NASA Technical Reports Server (NTRS)
Michailova, M N; Neumann, M B
1936-01-01
In the present report a comparison is made between the scale obtained with mixtures of cetane and l-methyl naphthalene in a bomb, and that obtained with the same fuels in a Waukesha engine. The tests were conducted in a metal bomb heated by a Nichrome spiral. The fuel was injected into the bomb from a Bosch jet by means of a specially constructed plunger pump. The instant injection and the pressure curve in the bomb were registered by a beam of light which was reflected from a mirror connected to the needle of the jet and to a membrane indicator.
NASA Astrophysics Data System (ADS)
Shin, Philip
Number relativity 1.Every equation of the relativity is just the way to understand through to solve one question of the math problem. We just add the hypothesis into the number. 2. Sequence of number is the machine physics for software(computer) as the number order is program equation as calculator. 3. When zero is denominator, it is not existing as it is doing something by nothing. So nothing means time as we put zero denominator into time. My personal physics imagine.
ERIC Educational Resources Information Center
Herrera, Terese A.
2004-01-01
This article features Number Time, a site developed by the British Broadcasting Corporation (BBC) for young mathematics learners, located at www.bbc.co.uk/schools/numbertime. The site uses interactive animation to help children in pre-K through grade 2 understand and practice number basics. Users will find online games, videos that tell number…
ERIC Educational Resources Information Center
Sezin, Fatin
2009-01-01
It is instructive and interesting to find hidden numbers by using different positional numeration systems. Most of the present guessing techniques use the binary system expressed as less-than, greater-than or present-absent type information. This article describes how, by employing four cards having integers 1-64 written in different colours, one…
ERIC Educational Resources Information Center
Thelin, John R.
2013-01-01
What topic would you choose if you had the luxury of writing forever? In this article, John Thelin provides his response: He would opt to write about the history of higher education in a way that relies on quantitative data. "Numbers, please!" is his research request in taking on a longitudinal study of colleges and universities over…
ERIC Educational Resources Information Center
Kathotia, Vinay
2009-01-01
This article reports on work undertaken by schools as part of Qualifications and Curriculum Authority's (QCA's) "Engaging mathematics for all learners" project. The goal was to use in the classroom, materials and approaches from a Royal Institution (Ri) Year 10 master-class, "Number Sense", which was inspired by examples from…
ERIC Educational Resources Information Center
Galbraith, Mary J.
1974-01-01
Examination of models for representing integers demonstrates that formal operational thought is required for establishing the operations on integers. Advocated is the use of many models for introducing negative numbers but, apart from addition, it is recommended that operations on integers be delayed until the formal operations stage. (JP)
Moretto, Giovanna; di Pellegrino, Giuseppe
2008-07-01
Both theoretical and empirical studies suggest that numerical processing is intimately linked to representations of goal-directed hand actions. Further evidence for this possibility is provided here by the results of two experiments, both of which revealed a powerful influence of numerical magnitude on the selection of hand grasping movements. Human participants performed either power or precision grip responses based on the semantic properties (e.g., parity) of visual Arabic numerals, in Experiment 1, or depending on their surface characteristics (e.g., colour), in Experiment 2. In both the experiments, it was found that small numerical values facilitated precision grip (commonly used to grasp small objects), while large numerical value potentiated power grip (commonly used to grasp large objects). These findings reveal that perceiving numbers can automatically prime grasping gestures, in a similar manner to viewing physical objects. This result is coherent with the view that processing of symbolic (numerical) and physical quantitative information converges onto a shared magnitude system representing the coordinates of action.
Number Concepts with "Number Worlds": Thickening Understandings
ERIC Educational Resources Information Center
Liljedahl, Peter; Sinclair, Nathalie; Zazkis, Rina
2006-01-01
This study focuses on the nature of preservice elementary school teachers' understandings of several concepts in elementary number theory that are evoked by a computer-based microworld called "Number Worlds". In particular, the focus is on the concepts of factor, multiple and prime number. The notion of "thickness" is examined with respect to…
On Multiplying Negative Numbers.
ERIC Educational Resources Information Center
Crowley, Mary L.; Dunn, Kenneth A.
1985-01-01
Comments on the history of negative numbers, some methods that can be used to introduce the multiplication of negative numbers to students, and an explanation of why the product of two negative numbers is a positive number are included. (MNS)
All Square Chiliagonal Numbers
ERIC Educational Resources Information Center
A?iru, Muniru A.
