Asset surveillance system: apparatus and method

NASA Technical Reports Server (NTRS)

Bickford, Randall L. (Inventor)

2007-01-01

System and method for providing surveillance of an asset comprised of numerically fitting at least one mathematical model to obtained residual data correlative to asset operation; storing at least one mathematical model in a memory; obtaining a current set of signal data from the asset; retrieving at least one mathematical model from the memory, using the retrieved mathematical model in a sequential hypothesis test for determining if the current set of signal data is indicative of a fault condition; determining an asset fault cause correlative to a determined indication of a fault condition; providing an indication correlative to a determined fault cause, and an action when warranted. The residual data can be mode partitioned, a current mode of operation can be determined from the asset, and at least one mathematical model can be retrieved from the memory as a function of the determined mode of operation.

[Rational bases for cooperation between epidemiologists and mathematicians].

PubMed

Favorova, L A; Shatrov, I I

1977-10-01

The authors consider rational foundations underlying creatin of realistic models. The principal condition for the successful mathematical modelling is obtaining of the most full value primary materials on the course of the epidemic process. For this purpose the authors suggest definite principles of the methodical approach to the mathematical modelling. Possibilities of the use of mathematical methods for various groups of infections are consideder. Particular attention is paid to the works on the study of the infection risk in "small" collective bodies.

Automated method for the systematic interpretation of resonance peaks in spectrum data

DOEpatents

Damiano, Brian; Wood, Richard T.

1997-01-01

A method for spectral signature interpretation. The method includes the creation of a mathematical model of a system or process. A neural network training set is then developed based upon the mathematical model. The neural network training set is developed by using the mathematical model to generate measurable phenomena of the system or process based upon model input parameter that correspond to the physical condition of the system or process. The neural network training set is then used to adjust internal parameters of a neural network. The physical condition of an actual system or process represented by the mathematical model is then monitored by extracting spectral features from measured spectra of the actual process or system. The spectral features are then input into said neural network to determine the physical condition of the system or process represented by the mathematical. More specifically, the neural network correlates the spectral features (i.e. measurable phenomena) of the actual process or system with the corresponding model input parameters. The model input parameters relate to specific components of the system or process, and, consequently, correspond to the physical condition of the process or system.

Students’ errors in solving combinatorics problems observed from the characteristics of RME modeling

NASA Astrophysics Data System (ADS)

Meika, I.; Suryadi, D.; Darhim

2018-01-01

This article was written based on the learning evaluation results of students’ errors in solving combinatorics problems observed from the characteristics of Realistic Mathematics Education (RME); that is modeling. Descriptive method was employed by involving 55 students from two international-based pilot state senior high schools in Banten. The findings of the study suggested that the students still committed errors in simplifying the problem as much 46%; errors in making mathematical model (horizontal mathematization) as much 60%; errors in finishing mathematical model (vertical mathematization) as much 65%; and errors in interpretation as well as validation as much 66%.

The effect of Missouri mathematics project learning model on students’ mathematical problem solving ability

NASA Astrophysics Data System (ADS)

Handayani, I.; Januar, R. L.; Purwanto, S. E.

2018-01-01

This research aims to know the influence of Missouri Mathematics Project Learning Model to Mathematical Problem-solving Ability of Students at Junior High School. This research is a quantitative research and uses experimental research method of Quasi Experimental Design. The research population includes all student of grade VII of Junior High School who are enrolled in the even semester of the academic year 2016/2017. The Sample studied are 76 students from experimental and control groups. The sampling technique being used is cluster sampling method. The instrument is consisted of 7 essay questions whose validity, reliability, difficulty level and discriminating power have been tested. Before analyzing the data by using t-test, the data has fulfilled the requirement for normality and homogeneity. The result of data shows that there is the influence of Missouri mathematics project learning model to mathematical problem-solving ability of students at junior high school with medium effect.

Phase demodulation method from a single fringe pattern based on correlation with a polynomial form.

PubMed

Robin, Eric; Valle, Valéry; Brémand, Fabrice

2005-12-01

The method presented extracts the demodulated phase from only one fringe pattern. Locally, this method approaches the fringe pattern morphology with the help of a mathematical model. The degree of similarity between the mathematical model and the real fringe is estimated by minimizing a correlation function. To use an optimization process, we have chosen a polynomial form such as a mathematical model. However, the use of a polynomial form induces an identification procedure with the purpose of retrieving the demodulated phase. This method, polynomial modulated phase correlation, is tested on several examples. Its performance, in terms of speed and precision, is presented on very noised fringe patterns.

Genomic similarity and kernel methods I: advancements by building on mathematical and statistical foundations.

PubMed

Schaid, Daniel J

2010-01-01

Measures of genomic similarity are the basis of many statistical analytic methods. We review the mathematical and statistical basis of similarity methods, particularly based on kernel methods. A kernel function converts information for a pair of subjects to a quantitative value representing either similarity (larger values meaning more similar) or distance (smaller values meaning more similar), with the requirement that it must create a positive semidefinite matrix when applied to all pairs of subjects. This review emphasizes the wide range of statistical methods and software that can be used when similarity is based on kernel methods, such as nonparametric regression, linear mixed models and generalized linear mixed models, hierarchical models, score statistics, and support vector machines. The mathematical rigor for these methods is summarized, as is the mathematical framework for making kernels. This review provides a framework to move from intuitive and heuristic approaches to define genomic similarities to more rigorous methods that can take advantage of powerful statistical modeling and existing software. A companion paper reviews novel approaches to creating kernels that might be useful for genomic analyses, providing insights with examples [1]. Copyright © 2010 S. Karger AG, Basel.

Mathematical modeling of ignition of woodlands resulted from accident on the pipeline

NASA Astrophysics Data System (ADS)

Perminov, V. A.; Loboda, E. L.; Reyno, V. V.

2014-11-01

Accidents occurring at the sites of pipelines, accompanied by environmental damage, economic loss, and sometimes loss of life. In this paper we calculated the sizes of the possible ignition zones in emergency situations on pipelines located close to the forest, accompanied by the appearance of fireballs. In this paper, using the method of mathematical modeling calculates the maximum size of the ignition zones of vegetation as a result of accidental releases of flammable substances. The paper suggested in the context of the general mathematical model of forest fires give a new mathematical setting and method of numerical solution of a problem of a forest fire modeling. The boundary-value problem is solved numerically using the method of splitting according to physical processes. The dependences of the size of the forest fuel for different amounts of leaked flammable substances and moisture content of vegetation.

Mathematical estimation of the level of microbial contamination on spacecraft surfaces by volumetric air sampling

NASA Technical Reports Server (NTRS)

Oxborrow, G. S.; Roark, A. L.; Fields, N. D.; Puleo, J. R.

1974-01-01

Microbiological sampling methods presently used for enumeration of microorganisms on spacecraft surfaces require contact with easily damaged components. Estimation of viable particles on surfaces using air sampling methods in conjunction with a mathematical model would be desirable. Parameters necessary for the mathematical model are the effect of angled surfaces on viable particle collection and the number of viable cells per viable particle. Deposition of viable particles on angled surfaces closely followed a cosine function, and the number of viable cells per viable particle was consistent with a Poisson distribution. Other parameters considered by the mathematical model included deposition rate and fractional removal per unit time. A close nonlinear correlation between volumetric air sampling and airborne fallout on surfaces was established with all fallout data points falling within the 95% confidence limits as determined by the mathematical model.

Correlation Educational Model in Primary Education Curriculum of Mathematics and Computer Science

ERIC Educational Resources Information Center

Macinko Kovac, Maja; Eret, Lidija

2012-01-01

This article gives insight into methodical correlation model of teaching mathematics and computer science. The model shows the way in which the related areas of computer science and mathematics can be supplemented, if it transforms the way of teaching and creates a "joint" lessons. Various didactic materials are designed, in which all…

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.

Mathematics Teachers' Criteria of Dimension

ERIC Educational Resources Information Center

Ural, Alattin

2014-01-01

The aim of the study is to determine mathematics teachers' decisions about dimensions of the geometric figures, criteria of dimension and consistency of decision-criteria. The research is a qualitative research and the model applied in the study is descriptive method on the basis of general scanning model. 15 mathematics teachers attended the…

Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model.

PubMed

Said, Nadia; Engelhart, Michael; Kirches, Christian; Körkel, Stefan; Holt, Daniel V

2016-01-01

Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods.

Mathematical modeling of the aerodynamics of high-angle-of-attack maneuvers

NASA Technical Reports Server (NTRS)

Schiff, L. B.; Tobak, M.; Malcolm, G. N.

1980-01-01

This paper is a review of the current state of aerodynamic mathematical modeling for aircraft motions at high angles of attack. The mathematical model serves to define a set of characteristic motions from whose known aerodynamic responses the aerodynamic response to an arbitrary high angle-of-attack flight maneuver can be predicted. Means are explored of obtaining stability parameter information in terms of the characteristic motions, whether by wind-tunnel experiments, computational methods, or by parameter-identification methods applied to flight-test data. A rationale is presented for selecting and verifying the aerodynamic mathematical model at the lowest necessary level of complexity. Experimental results describing the wing-rock phenomenon are shown to be accommodated within the most recent mathematical model by admitting the existence of aerodynamic hysteresis in the steady-state variation of the rolling moment with roll angle. Interpretation of the experimental results in terms of bifurcation theory reveals the general conditions under which aerodynamic hysteresis must exist.

Ocular hemodynamics and glaucoma: the role of mathematical modeling.

PubMed

Harris, Alon; Guidoboni, Giovanna; Arciero, Julia C; Amireskandari, Annahita; Tobe, Leslie A; Siesky, Brent A

2013-01-01

To discuss the role of mathematical modeling in studying ocular hemodynamics, with a focus on glaucoma. We reviewed recent literature on glaucoma, ocular blood flow, autoregulation, the optic nerve head, and the use of mathematical modeling in ocular circulation. Many studies suggest that alterations in ocular hemodynamics play a significant role in the development, progression, and incidence of glaucoma. Although there is currently a limited number of studies involving mathematical modeling of ocular blood flow, regulation, and diseases (such as glaucoma), preliminary modeling work shows the potential of mathematical models to elucidate the mechanisms that contribute most significantly to glaucoma progression. Mathematical modeling is a useful tool when used synergistically with clinical and laboratory data in the study of ocular blood flow and glaucoma. The development of models to investigate the relationship between ocular hemodynamic alterations and glaucoma progression will provide a unique and useful method for studying the pathophysiology of glaucoma.

10 CFR 431.197 - Manufacturer's determination of efficiency for distribution transformers.

Code of Federal Regulations, 2010 CFR

2010-01-01

... methods used; the mathematical model, the engineering or statistical analysis, computer simulation or... (b)(3) of this section, or by application of an alternative efficiency determination method (AEDM... section only if: (i) The AEDM has been derived from a mathematical model that represents the electrical...

Method and system to perform energy-extraction based active noise control

NASA Technical Reports Server (NTRS)

Kelkar, Atul (Inventor); Joshi, Suresh M. (Inventor)

2009-01-01

A method to provide active noise control to reduce noise and vibration in reverberant acoustic enclosures such as aircraft, vehicles, appliances, instruments, industrial equipment and the like is presented. A continuous-time multi-input multi-output (MIMO) state space mathematical model of the plant is obtained via analytical modeling and system identification. Compensation is designed to render the mathematical model passive in the sense of mathematical system theory. The compensated system is checked to ensure robustness of the passive property of the plant. The check ensures that the passivity is preserved if the mathematical model parameters are perturbed from nominal values. A passivity-based controller is designed and verified using numerical simulations and then tested. The controller is designed so that the resulting closed-loop response shows the desired noise reduction.

Mathematical Modeling of Diverse Phenomena

NASA Technical Reports Server (NTRS)

Howard, J. C.

1979-01-01

Tensor calculus is applied to the formulation of mathematical models of diverse phenomena. Aeronautics, fluid dynamics, and cosmology are among the areas of application. The feasibility of combining tensor methods and computer capability to formulate problems is demonstrated. The techniques described are an attempt to simplify the formulation of mathematical models by reducing the modeling process to a series of routine operations, which can be performed either manually or by computer.

Neutral model analysis of landscape patterns from mathematical morphology

Treesearch

Kurt H. Riitters; Peter Vogt; Pierre Soille; Jacek Kozak; Christine Estreguil

2007-01-01

Mathematical morphology encompasses methods for characterizing land-cover patterns in ecological research and biodiversity assessments. This paper reports a neutral model analysis of patterns in the absence of a structuring ecological process, to help set standards for comparing and interpreting patterns identified by mathematical morphology on real land-cover maps. We...

PENDISC: a simple method for constructing a mathematical model from time-series data of metabolite concentrations.

PubMed

Sriyudthsak, Kansuporn; Iwata, Michio; Hirai, Masami Yokota; Shiraishi, Fumihide

2014-06-01

The availability of large-scale datasets has led to more effort being made to understand characteristics of metabolic reaction networks. However, because the large-scale data are semi-quantitative, and may contain biological variations and/or analytical errors, it remains a challenge to construct a mathematical model with precise parameters using only these data. The present work proposes a simple method, referred to as PENDISC (Parameter Estimation in a N on- DImensionalized S-system with Constraints), to assist the complex process of parameter estimation in the construction of a mathematical model for a given metabolic reaction system. The PENDISC method was evaluated using two simple mathematical models: a linear metabolic pathway model with inhibition and a branched metabolic pathway model with inhibition and activation. The results indicate that a smaller number of data points and rate constant parameters enhances the agreement between calculated values and time-series data of metabolite concentrations, and leads to faster convergence when the same initial estimates are used for the fitting. This method is also shown to be applicable to noisy time-series data and to unmeasurable metabolite concentrations in a network, and to have a potential to handle metabolome data of a relatively large-scale metabolic reaction system. Furthermore, it was applied to aspartate-derived amino acid biosynthesis in Arabidopsis thaliana plant. The result provides confirmation that the mathematical model constructed satisfactorily agrees with the time-series datasets of seven metabolite concentrations.

Research Methods in Healthcare Epidemiology and Antimicrobial Stewardship-Mathematical Modeling.

PubMed

Barnes, Sean L; Kasaie, Parastu; Anderson, Deverick J; Rubin, Michael

2016-11-01

Mathematical modeling is a valuable methodology used to study healthcare epidemiology and antimicrobial stewardship, particularly when more traditional study approaches are infeasible, unethical, costly, or time consuming. We focus on 2 of the most common types of mathematical modeling, namely compartmental modeling and agent-based modeling, which provide important advantages-such as shorter developmental timelines and opportunities for extensive experimentation-over observational and experimental approaches. We summarize these advantages and disadvantages via specific examples and highlight recent advances in the methodology. A checklist is provided to serve as a guideline in the development of mathematical models in healthcare epidemiology and antimicrobial stewardship. Infect Control Hosp Epidemiol 2016;1-7.

Assessment and Learning of Mathematics.

ERIC Educational Resources Information Center

Leder, Gilah C., Ed.

This book addresses the link between student learning of mathematics, the teaching method adopted in the mathematics classroom, and the assessment procedures used to determine and measure student knowledge. Fifteen chapters address issues that include a review of different models of mathematics learning and assessment practices, three contrasting…

Mathematical-Artificial Neural Network Hybrid Model to Predict Roll Force during Hot Rolling of Steel

NASA Astrophysics Data System (ADS)

Rath, S.; Sengupta, P. P.; Singh, A. P.; Marik, A. K.; Talukdar, P.

2013-07-01

Accurate prediction of roll force during hot strip rolling is essential for model based operation of hot strip mills. Traditionally, mathematical models based on theory of plastic deformation have been used for prediction of roll force. In the last decade, data driven models like artificial neural network have been tried for prediction of roll force. Pure mathematical models have accuracy limitations whereas data driven models have difficulty in convergence when applied to industrial conditions. Hybrid models by integrating the traditional mathematical formulations and data driven methods are being developed in different parts of world. This paper discusses the methodology of development of an innovative hybrid mathematical-artificial neural network model. In mathematical model, the most important factor influencing accuracy is flow stress of steel. Coefficients of standard flow stress equation, calculated by parameter estimation technique, have been used in the model. The hybrid model has been trained and validated with input and output data collected from finishing stands of Hot Strip Mill, Bokaro Steel Plant, India. It has been found that the model accuracy has been improved with use of hybrid model, over the traditional mathematical model.

A Model for Minimizing Numeric Function Generator Complexity and Delay

DTIC Science & Technology

2007-12-01

allow computation of difficult mathematical functions in less time and with less hardware than commonly employed methods. They compute piecewise...Programmable Gate Arrays (FPGAs). The algorithms and estimation techniques apply to various NFG architectures and mathematical functions. This...thesis compares hardware utilization and propagation delay for various NFG architectures, mathematical functions, word widths, and segmentation methods

Mathematic models for a ray tracing method and its applications in wireless optical communications.

PubMed

Zhang, Minglun; Zhang, Yangan; Yuan, Xueguang; Zhang, Jinnan

2010-08-16

This paper presents a new ray tracing method, which contains a whole set of mathematic models, and its validity is verified by simulations. In addition, both theoretical analysis and simulation results show that the computational complexity of the method is much lower than that of previous ones. Therefore, the method can be used to rapidly calculate the impulse response of wireless optical channels for complicated systems.

The implementation of multiple intelligences based teaching model to improve mathematical problem solving ability for student of junior high school

NASA Astrophysics Data System (ADS)

Fasni, Nurli; Fatimah, Siti; Yulanda, Syerli

2017-05-01

This research aims to achieve some purposes such as: to know whether mathematical problem solving ability of students who have learned mathematics using Multiple Intelligences based teaching model is higher than the student who have learned mathematics using cooperative learning; to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using Multiple Intelligences based teaching model., to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using cooperative learning; to know the attitude of the students to Multiple Intelligences based teaching model. The method employed here is quasi-experiment which is controlled by pre-test and post-test. The population of this research is all of VII grade in SMP Negeri 14 Bandung even-term 2013/2014, later on two classes of it were taken for the samples of this research. A class was taught using Multiple Intelligences based teaching model and the other one was taught using cooperative learning. The data of this research were gotten from the test in mathematical problem solving, scale questionnaire of the student attitudes, and observation. The results show the mathematical problem solving of the students who have learned mathematics using Multiple Intelligences based teaching model learning is higher than the student who have learned mathematics using cooperative learning, the mathematical problem solving ability of the student who have learned mathematics using cooperative learning and Multiple Intelligences based teaching model are in intermediate level, and the students showed the positive attitude in learning mathematics using Multiple Intelligences based teaching model. As for the recommendation for next author, Multiple Intelligences based teaching model can be tested on other subject and other ability.

[Mathematical calculation of strength of the vertebral column in surgical treatment of unstable fractures of the spine].

PubMed

Orlov, S V; Kanykin, A Iu; Moskalev, V P; Shchedrenok, V V; Sedov, R L

2009-01-01

A mathematical model of a three-vertebra complex was developed in order to make an exact calculation of loss of supporting ability of the vertebral column in trauma. Mathematical description of the dynamic processes was based on Lagrange differential equation of the second order. The degree of compression and instability of the three-vertebra complex, established using mathematical modeling, determines the decision on the surgical treatment and might be considered as a prognostic criterion of the course of the compression trauma of the spine. The method of mathematical modeling of supporting ability of the vertebral column was used in 72 patients.

A mathematical method for precisely calculating the radiographic angles of the cup after total hip arthroplasty.

PubMed

Zhao, Jing-Xin; Su, Xiu-Yun; Xiao, Ruo-Xiu; Zhao, Zhe; Zhang, Li-Hai; Zhang, Li-Cheng; Tang, Pei-Fu

2016-11-01

We established a mathematical method to precisely calculate the radiographic anteversion (RA) and radiographic inclination (RI) angles of the acetabular cup based on anterior-posterior (AP) pelvic radiographs after total hip arthroplasty. Using Mathematica software, a mathematical model for an oblique cone was established to simulate how AP pelvic radiographs are obtained and to address the relationship between the two-dimensional and three-dimensional geometry of the opening circle of the cup. In this model, the vertex was the X-ray beam source, and the generatrix was the ellipse in radiographs projected from the opening circle of the acetabular cup. Using this model, we established a series of mathematical formulas to reveal the differences between the true RA and RI cup angles and the measurements results achieved using traditional methods and AP pelvic radiographs and to precisely calculate the RA and RI cup angles based on post-operative AP pelvic radiographs. Statistical analysis indicated that traditional methods should be used with caution if traditional measurements methods are used to calculate the RA and RI cup angles with AP pelvic radiograph. The entire calculation process could be performed by an orthopedic surgeon with mathematical knowledge of basic matrix and vector equations. Copyright © 2016 IPEM. Published by Elsevier Ltd. All rights reserved.

On the Shoulders of Giants: New Approaches to Numeracy.

ERIC Educational Resources Information Center

Steen, Lynn Arthur, Ed.

Forces created by the proliferation of computer hardware and software, by innovative methods of mathematical modelling and applications, by broader demographic considerations, and by schools themselves are profoundly changing the way mathematics is practiced, the way mathematics is taught, and the way mathematics is learned. In this volume, a…

Think Pair Share Using Realistic Mathematics Education Approach in Geometry Learning

NASA Astrophysics Data System (ADS)

Afthina, H.; Mardiyana; Pramudya, I.

2017-09-01

This research aims to determine the impact of mathematics learning applying Think Pair Share (TPS) using Realistic Mathematics Education (RME) viewed from mathematical-logical intelligence in geometry learning. Method that used in this research is quasi experimental research The result of this research shows that (1) mathematics achievement applying TPS using RME approach gives a better result than those applying direct learning model; (2) students with high mathematical-logical intelligence can reach a better mathematics achievement than those with average and low one, whereas students with average mathematical-logical intelligence can reach a better achievement than those with low one; (3) there is no interaction between learning model and the level of students’ mathematical-logical intelligence in giving a mathematics achievement. The impact of this research is that TPS model using RME approach can be applied in mathematics learning so that students can learn more actively and understand the material more, and mathematics learning become more meaningful. On the other hand, internal factors of students must become a consideration toward the success of students’ mathematical achievement particularly in geometry material.

Construction of mathematical model for measuring material concentration by colorimetric method

NASA Astrophysics Data System (ADS)

Liu, Bing; Gao, Lingceng; Yu, Kairong; Tan, Xianghua

2018-06-01

This paper use the method of multiple linear regression to discuss the data of C problem of mathematical modeling in 2017. First, we have established a regression model for the concentration of 5 substances. But only the regression model of the substance concentration of urea in milk can pass through the significance test. The regression model established by the second sets of data can pass the significance test. But this model exists serious multicollinearity. We have improved the model by principal component analysis. The improved model is used to control the system so that it is possible to measure the concentration of material by direct colorimetric method.

Biological system interactions.

PubMed Central

Adomian, G; Adomian, G E; Bellman, R E

1984-01-01

Mathematical modeling of cellular population growth, interconnected subsystems of the body, blood flow, and numerous other complex biological systems problems involves nonlinearities and generally randomness as well. Such problems have been dealt with by mathematical methods often changing the actual model to make it tractable. The method presented in this paper (and referenced works) allows much more physically realistic solutions. PMID:6585837

Application of differential transformation method for solving dengue transmission mathematical model

NASA Astrophysics Data System (ADS)

Ndii, Meksianis Z.; Anggriani, Nursanti; Supriatna, Asep K.

2018-03-01

The differential transformation method (DTM) is a semi-analytical numerical technique which depends on Taylor series and has application in many areas including Biomathematics. The aim of this paper is to employ the differential transformation method (DTM) to solve system of non-linear differential equations for dengue transmission mathematical model. Analytical and numerical solutions are determined and the results are compared to that of Runge-Kutta method. We found a good agreement between DTM and Runge-Kutta method.

Mathematical modelling and quantitative methods.

PubMed

Edler, L; Poirier, K; Dourson, M; Kleiner, J; Mileson, B; Nordmann, H; Renwick, A; Slob, W; Walton, K; Würtzen, G

2002-01-01

The present review reports on the mathematical methods and statistical techniques presently available for hazard characterisation. The state of the art of mathematical modelling and quantitative methods used currently for regulatory decision-making in Europe and additional potential methods for risk assessment of chemicals in food and diet are described. Existing practices of JECFA, FDA, EPA, etc., are examined for their similarities and differences. A framework is established for the development of new and improved quantitative methodologies. Areas for refinement, improvement and increase of efficiency of each method are identified in a gap analysis. Based on this critical evaluation, needs for future research are defined. It is concluded from our work that mathematical modelling of the dose-response relationship would improve the risk assessment process. An adequate characterisation of the dose-response relationship by mathematical modelling clearly requires the use of a sufficient number of dose groups to achieve a range of different response levels. This need not necessarily lead to an increase in the total number of animals in the study if an appropriate design is used. Chemical-specific data relating to the mode or mechanism of action and/or the toxicokinetics of the chemical should be used for dose-response characterisation whenever possible. It is concluded that a single method of hazard characterisation would not be suitable for all kinds of risk assessments, and that a range of different approaches is necessary so that the method used is the most appropriate for the data available and for the risk characterisation issue. Future refinements to dose-response characterisation should incorporate more clearly the extent of uncertainty and variability in the resulting output.

Mathematical Model of Stress-Strain State of Curved Tube of Non-Circular Cross-Section with Account of Technological Wall Thickness Variation

NASA Astrophysics Data System (ADS)

Pirogov, S. P.; Ustinov, N. N.; Smolin, N. I.

2018-05-01

A mathematical model of the stress-strain state of a curved tube of a non-circular cross-section is presented, taking into account the technological wall thickness variation. On the basis of the semi-membrane shell theory, a system of linear differential equations describing the deformation of a tube under the effect of pressure is obtained. To solve the boundary value problem, the method of shooting is applied. The adequacy of the proposed mathematical model is verified by comparison with the experimental data and the results of the calculation of tubes by the energy method.

The Prediction of the Students' Academic Underachievement in Mathematics Using the DEA Model: A Developing Country Case Study

ERIC Educational Resources Information Center

Moradi, Fatemeh; Amiripour, Parvaneh

2017-01-01

In this study, an attempt was made to predict the students' mathematical academic underachievement at the Islamic Azad University-Yadegare-Imam branch and the appropriate strategies in mathematical academic achievement to be applied using the Data Envelopment Analysis (DEA) model. Survey research methods were used to select 91 students from the…

Capability of GPGPU for Faster Thermal Analysis Used in Data Assimilation

NASA Astrophysics Data System (ADS)

Takaki, Ryoji; Akita, Takeshi; Shima, Eiji

A thermal mathematical model plays an important role in operations on orbit as well as spacecraft thermal designs. The thermal mathematical model has some uncertain thermal characteristic parameters, such as thermal contact resistances between components, effective emittances of multilayer insulation (MLI) blankets, discouraging make up efficiency and accuracy of the model. A particle filter which is one of successive data assimilation methods has been applied to construct spacecraft thermal mathematical models. This method conducts a lot of ensemble computations, which require large computational power. Recently, General Purpose computing in Graphics Processing Unit (GPGPU) has been attracted attention in high performance computing. Therefore GPGPU is applied to increase the computational speed of thermal analysis used in the particle filter. This paper shows the speed-up results by using GPGPU as well as the application method of GPGPU.

Projects, Puzzles and Other Pedagogies: Working with Kids to Solve Local Problems

ERIC Educational Resources Information Center

Marshman, Margaret

2012-01-01

Engaging and extending middle years students in mathematics is a continual challenge. One of the aims of the "Australian Curriculum: Mathematics" is to ensure that students are "confident, creative users and communicators of mathematics" (ACARA, 2011). Use of mathematical models and/or problems has been suggested as methods of…

Using Mathematical Analyses Activities to Improve Manipulative Discrimination in Early Childhood Teacher Education

ERIC Educational Resources Information Center

Ertle, Barbrina B.

2017-01-01

This article reports on the findings of manipulative analyses performed by preservice and in-service teachers in an early childhood teacher education program mathematics methods course. The activities are intended to model and promote mathematical analyses for better discrimination between mathematics manipulatives by early childhood teachers.…

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.

A mathematical model for describing the mechanical behaviour of root canal instruments.

PubMed

Zhang, E W; Cheung, G S P; Zheng, Y F

2011-01-01

The purpose of this study was to establish a general mathematical model for describing the mechanical behaviour of root canal instruments by combining a theoretical analytical approach with a numerical finite-element method. Mathematical formulas representing the longitudinal (taper, helical angle and pitch) and cross-sectional configurations and area, the bending and torsional inertia, the curvature of the boundary point and the (geometry of) loading condition were derived. Torsional and bending stresses and the resultant deformation were expressed mathematically as a function of these geometric parameters, modulus of elasticity of the material and the applied load. As illustrations, three brands of NiTi endodontic files of different cross-sectional configurations (ProTaper, Hero 642, and Mani NRT) were analysed under pure torsion and pure bending situation by entering the model into a finite-element analysis package (ANSYS). Numerical results confirmed that mathematical models were a feasible method to analyse the mechanical properties and predict the stress and deformation for root canal instruments during root canal preparation. Mathematical and numerical model can be a suitable way to examine mechanical behaviours as a criterion of the instrument design and to predict the stress and strain experienced by the endodontic instruments during root canal preparation. © 2010 International Endodontic Journal.

Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century.

PubMed

Ganusov, Vitaly V

2016-01-01

While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest "strong inference in mathematical modeling" as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century.

Discrete Dynamical Modeling.

ERIC Educational Resources Information Center

Sandefur, James T.

1991-01-01

Discussed is the process of translating situations involving changing quantities into mathematical relationships. This process, called dynamical modeling, allows students to learn new mathematics while sharpening their algebraic skills. A description of dynamical systems, problem-solving methods, a graphical analysis, and available classroom…

Mathematical modeling of ethanol production in solid-state fermentation based on solid medium' dry weight variation.

PubMed

Mazaheri, Davood; Shojaosadati, Seyed Abbas; Zamir, Seyed Morteza; Mousavi, Seyyed Mohammad

2018-04-21

In this work, mathematical modeling of ethanol production in solid-state fermentation (SSF) has been done based on the variation in the dry weight of solid medium. This method was previously used for mathematical modeling of enzyme production; however, the model should be modified to predict the production of a volatile compound like ethanol. The experimental results of bioethanol production from the mixture of carob pods and wheat bran by Zymomonas mobilis in SSF were used for the model validation. Exponential and logistic kinetic models were used for modeling the growth of microorganism. In both cases, the model predictions matched well with the experimental results during the exponential growth phase, indicating the good ability of solid medium weight variation method for modeling a volatile product formation in solid-state fermentation. In addition, using logistic model, better predictions were obtained.

Mathematical Practice in Textbooks Analysis: Praxeological Reference Models, the Case of Proportion

ERIC Educational Resources Information Center

Wijayanti, Dyana; Winsløw, Carl

2017-01-01

We present a new method in textbook analysis, based on so-called praxeological reference models focused on specific content at task level. This method implies that the mathematical contents of a textbook (or textbook part) is analyzed in terms of the tasks and techniques which are exposed to or demanded from readers; this can then be interpreted…

Reduced modeling of signal transduction – a modular approach

PubMed Central

Koschorreck, Markus; Conzelmann, Holger; Ebert, Sybille; Ederer, Michael; Gilles, Ernst Dieter

2007-01-01

Background Combinatorial complexity is a challenging problem in detailed and mechanistic mathematical modeling of signal transduction. This subject has been discussed intensively and a lot of progress has been made within the last few years. A software tool (BioNetGen) was developed which allows an automatic rule-based set-up of mechanistic model equations. In many cases these models can be reduced by an exact domain-oriented lumping technique. However, the resulting models can still consist of a very large number of differential equations. Results We introduce a new reduction technique, which allows building modularized and highly reduced models. Compared to existing approaches further reduction of signal transduction networks is possible. The method also provides a new modularization criterion, which allows to dissect the model into smaller modules that are called layers and can be modeled independently. Hallmarks of the approach are conservation relations within each layer and connection of layers by signal flows instead of mass flows. The reduced model can be formulated directly without previous generation of detailed model equations. It can be understood and interpreted intuitively, as model variables are macroscopic quantities that are converted by rates following simple kinetics. The proposed technique is applicable without using complex mathematical tools and even without detailed knowledge of the mathematical background. However, we provide a detailed mathematical analysis to show performance and limitations of the method. For physiologically relevant parameter domains the transient as well as the stationary errors caused by the reduction are negligible. Conclusion The new layer based reduced modeling method allows building modularized and strongly reduced models of signal transduction networks. Reduced model equations can be directly formulated and are intuitively interpretable. Additionally, the method provides very good approximations especially for macroscopic variables. It can be combined with existing reduction methods without any difficulties. PMID:17854494

Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century

PubMed Central

Ganusov, Vitaly V.

2016-01-01

While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest “strong inference in mathematical modeling” as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century. PMID:27499750

Mathematical modelling of an electromagnetics automobile suspension

NASA Astrophysics Data System (ADS)

Amin, Ahmad Zaki Mohamad; Ahmad, Shamsuddin; Hoe, Yeak Su

2017-04-01

The mathematical modelling of the electromagnetic automobile suspension (EAS) is presented. The solution of the model is found using Runge-Kutta Method via MAPLE. The graphs of the vertical displacement, different vertical displacement and road profiles and acceleration of car body against time are investigated and validated using certain criteria.

Mathematical modelling of the growth of human fetus anatomical structures.

PubMed

Dudek, Krzysztof; Kędzia, Wojciech; Kędzia, Emilia; Kędzia, Alicja; Derkowski, Wojciech

2017-09-01

The goal of this study was to present a procedure that would enable mathematical analysis of the increase of linear sizes of human anatomical structures, estimate mathematical model parameters and evaluate their adequacy. Section material consisted of 67 foetuses-rectus abdominis muscle and 75 foetuses- biceps femoris muscle. The following methods were incorporated to the study: preparation and anthropologic methods, image digital acquisition, Image J computer system measurements and statistical analysis method. We used an anthropologic method based on age determination with the use of crown-rump length-CRL (V-TUB) by Scammon and Calkins. The choice of mathematical function should be based on a real course of the curve presenting growth of anatomical structure linear size Ύ in subsequent weeks t of pregnancy. Size changes can be described with a segmental-linear model or one-function model with accuracy adequate enough for clinical purposes. The interdependence of size-age is described with many functions. However, the following functions are most often considered: linear, polynomial, spline, logarithmic, power, exponential, power-exponential, log-logistic I and II, Gompertz's I and II and von Bertalanffy's function. With the use of the procedures described above, mathematical models parameters were assessed for V-PL (the total length of body) and CRL body length increases, rectus abdominis total length h, its segments hI, hII, hIII, hIV, as well as biceps femoris length and width of long head (LHL and LHW) and of short head (SHL and SHW). The best adjustments to measurement results were observed in the exponential and Gompertz's models.

What’s about Peer Tutoring Learning Model?

NASA Astrophysics Data System (ADS)

Muthma'innah, M.

2017-09-01

Mathematics learning outcomes in Indonesia in general is still far from satisfactory. One effort that could be expected to solve the problem is to apply the model of peer tutoring learning in mathematics. This study aims to determine whether the results of students’ mathematics learning can be enhanced through peer tutoring learning models. This type of research is the study of literature, so that the method used is to summarize and analyze the results of relevant research that has been done. Peer tutoring learning model is a model of learning in which students learn in small groups that are grouped with different ability levels, all group members to work together and help each other to understand the material. By paying attention to the syntax of the learning, then learning will be invaluable peer tutoring for students who served as teachers and students are taught. In mathematics, the implementation of this learning model can make students understand each other mathematical concepts and help students in solving mathematical problems that are poorly understood, due to the interaction between students in learning. Then it will be able to improve learning outcomes in mathematics. The impact, it can be applied in mathematics learning.

Analysis of mathematical literacy ability based on goal orientation in model eliciting activities learning with murder strategy

NASA Astrophysics Data System (ADS)

Wijayanti, R.; Waluya, S. B.; Masrukan

2018-03-01

The purpose of this research are (1) to analyze the learning quality of MEAs with MURDER strategy, (2) to analyze students’ mathematical literacy ability based on goal orientation in MEAs learning with MURDER strategy. This research is a mixed method research of concurrent embedded type where qualitative method as the primary method. The data were obtained using the methods of scale, observation, test and interviews. The results showed that (1) MEAs Learning with MURDER strategy on students' mathematical literacy ability is qualified, (2) Students who have mastery goal characteristics are able to master the seven components of mathematical literacy process although there are still two components that the solution is less than the maximum. Students who have performance goal characteristics have not mastered the components of mathematical literacy process with the maximum, they are only able to master the ability of using mathematics tool and the other components of mathematical literacy process is quite good.

Mathematical Modelling as a Tool to Understand Cell Self-renewal and Differentiation.

PubMed

Getto, Philipp; Marciniak-Czochra, Anna

2015-01-01

Mathematical modeling is a powerful technique to address key questions and paradigms in a variety of complex biological systems and can provide quantitative insights into cell kinetics, fate determination and development of cell populations. The chapter is devoted to a review of modeling of the dynamics of stem cell-initiated systems using mathematical methods of ordinary differential equations. Some basic concepts and tools for cell population dynamics are summarized and presented as a gentle introduction to non-mathematicians. The models take into account different plausible mechanisms regulating homeostasis. Two mathematical frameworks are proposed reflecting, respectively, a discrete (punctuated by division events) and a continuous character of transitions between differentiation stages. Advantages and constraints of the mathematical approaches are presented on examples of models of blood systems and compared to patients data on healthy hematopoiesis.

A mathematical programming method for formulating a fuzzy regression model based on distance criterion.

PubMed

Chen, Liang-Hsuan; Hsueh, Chan-Ching

2007-06-01

Fuzzy regression models are useful to investigate the relationship between explanatory and response variables with fuzzy observations. Different from previous studies, this correspondence proposes a mathematical programming method to construct a fuzzy regression model based on a distance criterion. The objective of the mathematical programming is to minimize the sum of distances between the estimated and observed responses on the X axis, such that the fuzzy regression model constructed has the minimal total estimation error in distance. Only several alpha-cuts of fuzzy observations are needed as inputs to the mathematical programming model; therefore, the applications are not restricted to triangular fuzzy numbers. Three examples, adopted in the previous studies, and a larger example, modified from the crisp case, are used to illustrate the performance of the proposed approach. The results indicate that the proposed model has better performance than those in the previous studies based on either distance criterion or Kim and Bishu's criterion. In addition, the efficiency and effectiveness for solving the larger example by the proposed model are also satisfactory.

Program Helps Generate Boundary-Element Mathematical Models

NASA Technical Reports Server (NTRS)

Goldberg, R. K.

1995-01-01

Composite Model Generation-Boundary Element Method (COM-GEN-BEM) computer program significantly reduces time and effort needed to construct boundary-element mathematical models of continuous-fiber composite materials at micro-mechanical (constituent) scale. Generates boundary-element models compatible with BEST-CMS boundary-element code for anlaysis of micromechanics of composite material. Written in PATRAN Command Language (PCL).

Assessing metacognition of grade 2 and grade 4 students using an adaptation of multi-method interview approach during mathematics problem-solving

NASA Astrophysics Data System (ADS)

Kuzle, A.

2018-06-01

The important role that metacognition plays as a predictor for student mathematical learning and for mathematical problem-solving, has been extensively documented. But only recently has attention turned to primary grades, and more research is needed at this level. The goals of this paper are threefold: (1) to present metacognitive framework during mathematics problem-solving, (2) to describe their multi-method interview approach developed to study student mathematical metacognition, and (3) to empirically evaluate the utility of their model and the adaptation of their approach in the context of grade 2 and grade 4 mathematics problem-solving. The results are discussed not only with regard to further development of the adapted multi-method interview approach, but also with regard to their theoretical and practical implications.

Characterizing Preservice Teachers' Mathematical Understanding of Algebraic Relationships

ERIC Educational Resources Information Center

Nillas, Leah A.

2010-01-01

Qualitative research methods were employed to investigate characterization of preservice teachers' mathematical understanding. Responses on test items involving algebraic relationships were analyzed using with-in case analysis (Miles and Huberman, 1994) and Pirie and Kieren's (1994) model of growth of mathematical understanding. Five elementary…

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.

Envisioning migration: Mathematics in both experimental analysis and modeling of cell behavior

PubMed Central

Zhang, Elizabeth R.; Wu, Lani F.; Altschuler, Steven J.

2013-01-01

The complex nature of cell migration highlights the power and challenges of applying mathematics to biological studies. Mathematics may be used to create model equations that recapitulate migration, which can predict phenomena not easily uncovered by experiments or intuition alone. Alternatively, mathematics may be applied to interpreting complex data sets with better resolution—potentially empowering scientists to discern subtle patterns amid the noise and heterogeneity typical of migrating cells. Iteration between these two methods is necessary in order to reveal connections within the cell migration signaling network, as well as to understand the behavior that arises from those connections. Here, we review recent quantitative analysis and mathematical modeling approaches to the cell migration problem. PMID:23660413

Envisioning migration: mathematics in both experimental analysis and modeling of cell behavior.

PubMed

Zhang, Elizabeth R; Wu, Lani F; Altschuler, Steven J

2013-10-01

The complex nature of cell migration highlights the power and challenges of applying mathematics to biological studies. Mathematics may be used to create model equations that recapitulate migration, which can predict phenomena not easily uncovered by experiments or intuition alone. Alternatively, mathematics may be applied to interpreting complex data sets with better resolution--potentially empowering scientists to discern subtle patterns amid the noise and heterogeneity typical of migrating cells. Iteration between these two methods is necessary in order to reveal connections within the cell migration signaling network, as well as to understand the behavior that arises from those connections. Here, we review recent quantitative analysis and mathematical modeling approaches to the cell migration problem. Copyright © 2013 Elsevier Ltd. All rights reserved.

Will the digital computer transform classical mathematics?

PubMed

Rotman, Brian

2003-08-15

Mathematics and machines have influenced each other for millennia. The advent of the digital computer introduced a powerfully new element that promises to transform the relation between them. This paper outlines the thesis that the effect of the digital computer on mathematics, already widespread, is likely to be radical and far-reaching. To articulate this claim, an abstract model of doing mathematics is introduced based on a triad of actors of which one, the 'agent', corresponds to the function performed by the computer. The model is used to frame two sorts of transformation. The first is pragmatic and involves the alterations and progressive colonization of the content and methods of enquiry of various mathematical fields brought about by digital methods. The second is conceptual and concerns a fundamental antagonism between the infinity enshrined in classical mathematics and physics (continuity, real numbers, asymptotic definitions) and the inherently real and material limit of processes associated with digital computation. An example which lies in the intersection of classical mathematics and computer science, the P=NP problem, is analysed in the light of this latter issue.

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

Yan, Ruqiang; Chen, Xuefeng; Li, Weihua

Modern mathematics has commonly been utilized as an effective tool to model mechanical equipment so that their dynamic characteristics can be studied analytically. This will help identify potential failures of mechanical equipment by observing change in the equipment’s dynamic parameters. On the other hand, dynamic signals are also important and provide reliable information about the equipment’s working status. Modern mathematics has also provided us with a systematic way to design and implement various signal processing methods, which are used to analyze these dynamic signals, and to enhance intrinsic signal components that are directly related to machine failures. This special issuemore » is aimed at stimulating not only new insights on mathematical methods for modeling but also recently developed signal processing methods, such as sparse decomposition with potential applications in machine fault diagnosis. Finally, the papers included in this special issue provide a glimpse into some of the research and applications in the field of machine fault diagnosis through applications of the modern mathematical methods.« less

Comparison effectiveness of cooperative learning type STAD with cooperative learning type TPS in terms of mathematical method of Junior High School students

NASA Astrophysics Data System (ADS)

Wahyuni, A.

2018-05-01

This research is aimed to find out whether the model of cooperative learning type Student Team Achievement Division (STAD) is more effective than cooperative learning type Think-Pair-Share in SMP Negeri 7 Yogyakarta. This research was a quasi-experimental research, using two experimental groups. The population of research was all students of 7thclass in SMP Negeri 7 Yogyakarta that consists of 5 Classes. From the population were taken 2 classes randomly which used as sample. The instrument to collect data was a description test. Measurement of instrument validity use content validity and construct validity, while measuring instrument reliability use Cronbach Alpha formula. To investigate the effectiveness of cooperative learning type STAD and cooperative learning type TPS on the aspect of student’s mathematical method, the datas were analyzed by one sample test. Comparing the effectiveness of cooperative learning type STAD and TPS in terms of mathematical communication skills by using t-test. Normality test was not conducted because the sample of research more than 30 students, while homogeneity tested by using Kolmogorov Smirnov test. The analysis was performed at 5% confidence level.The results show as follows : 1) The model of cooperative learning type STAD and TPS are effective in terms of mathematical method of junior high school students. 2). STAD type cooperative learning model is more effective than TPS type cooperative learning model in terms of mathematical methods of junior high school students.

A mathematical modeling approach to resource allocation for railroad-highway crossing safety upgrades.

PubMed

Konur, Dinçer; Golias, Mihalis M; Darks, Brandon

2013-03-01

State Departments of Transportation (S-DOT's) periodically allocate budget for safety upgrades at railroad-highway crossings. Efficient resource allocation is crucial for reducing accidents at railroad-highway crossings and increasing railroad as well as highway transportation safety. While a specific method is not restricted to S-DOT's, sorting type of procedures are recommended by the Federal Railroad Administration (FRA), United States Department of Transportation for the resource allocation problem. In this study, a generic mathematical model is proposed for the resource allocation problem for railroad-highway crossing safety upgrades. The proposed approach is compared to sorting based methods for safety upgrades of public at-grade railroad-highway crossings in Tennessee. The comparison shows that the proposed mathematical modeling approach is more efficient than sorting methods in reducing accidents and severity. Copyright © 2012 Elsevier Ltd. All rights reserved.

