary differential equations. Then the reduced equations are solved explicitly by using homotopy analysis method (HAM). The resulting solutions are investigated for heat transfer effects on velocity and temperature profiles.

Theoretical foundations for a quantitative approach to paleogenetics. I, II.

NASA Technical Reports Server (NTRS)

Holmquist, R.

1972-01-01

It is shown that by neglecting the phenomena of multiple hits, back mutation, and chance coincidence errors larger than 100% can be introduced in the calculated value of the average number of nucleotide base differences to be expected between two homologous polynucleotides. Mathematical formulas are derived to correct quantitatively for these effects. It is pointed out that the effects change materially the quantitative aspects of phylogenics, such as the length of the legs of the trees. A number of problems are solved without approximation.-

Representations, Approximations, and Algorithms for Mathematical Speech Processing

DTIC Science & Technology

1998-06-16

location on the basilar membrane was very low (i.e., any given location responded well to a broad range of frequencies ); so theorists had trouble...are variants of the signal-to- noise ratio (SNR). SNR measures compare the energy of the signal with the energy of the noise (defined as the difference...segment m and frequency band j, and 0"^ • and cr^mj- are the variances for band j and segment m of the original speech and noise , respectively

Analysis, approximation, and computation of a coupled solid/fluid temperature control problem

NASA Technical Reports Server (NTRS)

Gunzburger, Max D.; Lee, Hyung C.

1993-01-01

An optimization problem is formulated motivated by the desire to remove temperature peaks, i.e., 'hot spots', along the bounding surfaces of containers of fluid flows. The heat equation of the solid container is coupled to the energy equations for the fluid. Heat sources can be located in the solid body, the fluid, or both. Control is effected by adjustments to the temperature of the fluid at the inflow boundary. Both mathematical analyses and computational experiments are given.

The credibility crisis in research: Can economics tools help?

PubMed Central

Gall, Thomas; Ioannidis, John P. A.; Maniadis, Zacharias

2017-01-01

The issue of nonreplicable evidence has attracted considerable attention across biomedical and other sciences. This concern is accompanied by an increasing interest in reforming research incentives and practices. How to optimally perform these reforms is a scientific problem in itself, and economics has several scientific methods that can help evaluate research reforms. Here, we review these methods and show their potential. Prominent among them are mathematical modeling and laboratory experiments that constitute affordable ways to approximate the effects of policies with wide-ranging implications. PMID:28445470

The credibility crisis in research: Can economics tools help?

PubMed

Gall, Thomas; Ioannidis, John P A; Maniadis, Zacharias

2017-04-01

The issue of nonreplicable evidence has attracted considerable attention across biomedical and other sciences. This concern is accompanied by an increasing interest in reforming research incentives and practices. How to optimally perform these reforms is a scientific problem in itself, and economics has several scientific methods that can help evaluate research reforms. Here, we review these methods and show their potential. Prominent among them are mathematical modeling and laboratory experiments that constitute affordable ways to approximate the effects of policies with wide-ranging implications.

kappa-Version of Finite Element Method: A New Mathematical and Computational Framework for BVP and IVP

DTIC Science & Technology

2007-01-01

differentiability, fluid-solid interaction, error estimation, re-discretization, moving meshes 16. SECURITY CLASSIFICATION OF: 17 . LIMITATION OF 18. NUMBER...method the weight function is an indepen- dent function v = 0 6 4Ph , with v = 0 on F, if W = W0 on F1. 2. Galerkin method (GM): If Wh is an approximation...This can be demonstrated by considering a simple I-D case (like described above) in which the discretization 17 is uniform with characteristic length

A Characterization of an Element of Best Simultaneous Approximation.