2016-01-01
A square chiliagonal number is a number which is simultaneously a chiliagonal number and a perfect square (just as the well-known square triangular number is both triangular and square). In this work, we determine which of the chiliagonal numbers are perfect squares and provide the indices of the corresponding chiliagonal numbers and square…
ERIC Educational Resources Information Center
Gurganus, Susan
2004-01-01
"Number sense" is "an intuition about numbers that is drawn from all varied meanings of number" (NCTM, 1989, p. 39). Students with number sense understand that numbers are representative of objects, magnitudes, relationships, and other attributes; that numbers can be operated on, compared, and used for communication. It is fundamental knowledge…
Numbers Defy the Law of Large Numbers
ERIC Educational Resources Information Center
Falk, Ruma; Lann, Avital Lavie
2015-01-01
As the number of independent tosses of a fair coin grows, the rates of heads and tails tend to equality. This is misinterpreted by many students as being true also for the absolute numbers of the two outcomes, which, conversely, depart unboundedly from each other in the process. Eradicating that misconception, as by coin-tossing experiments,…
ERIC Educational Resources Information Center
Wilkie, James E. B.; Bodenhausen, Galen V.
2012-01-01
We examined the possibility that nonsocial, highly generic concepts are gendered. Specifically, we investigated the gender connotations of Arabic numerals. Across several experiments, we show that the number 1 and other odd numbers are associated with masculinity, whereas the number 2 and other even numbers are associated with femininity, in ways…
ERIC Educational Resources Information Center
Burkhart, Jerry
2009-01-01
Prime numbers are often described as the "building blocks" of natural numbers. This article shows how the author and his students took this idea literally by using prime factorizations to build numbers with blocks. In this activity, students explore many concepts of number theory, including the relationship between greatest common factors and…
Sierpinski and Carmichael Numbers
2013-01-16
prove that almost all odd natural numbers k have the property that 2nk + 1 is not a Carmichael number for any n 2 N; this implies the existence of a...Sierpiński and Riesel numbers. First, we prove that almost all odd natural numbers k have the property that 2nk + 1 is not a Carmichael number for any n...Sierpiński [25] showed that there are infinitely many odd natural numbers k with the property that 2nk + 1 is composite for every natural number n; such an
PET: [number sign]1 is number one
Miller, C.
1994-09-01
Subsidized in the beginning by bottle deposits, now spurred by the ability of curbside recycling to collect more than soda bottles, polyethylene terephthalate (PET) recycling has made great strides in the last 10 years. Its growth rate and increased market demand are the envy of many other materials. Appropriate, if not deliberately, this number-one resin is listed under the Society for the Plastics Industry's resin identification code as [number sign]1. Unlike most recyclables, the market demand for recycled PET is greater than the supply. As a result, demand not supply, is fueling the increase in PET recycling.
Rips, Lance J; Thompson, Samantha
2014-03-01
Number systems-such as the natural numbers, integers, rationals, reals, or complex numbers-play a foundational role in mathematics, but these systems can present difficulties for students. In the studies reported here, we probed the boundaries of people's concept of a number system by asking them whether "number lines" of varying shapes qualify as possible number systems. In Experiment 1, participants rated each of a set of number lines as a possible number system, where the number lines differed in their structures (a single straight line, a step-shaped line, a double line, or two branching structures) and in their boundedness (unbounded, bounded below, bounded above, bounded above and below, or circular). Participants also rated each of a group of mathematical properties (e.g., associativity) for its importance to number systems. Relational properties, such as associativity, predicted whether participants believed that particular forms were number systems, as did the forms' ability to support arithmetic operations, such as addition. In Experiment 2, we asked participants to produce properties that were important for number systems. Relational, operation, and use-based properties from this set again predicted ratings of whether the number lines were possible number systems. In Experiment 3, we found similar results when the number lines indicated the positions of the individual numbers. The results suggest that people believe that number systems should be well-behaved with respect to basic arithmetic operations, and that they reject systems for which these operations produce ambiguous answers. People care much less about whether the systems have particular numbers (e.g., 0) or sets of numbers (e.g., the positives).