Mathematical modeling and hydrodynamics of Electrochemical deburring process

NASA Astrophysics Data System (ADS)

Prabhu, Satisha; Abhishek Kumar, K., Dr

2018-04-01

The electrochemical deburring (ECD) is a variation of electrochemical machining is considered as one of the efficient methods for deburring of intersecting features and internal parts. Since manual deburring costs are comparatively high one can potentially use this method in both batch production and flow production. The other advantage of this process is that time of deburring as is on the order of seconds as compared to other methods. In this paper, the mathematical modeling of Electrochemical deburring is analysed from its deburring time and base metal removal point of view. Simultaneously material removal rate is affected by electrolyte temperature and bubble formation. The mathematical model and hydrodynamics of the process throw limelight upon optimum velocity calculations which can be theoretically determined. The analysis can be the powerful tool for prediction of the above-mentioned parameters by experimentation.

Mathematical models of the simplest fuzzy PI/PD controllers with skewed input and output fuzzy sets.

PubMed

Mohan, B M; Sinha, Arpita

2008-07-01

This paper unveils mathematical models for fuzzy PI/PD controllers which employ two skewed fuzzy sets for each of the two-input variables and three skewed fuzzy sets for the output variable. The basic constituents of these models are Gamma-type and L-type membership functions for each input, trapezoidal/triangular membership functions for output, intersection/algebraic product triangular norm, maximum/drastic sum triangular conorm, Mamdani minimum/Larsen product/drastic product inference method, and center of sums defuzzification method. The existing simplest fuzzy PI/PD controller structures derived via symmetrical fuzzy sets become special cases of the mathematical models revealed in this paper. Finally, a numerical example along with its simulation results are included to demonstrate the effectiveness of the simplest fuzzy PI controllers.

Modeling Electromagnetic Scattering From Complex Inhomogeneous Objects

NASA Technical Reports Server (NTRS)

Deshpande, Manohar; Reddy, C. J.

2011-01-01

This software innovation is designed to develop a mathematical formulation to estimate the electromagnetic scattering characteristics of complex, inhomogeneous objects using the finite-element-method (FEM) and method-of-moments (MoM) concepts, as well as to develop a FORTRAN code called FEMOM3DS (Finite Element Method and Method of Moments for 3-Dimensional Scattering), which will implement the steps that are described in the mathematical formulation. Very complex objects can be easily modeled, and the operator of the code is not required to know the details of electromagnetic theory to study electromagnetic scattering.

Preface of the "Symposium on Mathematical Models and Methods to investigate Heterogeneity in Cell and Cell Population Biology"

NASA Astrophysics Data System (ADS)

Clairambault, Jean

2016-06-01

This session investigates hot topics related to mathematical representations of cell and cell population dynamics in biology and medicine, in particular, but not only, with applications to cancer. Methods in mathematical modelling and analysis, and in statistical inference using single-cell and cell population data, should contribute to focus this session on heterogeneity in cell populations. Among other methods are proposed: a) Intracellular protein dynamics and gene regulatory networks using ordinary/partial/delay differential equations (ODEs, PDEs, DDEs); b) Representation of cell population dynamics using agent-based models (ABMs) and/or PDEs; c) Hybrid models and multiscale models to integrate single-cell dynamics into cell population behaviour; d) Structured cell population dynamics and asymptotic evolution w.r.t. relevant traits; e) Heterogeneity in cancer cell populations: origin, evolution, phylogeny and methods of reconstruction; f) Drug resistance as an evolutionary phenotype: predicting and overcoming it in therapeutics; g) Theoretical therapeutic optimisation of combined drug treatments in cancer cell populations and in populations of other organisms, such as bacteria.

Examining the Implementation of a Problem-Based Learning and Traditional Hybrid Model of Instruction in Remedial Mathematics Classes Designed for State Testing Preparation of Eleventh Grade Students

ERIC Educational Resources Information Center

Rodgers, Lindsay D.

2011-01-01

The following paper examined the effects of a new method of teaching for remedial mathematics, named the hybrid model of instruction. Due to increasing importance of high stakes testing, the study sought to determine if this method of instruction, that blends traditional teaching and problem-based learning, had different learning effects on…

Algorithm for repairing the damaged images of grain structures obtained from the cellular automata and measurement of grain size

NASA Astrophysics Data System (ADS)

Ramírez-López, A.; Romero-Romo, M. A.; Muñoz-Negron, D.; López-Ramírez, S.; Escarela-Pérez, R.; Duran-Valencia, C.

2012-10-01

Computational models are developed to create grain structures using mathematical algorithms based on the chaos theory such as cellular automaton, geometrical models, fractals, and stochastic methods. Because of the chaotic nature of grain structures, some of the most popular routines are based on the Monte Carlo method, statistical distributions, and random walk methods, which can be easily programmed and included in nested loops. Nevertheless, grain structures are not well defined as the results of computational errors and numerical inconsistencies on mathematical methods. Due to the finite definition of numbers or the numerical restrictions during the simulation of solidification, damaged images appear on the screen. These images must be repaired to obtain a good measurement of grain geometrical properties. Some mathematical algorithms were developed to repair, measure, and characterize grain structures obtained from cellular automata in the present work. An appropriate measurement of grain size and the corrected identification of interfaces and length are very important topics in materials science because they are the representation and validation of mathematical models with real samples. As a result, the developed algorithms are tested and proved to be appropriate and efficient to eliminate the errors and characterize the grain structures.

Curve fitting methods for solar radiation data modeling

NASA Astrophysics Data System (ADS)

Karim, Samsul Ariffin Abdul; Singh, Balbir Singh Mahinder

2014-10-01

This paper studies the use of several type of curve fitting method to smooth the global solar radiation data. After the data have been fitted by using curve fitting method, the mathematical model of global solar radiation will be developed. The error measurement was calculated by using goodness-fit statistics such as root mean square error (RMSE) and the value of R2. The best fitting methods will be used as a starting point for the construction of mathematical modeling of solar radiation received in Universiti Teknologi PETRONAS (UTP) Malaysia. Numerical results indicated that Gaussian fitting and sine fitting (both with two terms) gives better results as compare with the other fitting methods.

Curve fitting methods for solar radiation data modeling

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

Karim, Samsul Ariffin Abdul, E-mail: samsul-ariffin@petronas.com.my, E-mail: balbir@petronas.com.my; Singh, Balbir Singh Mahinder, E-mail: samsul-ariffin@petronas.com.my, E-mail: balbir@petronas.com.my

2014-10-24

This paper studies the use of several type of curve fitting method to smooth the global solar radiation data. After the data have been fitted by using curve fitting method, the mathematical model of global solar radiation will be developed. The error measurement was calculated by using goodness-fit statistics such as root mean square error (RMSE) and the value of R{sup 2}. The best fitting methods will be used as a starting point for the construction of mathematical modeling of solar radiation received in Universiti Teknologi PETRONAS (UTP) Malaysia. Numerical results indicated that Gaussian fitting and sine fitting (both withmore » two terms) gives better results as compare with the other fitting methods.« less

Female Preservice Teachers and Mathematics: Anxiety, Beliefs, and Stereotypes

ERIC Educational Resources Information Center

Lake, Vickie E.; Kelly, Loreen

2014-01-01

The purpose of the current study was to examine if preservice teachers' (PSTs) mathematics anxiety decreased and if their beliefs and stereotypes changed after they completed their early childhood mathematics methods course. It was hypothesized that by using and modeling concrete materials or manipulatives (Thompson, 1992; Vinson, 2001) and…

A mathematical model of microbial enhanced oil recovery (MEOR) method for mixed type rock

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

Sitnikov, A.A.; Eremin, N.A.; Ibattulin, R.R.

1994-12-31

This paper deals with the microbial enhanced oil recovery method. It covers: (1) Mechanism of microbial influence on the reservoir was analyzed; (2) The main groups of metabolites affected by the hydrodynamic characteristics of the reservoir were determined; (3) The criterions of use of microbial influence method on the reservoir are defined. The mathematical model of microbial influence on the reservoir was made on this basis. The injection of molasse water solution with Clostridium bacterias into the mixed type of rock was used in this model. And the results of calculations were compared with experimental data.

Quantitative assessment model for gastric cancer screening

PubMed Central

Chen, Kun; Yu, Wei-Ping; Song, Liang; Zhu, Yi-Min

2005-01-01

AIM: To set up a mathematic model for gastric cancer screening and to evaluate its function in mass screening for gastric cancer. METHODS: A case control study was carried on in 66 patients and 198 normal people, then the risk and protective factors of gastric cancer were determined, including heavy manual work, foods such as small yellow-fin tuna, dried small shrimps, squills, crabs, mothers suffering from gastric diseases, spouse alive, use of refrigerators and hot food, etc. According to some principles and methods of probability and fuzzy mathematics, a quantitative assessment model was established as follows: first, we selected some factors significant in statistics, and calculated weight coefficient for each one by two different methods; second, population space was divided into gastric cancer fuzzy subset and non gastric cancer fuzzy subset, then a mathematic model for each subset was established, we got a mathematic expression of attribute degree (AD). RESULTS: Based on the data of 63 patients and 693 normal people, AD of each subject was calculated. Considering the sensitivity and specificity, the thresholds of AD values calculated were configured with 0.20 and 0.17, respectively. According to these thresholds, the sensitivity and specificity of the quantitative model were about 69% and 63%. Moreover, statistical test showed that the identification outcomes of these two different calculation methods were identical (P>0.05). CONCLUSION: The validity of this method is satisfactory. It is convenient, feasible, economic and can be used to determine individual and population risks of gastric cancer. PMID:15655813

Problem-Based Learning--Buginese Cultural Knowledge Model--Case Study: Teaching Mathematics at Junior High School

ERIC Educational Resources Information Center

Cheriani, Cheriani; Mahmud, Alimuddin; Tahmir, Suradi; Manda, Darman; Dirawan, Gufran Darma

2015-01-01

This study aims to determine the differences in learning output by using Problem Based Model combines with the "Buginese" Local Cultural Knowledge (PBL-Culture). It is also explores the students activities in learning mathematics subject by using PBL-Culture Models. This research is using Mixed Methods approach that combined quantitative…

Complex Applications of HLM in Studies of Science and Mathematics Achievement: Cross-Classified Random Effects Models

ERIC Educational Resources Information Center

Moreno, Mario; Harwell, Michael; Guzey, S. Selcen; Phillips, Alison; Moore, Tamara J.

2016-01-01

Hierarchical linear models have become a familiar method for accounting for a hierarchical data structure in studies of science and mathematics achievement. This paper illustrates the use of cross-classified random effects models (CCREMs), which are likely less familiar. The defining characteristic of CCREMs is a hierarchical data structure…

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

Mathematical modelling and numerical simulation of forces in milling process

NASA Astrophysics Data System (ADS)

Turai, Bhanu Murthy; Satish, Cherukuvada; Prakash Marimuthu, K.

2018-04-01

Machining of the material by milling induces forces, which act on the work piece material, tool and which in turn act on the machining tool. The forces involved in milling process can be quantified, mathematical models help to predict these forces. A lot of research has been carried out in this area in the past few decades. The current research aims at developing a mathematical model to predict forces at different levels which arise machining of Aluminium6061 alloy. Finite element analysis was used to develop a FE model to predict the cutting forces. Simulation was done for varying cutting conditions. Different experiments was designed using Taguchi method. A L9 orthogonal array was designed and the output was measure for the different experiments. The same was used to develop the mathematical model.

Mathematical modeling of physiological systems: an essential tool for discovery.

PubMed

Glynn, Patric; Unudurthi, Sathya D; Hund, Thomas J

2014-08-28

Mathematical models are invaluable tools for understanding the relationships between components of a complex system. In the biological context, mathematical models help us understand the complex web of interrelations between various components (DNA, proteins, enzymes, signaling molecules etc.) in a biological system, gain better understanding of the system as a whole, and in turn predict its behavior in an altered state (e.g. disease). Mathematical modeling has enhanced our understanding of multiple complex biological processes like enzyme kinetics, metabolic networks, signal transduction pathways, gene regulatory networks, and electrophysiology. With recent advances in high throughput data generation methods, computational techniques and mathematical modeling have become even more central to the study of biological systems. In this review, we provide a brief history and highlight some of the important applications of modeling in biological systems with an emphasis on the study of excitable cells. We conclude with a discussion about opportunities and challenges for mathematical modeling going forward. In a larger sense, the review is designed to help answer a simple but important question that theoreticians frequently face from interested but skeptical colleagues on the experimental side: "What is the value of a model?" Copyright © 2014 Elsevier Inc. All rights reserved.

Optimization of a new mathematical model for bacterial growth

USDA-ARS?s Scientific Manuscript database

The objective of this research is to optimize a new mathematical equation as a primary model to describe the growth of bacteria under constant temperature conditions. An optimization algorithm was used in combination with a numerical (Runge-Kutta) method to solve the differential form of the new gr...

Mathematical Model Taking into Account Nonlocal Effects of Plasmonic Structures on the Basis of the Discrete Source Method

NASA Astrophysics Data System (ADS)

Eremin, Yu. A.; Sveshnikov, A. G.

2018-04-01

The discrete source method is used to develop and implement a mathematical model for solving the problem of scattering electromagnetic waves by a three-dimensional plasmonic scatterer with nonlocal effects taken into account. Numerical results are presented whereby the features of the scattering properties of plasmonic particles with allowance for nonlocal effects are demonstrated depending on the direction and polarization of the incident wave.

Application of the Analog Method to Modelling Heat Waves: A Case Study with Power Transformers

DTIC Science & Technology

2017-04-21

UNCLASSIFIED Massachusetts Institute of Technology Lincoln Laboratory APPLICATION OF THE ANALOG METHOD TO MODELLING HEAT WAVES: A CASE STUDY WITH...18 2 Calibration and validation statistics with the use of five atmospheric vari- ables to construct analogue diagnostics for JJA of transformer T2...electrical grid as a series of nodes (transformers) and edges (transmission lines) so that basic mathematical anal- ysis can be performed. The mathematics

An overview of the mathematical and statistical analysis component of RICIS

NASA Technical Reports Server (NTRS)

Hallum, Cecil R.

1987-01-01

Mathematical and statistical analysis components of RICIS (Research Institute for Computing and Information Systems) can be used in the following problem areas: (1) quantification and measurement of software reliability; (2) assessment of changes in software reliability over time (reliability growth); (3) analysis of software-failure data; and (4) decision logic for whether to continue or stop testing software. Other areas of interest to NASA/JSC where mathematical and statistical analysis can be successfully employed include: math modeling of physical systems, simulation, statistical data reduction, evaluation methods, optimization, algorithm development, and mathematical methods in signal processing.

Development and Validation of a Mathematical Model for Olive Oil Oxidation

NASA Astrophysics Data System (ADS)

Rahmouni, K.; Bouhafa, H.; Hamdi, S.

2009-03-01

A mathematical model describing the stability or the susceptibility to oxidation of extra virgin olive oil has been developed. The model has been resolved by an iterative method using differential finite method. It was validated by experimental data of extra virgin olive oil (EVOO) oxidation. EVOO stability was tested by using a Rancimat at four different temperatures 60, 70, 80 and 90° C until peroxide accumulation reached 20 [meq/kg]. Peroxide formation is speed relatively slow; fits zero order reaction with linear regression coefficients varying from 0, 98 to 0, 99. The mathematical model was used to predict the shelf life of bulk conditioned olive oil. This model described peroxide accumulation inside a container in excess of oxygen as a function of time at various positions from the interface air/oil. Good correlations were obtained between theoretical and experimental values.

Comparing the cognitive differences resulting from modeling instruction: Using computer microworld and physical object instruction to model real world problems

NASA Astrophysics Data System (ADS)

Oursland, Mark David

This study compared the modeling achievement of students receiving mathematical modeling instruction using the computer microworld, Interactive Physics, and students receiving instruction using physical objects. Modeling instruction included activities where students applied the (a) linear model to a variety of situations, (b) linear model to two-rate situations with a constant rate, (c) quadratic model to familiar geometric figures. Both quantitative and qualitative methods were used to analyze achievement differences between students (a) receiving different methods of modeling instruction, (b) with different levels of beginning modeling ability, or (c) with different levels of computer literacy. Student achievement was analyzed quantitatively through a three-factor analysis of variance where modeling instruction, beginning modeling ability, and computer literacy were used as the three independent factors. The SOLO (Structure of the Observed Learning Outcome) assessment framework was used to design written modeling assessment instruments to measure the students' modeling achievement. The same three independent factors were used to collect and analyze the interviews and observations of student behaviors. Both methods of modeling instruction used the data analysis approach to mathematical modeling. The instructional lessons presented problem situations where students were asked to collect data, analyze the data, write a symbolic mathematical equation, and use equation to solve the problem. The researcher recommends the following practice for modeling instruction based on the conclusions of this study. A variety of activities with a common structure are needed to make explicit the modeling process of applying a standard mathematical model. The modeling process is influenced strongly by prior knowledge of the problem context and previous modeling experiences. The conclusions of this study imply that knowledge of the properties about squares improved the students' ability to model a geometric problem more than instruction in data analysis modeling. The uses of computer microworlds such as Interactive Physics in conjunction with cooperative groups are a viable method of modeling instruction.

Mathematic modeling of the Earth's surface and the process of remote sensing

NASA Technical Reports Server (NTRS)

Balter, B. M.

1979-01-01

It is shown that real data from remote sensing of the Earth from outer space are not best suited to the search for optimal procedures with which to process such data. To work out the procedures, it was proposed that data synthesized with the help of mathematical modeling be used. A criterion for simularity to reality was formulated. The basic principles for constructing methods for modeling the data from remote sensing are recommended. A concrete method is formulated for modeling a complete cycle of radiation transformations in remote sensing. A computer program is described which realizes the proposed method. Some results from calculations are presented which show that the method satisfies the requirements imposed on it.

Mathematical model of rolling an elastic wheel over deformable support base

NASA Astrophysics Data System (ADS)

Volskaia, V. N.; Zhileykin, M. M.; Zakharov, A. Y.

2018-02-01

One of the main direction of economic growth in Russia remains to be a speedy development of north and northeast regions that are the constituents of the 60 percent of the country territory. The further development of these territories requires new methods and technologies for solving transport and technological problems when off-road transportation of cargoes and people is conducting. One of the fundamental methods of patency prediction is imitation modeling of wheeled vehicles movement in different operating conditions. Both deformable properties of tires and physical and mechanical properties of the ground: normal tire deflection and gauge depth; variation of contact patch area depending on the load and pressure of air in the tire; existence of hysteresis losses in the tire material which are influencing on the rolling resistance due to friction processes between tire and ground in the contact patch; existence of the tangential reaction from the ground by entire contact area influence on the tractive patency. Nowadays there are two main trends in theoretical research of interaction wheeled propulsion device with ground: analytical method involving mathematical description of explored process and finite element method based on computational modeling. Mathematical models of interaction tire with the ground are used both in processes of interaction individual wheeled propulsion device with ground and researches of mobile vehicle dynamical models operated in specific road and climate conditions. One of the most significant imperfection of these models is the description of interaction wheel with flat deformable support base whereas profile of real support base surface has essential height of unevenness which is commensurate with radius of the wheel. The description of processes taking place in the ground under influence of the wheeled propulsion device using the finite element method is relatively new but most applicable lately. The application of this method allows to provide the most accurate description of the interaction process of a wheeled propulsion devices and the ground, also this method allows to define tension in the ground, deformation of the ground and the tire and ground’s compression. However, the high laboriousness of computations is essential shortcoming of that method therefore it’s hard to use these models as part of the general motion model of multi-axis wheeled vehicles. The purpose of this research is the elaboration of mathematical model of elastic wheel rolling over deformable rough support base taking into account the contact patch deformation. The mathematical model of rectilinear rolling an elastic wheel over rough deformable support base, taking into account variation of contact patch area and variation in the direction of the radial and tangential reactions also load bearing capacity of the ground, is developed. The efficiency of developed mathematical model of rectilinear rolling an elastic wheel over rough deformable support base is proved by the simulation methods.

Airflow and Particle Transport Through Human Airways: A Systematic Review

NASA Astrophysics Data System (ADS)

Kharat, S. B.; Deoghare, A. B.; Pandey, K. M.

2017-08-01

This paper describes review of the relevant literature about two phase analysis of air and particle flow through human airways. An emphasis of the review is placed on elaborating the steps involved in two phase analysis, which are Geometric modelling methods and Mathematical models. The first two parts describes various approaches that are followed for constructing an Airway model upon which analysis are conducted. Broad two categories of geometric modelling viz. Simplified modelling and Accurate modelling using medical scans are discussed briefly. Ease and limitations of simplified models, then examples of CT based models are discussed. In later part of the review different mathematical models implemented by researchers for analysis are briefed. Mathematical models used for Air and Particle phases are elaborated separately.

Mathematical model of a DIC position sensing system within an optical trap

NASA Astrophysics Data System (ADS)

Wulff, Kurt D.; Cole, Daniel G.; Clark, Robert L.

2005-08-01

The quantitative study of displacements and forces of motor proteins and processes that occur at the microscopic level and below require a high level of sensitivity. For optical traps, two techniques for position sensing have been accepted and used quite extensively: quadrant photodiodes and an interferometric position sensing technique based on DIC imaging. While quadrant photodiodes have been studied in depth and mathematically characterized, a mathematical characterization of the interferometric position sensor has not been presented to the authors' knowledge. The interferometric position sensing method works off of the DIC imaging capabilities of a microscope. Circularly polarized light is sent into the microscope and the Wollaston prism used for DIC imaging splits the beam into its orthogonal components, displacing them by a set distance determined by the user. The distance between the axes of the beams is set so the beams overlap at the specimen plane and effectively share the trapped microsphere. A second prism then recombines the light beams and the exiting laser light's polarization is measured and related to position. In this paper we outline the mathematical characterization of a microsphere suspended in an optical trap using a DIC position sensing method. The sensitivity of this mathematical model is then compared to the QPD model. The mathematical model of a microsphere in an optical trap can serve as a calibration curve for an experimental setup.

On dependency properties of the ISIs generated by a two-compartmental neuronal model.

PubMed

Benedetto, Elisa; Sacerdote, Laura

2013-02-01

One-dimensional leaky integrate and fire neuronal models describe interspike intervals (ISIs) of a neuron as a renewal process and disregarding the neuron geometry. Many multi-compartment models account for the geometrical features of the neuron but are too complex for their mathematical tractability. Leaky integrate and fire two-compartment models seem a good compromise between mathematical tractability and an improved realism. They indeed allow to relax the renewal hypothesis, typical of one-dimensional models, without introducing too strong mathematical difficulties. Here, we pursue the analysis of the two-compartment model studied by Lansky and Rodriguez (Phys D 132:267-286, 1999), aiming of introducing some specific mathematical results used together with simulation techniques. With the aid of these methods, we investigate dependency properties of ISIs for different values of the model parameters. We show that an increase of the input increases the strength of the dependence between successive ISIs.

Comparison of Intelligent Systems in Detecting a Child's Mathematical Gift

ERIC Educational Resources Information Center

Pavlekovic, Margita; Zekic-Susac, Marijana; Djurdjevic, Ivana

2009-01-01

This paper compares the efficiency of two intelligent methods: expert systems and neural networks, in detecting children's mathematical gift at the fourth grade of elementary school. The input space for the expert system and the neural network model consisted of 60 variables describing five basic components of a child's mathematical gift…

Engaging Life-Sciences Students with Mathematical Models: Does Authenticity Help?

ERIC Educational Resources Information Center

Poladian, Leon

2013-01-01

Compulsory mathematics service units for the life sciences present unique challenges: even students who learn some specific skills maintain a negative attitude to mathematics and do not see the relevance of the unit towards their degree. The focus on authentic content and the presentation and teaching of global or qualitative methods before…

Comparison of genetic algorithms with conjugate gradient methods

NASA Technical Reports Server (NTRS)

Bosworth, J. L.; Foo, N. Y.; Zeigler, B. P.

1972-01-01

Genetic algorithms for mathematical function optimization are modeled on search strategies employed in natural adaptation. Comparisons of genetic algorithms with conjugate gradient methods, which were made on an IBM 1800 digital computer, show that genetic algorithms display superior performance over gradient methods for functions which are poorly behaved mathematically, for multimodal functions, and for functions obscured by additive random noise. Genetic methods offer performance comparable to gradient methods for many of the standard functions.

Analytic uncertainty and sensitivity analysis of models with input correlations

NASA Astrophysics Data System (ADS)

Zhu, Yueying; Wang, Qiuping A.; Li, Wei; Cai, Xu

2018-03-01

Probabilistic uncertainty analysis is a common means of evaluating mathematical models. In mathematical modeling, the uncertainty in input variables is specified through distribution laws. Its contribution to the uncertainty in model response is usually analyzed by assuming that input variables are independent of each other. However, correlated parameters are often happened in practical applications. In the present paper, an analytic method is built for the uncertainty and sensitivity analysis of models in the presence of input correlations. With the method, it is straightforward to identify the importance of the independence and correlations of input variables in determining the model response. This allows one to decide whether or not the input correlations should be considered in practice. Numerical examples suggest the effectiveness and validation of our analytic method in the analysis of general models. A practical application of the method is also proposed to the uncertainty and sensitivity analysis of a deterministic HIV model.

System and method for anomaly detection

DOEpatents

Scherrer, Chad

2010-06-15

A system and method for detecting one or more anomalies in a plurality of observations is provided. In one illustrative embodiment, the observations are real-time network observations collected from a stream of network traffic. The method includes performing a discrete decomposition of the observations, and introducing derived variables to increase storage and query efficiencies. A mathematical model, such as a conditional independence model, is then generated from the formatted data. The formatted data is also used to construct frequency tables which maintain an accurate count of specific variable occurrence as indicated by the model generation process. The formatted data is then applied to the mathematical model to generate scored data. The scored data is then analyzed to detect anomalies.

Mathematical model for the dc-ac inverter for the Space Shuttle

NASA Technical Reports Server (NTRS)

Berry, Frederick C.

1987-01-01

The reader is informed of what was done for the mathematical modeling of the dc-ac inverter for the Space Shuttle. The mathematical modeling of the dc-ac inverter is an essential element in the modeling of the electrical power distribution system of the Space Shuttle. The electrical power distribution system which is present on the Space Shuttle is made up to 3 strings each having a fuel cell which provides dc to those systems which require dc, and the inverters which convert the dc to ac for those elements which require ac. The inverters are units which are 2 wire structures for the main dc inputs and 2 wire structures for the ac output. When 3 are connected together a 4 wire wye connection results on the ac side. The method of modeling is performed by using a Least Squares curve fitting method. A computer program is presented for implementation of the model along with graphs and tables to demonstrate the accuracy of the model.

A Quantitative Analysis of Methods Used for Avoidance and Acceleration of Developmental Mathematics Sequences in Community College

ERIC Educational Resources Information Center

Travers, Steven T.

2017-01-01

Many developmental mathematics programs at community colleges in recent years have undergone a process of redesign in an attempt increase the historical poor rate of student successful completion of required developmental coursework. Various curriculum and instructional design models that incorporate methods of avoiding and accelerating the…

Mathematical supply-chain modelling: Product analysis of cost and time

NASA Astrophysics Data System (ADS)

Easters, D. J.

2014-03-01

Establishing a mathematical supply-chain model is a proposition that has received attention due to its inherent benefits of evolving global supply-chain efficiencies. This paper discusses the prevailing relationships found within apparel supply-chain environments, and contemplates the complex issues indicated for constituting a mathematical model. Principal results identified within the data suggest, that the multifarious nature of global supply-chain activities require a degree of simplification in order to fully dilate the necessary factors which affect, each sub-section of the chain. Subsequently, the research findings allowed the division of supply-chain components into sub-sections, which amassed a coherent method of product development activity. Concurrently, the supply-chain model was found to allow systematic mathematical formulae analysis, of cost and time, within the multiple contexts of each subsection encountered. The paper indicates the supply-chain model structure, the mathematics, and considers how product analysis of cost and time can improve the comprehension of product lifecycle management.

Mathematical Modeling For Control Of A Flexible Manipulator

NASA Technical Reports Server (NTRS)

Hu, Anren

1996-01-01

Improved method of mathematical modeling of dynamics of flexible robotic manipulators developed for use in controlling motions of manipulators. Involves accounting for effect, upon modes of vibration of manipulator, of changes in configuration of manipulator and manipulated payload(s). Flexible manipulator has one or more long, slender articulated link(s), like those used in outer space, method also applicable to terrestrial industrial robotic manipulators with relatively short, stiff links, or to such terrestrial machines as construction cranes.

The art of fault-tolerant system reliability modeling

NASA Technical Reports Server (NTRS)

Butler, Ricky W.; Johnson, Sally C.

1990-01-01

A step-by-step tutorial of the methods and tools used for the reliability analysis of fault-tolerant systems is presented. Emphasis is on the representation of architectural features in mathematical models. Details of the mathematical solution of complex reliability models are not presented. Instead the use of several recently developed computer programs--SURE, ASSIST, STEM, PAWS--which automate the generation and solution of these models is described.

Two Mathematical Models of Nonlinear Vibrations

NASA Technical Reports Server (NTRS)

Brugarolas, Paul; Bayard, David; Spanos, John; Breckenridge, William

2007-01-01

Two innovative mathematical models of nonlinear vibrations, and methods of applying them, have been conceived as byproducts of an effort to develop a Kalman filter for highly precise estimation of bending motions of a large truss structure deployed in outer space from a space-shuttle payload bay. These models are also applicable to modeling and analysis of vibrations in other engineering disciplines, on Earth as well as in outer space.

Evaluation of Turkish and Mathematics Curricula According to Value-Based Evaluation Model

ERIC Educational Resources Information Center

Duman, Serap Nur; Akbas, Oktay

2017-01-01

This study evaluated secondary school seventh-grade Turkish and mathematics programs using the Context-Input-Process-Product Evaluation Model based on student, teacher, and inspector views. The convergent parallel mixed method design was used in the study. Student values were identified using the scales for socio-level identification, traditional…

Matched field localization based on CS-MUSIC algorithm

NASA Astrophysics Data System (ADS)

Guo, Shuangle; Tang, Ruichun; Peng, Linhui; Ji, Xiaopeng

2016-04-01

The problem caused by shortness or excessiveness of snapshots and by coherent sources in underwater acoustic positioning is considered. A matched field localization algorithm based on CS-MUSIC (Compressive Sensing Multiple Signal Classification) is proposed based on the sparse mathematical model of the underwater positioning. The signal matrix is calculated through the SVD (Singular Value Decomposition) of the observation matrix. The observation matrix in the sparse mathematical model is replaced by the signal matrix, and a new concise sparse mathematical model is obtained, which means not only the scale of the localization problem but also the noise level is reduced; then the new sparse mathematical model is solved by the CS-MUSIC algorithm which is a combination of CS (Compressive Sensing) method and MUSIC (Multiple Signal Classification) method. The algorithm proposed in this paper can overcome effectively the difficulties caused by correlated sources and shortness of snapshots, and it can also reduce the time complexity and noise level of the localization problem by using the SVD of the observation matrix when the number of snapshots is large, which will be proved in this paper.

Rigorous mathematical modelling for a Fast Corrector Power Supply in TPS

NASA Astrophysics Data System (ADS)

Liu, K.-B.; Liu, C.-Y.; Chien, Y.-C.; Wang, B.-S.; Wong, Y. S.

2017-04-01

To enhance the stability of beam orbit, a Fast Orbit Feedback System (FOFB) eliminating undesired disturbances was installed and tested in the 3rd generation synchrotron light source of Taiwan Photon Source (TPS) of National Synchrotron Radiation Research Center (NSRRC). The effectiveness of the FOFB greatly depends on the output performance of Fast Corrector Power Supply (FCPS); therefore, the design and implementation of an accurate FCPS is essential. A rigorous mathematical modelling is very useful to shorten design time and improve design performance of a FCPS. A rigorous mathematical modelling derived by the state-space averaging method for a FCPS in the FOFB of TPS composed of a full-bridge topology is therefore proposed in this paper. The MATLAB/SIMULINK software is used to construct the proposed mathematical modelling and to conduct the simulations of the FCPS. Simulations for the effects of the different resolutions of ADC on the output accuracy of the FCPS are investigated. A FCPS prototype is realized to demonstrate the effectiveness of the proposed rigorous mathematical modelling for the FCPS. Simulation and experimental results show that the proposed mathematical modelling is helpful for selecting the appropriate components to meet the accuracy requirements of a FCPS.

Analysis of creative mathematic thinking ability in problem based learning model based on self-regulation learning

NASA Astrophysics Data System (ADS)

Munahefi, D. N.; Waluya, S. B.; Rochmad

2018-03-01

The purpose of this research identified the effectiveness of Problem Based Learning (PBL) models based on Self Regulation Leaning (SRL) on the ability of mathematical creative thinking and analyzed the ability of mathematical creative thinking of high school students in solving mathematical problems. The population of this study was students of grade X SMA N 3 Klaten. The research method used in this research was sequential explanatory. Quantitative stages with simple random sampling technique, where two classes were selected randomly as experimental class was taught with the PBL model based on SRL and control class was taught with expository model. The selection of samples at the qualitative stage was non-probability sampling technique in which each selected 3 students were high, medium, and low academic levels. PBL model with SRL approach effectived to students’ mathematical creative thinking ability. The ability of mathematical creative thinking of low academic level students with PBL model approach of SRL were achieving the aspect of fluency and flexibility. Students of academic level were achieving fluency and flexibility aspects well. But the originality of students at the academic level was not yet well structured. Students of high academic level could reach the aspect of originality.

Simulation of car movement along circular path

NASA Astrophysics Data System (ADS)

Fedotov, A. I.; Tikhov-Tinnikov, D. A.; Ovchinnikova, N. I.; Lysenko, A. V.

2017-10-01

Under operating conditions, suspension system performance changes which negatively affects vehicle stability and handling. The paper aims to simulate the impact of changes in suspension system performance on vehicle stability and handling. Methods. The paper describes monitoring of suspension system performance, testing of vehicle stability and handling, analyzes methods of suspension system performance monitoring under operating conditions. The mathematical model of a car movement along a circular path was developed. Mathematical tools describing a circular movement of a vehicle along a horizontal road were developed. Turning car movements were simulated. Calculation and experiment results were compared. Simulation proves the applicability of a mathematical model for assessment of the impact of suspension system performance on vehicle stability and handling.

Computational model, method, and system for kinetically-tailoring multi-drug chemotherapy for individuals

DOEpatents

Gardner, Shea Nicole

2007-10-23

A method and system for tailoring treatment regimens to individual patients with diseased cells exhibiting evolution of resistance to such treatments. A mathematical model is provided which models rates of population change of proliferating and quiescent diseased cells using cell kinetics and evolution of resistance of the diseased cells, and pharmacokinetic and pharmacodynamic models. Cell kinetic parameters are obtained from an individual patient and applied to the mathematical model to solve for a plurality of treatment regimens, each having a quantitative efficacy value associated therewith. A treatment regimen may then be selected from the plurlaity of treatment options based on the efficacy value.

New techniques for the analysis of manual control systems. [mathematical models of human operator behavior

NASA Technical Reports Server (NTRS)

Bekey, G. A.

1971-01-01

Studies are summarized on the application of advanced analytical and computational methods to the development of mathematical models of human controllers in multiaxis manual control systems. Specific accomplishments include the following: (1) The development of analytical and computer methods for the measurement of random parameters in linear models of human operators. (2) Discrete models of human operator behavior in a multiple display situation were developed. (3) Sensitivity techniques were developed which make possible the identification of unknown sampling intervals in linear systems. (4) The adaptive behavior of human operators following particular classes of vehicle failures was studied and a model structure proposed.

Computational Methods for Structural Mechanics and Dynamics, part 1

NASA Technical Reports Server (NTRS)

Stroud, W. Jefferson (Editor); Housner, Jerrold M. (Editor); Tanner, John A. (Editor); Hayduk, Robert J. (Editor)

1989-01-01

The structural analysis methods research has several goals. One goal is to develop analysis methods that are general. This goal of generality leads naturally to finite-element methods, but the research will also include other structural analysis methods. Another goal is that the methods be amenable to error analysis; that is, given a physical problem and a mathematical model of that problem, an analyst would like to know the probable error in predicting a given response quantity. The ultimate objective is to specify the error tolerances and to use automated logic to adjust the mathematical model or solution strategy to obtain that accuracy. A third goal is to develop structural analysis methods that can exploit parallel processing computers. The structural analysis methods research will focus initially on three types of problems: local/global nonlinear stress analysis, nonlinear transient dynamics, and tire modeling.

Analysis of critical thinking ability of VII grade students based on the mathematical anxiety level through learning cycle 7E model

NASA Astrophysics Data System (ADS)

Widyaningsih, E.; Waluya, S. B.; Kurniasih, A. W.

2018-03-01

This study aims to know mastery learning of students’ critical thinking ability with learning cycle 7E, determine whether the critical thinking ability of the students with learning cycle 7E is better than students’ critical thinking ability with expository model, and describe the students’ critical thinking phases based on the mathematical anxiety level. The method is mixed method with concurrent embedded. The population is VII grade students of SMP Negeri 3 Kebumen academic year 2016/2017. Subjects are determined by purposive sampling, selected two students from each level of mathematical anxiety. Data collection techniques include test, questionnaire, interview, and documentation. Quantitative data analysis techniques include mean test, proportion test, difference test of two means, difference test of two proportions and for qualitative data used Miles and Huberman model. The results show that: (1) students’ critical thinking ability with learning cycle 7E achieve mastery learning; (2) students’ critical thinking ability with learning cycle 7E is better than students’ critical thinking ability with expository model; (3) description of students’ critical thinking phases based on the mathematical anxiety level that is the lower the mathematical anxiety level, the subjects have been able to fulfil all of the indicators of clarification, assessment, inference, and strategies phases.

Parametric diagnosis of the adaptive gas path in the automatic control system of the aircraft engine

NASA Astrophysics Data System (ADS)

Kuznetsova, T. A.

2017-01-01

The paper dwells on the adaptive multimode mathematical model of the gas-turbine aircraft engine (GTE) embedded in the automatic control system (ACS). The mathematical model is based on the throttle performances, and is characterized by high accuracy of engine parameters identification in stationary and dynamic modes. The proposed on-board engine model is the state space linearized low-level simulation. The engine health is identified by the influence of the coefficient matrix. The influence coefficient is determined by the GTE high-level mathematical model based on measurements of gas-dynamic parameters. In the automatic control algorithm, the sum of squares of the deviation between the parameters of the mathematical model and real GTE is minimized. The proposed mathematical model is effectively used for gas path defects detecting in on-line GTE health monitoring. The accuracy of the on-board mathematical model embedded in ACS determines the quality of adaptive control and reliability of the engine. To improve the accuracy of identification solutions and sustainability provision, the numerical method of Monte Carlo was used. The parametric diagnostic algorithm based on the LPτ - sequence was developed and tested. Analysis of the results suggests that the application of the developed algorithms allows achieving higher identification accuracy and reliability than similar models used in practice.

Will big data yield new mathematics? An evolving synergy with neuroscience

PubMed Central

Feng, S.; Holmes, P.

2016-01-01

New mathematics has often been inspired by new insights into the natural world. Here we describe some ongoing and possible future interactions among the massive data sets being collected in neuroscience, methods for their analysis and mathematical models of the underlying, still largely uncharted neural substrates that generate these data. We start by recalling events that occurred in turbulence modelling when substantial space-time velocity field measurements and numerical simulations allowed a new perspective on the governing equations of fluid mechanics. While no analogous global mathematical model of neural processes exists, we argue that big data may enable validation or at least rejection of models at cellular to brain area scales and may illuminate connections among models. We give examples of such models and survey some relatively new experimental technologies, including optogenetics and functional imaging, that can report neural activity in live animals performing complex tasks. The search for analytical techniques for these data is already yielding new mathematics, and we believe their multi-scale nature may help relate well-established models, such as the Hodgkin–Huxley equations for single neurons, to more abstract models of neural circuits, brain areas and larger networks within the brain. In brief, we envisage a closer liaison, if not a marriage, between neuroscience and mathematics. PMID:27516705

Will big data yield new mathematics? An evolving synergy with neuroscience.

PubMed

Feng, S; Holmes, P

2016-06-01

New mathematics has often been inspired by new insights into the natural world. Here we describe some ongoing and possible future interactions among the massive data sets being collected in neuroscience, methods for their analysis and mathematical models of the underlying, still largely uncharted neural substrates that generate these data. We start by recalling events that occurred in turbulence modelling when substantial space-time velocity field measurements and numerical simulations allowed a new perspective on the governing equations of fluid mechanics. While no analogous global mathematical model of neural processes exists, we argue that big data may enable validation or at least rejection of models at cellular to brain area scales and may illuminate connections among models. We give examples of such models and survey some relatively new experimental technologies, including optogenetics and functional imaging, that can report neural activity in live animals performing complex tasks. The search for analytical techniques for these data is already yielding new mathematics, and we believe their multi-scale nature may help relate well-established models, such as the Hodgkin-Huxley equations for single neurons, to more abstract models of neural circuits, brain areas and larger networks within the brain. In brief, we envisage a closer liaison, if not a marriage, between neuroscience and mathematics.

Redundancy management of electrohydraulic servoactuators by mathematical model referencing

NASA Technical Reports Server (NTRS)

Campbell, R. A.

1971-01-01

A description of a mathematical model reference system is presented which provides redundancy management for an electrohydraulic servoactuator. The mathematical model includes a compensation network that calculates reference parameter perturbations induced by external disturbance forces. This is accomplished by using the measured pressure differential data taken from the physical system. This technique was experimentally verified by tests performed using the H-1 engine thrust vector control system for Saturn IB. The results of these tests are included in this report. It was concluded that this technique improves the tracking accuracy of the model reference system to the extent that redundancy management of electrohydraulic servosystems may be performed using this method.

Modeling Scientific Processes with Mathematics Equations Enhances Student Qualitative Conceptual Understanding and Quantitative Problem Solving

ERIC Educational Resources Information Center

Schuchardt, Anita M.; Schunn, Christian D.

2016-01-01

Amid calls for integrating science, technology, engineering, and mathematics (iSTEM) in K-12 education, there is a pressing need to uncover productive methods of integration. Prior research has shown that increasing contextual linkages between science and mathematics is associated with student problem solving and conceptual understanding. However,…

Family Mathematics Nights: An Opportunity to Improve Preservice Teachers' Understanding of Parents' Roles and Expectations

ERIC Educational Resources Information Center

Bofferding, Laura; Kastberg, Signe; Hoffman, Andrew

2016-01-01

Providing preservice teachers with opportunities to engage with parents and begin to see them as collaborators in their children's education is a persistent challenge in mathematics methods courses and teacher preparation programs more broadly. We describe the use of family mathematics nights as a model for engaging parents and preservice…

Correlation of spacecraft thermal mathematical models to reference data

NASA Astrophysics Data System (ADS)

Torralbo, Ignacio; Perez-Grande, Isabel; Sanz-Andres, Angel; Piqueras, Javier

2018-03-01

Model-to-test correlation is a frequent problem in spacecraft-thermal control design. The idea is to determine the values of the parameters of the thermal mathematical model (TMM) that allows reaching a good fit between the TMM results and test data, in order to reduce the uncertainty of the mathematical model. Quite often, this task is performed manually, mainly because a good engineering knowledge and experience is needed to reach a successful compromise, but the use of a mathematical tool could facilitate this work. The correlation process can be considered as the minimization of the error of the model results with regard to the reference data. In this paper, a simple method is presented suitable to solve the TMM-to-test correlation problem, using Jacobian matrix formulation and Moore-Penrose pseudo-inverse, generalized to include several load cases. Aside, in simple cases, this method also allows for analytical solutions to be obtained, which helps to analyze some problems that appear when the Jacobian matrix is singular. To show the implementation of the method, two problems have been considered, one more academic, and the other one the TMM of an electronic box of PHI instrument of ESA Solar Orbiter mission, to be flown in 2019. The use of singular value decomposition of the Jacobian matrix to analyze and reduce these models is also shown. The error in parameter space is used to assess the quality of the correlation results in both models.

The Effects of an Undergraduate Programme of Preschool Teaching on Preservice Teachers' Attitudes Towards Early Mathematics Education in Turkey: A Longitudinal Study

ERIC Educational Resources Information Center

Kesicioglu, Oguz Serdar

2015-01-01

The aim of this study is to set forth preservice teachers' attitudes towards early mathematics education. For this purpose, quantitative and qualitative research methods were used conjunctively and the research was planned in accordance with a "screening model". The longitudinal screening model, one of the screening models, was used in…

Effects of rotor model degradation on the accuracy of rotorcraft real time simulation

NASA Technical Reports Server (NTRS)

Houck, J. A.; Bowles, R. L.

1976-01-01

The effects are studied of degrading a rotating blade element rotor mathematical model to meet various real-time simulation requirements of rotorcraft. Three methods of degradation were studied: reduction of number of blades, reduction of number of blade segments, and increasing the integration interval, which has the corresponding effect of increasing blade azimuthal advance angle. The three degradation methods were studied through static trim comparisons, total rotor force and moment comparisons, single blade force and moment comparisons over one complete revolution, and total vehicle dynamic response comparisons. Recommendations are made concerning model degradation which should serve as a guide for future users of this mathematical model, and in general, they are in order of minimum impact on model validity: (1) reduction of number of blade segments, (2) reduction of number of blades, and (3) increase of integration interval and azimuthal advance angle. Extreme limits are specified beyond which the rotating blade element rotor mathematical model should not be used.

Models of Pilot Behavior and Their Use to Evaluate the State of Pilot Training

NASA Astrophysics Data System (ADS)

Jirgl, Miroslav; Jalovecky, Rudolf; Bradac, Zdenek

2016-07-01

This article discusses the possibilities of obtaining new information related to human behavior, namely the changes or progressive development of pilots' abilities during training. The main assumption is that a pilot's ability can be evaluated based on a corresponding behavioral model whose parameters are estimated using mathematical identification procedures. The mean values of the identified parameters are obtained via statistical methods. These parameters are then monitored and their changes evaluated. In this context, the paper introduces and examines relevant mathematical models of human (pilot) behavior, the pilot-aircraft interaction, and an example of the mathematical analysis.