DTIC Science & Technology

1983-09-01

space Work Unit Number 3 - Numerical Analysis and Scientific Computing C . R. Category: G.1.2 * Department of Mathematics, Lewis and Clark College...Portland, OR 97219, USA. Sponsored by the United States Army under Contract No. DAAG29-80- C -0041. - ,1I K SIGNIFICANCE AND EXPLANATION A basic problem of...under Contract No. DAAG29-80- C -0041. others, e.g. Goel et.al. [8], ltilman (14], and Phillips et.al. [15], give characterizations in terms of one or

Distribution of thermal neutrons in a temperature gradient

NASA Astrophysics Data System (ADS)

Molinari, V. G.; Pollachini, L.

A method to determine the spatial distribution of the thermal spectrum of neutrons in heterogeneous systems is presented. The method is based on diffusion concepts and has a simple mathematical structure which increases computing efficiency. The application of this theory to the neutron thermal diffusion induced by a temperature gradient, as found in nuclear reactors, is described. After introducing approximations, a nonlinear equation system representing the neutron temperature is given. Values of the equation parameters and its dependence on geometrical factors and media characteristics are discussed.

Selection theory of free dendritic growth in a potential flow.

PubMed

von Kurnatowski, Martin; Grillenbeck, Thomas; Kassner, Klaus

2013-04-01

The Kruskal-Segur approach to selection theory in diffusion-limited or Laplacian growth is extended via combination with the Zauderer decomposition scheme. This way nonlinear bulk equations become tractable. To demonstrate the method, we apply it to two-dimensional crystal growth in a potential flow. We omit the simplifying approximations used in a preliminary calculation for the same system [Fischaleck, Kassner, Europhys. Lett. 81, 54004 (2008)], thus exhibiting the capability of the method to extend mathematical rigor to more complex problems than hitherto accessible.

From correspondence to complementarity: The emergence of Bohr's Copenhagen interpretation of quantum mechanics

NASA Astrophysics Data System (ADS)

Tanona, Scott Daniel

I develop a new analysis of Niels Bohr's Copenhagen interpretation of quantum mechanics by examining the development of his views from his earlier use of the correspondence principle in the so-called 'old quantum theory' to his articulation of the idea of complementarity in the context of the novel mathematical formalism of quantum mechanics. I argue that Bohr was motivated not by controversial and perhaps dispensable epistemological ideas---positivism or neo-Kantianism, for example---but by his own unique perspective on the difficulties of creating a new working physics of the internal structure of the atom. Bohr's use of the correspondence principle in the old quantum theory was associated with an empirical methodology that used this principle as an epistemological bridge to connect empirical phenomena with quantum models. The application of the correspondence principle required that one determine the validity of the idealizations and approximations necessary for the judicious use of classical physics within quantum theory. Bohr's interpretation of the new quantum mechanics then focused on the largely unexamined ways in which the developing abstract mathematical formalism is given empirical content by precisely this process of approximation. Significant consistency between his later interpretive framework and his forms of argument with the correspondence principle indicate that complementarity is best understood as a relationship among the various approximations and idealizations that must be made when one connects otherwise meaningless quantum mechanical symbols to empirical situations or 'experimental arrangements' described using concepts from classical physics. We discover that this relationship is unavoidable not through any sort of a priori analysis of the priority of classical concepts, but because quantum mechanics incorporates the correspondence approach in the way in which it represents quantum properties with matrices of transition probabilities, the empirical meaning of which depend on the situation but in general are tied to the correspondence connection to the spectra. For Bohr, it is then the commutation relations, which arise from the formalism, which inform us of the complementary nature of this approximate representation of quantum properties via the classical equations through which we connect them to experiments.

Travelling wave ultrasonic motors, Part I: Working principle and mathematical modelling of the stator

NASA Astrophysics Data System (ADS)

Hagedorn, P.; Wallaschek, J.