Number Sense Made Simple Using Number Patterns
ERIC Educational Resources Information Center
Su, Hui Fang Huang; Marinas, Carol; Furner, Joseph
2011-01-01
This article highlights investigating intriguing number patterns utilising an emerging technology called the Square Tool. Mathematics teachers of grades K-12 will find the Square Tool useful in making connections and bridging the gap from the concrete to the abstract. Pattern recognition helps students discover various mathematical concepts. With…
ERIC Educational Resources Information Center
Allen, G. Donald
2014-01-01
In human history, the origin of the numbers came from definite practical needs. Indeed, there is strong evidence that numbers were created before writing. The number "1", dating back at least 20,000 years, was found as a counting symbol on a bone. The famous statement by the German mathematician Leopold Kronecker (1823-1891), "God…
ERIC Educational Resources Information Center
Landy, David; Silbert, Noah; Goldin, Aleah
2013-01-01
Despite their importance in public discourse, numbers in the range of 1 million to 1 trillion are notoriously difficult to understand. We examine magnitude estimation by adult Americans when placing large numbers on a number line and when qualitatively evaluating descriptions of imaginary geopolitical scenarios. Prior theoretical conceptions…
ERIC Educational Resources Information Center
de Mestre, Neville
2008-01-01
Prime numbers are important as the building blocks for the set of all natural numbers, because prime factorisation is an important and useful property of all natural numbers. Students can discover them by using the method known as the Sieve of Eratosthenes, named after the Greek geographer and astronomer who lived from c. 276-194 BC. Eratosthenes…
ERIC Educational Resources Information Center
Kissner, Emily
2000-01-01
Describes the activity of numbering trees in which students number trees or find the numbered trees and observe other features according to class time. This activity aims to increase student tracking, mapping, and writing skills and integrate them with math skills. Suggests follow up activities that focus on reading, writing, and language skills.…
ERIC Educational Resources Information Center
Shi, Yixun
2010-01-01
Starting with an interesting number game sometimes used by school teachers to demonstrate the factorization of integers, "sum-difference numbers" are defined. A positive integer n is a "sum-difference number" if there exist positive integers "x, y, w, z" such that n = xy = wz and x ? y = w + z. This paper characterizes all sum-difference numbers…
Convoluted Convolved Fibonacci Numbers
NASA Astrophysics Data System (ADS)
Moree, Pieter
2004-04-01
The convolved Fibonacci numbers F_j^(r) are defined by (1-x-x^2)^{-r}=sum_{j>= 0}F_{j+1}^(r)x^j. In this note we consider some related numbers that can be expressed in terms of convolved Fibonacci numbers. These numbers appear in the numerical evaluation of a constant arising in the study of the average density of elements in a finite field having order congruent to a (mod d). We derive a formula expressing these numbers in terms of ordinary Fibonacci and Lucas numbers. The non-negativity of these numbers can be inferred from Witt's dimension formula for free Lie algebras. This note is a case study of the transform 1/n sum_{d|}n mu(d)f(z^d)^{n/d} (with f any formal series), which was introduced and studied in a companion paper by Moree.
Versatile page numbering analysis
NASA Astrophysics Data System (ADS)
Déjean, Hervé; Meunier, Jean-Luc
2008-01-01
In this paper, we revisit the problem of detecting the page numbers of a document. This work is motivated by a need for a generic method which applies on a large variety of documents, as well as the need for analyzing the document page numbering scheme rather than spotting one number per page. We propose here a novel method, based on the notion of sequence, which goes beyond any previous described work, and we report on an extensive evaluation of its performance.
Curvature and Tachibana numbers
Stepanov, Sergey E
2011-07-31
The aim of this paper is to define the rth Tachibana number t{sub r} of an n-dimensional compact oriented Riemannian manifold as the dimension of the space of conformally Killing r-forms, for r=1,2,...,n-1. We also describe properties of these numbers, by analogy with properties of the Betti numbers b{sub r} of a compact oriented Riemannian manifold. Bibliography: 25 titles.
NASA Technical Reports Server (NTRS)
Baals, D. D. (Editor)
1977-01-01
Fundamental aerodynamic questions for which high Reynolds number experimental capability is required are discussed. The operational characteristics and design features of the National Transonic Facility are reviewed.
Lloyd, G. Scott
2016-09-17
This floating-point arithmetic library contains a software implementation of Universal Numbers (unums) as described by John Gustafson [1]. The unum format is a superset of IEEE 754 floating point with several advantages. Computing with unums provides more accurate answers without rounding errors, underflow or overflow. In contrast to fixed-sized IEEE numbers, a variable number of bits can be used to encode unums. This all allows number with only a few significant digits or with a small dynamic range to be represented more compactly.