Inattentive Drivers: Making the Solution Method the Model

ERIC Educational Resources Information Center

McCartney, Mark

2003-01-01

A simple car following model based on the solution of coupled ordinary differential equations is considered. The model is solved using Euler's method and this method of solution is itself interpreted as a mathematical model for car following. Examples of possible classroom use are given. (Contains 6 figures.)

Anaerobic Threshold by Mathematical Model in Healthy and Post-Myocardial Infarction Men.

PubMed

Novais, L D; Silva, E; Simões, R P; Sakabe, D I; Martins, L E B; Oliveira, L; Diniz, C A R; Gallo, L; Catai, A M

2016-02-01

The aim of this study was to determine the anaerobic threshold (AT) in a population of healthy and post-myocardial infarction men by applying Hinkley's mathematical method and comparing its performance to the ventilatory visual method. This mathematical model, in lieu of observer-dependent visual determination, can produce more reliable results due to the uniformity of the procedure. 17 middle-aged men (55±3 years) were studied in 2 groups: 9 healthy men (54±2 years); and 8 men with previous myocardial infarction (57±3 years). All subjects underwent an incremental ramp exercise test until physical exhaustion. Breath-by-breath ventilatory variables, heart rate (HR), and vastus lateralis surface electromyography (sEMG) signal were collected throughout the test. Carbon dioxide output (V˙CO2), HR, and sEMG were studied, and the AT determination methods were compared using correlation coefficients and Bland-Altman plots. Parametric statistical tests were applied with significance level set at 5%. No significant differences were found in the HR, sEMG, and ventilatory variables at AT between the different methods, such as the intensity of effort relative to AT. Moreover, important concordance and significant correlations were observed between the methods. We concluded that the mathematical model was suitable for detecting the AT in both healthy and myocardial infarction subjects. © Georg Thieme Verlag KG Stuttgart · New York.

The human body metabolism process mathematical simulation based on Lotka-Volterra model

NASA Astrophysics Data System (ADS)

Oliynyk, Andriy; Oliynyk, Eugene; Pyptiuk, Olexandr; DzierŻak, RóŻa; Szatkowska, Małgorzata; Uvaysova, Svetlana; Kozbekova, Ainur

2017-08-01

The mathematical model of metabolism process in human organism based on Lotka-Volterra model has beeng proposed, considering healing regime, nutrition system, features of insulin and sugar fragmentation process in the organism. The numerical algorithm of the model using IV-order Runge-Kutta method has been realized. After the result of calculations the conclusions have been made, recommendations about using the modeling results have been showed, the vectors of the following researches are defined.

System Identification Methods for Aircraft Flight Control Development and Validation

DOT National Transportation Integrated Search

1995-10-01

System-identification methods compose a mathematical model, or series of models, : from measurements of inputs and outputs of dynamic systems. This paper : discusses the use of frequency-domain system-identification methods for the : development and ...

Predicting disease progression from short biomarker series using expert advice algorithm

NASA Astrophysics Data System (ADS)

Morino, Kai; Hirata, Yoshito; Tomioka, Ryota; Kashima, Hisashi; Yamanishi, Kenji; Hayashi, Norihiro; Egawa, Shin; Aihara, Kazuyuki

2015-05-01

Well-trained clinicians may be able to provide diagnosis and prognosis from very short biomarker series using information and experience gained from previous patients. Although mathematical methods can potentially help clinicians to predict the progression of diseases, there is no method so far that estimates the patient state from very short time-series of a biomarker for making diagnosis and/or prognosis by employing the information of previous patients. Here, we propose a mathematical framework for integrating other patients' datasets to infer and predict the state of the disease in the current patient based on their short history. We extend a machine-learning framework of ``prediction with expert advice'' to deal with unstable dynamics. We construct this mathematical framework by combining expert advice with a mathematical model of prostate cancer. Our model predicted well the individual biomarker series of patients with prostate cancer that are used as clinical samples.

Predicting disease progression from short biomarker series using expert advice algorithm.

PubMed

Morino, Kai; Hirata, Yoshito; Tomioka, Ryota; Kashima, Hisashi; Yamanishi, Kenji; Hayashi, Norihiro; Egawa, Shin; Aihara, Kazuyuki

2015-05-20

Well-trained clinicians may be able to provide diagnosis and prognosis from very short biomarker series using information and experience gained from previous patients. Although mathematical methods can potentially help clinicians to predict the progression of diseases, there is no method so far that estimates the patient state from very short time-series of a biomarker for making diagnosis and/or prognosis by employing the information of previous patients. Here, we propose a mathematical framework for integrating other patients' datasets to infer and predict the state of the disease in the current patient based on their short history. We extend a machine-learning framework of "prediction with expert advice" to deal with unstable dynamics. We construct this mathematical framework by combining expert advice with a mathematical model of prostate cancer. Our model predicted well the individual biomarker series of patients with prostate cancer that are used as clinical samples.

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.

Using Confirmatory Factor Analysis to Understand Executive Control in Preschool Children: Sources of Variation in Emergent Mathematic Achievement

ERIC Educational Resources Information Center

Bull, Rebecca; Espy, Kimberly Andrews; Wiebe, Sandra A.; Sheffield, Tiffany D.; Nelson, Jennifer Mize

2011-01-01

Latent variable modeling methods have demonstrated utility for understanding the structure of executive control (EC) across development. These methods are utilized to better characterize the relation between EC and mathematics achievement in the preschool period, and to understand contributing sources of individual variation. Using the sample and…

Manual of phosphoric acid fuel cell stack three-dimensional model and computer program

NASA Technical Reports Server (NTRS)

Lu, C. Y.; Alkasab, K. A.

1984-01-01

A detailed distributed mathematical model of phosphoric acid fuel cell stack have been developed, with the FORTRAN computer program, for analyzing the temperature distribution in the stack and the associated current density distribution on the cell plates. Energy, mass, and electrochemical analyses in the stack were combined to develop the model. Several reasonable assumptions were made to solve this mathematical model by means of the finite differences numerical method.

Model correlation and damage location for large space truss structures: Secant method development and evaluation

NASA Technical Reports Server (NTRS)

Smith, Suzanne Weaver; Beattie, Christopher A.

1991-01-01

On-orbit testing of a large space structure will be required to complete the certification of any mathematical model for the structure dynamic response. The process of establishing a mathematical model that matches measured structure response is referred to as model correlation. Most model correlation approaches have an identification technique to determine structural characteristics from the measurements of the structure response. This problem is approached with one particular class of identification techniques - matrix adjustment methods - which use measured data to produce an optimal update of the structure property matrix, often the stiffness matrix. New methods were developed for identification to handle problems of the size and complexity expected for large space structures. Further development and refinement of these secant-method identification algorithms were undertaken. Also, evaluation of these techniques is an approach for model correlation and damage location was initiated.

The image of mathematics held by Irish post-primary students

NASA Astrophysics Data System (ADS)

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

2014-08-01

The image of mathematics held by Irish post-primary students was examined and a model for the image found was constructed. Initially, a definition for 'image of mathematics' was adopted with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. Research focused on students studying ordinary level mathematics for the Irish Leaving Certificate examination - the final examination for students in second-level or post-primary education. Students were aged between 15 and 18 years. A questionnaire was constructed with both quantitative and qualitative aspects. The questionnaire survey was completed by 356 post-primary students. Responses were analysed quantitatively using Statistical Package for the Social Sciences (SPSS) and qualitatively using the constant comparative method of analysis and by reviewing individual responses. Findings provide an insight into Irish post-primary students' images of mathematics and offer a means for constructing a theoretical model of image of mathematics which could be beneficial for future research.

Gompertzian stochastic model with delay effect to cervical cancer growth

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

Mazlan, Mazma Syahidatul Ayuni binti; Rosli, Norhayati binti; Bahar, Arifah

2015-02-03

In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.

Mathematical interpretation of Brownian motor model: Limit cycles and directed transport phenomena

NASA Astrophysics Data System (ADS)

Yang, Jianqiang; Ma, Hong; Zhong, Suchuang

2018-03-01

In this article, we first suggest that the attractor of Brownian motor model is one of the reasons for the directed transport phenomenon of Brownian particle. We take the classical Smoluchowski-Feynman (SF) ratchet model as an example to investigate the relationship between limit cycles and directed transport phenomenon of the Brownian particle. We study the existence and variation rule of limit cycles of SF ratchet model at changing parameters through mathematical methods. The influences of these parameters on the directed transport phenomenon of a Brownian particle are then analyzed through numerical simulations. Reasonable mathematical explanations for the directed transport phenomenon of Brownian particle in SF ratchet model are also formulated on the basis of the existence and variation rule of the limit cycles and numerical simulations. These mathematical explanations provide a theoretical basis for applying these theories in physics, biology, chemistry, and engineering.

Effectiveness of discovery learning model on mathematical problem solving

NASA Astrophysics Data System (ADS)

Herdiana, Yunita; Wahyudin, Sispiyati, Ririn

2017-08-01

This research is aimed to describe the effectiveness of discovery learning model on mathematical problem solving. This research investigate the students' problem solving competency before and after learned by using discovery learning model. The population used in this research was student in grade VII in one of junior high school in West Bandung Regency. From nine classes, class VII B were randomly selected as the sample of experiment class, and class VII C as control class, which consist of 35 students every class. The method in this research was quasi experiment. The instrument in this research is pre-test, worksheet and post-test about problem solving of mathematics. Based on the research, it can be conclude that the qualification of problem solving competency of students who gets discovery learning model on level 80%, including in medium category and it show that discovery learning model effective to improve mathematical problem solving.

Realistic Real World Contexts: Model Eliciting Activities

ERIC Educational Resources Information Center

Doruk, Bekir Kürsat

2016-01-01

Researchers have proposed a variety of methods to make a connection between real life and mathematics so that it can be learned in a practical way and enable people to utilise mathematics in their daily lives. Model-eliciting activities (MEAs) were developed to fulfil this need and are very capable of serving this purpose. The reason MEAs are so…

Teaching Methods for Modelling Problems and Students' Task-Specific Enjoyment, Value, Interest and Self-Efficacy Expectations

ERIC Educational Resources Information Center

Schukajlow, Stanislaw; Leiss, Dominik; Pekrun, Reinhard; Blum, Werner; Muller, Marcel; Messner, Rudolf

2012-01-01

In this study which was part of the DISUM-project, 224 ninth graders from 14 German classes from middle track schools (Realschule) were asked about their enjoyment, interest, value and self-efficacy expectations concerning three types of mathematical problems: intra-mathematical problems, word problems and modelling problems. Enjoyment, interest,…

Load influence on gear noise. [mathematical model for determining acoustic pressure level as function of load

NASA Technical Reports Server (NTRS)

Merticaru, V.

1974-01-01

An original mathematical model is proposed to derive equations for calculation of gear noise. These equations permit the acoustic pressure level to be determined as a function of load. Application of this method to three parallel gears is reported. The logical calculation scheme is given, as well as the results obtained.

A mathematical model for predicting fire spread in wildland fuels

Treesearch

Richard C. Rothermel

1972-01-01

A mathematical fire model for predicting rate of spread and intensity that is applicable to a wide range of wildland fuels and environment is presented. Methods of incorporating mixtures of fuel sizes are introduced by weighting input parameters by surface area. The input parameters do not require a prior knowledge of the burning characteristics of the fuel.

Mathematical modeling relevant to closed artificial ecosystems

USGS Publications Warehouse

DeAngelis, D.L.

2003-01-01

The mathematical modeling of ecosystems has contributed much to the understanding of the dynamics of such systems. Ecosystems can include not only the natural variety, but also artificial systems designed and controlled by humans. These can range from agricultural systems and activated sludge plants, down to mesocosms, microcosms, and aquaria, which may have practical or research applications. Some purposes may require the design of systems that are completely closed, as far as material cycling is concerned. In all cases, mathematical modeling can help not only to understand the dynamics of the system, but also to design methods of control to keep the system operating in desired ranges. This paper reviews mathematical modeling relevant to the simulation and control of closed or semi-closed artificial ecosystems designed for biological production and recycling in applications in space. Published by Elsevier Science Ltd on behalf of COSPAR.

Introducing Seismic Tomography with Computational Modeling

NASA Astrophysics Data System (ADS)

Neves, R.; Neves, M. L.; Teodoro, V.

2011-12-01

Learning seismic tomography principles and techniques involves advanced physical and computational knowledge. In depth learning of such computational skills is a difficult cognitive process that requires a strong background in physics, mathematics and computer programming. The corresponding learning environments and pedagogic methodologies should then involve sets of computational modelling activities with computer software systems which allow students the possibility to improve their mathematical or programming knowledge and simultaneously focus on the learning of seismic wave propagation and inverse theory. To reduce the level of cognitive opacity associated with mathematical or programming knowledge, several computer modelling systems have already been developed (Neves & Teodoro, 2010). Among such systems, Modellus is particularly well suited to achieve this goal because it is a domain general environment for explorative and expressive modelling with the following main advantages: 1) an easy and intuitive creation of mathematical models using just standard mathematical notation; 2) the simultaneous exploration of images, tables, graphs and object animations; 3) the attribution of mathematical properties expressed in the models to animated objects; and finally 4) the computation and display of mathematical quantities obtained from the analysis of images and graphs. Here we describe virtual simulations and educational exercises which enable students an easy grasp of the fundamental of seismic tomography. The simulations make the lecture more interactive and allow students the possibility to overcome their lack of advanced mathematical or programming knowledge and focus on the learning of seismological concepts and processes taking advantage of basic scientific computation methods and tools.

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.

The Dynamics of Drug Resistance: A Mathematical Perspective

PubMed Central

Lavi, Orit; Gottesman, Michael M.; Levy, Doron

2012-01-01

Resistance to chemotherapy is a key impediment to successful cancer treatment that has been intensively studied for the last three decades. Several central mechanisms have been identified as contributing to the resistance. In the case of multidrug resistance (MDR), the cell becomes resistant to a variety of structurally and mechanistically unrelated drugs in addition to the drug initially administered. Mathematical models of drug resistance have dealt with many of the known aspects of this field, such as pharmacologic sanctuary and location/diffusion resistance, intrinsic resistance that is therapy independent, therapy-dependent cellular alterations including induced resistance (dose-dependent) and acquired resistance (dose-independent). In addition, there are mathematical models that take into account the kinetic/phase resistance, and models that investigate intra-cellular mechanisms based on specific biological functions (such as ABC transporters, apoptosis and repair mechanisms). This review covers aspects of MDR that have been mathematically studied, and explains how, from a methodological perspective, mathematics can be used to study drug resistance. We discuss quantitative approaches of mathematical analysis, and demonstrate how mathematics can be used in combination with other experimental and clinical tools. We emphasize the potential benefits of integrating analytical and mathematical methods into future clinical and experimental studies of drug resistance. PMID:22387162

Improving students’ mathematical critical thinking through rigorous teaching and learning model with informal argument

NASA Astrophysics Data System (ADS)

Hamid, H.

2018-01-01

The purpose of this study is to analyze an improvement of students’ mathematical critical thinking (CT) ability in Real Analysis course by using Rigorous Teaching and Learning (RTL) model with informal argument. In addition, this research also attempted to understand students’ CT on their initial mathematical ability (IMA). This study was conducted at a private university in academic year 2015/2016. The study employed the quasi-experimental method with pretest-posttest control group design. The participants of the study were 83 students in which 43 students were in the experimental group and 40 students were in the control group. The finding of the study showed that students in experimental group outperformed students in control group on mathematical CT ability based on their IMA (high, medium, low) in learning Real Analysis. In addition, based on medium IMA the improvement of mathematical CT ability of students who were exposed to RTL model with informal argument was greater than that of students who were exposed to CI (conventional instruction). There was also no effect of interaction between RTL model and CI model with both (high, medium, and low) IMA increased mathematical CT ability. Finally, based on (high, medium, and low) IMA there was a significant improvement in the achievement of all indicators of mathematical CT ability of students who were exposed to RTL model with informal argument than that of students who were exposed to CI.

Development of a Predictive Corrosion Model Using Locality-Specific Corrosion Indices

DTIC Science & Technology

2017-09-12

6 3.2.1 Statistical data analysis methods ...6 3.2.2 Algorithm development method ...components, and method ) were compiled into an executable program that uses mathematical models of materials degradation, and statistical calcula- tions

Dispersive traveling wave solutions of the Equal-Width and Modified Equal-Width equations via mathematical methods and its applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

The Equal-Width and Modified Equal-Width equations are used as a model in partial differential equations for the simulation of one-dimensional wave transmission in nonlinear media with dispersion processes. In this article we have employed extend simple equation method and the exp(-varphi(ξ)) expansion method to construct the exact traveling wave solutions of equal width and modified equal width equations. The obtained results are novel and have numerous applications in current areas of research in mathematical physics. It is exposed that our method, with the help of symbolic computation, provides a effective and powerful mathematical tool for solving different kind nonlinear wave problems.

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.

Full nonlinear treatment of the global thermospheric wind system. Part 1: Mathematical method and analysis of forces

NASA Technical Reports Server (NTRS)

Blum, P. W.; Harris, I.

1973-01-01

The equations of horizontal motion of the neutral atmosphere between 120 and 500 km are integrated with the inclusion of all the nonlinear terms of the convective derivative and the viscous forces due to vertical and horizontal velocity gradients. Empirical models of the distribution of neutral and charged particles are assumed to be known. The model of velocities developed is a steady state model. In part 1 the mathematical method used in the integration of the Navier-Stokes equations is described and the various forces are analysed.

Data-Based Detection of Potential Terrorist Attacks: Statistical and Graphical Methods

DTIC Science & Technology

2010-06-01

Naren; Vasquez-Robinet, Cecilia; Watkinson, Jonathan: "A General Probabilistic Model of the PCR Process," Applied Mathematics and Computation 182(1...September 2006. Seminar, Measuring the effect of Length biased sampling, Mathematical Sciences Section, National Security Agency, 19 September 2006...Committee on National Statistics, 9 February 2007. Invited seminar, Statistical Tests for Bullet Lead Comparisons, Department of Mathematics , Butler

Structure and Maintenance of a Mathematical Creative Lesson as a Mean of Pupils' Meta-Subject Results Achievement

ERIC Educational Resources Information Center

Gorev, Pavel M.; Aydar M. Kalimullin

2017-01-01

The purpose of the research is to study and change the structure of a mathematical lesson to improve quality of pupils' mathematical training and design mechanisms of inclusion the systems of open type tasks in educational process considering specifics of pupils' creative personality development. The leading method is modeling of a mathematical…

Development of the mathematical model for design and verification of acoustic modal analysis methods

NASA Astrophysics Data System (ADS)

Siner, Alexander; Startseva, Maria

2016-10-01

To reduce the turbofan noise it is necessary to develop methods for the analysis of the sound field generated by the blade machinery called modal analysis. Because modal analysis methods are very difficult and their testing on the full scale measurements are very expensive and tedious it is necessary to construct some mathematical models allowing to test modal analysis algorithms fast and cheap. At this work the model allowing to set single modes at the channel and to analyze generated sound field is presented. Modal analysis of the sound generated by the ring array of point sound sources is made. Comparison of experimental and numerical modal analysis results is presented at this work.

Computational aspects of real-time simulation of rotary-wing aircraft. M.S. Thesis

NASA Technical Reports Server (NTRS)

Houck, J. A.

1976-01-01

A study was conducted to determine the effects of degrading a rotating blade element rotor mathematical model suitable for real-time simulation of rotorcraft. Three methods of degradation were studied, reduction of number of blades, reduction of number of blade segments, and increasing the integration interval, which has the corresponding effect of increasing blade azimuthal advance angle. The three degradation methods were studied through static trim comparisons, total rotor force and moment comparisons, single blade force and moment comparisons over one complete revolution, and total vehicle dynamic response comparisons. Recommendations are made concerning model degradation which should serve as a guide for future users of this mathematical model, and in general, they are in order of minimum impact on model validity: (1) reduction of number of blade segments; (2) reduction of number of blades; and (3) increase of integration interval and azimuthal advance angle. Extreme limits are specified beyond which a different rotor mathematical model should be used.

Improving science and mathematics education with computational modelling in interactive engagement environments

NASA Astrophysics Data System (ADS)

Neves, Rui Gomes; Teodoro, Vítor Duarte

2012-09-01

A teaching approach aiming at an epistemologically balanced integration of computational modelling in science and mathematics education is presented. The approach is based on interactive engagement learning activities built around computational modelling experiments that span the range of different kinds of modelling from explorative to expressive modelling. The activities are designed to make a progressive introduction to scientific computation without requiring prior development of a working knowledge of programming, generate and foster the resolution of cognitive conflicts in the understanding of scientific and mathematical concepts and promote performative competency in the manipulation of different and complementary representations of mathematical models. The activities are supported by interactive PDF documents which explain the fundamental concepts, methods and reasoning processes using text, images and embedded movies, and include free space for multimedia enriched student modelling reports and teacher feedback. To illustrate, an example from physics implemented in the Modellus environment and tested in undergraduate university general physics and biophysics courses is discussed.

Mathematics in modern immunology

DOE PAGES

Castro, Mario; Lythe, Grant; Molina-París, Carmen; ...

2016-02-19

Mathematical and statistical methods enable multidisciplinary approaches that catalyse discovery. Together with experimental methods, they identify key hypotheses, define measurable observables and reconcile disparate results. Here, we collect a representative sample of studies in T-cell biology that illustrate the benefits of modelling–experimental collaborations and that have proven valuable or even groundbreaking. Furthermore, we conclude that it is possible to find excellent examples of synergy between mathematical modelling and experiment in immunology, which have brought significant insight that would not be available without these collaborations, but that much remains to be discovered.

Mathematics in modern immunology

PubMed Central

Castro, Mario; Lythe, Grant; Molina-París, Carmen; Ribeiro, Ruy M.

2016-01-01

Mathematical and statistical methods enable multidisciplinary approaches that catalyse discovery. Together with experimental methods, they identify key hypotheses, define measurable observables and reconcile disparate results. We collect a representative sample of studies in T-cell biology that illustrate the benefits of modelling–experimental collaborations and that have proven valuable or even groundbreaking. We conclude that it is possible to find excellent examples of synergy between mathematical modelling and experiment in immunology, which have brought significant insight that would not be available without these collaborations, but that much remains to be discovered. PMID:27051512

Mathematical model of compact type evaporator

NASA Astrophysics Data System (ADS)

Borovička, Martin; Hyhlík, Tomáš

2018-06-01

In this paper, development of the mathematical model for evaporator used in heat pump circuits is covered, with focus on air dehumidification application. Main target of this ad-hoc numerical model is to simulate heat and mass transfer in evaporator for prescribed inlet conditions and different geometrical parameters. Simplified 2D mathematical model is developed in MATLAB SW. Solvers for multiple heat and mass transfer problems - plate surface temperature, condensate film temperature, local heat and mass transfer coefficients, refrigerant temperature distribution, humid air enthalpy change are included as subprocedures of this model. An automatic procedure of data transfer is developed in order to use results of MATLAB model in more complex simulation within commercial CFD code. In the end, Proper Orthogonal Decomposition (POD) method is introduced and implemented into MATLAB model.

A study of direct moxibustion using mathematical methods.

PubMed

Liu, Miao; Kauh, Sang Ken; Lim, Sabina

2012-01-01

Direct moxibustion is an important and widely used treatment method in traditional medical science. The use of a mathematical method to analyse direct moxibustion treatment is necessary and helpful in exploring the new direct moxibustion instruments and their standardisation. Thus, this paper aims to use a mathematical method to study direct moxibustion in skin to demonstrate a direct relationship between direct moxibustion and skin stimuli. In this paper, the transient thermal response of skin layers is analysed to study direct moxibustion using the data got from standardised method to measure the temperature of a burning moxa cone. Numerical simulations based on an appropriate finite element model are developed to predict the heat transfer, thermal damage and thermal stress distribution of barley moxa cones and jujube moxa cones in the skin tissue. The results are verified by the ancient literatures of traditional Chinese medicine and clinical application, and showed that mathematical method can be a good interface between moxa cone and skin tissue providing the numerical value basis for moxibustion.

The application of brain-based learning principles aided by GeoGebra to improve mathematical representation ability

NASA Astrophysics Data System (ADS)

Priatna, Nanang

2017-08-01

The use of Information and Communication Technology (ICT) in mathematics instruction will help students in building conceptual understanding. One of the software products used in mathematics instruction is GeoGebra. The program enables simple visualization of complex geometric concepts and helps improve students' understanding of geometric concepts. Instruction applying brain-based learning principles is one oriented at the efforts of naturally empowering the brain potentials which enable students to build their own knowledge. One of the goals of mathematics instruction in school is to develop mathematical communication ability. Mathematical representation is regarded as a part of mathematical communication. It is a description, expression, symbolization, or modeling of mathematical ideas/concepts as an attempt of clarifying meanings or seeking for solutions to the problems encountered by students. The research aims to develop a learning model and teaching materials by applying the principles of brain-based learning aided by GeoGebra to improve junior high school students' mathematical representation ability. It adopted a quasi-experimental method with the non-randomized control group pretest-posttest design and the 2x3 factorial model. Based on analysis of the data, it is found that the increase in the mathematical representation ability of students who were treated with mathematics instruction applying the brain-based learning principles aided by GeoGebra was greater than the increase of the students given conventional instruction, both as a whole and based on the categories of students' initial mathematical ability.

Evaluation of an S-system root-finding method for estimating parameters in a metabolic reaction model.

PubMed

Iwata, Michio; Miyawaki-Kuwakado, Atsuko; Yoshida, Erika; Komori, Soichiro; Shiraishi, Fumihide

2018-02-02

In a mathematical model, estimation of parameters from time-series data of metabolic concentrations in cells is a challenging task. However, it seems that a promising approach for such estimation has not yet been established. Biochemical Systems Theory (BST) is a powerful methodology to construct a power-law type model for a given metabolic reaction system and to then characterize it efficiently. In this paper, we discuss the use of an S-system root-finding method (S-system method) to estimate parameters from time-series data of metabolite concentrations. We demonstrate that the S-system method is superior to the Newton-Raphson method in terms of the convergence region and iteration number. We also investigate the usefulness of a translocation technique and a complex-step differentiation method toward the practical application of the S-system method. The results indicate that the S-system method is useful to construct mathematical models for a variety of metabolic reaction networks. Copyright © 2018 Elsevier Inc. All rights reserved.

Computing the stability of steady-state solutions of mathematical models of the electrical activity in the heart.

PubMed

Tveito, Aslak; Skavhaug, Ola; Lines, Glenn T; Artebrant, Robert

2011-08-01

Instabilities in the electro-chemical resting state of the heart can generate ectopic waves that in turn can initiate arrhythmias. We derive methods for computing the resting state for mathematical models of the electro-chemical process underpinning a heartbeat, and we estimate the stability of the resting state by invoking the largest real part of the eigenvalues of a linearized model. The implementation of the methods is described and a number of numerical experiments illustrate the feasibility of the methods. In particular, we test the methods for problems where we can compare the solutions with analytical results, and problems where we have solutions computed by independent software. The software is also tested for a fairly realistic 3D model. Copyright © 2011 Elsevier Ltd. All rights reserved.

Do Teachers Make Decisions Like Firefighters? Applying Naturalistic Decision-Making Methods to Teachers' In-Class Decision Making in Mathematics

ERIC Educational Resources Information Center

Jazby, Dan

2014-01-01

Research into human decision making (DM) processes from outside of education paint a different picture of DM than current DM models in education. This pilot study assesses the use of critical decision method (CDM)--developed from observations of firefighters' DM -- in the context of primary mathematics teachers' in-class DM. Preliminary results…

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

Jablonská, Jana, E-mail: jana.jablonska@vsb.cz; Kozubková, Milada, E-mail: milada.kozubkova@vsb.cz

Cavitation today is a very important problem that is solved by means of experimental and mathematical methods. The article deals with the generation of cavitation in convergent divergent nozzle of rectangular cross section. Measurement of pressure, flow rate, temperature, amount of dissolved air in the liquid and visualization of cavitation area using high-speed camera was performed for different flow rates. The measurement results were generalized by dimensionless analysis, which allows easy detection of cavitation in the nozzle. For numerical simulation the multiphase mathematical model of cavitation consisting of water and vapor was created. During verification the disagreement with the measurementsmore » for higher flow rates was proved, therefore the model was extended to multiphase mathematical model (water, vapor and air), due to release of dissolved air. For the mathematical modeling the multiphase turbulence RNG k-ε model for low Reynolds number flow with vapor and air cavitation was used. Subsequently the sizes of the cavitation area were verified. In article the inlet pressure and loss coefficient depending on the amount of air added to the mathematical model are evaluated. On the basis of the approach it may be create a methodology to estimate the amount of released air added at the inlet to the modeled area.« less

Enhancing mathematics teachers' quality through Lesson Study.

PubMed

Lomibao, Laila S

2016-01-01

The efficiency and effectivity of the learning experience is dependent on the teacher quality, thus, enhancing teacher's quality is vital in improving the students learning outcome. Since, the usual top-down one-shot cascading model practice for teachers' professional development in Philippines has been observed to have much information dilution, and the Southeast Asian Ministers of Education Organization demanded the need to develop mathematics teachers' quality standards through the Southeast Asia Regional Standards for Mathematics Teachers (SEARS-MT), thus, an intensive, ongoing professional development model should be provided to teachers. This study was undertaken to determine the impact of Lesson Study on Bulua National High School mathematics teachers' quality level in terms of SEARS-MT dimensions. A mixed method of quantitative-qualitative research design was employed. Results of the analysis revealed that Lesson Study effectively enhanced mathematics teachers' quality and promoted teachers professional development. Teachers positively perceived Lesson Study to be beneficial for them to become a better mathematics teacher.

Applying multibeam sonar and mathematical modeling for mapping seabed substrate and biota of offshore shallows

NASA Astrophysics Data System (ADS)

Herkül, Kristjan; Peterson, Anneliis; Paekivi, Sander

2017-06-01

Both basic science and marine spatial planning are in a need of high resolution spatially continuous data on seabed habitats and biota. As conventional point-wise sampling is unable to cover large spatial extents in high detail, it must be supplemented with remote sensing and modeling in order to fulfill the scientific and management needs. The combined use of in situ sampling, sonar scanning, and mathematical modeling is becoming the main method for mapping both abiotic and biotic seabed features. Further development and testing of the methods in varying locations and environmental settings is essential for moving towards unified and generally accepted methodology. To fill the relevant research gap in the Baltic Sea, we used multibeam sonar and mathematical modeling methods - generalized additive models (GAM) and random forest (RF) - together with underwater video to map seabed substrate and epibenthos of offshore shallows. In addition to testing the general applicability of the proposed complex of techniques, the predictive power of different sonar-based variables and modeling algorithms were tested. Mean depth, followed by mean backscatter, were the most influential variables in most of the models. Generally, mean values of sonar-based variables had higher predictive power than their standard deviations. The predictive accuracy of RF was higher than that of GAM. To conclude, we found the method to be feasible and with predictive accuracy similar to previous studies of sonar-based mapping.

Mathematical modeling of the heat transfer for determining the depth of thawing basin buildings with long service life

NASA Astrophysics Data System (ADS)

Sirditov, Ivan; Stepanov, Sergei

2017-11-01

In this paper, a numerical study of the problem of determining a thawing basin in the permafrost soil for buildings with a long service life is carried out using two methods, with the formulas of set of rules 25.13330.2012 "Soil bases and foundations on permafrost soils" and using a mathematical model.

[Influence of sample surface roughness on mathematical model of NIR quantitative analysis of wood density].

PubMed

Huang, An-Min; Fei, Ben-Hua; Jiang, Ze-Hui; Hse, Chung-Yun

2007-09-01

Near infrared spectroscopy is widely used as a quantitative method, and the main multivariate techniques consist of regression methods used to build prediction models, however, the accuracy of analysis results will be affected by many factors. In the present paper, the influence of different sample roughness on the mathematical model of NIR quantitative analysis of wood density was studied. The result of experiments showed that if the roughness of predicted samples was consistent with that of calibrated samples, the result was good, otherwise the error would be much higher. The roughness-mixed model was more flexible and adaptable to different sample roughness. The prediction ability of the roughness-mixed model was much better than that of the single-roughness model.

Specific modes of vibratory technological machines: mathematical models, peculiarities of interaction of system elements

NASA Astrophysics Data System (ADS)

Eliseev, A. V.; Sitov, I. S.; Eliseev, S. V.

2018-03-01

The methodological basis of constructing mathematical models of vibratory technological machines is developed in the article. An approach is proposed that makes it possible to introduce a vibration table in a specific mode that provides conditions for the dynamic damping of oscillations for the zone of placement of a vibration exciter while providing specified vibration parameters in the working zone of the vibration table. The aim of the work is to develop methods of mathematical modeling, oriented to technological processes with long cycles. The technologies of structural mathematical modeling are used with structural schemes, transfer functions and amplitude-frequency characteristics. The concept of the work is to test the possibilities of combining the conditions for reducing loads with working components of a vibration exciter while simultaneously maintaining sufficiently wide limits in variating the parameters of the vibrational field.

Transient Mathematical Modeling for Liquid Rocket Engine Systems: Methods, Capabilities, and Experience

NASA Technical Reports Server (NTRS)

Seymour, David C.; Martin, Michael A.; Nguyen, Huy H.; Greene, William D.

2005-01-01

The subject of mathematical modeling of the transient operation of liquid rocket engines is presented in overview form from the perspective of engineers working at the NASA Marshall Space Flight Center. The necessity of creating and utilizing accurate mathematical models as part of liquid rocket engine development process has become well established and is likely to increase in importance in the future. The issues of design considerations for transient operation, development testing, and failure scenario simulation are discussed. An overview of the derivation of the basic governing equations is presented along with a discussion of computational and numerical issues associated with the implementation of these equations in computer codes. Also, work in the field of generating usable fluid property tables is presented along with an overview of efforts to be undertaken in the future to improve the tools use for the mathematical modeling process.

Transient Mathematical Modeling for Liquid Rocket Engine Systems: Methods, Capabilities, and Experience

NASA Technical Reports Server (NTRS)

Martin, Michael A.; Nguyen, Huy H.; Greene, William D.; Seymout, David C.

2003-01-01

The subject of mathematical modeling of the transient operation of liquid rocket engines is presented in overview form from the perspective of engineers working at the NASA Marshall Space Flight Center. The necessity of creating and utilizing accurate mathematical models as part of liquid rocket engine development process has become well established and is likely to increase in importance in the future. The issues of design considerations for transient operation, development testing, and failure scenario simulation are discussed. An overview of the derivation of the basic governing equations is presented along with a discussion of computational and numerical issues associated with the implementation of these equations in computer codes. Also, work in the field of generating usable fluid property tables is presented along with an overview of efforts to be undertaken in the future to improve the tools use for the mathematical modeling process.

Mathematics teacher professional development in and through internet use: reflections on an ethnographic study

NASA Astrophysics Data System (ADS)

Patahuddin, Sitti Maesuri

2013-12-01

This paper is a reflection on a model for mathematics teacher professional development with respect to technology. The model was informed by three interrelated concepts: (1) a theory of teacher professional development from analysis of the field, (2) the zone theory of teacher professional learning, and (3) ethnography as a method. The model was applied in a study that focused on the uses of the Internet for primary mathematics teacher professional development, particularly to exploit the potential of the Internet for professional learning and to use it in professional work. This is illustrated through selected critical events over an eight-month ethnographic intervention in a primary mathematics classroom in Australia. Though the model is theoretically grounded, it opens up questions about the power, potential, and challenges as well as its feasibility, with respect to not only the teacher but also the ethnographer.

Analysis mathematical literacy skills in terms of the students’ metacognition on PISA-CPS model

NASA Astrophysics Data System (ADS)

Ovan; Waluya, S. B.; Nugroho, S. E.

2018-03-01

This research was aimed to know the effectiveness of PISA-CPS model and desceibe the mathematical literacy skills (KLM) in terms of the students’ metacognition. This study used Mixed Methods approaches with the concurrent embedded desaign. The technique of data analysis on quantitative research done analysis of lesson plan, prerequisite test, test hypotesis 1 and hypotesis test. While qualitative research done data reduction, data presentation, and drawing conclution and data verification. The subject of this study was the students of Grade Eight (VIII) of SMP Islam Sultan Agung 4 Semarang, Central Java. The writer analyzed the data with quantitative and qualitative approaches based on the metacognition of the students in low, medium and high groups. Subsequently, taken the mathematical literacy skills (KLM) from students’ metacognition in low, medium, and high . The results of the study showed that the PISA-CPS model was complete and the students’ mathematical literacy skills in terms of the students’ metacognition taught by the PISA-CPS model was higher than the expository learning. metacognitions’ students classified low hadmathematical literacy skills (KLM) less good, metacognitions’ students classified medium had mathematical literacy skills (KLM) good enough, metacognitions’ students classified high had mathematical literacy skills (KLM) very good. Based onresult analysis got conclusion that the PISA-CPS model was effective toward the students’ mathematical literacy skills (KLM). To increase the students’ mathematical literacy skills (KLM), the teachers need to provide reinforcements in the form of the exercises so that the student’s mathematical literacy was achieved at level 5 and level 6.

The averaging method in applied problems

NASA Astrophysics Data System (ADS)

Grebenikov, E. A.

1986-04-01

The totality of methods, allowing to research complicated non-linear oscillating systems, named in the literature "averaging method" has been given. THe author is describing the constructive part of this method, or a concrete form and corresponding algorithms, on mathematical models, sufficiently general , but built on concrete problems. The style of the book is that the reader interested in the Technics and algorithms of the asymptotic theory of the ordinary differential equations, could solve individually such problems. For specialists in the area of applied mathematics and mechanics.

Annotated Computer Output for Illustrative Examples of Clustering Using the Mixture Method and Two Comparable Methods from SAS.

DTIC Science & Technology

1987-06-26

BUREAU OF STANDAR-S1963-A Nw BOM -ILE COPY -. 4eo .?3sa.9"-,,A WIN* MAT HEMATICAL SCIENCES _*INSTITUTE AD-A184 687 DTICS!ELECTE ANNOTATED COMPUTER OUTPUT...intoduction to the use of mixture models in clustering. Cornell University Biometrics Unit Technical Report BU-920-M and Mathematical Sciences Institute...mixture method and two comparable methods from SAS. Cornell University Biometrics Unit Technical Report BU-921-M and Mathematical Sciences Institute

Mathematical Modeling of Loop Heat Pipes

NASA Technical Reports Server (NTRS)

Kaya, Tarik; Ku, Jentung; Hoang, Triem T.; Cheung, Mark L.

1998-01-01

The primary focus of this study is to model steady-state performance of a Loop Heat Pipe (LHP). The mathematical model is based on the steady-state energy balance equations at each component of the LHP. The heat exchange between each LHP component and the surrounding is taken into account. Both convection and radiation environments are modeled. The loop operating temperature is calculated as a function of the applied power at a given loop condition. Experimental validation of the model is attempted by using two different LHP designs. The mathematical model is tested at different sink temperatures and at different elevations of the loop. Tbc comparison of the calculations and experimental results showed very good agreement (within 3%). This method proved to be a useful tool in studying steady-state LHP performance characteristics.

Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations

NASA Astrophysics Data System (ADS)

Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher

2015-07-01

Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.

Assessing the Effectiveness of STAD Model and Problem Based Learning in Mathematics Learning Achievement and Problem Solving Ability

ERIC Educational Resources Information Center

Rattanatumma, Tawachai; Puncreobutr, Vichian

2016-01-01

The objective of this study was to compare the effectiveness of teaching methods in improving Mathematics Learning Achievement and Problem solving ability of students at an international college. This is a Quasi-Experimental Research which was done the study with the first year students who have registered to study Mathematics subject at St.…

A mathematical model for ethanol fermentation from oil palm trunk sap using Saccharomyces cerevisiae

NASA Astrophysics Data System (ADS)

Sultana, S.; Jamil, Norazaliza Mohd; Saleh, E. A. M.; Yousuf, A.; Faizal, Che Ku M.

2017-09-01

This paper presents a mathematical model and solution strategy of ethanol fermentation for oil palm trunk (OPT) sap by considering the effect of substrate limitation, substrate inhibition product inhibition and cell death. To investigate the effect of cell death rate on the fermentation process we extended and improved the current mathematical model. The kinetic parameters of the model were determined by nonlinear regression using maximum likelihood function. The temporal profiles of sugar, cell and ethanol concentrations were modelled by a set of ordinary differential equations, which were solved numerically by the 4th order Runge-Kutta method. The model was validated by the experimental data and the agreement between the model and experimental results demonstrates that the model is reasonable for prediction of the dynamic behaviour of the fermentation process.

Analysis of mathematical literacy ability based on self-efficacy in model eliciting activities using metaphorical thinking approach

NASA Astrophysics Data System (ADS)

Setiani, C.; Waluya, S. B.; Wardono

2018-03-01

The purposes of this research are: (1) to identify learning quality in Model Eliciting Activities (MEAs) using a Metaphorical Thinking (MT) approach regarding qualitative and quantitative; (2) to analyze mathematical literacy of students based on Self-Efficacy (SE). This research is mixed method concurrent embedded design with qualitative research as the primary method. The quantitative research used quasi-experimental with non-equivalent control group design. The population is VIII grade students of SMP Negeri 3 Semarang Indonesia. Quantitative data is examined by conducting completeness mean test, standard completeness test, mean differentiation test and proportional differentiation test. Qualitative data is analyzed descriptively. The result of this research shows that MEAs learning using MT approach accomplishes good criteria both quantitatively and qualitatively. Students with low self-efficacy can identify problems, but they are lack ability to arrange problem-solving strategy on mathematical literacy questions. Students with medium self-efficacy can identify information provided in issues, but they find difficulties to use math symbols in making a representation. Students with high self-efficacy are excellent to represent problems into mathematical models as well as figures by using appropriate symbols and tools, so they can arrange strategy easily to solve mathematical literacy questions.

A Double Layer Model of the Electromagnetic and Thermal Processes in Induction Heating of Ferromagnetic Material

NASA Astrophysics Data System (ADS)

Gilev, B.; Kraev, G.; Venkov, G. I.

2007-10-01

This paper presents the modeling of electromagnetic and heating processes in an inductor, where cylindrical ferromagnetic material has been placed. In the first part the electromagnetic mathematical problem is solved, as a result the power density is obtained. The power density takes part in the heat conduction equation. In the second part the thermal mathematical problem is solved, as a result the alteration of the temperature of the ferromagnetic material during the heating process is obtained. The parameters in both mathematical problems depend on the temperature. Because of that the stitching method is used for their finding. In [3, 4] the same mathematical problems are solved by the finite elements method. Comparing our results to those from [3] shows that they are similar. In contrast to [3, 4] our method allows the continuation of the analysis with the finding of the load power during the heating process. Thus result permits the determination of the load power alteration in the supplying inverter [1]. It is well-known that during the induction hardening it is necessary to maintain constant current amplitude in the load circuit of the inverter. So the next aim of this research is to build up a controller, based on the developed model, which will procure the necessary mode.

Mathematical modeling of silica deposition in Tongonan-I reinjection wells, Philippines

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

Malate, R.C.M.; O`Sullivan, M.J.

1993-10-01

Mathematical models of silica deposition are derived using the method of characteristics for the problem of variable rate injection into a well producing radially symmetric flow. Solutions are developed using the first order rate equation of silica deposition suggested by Rimstidt and Barnes (1980). The changes in porosity and permeability resulting from deposition are included in the models. The models developed are successfully applied in simulating the changes in injection capacity in some of the reinjection wells in Tongonan geothermal field, Philippines.

Pyroelectric effect in tryglicyne sulphate single crystals - Differential measurement method

NASA Astrophysics Data System (ADS)

Trybus, M.

2018-06-01

A simple mathematical model of the pyroelectric phenomenon was used to explain the electric response of the TGS (triglycine sulphate) samples in the linear heating process in ferroelectric and paraelectric phases. Experimental verification of mathematical model was realized. TGS single crystals were grown and four electrode samples were fabricated. Differential measurements of the pyroelectric response of two different regions of the samples were performed and the results were compared with data obtained from the model. Experimental results are in good agreement with model calculations.

A Mathematical Model of the Thermo-Anemometric Flowmeter

PubMed Central

Korobiichuk, Igor; Bezvesilna, Olena; Ilchenko, Andriі; Shadura, Valentina; Nowicki, Michał; Szewczyk, Roman

2015-01-01

A thermo-anemometric flowmeter design and the principles of its work are presented in the article. A mathematical model of the temperature field in a stream of biofuel is proposed. This model allows one to determine the fuel consumption with high accuracy. Numerical modeling of the heater heat balance in the fuel flow of a thermo-anemometric flowmeter is conducted and the results are analyzed. Methods for increasing the measurement speed and accuracy of a thermo-anemometric flowmeter are proposed. PMID:26378535

A Mathematical Model of the Thermo-Anemometric Flowmeter.

PubMed

Korobiichuk, Igor; Bezvesilna, Olena; Ilchenko, Andriі; Shadura, Valentina; Nowicki, Michał; Szewczyk, Roman

2015-09-11

A thermo-anemometric flowmeter design and the principles of its work are presented in the article. A mathematical model of the temperature field in a stream of biofuel is proposed. This model allows one to determine the fuel consumption with high accuracy. Numerical modeling of the heater heat balance in the fuel flow of a thermo-anemometric flowmeter is conducted and the results are analyzed. Methods for increasing the measurement speed and accuracy of a thermo-anemometric flowmeter are proposed.

A numerical solution of the problem of crown forest fire initiation and spread

NASA Astrophysics Data System (ADS)

Marzaeva, S. I.; Galtseva, O. V.

2018-05-01

Mathematical model of forest fire was based on an analysis of known experimental data and using concept and methods from reactive media mechanics. The study takes in to account the mutual interaction of the forest fires and three-dimensional atmosphere flows. The research is done by means of mathematical modeling of physical processes. It is based on numerical solution of Reynolds equations for chemical components and equations of energy conservation for gaseous and condensed phases. It is assumed that the forest during a forest fire can be modeled as a two-temperature multiphase non-deformable porous reactive medium. A discrete analog for the system of equations was obtained by means of the control volume method. The developed model of forest fire initiation and spreading would make it possible to obtain a detailed picture of the variation in the velocity, temperature and chemical species concentration fields with time. Mathematical model and the result of the calculation give an opportunity to evaluate critical conditions of the forest fire initiation and spread which allows applying the given model for of means for preventing fires.