1992-05-01

Travelling wave ultrasonic motors have recently been attracting considerable attention: they may possibly soon replace—at least in certain areas—small electromagnetic motors. This development has been made possible by recent advances in power electronics, material research and digital control, which allow utilization of the piezoelectric effect for low power motors. In these motors the mechanical energy is generated with frequencies of the order of 40 kHz via piezo-elements producing bending waves in a stator, which has approximately the form of a circular plate. The rotor is then driven by the stator via contact forces, and with an extremely simple mechanism frequency reductions of 1:40 000 and more are obtained between the stator vibration and the rotor motion. As a consequence, one can work in the 40 kHz range on the electrical side, while a low frequency rotation is obtained on the mechanical side, as is desirable for many applications. In the present paper, which is the first of a series, the working principle of travelling wave ultrasonic motors is reviewed, and the main phenomena are mathematically modelled. In further papers a detailed mathematical description of the stator vibration and a first model of the contact problem will be given.

Hybrid model based unified scheme for endoscopic Cerenkov and radio-luminescence tomography: Simulation demonstration

NASA Astrophysics Data System (ADS)

Wang, Lin; Cao, Xin; Ren, Qingyun; Chen, Xueli; He, Xiaowei

2018-05-01

Cerenkov luminescence imaging (CLI) is an imaging method that uses an optical imaging scheme to probe a radioactive tracer. Application of CLI with clinically approved radioactive tracers has opened an opportunity for translating optical imaging from preclinical to clinical applications. Such translation was further improved by developing an endoscopic CLI system. However, two-dimensional endoscopic imaging cannot identify accurate depth and obtain quantitative information. Here, we present an imaging scheme to retrieve the depth and quantitative information from endoscopic Cerenkov luminescence tomography, which can also be applied for endoscopic radio-luminescence tomography. In the scheme, we first constructed a physical model for image collection, and then a mathematical model for characterizing the luminescent light propagation from tracer to the endoscopic detector. The mathematical model is a hybrid light transport model combined with the 3rd order simplified spherical harmonics approximation, diffusion, and radiosity equations to warrant accuracy and speed. The mathematical model integrates finite element discretization, regularization, and primal-dual interior-point optimization to retrieve the depth and the quantitative information of the tracer. A heterogeneous-geometry-based numerical simulation was used to explore the feasibility of the unified scheme, which demonstrated that it can provide a satisfactory balance between imaging accuracy and computational burden.

Predicting academic self-handicapping in different age groups: the role of personal achievement goals and social goals.

PubMed

Leondari, Angeliki; Gonida, Eleftheria

2007-09-01

Academic self-handicapping refers to the use of impediments to successful performance on academic tasks. Previous studies have shown that it is related to personal achievement goals. A performance goal orientation is a positive predictor of self-handicapping, whereas a task goal orientation is unrelated to self-handicapping. The aim of this study was to examine the relationship between academic self-handicapping, goal orientations (task, performance-approach, performance-avoidance), social goals, future consequences and achievement in mathematics. An additional aim was to investigate grade-level and gender differences in relation to academic self-handicapping. Participants were 702 upper elementary, junior and senior high school students with approximately equal numbers of girls and boys. There were no grade-level or gender differences as regards the use of self-handicapping. The correlations among the variables revealed that, when the whole sample was considered, self-handicapping was positively related to performance goal orientations and pleasing significant others and negatively to achievement in mathematics. The results of hierarchical regression analysis showed that, in upper elementary and junior high schools, the association between achievement in mathematics and self-handicapping was mediated by performance-avoidance goals. In senior high school, only task goal orientation was a negative predictor of self-handicapping.

Mathematical modeling of simultaneous carbon-nitrogen-sulfur removal from industrial wastewater.