ERIC Educational Resources Information Center
Onstad, Torgeir
1991-01-01
After a brief historical account of Leonardo Pisano Fibonacci, some basic results concerning the Fibonacci numbers are developed and proved, and entertaining examples are described. Connections are made between the Fibonacci numbers and the Golden Ratio, biological nature, and other combinatorics examples. (MDH)
Templates, Numbers & Watercolors.
ERIC Educational Resources Information Center
Clemesha, David J.
1990-01-01
Describes how a second-grade class used large templates to draw and paint five-digit numbers. The lesson integrated artistic knowledge and vocabulary with their mathematics lesson in place value. Students learned how draftspeople use templates, and they studied number paintings by Charles Demuth and Jasper Johns. (KM)
Avogadro's Number Ferromagnetically
ERIC Educational Resources Information Center
Houari, Ahmed
2010-01-01
Avogadro's number, usually denoted by N[subscript A], plays a fundamental role in both physics and chemistry. It defines the extremely useful concept of the mole, which is the base unit of the amount of matter in the international system of units. The fundamental character of this number can also be illustrated by its appearance in the definitions…
ERIC Educational Resources Information Center
Leadership, 2007
2007-01-01
Education, it seems, is increasingly driven by the numbers. Whether it is measuring student performance or a school district's ability to balance the books, one will find data out there about it. So much data, in fact, that it is difficult to sort through all the numbers to get the needed information. This article describes California's Ed-Data…
ERIC Educational Resources Information Center
Cole, Milton W.
2009-01-01
Numbers--of publications, grant money, PhD students, and invited talks, for example--play too large a role in assessments of faculty. The author's thirty-five years of experience in higher education have convinced him that overreliance on such numbers is a big problem, especially, but not exclusively, in the sciences. Every scientist recognizes…
Rugani, Rosa; Sartori, Luisa
2016-01-01
Humans show a remarkable tendency to describe and think of numbers as being placed on a mental number line (MNL), with smaller numbers located on the left and larger ones on the right. Faster responses to small numbers are indeed performed on the left side of space, while responses to large numbers are facilitated on the right side of space (spatial-numerical association of response codes, SNARC effect). This phenomenon is considered the experimental demonstration of the MNL and has been extensively replicated throughout a variety of paradigms. Nevertheless, the majority of previous literature has mainly investigated this effect by means of response times and accuracy, whereas studies considering more subtle and automatic measures such as kinematic parameters are rare (e.g., in a reaching-to-grasp movement, the grip aperture is enlarged in responding to larger numbers than in responding to small numbers). In this brief review we suggest that numerical magnitude can also affect the what and how of action execution (i.e., temporal and spatial components of movement). This evidence could have large implications in the strongly debated issue concerning the effect of experience and culture on the orientation of MNL. PMID:27524965
Rugani, Rosa; Sartori, Luisa
2016-01-01
Humans show a remarkable tendency to describe and think of numbers as being placed on a mental number line (MNL), with smaller numbers located on the left and larger ones on the right. Faster responses to small numbers are indeed performed on the left side of space, while responses to large numbers are facilitated on the right side of space (spatial-numerical association of response codes, SNARC effect). This phenomenon is considered the experimental demonstration of the MNL and has been extensively replicated throughout a variety of paradigms. Nevertheless, the majority of previous literature has mainly investigated this effect by means of response times and accuracy, whereas studies considering more subtle and automatic measures such as kinematic parameters are rare (e.g., in a reaching-to-grasp movement, the grip aperture is enlarged in responding to larger numbers than in responding to small numbers). In this brief review we suggest that numerical magnitude can also affect the what and how of action execution (i.e., temporal and spatial components of movement). This evidence could have large implications in the strongly debated issue concerning the effect of experience and culture on the orientation of MNL.
Quantum random number generators
NASA Astrophysics Data System (ADS)
Herrero-Collantes, Miguel; Garcia-Escartin, Juan Carlos
2017-01-01
Random numbers are a fundamental resource in science and engineering with important applications in simulation and cryptography. The inherent randomness at the core of quantum mechanics makes quantum systems a perfect source of entropy. Quantum random number generation is one of the most mature quantum technologies with many alternative generation methods. This review discusses the different technologies in quantum random number generation from the early devices based on radioactive decay to the multiple ways to use the quantum states of light to gather entropy from a quantum origin. Randomness extraction and amplification and the notable possibility of generating trusted random numbers even with untrusted hardware using device-independent generation protocols are also discussed.