Applications of numerical methods to simulate the movement of contaminants in groundwater.

PubMed Central

Sun, N Z

1989-01-01

This paper reviews mathematical models and numerical methods that have been extensively used to simulate the movement of contaminants through the subsurface. The major emphasis is placed on the numerical methods of advection-dominated transport problems and inverse problems. Several mathematical models that are commonly used in field problems are listed. A variety of numerical solutions for three-dimensional models are introduced, including the multiple cell balance method that can be considered a variation of the finite element method. The multiple cell balance method is easy to understand and convenient for solving field problems. When the advection transport dominates the dispersion transport, two kinds of numerical difficulties, overshoot and numerical dispersion, are always involved in solving standard, finite difference methods and finite element methods. To overcome these numerical difficulties, various numerical techniques are developed, such as upstream weighting methods and moving point methods. A complete review of these methods is given and we also mention the problems of parameter identification, reliability analysis, and optimal-experiment design that are absolutely necessary for constructing a practical model. PMID:2695327

Progress in Mathematical Modeling of Gastrointestinal Slow Wave Abnormalities

PubMed Central

Du, Peng; Calder, Stefan; Angeli, Timothy R.; Sathar, Shameer; Paskaranandavadivel, Niranchan; O'Grady, Gregory; Cheng, Leo K.

2018-01-01

Gastrointestinal (GI) motility is regulated in part by electrophysiological events called slow waves, which are generated by the interstitial cells of Cajal (ICC). Slow waves propagate by a process of “entrainment,” which occurs over a decreasing gradient of intrinsic frequencies in the antegrade direction across much of the GI tract. Abnormal initiation and conduction of slow waves have been demonstrated in, and linked to, a number of GI motility disorders. A range of mathematical models have been developed to study abnormal slow waves and applied to propose novel methods for non-invasive detection and therapy. This review provides a general outline of GI slow wave abnormalities and their recent classification using multi-electrode (high-resolution) mapping methods, with a particular emphasis on the spatial patterns of these abnormal activities. The recently-developed mathematical models are introduced in order of their biophysical scale from cellular to whole-organ levels. The modeling techniques, main findings from the simulations, and potential future directions arising from notable studies are discussed. PMID:29379448

Mathematical Modeling of Microbial Community Dynamics: A Methodological Review

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

Song, Hyun-Seob; Cannon, William R.; Beliaev, Alex S.

Microorganisms in nature form diverse communities that dynamically change in structure and function in response to environmental variations. As a complex adaptive system, microbial communities show higher-order properties that are not present in individual microbes, but arise from their interactions. Predictive mathematical models not only help to understand the underlying principles of the dynamics and emergent properties of natural and synthetic microbial communities, but also provide key knowledge required for engineering them. In this article, we provide an overview of mathematical tools that include not only current mainstream approaches, but also less traditional approaches that, in our opinion, can bemore » potentially useful. We discuss a broad range of methods ranging from low-resolution supra-organismal to high-resolution individual-based modeling. Particularly, we highlight the integrative approaches that synergistically combine disparate methods. In conclusion, we provide our outlook for the key aspects that should be further developed to move microbial community modeling towards greater predictive power.« less

Evolutionary game theory using agent-based methods.

PubMed

Adami, Christoph; Schossau, Jory; Hintze, Arend

2016-12-01

Evolutionary game theory is a successful mathematical framework geared towards understanding the selective pressures that affect the evolution of the strategies of agents engaged in interactions with potential conflicts. While a mathematical treatment of the costs and benefits of decisions can predict the optimal strategy in simple settings, more realistic settings such as finite populations, non-vanishing mutations rates, stochastic decisions, communication between agents, and spatial interactions, require agent-based methods where each agent is modeled as an individual, carries its own genes that determine its decisions, and where the evolutionary outcome can only be ascertained by evolving the population of agents forward in time. While highlighting standard mathematical results, we compare those to agent-based methods that can go beyond the limitations of equations and simulate the complexity of heterogeneous populations and an ever-changing set of interactors. We conclude that agent-based methods can predict evolutionary outcomes where purely mathematical treatments cannot tread (for example in the weak selection-strong mutation limit), but that mathematics is crucial to validate the computational simulations. Copyright © 2016 Elsevier B.V. All rights reserved.

The Effects of Web-Based Interactive Virtual Tours on the Development of Prospective Mathematics Teachers' Spatial Skills

ERIC Educational Resources Information Center

Kurtulus, Aytac

2013-01-01

The aim of this study was to investigate the effects of web-based interactive virtual tours on the development of prospective mathematics teachers' spatial skills. The study was designed based on experimental method. The "one-group pre-test post-test design" of this method was taken as the research model. The study was conducted with 3rd year…

Road simulation for four-wheel vehicle whole input power spectral density

NASA Astrophysics Data System (ADS)

Wang, Jiangbo; Qiang, Baomin

2017-05-01

As the vibration of running vehicle mainly comes from road and influence vehicle ride performance. So the road roughness power spectral density simulation has great significance to analyze automobile suspension vibration system parameters and evaluate ride comfort. Firstly, this paper based on the mathematical model of road roughness power spectral density, established the integral white noise road random method. Then in the MATLAB/Simulink environment, according to the research method of automobile suspension frame from simple two degree of freedom single-wheel vehicle model to complex multiple degrees of freedom vehicle model, this paper built the simple single incentive input simulation model. Finally the spectrum matrix was used to build whole vehicle incentive input simulation model. This simulation method based on reliable and accurate mathematical theory and can be applied to the random road simulation of any specified spectral which provides pavement incentive model and foundation to vehicle ride performance research and vibration simulation.

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.

Numerical simulation of the structure of the high-latitude ionospheric F region during meridional HF propagation

NASA Astrophysics Data System (ADS)

Andreev, M. Yu.; Mingaleva, G. I.; Mingalev, V. S.

2007-08-01

A previously developed model of the high-latitude ionosphere is used to calculate the distribution of the ionospheric parameters in the polar region. A specific method for specifying input parameters of the mathematical model, using the experimental data obtained by the method of satellite radio tomography, is used in this case. The spatial distributions of the ionospheric parameters characterized by a complex inhomogeneous structure in the high-latitude region, calculated with the help of the mathematical model, are used to simulate the HF propagation along the meridionally oriented radio paths extending from middle to high latitudes. The method for improving the HF communication between a midlatitude transmitter and a polar-cap receiver is proposed.

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.

Connectivity inference from neural recording data: Challenges, mathematical bases and research directions.

PubMed

Magrans de Abril, Ildefons; Yoshimoto, Junichiro; Doya, Kenji

2018-06-01

This article presents a review of computational methods for connectivity inference from neural activity data derived from multi-electrode recordings or fluorescence imaging. We first identify biophysical and technical challenges in connectivity inference along the data processing pipeline. We then review connectivity inference methods based on two major mathematical foundations, namely, descriptive model-free approaches and generative model-based approaches. We investigate representative studies in both categories and clarify which challenges have been addressed by which method. We further identify critical open issues and possible research directions. Copyright © 2018 The Author(s). Published by Elsevier Ltd.. All rights reserved.

An analytic model for footprint dispersions and its application to mission design

NASA Technical Reports Server (NTRS)

Rao, J. R. Jagannatha; Chen, Yi-Chao

1992-01-01

This is the final report on our recent research activities that are complementary to those conducted by our colleagues, Professor Farrokh Mistree and students, in the context of the Taguchi method. We have studied the mathematical model that forms the basis of the Simulation and Optimization of Rocket Trajectories (SORT) program and developed an analytic method for determining mission reliability with a reduced number of flight simulations. This method can be incorporated in a design algorithm to mathematically optimize different performance measures of a mission, thus leading to a robust and easy-to-use methodology for mission planning and design.

The effect of creative problem solving on students’ mathematical adaptive reasoning

NASA Astrophysics Data System (ADS)

Muin, A.; Hanifah, S. H.; Diwidian, F.

2018-01-01

This research was conducted to analyse the effect of creative problem solving (CPS) learning model on the students’ mathematical adaptive reasoning. The method used in this study was a quasi-experimental with randomized post-test only control group design. Samples were taken as many as two classes by cluster random sampling technique consisting of experimental class (CPS) as many as 40 students and control class (conventional) as many as 40 students. Based on the result of hypothesis testing with the t-test at the significance level of 5%, it was obtained that significance level of 0.0000 is less than α = 0.05. This shows that the students’ mathematical adaptive reasoning skills who were taught by CPS model were higher than the students’ mathematical adaptive reasoning skills of those who were taught by conventional model. The result of this research showed that the most prominent aspect of adaptive reasoning that could be developed through a CPS was inductive intuitive. Two aspects of adaptive reasoning, which were inductive intuitive and deductive intuitive, were mostly balanced. The different between inductive intuitive and deductive intuitive aspect was not too big. CPS model can develop student mathematical adaptive reasoning skills. CPS model can facilitate development of mathematical adaptive reasoning skills thoroughly.

Circular Samples as Objects for Magnetic Resonance Imaging - Mathematical Simulation, Experimental Results

NASA Astrophysics Data System (ADS)

Frollo, Ivan; Krafčík, Andrej; Andris, Peter; Přibil, Jiří; Dermek, Tomáš

2015-12-01

Circular samples are the frequent objects of "in-vitro" investigation using imaging method based on magnetic resonance principles. The goal of our investigation is imaging of thin planar layers without using the slide selection procedure, thus only 2D imaging or imaging of selected layers of samples in circular vessels, eppendorf tubes,.. compulsorily using procedure "slide selection". In spite of that the standard imaging methods was used, some specificity arise when mathematical modeling of these procedure is introduced. In the paper several mathematical models were presented that were compared with real experimental results. Circular magnetic samples were placed into the homogenous magnetic field of a low field imager based on nuclear magnetic resonance. For experimental verification an MRI 0.178 Tesla ESAOTE Opera imager was used.

An analysis of mathematical connection ability based on student learning style on visualization auditory kinesthetic (VAK) learning model with self-assessment

NASA Astrophysics Data System (ADS)

Apipah, S.; Kartono; Isnarto

2018-03-01

This research aims to analyze the quality of VAK learning with self-assessment toward the ability of mathematical connection performed by students and to analyze students’ mathematical connection ability based on learning styles in VAK learning model with self-assessment. This research applies mixed method type with concurrent embedded design. The subject of this research consists of VIII grade students from State Junior High School 9 Semarang who apply visual learning style, auditory learning style, and kinesthetic learning style. The data of learning style is collected by using questionnaires, the data of mathematical connection ability is collected by performing tests, and the data of self-assessment is collected by using assessment sheets. The quality of learning is qualitatively valued from planning stage, realization stage, and valuation stage. The result of mathematical connection ability test is analyzed quantitatively by mean test, conducting completeness test, mean differentiation test, and mean proportional differentiation test. The result of the research shows that VAK learning model results in well-qualified learning regarded from qualitative and quantitative sides. Students with visual learning style perform the highest mathematical connection ability, students with kinesthetic learning style perform average mathematical connection ability, and students with auditory learning style perform the lowest mathematical connection ability.

Mathematical modeling of aeroelastic systems

NASA Astrophysics Data System (ADS)

Velmisov, Petr A.; Ankilov, Andrey V.; Semenova, Elizaveta P.

2017-12-01

In the paper, the stability of elastic elements of a class of designs that are in interaction with a gas or liquid flow is investigated. The definition of the stability of an elastic body corresponds to the concept of stability of dynamical systems by Lyapunov. As examples the mathematical models of flowing channels (models of vibration devices) at a subsonic flow and the mathematical models of protective surface at a supersonic flow are considered. Models are described by the related systems of the partial differential equations. An analytic investigation of stability is carried out on the basis of the construction of Lyapunov-type functionals, a numerical investigation is carried out on the basis of the Galerkin method. The various models of the gas-liquid environment (compressed, incompressible) and the various models of a deformable body (elastic linear and elastic nonlinear) are considered.

The Value of 18F-FDG PET/CT Mathematical Prediction Model in Diagnosis of Solitary Pulmonary Nodules

PubMed Central

Chen, Yao; Tang, Kun; Lin, Jie

2018-01-01

Purpose To establish an 18F-fluorodeoxyglucose (18F-FDG) positron emission tomography/computed tomography (PET/CT) mathematical prediction model to improve the diagnosis of solitary pulmonary nodules (SPNs). Materials and Methods We retrospectively reviewed 177 consecutive patients who underwent 18F-FDG PET/CT for evaluation of SPNs. The mathematical model was established by logistic regression analysis. The diagnostic capabilities of the model were calculated, and the areas under the receiver operating characteristic curve (AUC) were compared with Mayo and VA model. Results The mathematical model was y = exp⁡(x)/[1 + exp⁡(x)], x = −7.363 + 0.079 × age + 1.900 × lobulation + 1.024 × vascular convergence + 1.530 × pleural retraction + 0.359 × the maximum of standardized uptake value (SUVmax). When the cut-off value was set at 0.56, the sensitivity, specificity, and accuracy of our model were 86.55%, 74.14%, and 81.4%, respectively. The area under the receiver operating characteristic curve (AUC) of our model was 0.903 (95% confidence interval (CI): 0.860 to 0.946). The AUC of our model was greater than that of the Mayo model, the VA model, and PET (P < 0.05) and has no difference with that of PET/CT (P > 0.05). Conclusion The mathematical predictive model has high accuracy in estimating the malignant probability of patients with SPNs. PMID:29789808

Techniques for modeling the reliability of fault-tolerant systems with the Markov state-space approach

NASA Technical Reports Server (NTRS)

Butler, Ricky W.; Johnson, Sally C.

1995-01-01

This paper presents a step-by-step tutorial of the methods and the tools that were used for the reliability analysis of fault-tolerant systems. The approach used in this paper is the Markov (or semi-Markov) state-space method. The paper is intended for design engineers with a basic understanding of computer architecture and fault tolerance, but little knowledge of reliability modeling. The representation of architectural features in mathematical models is emphasized. This paper does not present details of the mathematical solution of complex reliability models. Instead, it describes the use of several recently developed computer programs SURE, ASSIST, STEM, and PAWS that automate the generation and the solution of these models.

Mathematical model of an indirect action fuel flow controller for aircraft jet engines

NASA Astrophysics Data System (ADS)

Tudosie, Alexandru-Nicolae

2017-06-01

The paper deals with a fuel mass flow rate controller with indirect action for aircraft jet engines. The author has identified fuel controller's main parts and its operation mode, then, based on these observations, one has determined motion equations of each main part, which have built system's non-linear mathematical model. In order to realize a better study this model was linearised (using the finite differences method) and then adimensionalized. Based on this new form of the mathematical model, after applying Laplace transformation, the embedded system (controller+engine) was described by the block diagram with transfer functions. Some Simulink-Matlab simulations were performed, concerning system's time behavior for step input, which lead to some useful conclusions and extension possibilities.

Aspects of Mathematical Modelling of Pressure Retarded Osmosis

PubMed Central

Anissimov, Yuri G.

2016-01-01

In power generating terms, a pressure retarded osmosis (PRO) energy generating plant, on a river entering a sea or ocean, is equivalent to a hydroelectric dam with a height of about 60 meters. Therefore, PRO can add significantly to existing renewable power generation capacity if economical constrains of the method are resolved. PRO energy generation relies on a semipermeable membrane that is permeable to water and impermeable to salt. Mathematical modelling plays an important part in understanding flows of water and salt near and across semipermeable membranes and helps to optimize PRO energy generation. Therefore, the modelling can help realizing PRO energy generation potential. In this work, a few aspects of mathematical modelling of the PRO process are reviewed and discussed. PMID:26848696

Facultative Stabilization Pond: Measuring Biological Oxygen Demand using Mathematical Approaches

NASA Astrophysics Data System (ADS)

Wira S, Ihsan; Sunarsih, Sunarsih

2018-02-01

Pollution is a man-made phenomenon. Some pollutants which discharged directly to the environment could create serious pollution problems. Untreated wastewater will cause contamination and even pollution on the water body. Biological Oxygen Demand (BOD) is the amount of oxygen required for the oxidation by bacteria. The higher the BOD concentration, the greater the organic matter would be. The purpose of this study was to predict the value of BOD contained in wastewater. Mathematical modeling methods were chosen in this study to depict and predict the BOD values contained in facultative wastewater stabilization ponds. Measurements of sampling data were carried out to validate the model. The results of this study indicated that a mathematical approach can be applied to predict the BOD contained in the facultative wastewater stabilization ponds. The model was validated using Absolute Means Error with 10% tolerance limit, and AME for model was 7.38% (< 10%), so the model is valid. Furthermore, a mathematical approach can also be applied to illustrate and predict the contents of wastewater.

A Mathematical Model for the Exhaust Gas Temperature Profile of a Diesel Engine

NASA Astrophysics Data System (ADS)

Brito, C. H. G.; Maia, C. B.; Sodré, J. R.

2015-09-01

This work presents a heat transfer model for the exhaust gas of a diesel power generator to determine the gas temperature profile in the exhaust pipe. The numerical methodology to solve the mathematical model was developed using a finite difference method approach for energy equation resolution and determination of temperature profiles considering turbulent fluid flow and variable fluid properties. The simulation was carried out for engine operation under loads from 0 kW to 40 kW. The model was compared with results obtained using the multidimensional Ansys CFX software, which was applied to solve the governor equations of turbulent fluid flow. The results for the temperature profiles in the exhaust pipe show a good proximity between the mathematical model developed and the multidimensional software.

Mathematical neuroscience: from neurons to circuits to systems.

PubMed

Gutkin, Boris; Pinto, David; Ermentrout, Bard

2003-01-01

Applications of mathematics and computational techniques to our understanding of neuronal systems are provided. Reduction of membrane models to simplified canonical models demonstrates how neuronal spike-time statistics follow from simple properties of neurons. Averaging over space allows one to derive a simple model for the whisker barrel circuit and use this to explain and suggest several experiments. Spatio-temporal pattern formation methods are applied to explain the patterns seen in the early stages of drug-induced visual hallucinations.

Mathematical Astronomy in India

NASA Astrophysics Data System (ADS)

Plofker, Kim

Astronomy in South Asia's Sanskrit tradition, apparently originating in simple calendric computations regulating the timing of ancient ritual practices, expanded over the course of two or three millennia to include detailed spherical models, an endless variety of astrological systems, and academic mathematics in general. Assimilating various technical models, methods, and genres from the astronomy of neighboring cultures, Indian astronomers created new forms that were in turn borrowed by their foreign counterparts. Always recognizably related to the main themes of Eurasian geocentric mathematical astronomy, Indian astral science nonetheless maintained its culturally distinct character until Keplerian heliocentrism and Newtonian mechanics replaced it in colonial South Asia's academic mainstream.

Multiscale modeling of brain dynamics: from single neurons and networks to mathematical tools.

PubMed

Siettos, Constantinos; Starke, Jens

2016-09-01

The extreme complexity of the brain naturally requires mathematical modeling approaches on a large variety of scales; the spectrum ranges from single neuron dynamics over the behavior of groups of neurons to neuronal network activity. Thus, the connection between the microscopic scale (single neuron activity) to macroscopic behavior (emergent behavior of the collective dynamics) and vice versa is a key to understand the brain in its complexity. In this work, we attempt a review of a wide range of approaches, ranging from the modeling of single neuron dynamics to machine learning. The models include biophysical as well as data-driven phenomenological models. The discussed models include Hodgkin-Huxley, FitzHugh-Nagumo, coupled oscillators (Kuramoto oscillators, Rössler oscillators, and the Hindmarsh-Rose neuron), Integrate and Fire, networks of neurons, and neural field equations. In addition to the mathematical models, important mathematical methods in multiscale modeling and reconstruction of the causal connectivity are sketched. The methods include linear and nonlinear tools from statistics, data analysis, and time series analysis up to differential equations, dynamical systems, and bifurcation theory, including Granger causal connectivity analysis, phase synchronization connectivity analysis, principal component analysis (PCA), independent component analysis (ICA), and manifold learning algorithms such as ISOMAP, and diffusion maps and equation-free techniques. WIREs Syst Biol Med 2016, 8:438-458. doi: 10.1002/wsbm.1348 For further resources related to this article, please visit the WIREs website. © 2016 Wiley Periodicals, Inc.

Application of geologic-mathematical 3D modeling for complex structure deposits by the example of Lower- Cretaceous period depositions in Western Ust - Balykh oil field (Khanty-Mansiysk Autonomous District)

NASA Astrophysics Data System (ADS)

Perevertailo, T.; Nedolivko, N.; Prisyazhnyuk, O.; Dolgaya, T.

2015-11-01

The complex structure of the Lower-Cretaceous formation by the example of the reservoir BC101 in Western Ust - Balykh Oil Field (Khanty-Mansiysk Autonomous District) has been studied. Reservoir range relationships have been identified. 3D geologic- mathematical modeling technique considering the heterogeneity and variability of a natural reservoir structure has been suggested. To improve the deposit geological structure integrity methods of mathematical statistics were applied, which, in its turn, made it possible to obtain equal probability models with similar input data and to consider the formation conditions of reservoir rocks and cap rocks.

The oxygen uptake slow component at submaximal intensities in breaststroke swimming

PubMed Central

Oliveira, Diogo R.; Gonçalves, Lio F.; Reis, António M.; Fernandes, Ricardo J.; Garrido, Nuno D.

2016-01-01

Abstract The present work proposed to study the oxygen uptake slow component (VO2 SC) of breaststroke swimmers at four different intensities of submaximal exercise, via mathematical modeling of a multi-exponential function. The slow component (SC) was also assessed with two different fixed interval methods and the three methods were compared. Twelve male swimmers performed a test comprising four submaximal 300 m bouts at different intensities where all expired gases were collected breath by breath. Multi-exponential modeling showed values above 450 ml·min−1 of the SC in the two last bouts of exercise (those with intensities above the lactate threshold). A significant effect of the method that was used to calculate the VO2 SC was revealed. Higher mean values were observed when using mathematical modeling compared with the fixed interval 3rd min method (F=7.111; p=0.012; η2=0.587); furthermore, differences were detected among the two fixed interval methods. No significant relationship was found between the SC determined by any method and the blood lactate measured at each of the four exercise intensities. In addition, no significant association between the SC and peak oxygen uptake was found. It was concluded that in trained breaststroke swimmers, the presence of the VO2 SC may be observed at intensities above that corresponding to the 3.5 mM-1 threshold. Moreover, mathematical modeling of the oxygen uptake on-kinetics tended to show a higher slow component as compared to fixed interval methods. PMID:28149379

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.

Detecting isotopic ratio outliers

NASA Astrophysics Data System (ADS)

Bayne, C. K.; Smith, D. H.

An alternative method is proposed for improving isotopic ratio estimates. This method mathematically models pulse-count data and uses iterative reweighted Poisson regression to estimate model parameters to calculate the isotopic ratios. This computer-oriented approach provides theoretically better methods than conventional techniques to establish error limits and to identify outliers.

Mathematical Modeling of Chemical Stoichiometry

ERIC Educational Resources Information Center

Croteau, Joshua; Fox, William P.; Varazo, Kristofoland

2007-01-01

In beginning chemistry classes, students are taught a variety of techniques for balancing chemical equations. The most common method is inspection. This paper addresses using a system of linear mathematical equations to solve for the stoichiometric coefficients. Many linear algebra books carry the standard balancing of chemical equations as an…

Satellite orbit computation methods

NASA Technical Reports Server (NTRS)

1977-01-01

Mathematical and algorithmical techniques for solution of problems in satellite dynamics were developed, along with solutions to satellite orbit motion. Dynamical analysis of shuttle on-orbit operations were conducted. Computer software routines for use in shuttle mission planning were developed and analyzed, while mathematical models of atmospheric density were formulated.

40 CFR 227.29 - Initial mixing.

Code of Federal Regulations, 2010 CFR

2010-07-01

... estimated by one of these methods, in order of preference: (1) When field data on the proposed dumping are... conjunction with an appropriate mathematical model acceptable to EPA or the District Engineer, as appropriate... proposed for discharge are available, these shall be used in conjunction with an appropriate mathematical...

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

A mathematical framework for modelling cambial surface evolution using a level set method

PubMed Central

Sellier, Damien; Plank, Michael J.; Harrington, Jonathan J.

2011-01-01

Background and Aims During their lifetime, tree stems take a series of successive nested shapes. Individual tree growth models traditionally focus on apical growth and architecture. However, cambial growth, which is distributed over a surface layer wrapping the whole organism, equally contributes to plant form and function. This study aims at providing a framework to simulate how organism shape evolves as a result of a secondary growth process that occurs at the cellular scale. Methods The development of the vascular cambium is modelled as an expanding surface using the level set method. The surface consists of multiple compartments following distinct expansion rules. Growth behaviour can be formulated as a mathematical function of surface state variables and independent variables to describe biological processes. Key Results The model was coupled to an architectural model and to a forest stand model to simulate cambium dynamics and wood formation at the scale of the organism. The model is able to simulate competition between cambia, surface irregularities and local features. Predicting the shapes associated with arbitrarily complex growth functions does not add complexity to the numerical method itself. Conclusions Despite their slenderness, it is sometimes useful to conceive of trees as expanding surfaces. The proposed mathematical framework provides a way to integrate through time and space the biological and physical mechanisms underlying cambium activity. It can be used either to test growth hypotheses or to generate detailed maps of wood internal structure. PMID:21470972

Optimizing Chemotherapy Dose and Schedule by Norton-Simon Mathematical Modeling

PubMed Central

Traina, Tiffany A.; Dugan, Ute; Higgins, Brian; Kolinsky, Kenneth; Theodoulou, Maria; Hudis, Clifford A.; Norton, Larry

2011-01-01

Background To hasten and improve anticancer drug development, we created a novel approach to generating and analyzing preclinical dose-scheduling data so as to optimize benefit-to-toxicity ratios. Methods We applied mathematical methods based upon Norton-Simon growth kinetic modeling to tumor-volume data from breast cancer xenografts treated with capecitabine (Xeloda®, Roche) at the conventional schedule of 14 days of treatment followed by a 7-day rest (14 - 7). Results The model predicted that 7 days of treatment followed by a 7-day rest (7 - 7) would be superior. Subsequent preclinical studies demonstrated that this biweekly capecitabine schedule allowed for safe delivery of higher daily doses, improved tumor response, and prolonged animal survival. Conclusions We demonstrated that the application of Norton-Simon modeling to the design and analysis of preclinical data predicts an improved capecitabine dosing schedule in xenograft models. This method warrants further investigation and application in clinical drug development. PMID:20519801

On the interplay between mathematics and biology. Hallmarks toward a new systems biology

NASA Astrophysics Data System (ADS)

Bellomo, Nicola; Elaiw, Ahmed; Althiabi, Abdullah M.; Alghamdi, Mohammed Ali

2015-03-01

This paper proposes a critical analysis of the existing literature on mathematical tools developed toward systems biology approaches and, out of this overview, develops a new approach whose main features can be briefly summarized as follows: derivation of mathematical structures suitable to capture the complexity of biological, hence living, systems, modeling, by appropriate mathematical tools, Darwinian type dynamics, namely mutations followed by selection and evolution. Moreover, multiscale methods to move from genes to cells, and from cells to tissue are analyzed in view of a new systems biology approach.

An Evaluation Model Applied to a Mathematics-Methods Program Involving Three Characteristics of Teaching Style and Their Relationship to Pupil Achievement. Teacher Education Forum; Volume 3, Number 4.

ERIC Educational Resources Information Center

Dodd, Carol Ann

This study explores a technique for evaluating teacher education programs in terms of teaching competencies, as applied to the Indiana University Mathematics Methods Program (MMP). The evaluation procedures formulated for the study include a process product design in combination with a modification of Pophan's performance test paradigm and Gage's…

Using confirmatory factor analysis to understand executive control in preschool children: sources of variation in emergent mathematic achievement

PubMed Central

Bull, Rebecca; Espy, Kimberly Andrews; Wiebe, Sandra A.; Sheffield, Tiffany D.; Nelson, Jennifer Mize

2010-01-01

Latent variable modeling methods have demonstrated utility for understanding the structure of executive control (EC) across development. These methods are utilized to better characterize the relation between EC and mathematics achievement in the preschool period, and to understand contributing sources of individual variation. Using the sample and battery of laboratory tasks described in Wiebe, Espy and Charak (2008), latent EC was related strongly to emergent mathematics achievement in preschool, and was robust after controlling for crystallized intellectual skills. The relation between crystallized skills and emergent mathematics differed between girls and boys, although the predictive association between EC and mathematics did not. Two dimensions of the child’s social environment contributed to mathematics achievement: social network support through its relation to EC and environmental stressors through its relation with crystallized skills. These findings underscore the need to examine the dimensions, mechanisms, and individual pathways that influence the development of early competence in basic cognitive processes that underpin early academic achievement. PMID:21676089

Using confirmatory factor analysis to understand executive control in preschool children: sources of variation in emergent mathematic achievement.

PubMed

Bull, Rebecca; Espy, Kimberly Andrews; Wiebe, Sandra A; Sheffield, Tiffany D; Nelson, Jennifer Mize

2011-07-01

Latent variable modeling methods have demonstrated utility for understanding the structure of executive control (EC) across development. These methods are utilized to better characterize the relation between EC and mathematics achievement in the preschool period, and to understand contributing sources of individual variation. Using the sample and battery of laboratory tasks described in Wiebe, Espy and Charak (2008), latent EC was related strongly to emergent mathematics achievement in preschool, and was robust after controlling for crystallized intellectual skills. The relation between crystallized skills and emergent mathematics differed between girls and boys, although the predictive association between EC and mathematics did not. Two dimensions of the child 's social environment contributed to mathematics achievement: social network support through its relation to EC and environmental stressors through its relation with crystallized skills. These findings underscore the need to examine the dimensions, mechanisms, and individual pathways that influence the development of early competence in basic cognitive processes that underpin early academic achievement. © 2010 Blackwell Publishing Ltd.

Understanding the Impact of Interventions to Prevent Antimicrobial Resistant Infections in the Long-Term Care Facility: A Review and Practical Guide to Mathematical Modeling.

PubMed

Rosello, Alicia; Horner, Carolyne; Hopkins, Susan; Hayward, Andrew C; Deeny, Sarah R

2017-02-01

OBJECTIVES (1) To systematically search for all dynamic mathematical models of infectious disease transmission in long-term care facilities (LTCFs); (2) to critically evaluate models of interventions against antimicrobial resistance (AMR) in this setting; and (3) to develop a checklist for hospital epidemiologists and policy makers by which to distinguish good quality models of AMR in LTCFs. METHODS The CINAHL, EMBASE, Global Health, MEDLINE, and Scopus databases were systematically searched for studies of dynamic mathematical models set in LTCFs. Models of interventions targeting methicillin-resistant Staphylococcus aureus in LTCFs were critically assessed. Using this analysis, we developed a checklist for good quality mathematical models of AMR in LTCFs. RESULTS AND DISCUSSION Overall, 18 papers described mathematical models that characterized the spread of infectious diseases in LTCFs, but no models of AMR in gram-negative bacteria in this setting were described. Future models of AMR in LTCFs require a more robust methodology (ie, formal model fitting to data and validation), greater transparency regarding model assumptions, setting-specific data, realistic and current setting-specific parameters, and inclusion of movement dynamics between LTCFs and hospitals. CONCLUSIONS Mathematical models of AMR in gram-negative bacteria in the LTCF setting, where these bacteria are increasingly becoming prevalent, are needed to help guide infection prevention and control. Improvements are required to develop outputs of sufficient quality to help guide interventions and policy in the future. We suggest a checklist of criteria to be used as a practical guide to determine whether a model is robust enough to test policy. Infect Control Hosp Epidemiol 2017;38:216-225.

Classroom observation data and instruction in primary mathematics education: improving design and rigour

NASA Astrophysics Data System (ADS)

Thompson, Carla J.; Davis, Sandra B.

2014-06-01

The use of formal observation in primary mathematics classrooms is supported in the literature as a viable method of determining effective teaching strategies and appropriate tasks for inclusion in the early years of mathematics learning. The twofold aim of this study was to (a) investigate predictive relationships between primary mathematics classroom observational data and student achievement data, and (b) to examine the impact of providing periodic classroom observational data feedback to teachers using a Relational-Feedback-Intervention (RFI) Database Model. This observational research effort focused on an empirical examination of student engagement levels in time spent on specific learning activities observed in primary mathematics classrooms as predictors of student competency outcomes in mathematics. Data were collected from more than 2,000 primary classroom observations in 17 primary schools during 2009-2011 and from standardised end-of-year tests for mathematics achievement. Results revealed predictive relationships among several types of teaching and learning tasks with student achievement. Specifically, the use of mathematics concepts, technology and hands-on materials in primary mathematics classrooms was found to produce substantive predictors of increased student mathematics achievement. Additional findings supported the use of periodic classroom observation data reporting as a positive influence on teachers' decisions in determining instructional tasks for inclusion in primary mathematics classrooms. Study results indicate classroom observational research involving a RFI Database Model is a productive tool for improving teaching and learning in primary mathematics classrooms.

The Model Method: Singapore Children's Tool for Representing and Solving Algebraic Word Problems

ERIC Educational Resources Information Center

Ng, Swee Fong; Lee, Kerry

2009-01-01

Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to…

Aspects of job scheduling

NASA Technical Reports Server (NTRS)

Phillips, K.

1976-01-01

A mathematical model for job scheduling in a specified context is presented. The model uses both linear programming and combinatorial methods. While designed with a view toward optimization of scheduling of facility and plant operations at the Deep Space Communications Complex, the context is sufficiently general to be widely applicable. The general scheduling problem including options for scheduling objectives is discussed and fundamental parameters identified. Mathematical algorithms for partitioning problems germane to scheduling are presented.

A Categorization Model for Educational Values of the History of Mathematics. An Empirical Study

NASA Astrophysics Data System (ADS)

Wang, Xiao-qin; Qi, Chun-yan; Wang, Ke

2017-11-01

There is not a clear consensus on the categorization framework of the educational values of the history of mathematics. By analyzing 20 Chinese teaching cases on integrating the history of mathematics into mathematics teaching based on the relevant literature, this study examined a new categorization framework of the educational values of the history of mathematics by combining the objectives of high school mathematics curriculum in China. This framework includes six dimensions: the harmony of knowledge, the beauty of ideas or methods, the pleasure of inquiries, the improvement of capabilities, the charm of cultures, and the availability of moral education. The results show that this framework better explained the all-educational values of the history of mathematics that all teaching cases showed. Therefore, the framework can guide teachers to better integrate the history of mathematics into teaching.

Thermal Network Modelling Handbook

NASA Technical Reports Server (NTRS)

1972-01-01

Thermal mathematical modelling is discussed in detail. A three-fold purpose was established: (1) to acquaint the new user with the terminology and concepts used in thermal mathematical modelling, (2) to present the more experienced and occasional user with quick formulas and methods for solving everyday problems, coupled with study cases which lend insight into the relationships that exist among the various solution techniques and parameters, and (3) to begin to catalog in an orderly fashion the common formulas which may be applied to automated conversational language techniques.

Mathematical Modeling of Ultraporous Nonmetallic Reticulated Materials

NASA Astrophysics Data System (ADS)

Alifanov, O. M.; Cherepanov, V. V.; Morzhukhina, A. V.

2015-01-01

We have developed an imitation statistical mathematical model reflecting the structure and the thermal, electrophysical, and optical properties of nonmetallic ultraporous reticulated materials. This model, in combination with a nonstationary thermal experiment and methods of the theory of inverse heat transfer problems, permits determining the little-studied characteristics of the above materials such as the radiative and conductive heat conductivities, the spectral scattering and absorption coefficients, the scattering indicatrix, and the dielectric constants, which are of great practical interest but are difficult to investigate.

Mathematical programming formulations for satellite synthesis

NASA Technical Reports Server (NTRS)

Bhasin, Puneet; Reilly, Charles H.

1987-01-01

The problem of satellite synthesis can be described as optimally allotting locations and sometimes frequencies and polarizations, to communication satellites so that interference from unwanted satellite signals does not exceed a specified threshold. In this report, mathematical programming models and optimization methods are used to solve satellite synthesis problems. A nonlinear programming formulation which is solved using Zoutendijk's method and a gradient search method is described. Nine mixed integer programming models are considered. Results of computer runs with these nine models and five geographically compatible scenarios are presented and evaluated. A heuristic solution procedure is also used to solve two of the models studied. Heuristic solutions to three large synthesis problems are presented. The results of our analysis show that the heuristic performs very well, both in terms of solution quality and solution time, on the two models to which it was applied. It is concluded that the heuristic procedure is the best of the methods considered for solving satellite synthesis problems.

Methods to achieve accurate projection of regional and global raster databases

USGS Publications Warehouse

Usery, E. Lynn; Seong, Jeong Chang; Steinwand, Dan

2002-01-01

Modeling regional and global activities of climatic and human-induced change requires accurate geographic data from which we can develop mathematical and statistical tabulations of attributes and properties of the environment. Many of these models depend on data formatted as raster cells or matrices of pixel values. Recently, it has been demonstrated that regional and global raster datasets are subject to significant error from mathematical projection and that these errors are of such magnitude that model results may be jeopardized (Steinwand, et al., 1995; Yang, et al., 1996; Usery and Seong, 2001; Seong and Usery, 2001). There is a need to develop methods of projection that maintain the accuracy of these datasets to support regional and global analyses and modeling

Assessing adult mortality in HIV-1-afflicted Zimbabwe (1998 -2003).

PubMed Central

Lopman, Ben A.; Barnabas, Ruanne; Hallett, Timothy B.; Nyamukapa, Constance; Mundandi, Costa; Mushati, Phyllis; Garnett, Geoff P.; Gregson, Simon

2006-01-01

OBJECTIVE: To compare alternative methods to vital registration systems for estimating adult mortality, and describe patterns of mortality in Manicaland, Zimbabwe, which has been severely affected by HIV. METHODS: We compared estimates of adult mortality from (1) a single question on household mortality, (2) repeated household censuses, and (3) an adult cohort study with linked HIV testing from Manicaland, with a mathematical model fitted to local age-specific HIV prevalence (1998 -2000). FINDINGS: The crude death rate from the single question (29 per 1000 person-years) was roughly consistent with that from the mathematical model (22 -25 per 1000 person-years), but much higher than that from the household censuses (12 per 1000 person-years). Adult mortality in the household censuses (males 0.65; females 0.51) was lower than in the cohort study (males 0.77; females 0.57), while mathematical models gave a much higher estimate, especially for females (males 0.80 -0.83; females 0.75 -0.80). The population attributable fraction of adult deaths due to HIV was 0.61 for men and 0.70 for women, with life expectancy estimated to be 34.3 years for males and 38.2 years for females. CONCLUSION: Each method for estimating adult mortality had limitations in terms of loss to follow-up (cohort study), under-ascertainment (household censuses), transparency of underlying processes (single question), and sensitivity to parameterization (mathematical model). However, these analyses make clear the advantages of longitudinal cohort data, which provide more complete ascertainment than household censuses, highlight possible inaccuracies in model assumptions, and allow direct quantification of the impact of HIV. PMID:16583077

Collective Properties of Neural Systems and Their Relation to Other Physical Models

DTIC Science & Technology

1988-08-05

been computed explicitly. This has been achieved algorithmically by utilizing methods introduced earlier. It should be emphasized that in addition to...Research Institute for Mathematical Sciences. K’oto Universin. K roto 606. .apan and E. BAROUCH Department of Mathematics and Computer Sciene. Clarkon...Mathematics and Computer Science, Clarkson University, where this work was collaborated. References I. IBabu, S. V. and Barouch E., An exact soIlution for the

A log-linear model approach to estimation of population size using the line-transect sampling method

USGS Publications Warehouse

Anderson, D.R.; Burnham, K.P.; Crain, B.R.

1978-01-01

The technique of estimating wildlife population size and density using the belt or line-transect sampling method has been used in many past projects, such as the estimation of density of waterfowl nestling sites in marshes, and is being used currently in such areas as the assessment of Pacific porpoise stocks in regions of tuna fishing activity. A mathematical framework for line-transect methodology has only emerged in the last 5 yr. In the present article, we extend this mathematical framework to a line-transect estimator based upon a log-linear model approach.

The application of virtual prototyping methods to determine the dynamic parameters of mobile robot

NASA Astrophysics Data System (ADS)

Kurc, Krzysztof; Szybicki, Dariusz; Burghardt, Andrzej; Muszyńska, Magdalena

2016-04-01

The paper presents methods used to determine the parameters necessary to build a mathematical model of an underwater robot with a crawler drive. The parameters present in the dynamics equation will be determined by means of advanced mechatronic design tools, including: CAD/CAE software andMES modules. The virtual prototyping process is described as well as the various possible uses (design adaptability) depending on the optional accessories added to the vehicle. A mathematical model is presented to show the kinematics and dynamics of the underwater crawler robot, essential for the design stage.

Thermal oil recovery method using self-contained windelectric sets

NASA Astrophysics Data System (ADS)

Belsky, A. A.; Korolyov, I. A.

2018-05-01

The paper reviews challenges associated with questions of efficiency of thermal methods of impact on productive oil strata. The concept of using electrothermal complexes with WEG power supply for the indicated purposes was proposed and justified, their operating principles, main advantages and disadvantages, as well as a schematechnical solution for the implementation of the intensification of oil extraction, were considered. A mathematical model for finding the operating characteristics of WEG is presented and its main energy parameters are determined. The adequacy of the mathematical model is confirmed by laboratory simulation stand tests with nominal parameters.

Mathematical Formulation of Multivariate Euclidean Models for Discrimination Methods.

ERIC Educational Resources Information Center

Mullen, Kenneth; Ennis, Daniel M.

1987-01-01

Multivariate models for the triangular and duo-trio methods are described, and theoretical methods are compared to a Monte Carlo simulation. Implications are discussed for a new theory of multidimensional scaling which challenges the traditional assumption that proximity measures and perceptual distances are monotonically related. (Author/GDC)

Mathematical methods to model rodent behavior in the elevated plus-maze.

PubMed

Arantes, Rafael; Tejada, Julián; Bosco, Geraldine G; Morato, Silvio; Roque, Antonio C

2013-11-15

The elevated plus maze is a widely used experimental test to study anxiety-like rodent behavior. It is made of four arms, two open and two closed, connected at a central area forming a plus shaped maze. The whole apparatus is elevated 50 cm from the floor. The anxiety of the animal is usually assessed by the number of entries and duration of stay in each arm type during a 5-min period. Different mathematical methods have been proposed to model the mechanisms that control the animal behavior in the maze, such as factor analysis, statistical inference on Markov chains and computational modeling. In this review we discuss these methods and propose possible extensions of them as a direction for future research. Copyright © 2013 Elsevier B.V. All rights reserved.

Human Modelling for Military Application (Applications militaires de la modelisation humaine)

DTIC Science & Technology

2010-10-01

techniques (rooted in the mathematics-centered analytic methods arising from World War I analyses by Lanchester 2 ). Recent requirements for research and...34Dry Shooting for Airplane Gunners - Popular Science Monthly". January 1919. p. 13-14. 2 Lanchester F.W., Mathematics in Warfare in The World of

Student Engagement and Teacher Guidance in Meaningful Mathematics: Enduring Principles

ERIC Educational Resources Information Center

Freeman, Gregory D.; Lucius, Lisa B.

2008-01-01

In mathematics, developing a conceptual understanding and observing properly modeled methods rarely lead to successful student performance. The student must participate. As with bike riding, participation with monitoring and guidance makes initial efforts meaningful and beneficial. In this article, the authors share a bike riding experience and…

Examination of Mathematics Teachers' Pedagogical Content Knowledge of Probability

ERIC Educational Resources Information Center

Danisman, Sahin; Tanisli, Dilek

2017-01-01

The aim of this study is to explore the probability-related pedagogical content knowledge (PCK) of secondary school mathematics teachers in terms of content knowledge, curriculum knowledge, student knowledge, and knowledge of teaching methods and strategies. Case study design, a qualitative research model, was used in the study, and the…

Ross, macdonald, and a theory for the dynamics and control of mosquito-transmitted pathogens.

PubMed

Smith, David L; Battle, Katherine E; Hay, Simon I; Barker, Christopher M; Scott, Thomas W; McKenzie, F Ellis

2012-01-01

Ronald Ross and George Macdonald are credited with developing a mathematical model of mosquito-borne pathogen transmission. A systematic historical review suggests that several mathematicians and scientists contributed to development of the Ross-Macdonald model over a period of 70 years. Ross developed two different mathematical models, Macdonald a third, and various "Ross-Macdonald" mathematical models exist. Ross-Macdonald models are best defined by a consensus set of assumptions. The mathematical model is just one part of a theory for the dynamics and control of mosquito-transmitted pathogens that also includes epidemiological and entomological concepts and metrics for measuring transmission. All the basic elements of the theory had fallen into place by the end of the Global Malaria Eradication Programme (GMEP, 1955-1969) with the concept of vectorial capacity, methods for measuring key components of transmission by mosquitoes, and a quantitative theory of vector control. The Ross-Macdonald theory has since played a central role in development of research on mosquito-borne pathogen transmission and the development of strategies for mosquito-borne disease prevention.