PubMed

Xu, Xi-Jun; Chen, Chuan; Wang, Ai-Jie; Ni, Bing-Jie; Guo, Wan-Qian; Yuan, Ye; Huang, Cong; Zhou, Xu; Wu, Dong-Hai; Lee, Duu-Jong; Ren, Nan-Qi

2017-01-05

A mathematical model of carbon, nitrogen and sulfur removal (C-N-S) from industrial wastewater was constructed considering the interactions of sulfate-reducing bacteria (SRB), sulfide-oxidizing bacteria (SOB), nitrate-reducing bacteria (NRB), facultative bacteria (FB), and methane producing archaea (MPA). For the kinetic network, the bioconversion of C-N by heterotrophic denitrifiers (NO 3 - →NO 2 - →N 2 ), and that of C-S by SRB (SO 4 2- →S 2- ) and SOB (S 2- →S 0 ) was proposed and calibrated based on batch experimental data. The model closely predicted the profiles of nitrate, nitrite, sulfate, sulfide, lactate, acetate, methane and oxygen under both anaerobic and micro-aerobic conditions. The best-fit kinetic parameters had small 95% confidence regions with mean values approximately at the center. The model was further validated using independent data sets generated under different operating conditions. This work was the first successful mathematical modeling of simultaneous C-N-S removal from industrial wastewater and more importantly, the proposed model was proven feasible to simulate other relevant processes, such as sulfate-reducing, sulfide-oxidizing process (SR-SO) and denitrifying sulfide removal (DSR) process. The model developed is expected to enhance our ability to predict the treatment of carbon-nitrogen-sulfur contaminated industrial wastewater. Copyright © 2016 Elsevier B.V. All rights reserved.

The role of under-determined approximations in engineering and science application

NASA Technical Reports Server (NTRS)

Carpenter, William C.

1992-01-01

There is currently a great deal of interest in using response surfaces in the optimization of aircraft performance. The objective function and/or constraint equations involved in these optimization problems may come from numerous disciplines such as structures, aerodynamics, environmental engineering, etc. In each of these disciplines, the mathematical complexity of the governing equations usually dictates that numerical results be obtained from large computer programs such as a finite element method program. Thus, when performing optimization studies, response surfaces are a convenient way of transferring information from the various disciplines to the optimization algorithm as opposed to bringing all the sundry computer programs together in a massive computer code. Response surfaces offer another advantage in the optimization of aircraft structures. A characteristic of these types of optimization problems is that evaluation of the objective function and response equations (referred to as a functional evaluation) can be very expensive in a computational sense. Because of the computational expense in obtaining functional evaluations, the present study was undertaken to investigate under-determinined approximations. An under-determined approximation is one in which there are fewer training pairs (pieces of information about a function) than there are undetermined parameters (coefficients or weights) associated with the approximation. Both polynomial approximations and neural net approximations were examined. Three main example problems were investigated: (1) a function of one design variable was considered; (2) a function of two design variables was considered; and (3) a 35 bar truss with 4 design variables was considered.

Stability analysis of wall driven nanofluid flow through a tube

NASA Astrophysics Data System (ADS)

Hossain, M. Mainul; Khan, M. A. H.

2017-06-01

Wall driven incompressible viscous fluid flow with nanoparticles through a tube is considered where two different nanofluids (Cu-water, SiO2-water) are used separately. Flow becomes gradually unstable due to movement of wall and existence of nanoparticles. However, Reynolds number, volume fraction and density ratio are responsible for flow instability. The mathematical model of the problem is constructed and solved by means of series solution method. Special type Hermite-Padé approximation method is used to improve the series solution. The critical point for Reynolds number, volume fraction and density ratio are determined and described using approximation technique and bifurcation diagram for both nanofluids. Moreover, Interaction between these three numbers and their effect on velocity profile are discussed. To indicate the nanofluid which is more effective for flow stability is our major concerned.

Tables of the Inverse Laplace Transform of the Function [Formula: see text].

PubMed

Dishon, Menachem; Bendler, John T; Weiss, George H

1990-01-01

The inverse transform, [Formula: see text], 0 < β < 1, is a stable law that arises in a number of different applications in chemical physics, polymer physics, solid-state physics, and applied mathematics. Because of its important applications, a number of investigators have suggested approximations to g ( t ). However, there have so far been no accurately calculated values available for checking or other purposes. We present here tables, accurate to six figures, of g ( t ) for a number of values of β between 0.25 and 0.999. In addition, since g ( t ), regarded as a function of β , is uni-modal with a peak occurring at t = t max we both tabulate and graph t max and 1/ g ( t max ) as a function of β , as well as giving polynomial approximations to 1/ g ( t max ).