NASA Astrophysics Data System (ADS)
Doeff, E.; Misiurewicz, M.
1997-11-01
This paper presents results on rotation numbers for orientation-preserving torus homeomorphisms homotopic to a Dehn twist. Rotation numbers and the rotation set for such homeomorphisms have been defined and initially investigated by the first author in a previous paper. Here we prove that each rotation number 0951-7715/10/6/017/img5 in the interior of the rotation set is realized by some compact invariant set, and that there is an ergodic measure on that set with mean rotation number 0951-7715/10/6/017/img5. It is also proved that the function which assigns its rotation set to such a homeomorphism is continuous. Finally, a counterexample is presented that shows that rational extremal points of the shear rotation set do not necessarily correspond to any periodic orbits.
Quantum random number generator
Pooser, Raphael C.
2016-05-10
A quantum random number generator (QRNG) and a photon generator for a QRNG are provided. The photon generator may be operated in a spontaneous mode below a lasing threshold to emit photons. Photons emitted from the photon generator may have at least one random characteristic, which may be monitored by the QRNG to generate a random number. In one embodiment, the photon generator may include a photon emitter and an amplifier coupled to the photon emitter. The amplifier may enable the photon generator to be used in the QRNG without introducing significant bias in the random number and may enable multiplexing of multiple random numbers. The amplifier may also desensitize the photon generator to fluctuations in power supplied thereto while operating in the spontaneous mode. In one embodiment, the photon emitter and amplifier may be a tapered diode amplifier.
Discovering Avogadro's Number.
ERIC Educational Resources Information Center
Rieck, William A.
1997-01-01
Illustrates the use of an inductive approach that leads students to the discovery of Avogadro's number while integrating thinking, mathematical, and calculator skills in the process. An understanding of scientific notation and a calculator are required. (DDR)
... View All Articles | Inside Life Science Home Page Genetics by the Numbers By Chelsea Toledo and Kirstie ... June 11, 2012 Scholars have been studying modern genetics since the mid-19th century, but even today ...
ERIC Educational Resources Information Center
Strawn, Candace A.
1998-01-01
Describes LOGO's turtle graphics capabilities based on a sixth-grade classroom's activities with negative numbers and Logo programming. A sidebar explains LOGO and offers suggestions to teachers for using LOGO effectively. (LRW)
ERIC Educational Resources Information Center
Brown, Ezra; Brunson, Cornelius
2008-01-01
Fibonacci's forgotten number is the sexagesimal number 1;22,7,42,33,4,40, which he described in 1225 as an approximation to the real root of x[superscript 3] + 2x[superscript 2] + 10x - 20. In decimal notation, this is 1.36880810785...and it is correct to nine decimal digits. Fibonacci did not reveal his method. How did he do it? There is also a…
Nelson, R.N.
1985-05-01
This publication lists all report number codes processed by the Office of Scientific and Technical Information. The report codes are substantially based on the American National Standards Institute, Standard Technical Report Number (STRN)-Format and Creation Z39.23-1983. The Standard Technical Report Number (STRN) provides one of the primary methods of identifying a specific technical report. The STRN consists of two parts: The report code and the sequential number. The report code identifies the issuing organization, a specific program, or a type of document. The sequential number, which is assigned in sequence by each report issuing entity, is not included in this publication. Part I of this compilation is alphabetized by report codes followed by issuing installations. Part II lists the issuing organization followed by the assigned report code(s). In both Parts I and II, the names of issuing organizations appear for the most part in the form used at the time the reports were issued. However, for some of the more prolific installations which have had name changes, all entries have been merged under the current name.
Schreuder, Michiel F
2012-10-01
A low nephron number is, according to Brenner's hyperfiltration hypothesis, associated with hypertension, glomerular damage and proteinuria, and starts a vicious cycle that ends in renal failure over the long term. Nephron endowment is set during foetal life, and there is no formation of nephrons after 34-36 weeks of gestation, indicating that many factors before that time-point may have an impact on kidney development and reduce nephron numbers. Such factors include maternal malnutrition, stress, diseases, such as diabetes, uteroplacental insufficiency, maternal and neonatal drugs and premature birth. However, other congenital anomalies, such as renal hypoplasia, unilateral renal agenesis or multicystic dysplastic kidney, may also lead to a reduced nephron endowment, with an increased risk for hypertension, renal dysfunction and the need for renal replacement therapy. This review focuses on the causes and consequences of a low nephron endowment and will illustrate why there is safety in glomerular numbers.