Ross, Macdonald, and a Theory for the Dynamics and Control of Mosquito-Transmitted Pathogens

PubMed Central

Smith, David L.; Battle, Katherine E.; Hay, Simon I.; Barker, Christopher M.; Scott, Thomas W.; McKenzie, F. Ellis

2012-01-01

Ronald Ross and George Macdonald are credited with developing a mathematical model of mosquito-borne pathogen transmission. A systematic historical review suggests that several mathematicians and scientists contributed to development of the Ross-Macdonald model over a period of 70 years. Ross developed two different mathematical models, Macdonald a third, and various “Ross-Macdonald” mathematical models exist. Ross-Macdonald models are best defined by a consensus set of assumptions. The mathematical model is just one part of a theory for the dynamics and control of mosquito-transmitted pathogens that also includes epidemiological and entomological concepts and metrics for measuring transmission. All the basic elements of the theory had fallen into place by the end of the Global Malaria Eradication Programme (GMEP, 1955–1969) with the concept of vectorial capacity, methods for measuring key components of transmission by mosquitoes, and a quantitative theory of vector control. The Ross-Macdonald theory has since played a central role in development of research on mosquito-borne pathogen transmission and the development of strategies for mosquito-borne disease prevention. PMID:22496640

10 CFR 431.173 - Requirements applicable to all manufacturers.

Code of Federal Regulations, 2011 CFR

2011-01-01

... COMMERCIAL AND INDUSTRIAL EQUIPMENT Provisions for Commercial Heating, Ventilating, Air-Conditioning and... is based on engineering or statistical analysis, computer simulation or modeling, or other analytic... method or methods used; (B) The mathematical model, the engineering or statistical analysis, computer...

MODELS AND MODELING METHODS FOR ASSESSING HUMAN EXPOSURE AND DOSE TO TOXIC CHEMICALS AND POLLUTANTS

EPA Science Inventory

This project aims to strengthen the general scientific foundation of EPA's exposure and risk assessment, management, and policy processes by developing state-of-the-art exposure to dose mathematical models and solution methods. The results of this research will be to produce a mo...

Differential Equations Models to Study Quorum Sensing.

PubMed

Pérez-Velázquez, Judith; Hense, Burkhard A

2018-01-01

Mathematical models to study quorum sensing (QS) have become an important tool to explore all aspects of this type of bacterial communication. A wide spectrum of mathematical tools and methods such as dynamical systems, stochastics, and spatial models can be employed. In this chapter, we focus on giving an overview of models consisting of differential equations (DE), which can be used to describe changing quantities, for example, the dynamics of one or more signaling molecule in time and space, often in conjunction with bacterial growth dynamics. The chapter is divided into two sections: ordinary differential equations (ODE) and partial differential equations (PDE) models of QS. Rates of change are represented mathematically by derivatives, i.e., in terms of DE. ODE models allow describing changes in one independent variable, for example, time. PDE models can be used to follow changes in more than one independent variable, for example, time and space. Both types of models often consist of systems (i.e., more than one equation) of equations, such as equations for bacterial growth and autoinducer concentration dynamics. Almost from the onset, mathematical modeling of QS using differential equations has been an interdisciplinary endeavor and many of the works we revised here will be placed into their biological context.

Application of the Refined Integral Method in the mathematical modeling of drug delivery from one-layer torus-shaped devices.

PubMed

Helbling, Ignacio M; Ibarra, Juan C D; Luna, Julio A

2012-02-28

A mathematical modeling of controlled release of drug from one-layer torus-shaped devices is presented. Analytical solutions based on Refined Integral Method (RIM) are derived. The validity and utility of the model are ascertained by comparison of the simulation results with matrix-type vaginal rings experimental release data reported in the literature. For the comparisons, the pair-wise procedure is used to measure quantitatively the fit of the theoretical predictions to the experimental data. A good agreement between the model prediction and the experimental data is observed. A comparison with a previously reported model is also presented. More accurate results are achieved for small A/C(s) ratios. Copyright © 2011 Elsevier B.V. All rights reserved.

Mathematical Ability and Socio-Economic Background: IRT Modeling to Estimate Genotype by Environment Interaction.

PubMed

Schwabe, Inga; Boomsma, Dorret I; van den Berg, Stéphanie M

2017-12-01

Genotype by environment interaction in behavioral traits may be assessed by estimating the proportion of variance that is explained by genetic and environmental influences conditional on a measured moderating variable, such as a known environmental exposure. Behavioral traits of interest are often measured by questionnaires and analyzed as sum scores on the items. However, statistical results on genotype by environment interaction based on sum scores can be biased due to the properties of a scale. This article presents a method that makes it possible to analyze the actually observed (phenotypic) item data rather than a sum score by simultaneously estimating the genetic model and an item response theory (IRT) model. In the proposed model, the estimation of genotype by environment interaction is based on an alternative parametrization that is uniquely identified and therefore to be preferred over standard parametrizations. A simulation study shows good performance of our method compared to analyzing sum scores in terms of bias. Next, we analyzed data of 2,110 12-year-old Dutch twin pairs on mathematical ability. Genetic models were evaluated and genetic and environmental variance components estimated as a function of a family's socio-economic status (SES). Results suggested that common environmental influences are less important in creating individual differences in mathematical ability in families with a high SES than in creating individual differences in mathematical ability in twin pairs with a low or average SES.

Dynamic deformation of soft soil media: Experimental studies and mathematical modeling

NASA Astrophysics Data System (ADS)

Balandin, V. V.; Bragov, A. M.; Igumnov, L. A.; Konstantinov, A. Yu.; Kotov, V. L.; Lomunov, A. K.

2015-05-01

A complex experimental-theoretical approach to studying the problem of high-rate strain of soft soil media is presented. This approach combines the following contemporary methods of dynamical tests: the modified Hopkinson-Kolsky method applied tomedium specimens contained in holders and the method of plane wave shock experiments. The following dynamic characteristics of sand soils are obtained: shock adiabatic curves, bulk compressibility curves, and shear resistance curves. The obtained experimental data are used to study the high-rate strain process in the system of a split pressure bar, and the constitutive relations of Grigoryan's mathematical model of soft soil medium are verified by comparing the results of computational and natural test experiments of impact and penetration.

Non-parametric correlative uncertainty quantification and sensitivity analysis: Application to a Langmuir bimolecular adsorption model

NASA Astrophysics Data System (ADS)

Feng, Jinchao; Lansford, Joshua; Mironenko, Alexander; Pourkargar, Davood Babaei; Vlachos, Dionisios G.; Katsoulakis, Markos A.

2018-03-01

We propose non-parametric methods for both local and global sensitivity analysis of chemical reaction models with correlated parameter dependencies. The developed mathematical and statistical tools are applied to a benchmark Langmuir competitive adsorption model on a close packed platinum surface, whose parameters, estimated from quantum-scale computations, are correlated and are limited in size (small data). The proposed mathematical methodology employs gradient-based methods to compute sensitivity indices. We observe that ranking influential parameters depends critically on whether or not correlations between parameters are taken into account. The impact of uncertainty in the correlation and the necessity of the proposed non-parametric perspective are demonstrated.

Personality, Motivation, and Math Achievement Among Turkish Students.

PubMed

Akben-Selcuk, Elif

2017-04-01

Using the Turkish portion of the Programme for International Student Assessment dataset ( N = 4,848; 51% boys, 49% girls; age, M = 15.81 years, SD = 0.28), this study investigated factors associated with mathematics achievement among Turkish students. Three different models were estimated using the method of balanced repeated replication with Fay's method and taking into account the presence of five plausible values of the dependent variable. Results showed that male students and older students had better mathematics proficiency. Socio-economic status and school resources also played a significant role in explaining student achievement in mathematics. Finally, students who were more open to problem solving, who attributed their failure to external factors, and who were intrinsically motivated to learn mathematics achieved higher scores. Policy implications are provided.

Higher-order automatic differentiation of mathematical functions

NASA Astrophysics Data System (ADS)

Charpentier, Isabelle; Dal Cappello, Claude

2015-04-01

Functions of mathematical physics such as the Bessel functions, the Chebyshev polynomials, the Gauss hypergeometric function and so forth, have practical applications in many scientific domains. On the one hand, differentiation formulas provided in reference books apply to real or complex variables. These do not account for the chain rule. On the other hand, based on the chain rule, the automatic differentiation has become a natural tool in numerical modeling. Nevertheless automatic differentiation tools do not deal with the numerous mathematical functions. This paper describes formulas and provides codes for the higher-order automatic differentiation of mathematical functions. The first method is based on Faà di Bruno's formula that generalizes the chain rule. The second one makes use of the second order differential equation they satisfy. Both methods are exemplified with the aforementioned functions.

Mathematical biology modules based on modern molecular biology and modern discrete mathematics.

PubMed

Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network.

Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics

PubMed Central

Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network. PMID:20810955

Problems of Mathematical Finance by Stochastic Control Methods

NASA Astrophysics Data System (ADS)

Stettner, Łukasz

The purpose of this paper is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. On the one hand stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control in the last two decades. We start with pricing of financial derivatives and modeling of asset prices, studying the conditions for the absence of arbitrage. Then we consider pricing of defaultable contingent claims. Investments in bonds lead us to the term structure modeling problems. Special attention is devoted to historical static portfolio analysis called Markowitz theory. We also briefly sketch dynamic portfolio problems using viscosity solutions to Hamilton-Jacobi-Bellman equation, martingale-convex analysis method or stochastic maximum principle together with backward stochastic differential equation. Finally, long time portfolio analysis for both risk neutral and risk sensitive functionals is introduced.

Discovery learning model with geogebra assisted for improvement mathematical visual thinking ability

NASA Astrophysics Data System (ADS)

Juandi, D.; Priatna, N.

2018-05-01

The main goal of this study is to improve the mathematical visual thinking ability of high school student through implementation the Discovery Learning Model with Geogebra Assisted. This objective can be achieved through study used quasi-experimental method, with non-random pretest-posttest control design. The sample subject of this research consist of 62 senior school student grade XI in one of school in Bandung district. The required data will be collected through documentation, observation, written tests, interviews, daily journals, and student worksheets. The results of this study are: 1) Improvement students Mathematical Visual Thinking Ability who obtain learning with applied the Discovery Learning Model with Geogebra assisted is significantly higher than students who obtain conventional learning; 2) There is a difference in the improvement of students’ Mathematical Visual Thinking ability between groups based on prior knowledge mathematical abilities (high, medium, and low) who obtained the treatment. 3) The Mathematical Visual Thinking Ability improvement of the high group is significantly higher than in the medium and low groups. 4) The quality of improvement ability of high and low prior knowledge is moderate category, in while the quality of improvement ability in the high category achieved by student with medium prior knowledge.

Mathematical Modeling of an Oscillating Droplet

NASA Technical Reports Server (NTRS)

Berry, S.; Hyers, R. W.; Racz, L. M.; Abedian, B.; Rose, M. Franklin (Technical Monitor)

2000-01-01

Oscillating droplets are of interest in a number of disciplines. A practical application is the oscillating drop method, which is a technique for measuring surface tension and viscosity of liquid metals. It is especially suited to undercooled and highly reactive metals, because it is performed by electromagnetic levitation. The natural oscillation frequency of the droplets is related to the surface tension of the material, and the decay of oscillations is related to its viscosity. The fluid flow inside the droplet must be laminar in order for this technique to yield good results. Because no experimental method has yet been developed to visualize flow in electromagnetically-levitated oscillating metal droplets, mathematical modeling is required to determine whether or not turbulence occurs. Three mathematical models of the flow: (1) assuming laminar conditions, (2) using the k-epsilon turbulence model, and (3) using the RNG turbulence model, respectively, are compared and contrasted to determine the physical characteristics of the flow. It is concluded that the RNG model is the best suited for describing this problem. The goal of the presented work was to characterize internal flow in an oscillating droplet of liquid metal, and to verify the accuracy of the characterization by comparing calculated surface tension and viscosity.

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.

A mathematical model for the virus medical imaging technique

NASA Astrophysics Data System (ADS)

Fioranelli, Massimo; Sepehri, Alireza

In this paper, we introduce a mathematical model for the virus medical imaging (VMI). In this method, first, by proposing a mathematical model, we show that there are two types of viruses that each of them produce one type of signal. Some of these signals can be received by males and others by females. Then, we will show that in the VMI technique, viruses can communicate with cells, interior to human’s body via two ways. (1) Viruses can form a wire that passes the skin and reaches to a special cell. (2) Viruses can communicate with viruses interior to body in the wireless form and send some signals for controlling evolutions of cells interior to human’s body.

Discrete mathematical model of wave diffraction on pre-fractal impedance strips. TM mode case

NASA Astrophysics Data System (ADS)

Nesvit, K. V.

2013-10-01

In this paper a transverse magnetic (TM) wave diffraction problem on pre-fractal impedance strips is considered. The overall aim of this work is to develop a discrete mathematical model of the boundary integral equations (IEs) with the help of special quadrature formulas with the nodes in the zeros of Chebyshev polynomials and to perform a numerical experiments with the help of an efficient discrete singularities method (DSM).

Mathematical modeling of processes of heat and mass transfer in channels of water evaporating coolers

NASA Astrophysics Data System (ADS)

Gulevsky, V. A.; Ryazantsev, A. A.; Nikulichev, A. A.; Menzhulova, A. S.

2018-05-01

The variety of cooling systems is dictated by a wide range of demands placed on them. This is the price, operating costs, quality of work, ecological safety, etc. These requirements in a positive sense are put into correspondence by water evaporating plate coolers. Currently, their widespread use is limited by a lack of theoretical base. To solve this problem, the best method is mathematical modeling.

Review Of Applied Mathematical Models For Describing The Behaviour Of Aqueous Humor In Eye Structures

NASA Astrophysics Data System (ADS)

Dzierka, M.; Jurczak, P.

2015-12-01

In the paper, currently used methods for modeling the flow of the aqueous humor through eye structures are presented. Then a computational model based on rheological models of Newtonian and non-Newtonian fluids is proposed. The proposed model may be used for modeling the flow of the aqueous humor through the trabecular meshwork. The trabecular meshwork is modeled as an array of rectilinear parallel capillary tubes. The flow of Newtonian and non-Newtonian fluids is considered. As a results of discussion mathematical equations of permeability of porous media and velocity of fluid flow through porous media have been received.

Identification and agreement of first turn point by mathematical analysis applied to heart rate, carbon dioxide output and electromyography

PubMed Central

Zamunér, Antonio R.; Catai, Aparecida M.; Martins, Luiz E. B.; Sakabe, Daniel I.; Silva, Ester Da

2013-01-01

Background The second heart rate (HR) turn point has been extensively studied, however there are few studies determining the first HR turn point. Also, the use of mathematical and statistical models for determining changes in dynamic characteristics of physiological variables during an incremental cardiopulmonary test has been suggested. Objectives To determine the first turn point by analysis of HR, surface electromyography (sEMG), and carbon dioxide output () using two mathematical models and to compare the results to those of the visual method. Method Ten sedentary middle-aged men (53.9±3.2 years old) were submitted to cardiopulmonary exercise testing on an electromagnetic cycle ergometer until exhaustion. Ventilatory variables, HR, and sEMG of the vastus lateralis were obtained in real time. Three methods were used to determine the first turn point: 1) visual analysis based on loss of parallelism between and oxygen uptake (); 2) the linear-linear model, based on fitting the curves to the set of data (Lin-Lin ); 3) a bi-segmental linear regression of Hinkley' s algorithm applied to HR (HMM-HR), (HMM- ), and sEMG data (HMM-RMS). Results There were no differences between workload, HR, and ventilatory variable values at the first ventilatory turn point as determined by the five studied parameters (p>0.05). The Bland-Altman plot showed an even distribution of the visual analysis method with Lin-Lin , HMM-HR, HMM-CO2, and HMM-RMS. Conclusion The proposed mathematical models were effective in determining the first turn point since they detected the linear pattern change and the deflection point of , HR responses, and sEMG. PMID:24346296

Modeling the Metabolism of Arabidopsis thaliana: Application of Network Decomposition and Network Reduction in the Context of Petri Nets.

PubMed

Koch, Ina; Nöthen, Joachim; Schleiff, Enrico

2017-01-01

Motivation: Arabidopsis thaliana is a well-established model system for the analysis of the basic physiological and metabolic pathways of plants. Nevertheless, the system is not yet fully understood, although many mechanisms are described, and information for many processes exists. However, the combination and interpretation of the large amount of biological data remain a big challenge, not only because data sets for metabolic paths are still incomplete. Moreover, they are often inconsistent, because they are coming from different experiments of various scales, regarding, for example, accuracy and/or significance. Here, theoretical modeling is powerful to formulate hypotheses for pathways and the dynamics of the metabolism, even if the biological data are incomplete. To develop reliable mathematical models they have to be proven for consistency. This is still a challenging task because many verification techniques fail already for middle-sized models. Consequently, new methods, like decomposition methods or reduction approaches, are developed to circumvent this problem. Methods: We present a new semi-quantitative mathematical model of the metabolism of Arabidopsis thaliana . We used the Petri net formalism to express the complex reaction system in a mathematically unique manner. To verify the model for correctness and consistency we applied concepts of network decomposition and network reduction such as transition invariants, common transition pairs, and invariant transition pairs. Results: We formulated the core metabolism of Arabidopsis thaliana based on recent knowledge from literature, including the Calvin cycle, glycolysis and citric acid cycle, glyoxylate cycle, urea cycle, sucrose synthesis, and the starch metabolism. By applying network decomposition and reduction techniques at steady-state conditions, we suggest a straightforward mathematical modeling process. We demonstrate that potential steady-state pathways exist, which provide the fixed carbon to nearly all parts of the network, especially to the citric acid cycle. There is a close cooperation of important metabolic pathways, e.g., the de novo synthesis of uridine-5-monophosphate, the γ-aminobutyric acid shunt, and the urea cycle. The presented approach extends the established methods for a feasible interpretation of biological network models, in particular of large and complex models.

Modeling the Metabolism of Arabidopsis thaliana: Application of Network Decomposition and Network Reduction in the Context of Petri Nets

PubMed Central

Koch, Ina; Nöthen, Joachim; Schleiff, Enrico

2017-01-01

Motivation: Arabidopsis thaliana is a well-established model system for the analysis of the basic physiological and metabolic pathways of plants. Nevertheless, the system is not yet fully understood, although many mechanisms are described, and information for many processes exists. However, the combination and interpretation of the large amount of biological data remain a big challenge, not only because data sets for metabolic paths are still incomplete. Moreover, they are often inconsistent, because they are coming from different experiments of various scales, regarding, for example, accuracy and/or significance. Here, theoretical modeling is powerful to formulate hypotheses for pathways and the dynamics of the metabolism, even if the biological data are incomplete. To develop reliable mathematical models they have to be proven for consistency. This is still a challenging task because many verification techniques fail already for middle-sized models. Consequently, new methods, like decomposition methods or reduction approaches, are developed to circumvent this problem. Methods: We present a new semi-quantitative mathematical model of the metabolism of Arabidopsis thaliana. We used the Petri net formalism to express the complex reaction system in a mathematically unique manner. To verify the model for correctness and consistency we applied concepts of network decomposition and network reduction such as transition invariants, common transition pairs, and invariant transition pairs. Results: We formulated the core metabolism of Arabidopsis thaliana based on recent knowledge from literature, including the Calvin cycle, glycolysis and citric acid cycle, glyoxylate cycle, urea cycle, sucrose synthesis, and the starch metabolism. By applying network decomposition and reduction techniques at steady-state conditions, we suggest a straightforward mathematical modeling process. We demonstrate that potential steady-state pathways exist, which provide the fixed carbon to nearly all parts of the network, especially to the citric acid cycle. There is a close cooperation of important metabolic pathways, e.g., the de novo synthesis of uridine-5-monophosphate, the γ-aminobutyric acid shunt, and the urea cycle. The presented approach extends the established methods for a feasible interpretation of biological network models, in particular of large and complex models. PMID:28713420

Modeling in the quality by design environment: Regulatory requirements and recommendations for design space and control strategy appointment.

PubMed

Djuris, Jelena; Djuric, Zorica

2017-11-30

Mathematical models can be used as an integral part of the quality by design (QbD) concept throughout the product lifecycle for variety of purposes, including appointment of the design space and control strategy, continual improvement and risk assessment. Examples of different mathematical modeling techniques (mechanistic, empirical and hybrid) in the pharmaceutical development and process monitoring or control are provided in the presented review. In the QbD context, mathematical models are predominantly used to support design space and/or control strategies. Considering their impact to the final product quality, models can be divided into the following categories: high, medium and low impact models. Although there are regulatory guidelines on the topic of modeling applications, review of QbD-based submission containing modeling elements revealed concerns regarding the scale-dependency of design spaces and verification of models predictions at commercial scale of manufacturing, especially regarding real-time release (RTR) models. Authors provide critical overview on the good modeling practices and introduce concepts of multiple-unit, adaptive and dynamic design space, multivariate specifications and methods for process uncertainty analysis. RTR specification with mathematical model and different approaches to multivariate statistical process control supporting process analytical technologies are also presented. Copyright © 2017 Elsevier B.V. All rights reserved.

The stability issues in problems of mathematical modeling

NASA Astrophysics Data System (ADS)

Mokin, A. Yu.; Savenkova, N. P.; Udovichenko, N. S.

2018-03-01

In the paper it is briefly considered various aspects of stability concepts, which are used in physics, mathematics and numerical methods of solution. The interrelation between these concepts is described, the questions of preliminary stability research before the numerical solution of the problem and the correctness of the mathematical statement of the physical problem are discussed. Examples of concrete mathematical statements of individual physical problems are given: a nonlocal problem for the heat equation, the Korteweg-de Fries equation with boundary conditions at infinity, the sine-Gordon equation, the problem of propagation of femtosecond light pulses in an area with a cubic nonlinearity.

On the interplay between mathematics and biology: hallmarks toward a new systems biology.

PubMed

Bellomo, Nicola; Elaiw, Ahmed; Althiabi, Abdullah M; Alghamdi, Mohammed Ali

2015-03-01

This paper proposes a critical analysis of the existing literature on mathematical tools developed toward systems biology approaches and, out of this overview, develops a new approach whose main features can be briefly summarized as follows: derivation of mathematical structures suitable to capture the complexity of biological, hence living, systems, modeling, by appropriate mathematical tools, Darwinian type dynamics, namely mutations followed by selection and evolution. Moreover, multiscale methods to move from genes to cells, and from cells to tissue are analyzed in view of a new systems biology approach. Copyright © 2014 Elsevier B.V. All rights reserved.

IDEF3 Formalization Report

DTIC Science & Technology

1991-10-01

SUBJECT TERMS 15. NUMBER OF PAGES engineering management information systems method formalization 60 information engineering process modeling 16 PRICE...CODE information systems requirements definition methods knowlede acquisition methods systems engineering 17. SECURITY CLASSIFICATION ji. SECURITY... Management , Inc., Santa Monica, California. CORYNEN, G. C., 1975, A Mathematical Theory of Modeling and Simula- tion. Ph.D. Dissertation, Department

Teacher Support, Instructional Practices, Student Motivation, and Mathematics Achievement in High School

ERIC Educational Resources Information Center

Yu, Rongrong; Singh, Kusum

2018-01-01

The authors examined the relationships among teacher classroom practices, student motivation, and mathematics achievement in high school. The data for this study was drawn from the base-year data of High School Longitudinal Study of 2009. Structural equation modeling method was used to estimate the relationships among variables. The results…

Student and School Factors Affecting Mathematics Achievement: International Comparisons between Korea, Japan and the USA

ERIC Educational Resources Information Center

Shin, Jongho; Lee, Hyunjoo; Kim, Yongnam

2009-01-01

The purpose of the study was to comparatively investigate student- and school-level factors affecting mathematics achievement of Korean, Japanese and American students. For international comparisons, the PISA 2003 data were analysed by using the Hierarchical Linear Modeling method. The variables of competitive-learning preference, instrumental…

Hispanic students' mathematics achievement in the context of their high school types as STEM and non-STEM schools

NASA Astrophysics Data System (ADS)

Bicer, Ali; Capraro, Robert M.; Capraro, Mary M.

2018-07-01

The purpose of this paper is to demonstrate Hispanic students' mathematics achievement growth rate in Inclusive science, technology, engineering, and mathematics (STEM) high schools compared to Hispanic students' mathematics achievement growth rate in traditional public schools. Twenty-eight schools, 14 of which were Texas STEM (T-STEM) academies and 14 of which were matched non-STEM schools, were included in this study. A hierarchical linear modelling method was conducted. The result of the present study revealed that there was no difference in Hispanic students' mathematics achievement growth rate in T-STEM academies compared to Hispanic students' mathematics achievement growth rate in comparison schools. However, in terms of gender, the results indicated that female Hispanic students in T-STEM academies outperformed female Hispanic students in comparison schools in their mathematics growth rate.

PASMet: a web-based platform for prediction, modelling and analyses of metabolic systems

PubMed Central

Sriyudthsak, Kansuporn; Mejia, Ramon Francisco; Arita, Masanori; Hirai, Masami Yokota

2016-01-01

PASMet (Prediction, Analysis and Simulation of Metabolic networks) is a web-based platform for proposing and verifying mathematical models to understand the dynamics of metabolism. The advantages of PASMet include user-friendliness and accessibility, which enable biologists and biochemists to easily perform mathematical modelling. PASMet offers a series of user-functions to handle the time-series data of metabolite concentrations. The functions are organised into four steps: (i) Prediction of a probable metabolic pathway and its regulation; (ii) Construction of mathematical models; (iii) Simulation of metabolic behaviours; and (iv) Analysis of metabolic system characteristics. Each function contains various statistical and mathematical methods that can be used independently. Users who may not have enough knowledge of computing or programming can easily and quickly analyse their local data without software downloads, updates or installations. Users only need to upload their files in comma-separated values (CSV) format or enter their model equations directly into the website. Once the time-series data or mathematical equations are uploaded, PASMet automatically performs computation on server-side. Then, users can interactively view their results and directly download them to their local computers. PASMet is freely available with no login requirement at http://pasmet.riken.jp/ from major web browsers on Windows, Mac and Linux operating systems. PMID:27174940

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.

A new process sensitivity index to identify important system processes under process model and parametric uncertainty

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

Dai, Heng; Ye, Ming; Walker, Anthony P.

Hydrological models are always composed of multiple components that represent processes key to intended model applications. When a process can be simulated by multiple conceptual-mathematical models (process models), model uncertainty in representing the process arises. While global sensitivity analysis methods have been widely used for identifying important processes in hydrologic modeling, the existing methods consider only parametric uncertainty but ignore the model uncertainty for process representation. To address this problem, this study develops a new method to probe multimodel process sensitivity by integrating the model averaging methods into the framework of variance-based global sensitivity analysis, given that the model averagingmore » methods quantify both parametric and model uncertainty. A new process sensitivity index is derived as a metric of relative process importance, and the index includes variance in model outputs caused by uncertainty in both process models and model parameters. For demonstration, the new index is used to evaluate the processes of recharge and geology in a synthetic study of groundwater reactive transport modeling. The recharge process is simulated by two models that converting precipitation to recharge, and the geology process is also simulated by two models of different parameterizations of hydraulic conductivity; each process model has its own random parameters. The new process sensitivity index is mathematically general, and can be applied to a wide range of problems in hydrology and beyond.« less

Stochastic growth logistic model with aftereffect for batch fermentation process

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

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah

2014-06-19

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Stochastic growth logistic model with aftereffect for batch fermentation process

NASA Astrophysics Data System (ADS)

Rosli, Norhayati; Ayoubi, Tawfiqullah; Bahar, Arifah; Rahman, Haliza Abdul; Salleh, Madihah Md

2014-06-01

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

Method of performing computational aeroelastic analyses

NASA Technical Reports Server (NTRS)

Silva, Walter A. (Inventor)

2011-01-01

Computational aeroelastic analyses typically use a mathematical model for the structural modes of a flexible structure and a nonlinear aerodynamic model that can generate a plurality of unsteady aerodynamic responses based on the structural modes for conditions defining an aerodynamic condition of the flexible structure. In the present invention, a linear state-space model is generated using a single execution of the nonlinear aerodynamic model for all of the structural modes where a family of orthogonal functions is used as the inputs. Then, static and dynamic aeroelastic solutions are generated using computational interaction between the mathematical model and the linear state-space model for a plurality of periodic points in time.

Use of mathematic modeling to compare and predict hemodynamic effects of the modified Blalock-Taussig and right ventricle-pulmonary artery shunts for hypoplastic left heart syndrome.

PubMed

Bove, Edward L; Migliavacca, Francesco; de Leval, Marc R; Balossino, Rossella; Pennati, Giancarlo; Lloyd, Thomas R; Khambadkone, Sachin; Hsia, Tain-Yen; Dubini, Gabriele

2008-08-01

Stage one reconstruction (Norwood operation) for hypoplastic left heart syndrome can be performed with either a modified Blalock-Taussig shunt or a right ventricle-pulmonary artery shunt. Both methods have certain inherent characteristics. It is postulated that mathematic modeling could help elucidate these differences. Three-dimensional computer models of the Blalock-Taussig shunt and right ventricle-pulmonary artery shunt modifications of the Norwood operation were developed by using the finite volume method. Conduits of 3, 3.5, and 4 mm were used in the Blalock-Taussig shunt model, whereas conduits of 4, 5, and 6 mm were used in the right ventricle-pulmonary artery shunt model. The hydraulic nets (lumped resistances, compliances, inertances, and elastances) were identical in the 2 models. A multiscale approach was adopted to couple the 3-dimensional models with the circulation net. Computer simulations were compared with postoperative catheterization data. Good correlation was found between predicted and observed data. For the right ventricle-pulmonary artery shunt modification, there was higher aortic diastolic pressure, decreased pulmonary artery pressure, lower Qp/Qs ratio, and higher coronary perfusion pressure. Mathematic modeling predicted minimal regurgitant flow in the right ventricle-pulmonary artery shunt model, which correlated with postoperative Doppler measurements. The right ventricle-pulmonary artery shunt demonstrated lower stroke work and a higher mechanical efficiency (stroke work/total mechanical energy). The close correlation between predicted and observed data supports the use of mathematic modeling in the design and assessment of surgical procedures. The potentially damaging effects of a systemic ventriculotomy in the right ventricle-pulmonary artery shunt modification of the Norwood operation have not been analyzed.

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.

Nonlinear-programming mathematical modeling of coal blending for power plant

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

Tang Longhua; Zhou Junhu; Yao Qiang

At present most of the blending works are guided by experience or linear-programming (LP) which can not reflect the coal complicated characteristics properly. Experimental and theoretical research work shows that most of the coal blend properties can not always be measured as a linear function of the properties of the individual coals in the blend. The authors introduced nonlinear functions or processes (including neural network and fuzzy mathematics), established on the experiments directed by the authors and other researchers, to quantitatively describe the complex coal blend parameters. Finally nonlinear-programming (NLP) mathematical modeling of coal blend is introduced and utilized inmore » the Hangzhou Coal Blending Center. Predictions based on the new method resulted in different results from the ones based on LP modeling. The authors concludes that it is very important to introduce NLP modeling, instead of NL modeling, into the work of coal blending.« less

Physical and mathematical modeling of antimicrobial photodynamic therapy

NASA Astrophysics Data System (ADS)

Bürgermeister, Lisa; López, Fernando Romero; Schulz, Wolfgang

2014-07-01

Antimicrobial photodynamic therapy (aPDT) is a promising method to treat local bacterial infections. The therapy is painless and does not cause bacterial resistances. However, there are gaps in understanding the dynamics of the processes, especially in periodontal treatment. This work describes the advances in fundamental physical and mathematical modeling of aPDT used for interpretation of experimental evidence. The result is a two-dimensional model of aPDT in a dental pocket phantom model. In this model, the propagation of laser light and the kinetics of the chemical reactions are described as coupled processes. The laser light induces the chemical processes depending on its intensity. As a consequence of the chemical processes, the local optical properties and distribution of laser light change as well as the reaction rates. The mathematical description of these coupled processes will help to develop treatment protocols and is the first step toward an inline feedback system for aPDT users.

Approaching mathematical model of the immune network based DNA Strand Displacement system.

PubMed

Mardian, Rizki; Sekiyama, Kosuke; Fukuda, Toshio

2013-12-01

One biggest obstacle in molecular programming is that there is still no direct method to compile any existed mathematical model into biochemical reaction in order to solve a computational problem. In this paper, the implementation of DNA Strand Displacement system based on nature-inspired computation is observed. By using the Immune Network Theory and Chemical Reaction Network, the compilation of DNA-based operation is defined and the formulation of its mathematical model is derived. Furthermore, the implementation on this system is compared with the conventional implementation by using silicon-based programming. From the obtained results, we can see a positive correlation between both. One possible application from this DNA-based model is for a decision making scheme of intelligent computer or molecular robot. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Design, processing and testing of LSI arrays: Hybrid microelectronics task

NASA Technical Reports Server (NTRS)

Himmel, R. P.; Stuhlbarg, S. M.; Ravetti, R. G.; Zulueta, P. J.

1979-01-01

Mathematical cost factors were generated for both hybrid microcircuit and printed wiring board packaging methods. A mathematical cost model was created for analysis of microcircuit fabrication costs. The costing factors were refined and reduced to formulae for computerization. Efficient methods were investigated for low cost packaging of LSI devices as a function of density and reliability. Technical problem areas such as wafer bumping, inner/outer leading bonding, testing on tape, and tape processing, were investigated.

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

Using Computational and Mechanical Models to Study Animal Locomotion

PubMed Central

Miller, Laura A.; Goldman, Daniel I.; Hedrick, Tyson L.; Tytell, Eric D.; Wang, Z. Jane; Yen, Jeannette; Alben, Silas

2012-01-01

Recent advances in computational methods have made realistic large-scale simulations of animal locomotion possible. This has resulted in numerous mathematical and computational studies of animal movement through fluids and over substrates with the purpose of better understanding organisms’ performance and improving the design of vehicles moving through air and water and on land. This work has also motivated the development of improved numerical methods and modeling techniques for animal locomotion that is characterized by the interactions of fluids, substrates, and structures. Despite the large body of recent work in this area, the application of mathematical and numerical methods to improve our understanding of organisms in the context of their environment and physiology has remained relatively unexplored. Nature has evolved a wide variety of fascinating mechanisms of locomotion that exploit the properties of complex materials and fluids, but only recently are the mathematical, computational, and robotic tools available to rigorously compare the relative advantages and disadvantages of different methods of locomotion in variable environments. Similarly, advances in computational physiology have only recently allowed investigators to explore how changes at the molecular, cellular, and tissue levels might lead to changes in performance at the organismal level. In this article, we highlight recent examples of how computational, mathematical, and experimental tools can be combined to ultimately answer the questions posed in one of the grand challenges in organismal biology: “Integrating living and physical systems.” PMID:22988026

Mathematical modeling of photovoltaic thermal PV/T system with v-groove collector

NASA Astrophysics Data System (ADS)

Zohri, M.; Fudholi, A.; Ruslan, M. H.; Sopian, K.

2017-07-01

The use of v-groove in solar collector has a higher thermal efficiency in references. Dropping the working heat of photovoltaic panel was able to raise the electrical efficiency performance. Electrical and thermal efficiency were produced by photovoltaic thermal (PV/T) system concurrently. Mathematical modeling based on steady-state thermal analysis of PV/T system with v-groove was conducted. With matrix inversion method, the energy balance equations are explained by means of the investigative method. The comparison results show that in the PV/T system with the V-groove collector is higher temperature, thermal and electrical efficiency than other collectors.

[METHODS OF MATHEMATICAL MODELING IN MORPHOLOGICAL DIAGNOSTICS OF CHORNOBYL FACTOR INFLUENCE ON PROSTATE GLAND OF COAL MINERS-- THE CHERNOBYL DISASTER FIGHTERS].

PubMed

Danylov, Iu V; Motkov, K V; Shevchenko, T I

2014-01-01

The morphometric estimation of parenchyma and stroma condition included the determination of 25 parameters in a prostate gland at 27 persons. The mathematical model of morphogenesis of prostate gland was created by Bayes' method. The method of differential diagnosis of a prostate gland tissues' changes conditioned by the influence of the Chernobyl factor and/or unfavorable terms of the work in underground coal mines have been worked out. Its practical use provides exactness and reliability of the diagnosis (not less than 95%), independence from the level of the qualification and personal experience of the doctor, allows us to unify, optimize and individualize the diagnostic algorithms, answer the requirements of evidential medicine.

[Methods of mathematical modeling in morphological diagnostics of Chernobyl factor influence on the testes of coal miners of Donbas--the Chernobyl disaster fighters].

PubMed

Danylov, Iu V; Motkov, K V; Shevchenko, T I

2014-01-01

The morphometric estimation of parenchyma and stroma condition included the determination of 29 parameters in testicles at 27 persons. The mathematical model of morphogenesis of testicles was created by Bayes' method. The method of differential diagnosis of testicles tissues' changes conditioned by the influence of the Chernobyl factor and/or unfavorable terms of the work in underground coal mines have been worked out. Its practical use provides exactness and reliability of the diagnosis (not less than 95%), independence from the level of the qualification and personal experience of the doctor, allows us to unify, optimize and individualize the diagnostic algorithms, answer the requirements of evidential medicine.

Surveillance theory applied to virus detection: a case for targeted discovery

USGS Publications Warehouse

Bogich, Tiffany L.; Anthony, Simon J.; Nichols, James D.

2013-01-01

Virus detection and mathematical modeling have gone through rapid developments in the past decade. Both offer new insights into the epidemiology of infectious disease and characterization of future risk; however, modeling has not yet been applied to designing the best surveillance strategies for viral and pathogen discovery. We review recent developments and propose methods to integrate viral and pathogen discovery and mathematical modeling through optimal surveillance theory, arguing for a more targeted approach to novel virus detection guided by the principles of adaptive management and structured decision-making.

Methods of mathematical modeling using polynomials of algebra of sets

NASA Astrophysics Data System (ADS)

Kazanskiy, Alexandr; Kochetkov, Ivan

2018-03-01

The article deals with the construction of discrete mathematical models for solving applied problems arising from the operation of building structures. Security issues in modern high-rise buildings are extremely serious and relevant, and there is no doubt that interest in them will only increase. The territory of the building is divided into zones for which it is necessary to observe. Zones can overlap and have different priorities. Such situations can be described using formulas algebra of sets. Formulas can be programmed, which makes it possible to work with them using computer models.

Determination of thermophysical characteristics of vulcanizable rubber products by the mathematical modeling method

NASA Astrophysics Data System (ADS)

Tikhomirov, S. G.; Pyatakov, Y. V.; Karmanova, O. V.; Maslov, A. A.

2018-03-01

The studies of the vulcanization kinetics of elastomers were carried out using a Truck tyre tread rubber compound. The formal kinetic scheme of vulcanization of rubbers sulfur-accelerator curing system was used which generalizes the set of reactions occurring in the curing process. A mathematical model is developed for determining the thermal parameters vulcanizable mixture comprising algorithms for solving direct and inverse problems for system of equations of heat conduction and kinetics of the curing process. The performance of the model is confirmed by the results of numerical experiments on model examples.

Hierarchical analytical and simulation modelling of human-machine systems with interference

NASA Astrophysics Data System (ADS)

Braginsky, M. Ya; Tarakanov, D. V.; Tsapko, S. G.; Tsapko, I. V.; Baglaeva, E. A.

2017-01-01

The article considers the principles of building the analytical and simulation model of the human operator and the industrial control system hardware and software. E-networks as the extension of Petri nets are used as the mathematical apparatus. This approach allows simulating complex parallel distributed processes in human-machine systems. The structural and hierarchical approach is used as the building method for the mathematical model of the human operator. The upper level of the human operator is represented by the logical dynamic model of decision making based on E-networks. The lower level reflects psychophysiological characteristics of the human-operator.

Multiscale Mathematics for Nano-Particle-Endowed Active Membranes and Films

DTIC Science & Technology

2016-08-03

Formation in Biofilms ,” Contemporary Mathematics (586), 2013, 105-116. 2. Yi Sun and Qi Wang, “Modeling and Simulations of Multicellular Aggregate Self...6402. 21. Hua Jiang, Hao Yang, Jun Zeng, Zhiyuan Zhou, Jin Peng, Qi Wang, Analytic Oncology, Electron J Metab Nutr Cancer ，Jun. 2015，Vol. 2， No. 2, 26...30. 22. Chen Chen, Dacheng Ren, Mingming Ren and Qi Wang, “3-D Spatial-Temporal Structures of Biofilms in A Water Channel,” Mathematical Methods

Formal verification of mathematical software

NASA Technical Reports Server (NTRS)

Sutherland, D.

1984-01-01

Methods are investigated for formally specifying and verifying the correctness of mathematical software (software which uses floating point numbers and arithmetic). Previous work in the field was reviewed. A new model of floating point arithmetic called the asymptotic paradigm was developed and formalized. Two different conceptual approaches to program verification, the classical Verification Condition approach and the more recently developed Programming Logic approach, were adapted to use the asymptotic paradigm. These approaches were then used to verify several programs; the programs chosen were simplified versions of actual mathematical software.

School Improvement Model to Foster Student Learning

ERIC Educational Resources Information Center

Rulloda, Rudolfo Barcena

2011-01-01

Many classroom teachers are still using the traditional teaching methods. The traditional teaching methods are one-way learning process, where teachers would introduce subject contents such as language arts, English, mathematics, science, and reading separately. However, the school improvement model takes into account that all students have…

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.

TIMSS 2011 Student and Teacher Predictors for Mathematics Achievement Explored and Identified via Elastic Net.

PubMed

Yoo, Jin Eun

2018-01-01

A substantial body of research has been conducted on variables relating to students' mathematics achievement with TIMSS. However, most studies have employed conventional statistical methods, and have focused on selected few indicators instead of utilizing hundreds of variables TIMSS provides. This study aimed to find a prediction model for students' mathematics achievement using as many TIMSS student and teacher variables as possible. Elastic net, the selected machine learning technique in this study, takes advantage of both LASSO and ridge in terms of variable selection and multicollinearity, respectively. A logistic regression model was also employed to predict TIMSS 2011 Korean 4th graders' mathematics achievement. Ten-fold cross-validation with mean squared error was employed to determine the elastic net regularization parameter. Among 162 TIMSS variables explored, 12 student and 5 teacher variables were selected in the elastic net model, and the prediction accuracy, sensitivity, and specificity were 76.06, 70.23, and 80.34%, respectively. This study showed that the elastic net method can be successfully applied to educational large-scale data by selecting a subset of variables with reasonable prediction accuracy and finding new variables to predict students' mathematics achievement. Newly found variables via machine learning can shed light on the existing theories from a totally different perspective, which in turn propagates creation of a new theory or complement of existing ones. This study also examined the current scale development convention from a machine learning perspective.

TIMSS 2011 Student and Teacher Predictors for Mathematics Achievement Explored and Identified via Elastic Net

PubMed Central

Yoo, Jin Eun

2018-01-01

A substantial body of research has been conducted on variables relating to students' mathematics achievement with TIMSS. However, most studies have employed conventional statistical methods, and have focused on selected few indicators instead of utilizing hundreds of variables TIMSS provides. This study aimed to find a prediction model for students' mathematics achievement using as many TIMSS student and teacher variables as possible. Elastic net, the selected machine learning technique in this study, takes advantage of both LASSO and ridge in terms of variable selection and multicollinearity, respectively. A logistic regression model was also employed to predict TIMSS 2011 Korean 4th graders' mathematics achievement. Ten-fold cross-validation with mean squared error was employed to determine the elastic net regularization parameter. Among 162 TIMSS variables explored, 12 student and 5 teacher variables were selected in the elastic net model, and the prediction accuracy, sensitivity, and specificity were 76.06, 70.23, and 80.34%, respectively. This study showed that the elastic net method can be successfully applied to educational large-scale data by selecting a subset of variables with reasonable prediction accuracy and finding new variables to predict students' mathematics achievement. Newly found variables via machine learning can shed light on the existing theories from a totally different perspective, which in turn propagates creation of a new theory or complement of existing ones. This study also examined the current scale development convention from a machine learning perspective. PMID:29599736

Coastal Modeling System: Mathematical Formulations and Numerical Methods

DTIC Science & Technology

2014-03-01

sediment transport , and morphology change. The CMS was designed and developed for coastal inlets and navigation applications, including channel...numerical methods of hydrodynamic, salinity and sediment transport , and morphology change model CMS-Flow. The CMS- Flow uses the Finite Volume...and the influence of coastal structures. The implicit hydrodynamic model is coupled to a nonequilibrium transport model of multiple-sized total

Modeling of polymer networks for application to solid propellant formulating

NASA Technical Reports Server (NTRS)

Marsh, H. E.

1979-01-01

Methods for predicting the network structural characteristics formed by the curing of pourable elastomers were presented; as well as the logic which was applied in the development of mathematical models. A universal approach for modeling was developed and verified by comparison with other methods in application to a complex system. Several applications of network models to practical problems are described.

Blooms' separation of the final exam of Engineering Mathematics II: Item reliability using Rasch measurement model

NASA Astrophysics Data System (ADS)

Fuaad, Norain Farhana Ahmad; Nopiah, Zulkifli Mohd; Tawil, Norgainy Mohd; Othman, Haliza; Asshaari, Izamarlina; Osman, Mohd Hanif; Ismail, Nur Arzilah

2014-06-01

In engineering studies and researches, Mathematics is one of the main elements which express physical, chemical and engineering laws. Therefore, it is essential for engineering students to have a strong knowledge in the fundamental of mathematics in order to apply the knowledge to real life issues. However, based on the previous results of Mathematics Pre-Test, it shows that the engineering students lack the fundamental knowledge in certain topics in mathematics. Due to this, apart from making improvements in the methods of teaching and learning, studies on the construction of questions (items) should also be emphasized. The purpose of this study is to assist lecturers in the process of item development and to monitor the separation of items based on Blooms' Taxonomy and to measure the reliability of the items itself usingRasch Measurement Model as a tool. By using Rasch Measurement Model, the final exam questions of Engineering Mathematics II (Linear Algebra) for semester 2 sessions 2012/2013 were analysed and the results will provide the details onthe extent to which the content of the item providesuseful information about students' ability. This study reveals that the items used in Engineering Mathematics II (Linear Algebra) final exam are well constructed but the separation of the items raises concern as it is argued that it needs further attention, as there is abig gap between items at several levels of Blooms' cognitive skill.