Tables of the Inverse Laplace Transform of the Function e−sβ

PubMed Central

Dishon, Menachem; Bendler, John T.; Weiss, George H.

1990-01-01

The inverse transform, g(t)=L−1(e−sβ), 0 < β < 1, is a stable law that arises in a number of different applications in chemical physics, polymer physics, solid-state physics, and applied mathematics. Because of its important applications, a number of investigators have suggested approximations to g(t). However, there have so far been no accurately calculated values available for checking or other purposes. We present here tables, accurate to six figures, of g(t) for a number of values of β between 0.25 and 0.999. In addition, since g(t), regarded as a function of β, is uni-modal with a peak occurring at t = tmax we both tabulate and graph tmax and 1/g(tmax) as a function of β, as well as giving polynomial approximations to 1/g(tmax). PMID:28179785

Nonlinear radiative peristaltic flow of hydromagnetic fluid through porous medium

NASA Astrophysics Data System (ADS)

Hussain, Q.; Latif, T.; Alvi, N.; Asghar, S.

2018-06-01

The radiative heat and mass transfer in wall induced flow of hydromagnetic fluid through porous medium in an asymmetric channel is analyzed. The fluid viscosity is considered temperature dependent. In the theory of peristalsis, the radiation effects are either ignored or taken as linear approximation of radiative heat flux. Such approximation is only possible when there is sufficiently small temperature differences in the flow field; however, nonlinear radiation effects are valid for large temperature differences as well (the new feature added in the present study). Mathematical modeling of the problems include the complicated system of highly nonlinear differential equations. Semi-analytical solutions are established in the wave reference frame. Results are displayed graphically and discussed in detail for the variation of various physical parameters with the special attention to viscosity, radiation, and temperature ratio parameters.

Verification of floating-point software

NASA Technical Reports Server (NTRS)

Hoover, Doug N.

1990-01-01

Floating point computation presents a number of problems for formal verification. Should one treat the actual details of floating point operations, or accept them as imprecisely defined, or should one ignore round-off error altogether and behave as if floating point operations are perfectly accurate. There is the further problem that a numerical algorithm usually only approximately computes some mathematical function, and we often do not know just how good the approximation is, even in the absence of round-off error. ORA has developed a theory of asymptotic correctness which allows one to verify floating point software with a minimum entanglement in these problems. This theory and its implementation in the Ariel C verification system are described. The theory is illustrated using a simple program which finds a zero of a given function by bisection. This paper is presented in viewgraph form.

Mathematical Modeling of Electrodynamics Near the Surface of Earth and Planetary Water Worlds

NASA Technical Reports Server (NTRS)

Tyler, Robert H.

2017-01-01

An interesting feature of planetary bodies with hydrospheres is the presence of an electrically conducting shell near the global surface. This conducting shell may typically lie between relatively insulating rock, ice, or atmosphere, creating a strong constraint on the flow of large-scale electric currents. All or parts of the shell may be in fluid motion relative to main components of the rotating planetary magnetic field (as well as the magnetic fields due to external bodies), creating motionally-induced electric currents that would not otherwise be present. As such, one may expect distinguishing features in the types of electrodynamic processes that occur, as well as an opportunity for imposing specialized mathematical methods that efficiently address this class of application. The purpose of this paper is to present and discuss such specialized methods. Specifically, thin-shell approximations for both the electrodynamics and fluid dynamics are combined to derive simplified mathematical formulations describing the behavior of these electric currents as well as their associated electric and magnetic fields. These simplified formulae allow analytical solutions featuring distinct aspects of the thin-shell electrodynamics in idealized cases. A highly efficient numerical method is also presented that is useful for calculations under inhomogeneous parameter distributions. Finally, the advantages as well as limitations in using this mathematical approach are evaluated. This evaluation is presented primarily for the generic case of bodies with water worlds or other thin spherical conducting shells. More specific discussion is given for the case of Earth, but also Europa and other satellites with suspected oceans.