Modeling of Geometric Error in Linear Guide Way to Improved the vertical three-axis CNC Milling machine’s accuracy

NASA Astrophysics Data System (ADS)

Kwintarini, Widiyanti; Wibowo, Agung; Arthaya, Bagus M.; Yuwana Martawirya, Yatna

2018-03-01

The purpose of this study was to improve the accuracy of three-axis CNC Milling Vertical engines with a general approach by using mathematical modeling methods of machine tool geometric errors. The inaccuracy of CNC machines can be caused by geometric errors that are an important factor during the manufacturing process and during the assembly phase, and are factors for being able to build machines with high-accuracy. To improve the accuracy of the three-axis vertical milling machine, by knowing geometric errors and identifying the error position parameters in the machine tool by arranging the mathematical modeling. The geometric error in the machine tool consists of twenty-one error parameters consisting of nine linear error parameters, nine angle error parameters and three perpendicular error parameters. The mathematical modeling approach of geometric error with the calculated alignment error and angle error in the supporting components of the machine motion is linear guide way and linear motion. The purpose of using this mathematical modeling approach is the identification of geometric errors that can be helpful as reference during the design, assembly and maintenance stages to improve the accuracy of CNC machines. Mathematically modeling geometric errors in CNC machine tools can illustrate the relationship between alignment error, position and angle on a linear guide way of three-axis vertical milling machines.

Mathematical methods for protein science

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

Hart, W.; Istrail, S.; Atkins, J.

1997-12-31

Understanding the structure and function of proteins is a fundamental endeavor in molecular biology. Currently, over 100,000 protein sequences have been determined by experimental methods. The three dimensional structure of the protein determines its function, but there are currently less than 4,000 structures known to atomic resolution. Accordingly, techniques to predict protein structure from sequence have an important role in aiding the understanding of the Genome and the effects of mutations in genetic disease. The authors describe current efforts at Sandia to better understand the structure of proteins through rigorous mathematical analyses of simple lattice models. The efforts have focusedmore » on two aspects of protein science: mathematical structure prediction, and inverse protein folding.« less

The effect of team accelerated instruction on students’ mathematics achievement and learning motivation

NASA Astrophysics Data System (ADS)

Sri Purnami, Agustina; Adi Widodo, Sri; Charitas Indra Prahmana, Rully

2018-01-01

This study aimed to know the improvement of achievement and motivation of learning mathematics by using Team Accelerated Instruction. The research method used was the experiment with descriptive pre-test post-test experiment. The population in this study was all students of class VIII junior high school in Jogjakarta. The sample was taken using cluster random sampling technique. The instrument used in this research was questionnaire and test. Data analysis technique used was Wilcoxon test. It concluded that there was an increase in motivation and student achievement of class VII on linear equation system material by using the learning model of Team Accelerated Instruction. Based on the results of the learning model Team Accelerated Instruction can be used as a variation model in learning mathematics.

A Cognitive Analysis of Students’ Mathematical Communication Ability on Geometry

NASA Astrophysics Data System (ADS)

Sari, D. S.; Kusnandi, K.; Suhendra, S.

2017-09-01

This study aims to analyze the difficulties of mathematical communication ability of students in one of secondary school on “three-dimensional space” topic. This research conducted by using quantitative approach with descriptive method. The population in this research was all students of that school and the sample was thirty students that was chosen by purposive sampling technique. Data of mathematical communication were collected through essay test. Furthermore, the data were analyzed with a descriptive way. The results of this study indicate that the percentage of achievement of student mathematical communication indicators as follows 1) Stating a situation, ideas, and mathematic correlation into images, graphics, or algebraic expressions is 35%; 2) Stating daily experience into a mathematic language / symbol, or a mathematic model is 35%; and 3) Associating images or diagrams into mathematical ideas is 53.3%. Based on the percentage of achievement on each indicator, it can be concluded that the level of achievement of students’ mathematical communication ability is still low. It can be caused the students were not used to convey or write their mathematical ideas systematically. Therefore students’ mathematical communication ability need to be improved.

The Objective Borderline Method: A Probabilistic Method for Standard Setting

ERIC Educational Resources Information Center

Shulruf, Boaz; Poole, Phillippa; Jones, Philip; Wilkinson, Tim

2015-01-01

A new probability-based standard setting technique, the Objective Borderline Method (OBM), was introduced recently. This was based on a mathematical model of how test scores relate to student ability. The present study refined the model and tested it using 2500 simulated data-sets. The OBM was feasible to use. On average, the OBM performed well…

Wave processes in the human cardiovascular system: The measuring complex, computing models, and diagnostic analysis

NASA Astrophysics Data System (ADS)

Ganiev, R. F.; Reviznikov, D. L.; Rogoza, A. N.; Slastushenskiy, Yu. V.; Ukrainskiy, L. E.

2017-03-01

A description of a complex approach to investigation of nonlinear wave processes in the human cardiovascular system based on a combination of high-precision methods of measuring a pulse wave, mathematical methods of processing the empirical data, and methods of direct numerical modeling of hemodynamic processes in an arterial tree is given.

A mathematical modeling method for determination of local vibroacoustic characteristics of structures

NASA Technical Reports Server (NTRS)

Tartakovskiy, B. D.; Dubner, A. B.

1973-01-01

A method is proposed for determining vibroacoustic characteristics from the results of measurements of the distribution of vibrational energy in a structure. The method is based on an energy model of a structure studied earlier. Equations are written to describe the distribution of vibrational energy in a hypothetical diffuse energy state in structural elements.

Emulation of rocket trajectory based on a six degree of freedom model

NASA Astrophysics Data System (ADS)

Zhang, Wenpeng; Li, Fan; Wu, Zhong; Li, Rong

2008-10-01

In this paper, a 6-DOF motion mathematical model is discussed. It is consisted of body dynamics and kinematics block, aero dynamics block and atmosphere block. Based on Simulink, the whole rocket trajectory mathematical model is developed. In this model, dynamic system simulation becomes easy and visual. The method of modularization design gives more convenience to transplant. At last, relevant data is given to be validated by Monte Carlo means. Simulation results show that the flight trajectory of the rocket can be simulated preferably by means of this model, and it also supplies a necessary simulating tool for the development of control system.

Comparison among mathematical models of the photovoltaic cell for computer simulation purposes

NASA Astrophysics Data System (ADS)

Tofoli, Fernando Lessa; Pereira, Denis de Castro; Josias De Paula, Wesley; Moreira Vicente, Eduardo; Vicente, Paula dos Santos; Braga, Henrique Antonio Carvalho

2017-07-01

This paper presents a comparison among mathematical models used in the simulation of solar photovoltaic modules that can be easily integrated with power electronic converters. In order to perform the analysis, three models available in literature and also the physical model of the module in software PSIM® are used. Some results regarding the respective I × V and P × V curves are presented, while some advantages and eventual limitations are discussed. Besides, a DC-DC buck converter performs maximum power point tracking by using perturb and observe method, while the performance of each one of the aforementioned models is investigated.

Feasibility study for automatic reduction of phase change imagery

NASA Technical Reports Server (NTRS)

Nossaman, G. O.

1971-01-01

The feasibility of automatically reducing a form of pictorial aerodynamic heating data is discussed. The imagery, depicting the melting history of a thin coat of fusible temperature indicator painted on an aerodynamically heated model, was previously reduced by manual methods. Careful examination of various lighting theories and approaches led to an experimentally verified illumination concept capable of yielding high-quality imagery. Both digital and video image processing techniques were applied to reduction of the data, and it was demonstrated that either method can be used to develop superimposed contours. Mathematical techniques were developed to find the model-to-image and the inverse image-to-model transformation using six conjugate points, and methods were developed using these transformations to determine heating rates on the model surface. A video system was designed which is able to reduce the imagery rapidly, economically and accurately. Costs for this system were estimated. A study plan was outlined whereby the mathematical transformation techniques developed to produce model coordinate heating data could be applied to operational software, and methods were discussed and costs estimated for obtaining the digital information necessary for this software.

Construction of a model demonstrating neural pathways and reflex arcs.

PubMed

Chan, V; Pisegna, J M; Rosian, R L; DiCarlo, S E

1996-12-01

Employment opportunities in the future will require higher skills and an understanding of mathematics and science. As a result of the growing number of careers that require solid science and mathematics training, the methods of science education are undergoing major reform. To adequately equip students for technologically advanced positions, new teaching methods must be developed that prepare tomorrow's workforce for the challenges of the 21st century. One such method is the use of models. By actively building and manipulating concrete models that represent scientific concepts, students are involved in the most basic level of Piaget's learning scheme: the sensorimotor stage. Models are useful in reaching all students at the foundational levels of learning, and further learning experiences are rapidly moved through higher learning levels. This success ensures greater comprehension and understanding compared with the traditional methods of rote memorization. We developed an exercise for the construction of an inexpensive, easy-to-build model demonstrating neural pathways and reflex arcs. Our exercise also includes many supplemental teaching tools. The exercise is designed to fulfill the need of sound physiological teaching materials for high school students.

Chronology of DIC technique based on the fundamental mathematical modeling and dehydration impact.

PubMed

Alias, Norma; Saipol, Hafizah Farhah Saipan; Ghani, Asnida Che Abd

2014-12-01

A chronology of mathematical models for heat and mass transfer equation is proposed for the prediction of moisture and temperature behavior during drying using DIC (Détente Instantanée Contrôlée) or instant controlled pressure drop technique. DIC technique has the potential as most commonly used dehydration method for high impact food value including the nutrition maintenance and the best possible quality for food storage. The model is governed by the regression model, followed by 2D Fick's and Fourier's parabolic equation and 2D elliptic-parabolic equation in a rectangular slice. The models neglect the effect of shrinkage and radiation effects. The simulations of heat and mass transfer equations with parabolic and elliptic-parabolic types through some numerical methods based on finite difference method (FDM) have been illustrated. Intel®Core™2Duo processors with Linux operating system and C programming language have been considered as a computational platform for the simulation. Qualitative and quantitative differences between DIC technique and the conventional drying methods have been shown as a comparative.

Improving Mathematics Achievement of Indonesian 5th Grade Students through Guided Discovery Learning

ERIC Educational Resources Information Center

Yurniwati; Hanum, Latipa

2017-01-01

This research aims to find information about the improvement of mathematics achievement of grade five student through guided discovery learning. This research method is classroom action research using Kemmis and Taggart model consists of three cycles. Data used in this study is learning process and learning results. Learning process data is…

Covariation between Variables in a Modelling Process: The ACODESA (Collaborative Learning, Scientific Debate and Self-Reflection) Method

ERIC Educational Resources Information Center

Hitt, Fernando; González-Martín, Alejandro S.

2015-01-01

Semiotic representations have been an important topic of study in mathematics education. Previous research implicitly placed more importance on the development of institutional representations of mathematical concepts in students rather than other types of representations. In the context of an extensive research project, in progress since 2005,…

Mathematical modeling and Monte Carlo simulation of thermal inactivation of non-proteolytic Clostridium botulinum spores during continuous microwave-assisted pasteurization

USDA-ARS?s Scientific Manuscript database

The objective of this study is to develop a mathematical method to simulate the internal temperature history of products processed in a prototype microwave-assisted pasteurization system (MAPS) developed by Washington State University. Two products (10 oz. beef meatball trays and 16 oz. salmon fill...

The Effect of an Experiential Learning Program on Middle School Students' Motivation toward Mathematics and Science

ERIC Educational Resources Information Center

Weinberg, Andrea E.; Basile, Carole G.; Albright, Leonard

2011-01-01

A mixed methods design was used to evaluate the effects of four experiential learning programs on the interest and motivation of middle school students toward mathematics and science. The Expectancy-Value model provided a theoretical framework for the exploration of 336 middle school student participants. Initially, participants were generally…

Gamification for Non-Majors Mathematics: An Innovative Assignment Model

ERIC Educational Resources Information Center

Leong, Siow Hoo; Tang, Howe Eng

2017-01-01

The most important ingredient of the pedagogy for teaching non-majors is getting their engagement. This paper proposes to use gamification to engage non-majors. An innovative game termed as Cover the Hungarian's Zeros is designed to tackle the common weakness of non-majors mathematics in solving the assignment problem using the Hungarian Method.…

Contribution of Auditory Learning Style to Students’ Mathematical Connection Ability

NASA Astrophysics Data System (ADS)

Karlimah; Risfiani, F.

2017-09-01

This paper presents the results of the research on the relation of mathematical concept with mathematics, other subjects, and with everyday life. This research reveals study result of the students who had auditory learning style and correlates it with their ability of mathematical connection. In this research, the researchers used a combination model or sequential exploratory design method, which is the use of qualitative and quantitative research methods in sequence. The result proves that giving learning facilities which are not suitable for the class whose students have the auditory learning style results in the barely sufficient math connection ability. The average mathematical connection ability of the auditory students was initially in the medium level of qualification. Then, the improvement in the form of the varied learning that suited the auditory learning style still showed the average ability of mathematical connection in medium level of qualification. Nevertheless, there was increase in the frequency of students in the medium level of qualification and decrease in the very low and low level of qualification. This suggests that the learning facilities, which are appropriate for the student’s auditory learning style, contribute well enough to the students’ mathematical connection ability. Therefore, the mathematics learning for students who have an auditory learning style should consist of particular activity that is understanding the concepts of mathematics and their relations.

An Examination of Reading and Mathematic Achievement among Second Grade Students Who Have Received Instruction from Either Teachers Who Have Been Trained in Choice Theory/Reality Therapy Methods or Teachers Who Have Not Been Trained

ERIC Educational Resources Information Center

Hale, Jane V.

2011-01-01

The purpose of this study was to see if second grade students who were taught by teachers trained in choice theory/reality therapy (CT/RT) methods had higher achievement scores in mathematics/reading compared to students who were taught by teachers who were not trained. The American School Counselor Association (ASCA) National Model suggests that…

Investigation of vibration characteristics of electric motors

NASA Technical Reports Server (NTRS)

Bakshis, A. K.; Tamoshyunas, Y. K.

1973-01-01

The vibration characteristics of electric motors were analyzed using mathematical statistics methods. The equipment used and the method of conducting the test are described. Curves are developed to show the visualization of the electric motor vibrations in the vertical direction. Additional curves are included to show the amplitude-phase frequency characteristic of dynamic rotor-housing vibrations at the first lug and the same data for the second lug of the electric motor. Mathematical models were created to show the transmission function of the dynamic rotor housing 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.

10 CFR 431.445 - Determination of small electric motor efficiency.

Code of Federal Regulations, 2011 CFR

2011-01-01

... COMMERCIAL AND INDUSTRIAL EQUIPMENT Small Electric Motors Test Procedures § 431.445 Determination of small... the mechanical and electrical characteristics of that basic model, and (ii) Based on engineering or... Department of Energy records showing the method or methods used; the mathematical model, the engineering or...

Growth trajectories of mathematics achievement: Longitudinal tracking of student academic progress.

PubMed

Mok, Magdalena M C; McInerney, Dennis M; Zhu, Jinxin; Or, Anthony

2015-06-01

A number of methods to investigate growth have been reported in the literature, including hierarchical linear modelling (HLM), latent growth modelling (LGM), and multidimensional scaling applied to longitudinal profile analysis (LPAMS). This study aimed at modelling the mathematics growth of students over a span of 6 years from Grade 3 to Grade 9. The sample comprised secondary longitudinal data collected in three waves from n = 866 Hong Kong students when they were in Grade 3, Grade 6, and Grade 9. Mathematics achievement was measured thrice on a vertical scale linked with anchor items. Linear and nonlinear latent growth models were used to assess students' growth. Gender differences were also examined. A nonlinear latent growth curve with a decelerated rate had a good fit to the data. Initial achievement and growth rate were negatively correlated. No gender difference was found. Mathematics growth from Grade 6 to Grade 9 was slower than that from Grade 3 to Grade 6. Students with lower initial achievement improved at a faster rate than those who started at a higher level. Gender did not affect growth rate. © 2014 The British Psychological Society.

A Mathematical Model for Railway Control Systems

NASA Technical Reports Server (NTRS)

Hoover, D. N.

1996-01-01

We present a general method for modeling safety aspects of railway control systems. Using our modeling method, one can progressively refine an abstract railway safety model, sucessively adding layers of detail about how a real system actually operates, while maintaining a safety property that refines the original abstract safety property. This method supports a top-down approach to specification of railway control systems and to proof of a variety of safety-related properties. We demonstrate our method by proving safety of the classical block control system.

Improving students’ mathematical representational ability through RME-based progressive mathematization

NASA Astrophysics Data System (ADS)

Warsito; Darhim; Herman, T.

2018-01-01

This study aims to determine the differences in the improving of mathematical representation ability based on progressive mathematization with realistic mathematics education (PMR-MP) with conventional learning approach (PB). The method of research is quasi-experiments with non-equivalent control group designs. The study population is all students of class VIII SMPN 2 Tangerang consisting of 6 classes, while the sample was taken two classes with purposive sampling technique. The experimental class is treated with PMR-MP while the control class is treated with PB. The instruments used are test of mathematical representation ability. Data analysis was done by t-test, ANOVA test, post hoc test, and descriptive analysis. The result of analysis can be concluded that: 1) there are differences of mathematical representation ability improvement between students treated by PMR-MP and PB, 2) no interaction between learning approach (PMR-MP, PB) and prior mathematics knowledge (PAM) to improve students’ mathematical representation; 3) Students’ mathematical representation improvement in the level of higher PAM is better than medium, and low PAM students. Thus, based on the process of mathematization, it is very important when the learning direction of PMR-MP emphasizes on the process of building mathematics through a mathematical model.

A two-phase model of plantar tissue: a step toward prediction of diabetic foot ulceration.

PubMed

Sciumè, G; Boso, D P; Gray, W G; Cobelli, C; Schrefler, B A

2014-11-01

A new computational model, based on the thermodynamically constrained averaging theory, has been recently proposed to predict tumor initiation and proliferation. A similar mathematical approach is proposed here as an aid in diabetic ulcer prevention. The common aspects at the continuum level are the macroscopic balance equations governing the flow of the fluid phase, diffusion of chemical species, tissue mechanics, and some of the constitutive equations. The soft plantar tissue is modeled as a two-phase system: a solid phase consisting of the tissue cells and their extracellular matrix, and a fluid one (interstitial fluid and dissolved chemical species). The solid phase may become necrotic depending on the stress level and on the oxygen availability in the tissue. Actually, in diabetic patients, peripheral vascular disease impacts tissue necrosis; this is considered in the model via the introduction of an effective diffusion coefficient that governs transport of nutrients within the microvasculature. The governing equations of the mathematical model are discretized in space by the finite element method and in time domain using the θ-Wilson Method. While the full mathematical model is developed in this paper, the example is limited to the simulation of several gait cycles of a healthy foot. Copyright © 2014 John Wiley & Sons, Ltd.

Mathematical modeling of the gas extraction from the gas hydrate deposit taking into account the replacement technology

NASA Astrophysics Data System (ADS)

Musakaev, N. G.; Khasanov, M. K.; Borodin, S. L.

2018-03-01

In the work on the basis of methods and equations of mechanics of multiphase systems the mathematical model of the process of carbon dioxide burial in the reservoir saturated with methane hydrate is proposed. Estimates are obtained that allow for this problem to neglect diffusion mixing of carbon dioxide and methane. The features of the process of methane displacement from CH4 hydrate by filling them with carbon dioxide are studied.

Mathematical Modelling of Optimization of Structures of Monolithic Coverings Based on Liquid Rubbers

NASA Astrophysics Data System (ADS)

Turgumbayeva, R. Kh; Abdikarimov, M. N.; Mussabekov, R.; Sartayev, D. T.

2018-05-01

The paper considers optimization of monolithic coatings compositions using a computer and MPE methods. The goal of the paper was to construct a mathematical model of the complete factorial experiment taking into account its plan and conditions. Several regression equations were received. Dependence between content components and parameters of rubber, as well as the quantity of a rubber crumb, was considered. An optimal composition for manufacturing the material of monolithic coatings compositions was recommended based on experimental data.

Mathematical modeling of shell configurations made of homogeneous and composite materials experiencing intensive short actions and large displacements

NASA Astrophysics Data System (ADS)

Khairnasov, K. Z.

2018-04-01

The paper presents a mathematical model for solving the problem of behavior of shell configurations under the action of static and dynamic impacts. The problem is solved in geometrically nonlinear statement with regard to the finite element method. The composite structures with different material layers are considered. The obtained equations are used to study the behavior of shell configurations under the action of dynamic loads. The results agree well with the experimental data.

An investigation of the use of temporal decomposition in space mission scheduling

NASA Technical Reports Server (NTRS)

Bullington, Stanley E.; Narayanan, Venkat

1994-01-01

This research involves an examination of techniques for solving scheduling problems in long-duration space missions. The mission timeline is broken up into several time segments, which are then scheduled incrementally. Three methods are presented for identifying the activities that are to be attempted within these segments. The first method is a mathematical model, which is presented primarily to illustrate the structure of the temporal decomposition problem. Since the mathematical model is bound to be computationally prohibitive for realistic problems, two heuristic assignment procedures are also presented. The first heuristic method is based on dispatching rules for activity selection, and the second heuristic assigns performances of a model evenly over timeline segments. These heuristics are tested using a sample Space Station mission and a Spacelab mission. The results are compared with those obtained by scheduling the missions without any problem decomposition. The applicability of this approach to large-scale mission scheduling problems is also discussed.

A Mathematical Model for Storage and Recall of Images using Targeted Synchronization of Coupled Maps.

PubMed

Palaniyandi, P; Rangarajan, Govindan

2017-08-21

We propose a mathematical model for storage and recall of images using coupled maps. We start by theoretically investigating targeted synchronization in coupled map systems wherein only a desired (partial) subset of the maps is made to synchronize. A simple method is introduced to specify coupling coefficients such that targeted synchronization is ensured. The principle of this method is extended to storage/recall of images using coupled Rulkov maps. The process of adjusting coupling coefficients between Rulkov maps (often used to model neurons) for the purpose of storing a desired image mimics the process of adjusting synaptic strengths between neurons to store memories. Our method uses both synchronisation and synaptic weight modification, as the human brain is thought to do. The stored image can be recalled by providing an initial random pattern to the dynamical system. The storage and recall of the standard image of Lena is explicitly demonstrated.

Full non-linear treatment of the global thermospheric wind system. I - Mathematical method and analysis of forces. II - Results and comparison with observations

NASA Technical Reports Server (NTRS)

Blum, P. W.; Harris, I.

1975-01-01

The equations of horizontal motion of the neutral atmosphere between 120 and 500 km are integrated with the inclusion of all nonlinear terms of the convective derivative and the viscous forces due to vertical and horizontal velocity gradients. Empirical models of the distribution of neutral and charged particles are assumed to be known. The model of velocities developed is a steady state model. In Part I the mathematical method used in the integration of the Navier-Stokes equations is described and the various forces are analyzed. Results of the method given in Part I are presented with comparison with previous calculations and observations of upper atmospheric winds. Conclusions are that nonlinear effects are only significant in the equatorial region, especially at solstice conditions and that nonlinear effects do not produce any superrotation.

Combinatorial optimization in foundry practice

NASA Astrophysics Data System (ADS)

Antamoshkin, A. N.; Masich, I. S.

2016-04-01

The multicriteria mathematical model of foundry production capacity planning is suggested in the paper. The model is produced in terms of pseudo-Boolean optimization theory. Different search optimization methods were used to solve the obtained problem.

An engineering approach to modelling, decision support and control for sustainable systems.

PubMed

Day, W; Audsley, E; Frost, A R

2008-02-12

Engineering research and development contributes to the advance of sustainable agriculture both through innovative methods to manage and control processes, and through quantitative understanding of the operation of practical agricultural systems using decision models. This paper describes how an engineering approach, drawing on mathematical models of systems and processes, contributes new methods that support decision making at all levels from strategy and planning to tactics and real-time control. The ability to describe the system or process by a simple and robust mathematical model is critical, and the outputs range from guidance to policy makers on strategic decisions relating to land use, through intelligent decision support to farmers and on to real-time engineering control of specific processes. Precision in decision making leads to decreased use of inputs, less environmental emissions and enhanced profitability-all essential to sustainable systems.

Influence of drug-light-interval on photodynamic therapy of port wine stains--simulation and validation of mathematic models.

PubMed

Huang, Naiyan; Cheng, Gang; Li, Xiaosong; Gu, Ying; Liu, Fanguang; Zhong, Qiuhai; Wang, Ying; Zen, Jin; Qiu, Haixia; Chen, Hongxia

2008-06-01

We established mathematical models of photodynamic therapy (PDT) on port wine stains (PWS) to observe the effect of drug-light-interval (DLI) and optimize light dose. The mathematical simulations included determining (1) the distribution of laser light by Monte Carlo model, (2) the change of photosensitizer concentration in PWS vessels by a pharmacokinetics equation, (3) the change of photosensitizer distribution in tissue outside the vessels by a diffuse equation and photobleaching equation, and (4) the change of tissue oxygen concentration by the Fick's law with a consideration of the oxygen consumption during PDT. The concentration of singlet oxygen in the tissue model was calculated by the finite difference method. To validate those models, a PWS lesion of the same patient was divided into two areas and subjected to different DLIs and treated with different energy density. The color of lesion was assessed 8-12 weeks later. The simulation indicated the singlet oxygen concentration of the second treatment area (DLI=40 min) was lower than that of the first treatment area (DLI=0 min). However, it would be increased to a level similar to that of the first treatment area if the light irradiation time of the second treatment area was prolonged from 40 min to 55 min. Clinical results were consistent with the results predicted by the mathematical models. The mathematical models established in this study are helpful to optimize clinical protocol.

Forecasting in foodservice: model development, testing, and evaluation.

PubMed

Miller, J L; Thompson, P A; Orabella, M M

1991-05-01

This study was designed to develop, test, and evaluate mathematical models appropriate for forecasting menu-item production demand in foodservice. Data were collected from residence and dining hall foodservices at Ohio State University. Objectives of the study were to collect, code, and analyze the data; develop and test models using actual operation data; and compare forecasting results with current methods in use. Customer count was forecast using deseasonalized simple exponential smoothing. Menu-item demand was forecast by multiplying the count forecast by a predicted preference statistic. Forecasting models were evaluated using mean squared error, mean absolute deviation, and mean absolute percentage error techniques. All models were more accurate than current methods. A broad spectrum of forecasting techniques could be used by foodservice managers with access to a personal computer and spread-sheet and database-management software. The findings indicate that mathematical forecasting techniques may be effective in foodservice operations to control costs, increase productivity, and maximize profits.

Coupled oscillators in identification of nonlinear damping of a real parametric pendulum

NASA Astrophysics Data System (ADS)

Olejnik, Paweł; Awrejcewicz, Jan

2018-01-01

A damped parametric pendulum with friction is identified twice by means of its precise and imprecise mathematical model. A laboratory test stand designed for experimental investigations of nonlinear effects determined by a viscous resistance and the stick-slip phenomenon serves as the model mechanical system. An influence of accurateness of mathematical modeling on the time variability of the nonlinear damping coefficient of the oscillator is proved. A free decay response of a precisely and imprecisely modeled physical pendulum is dependent on two different time-varying coefficients of damping. The coefficients of the analyzed parametric oscillator are identified with the use of a new semi-empirical method based on a coupled oscillators approach, utilizing the fractional order derivative of the discrete measurement series treated as an input to the numerical model. Results of application of the proposed method of identification of the nonlinear coefficients of the damped parametric oscillator have been illustrated and extensively discussed.

Impact of Seasonal Heat Accumulation on Operation of Geothermal Heat Pump System with Vertical Ground Heat Exchanger

NASA Astrophysics Data System (ADS)

Timofeev, D. V.; Malyavina, E. G.

2017-11-01

The subject of the investigation was to find out the influence of heat pump operation in summer on its function in winter. For this purpose a mathematical model of a ground coupled heat pump system has been developed and programmed. The mathematical model of a system ground heat exchanger uses the finite difference method to describe the heat transfer in soil and the analytical method to specify the heat transfer in the U-tubes heat exchanger. The thermal diffusivity by the heat transfer in the soil changes during gradual freezing of the pore moisture and thus slows soil freezing. The mathematical model of a heat pump includes the description of a scroll compressor and the simplified descriptions of the evaporator and condenser. The analysis showed that heating during the cold season and cooling in the warm season affect the average heat transfer medium temperature in the soil loop in the winter season. It has been also showed that the degree of this effect depends on the clay content in the soil.

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.

EpiModel: An R Package for Mathematical Modeling of Infectious Disease over Networks.

PubMed

Jenness, Samuel M; Goodreau, Steven M; Morris, Martina

2018-04-01

Package EpiModel provides tools for building, simulating, and analyzing mathematical models for the population dynamics of infectious disease transmission in R. Several classes of models are included, but the unique contribution of this software package is a general stochastic framework for modeling the spread of epidemics on networks. EpiModel integrates recent advances in statistical methods for network analysis (temporal exponential random graph models) that allow the epidemic modeling to be grounded in empirical data on contacts that can spread infection. This article provides an overview of both the modeling tools built into EpiModel , designed to facilitate learning for students new to modeling, and the application programming interface for extending package EpiModel , designed to facilitate the exploration of novel research questions for advanced modelers.

EpiModel: An R Package for Mathematical Modeling of Infectious Disease over Networks

PubMed Central

Jenness, Samuel M.; Goodreau, Steven M.; Morris, Martina

2018-01-01

Package EpiModel provides tools for building, simulating, and analyzing mathematical models for the population dynamics of infectious disease transmission in R. Several classes of models are included, but the unique contribution of this software package is a general stochastic framework for modeling the spread of epidemics on networks. EpiModel integrates recent advances in statistical methods for network analysis (temporal exponential random graph models) that allow the epidemic modeling to be grounded in empirical data on contacts that can spread infection. This article provides an overview of both the modeling tools built into EpiModel, designed to facilitate learning for students new to modeling, and the application programming interface for extending package EpiModel, designed to facilitate the exploration of novel research questions for advanced modelers. PMID:29731699

Real-time control data wrangling for development of mathematical control models of technological processes

NASA Astrophysics Data System (ADS)

Vasilyeva, N. V.; Koteleva, N. I.; Fedorova, E. R.

2018-05-01

The relevance of the research is due to the need to stabilize the composition of the melting products of copper-nickel sulfide raw materials in the Vanyukov furnace. The goal of this research is to identify the most suitable methods for the aggregation of the real time data for the development of a mathematical model for control of the technological process of melting copper-nickel sulfide raw materials in the Vanyukov furnace. Statistical methods of analyzing the historical data of the real technological object and the correlation analysis of process parameters are described. Factors that exert the greatest influence on the main output parameter (copper content in matte) and ensure the physical-chemical transformations are revealed. An approach to the processing of the real time data for the development of a mathematical model for control of the melting process is proposed. The stages of processing the real time information are considered. The adopted methodology for the aggregation of data suitable for the development of a control model for the technological process of melting copper-nickel sulfide raw materials in the Vanyukov furnace allows us to interpret the obtained results for their further practical application.

Equivalent model of a dually-fed machine for electric drive control systems

NASA Astrophysics Data System (ADS)

Ostrovlyanchik, I. Yu; Popolzin, I. Yu

2018-05-01

The article shows that the mathematical model of a dually-fed machine is complicated because of the presence of a controlled voltage source in the rotor circuit. As a method of obtaining a mathematical model, the method of a generalized two-phase electric machine is applied and a rotating orthogonal coordinate system is chosen that is associated with the representing vector of a stator current. In the chosen coordinate system in the operator form the differential equations of electric equilibrium for the windings of the generalized machine (the Kirchhoff equation) are written together with the expression for the moment, which determines the electromechanical energy transformation in the machine. Equations are transformed so that they connect the currents of the windings, that determine the moment of the machine, and the voltages on these windings. The structural diagram of the machine is assigned to the written equations. Based on the written equations and accepted assumptions, expressions were obtained for the balancing the EMF of windings, and on the basis of these expressions an equivalent mathematical model of a dually-fed machine is proposed, convenient for use in electric drive control systems.

An optimization model for metabolic pathways.

PubMed

Planes, F J; Beasley, J E

2009-10-15

Different mathematical methods have emerged in the post-genomic era to determine metabolic pathways. These methods can be divided into stoichiometric methods and path finding methods. In this paper we detail a novel optimization model, based upon integer linear programming, to determine metabolic pathways. Our model links reaction stoichiometry with path finding in a single approach. We test the ability of our model to determine 40 annotated Escherichia coli metabolic pathways. We show that our model is able to determine 36 of these 40 pathways in a computationally effective manner.

Calculation of skiving cutter blade

NASA Astrophysics Data System (ADS)

Xu, Lei; Lao, Qicheng; Shang, Zhiyi

2018-05-01

The gear skiving method is a kind of gear machining technology with high efficiency and high precision. According to the method of gear machining, a method for calculating the blade of skiving cutter in machining an involute gear is proposed. Based on the principle of meshing gear and the kinematic relationship between the machined flank and the gear skiving, the mathematical model of skiving for machining the internal gear is built and the gear tooth surface is obtained by solving the meshing equation. The mathematical model of the gear blade curve of the skiving cutter is obtained by choosing the proper rake face and the cutter tooth surface for intersection. Through the analysis of the simulation of the skiving gear, the feasibility and correctness of the skiving cutter blade design are verified.

Algorithms for Mathematical Programming with Emphasis on Bi-level Models

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

Goldfarb, Donald; Iyengar, Garud

2014-05-22

The research supported by this grant was focused primarily on first-order methods for solving large scale and structured convex optimization problems and convex relaxations of nonconvex problems. These include optimal gradient methods, operator and variable splitting methods, alternating direction augmented Lagrangian methods, and block coordinate descent methods.

WORKSHOP ON APPLICATION OF STATISTICAL METHODS TO BIOLOGICALLY-BASED PHARMACOKINETIC MODELING FOR RISK ASSESSMENT

EPA Science Inventory

Biologically-based pharmacokinetic models are being increasingly used in the risk assessment of environmental chemicals. These models are based on biological, mathematical, statistical and engineering principles. Their potential uses in risk assessment include extrapolation betwe...

Animal models for studying transport across the blood-brain barrier.

PubMed

Bonate, P L

1995-01-01

There are many reasons for wishing to determine the rate of uptake of a drug from blood into brain parenchyma. However, when faced with doing so for the first time, choosing a method can be a formidable task. There are at least 7 methods from which to choose: indicator dilution, brain uptake index, microdialysis, external registration, PET scanning, in situ perfusion, and compartmental modeling. Each method has advantages and disadvantages. Some methods require very little equipment while others require equipment that can cost millions of dollars. Some methods require very little technical experience whereas others require complex surgical manipulation. The mathematics alone for the various methods range from simple algebra to complex integral calculus and differential equations. Like most things in science, as the complexity of the technique increases, so does the quantity of information it provides. This review is meant to serve as a starting point for the researcher who wishes to study transport and uptake across the blood-brain barrier in animal models. An overview of the mathematical theory, as well as an introduction to the techniques, is presented.

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.

Identification and agreement of first turn point by mathematical analysis applied to heart rate, carbon dioxide output and electromyography.

PubMed

Zamunér, Antonio R; Catai, Aparecida M; Martins, Luiz E B; Sakabe, Daniel I; Da Silva, Ester

2013-01-01

The second heart rate (HR) turn point has been extensively studied, however there are few studies determining the first HR turn point. Also, the use of mathematical and statistical models for determining changes in dynamic characteristics of physiological variables during an incremental cardiopulmonary test has been suggested. To determine the first turn point by analysis of HR, surface electromyography (sEMG), and carbon dioxide output (VCO2) using two mathematical models and to compare the results to those of the visual method. Ten sedentary middle-aged men (53.9 ± 3.2 years old) were submitted to cardiopulmonary exercise testing on an electromagnetic cycle ergometer until exhaustion. Ventilatory variables, HR, and sEMG of the vastus lateralis were obtained in real time. Three methods were used to determine the first turn point: 1) visual analysis based on loss of parallelism between VCO2 and oxygen uptake (VO2); 2) the linear-linear model, based on fitting the curves to the set of VCO2 data (Lin-LinVCO2); 3) a bi-segmental linear regression of Hinkley's algorithm applied to HR (HMM-HR), VCO2 (HMM-VCO2), and sEMG data (HMM-RMS). There were no differences between workload, HR, and ventilatory variable values at the first ventilatory turn point as determined by the five studied parameters (p>0.05). The Bland-Altman plot showed an even distribution of the visual analysis method with Lin-LinVCO2, HMM-HR, HMM-VCO2, and HMM-RMS. The proposed mathematical models were effective in determining the first turn point since they detected the linear pattern change and the deflection point of VCO2, HR responses, and sEMG.

A hybrid modeling system designed to support decision making in the optimization of extrusion of inhomogeneous materials

NASA Astrophysics Data System (ADS)

Kryuchkov, D. I.; Zalazinsky, A. G.

2017-12-01

Mathematical models and a hybrid modeling system are developed for the implementation of the experimental-calculation method for the engineering analysis and optimization of the plastic deformation of inhomogeneous materials with the purpose of improving metal-forming processes and machines. The created software solution integrates Abaqus/CAE, a subroutine for mathematical data processing, with the use of Python libraries and the knowledge base. Practical application of the software solution is exemplified by modeling the process of extrusion of a bimetallic billet. The results of the engineering analysis and optimization of the extrusion process are shown, the material damage being monitored.

Development of dynamic Bayesian models for web application test management

NASA Astrophysics Data System (ADS)

Azarnova, T. V.; Polukhin, P. V.; Bondarenko, Yu V.; Kashirina, I. L.

2018-03-01

The mathematical apparatus of dynamic Bayesian networks is an effective and technically proven tool that can be used to model complex stochastic dynamic processes. According to the results of the research, mathematical models and methods of dynamic Bayesian networks provide a high coverage of stochastic tasks associated with error testing in multiuser software products operated in a dynamically changing environment. Formalized representation of the discrete test process as a dynamic Bayesian model allows us to organize the logical connection between individual test assets for multiple time slices. This approach gives an opportunity to present testing as a discrete process with set structural components responsible for the generation of test assets. Dynamic Bayesian network-based models allow us to combine in one management area individual units and testing components with different functionalities and a direct influence on each other in the process of comprehensive testing of various groups of computer bugs. The application of the proposed models provides an opportunity to use a consistent approach to formalize test principles and procedures, methods used to treat situational error signs, and methods used to produce analytical conclusions based on test results.

Feasibility of wake vortex monitoring systems for air terminals

NASA Technical Reports Server (NTRS)

Wilson, D. J.; Shrider, K. R.; Lawrence, T. R.

1972-01-01

Wake vortex monitoring systems, especially those using laser Doppler sensors, were investigated. The initial phases of the effort involved talking with potential users (air traffic controllers, pilots, etc.) of a wake vortex monitoring system to determine system requirements from the user's viewpoint. These discussions involved the volumes of airspace to be monitored for vortices, and potential methods of using the monitored vortex data once the data are available. A subsequent task led to determining a suitable mathematical model of the vortex phenomena and developing a mathematical model of the laser Doppler sensor for monitoring the vortex flow field. The mathematical models were used in combination to help evaluate the capability of laser Doppler instrumentation in monitoring vortex flow fields both in the near vicinity of the sensor (within 1 kilometer and at long ranges(10 kilometers).

Flight test planning and parameter extraction for rotorcraft system identification

NASA Technical Reports Server (NTRS)

Wang, J. C.; Demiroz, M. Y.; Talbot, P. D.

1986-01-01

The present study is concerned with the mathematical modelling of aircraft dynamics on the basis of an investigation conducted with the aid of the Rotor System Research Aircraft (RSRA). The particular characteristics of RSRA make it possible to investigate aircraft properties which cannot be readily studied elsewhere, for example in the wind tunnel. The considered experiment had mainly the objective to develop an improved understanding of the physics of rotor flapping dynamics and rotor loads in maneuvers. The employed approach is based on a utilization of parameter identification methodology (PID) with application to helicopters. A better understanding of the contribution of the main rotor to the overall aircraft forces and moments is also to be obtained. Attention is given to the mathematical model of a rotorcraft system, an integrated identification method, flight data processing, and the identification of RSRA mathematical models.

Mathematical modelling of powder material motion and transportation in high-temperature flow core during plasma coatings application

NASA Astrophysics Data System (ADS)

Bogdanovich, V. I.; Giorbelidze, M. G.

2018-03-01

A problem of mathematical modelling of powder material motion and transportation in gas thermal flow core has been addressed. Undertaken studies indicate significant impact on dynamics of motion of sprayed particles of phenomenological law for drag coefficient and accounting momentum loss of a plasma jet upon acceleration of these particles and their diameter. It is determined that at great dispersion of spraying particles, they reach detail surface at different velocity and significant particles separation takes place at spraying spot. According to the results of mathematical modelling, requirements for admissible dispersion of diameters of particles used for spraying have been formulated. Research has also allowed reducing separation of particles at the spraying spot due to the selection of the method of powder feed to the anode channel of the plasma torch.

Mathematical model of one-man air revitalization system

NASA Technical Reports Server (NTRS)

1976-01-01

A mathematical model was developed for simulating the steady state performance in electrochemical CO2 concentrators which utilize (NMe4)2 CO3 (aq.) electrolyte. This electrolyte, which accommodates a wide range of air relative humidity, is most suitable for one-man air revitalization systems. The model is based on the solution of coupled nonlinear ordinary differential equations derived from mass transport and rate equations for the processes which take place in the cell. The boundary conditions are obtained by solving the mass and energy transport equations. A shooting method is used to solve the differential equations.

Manufacturing and Cost Considerations in Multidisciplinary Aircraft Design (Research on Mathematical Modeling of Manufacturability Factors)

NASA Technical Reports Server (NTRS)

Rais-Rohani, Masoud

1996-01-01

The identification of airframe Manufacturability Factors/Cost Drivers (MFCD) and the method by which the relationships between MFCD and designer-controlled parameters could be properly modeled are described.

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

Bastian, Mark; Trigueros, Jose V.

Phoenix is a Java Virtual Machine (JVM) based library for performing mathematical and astrodynamics calculations. It consists of two primary sub-modules, phoenix-math and phoenix-astrodynamics. The mathematics package has a variety of mathematical classes for performing 3D transformations, geometric reasoning, and numerical analysis. The astrodynamics package has various classes and methods for computing locations, attitudes, accesses, and other values useful for general satellite modeling and simulation. Methods for computing celestial locations, such as the location of the Sun and Moon, are also included. Phoenix is meant to be used as a library within the context of a larger application. For example,more » it could be used for a web service, desktop client, or to compute simple values in a scripting environment.« less

Mathematical modeling and computational prediction of cancer drug resistance.

PubMed

Sun, Xiaoqiang; Hu, Bin

2017-06-23

Diverse forms of resistance to anticancer drugs can lead to the failure of chemotherapy. Drug resistance is one of the most intractable issues for successfully treating cancer in current clinical practice. Effective clinical approaches that could counter drug resistance by restoring the sensitivity of tumors to the targeted agents are urgently needed. As numerous experimental results on resistance mechanisms have been obtained and a mass of high-throughput data has been accumulated, mathematical modeling and computational predictions using systematic and quantitative approaches have become increasingly important, as they can potentially provide deeper insights into resistance mechanisms, generate novel hypotheses or suggest promising treatment strategies for future testing. In this review, we first briefly summarize the current progress of experimentally revealed resistance mechanisms of targeted therapy, including genetic mechanisms, epigenetic mechanisms, posttranslational mechanisms, cellular mechanisms, microenvironmental mechanisms and pharmacokinetic mechanisms. Subsequently, we list several currently available databases and Web-based tools related to drug sensitivity and resistance. Then, we focus primarily on introducing some state-of-the-art computational methods used in drug resistance studies, including mechanism-based mathematical modeling approaches (e.g. molecular dynamics simulation, kinetic model of molecular networks, ordinary differential equation model of cellular dynamics, stochastic model, partial differential equation model, agent-based model, pharmacokinetic-pharmacodynamic model, etc.) and data-driven prediction methods (e.g. omics data-based conventional screening approach for node biomarkers, static network approach for edge biomarkers and module biomarkers, dynamic network approach for dynamic network biomarkers and dynamic module network biomarkers, etc.). Finally, we discuss several further questions and future directions for the use of computational methods for studying drug resistance, including inferring drug-induced signaling networks, multiscale modeling, drug combinations and precision medicine. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Mathematization Competencies of Pre-Service Elementary Mathematics Teachers in the Mathematical Modelling Process

ERIC Educational Resources Information Center

Yilmaz, Suha; Tekin-Dede, Ayse

2016-01-01

Mathematization competency is considered in the field as the focus of modelling process. Considering the various definitions, the components of the mathematization competency are determined as identifying assumptions, identifying variables based on the assumptions and constructing mathematical model/s based on the relations among identified…

Optimal back-extrapolation method for estimating plasma volume in humans using the indocyanine green dilution method.

PubMed

Polidori, David; Rowley, Clarence

2014-07-22

The indocyanine green dilution method is one of the methods available to estimate plasma volume, although some researchers have questioned the accuracy of this method. We developed a new, physiologically based mathematical model of indocyanine green kinetics that more accurately represents indocyanine green kinetics during the first few minutes postinjection than what is assumed when using the traditional mono-exponential back-extrapolation method. The mathematical model is used to develop an optimal back-extrapolation method for estimating plasma volume based on simulated indocyanine green kinetics obtained from the physiological model. Results from a clinical study using the indocyanine green dilution method in 36 subjects with type 2 diabetes indicate that the estimated plasma volumes are considerably lower when using the traditional back-extrapolation method than when using the proposed back-extrapolation method (mean (standard deviation) plasma volume = 26.8 (5.4) mL/kg for the traditional method vs 35.1 (7.0) mL/kg for the proposed method). The results obtained using the proposed method are more consistent with previously reported plasma volume values. Based on the more physiological representation of indocyanine green kinetics and greater consistency with previously reported plasma volume values, the new back-extrapolation method is proposed for use when estimating plasma volume using the indocyanine green dilution method.

Mathematical modelling of tissue formation in chondrocyte filter cultures.