Mathematical modeling of nitrous oxide (N2O) emissions from full-scale wastewater treatment plants.

PubMed

Ni, Bing-Jie; Ye, Liu; Law, Yingyu; Byers, Craig; Yuan, Zhiguo

2013-07-16

Mathematical modeling of N2O emissions is of great importance toward understanding the whole environmental impact of wastewater treatment systems. However, information on modeling of N2O emissions from full-scale wastewater treatment plants (WWTP) is still sparse. In this work, a mathematical model based on currently known or hypothesized metabolic pathways for N2O productions by heterotrophic denitrifiers and ammonia-oxidizing bacteria (AOB) is developed and calibrated to describe the N2O emissions from full-scale WWTPs. The model described well the dynamic ammonium, nitrite, nitrate, dissolved oxygen (DO) and N2O data collected from both an open oxidation ditch (OD) system with surface aerators and a sequencing batch reactor (SBR) system with bubbling aeration. The obtained kinetic parameters for N2O production are found to be reasonable as the 95% confidence regions of the estimates are all small with mean values approximately at the center. The model is further validated with independent data sets collected from the same two WWTPs. This is the first time that mathematical modeling of N2O emissions is conducted successfully for full-scale WWTPs. While clearly showing that the NH2OH related pathways could well explain N2O production and emission in the two full-scale plants studied, the modeling results do not prove the dominance of the NH2OH pathways in these plants, nor rule out the possibility of AOB denitrification being a potentially dominating pathway in other WWTPs that are designed or operated differently.

Dynamic ambulance reallocation for the reduction of ambulance response times using system status management.

PubMed

Lam, Sean Shao Wei; Zhang, Ji; Zhang, Zhong Cheng; Oh, Hong Choon; Overton, Jerry; Ng, Yih Yng; Ong, Marcus Eng Hock

2015-02-01

Dynamically reassigning ambulance deployment locations throughout a day to balance ambulance availability and demands can be effective in reducing response times. The objectives of this study were to model dynamic ambulance allocation plans in Singapore based on the system status management (SSM) strategy and to evaluate the dynamic deployment plans using a discrete event simulation (DES) model. The geographical information system-based analysis and mathematical programming were used to develop the dynamic ambulance deployment plans for SSM based on ambulance calls data from January 1, 2011, to June 30, 2011. A DES model that incorporated these plans was used to compare the performance of the dynamic SSM strategy against static reallocation policies under various demands and travel time uncertainties. When the deployment plans based on the SSM strategy were followed strictly, the DES model showed that the geographical information system-based plans resulted in approximately 13-second reduction in the median response times compared to the static reallocation policy, whereas the mathematical programming-based plans resulted in approximately a 44-second reduction. The response times and coverage performances were still better than the static policy when reallocations happened for only 60% of all the recommended moves. Dynamically reassigning ambulance deployment locations based on the SSM strategy can result in superior response times and coverage performance compared to static reallocation policies even when the dynamic plans were not followed strictly. Copyright © 2014 Elsevier Inc. All rights reserved.

The contribution of general cognitive abilities and approximate number system to early mathematics.