PubMed

Catt, C J; Schuurman, W; Sengers, B G; van Weeren, P R; Dhert, W J A; Please, C P; Malda, J

2011-12-17

In the field of cartilage tissue engineering, filter cultures are a frequently used three-dimensional differentiation model. However, understanding of the governing processes of in vitro growth and development of tissue in these models is limited. Therefore, this study aimed to further characterise these processes by means of an approach combining both experimental and applied mathematical methods. A mathematical model was constructed, consisting of partial differential equations predicting the distribution of cells and glycosaminoglycans (GAGs), as well as the overall thickness of the tissue. Experimental data was collected to allow comparison with the predictions of the simulation and refinement of the initial models. Healthy mature equine chondrocytes were expanded and subsequently seeded on collagen-coated filters and cultured for up to 7 weeks. Resulting samples were characterised biochemically, as well as histologically. The simulations showed a good representation of the experimentally obtained cell and matrix distribution within the cultures. The mathematical results indicate that the experimental GAG and cell distribution is critically dependent on the rate at which the cell differentiation process takes place, which has important implications for interpreting experimental results. This study demonstrates that large regions of the tissue are inactive in terms of proliferation and growth of the layer. In particular, this would imply that higher seeding densities will not significantly affect the growth rate. A simple mathematical model was developed to predict the observed experimental data and enable interpretation of the principal underlying mechanisms controlling growth-related changes in tissue composition.

Skolem and pessimism about proof in mathematics.

PubMed

Cohen, Paul J

2005-10-15

Attitudes towards formalization and proof have gone through large swings during the last 150 years. We sketch the development from Frege's first formalization, to the debates over intuitionism and other schools, through Hilbert's program and the decisive blow of the Gödel Incompleteness Theorem. A critical role is played by the Skolem-Lowenheim Theorem, which showed that no first-order axiom system can characterize a unique infinite model. Skolem himself regarded this as a body blow to the belief that mathematics can be reliably founded only on formal axiomatic systems. In a remarkably prescient paper, he even sketches the possibility of interesting new models for set theory itself, something later realized by the method of forcing. This is in contrast to Hilbert's belief that mathematics could resolve all its questions. We discuss the role of new axioms for set theory, questions in set theory itself, and their relevance for number theory. We then look in detail at what the methods of the predicate calculus, i.e. mathematical reasoning, really entail. The conclusion is that there is no reasonable basis for Hilbert's assumption. The vast majority of questions even in elementary number theory, of reasonable complexity, are beyond the reach of any such reasoning. Of course this cannot be proved and we present only plausibility arguments. The great success of mathematics comes from considering 'natural problems', those which are related to previous work and offer a good chance of being solved. The great glories of human reasoning, beginning with the Greek discovery of geometry, are in no way diminished by this pessimistic view. We end by wishing good health to present-day mathematics and the mathematics of many centuries to come.

Mathematical model of bone drilling for virtual surgery system

NASA Astrophysics Data System (ADS)

Alaytsev, Innokentiy K.; Danilova, Tatyana V.; Manturov, Alexey O.; Mareev, Gleb O.; Mareev, Oleg V.

2018-04-01

The bone drilling is an essential part of surgeries in ENT and Dentistry. A proper training of drilling machine handling skills is impossible without proper modelling of the drilling process. Utilization of high precision methods like FEM is limited due to the requirement of 1000 Hz update rate for haptic feedback. The study presents a mathematical model of the drilling process that accounts the properties of materials, the geometry and the rotation rate of a burr to compute the removed material volume. The simplicity of the model allows for integrating it in the high-frequency haptic thread. The precision of the model is enough for a virtual surgery system targeted on the training of the basic surgery skills.

In-vitro development of vitrified-warmed bovine oocytes after activation may be predicted based on mathematical modelling of cooling and warming rates during vitrification, storage and sample removal.

PubMed

Sansinena, Marina; Santos, Maria Victoria; Chirife, Jorge; Zaritzky, Noemi

2018-05-01

Heat transfer during cooling and warming is difficult to measure in cryo-devices; mathematical modelling is an alternative method that can describe these processes. In this study, we tested the validity of one such model by assessing in-vitro development of vitrified and warmed bovine oocytes after parthenogenetic activation and culture. The viability of oocytes vitrified in four different cryo-devices was assessed. Consistent with modelling predictions, oocytes vitrified using cryo-devices with the highest modelled cooling rates had significantly (P < 0.05) better cleavage and blastocyst formation rates. We then evaluated a two-step sample removal process, in which oocytes were held in nitrogen vapour for 15 s to simulate sample identification during clinical application, before being removed completely and warmed. Oocytes exposed to this procedure showed reduced developmental potential, according to the model, owing to thermodynamic instability and devitrification at relatively low temperatures. These findings suggest that cryo-device selection and handling, including method of removal from nitrogen storage, are critical to survival of vitrified oocytes. Limitations of the study include use of parthenogenetically activated rather than fertilized ova and lack of physical measurement of recrystallization. We suggest mathematical modelling could be used to predict the effect of critical steps in cryopreservation. Copyright © 2018 Reproductive Healthcare Ltd. Published by Elsevier Ltd. All rights reserved.

Integrated Modeling of Complex Optomechanical Systems

NASA Astrophysics Data System (ADS)

Andersen, Torben; Enmark, Anita

2011-09-01

Mathematical modeling and performance simulation are playing an increasing role in large, high-technology projects. There are two reasons; first, projects are now larger than they were before, and the high cost calls for detailed performance prediction before construction. Second, in particular for space-related designs, it is often difficult to test systems under realistic conditions beforehand, and mathematical modeling is then needed to verify in advance that a system will work as planned. Computers have become much more powerful, permitting calculations that were not possible before. At the same time mathematical tools have been further developed and found acceptance in the community. Particular progress has been made in the fields of structural mechanics, optics and control engineering, where new methods have gained importance over the last few decades. Also, methods for combining optical, structural and control system models into global models have found widespread use. Such combined models are usually called integrated models and were the subject of this symposium. The objective was to bring together people working in the fields of groundbased optical telescopes, ground-based radio telescopes, and space telescopes. We succeeded in doing so and had 39 interesting presentations and many fruitful discussions during coffee and lunch breaks and social arrangements. We are grateful that so many top ranked specialists found their way to Kiruna and we believe that these proceedings will prove valuable during much future work.

Predicting Drug Combination Index and Simulating the Network-Regulation Dynamics by Mathematical Modeling of Drug-Targeted EGFR-ERK Signaling Pathway

NASA Astrophysics Data System (ADS)

Huang, Lu; Jiang, Yuyang; Chen, Yuzong

2017-01-01

Synergistic drug combinations enable enhanced therapeutics. Their discovery typically involves the measurement and assessment of drug combination index (CI), which can be facilitated by the development and applications of in-silico CI predictive tools. In this work, we developed and tested the ability of a mathematical model of drug-targeted EGFR-ERK pathway in predicting CIs and in analyzing multiple synergistic drug combinations against observations. Our mathematical model was validated against the literature reported signaling, drug response dynamics, and EGFR-MEK drug combination effect. The predicted CIs and combination therapeutic effects of the EGFR-BRaf, BRaf-MEK, FTI-MEK, and FTI-BRaf inhibitor combinations showed consistent synergism. Our results suggest that existing pathway models may be potentially extended for developing drug-targeted pathway models to predict drug combination CI values, isobolograms, and drug-response surfaces as well as to analyze the dynamics of individual and combinations of drugs. With our model, the efficacy of potential drug combinations can be predicted. Our method complements the developed in-silico methods (e.g. the chemogenomic profile and the statistically-inferenced network models) by predicting drug combination effects from the perspectives of pathway dynamics using experimental or validated molecular kinetic constants, thereby facilitating the collective prediction of drug combination effects in diverse ranges of disease systems.

Safety Verification of the Small Aircraft Transportation System Concept of Operations

NASA Technical Reports Server (NTRS)

Carreno, Victor; Munoz, Cesar

2005-01-01

A critical factor in the adoption of any new aeronautical technology or concept of operation is safety. Traditionally, safety is accomplished through a rigorous process that involves human factors, low and high fidelity simulations, and flight experiments. As this process is usually performed on final products or functional prototypes, concept modifications resulting from this process are very expensive to implement. This paper describe an approach to system safety that can take place at early stages of a concept design. It is based on a set of mathematical techniques and tools known as formal methods. In contrast to testing and simulation, formal methods provide the capability of exhaustive state exploration analysis. We present the safety analysis and verification performed for the Small Aircraft Transportation System (SATS) Concept of Operations (ConOps). The concept of operations is modeled using discrete and hybrid mathematical models. These models are then analyzed using formal methods. The objective of the analysis is to show, in a mathematical framework, that the concept of operation complies with a set of safety requirements. It is also shown that the ConOps has some desirable characteristic such as liveness and absence of dead-lock. The analysis and verification is performed in the Prototype Verification System (PVS), which is a computer based specification language and a theorem proving assistant.

Dynamics of Longitudinal Impact in the Variable Cross-Section Rods

NASA Astrophysics Data System (ADS)

Stepanov, R.; Romenskyi, D.; Tsarenko, S.

2018-03-01

Dynamics of longitudinal impact in rods of variable cross-section is considered. Rods of various configurations are used as elements of power pulse systems. There is no single method to the construction of a mathematical model of longitudinal impact on rods. The creation of a general method for constructing a mathematical model of longitudinal impact for rods of variable cross-section is the goal of the article. An elastic rod is considered with a cross-sectional area varying in powers of law from the longitudinal coordinate. The solution of the wave equation is obtained using the Fourier method. Special functions are introduced on the basis of recurrence relations for Bessel functions for solving boundary value problems. The expression for the square of the norm is obtained taking into account the orthogonality property of the eigen functions with weight. For example, the impact of an inelastic mass along the wide end of a conical rod is considered. The expressions for the displacements, forces and stresses of the rod sections are obtained for the cases of sudden velocity communication and the application of force. The proposed mathematical model makes it possible to carry out investigations of the stress-strain state in rods of variable and constant cross-section for various conditions of dynamic effects.

Visual-spatial abilities relate to mathematics achievement in children with heavy prenatal alcohol exposure

PubMed Central

Crocker, N.; Riley, E.P.; Mattson, S.N.

2014-01-01

Objective The current study examined the relationship between mathematics and attention, working memory, and visual memory in children with heavy prenatal alcohol exposure and controls. Method Fifty-six children (29 AE, 27 CON) were administered measures of global mathematics achievement (WRAT-3 Arithmetic & WISC-III Written Arithmetic), attention, (WISC-III Digit Span forward and Spatial Span forward), working memory (WISC-III Digit Span backward and Spatial Span backward), and visual memory (CANTAB Spatial Recognition Memory and Pattern Recognition Memory). The contribution of cognitive domains to mathematics achievement was analyzed using linear regression techniques. Attention, working memory and visual memory data were entered together on step 1 followed by group on step 2, and the interaction terms on step 3. Results Model 1 accounted for a significant amount of variance in both mathematics achievement measures, however, model fit improved with the addition of group on step 2. Significant predictors of mathematics achievement were Spatial Span forward and backward and Spatial Recognition Memory. Conclusions These findings suggest that deficits in spatial processing may be related to math impairments seen in FASD. In addition, prenatal alcohol exposure was associated with deficits in mathematics achievement, above and beyond the contribution of general cognitive abilities. PMID:25000323

Mathematics Pedagogical Standards: A Suggested Model of Instruction in Enhancing the Mathematics Teacher’s Quality of Instruction

NASA Astrophysics Data System (ADS)

Saad, N. S.; Jemali, M.; Zakaria, Z. Hj; Yusof, Q.

2018-01-01

The paper aims at identifying the standards for teaching and learning of mathematics based on National Council of Teacher of Mathematics (NCTM, 2000), The Australian Association of Mathematics Teachers (AAMT, 2006) and Training and Development Agency for School (TDA, 2007). These known standards were used as a guide in identifying the constructs of the mathematics teacher’s instruction in the classroom. The survey method used in which a questionnaire instrument encompassed on the four identified constructs on the standards for teaching and learning of mathematics, namely professional practices, professional attributes, professional knowledge, and professional instructional processes. The instrument was tested during a pilot study and a Cronbach’s Alpha reliability index of greater than 0.85 was obtained. The actual research was carried out in Peninsular Malaysia involving 224 secondary schools with 1.120 mathematics teachers and 108 primary schools with 540 mathematics teachers. From the selected schools, only 820 secondary mathematics teachers (73.2%) and 361 primary teachers (66.9%) gave a response to the mailed questionnaires. The findings of the study revealed that the secondary and primary mathematics teachers strongly agreed on three constructs; professional practices, professional attributes and professional instructional processes.

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.

Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

ERIC Educational Resources Information Center

Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem

2014-01-01

Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…

Elementary Preservice Teachers' and Elementary Inservice Teachers' Knowledge of Mathematical Modeling

ERIC Educational Resources Information Center

Schwerdtfeger, Sara

2017-01-01

This study examined the differences in knowledge of mathematical modeling between a group of elementary preservice teachers and a group of elementary inservice teachers. Mathematical modeling has recently come to the forefront of elementary mathematics classrooms because of the call to add mathematical modeling tasks in mathematics classes through…

Comparison of anaerobic threshold determined by visual and mathematical methods in healthy women.

PubMed

Higa, M N; Silva, E; Neves, V F C; Catai, A M; Gallo, L; Silva de Sá, M F

2007-04-01

Several methods are used to estimate anaerobic threshold (AT) during exercise. The aim of the present study was to compare AT obtained by a graphic visual method for the estimate of ventilatory and metabolic variables (gold standard), to a bi-segmental linear regression mathematical model of Hinkley's algorithm applied to heart rate (HR) and carbon dioxide output (VCO2) data. Thirteen young (24 +/- 2.63 years old) and 16 postmenopausal (57 +/- 4.79 years old) healthy and sedentary women were submitted to a continuous ergospirometric incremental test on an electromagnetic braking cycloergometer with 10 to 20 W/min increases until physical exhaustion. The ventilatory variables were recorded breath-to-breath and HR was obtained beat-to-beat over real time. Data were analyzed by the nonparametric Friedman test and Spearman correlation test with the level of significance set at 5%. Power output (W), HR (bpm), oxygen uptake (VO2; mL kg(-1) min(-1)), VO2 (mL/min), VCO2 (mL/min), and minute ventilation (VE; L/min) data observed at the AT level were similar for both methods and groups studied (P > 0.05). The VO2 (mL kg(-1) min(-1)) data showed significant correlation (P < 0.05) between the gold standard method and the mathematical model when applied to HR (rs = 0.75) and VCO2 (rs = 0.78) data for the subjects as a whole (N = 29). The proposed mathematical method for the detection of changes in response patterns of VCO2 and HR was adequate and promising for AT detection in young and middle-aged women, representing a semi-automatic, non-invasive and objective AT measurement.

Establishment of the mathematical model for diagnosing the engine valve faults by genetic programming

NASA Astrophysics Data System (ADS)

Yang, Wen-Xian

2006-05-01

Available machine fault diagnostic methods show unsatisfactory performances on both on-line and intelligent analyses because their operations involve intensive calculations and are labour intensive. Aiming at improving this situation, this paper describes the development of an intelligent approach by using the Genetic Programming (abbreviated as GP) method. Attributed to the simple calculation of the mathematical model being constructed, different kinds of machine faults may be diagnosed correctly and quickly. Moreover, human input is significantly reduced in the process of fault diagnosis. The effectiveness of the proposed strategy is validated by an illustrative example, in which three kinds of valve states inherent in a six-cylinders/four-stroke cycle diesel engine, i.e. normal condition, valve-tappet clearance and gas leakage faults, are identified. In the example, 22 mathematical functions have been specially designed and 8 easily obtained signal features are used to construct the diagnostic model. Different from existing GPs, the diagnostic tree used in the algorithm is constructed in an intelligent way by applying a power-weight coefficient to each feature. The power-weight coefficients vary adaptively between 0 and 1 during the evolutionary process. Moreover, different evolutionary strategies are employed, respectively for selecting the diagnostic features and functions, so that the mathematical functions are sufficiently utilized and in the meantime, the repeated use of signal features may be fully avoided. The experimental results are illustrated diagrammatically in the following sections.

A Bionic Polarization Navigation Sensor and Its Calibration Method.

PubMed

Zhao, Huijie; Xu, Wujian

2016-08-03

The polarization patterns of skylight which arise due to the scattering of sunlight in the atmosphere can be used by many insects for deriving compass information. Inspired by insects' polarized light compass, scientists have developed a new kind of navigation method. One of the key techniques in this method is the polarimetric sensor which is used to acquire direction information from skylight. In this paper, a polarization navigation sensor is proposed which imitates the working principles of the polarization vision systems of insects. We introduce the optical design and mathematical model of the sensor. In addition, a calibration method based on variable substitution and non-linear curve fitting is proposed. The results obtained from the outdoor experiments provide support for the feasibility and precision of the sensor. The sensor's signal processing can be well described using our mathematical model. A relatively high degree of accuracy in polarization measurement can be obtained without any error compensation.

Mathematic modeling the relationship of bacteria number in a dairy product and the color difference measured by a CCD image sensor

NASA Astrophysics Data System (ADS)

Zhou, Zhen; Zhao, Zhigang; Chen, Dongkui; Liu, Yuping

2005-01-01

Although many methods, such as bacteria plate count, flow cytometry and impedance method have been broadly used in the dairy industry to quantitate bacteria numbers around the world, none of them is a quick, low cost and easy one. In this study, we proposed to apply the color difference theory in this field to establish a mathematic model to quantitate bacteria number in fresh milk. Preliminary testing results not only indicate that the application of the color difference theory to the new system is practical, but also confirm the theoretical relationship between the numbers of bacteria, incubation time and color difference. The proof of the principal study in this article further suggests that the novel method has the potential to replace the traditional methods to determine bacteria numbers for the food industry.

A novel no-reference objective stereoscopic video quality assessment method based on visual saliency analysis

NASA Astrophysics Data System (ADS)

Yang, Xinyan; Zhao, Wei; Ye, Long; Zhang, Qin

2017-07-01

This paper proposes a no-reference objective stereoscopic video quality assessment method with the motivation that making the effect of objective experiments close to that of subjective way. We believe that the image regions with different visual salient degree should not have the same weights when designing an assessment metric. Therefore, we firstly use GBVS algorithm to each frame pairs and separate both the left and right viewing images into the regions with strong, general and week saliency. Besides, local feature information like blockiness, zero-crossing and depth are extracted and combined with a mathematical model to calculate a quality assessment score. Regions with different salient degree are assigned with different weights in the mathematical model. Experiment results demonstrate the superiority of our method compared with the existed state-of-the-art no-reference objective Stereoscopic video quality assessment methods.

A Bionic Polarization Navigation Sensor and Its Calibration Method

PubMed Central

Zhao, Huijie; Xu, Wujian

2016-01-01

The polarization patterns of skylight which arise due to the scattering of sunlight in the atmosphere can be used by many insects for deriving compass information. Inspired by insects’ polarized light compass, scientists have developed a new kind of navigation method. One of the key techniques in this method is the polarimetric sensor which is used to acquire direction information from skylight. In this paper, a polarization navigation sensor is proposed which imitates the working principles of the polarization vision systems of insects. We introduce the optical design and mathematical model of the sensor. In addition, a calibration method based on variable substitution and non-linear curve fitting is proposed. The results obtained from the outdoor experiments provide support for the feasibility and precision of the sensor. The sensor’s signal processing can be well described using our mathematical model. A relatively high degree of accuracy in polarization measurement can be obtained without any error compensation. PMID:27527171

Robust Takagi-Sugeno fuzzy control for fractional order hydro-turbine governing system.

PubMed

Wang, Bin; Xue, Jianyi; Wu, Fengjiao; Zhu, Delan

2016-11-01

A robust fuzzy control method for fractional order hydro-turbine governing system (FOHGS) in the presence of random disturbances is investigated in this paper. Firstly, the mathematical model of FOHGS is introduced, and based on Takagi-Sugeno (T-S) fuzzy rules, the generalized T-S fuzzy model of FOHGS is presented. Secondly, based on fractional order Lyapunov stability theory, a novel T-S fuzzy control method is designed for the stability control of FOHGS. Thirdly, the relatively loose sufficient stability condition is acquired, which could be transformed into a group of linear matrix inequalities (LMIs) via Schur complement as well as the strict mathematical derivation is given. Furthermore, the control method could resist random disturbances, which shows the good robustness. Simulation results indicate the designed fractional order T-S fuzzy control scheme works well compared with the existing method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

A Case Study of Teachers' Development of Well-Structured Mathematical Modelling Activities

ERIC Educational Resources Information Center

Stohlmann, Micah; Maiorca, Cathrine; Allen, Charlie

2017-01-01

This case study investigated how three teachers developed mathematical modelling activities integrated with content standards through participation in a course on mathematical modelling. The class activities involved experiencing a mathematical modelling activity, reading and rating example mathematical modelling activities, reading articles about…

A Person-Oriented Approach: Methods for Today and Methods for Tomorrow

ERIC Educational Resources Information Center

Bergman, Lars R.; El-Khouri, Bassam M.

2003-01-01

Methodological implications of a person-oriented, holistic-interactionistic perspective in research on individual development are outlined, desirable properties of a mathematical model of a phenomenon are discussed, and selected methods for carrying out person-oriented research are briefly overviewed. These methods are: (1) the classificatory…

Mathematical simulation of bearing ring grinding process

NASA Astrophysics Data System (ADS)

Koltunov, I. I.; Gorbunova, T. N.; Tumanova, M. B.

2018-03-01

The paper suggests the method of forming a solid finite element model of the bearing ring. Implementation of the model allowed one to evaluate the influence of the inner cylindrical surface grinding scheme on the ring shape error.

Use of open-ended problems as the basis for the mathematical creativity growth disclosure of student

NASA Astrophysics Data System (ADS)

Suyitno, A.; Suyitno, H.; Rochmad; Dwijanto

2018-03-01

Mathematical creativity is the essence of learning in mathematics. However, mathematical creativity had not yet grown among students. Means there was a gap between needs and reality. This gap must be bridged through by scientific studies, and there were novelty findings, namely the discovery of stages to cultivate of Mathematical Creativity. The problem formulation: How to use of open-ended problems as the basis for the mathematical creativity growth disclosure of student? The goal was to use of open issues as the basis for the mathematical creativity growth disclosure of student. Research method with a qualitative approach. After data was collected then activity in data analysis, include data reduction, data presentation, data interpretation, and conclusion/verification. The results of the research: After the learning by applying the modification of RTTW learning model, then the students were trained to do the open-ended problems and by looking at the UTS and UAS values then qualitatively the results: (1) There was a significant increase of the student's final score. (2) The category of the growth of mathematical creativity of students, the Very Good there were three students, the Good there were six students, There were 17 students, and there were six students. The validation of these results was reinforced by interviews and triangulation. (3) Stage to cultivate mathematical creativity: lecturers should need to provide inputs on student work; Apply an appropriate learning model, and train students to work on the continuing problems.

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.

Mathematical Modelling Approach in Mathematics Education

ERIC Educational Resources Information Center

Arseven, Ayla

2015-01-01

The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…

Mathematical Modelling in the Junior Secondary Years: An Approach Incorporating Mathematical Technology

ERIC Educational Resources Information Center

Lowe, James; Carter, Merilyn; Cooper, Tom

2018-01-01

Mathematical models are conceptual processes that use mathematics to describe, explain, and/or predict the behaviour of complex systems. This article is written for teachers of mathematics in the junior secondary years (including out-of-field teachers of mathematics) who may be unfamiliar with mathematical modelling, to explain the steps involved…

Mathematics teachers' conceptions about modelling activities and its reflection on their beliefs about mathematics

NASA Astrophysics Data System (ADS)

Shahbari, Juhaina Awawdeh

2018-07-01

The current study examines whether the engagement of mathematics teachers in modelling activities and subsequent changes in their conceptions about these activities affect their beliefs about mathematics. The sample comprised 52 mathematics teachers working in small groups in four modelling activities. The data were collected from teachers' Reports about features of each activity, interviews and questionnaires on teachers' beliefs about mathematics. The findings indicated changes in teachers' conceptions about the modelling activities. Most teachers referred to the first activity as a mathematical problem but emphasized only the mathematical notions or the mathematical operations in the modelling process; changes in their conceptions were gradual. Most of the teachers referred to the fourth activity as a mathematical problem and emphasized features of the whole modelling process. The results of the interviews indicated that changes in the teachers' conceptions can be attributed to structure of the activities, group discussions, solution paths and elicited models. These changes about modelling activities were reflected in teachers' beliefs about mathematics. The quantitative findings indicated that the teachers developed more constructive beliefs about mathematics after engagement in the modelling activities and that the difference was significant, however there was no significant difference regarding changes in their traditional beliefs.

Mathematical modeling of heat treatment processes conserving biological activity of plant bioresources

NASA Astrophysics Data System (ADS)

Rodionova, N. S.; Popov, E. S.; Pozhidaeva, E. A.; Pynzar, S. S.; Ryaskina, L. O.

2018-05-01

The aim of this study is to develop a mathematical model of the heat exchange process of LT-processing to estimate the dynamics of temperature field changes and optimize the regime parameters, due to the non-stationarity process, the physicochemical and thermophysical properties of food systems. The application of LT-processing, based on the use of low-temperature modes in thermal culinary processing of raw materials with preliminary vacuum packaging in a polymer heat- resistant film is a promising trend in the development of technics and technology in the catering field. LT-processing application of food raw materials guarantees the preservation of biologically active substances in food environments, which are characterized by a certain thermolability, as well as extend the shelf life and high consumer characteristics of food systems that are capillary-porous bodies. When performing the mathematical modeling of the LT-processing process, the packet of symbolic mathematics “Maple” was used, as well as the mathematical packet flexPDE that uses the finite element method for modeling objects with distributed parameters. The processing of experimental results was evaluated with the help of the developed software in the programming language Python 3.4. To calculate and optimize the parameters of the LT processing process of polycomponent food systems, the differential equation of non-stationary thermal conductivity was used, the solution of which makes it possible to identify the temperature change at any point of the solid at different moments. The present study specifies data on the thermophysical characteristics of the polycomponent food system based on plant raw materials, with the help of which the physico-mathematical model of the LT- processing process has been developed. The obtained mathematical model allows defining of the dynamics of the temperature field in different sections of the LT-processed polycomponent food systems on the basis of calculating the evolution profiles of temperature fields, which enable one to analyze the efficiency of the regime parameters of heat treatment.

Ordinary differential equations with applications in molecular biology.

PubMed

Ilea, M; Turnea, M; Rotariu, M

2012-01-01

Differential equations are of basic importance in molecular biology mathematics because many biological laws and relations appear mathematically in the form of a differential equation. In this article we presented some applications of mathematical models represented by ordinary differential equations in molecular biology. The vast majority of quantitative models in cell and molecular biology are formulated in terms of ordinary differential equations for the time evolution of concentrations of molecular species. Assuming that the diffusion in the cell is high enough to make the spatial distribution of molecules homogenous, these equations describe systems with many participating molecules of each kind. We propose an original mathematical model with small parameter for biological phospholipid pathway. All the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. If we reduce the size of the solution region the same small epsilon will result in a different condition number. It is clear that the solution for a smaller region is less difficult. We introduce the mathematical technique known as boundary function method for singular perturbation system. In this system, the small parameter is an asymptotic variable, different from the independent variable. In general, the solutions of such equations exhibit multiscale phenomena. Singularly perturbed problems form a special class of problems containing a small parameter which may tend to zero. Many molecular biology processes can be quantitatively characterized by ordinary differential equations. Mathematical cell biology is a very active and fast growing interdisciplinary area in which mathematical concepts, techniques, and models are applied to a variety of problems in developmental medicine and bioengineering. Among the different modeling approaches, ordinary differential equations (ODE) are particularly important and have led to significant advances. Ordinary differential equations are used to model biological processes on various levels ranging from DNA molecules or biosynthesis phospholipids on the cellular level.

Evaluating the efficacies of Maximum Tolerated Dose and metronomic chemotherapies: A mathematical approach

NASA Astrophysics Data System (ADS)

Guiraldello, Rafael T.; Martins, Marcelo L.; Mancera, Paulo F. A.

2016-08-01

We present a mathematical model based on partial differential equations that is applied to understand tumor development and its response to chemotherapy. Our primary aim is to evaluate comparatively the efficacies of two chemotherapeutic protocols, Maximum Tolerated Dose (MTD) and metronomic, as well as two methods of drug delivery. Concerning therapeutic outcomes, the metronomic protocol proves more effective in prolonging the patient's life than MTD. Moreover, a uniform drug delivery method combined with the metronomic protocol is the most efficient strategy to reduce tumor density.

Mathematic modeling of the method of measurement relative dielectric permeability

NASA Astrophysics Data System (ADS)

Plotnikova, I. V.; Chicherina, N. V.; Stepanov, A. B.

2018-05-01

The method of measuring relative permittivity’s and the position of the interface between layers of a liquid medium is considered in the article. An electric capacitor is a system consisting of two conductors that are separated by a dielectric layer. It is mathematically proven that at any given time it is possible to obtain the values of the relative permittivity in the layers of the liquid medium and to determine the level of the interface between the layers of the two-layer liquid. The estimation of measurement errors is made.

The reliability of nonlinear least-squares algorithm for data analysis of neural response activity during sinusoidal rotational stimulation in semicircular canal neurons.

PubMed

Ren, Pengyu; Li, Bowen; Dong, Shiyao; Chen, Lin; Zhang, Yuelin

2018-01-01

Although many mathematical methods were used to analyze the neural activity under sinusoidal stimulation within linear response range in vestibular system, the reliabilities of these methods are still not reported, especially in nonlinear response range. Here we chose nonlinear least-squares algorithm (NLSA) with sinusoidal model to analyze the neural response of semicircular canal neurons (SCNs) during sinusoidal rotational stimulation (SRS) over a nonlinear response range. Our aim was to acquire a reliable mathematical method for data analysis under SRS in vestibular system. Our data indicated that the reliability of this method in an entire SCNs population was quite satisfactory. However, the reliability was strongly negatively depended on the neural discharge regularity. In addition, stimulation parameters were the vital impact factors influencing the reliability. The frequency had a significant negative effect but the amplitude had a conspicuous positive effect on the reliability. Thus, NLSA with sinusoidal model resulted a reliable mathematical tool for data analysis of neural response activity under SRS in vestibular system and more suitable for those under the stimulation with low frequency but high amplitude, suggesting that this method can be used in nonlinear response range. This method broke out of the restriction of neural activity analysis under nonlinear response range and provided a solid foundation for future study in nonlinear response range in vestibular system.

The reliability of nonlinear least-squares algorithm for data analysis of neural response activity during sinusoidal rotational stimulation in semicircular canal neurons

PubMed Central

Li, Bowen; Dong, Shiyao; Chen, Lin; Zhang, Yuelin

2018-01-01

Although many mathematical methods were used to analyze the neural activity under sinusoidal stimulation within linear response range in vestibular system, the reliabilities of these methods are still not reported, especially in nonlinear response range. Here we chose nonlinear least-squares algorithm (NLSA) with sinusoidal model to analyze the neural response of semicircular canal neurons (SCNs) during sinusoidal rotational stimulation (SRS) over a nonlinear response range. Our aim was to acquire a reliable mathematical method for data analysis under SRS in vestibular system. Our data indicated that the reliability of this method in an entire SCNs population was quite satisfactory. However, the reliability was strongly negatively depended on the neural discharge regularity. In addition, stimulation parameters were the vital impact factors influencing the reliability. The frequency had a significant negative effect but the amplitude had a conspicuous positive effect on the reliability. Thus, NLSA with sinusoidal model resulted a reliable mathematical tool for data analysis of neural response activity under SRS in vestibular system and more suitable for those under the stimulation with low frequency but high amplitude, suggesting that this method can be used in nonlinear response range. This method broke out of the restriction of neural activity analysis under nonlinear response range and provided a solid foundation for future study in nonlinear response range in vestibular system. PMID:29304173

Symbolic Drawings Reveal Changes in Preservice Teacher Mathematics Attitudes after a Mathematics Methods Course

ERIC Educational Resources Information Center

Rule, Audrey C.; Harrell, Mary H.

2006-01-01

A new method of analyzing mathematics attitudes through symbolic drawings, situated within the field of Jungian-oriented analytical psychology, was applied to 52 preservice elementary teachers before and after a mathematics methods course. In this triangulation mixed methods design study, pretest images related to past mathematics experiences…

Mathematical Methods of Subjective Modeling in Scientific Research: I. The Mathematical and Empirical Basis

NASA Astrophysics Data System (ADS)

Pyt'ev, Yu. P.

2018-01-01

mathematical formalism for subjective modeling, based on modelling of uncertainty, reflecting unreliability of subjective information and fuzziness that is common for its content. The model of subjective judgments on values of an unknown parameter x ∈ X of the model M( x) of a research object is defined by the researcher-modeler as a space1 ( X, p( X), P{I^{\\bar x}}, Be{l^{\\bar x}}) with plausibility P{I^{\\bar x}} and believability Be{l^{\\bar x}} measures, where x is an uncertain element taking values in X that models researcher—modeler's uncertain propositions about an unknown x ∈ X, measures P{I^{\\bar x}}, Be{l^{\\bar x}} model modalities of a researcher-modeler's subjective judgments on the validity of each x ∈ X: the value of P{I^{\\bar x}}(\\tilde x = x) determines how relatively plausible, in his opinion, the equality (\\tilde x = x) is, while the value of Be{l^{\\bar x}}(\\tilde x = x) determines how the inequality (\\tilde x = x) should be relatively believed in. Versions of plausibility Pl and believability Bel measures and pl- and bel-integrals that inherit some traits of probabilities, psychophysics and take into account interests of researcher-modeler groups are considered. It is shown that the mathematical formalism of subjective modeling, unlike "standard" mathematical modeling, •enables a researcher-modeler to model both precise formalized knowledge and non-formalized unreliable knowledge, from complete ignorance to precise knowledge of the model of a research object, to calculate relative plausibilities and believabilities of any features of a research object that are specified by its subjective model M(\\tilde x), and if the data on observations of a research object is available, then it: •enables him to estimate the adequacy of subjective model to the research objective, to correct it by combining subjective ideas and the observation data after testing their consistency, and, finally, to empirically recover the model of a research object.

An Evaluation into the Views of Candidate Mathematics Teachers over "Tablet Computers" to be Applied in Secondary Schools

ERIC Educational Resources Information Center

Aksu, Hasan Hüseyin

2014-01-01

This study aims to investigate, in terms of different variables, the views of prospective Mathematics teachers on tablet computers to be used in schools as an outcome of the Fatih Project, which was initiated by the Ministry of National Education. In the study, scanning model, one of the quantitative research methods, was used. In the population…

Effects of Singapore Model Method with Explicit Instruction on Math Problem Solving Skills of Students at Risk for or Identified with Learning Disabilities

ERIC Educational Resources Information Center

Preston, Angela Irene

2016-01-01

Over the last two decades, students in Singapore consistently scored above students from other nations on the Trends in International Mathematics and Science Study (TIMSS; Provasnik et al., 2012). In contrast, students in the United States have not performed as well on international and national mathematics assessments and students with…

The Efforts to Improve Mathematics Learning Achievement Results of High School Students as Required by Competency-Based Curriculum and Lesson Level-Based Curriculum

ERIC Educational Resources Information Center

Sidabutar, Ropinus

2016-01-01

The research was aimed to investigate the effect of various, innovated teaching models to improved the student's achievement in various topic in Mathematics. The study was conduct experiment by using innovated teaching with contextual, media and web which are the compared. with conventional teaching method. The result showed the innovation in the…

Study on China’s Earthquake Prediction by Mathematical Analysis and its Application in Catastrophe Insurance

NASA Astrophysics Data System (ADS)

Jianjun, X.; Bingjie, Y.; Rongji, W.

2018-03-01

The purpose of this paper was to improve catastrophe insurance level. Firstly, earthquake predictions were carried out using mathematical analysis method. Secondly, the foreign catastrophe insurances’ policies and models were compared. Thirdly, the suggestions on catastrophe insurances to China were discussed. The further study should be paid more attention on the earthquake prediction by introducing big data.

The Equation, the Whole Equation, and Nothing but the Equation! One Approach to the Teaching of Linear Equations.

ERIC Educational Resources Information Center

Pirie, Susan E. B.; Martin, Lyndon

1997-01-01

Presents the results of a case study which looked at the mathematics classroom of one teacher trying to teach mathematics with meaning to pupils or lower ability at the secondary level. Contrasts methods of teaching linear equations to a variety of ability levels and uses the Pirie-Kieren model to account for the successful growth in understanding…

On continuous and discontinuous approaches for modeling groundwater flow in heterogeneous media using the Numerical Manifold Method: Model development and comparison

NASA Astrophysics Data System (ADS)

Hu, Mengsu; Wang, Yuan; Rutqvist, Jonny

2015-06-01

One major challenge in modeling groundwater flow within heterogeneous geological media is that of modeling arbitrarily oriented or intersected boundaries and inner material interfaces. The Numerical Manifold Method (NMM) has recently emerged as a promising method for such modeling, in its ability to handle boundaries, its flexibility in constructing physical cover functions (continuous or with gradient jump), its meshing efficiency with a fixed mathematical mesh (covers), its convenience for enhancing approximation precision, and its integration precision, achieved by simplex integration. In this paper, we report on developing and comparing two new approaches for boundary constraints using the NMM, namely a continuous approach with jump functions and a discontinuous approach with Lagrange multipliers. In the discontinuous Lagrange multiplier method (LMM), the material interfaces are regarded as discontinuities which divide mathematical covers into different physical covers. We define and derive stringent forms of Lagrange multipliers to link the divided physical covers, thus satisfying the continuity requirement of the refraction law. In the continuous Jump Function Method (JFM), the material interfaces are regarded as inner interfaces contained within physical covers. We briefly define jump terms to represent the discontinuity of the head gradient across an interface to satisfy the refraction law. We then make a theoretical comparison between the two approaches in terms of global degrees of freedom, treatment of multiple material interfaces, treatment of small area, treatment of moving interfaces, the feasibility of coupling with mechanical analysis and applicability to other numerical methods. The newly derived boundary-constraint approaches are coded into a NMM model for groundwater flow analysis, and tested for precision and efficiency on different simulation examples. We first test the LMM for a Dirichlet boundary and then test both LMM and JFM for an idealized heterogeneous model, comparing the numerical results with analytical solutions. Then we test both approaches for a heterogeneous model and compare the results of hydraulic head and specific discharge. We show that both approaches are suitable for modeling material boundaries, considering high accuracy for the boundary constraints, the capability to deal with arbitrarily oriented or complexly intersected boundaries, and their efficiency using a fixed mathematical mesh.

Mathematical modelling of risk reduction in reinsurance

NASA Astrophysics Data System (ADS)

Balashov, R. B.; Kryanev, A. V.; Sliva, D. E.

2017-01-01

The paper presents a mathematical model of efficient portfolio formation in the reinsurance markets. The presented approach provides the optimal ratio between the expected value of return and the risk of yield values below a certain level. The uncertainty in the return values is conditioned by use of expert evaluations and preliminary calculations, which result in expected return values and the corresponding risk levels. The proposed method allows for implementation of computationally simple schemes and algorithms for numerical calculation of the numerical structure of the efficient portfolios of reinsurance contracts of a given insurance company.

Mathematical modeling of heat transfer problems in the permafrost

NASA Astrophysics Data System (ADS)

Gornov, V. F.; Stepanov, S. P.; Vasilyeva, M. V.; Vasilyev, V. I.

2014-11-01

In this work we present results of numerical simulation of three-dimensional temperature fields in soils for various applied problems: the railway line in the conditions of permafrost for different geometries, the horizontal tunnel underground storage and greenhouses of various designs in the Far North. Mathematical model of the process is described by a nonstationary heat equation with phase transitions of pore water. The numerical realization of the problem is based on the finite element method using a library of scientific computing FEniCS. For numerical calculations we use high-performance computing systems.

The electromagnetic pendulum in quickly changing magnetic field of constant intensity

NASA Astrophysics Data System (ADS)

Rodyukov, F. F.; Shepeljavyi, A. I.

2018-05-01

The Lagrange-Maxwell equations for the pendulum in the form of a conductive frame, which is suspended in a uniform sinusoidal electromagnetic field of constant intensity, are obtained. The procedure for obtaining simplified mathematical models by a traditional method of separating fast and slow motions with subsiquent averaging a fast time is used. It is shown that this traditional approach may lead to inappropriate mathematical models. Suggested ways on how this can be avoided for the case are considered. The main statements by numerical experiments are illustrated.

Extreme-Scale Bayesian Inference for Uncertainty Quantification of Complex Simulations

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

Biros, George

Uncertainty quantification (UQ)—that is, quantifying uncertainties in complex mathematical models and their large-scale computational implementations—is widely viewed as one of the outstanding challenges facing the field of CS&E over the coming decade. The EUREKA project set to address the most difficult class of UQ problems: those for which both the underlying PDE model as well as the uncertain parameters are of extreme scale. In the project we worked on these extreme-scale challenges in the following four areas: 1. Scalable parallel algorithms for sampling and characterizing the posterior distribution that exploit the structure of the underlying PDEs and parameter-to-observable map. Thesemore » include structure-exploiting versions of the randomized maximum likelihood method, which aims to overcome the intractability of employing conventional MCMC methods for solving extreme-scale Bayesian inversion problems by appealing to and adapting ideas from large-scale PDE-constrained optimization, which have been very successful at exploring high-dimensional spaces. 2. Scalable parallel algorithms for construction of prior and likelihood functions based on learning methods and non-parametric density estimation. Constructing problem-specific priors remains a critical challenge in Bayesian inference, and more so in high dimensions. Another challenge is construction of likelihood functions that capture unmodeled couplings between observations and parameters. We will create parallel algorithms for non-parametric density estimation using high dimensional N-body methods and combine them with supervised learning techniques for the construction of priors and likelihood functions. 3. Bayesian inadequacy models, which augment physics models with stochastic models that represent their imperfections. The success of the Bayesian inference framework depends on the ability to represent the uncertainty due to imperfections of the mathematical model of the phenomena of interest. This is a central challenge in UQ, especially for large-scale models. We propose to develop the mathematical tools to address these challenges in the context of extreme-scale problems. 4. Parallel scalable algorithms for Bayesian optimal experimental design (OED). Bayesian inversion yields quantified uncertainties in the model parameters, which can be propagated forward through the model to yield uncertainty in outputs of interest. This opens the way for designing new experiments to reduce the uncertainties in the model parameters and model predictions. Such experimental design problems have been intractable for large-scale problems using conventional methods; we will create OED algorithms that exploit the structure of the PDE model and the parameter-to-output map to overcome these challenges. Parallel algorithms for these four problems were created, analyzed, prototyped, implemented, tuned, and scaled up for leading-edge supercomputers, including UT-Austin’s own 10 petaflops Stampede system, ANL’s Mira system, and ORNL’s Titan system. While our focus is on fundamental mathematical/computational methods and algorithms, we will assess our methods on model problems derived from several DOE mission applications, including multiscale mechanics and ice sheet dynamics.« less

Mathematical model of silicon smelting process basing on pelletized charge from technogenic raw materials

NASA Astrophysics Data System (ADS)

Nemchinova, N. V.; Tyutrin, A. A.; Salov, V. M.

2018-03-01

The silicon production process in the electric arc reduction furnaces (EAF) is studied using pelletized charge as an additive to the standard on the basis of the generated mathematical model. The results obtained due to the model will contribute to the analysis of the charge components behavior during melting with the achievement of optimum final parameters of the silicon production process. The authors proposed using technogenic waste as a raw material for the silicon production in a pelletized form using liquid glass and aluminum production dust from the electrostatic precipitators as a binder. The method of mathematical modeling with the help of the ‘Selector’ software package was used as a basis for the theoretical study. A model was simulated with the imitation of four furnace temperature zones and a crystalline silicon phase (25 °C). The main advantage of the created model is the ability to analyze the behavior of all burden materials (including pelletized charge) in the carbothermic process. The behavior analysis is based on the thermodynamic probability data of the burden materials interactions in the carbothermic process. The model accounts for 17 elements entering the furnace with raw materials, electrodes and air. The silicon melt, obtained by the modeling, contained 91.73 % wt. of the target product. The simulation results showed that in the use of the proposed combined charge, the recovery of silicon reached 69.248 %, which is in good agreement with practical data. The results of the crystalline silicon chemical composition modeling are compared with the real silicon samples of chemical analysis data, which showed the results of convergence. The efficiency of the mathematical modeling methods in the studying of the carbothermal silicon obtaining process with complex interphase transformations and the formation of numerous intermediate compounds using a pelletized charge as an additive to the traditional one is shown.

The Relationship of Mathematics Anxiety and Mathematical Knowledge to the Learning of Mathematical Pedagogy by Preservice Elementary Teachers.

ERIC Educational Resources Information Center

Battista, Michael T.

1986-01-01

Examined how preservice elementary teachers' (N=38) mathematical knowledge and mathematics anxiety affect their success in a mathematics methods course. Also examined the hypothesis that a mathematics methods course can reduce the mathematics anxiety of these teachers. One finding is that mathematics anxiety does not inhibit their learning of…

The 24-Hour Mathematical Modeling Challenge

ERIC Educational Resources Information Center

Galluzzo, Benjamin J.; Wendt, Theodore J.

2015-01-01

Across the mathematics curriculum there is a renewed emphasis on applications of mathematics and on mathematical modeling. Providing students with modeling experiences beyond the ordinary classroom setting remains a challenge, however. In this article, we describe the 24-hour Mathematical Modeling Challenge, an extracurricular event that exposes…

Quantifying Aluminum Crystal Size Part 2: The Model-Development Sequence

ERIC Educational Resources Information Center

Hjalmarson, Margret; Diefes-Dux, Heidi A.; Bowman, Keith; Zawojewski, Judith S.