PubMed

Passolunghi, Maria Chiara; Cargnelutti, Elisa; Pastore, Massimiliano

2014-12-01

Math learning is a complex process that entails a wide range of cognitive abilities to be fulfilled. There is sufficient evidence that both general and specific cognitive skills assume a fundamental role, despite the absence of shared consensus about the relative extent of their involvement. Moreover, regarding general abilities, there is no agreement about the recruitment of the different memory components or of intelligence. In relation to specific factors, great debate subsists regarding the role of the approximate number system (ANS). Starting from these considerations, we wanted to conduct a wide assessment of memory components and ANS, by controlling for the effects associated with intelligence and also exploring possible relationships between all precursors. To achieve this purpose, a sample of 157 children was tested at both beginning and end of their Grade 1. Both general (memory and intelligence) and specific (ANS) precursors were evaluated by a wide battery of tests and put in relation to concurrent and subsequent math skills. Memory was explored in passive and active aspects involving both verbal and visuo-spatial components. Path analysis results demonstrated that memory, and especially the more active processes, and intelligence were the strongest precursors in both assessment times. ANS had a milder role which lost significance by the end of the school year. Memory and ANS seemed to influence early mathematics almost independently. Both general and specific precursors seemed to have a crucial role in early math competences, despite the lower involvement of ANS. © 2014 The British Psychological Society.

Development and evaluation of thermal model reduction algorithms for spacecraft

NASA Astrophysics Data System (ADS)

Deiml, Michael; Suderland, Martin; Reiss, Philipp; Czupalla, Markus

2015-05-01

This paper is concerned with the topic of the reduction of thermal models of spacecraft. The work presented here has been conducted in cooperation with the company OHB AG, formerly Kayser-Threde GmbH, and the Institute of Astronautics at Technische Universität München with the goal to shorten and automatize the time-consuming and manual process of thermal model reduction. The reduction of thermal models can be divided into the simplification of the geometry model for calculation of external heat flows and radiative couplings and into the reduction of the underlying mathematical model. For simplification a method has been developed which approximates the reduced geometry model with the help of an optimization algorithm. Different linear and nonlinear model reduction techniques have been evaluated for their applicability in reduction of the mathematical model. Thereby the compatibility with the thermal analysis tool ESATAN-TMS is of major concern, which restricts the useful application of these methods. Additional model reduction methods have been developed, which account to these constraints. The Matrix Reduction method allows the approximation of the differential equation to reference values exactly expect for numerical errors. The summation method enables a useful, applicable reduction of thermal models that can be used in industry. In this work a framework for model reduction of thermal models has been created, which can be used together with a newly developed graphical user interface for the reduction of thermal models in industry.

Spheroidal Integral Equations for Geodetic Inversion of Geopotential Gradients

NASA Astrophysics Data System (ADS)

Novák, Pavel; Šprlák, Michal

2018-03-01

The static Earth's gravitational field has traditionally been described in geodesy and geophysics by the gravitational potential (geopotential for short), a scalar function of 3-D position. Although not directly observable, geopotential functionals such as its first- and second-order gradients are routinely measured by ground, airborne and/or satellite sensors. In geodesy, these observables are often used for recovery of the static geopotential at some simple reference surface approximating the actual Earth's surface. A generalized mathematical model is represented by a surface integral equation which originates in solving Dirichlet's boundary-value problem of the potential theory defined for the harmonic geopotential, spheroidal boundary and globally distributed gradient data. The mathematical model can be used for combining various geopotential gradients without necessity of their re-sampling or prior continuation in space. The model extends the apparatus of integral equations which results from solving boundary-value problems of the potential theory to all geopotential gradients observed by current ground, airborne and satellite sensors. Differences between spherical and spheroidal formulations of integral kernel functions of Green's kind are investigated. Estimated differences reach relative values at the level of 3% which demonstrates the significance of spheroidal approximation for flattened bodies such as the Earth. The observation model can be used for combined inversion of currently available geopotential gradients while exploring their spectral and stochastic characteristics. The model would be even more relevant to gravitational field modelling of other bodies in space with more pronounced spheroidal geometry than that of the Earth.

Beauty is in the ease of the beholding: A neurophysiological test of the averageness theory of facial attractiveness

PubMed Central

Trujillo, Logan T.; Jankowitsch, Jessica M.; Langlois, Judith H.