2006-01-01

We have designed model-development sequences using a common context to provide authentic problem-solving experiences for first-year students. The model-development sequence takes a model-eliciting activity a step further by engaging students in the exploration and adaptation of a mathematical model (e.g., procedure, algorithm, method) for solving…

Runge-Kutta method for wall shear stress of blood flow in stenosed artery

NASA Astrophysics Data System (ADS)

Awaludin, Izyan Syazana; Ahmad, Rokiah@Rozita

2014-06-01

A mathematical model of blood flow through stenotic artery is considered. A stenosis is defined as the partial occlusion of the blood vessels due to the accumulation of cholesterols, fats and the abnormal growth of tissue on the artery walls. The development of stenosis in the artery is one of the factors that cause problem in blood circulation system. This study was conducted to determine the wall shear stress of blood flow in stenosed artery. Modified mathematical model is used to analyze the relationship of the wall shear stress versus the length and height of stenosis. The existing models that have been created by previous researchers are solved using fourth order Runge-Kutta method. Numerical results show that the wall shear stress is proportionate to the length and height of stenosis.

Optimal descriptor as a translator of eclectic data into endpoint prediction: mutagenicity of fullerene as a mathematical function of conditions.

PubMed

Toropov, Andrey A; Toropova, Alla P

2014-06-01

The experimental data on the bacterial reverse mutation test on C60 nanoparticles (TA100) is examined as an endpoint. By means of the optimal descriptors calculated with the Monte Carlo method a mathematical model of the endpoint has been built up. The model is the mathematical function of (i) dose (g/plate); (ii) metabolic activation (i.e. with S9 mix or without S9 mix); and (iii) illumination (i.e. dark or irradiation). The statistical quality of the model is the following: n=10, r(2)=0.7549, q(2)=0.5709, s=7.67, F=25 (Training set); n=5, r(2)=0.8987, s=18.4 (Calibration set); and n=5, r(2)=0.6968, s=10.9 (Validation set). Copyright © 2013 Elsevier Ltd. All rights reserved.

Study of Adaptive Mathematical Models for Deriving Automated Pilot Performance Measurement Techniques. Volume I. Model Development.

ERIC Educational Resources Information Center

Connelly, Edward A.; And Others

A new approach to deriving human performance measures and criteria for use in automatically evaluating trainee performance is documented in this report. The ultimate application of the research is to provide methods for automatically measuring pilot performance in a flight simulator or from recorded in-flight data. An efficient method of…

Resampling and Distribution of the Product Methods for Testing Indirect Effects in Complex Models

ERIC Educational Resources Information Center

Williams, Jason; MacKinnon, David P.

2008-01-01

Recent advances in testing mediation have found that certain resampling methods and tests based on the mathematical distribution of 2 normal random variables substantially outperform the traditional "z" test. However, these studies have primarily focused only on models with a single mediator and 2 component paths. To address this limitation, a…

Methods and Models for the Construction of Weakly Parallel Tests. Research Report 90-4.

ERIC Educational Resources Information Center

Adema, Jos J.

Methods are proposed for the construction of weakly parallel tests, that is, tests with the same test information function. A mathematical programing model for constructing tests with a prespecified test information function and a heuristic for assigning items to tests such that their information functions are equal play an important role in the…

Estimating Sobol Sensitivity Indices Using Correlations

EPA Science Inventory

Sensitivity analysis is a crucial tool in the development and evaluation of complex mathematical models. Sobol's method is a variance-based global sensitivity analysis technique that has been applied to computational models to assess the relative importance of input parameters on...

Proceedings of the 3rd Annual SCOLE Workshop

NASA Technical Reports Server (NTRS)

Taylor, Lawrence W., Jr. (Compiler)

1987-01-01

Topics addressed include: modeling and controlling the Spacecraft Control Laboratory Experiment (SCOLE) configurations; slewing maneuvers; mathematical models; vibration damping; gravitational effects; structural dynamics; finite element method; distributed parameter system; on-line pulse control; stability augmentation; and stochastic processes.

International Energy Module - NEMS Documentation

EIA Publications

2014-01-01

Summarizes the overall structure of the International Energy Model and its interface with other NEMS modules, mathematical specifications of behavioral relationships, and data sources and estimation methods.

Deflection angle detecting system for the large-angle and high-linearity fast steering mirror using quadrant detector

NASA Astrophysics Data System (ADS)

Ni, Yingxue; Wu, Jiabin; San, Xiaogang; Gao, Shijie; Ding, Shaohang; Wang, Jing; Wang, Tao

2018-02-01

A deflection angle detecting system (DADS) using a quadrant detector (QD) is developed to achieve the large deflection angle and high linearity for the fast steering mirror (FSM). The mathematical model of the DADS is established by analyzing the principle of position detecting and error characteristics of the QD. Based on this mathematical model, the method of optimizing deflection angle and linearity of FSM is demonstrated, which is proved feasible by simulation and experimental results. Finally, a QD-based FSM is designed and tested. The results show that it achieves 0.72% nonlinearity, ±2.0 deg deflection angle, and 1.11-μrad resolution. Therefore, the application of this method will be beneficial to design the FSM.

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.

Mathematical models for exploring different aspects of genotoxicity and carcinogenicity databases.

PubMed

Benigni, R; Giuliani, A

1991-12-01

One great obstacle to understanding and using the information contained in the genotoxicity and carcinogenicity databases is the very size of such databases. Their vastness makes them difficult to read; this leads to inadequate exploitation of the information, which becomes costly in terms of time, labor, and money. In its search for adequate approaches to the problem, the scientific community has, curiously, almost entirely neglected an existent series of very powerful methods of data analysis: the multivariate data analysis techniques. These methods were specifically designed for exploring large data sets. This paper presents the multivariate techniques and reports a number of applications to genotoxicity problems. These studies show how biology and mathematical modeling can be combined and how successful this combination is.

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 Relationship between Students' Performance on Conventional Standardized Mathematics Assessments and Complex Mathematical Modeling Problems

ERIC Educational Resources Information Center

Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.

2016-01-01

Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…

Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics

ERIC Educational Resources Information Center

Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.

2016-01-01

Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…

Mathematical and Computational Modeling for Tumor Virotherapy with Mediated Immunity.

PubMed

Timalsina, Asim; Tian, Jianjun Paul; Wang, Jin

2017-08-01

We propose a new mathematical modeling framework based on partial differential equations to study tumor virotherapy with mediated immunity. The model incorporates both innate and adaptive immune responses and represents the complex interaction among tumor cells, oncolytic viruses, and immune systems on a domain with a moving boundary. Using carefully designed computational methods, we conduct extensive numerical simulation to the model. The results allow us to examine tumor development under a wide range of settings and provide insight into several important aspects of the virotherapy, including the dependence of the efficacy on a few key parameters and the delay in the adaptive immunity. Our findings also suggest possible ways to improve the virotherapy for tumor treatment.

A mathematical model of the maximum power density attainable in an alkaline hydrogen/oxygen fuel cell

NASA Technical Reports Server (NTRS)

Kimble, Michael C.; White, Ralph E.

1991-01-01

A mathematical model of a hydrogen/oxygen alkaline fuel cell is presented that can be used to predict the polarization behavior under various power loads. The major limitations to achieving high power densities are indicated and methods to increase the maximum attainable power density are suggested. The alkaline fuel cell model describes the phenomena occurring in the solid, liquid, and gaseous phases of the anode, separator, and cathode regions based on porous electrode theory applied to three phases. Fundamental equations of chemical engineering that describe conservation of mass and charge, species transport, and kinetic phenomena are used to develop the model by treating all phases as a homogeneous continuum.

On two mathematical problems of canonical quantization. IV

NASA Astrophysics Data System (ADS)

Kirillov, A. I.

1992-11-01

A method for solving the problem of reconstructing a measure beginning with its logarithmic derivative is presented. The method completes that of solving the stochastic differential equation via Dirichlet forms proposed by S. Albeverio and M. Rockner. As a result one obtains the mathematical apparatus for the stochastic quantization. The apparatus is applied to prove the existence of the Feynman-Kac measure of the sine-Gordon and λφ2n/(1 + K2φ2n)-models. A synthesis of both mathematical problems of canonical quantization is obtained in the form of a second-order martingale problem for vacuum noise. It is shown that in stochastic mechanics the martingale problem is an analog of Newton's second law and enables us to find the Nelson's stochastic trajectories without determining the wave functions.

Dynamic Modeling of Cell-Free Biochemical Networks Using Effective Kinetic Models

DTIC Science & Technology

2015-03-16

sensitivity value was the maximum uncertainty in that value estimated by the Sobol method. 2.4. Global Sensitivity Analysis of the Reduced Order Coagulation...sensitivity analysis, using the variance-based method of Sobol , to estimate which parameters controlled the performance of the reduced order model [69]. We...Environment. Comput. Sci. Eng. 2007, 9, 90–95. 69. Sobol , I. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates

Mathematical Modeling: A Bridge to STEM Education

ERIC Educational Resources Information Center

Kertil, Mahmut; Gurel, Cem

2016-01-01

The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may…

METHODS FOR MODELING PARTICLE DEPOSITION AS A FUNCTION OF AGE. (R827352C004)

EPA Science Inventory

The purpose of this paper is to review the application of mathematical models of inhaled particle deposition to people of various ages. The basic considerations of aerosol physics, biological characteristics and model structure are presented along with limitations inherent in ...

Computational Evaluation of the Traceback Method

ERIC Educational Resources Information Center

Kol, Sheli; Nir, Bracha; Wintner, Shuly

2014-01-01

Several models of language acquisition have emerged in recent years that rely on computational algorithms for simulation and evaluation. Computational models are formal and precise, and can thus provide mathematically well-motivated insights into the process of language acquisition. Such models are amenable to robust computational evaluation,…

Modeling and optimization of dough recipe for breadsticks

NASA Astrophysics Data System (ADS)

Krivosheev, A. Yu; Ponomareva, E. I.; Zhuravlev, A. A.; Lukina, S. I.; Alekhina, N. N.

2018-05-01

During the work, the authors studied the combined effect of non-traditional raw materials on indicators of quality breadsticks, mathematical methods of experiment planning were applied. The main factors chosen were the dosages of flaxseed flour and grape seed oil. The output parameters were the swelling factor of the products and their strength. Optimization of the formulation composition of the dough for bread sticks was carried out by experimental- statistical methods. As a result of the experiment, mathematical models were constructed in the form of regression equations, adequately describing the process of studies. The statistical processing of the experimental data was carried out by the criteria of Student, Cochran and Fisher (with a confidence probability of 0.95). A mathematical interpretation of the regression equations was given. Optimization of the formulation of the dough for bread sticks was carried out by the method of uncertain Lagrange multipliers. The rational values of the factors were determined: the dosage of flaxseed flour - 14.22% and grape seed oil - 7.8%, ensuring the production of products with the best combination of swelling ratio and strength. On the basis of the data obtained, a recipe and a method for the production of breadsticks "Idea" were proposed (TU (Russian Technical Specifications) 9117-443-02068106-2017).

Optimization Research of Generation Investment Based on Linear Programming Model

NASA Astrophysics Data System (ADS)

Wu, Juan; Ge, Xueqian

Linear programming is an important branch of operational research and it is a mathematical method to assist the people to carry out scientific management. GAMS is an advanced simulation and optimization modeling language and it will combine a large number of complex mathematical programming, such as linear programming LP, nonlinear programming NLP, MIP and other mixed-integer programming with the system simulation. In this paper, based on the linear programming model, the optimized investment decision-making of generation is simulated and analyzed. At last, the optimal installed capacity of power plants and the final total cost are got, which provides the rational decision-making basis for optimized investments.

Mathematic model analysis of Gaussian beam propagation through an arbitrary thickness random phase screen.

PubMed

Tian, Yuzhen; Guo, Jin; Wang, Rui; Wang, Tingfeng

2011-09-12

In order to research the statistical properties of Gaussian beam propagation through an arbitrary thickness random phase screen for adaptive optics and laser communication application in the laboratory, we establish mathematic models of statistical quantities, which are based on the Rytov method and the thin phase screen model, involved in the propagation process. And the analytic results are developed for an arbitrary thickness phase screen based on the Kolmogorov power spectrum. The comparison between the arbitrary thickness phase screen and the thin phase screen shows that it is more suitable for our results to describe the generalized case, especially the scintillation index.

A review of methods for predicting air pollution dispersion

NASA Technical Reports Server (NTRS)

Mathis, J. J., Jr.; Grose, W. L.

1973-01-01

Air pollution modeling, and problem areas in air pollution dispersion modeling were surveyed. Emission source inventory, meteorological data, and turbulent diffusion are discussed in terms of developing a dispersion model. Existing mathematical models of urban air pollution, and highway and airport models are discussed along with their limitations. Recommendations for improving modeling capabilities are included.

Modelling the effect of structural QSAR parameters on skin penetration using genetic programming

NASA Astrophysics Data System (ADS)

Chung, K. K.; Do, D. Q.

2010-09-01

In order to model relationships between chemical structures and biological effects in quantitative structure-activity relationship (QSAR) data, an alternative technique of artificial intelligence computing—genetic programming (GP)—was investigated and compared to the traditional method—statistical. GP, with the primary advantage of generating mathematical equations, was employed to model QSAR data and to define the most important molecular descriptions in QSAR data. The models predicted by GP agreed with the statistical results, and the most predictive models of GP were significantly improved when compared to the statistical models using ANOVA. Recently, artificial intelligence techniques have been applied widely to analyse QSAR data. With the capability of generating mathematical equations, GP can be considered as an effective and efficient method for modelling QSAR data.

The influence of mathematics learning using SAVI approach on junior high school students’ mathematical modelling ability

NASA Astrophysics Data System (ADS)

Khusna, H.; Heryaningsih, N. Y.

2018-01-01

The aim of this research was to examine mathematical modeling ability who learn mathematics by using SAVI approach. This research was a quasi-experimental research with non-equivalent control group designed by using purposive sampling technique. The population of this research was the state junior high school students in Lembang while the sample consisted of two class at 8th grade. The instrument used in this research was mathematical modeling ability. Data analysis of this research was conducted by using SPSS 20 by Windows. The result showed that students’ ability of mathematical modeling who learn mathematics by using SAVI approach was better than students’ ability of mathematical modeling who learn mathematics using conventional learning.

The quest for a new modelling framework in mathematical biology. Comment on "On the interplay between mathematics and biology: Hallmarks towards a new systems biology" by N. Bellomo et al.

NASA Astrophysics Data System (ADS)

Eftimie, Raluca

2015-03-01

One of the main unsolved problems of modern physics is finding a "theory of everything" - a theory that can explain, with the help of mathematics, all physical aspects of the universe. While the laws of physics could explain some aspects of the biology of living systems (e.g., the phenomenological interpretation of movement of cells and animals), there are other aspects specific to biology that cannot be captured by physics models. For example, it is generally accepted that the evolution of a cell-based system is influenced by the activation state of cells (e.g., only activated and functional immune cells can fight diseases); on the other hand, the evolution of an animal-based system can be influenced by the psychological state (e.g., distress) of animals. Therefore, the last 10-20 years have seen also a quest for a "theory of everything"-approach extended to biology, with researchers trying to propose mathematical modelling frameworks that can explain various biological phenomena ranging from ecology to developmental biology and medicine [1,2,6]. The basic idea behind this approach can be found in a few reviews on ecology and cell biology [6,7,9-11], where researchers suggested that due to the parallel between the micro-scale dynamics and the emerging macro-scale phenomena in both cell biology and in ecology, many mathematical methods used for ecological processes could be adapted to cancer modelling [7,9] or to modelling in immunology [11]. However, this approach generally involved the use of different models to describe different biological aspects (e.g., models for cell and animal movement, models for competition between cells or animals, etc.).

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.

Multilevel modeling of damage accumulation processes in metals

NASA Astrophysics Data System (ADS)

Kurmoiartseva, K. A.; Trusov, P. V.; Kotelnikova, N. V.

2017-12-01

To predict the behavior of components and constructions it is necessary to develop the methods and mathematical models which take into account the self-organization of microstructural processes and the strain localization. The damage accumulation processes and the evolution of material properties during deformation are important to take into account. The heterogeneity of the process of damage accumulation is due to the appropriate physical mechanisms at the scale levels, which are lower than the macro-level. The purpose of this work is to develop a mathematical model for analyzing the behavior of polycrystalline materials that allows describing the damage accumulation processes. Fracture is the multistage and multiscale process of the build-up of micro- and mesodefects over the wide range of loading rates. The formation of microcracks by mechanisms is caused by the interactions of the dislocations of different slip systems, barriers, boundaries and the inclusions of the secondary phase. This paper provides the description of some of the most well-known models of crack nucleation and also suggests the structure of a mathematical model based on crystal plasticity and dislocation models of crack nucleation.

Mathematical modeling and simulation of aquatic and aerial animal locomotion

NASA Astrophysics Data System (ADS)

Hou, T. Y.; Stredie, V. G.; Wu, T. Y.

2007-08-01

In this paper, we investigate the locomotion of fish and birds by applying a new unsteady, flexible wing theory that takes into account the strong nonlinear dynamics semi-analytically. We also make extensive comparative study between the new approach and the modified vortex blob method inspired from Chorin's and Krasny's work. We first implement the modified vortex blob method for two examples and then discuss the numerical implementation of the nonlinear analytical mathematical model of Wu. We will demonstrate that Wu's method can capture the nonlinear effects very well by applying it to some specific cases and by comparing with the experiments available. In particular, we apply Wu's method to analyze Wagner's result for a wing abruptly undergoing an increase in incidence angle. Moreover, we study the vorticity generated by a wing in heaving, pitching and bending motion. In both cases, we show that the new method can accurately represent the vortex structure behind a flying wing and its influence on the bound vortex sheet on the wing.

The Modulus of Rupture from a Mathematical Point of View

NASA Astrophysics Data System (ADS)

Quintela, P.; Sánchez, M. T.

2007-04-01

The goal of this work is to present a complete mathematical study about the three-point bending experiments and the modulus of rupture of brittle materials. We will present the mathematical model associated to three-point bending experiments and we will use the asymptotic expansion method to obtain a new formula to calculate the modulus of rupture. We will compare the modulus of rupture of porcelain obtained with the previous formula with that obtained by using the classic theoretical formula. Finally, we will also present one and three-dimensional numerical simulations to compute the modulus of rupture.

Characterizing Topology of Probabilistic Biological Networks.

PubMed

Todor, Andrei; Dobra, Alin; Kahveci, Tamer

2013-09-06

Biological interactions are often uncertain events, that may or may not take place with some probability. Existing studies analyze the degree distribution of biological networks by assuming that all the given interactions take place under all circumstances. This strong and often incorrect assumption can lead to misleading results. Here, we address this problem and develop a sound mathematical basis to characterize networks in the presence of uncertain interactions. We develop a method that accurately describes the degree distribution of such networks. We also extend our method to accurately compute the joint degree distributions of node pairs connected by edges. The number of possible network topologies grows exponentially with the number of uncertain interactions. However, the mathematical model we develop allows us to compute these degree distributions in polynomial time in the number of interactions. It also helps us find an adequate mathematical model using maximum likelihood estimation. Our results demonstrate that power law and log-normal models best describe degree distributions for probabilistic networks. The inverse correlation of degrees of neighboring nodes shows that, in probabilistic networks, nodes with large number of interactions prefer to interact with those with small number of interactions more frequently than expected.

Application of Monte Carlo techniques to optimization of high-energy beam transport in a stochastic environment

NASA Technical Reports Server (NTRS)

Parrish, R. V.; Dieudonne, J. E.; Filippas, T. A.

1971-01-01

An algorithm employing a modified sequential random perturbation, or creeping random search, was applied to the problem of optimizing the parameters of a high-energy beam transport system. The stochastic solution of the mathematical model for first-order magnetic-field expansion allows the inclusion of state-variable constraints, and the inclusion of parameter constraints allowed by the method of algorithm application eliminates the possibility of infeasible solutions. The mathematical model and the algorithm were programmed for a real-time simulation facility; thus, two important features are provided to the beam designer: (1) a strong degree of man-machine communication (even to the extent of bypassing the algorithm and applying analog-matching techniques), and (2) extensive graphics for displaying information concerning both algorithm operation and transport-system behavior. Chromatic aberration was also included in the mathematical model and in the optimization process. Results presented show this method as yielding better solutions (in terms of resolutions) to the particular problem than those of a standard analog program as well as demonstrating flexibility, in terms of elements, constraints, and chromatic aberration, allowed by user interaction with both the algorithm and the stochastic model. Example of slit usage and a limited comparison of predicted results and actual results obtained with a 600 MeV cyclotron are given.

Examining spectral properties of Landsat 8 OLI for predicting above-ground carbon of Labanan Forest, Berau

NASA Astrophysics Data System (ADS)

Suhardiman, A.; Tampubolon, B. A.; Sumaryono, M.

2018-04-01

Many studies revealed significant correlation between satellite image properties and forest data attributes such as stand volume, biomass or carbon stock. However, further study is still relevant due to advancement of remote sensing technology as well as improvement on methods of data analysis. In this study, the properties of three vegetation indices derived from Landsat 8 OLI were tested upon above-ground carbon stock data from 50 circular sample plots (30-meter radius) from ground survey in PT. Inhutani I forest concession in Labanan, Berau, East Kalimantan. Correlation analysis using Pearson method exhibited a promising results when the coefficient of correlation (r-value) was higher than 0.5. Further regression analysis was carried out to develop mathematical model describing the correlation between sample plots data and vegetation index image using various mathematical models.Power and exponential model were demonstrated a good result for all vegetation indices. In order to choose the most adequate mathematical model for predicting Above-ground Carbon (AGC), the Bayesian Information Criterion (BIC) was applied. The lowest BIC value (i.e. -376.41) shown by Transformed Vegetation Index (TVI) indicates this formula, AGC = 9.608*TVI21.54, is the best predictor of AGC of study area.

Design and Development Computer-Based E-Learning Teaching Material for Improving Mathematical Understanding Ability and Spatial Sense of Junior High School Students

NASA Astrophysics Data System (ADS)

Nurjanah; Dahlan, J. A.; Wibisono, Y.

2017-02-01

This paper aims to make a design and development computer-based e-learning teaching material for improving mathematical understanding ability and spatial sense of junior high school students. Furthermore, the particular aims are (1) getting teaching material design, evaluation model, and intrument to measure mathematical understanding ability and spatial sense of junior high school students; (2) conducting trials computer-based e-learning teaching material model, asessment, and instrument to develop mathematical understanding ability and spatial sense of junior high school students; (3) completing teaching material models of computer-based e-learning, assessment, and develop mathematical understanding ability and spatial sense of junior high school students; (4) resulting research product is teaching materials of computer-based e-learning. Furthermore, the product is an interactive learning disc. The research method is used of this study is developmental research which is conducted by thought experiment and instruction experiment. The result showed that teaching materials could be used very well. This is based on the validation of computer-based e-learning teaching materials, which is validated by 5 multimedia experts. The judgement result of face and content validity of 5 validator shows that the same judgement result to the face and content validity of each item test of mathematical understanding ability and spatial sense. The reliability test of mathematical understanding ability and spatial sense are 0,929 and 0,939. This reliability test is very high. While the validity of both tests have a high and very high criteria.

AIR MONITOR SITING BY OBJECTIVE

EPA Science Inventory

A method is developed whereby measured pollutant concentrations can be used in conjunction with a mathematical air quality model to estimate the full spatial and temporal concentration distributions of the pollutants over a given region. The method is based on the application of ...

Health Risk of Exposure to Atmospheric Pollutant Particles

EPA Science Inventory

In relation to multi-component mixture nature of atmospheric PM, this presentation will discuss methods for estimating the respiratory internal dose by experiment and mathematical modeling, limitations of each method and interpretations of the results in the context of health ris...

Beyond Motivation: Exploring Mathematical Modeling as a Context for Deepening Students' Understandings of Curricular Mathematics

ERIC Educational Resources Information Center

Zbiek, Rose Mary; Conner, Annamarie

2006-01-01

Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical…

An Investigation of Mathematical Modeling with Pre-Service Secondary Mathematics Teachers

ERIC Educational Resources Information Center

Thrasher, Emily Plunkett

2016-01-01

The goal of this thesis was to investigate and enhance our understanding of what occurs while pre-service mathematics teachers engage in a mathematical modeling unit that is broadly based upon mathematical modeling as defined by the Common Core State Standards for Mathematics (National Governors Association Center for Best Practices & Council…

Optimal back-extrapolation method for estimating plasma volume in humans using the indocyanine green dilution method

PubMed Central

2014-01-01

Background The indocyanine green dilution method is one of the methods available to estimate plasma volume, although some researchers have questioned the accuracy of this method. Methods We developed a new, physiologically based mathematical model of indocyanine green kinetics that more accurately represents indocyanine green kinetics during the first few minutes postinjection than what is assumed when using the traditional mono-exponential back-extrapolation method. The mathematical model is used to develop an optimal back-extrapolation method for estimating plasma volume based on simulated indocyanine green kinetics obtained from the physiological model. Results Results from a clinical study using the indocyanine green dilution method in 36 subjects with type 2 diabetes indicate that the estimated plasma volumes are considerably lower when using the traditional back-extrapolation method than when using the proposed back-extrapolation method (mean (standard deviation) plasma volume = 26.8 (5.4) mL/kg for the traditional method vs 35.1 (7.0) mL/kg for the proposed method). The results obtained using the proposed method are more consistent with previously reported plasma volume values. Conclusions Based on the more physiological representation of indocyanine green kinetics and greater consistency with previously reported plasma volume values, the new back-extrapolation method is proposed for use when estimating plasma volume using the indocyanine green dilution method. PMID:25052018

System principles, mathematical models and methods to ensure high reliability of safety systems

NASA Astrophysics Data System (ADS)

Zaslavskyi, V.

2017-04-01

Modern safety and security systems are composed of a large number of various components designed for detection, localization, tracking, collecting, and processing of information from the systems of monitoring, telemetry, control, etc. They are required to be highly reliable in a view to correctly perform data aggregation, processing and analysis for subsequent decision making support. On design and construction phases of the manufacturing of such systems a various types of components (elements, devices, and subsystems) are considered and used to ensure high reliability of signals detection, noise isolation, and erroneous commands reduction. When generating design solutions for highly reliable systems a number of restrictions and conditions such as types of components and various constrains on resources should be considered. Various types of components perform identical functions; however, they are implemented using diverse principles, approaches and have distinct technical and economic indicators such as cost or power consumption. The systematic use of different component types increases the probability of tasks performing and eliminates the common cause failure. We consider type-variety principle as an engineering principle of system analysis, mathematical models based on this principle, and algorithms for solving optimization problems of highly reliable safety and security systems design. Mathematical models are formalized in a class of two-level discrete optimization problems of large dimension. The proposed approach, mathematical models, algorithms can be used for problem solving of optimal redundancy on the basis of a variety of methods and control devices for fault and defects detection in technical systems, telecommunication networks, and energy systems.

Scattering and Diffraction of Elastodynamic Waves in a Concentric Cylindrical Phantom for MR Elastography

PubMed Central

Schwartz, Benjamin L.; Yin, Ziying; Yaşar, Temel K.; Liu, Yifei; Khan, Altaf A.; Ye, Allen Q.; Royston, Thomas J.; Magin, Richard L.

2016-01-01

Aim The focus of this paper is to report on the design and construction of a multiply connected phantom for use in magnetic resonance elasography (MRE)–an imaging technique that allows for the non-invasive visualization of the displacement field throughout an object from externally driven harmonic motion–as well as its inverse modeling with a closed-form analytic solution which is derived herein from first principles. Methods Mathematically, the phantom is described as two infinite concentric circular cylinders with unequal complex shear moduli, harmonically vibrated at the exterior surface in a direction along their common axis. Each concentric cylinder is made of a hydrocolloid with its own specific solute concentration. They are assembled in a multi-step process for which custom scaffolding was designed and built. A customized spin-echo based MR elastography sequence with a sinusoidal motion-sensitizing gradient was used for data acquisition on a 9.4 T Agilent small-animal MR scanner. Complex moduli obtained from the inverse model are used to solve the forward problem with a finite element method. Results Both complex shear moduli show a significant frequency dependence (p < 0.001) in keeping with previous work. Conclusion The novel multiply connected phantom and mathematical model are validated as a viable tool for MRE studies. Significance On a small enough scale much of physiology can be mathematically modeled with basic geometric shapes, e.g. a cylinder representing a blood vessel. This work demonstrates the possibility of elegant mathematical analysis of phantoms specifically designed and carefully constructed for biomedical MRE studies. PMID:26886963

Effective groundwater model calibration: With analysis of data, sensitivities, predictions, and uncertainty

USGS Publications Warehouse

Hill, Mary C.; Tiedeman, Claire

2007-01-01

Methods and guidelines for developing and using mathematical modelsTurn to Effective Groundwater Model Calibration for a set of methods and guidelines that can help produce more accurate and transparent mathematical models. The models can represent groundwater flow and transport and other natural and engineered systems. Use this book and its extensive exercises to learn methods to fully exploit the data on hand, maximize the model's potential, and troubleshoot any problems that arise. Use the methods to perform:Sensitivity analysis to evaluate the information content of dataData assessment to identify (a) existing measurements that dominate model development and predictions and (b) potential measurements likely to improve the reliability of predictionsCalibration to develop models that are consistent with the data in an optimal mannerUncertainty evaluation to quantify and communicate errors in simulated results that are often used to make important societal decisionsMost of the methods are based on linear and nonlinear regression theory.Fourteen guidelines show the reader how to use the methods advantageously in practical situations.Exercises focus on a groundwater flow system and management problem, enabling readers to apply all the methods presented in the text. The exercises can be completed using the material provided in the book, or as hands-on computer exercises using instructions and files available on the text's accompanying Web site.Throughout the book, the authors stress the need for valid statistical concepts and easily understood presentation methods required to achieve well-tested, transparent models. Most of the examples and all of the exercises focus on simulating groundwater systems; other examples come from surface-water hydrology and geophysics.The methods and guidelines in the text are broadly applicable and can be used by students, researchers, and engineers to simulate many kinds systems.

An implementation framework for wastewater treatment models requiring a minimum programming expertise.

PubMed

Rodríguez, J; Premier, G C; Dinsdale, R; Guwy, A J

2009-01-01

Mathematical modelling in environmental biotechnology has been a traditionally difficult resource to access for researchers and students without programming expertise. The great degree of flexibility required from model implementation platforms to be suitable for research applications restricts their use to programming expert users. More user friendly software packages however do not normally incorporate the necessary flexibility for most research applications. This work presents a methodology based on Excel and Matlab-Simulink for both flexible and accessible implementation of mathematical models by researchers with and without programming expertise. The models are almost fully defined in an Excel file in which the names and values of the state variables and parameters are easily created. This information is automatically processed in Matlab to create the model structure and almost immediate model simulation, after only a minimum Matlab code definition, is possible. The framework proposed also provides programming expert researchers with a highly flexible and modifiable platform on which to base more complex model implementations. The method takes advantage of structural generalities in most mathematical models of environmental bioprocesses while enabling the integration of advanced elements (e.g. heuristic functions, correlations). The methodology has already been successfully used in a number of research studies.

Reflective Modeling in Teacher Education.

ERIC Educational Resources Information Center

Shealy, Barry E.

This paper describes mathematical modeling activities from a secondary mathematics teacher education course taken by fourth-year university students. Experiences with mathematical modeling are viewed as important in helping teachers develop a more intuitive understanding of mathematics, generate and evaluate mathematical interpretations, and…

Primary School Pre-Service Mathematics Teachers' Views on Mathematical Modeling

ERIC Educational Resources Information Center

Karali, Diren; Durmus, Soner

2015-01-01

The current study aimed to identify the views of pre-service teachers, who attended a primary school mathematics teaching department but did not take mathematical modeling courses. The mathematical modeling activity used by the pre-service teachers was developed with regards to the modeling activities utilized by Lesh and Doerr (2003) in their…

Heat pipe dynamic behavior

NASA Technical Reports Server (NTRS)

Issacci, F.; Roche, G. L.; Klein, D. B.; Catton, I.

1988-01-01

The vapor flow in a heat pipe was mathematically modeled and the equations governing the transient behavior of the core were solved numerically. The modeled vapor flow is transient, axisymmetric (or two-dimensional) compressible viscous flow in a closed chamber. The two methods of solution are described. The more promising method failed (a mixed Galerkin finite difference method) whereas a more common finite difference method was successful. Preliminary results are presented showing that multi-dimensional flows need to be treated. A model of the liquid phase of a high temperature heat pipe was developed. The model is intended to be coupled to a vapor phase model for the complete solution of the heat pipe problem. The mathematical equations are formulated consistent with physical processes while allowing a computationally efficient solution. The model simulates time dependent characteristics of concern to the liquid phase including input phase change, output heat fluxes, liquid temperatures, container temperatures, liquid velocities, and liquid pressure. Preliminary results were obtained for two heat pipe startup cases. The heat pipe studied used lithium as the working fluid and an annular wick configuration. Recommendations for implementation based on the results obtained are presented. Experimental studies were initiated using a rectangular heat pipe. Both twin beam laser holography and laser Doppler anemometry were investigated. Preliminary experiments were completed and results are reported.

Equation-free modeling unravels the behavior of complex ecological systems

USGS Publications Warehouse

DeAngelis, Donald L.; Yurek, Simeon

2015-01-01

Ye et al. (1) address a critical problem confronting the management of natural ecosystems: How can we make forecasts of possible future changes in populations to help guide management actions? This problem is especially acute for marine and anadromous fisheries, where the large interannual fluctuations of populations, arising from complex nonlinear interactions among species and with varying environmental factors, have defied prediction over even short time scales. The empirical dynamic modeling (EDM) described in Ye et al.’s report, the latest in a series of papers by Sugihara and his colleagues, offers a promising quantitative approach to building models using time series to successfully project dynamics into the future. With the term “equation-free” in the article title, Ye et al. (1) are suggesting broader implications of their approach, considering the centrality of equations in modern science. From the 1700s on, nature has been increasingly described by mathematical equations, with differential or difference equations forming the basic framework for describing dynamics. The use of mathematical equations for ecological systems came much later, pioneered by Lotka and Volterra, who showed that population cycles might be described in terms of simple coupled nonlinear differential equations. It took decades for Lotka–Volterra-type models to become established, but the development of appropriate differential equations is now routine in modeling ecological dynamics. There is no question that the injection of mathematical equations, by forcing “clarity and precision into conjecture” (2), has led to increased understanding of population and community dynamics. As in science in general, in ecology equations are a key method of communication and of framing hypotheses. These equations serve as compact representations of an enormous amount of empirical data and can be analyzed by the powerful methods of mathematics.

Efficient Asymptotic Preserving Deterministic methods for the Boltzmann Equation

DTIC Science & Technology

2011-04-01

history tracing back to Hilbert , Chapmann and Enskog (Cercignani, 1988) at the beginning of the last century. The mathematical difficulties related to the...accurate determin- istic computations of the stationary solutions, which may be treated by schemes aimed to capture the stationary state ( Greenberg and...Stokes model, can be considered using the Chapmann-Enskog and the Hilbert expansions. We refer to Levermore (1996) for a mathematical setting of the

Prospects of a mathematical theory of human behavior in complex man-machine systems tasks. [time sharing computer analogy of automobile driving

NASA Technical Reports Server (NTRS)

Johannsen, G.; Rouse, W. B.

1978-01-01

A hierarchy of human activities is derived by analyzing automobile driving in general terms. A structural description leads to a block diagram and a time-sharing computer analogy. The range of applicability of existing mathematical models is considered with respect to the hierarchy of human activities in actual complex tasks. Other mathematical tools so far not often applied to man machine systems are also discussed. The mathematical descriptions at least briefly considered here include utility, estimation, control, queueing, and fuzzy set theory as well as artificial intelligence techniques. Some thoughts are given as to how these methods might be integrated and how further work might be pursued.

Computational ecology as an emerging science

PubMed Central

Petrovskii, Sergei; Petrovskaya, Natalia

2012-01-01

It has long been recognized that numerical modelling and computer simulations can be used as a powerful research tool to understand, and sometimes to predict, the tendencies and peculiarities in the dynamics of populations and ecosystems. It has been, however, much less appreciated that the context of modelling and simulations in ecology is essentially different from those that normally exist in other natural sciences. In our paper, we review the computational challenges arising in modern ecology in the spirit of computational mathematics, i.e. with our main focus on the choice and use of adequate numerical methods. Somewhat paradoxically, the complexity of ecological problems does not always require the use of complex computational methods. This paradox, however, can be easily resolved if we recall that application of sophisticated computational methods usually requires clear and unambiguous mathematical problem statement as well as clearly defined benchmark information for model validation. At the same time, many ecological problems still do not have mathematically accurate and unambiguous description, and available field data are often very noisy, and hence it can be hard to understand how the results of computations should be interpreted from the ecological viewpoint. In this scientific context, computational ecology has to deal with a new paradigm: conventional issues of numerical modelling such as convergence and stability become less important than the qualitative analysis that can be provided with the help of computational techniques. We discuss this paradigm by considering computational challenges arising in several specific ecological applications. PMID:23565336

Method of Harmonic Balance in Full-Scale-Model Tests of Electrical Devices

NASA Astrophysics Data System (ADS)

Gorbatenko, N. I.; Lankin, A. M.; Lankin, M. V.

2017-01-01

Methods for determining the weber-ampere characteristics of electrical devices, one of which is based on solution of direct problem of harmonic balance and the other on solution of inverse problem of harmonic balance by the method of full-scale-model tests, are suggested. The mathematical model of the device is constructed using the describing function and simplex optimization methods. The presented results of experimental applications of the method show its efficiency. The advantage of the method is the possibility of application for nondestructive inspection of electrical devices in the processes of their production and operation.

Improving operating room efficiency by applying bin-packing and portfolio techniques to surgical case scheduling.

PubMed

Van Houdenhoven, Mark; van Oostrum, Jeroen M; Hans, Erwin W; Wullink, Gerhard; Kazemier, Geert

2007-09-01

An operating room (OR) department has adopted an efficient business model and subsequently investigated how efficiency could be further improved. The aim of this study is to show the efficiency improvement of lowering organizational barriers and applying advanced mathematical techniques. We applied advanced mathematical algorithms in combination with scenarios that model relaxation of various organizational barriers using prospectively collected data. The setting is the main inpatient OR department of a university hospital, which sets its surgical case schedules 2 wk in advance using a block planning method. The main outcome measures are the number of freed OR blocks and OR utilization. Lowering organizational barriers and applying mathematical algorithms can yield a 4.5% point increase in OR utilization (95% confidence interval 4.0%-5.0%). This is obtained by reducing the total required OR time. Efficient OR departments can further improve their efficiency. The paper shows that a radical cultural change that comprises the use of mathematical algorithms and lowering organizational barriers improves OR utilization.

The effect of brain based learning with contextual approach viewed from adversity quotient

NASA Astrophysics Data System (ADS)

Kartikaningtyas, V.; Kusmayadi, T. A.; Riyadi, R.

2018-05-01

The aim of this research was to find out the effect of Brain Based Learning (BBL) with contextual approach viewed from adversity quotient (AQ) on mathematics achievement. BBL-contextual is the model to optimize the brain in the new concept learning and real life problem solving by making the good environment. Adversity Quotient is the ability to response and faces the problems. In addition, it is also about how to turn the difficulties into chances. This AQ classified into quitters, campers, and climbers. The research method used in this research was quasi experiment by using 2x3 factorial designs. The sample was chosen by using stratified cluster random sampling. The instruments were test and questionnaire for the data of AQ. The results showed that (1) BBL-contextual is better than direct learning on mathematics achievement, (2) there is no significant difference between each types of AQ on mathematics achievement, and (3) there is no interaction between learning model and AQ on mathematics achievement.

Model-based optimal design of experiments - semidefinite and nonlinear programming formulations

PubMed Central

Duarte, Belmiro P.M.; Wong, Weng Kee; Oliveira, Nuno M.C.

2015-01-01

We use mathematical programming tools, such as Semidefinite Programming (SDP) and Nonlinear Programming (NLP)-based formulations to find optimal designs for models used in chemistry and chemical engineering. In particular, we employ local design-based setups in linear models and a Bayesian setup in nonlinear models to find optimal designs. In the latter case, Gaussian Quadrature Formulas (GQFs) are used to evaluate the optimality criterion averaged over the prior distribution for the model parameters. Mathematical programming techniques are then applied to solve the optimization problems. Because such methods require the design space be discretized, we also evaluate the impact of the discretization scheme on the generated design. We demonstrate the techniques for finding D–, A– and E–optimal designs using design problems in biochemical engineering and show the method can also be directly applied to tackle additional issues, such as heteroscedasticity in the model. Our results show that the NLP formulation produces highly efficient D–optimal designs but is computationally less efficient than that required for the SDP formulation. The efficiencies of the generated designs from the two methods are generally very close and so we recommend the SDP formulation in practice. PMID:26949279

Model-based optimal design of experiments - semidefinite and nonlinear programming formulations.

PubMed

Duarte, Belmiro P M; Wong, Weng Kee; Oliveira, Nuno M C

2016-02-15

We use mathematical programming tools, such as Semidefinite Programming (SDP) and Nonlinear Programming (NLP)-based formulations to find optimal designs for models used in chemistry and chemical engineering. In particular, we employ local design-based setups in linear models and a Bayesian setup in nonlinear models to find optimal designs. In the latter case, Gaussian Quadrature Formulas (GQFs) are used to evaluate the optimality criterion averaged over the prior distribution for the model parameters. Mathematical programming techniques are then applied to solve the optimization problems. Because such methods require the design space be discretized, we also evaluate the impact of the discretization scheme on the generated design. We demonstrate the techniques for finding D -, A - and E -optimal designs using design problems in biochemical engineering and show the method can also be directly applied to tackle additional issues, such as heteroscedasticity in the model. Our results show that the NLP formulation produces highly efficient D -optimal designs but is computationally less efficient than that required for the SDP formulation. The efficiencies of the generated designs from the two methods are generally very close and so we recommend the SDP formulation in practice.

A Mixed Methods Study of Teach for America Teachers' Mathematical Beliefs, Knowledge, and Classroom Teaching Practices during a Reform-Based University Mathematics Methods Course

ERIC Educational Resources Information Center

Swars, Susan Lee

2015-01-01

This mixed methods study examined the mathematical preparation of elementary teachers in a Teach for America (TFA) program, focal participants for whom there is scant extant research. Data collection occurred before and after a university mathematics methods course, with a particular focus on the participants' (n = 22) mathematical beliefs,…

Validation Methods Research for Fault-Tolerant Avionics and Control Systems Sub-Working Group Meeting. CARE 3 peer review

NASA Technical Reports Server (NTRS)

Trivedi, K. S. (Editor); Clary, J. B. (Editor)

1980-01-01

A computer aided reliability estimation procedure (CARE 3), developed to model the behavior of ultrareliable systems required by flight-critical avionics and control systems, is evaluated. The mathematical models, numerical method, and fault-tolerant architecture modeling requirements are examined, and the testing and characterization procedures are discussed. Recommendations aimed at enhancing CARE 3 are presented; in particular, the need for a better exposition of the method and the user interface is emphasized.

A stochastic method to characterize model uncertainty for a Nutrient TMDL

USDA-ARS?s Scientific Manuscript database

The U.S. EPA’s Total Maximum Daily Load (TMDL) program has encountered resistances in its implementation partly because of its strong dependence on mathematical models to set limitations on the release of impairing substances. The uncertainty associated with predictions of such models is often not s...

Application of positive-real functions in hyperstable discrete model-reference adaptive system design.

NASA Technical Reports Server (NTRS)

Karmarkar, J. S.

1972-01-01

Proposal of an algorithmic procedure, based on mathematical programming methods, to design compensators for hyperstable discrete model-reference adaptive systems (MRAS). The objective of the compensator is to render the MRAS insensitive to initial parameter estimates within a maximized hypercube in the model parameter space.

Improved method for calibration of exchange flows for a physical transport box model of Tampa Bay, FL USA

EPA Science Inventory

Results for both sequential and simultaneous calibration of exchange flows between segments of a 10-box, one-dimensional, well-mixed, bifurcated tidal mixing model for Tampa Bay are reported. Calibrations were conducted for three model options with different mathematical expressi...

Scaling issues and spatio-temporal variability in ecohydrological modeling on mountain topography: Methods for improving the VELMA model

EPA Science Inventory

The interactions between vegetation and hydrology in mountainous terrain are difficult to represent in mathematical models. There are at least three primary reasons for this difficulty. First, expanding plot-scale measurements to the watershed scale requires finding the balance...

Simulation of hardwood log sawing

Treesearch

D.B. Richards; W.K. Adkins; H. Hallock; E.H. Bulgrin

1979-01-01

Mathematical modeling computer programs for several hardwood sawing systems have been developed and are described. One has judgment capabilities. Several of the subroutines are common to all of the models. These models are the basis for further research which examines the question of best-grade sawing method in terms of lumber value yield.

A Method for Evaluating Information Security Governance (ISG) Components in Banking Environment

NASA Astrophysics Data System (ADS)

Ula, M.; Ula, M.; Fuadi, W.

2017-02-01

As modern banking increasingly relies on the internet and computer technologies to operate their businesses and market interactions, the threats and security breaches have highly increased in recent years. Insider and outsider attacks have caused global businesses lost trillions of Dollars a year. Therefore, that is a need for a proper framework to govern the information security in the banking system. The aim of this research is to propose and design an enhanced method to evaluate information security governance (ISG) implementation in banking environment. This research examines and compares the elements from the commonly used information security governance frameworks, standards and best practices. Their strength and weakness are considered in its approaches. The initial framework for governing the information security in banking system was constructed from document review. The framework was categorized into three levels which are Governance level, Managerial level, and technical level. The study further conducts an online survey for banking security professionals to get their professional judgment about the ISG most critical components and the importance for each ISG component that should be implemented in banking environment. Data from the survey was used to construct a mathematical model for ISG evaluation, component importance data used as weighting coefficient for the related component in the mathematical model. The research further develops a method for evaluating ISG implementation in banking based on the mathematical model. The proposed method was tested through real bank case study in an Indonesian local bank. The study evidently proves that the proposed method has sufficient coverage of ISG in banking environment and effectively evaluates the ISG implementation in banking environment.