2014-01-01

Multiple studies show that people prefer attractive over unattractive faces. But what is an attractive face and why is it preferred? Averageness theory claims that faces are perceived as attractive when their facial configuration approximates the mathematical average facial configuration of the population. Conversely, faces that deviate from this average configuration are perceived as unattractive. The theory predicts that both attractive and mathematically averaged faces should be processed more fluently than unattractive faces, whereas the averaged faces should be processed marginally more fluently than the attractive faces. We compared neurocognitive and behavioral responses to attractive, unattractive, and averaged human faces to test these predictions. We recorded event-related potentials (ERPs) and reaction times (RTs) from 48 adults while they discriminated between human and chimpanzee faces. Participants categorized averaged and high attractive faces as “human” faster than low attractive faces. The posterior N170 (150 – 225 ms) face-evoked ERP component was smaller in response to high attractive and averaged faces versus low attractive faces. Single-trial EEG analysis indicated that this reduced ERP response arose from the engagement of fewer neural resources and not from a change in the temporal consistency of how those resources were engaged. These findings provide novel evidence that faces are perceived as attractive when they approximate a facial configuration close to the population average and suggest that processing fluency underlies preferences for attractive faces. PMID:24326966

Modeling the reversible kinetics of neutrophil aggregation under hydrodynamic shear.

PubMed Central

Neelamegham, S; Taylor, A D; Hellums, J D; Dembo, M; Smith, C W; Simon, S I

1997-01-01

Neutrophil emigration into inflamed tissue is mediated by beta 2-integrin and L-selectin adhesion receptors. Homotypic neutrophil aggregation is also dependent on these molecules, and it provides a model system in which to study adhesion dynamics. In the current study we formulated a mathematical model for cellular aggregation in a linear shear field based on Smoluchowski's two-body collision theory. Neutrophil suspensions activated with chemotactic stimulus and sheared in a cone-plate viscometer rapidly aggregate. Over a range of shear rates (400-800 s-1), approximately 90% of the single cells were recruited into aggregates ranging from doublets to groupings larger than sextuplets. The adhesion efficiency fit to these kinetics reached maximum levels of > 70%. Formed aggregates remained intact and resistant to shear up to 120 s, at which time they spontaneously dissociated back to singlets. The rate of cell disaggregation was linearly proportional to the applied shear rate, and it was approximately 60% lower for doublets as compared to larger aggregates. By accounting for the time-dependent changes in adhesion efficiency, disaggregation rate, and the effects of aggregate geometry, we succeeded in predicting the reversible kinetics of aggregation over a wide range of shear rates and cell concentrations. The combination of viscometry with flow cytometry and mathematical analysis as presented here represents a novel approach to differentiating between the effects of hydrodynamics and the intrinsic biological processes that control cell adhesion. Images FIGURE 3 FIGURE 5 PMID:9083659

APOLLO: a general code for transport, slowing-down and thermalization calculations in heterogeneous media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kavenoky, A.

1973-01-01

From national topical meeting on mathematical models and computational techniques for analysis of nuclear systems; Ann Arbor, Michigan, USA (8 Apr 1973). In mathematical models and computational techniques for analysis of nuclear systems. APOLLO calculates the space-and-energy-dependent flux for a one dimensional medium, in the multigroup approximation of the transport equation. For a one dimensional medium, refined collision probabilities have been developed for the resolution of the integral form of the transport equation; these collision probabilities increase accuracy and save computing time. The interaction between a few cells can also be treated by the multicell option of APOLLO. The diffusionmore » coefficient and the material buckling can be computed in the various B and P approximations with a linearly anisotropic scattering law, even in the thermal range of the spectrum. Eventually this coefficient is corrected for streaming by use of Benoist's theory. The self-shielding of the heavy isotopes is treated by a new and accurate technique which preserves the reaction rates of the fundamental fine structure flux. APOLLO can perform a depletion calculation for one cell, a group of cells or a complete reactor. The results of an APOLLO calculation are the space-and-energy-dependent flux, the material buckling or any reaction rate; these results can also be macroscopic cross sections used as input data for a 2D or 3D depletion and diffusion code in reactor geometry. 10 references. (auth)« less