Cantlon, Jessica F.; Platt, Michael L.; Brannon, Elizabeth M.
2009-01-01
In a world without numbers, we would be unable to build a skyscraper, hold a national election, plan a wedding, or pay for a chicken at the market. The numerical symbols used in all these behaviors build on the approximate number system (ANS) which represents the number of discrete objects or events as a continuous mental magnitude. In this review, we first discuss evidence that the ANS bears a set of behavioral and brain signatures that are universally displayed across animal species, human cultures, and development. We then turn to the question of whether the ANS constitutes a specialized cognitive and neural domain--a question central to understanding how this system works, the nature of its evolutionary and developmental trajectory, and its physical instantiation in the brain. PMID:19131268
Quantum random number generation
Ma, Xiongfeng; Yuan, Xiao; Cao, Zhu; Zhang, Zhen; Qi, Bing
2016-06-28
Quantum physics can be exploited to generate true random numbers, which play important roles in many applications, especially in cryptography. Genuine randomness from the measurement of a quantum system reveals the inherent nature of quantumness -- coherence, an important feature that differentiates quantum mechanics from classical physics. The generation of genuine randomness is generally considered impossible with only classical means. Based on the degree of trustworthiness on devices, quantum random number generators (QRNGs) can be grouped into three categories. The first category, practical QRNG, is built on fully trusted and calibrated devices and typically can generate randomness at a high speed by properly modeling the devices. The second category is self-testing QRNG, where verifiable randomness can be generated without trusting the actual implementation. The third category, semi-self-testing QRNG, is an intermediate category which provides a tradeoff between the trustworthiness on the device and the random number generation speed.
Quantum random number generation
Ma, Xiongfeng; Yuan, Xiao; Cao, Zhu; ...
2016-06-28
Quantum physics can be exploited to generate true random numbers, which play important roles in many applications, especially in cryptography. Genuine randomness from the measurement of a quantum system reveals the inherent nature of quantumness -- coherence, an important feature that differentiates quantum mechanics from classical physics. The generation of genuine randomness is generally considered impossible with only classical means. Based on the degree of trustworthiness on devices, quantum random number generators (QRNGs) can be grouped into three categories. The first category, practical QRNG, is built on fully trusted and calibrated devices and typically can generate randomness at a highmore » speed by properly modeling the devices. The second category is self-testing QRNG, where verifiable randomness can be generated without trusting the actual implementation. The third category, semi-self-testing QRNG, is an intermediate category which provides a tradeoff between the trustworthiness on the device and the random number generation speed.« less
Quantum random number generation
NASA Astrophysics Data System (ADS)
Ma, Xiongfeng; Yuan, Xiao; Cao, Zhu; Qi, Bing; Zhang, Zhen
2016-06-01
Quantum physics can be exploited to generate true random numbers, which have important roles in many applications, especially in cryptography. Genuine randomness from the measurement of a quantum system reveals the inherent nature of quantumness—coherence, an important feature that differentiates quantum mechanics from classical physics. The generation of genuine randomness is generally considered impossible with only classical means. On the basis of the degree of trustworthiness on devices, quantum random number generators (QRNGs) can be grouped into three categories. The first category, practical QRNG, is built on fully trusted and calibrated devices and typically can generate randomness at a high speed by properly modelling the devices. The second category is self-testing QRNG, in which verifiable randomness can be generated without trusting the actual implementation. The third category, semi-self-testing QRNG, is an intermediate category that provides a tradeoff between the trustworthiness on the device and the random number generation speed.
2007-12-26
265–275. [7] H. G. Grundman, ‘ Sequences of consecutive Niven numbers’, Fibonacci Quart. 32 (1994), 174–175. [8] D. R. Heath-Brown and S. Konyagin...paper, we define a natural sequence in relation to q-Niven numbers. For a fixed but arbitrary k ∈ N and a base q ≥ 2, one may ask whether or not there...other words, ak is the smallest Niven number whose sum of the digits is a given positive integer k. We denote by ck the companion sequence ck = ak/k
ERIC Educational Resources Information Center
Trudgian, Timothy
2009-01-01
One of the difficulties in any teaching of mathematics is to bridge the divide between the abstract and the intuitive. Throughout school one encounters increasingly abstract notions, which are more and more difficult to relate to everyday experiences. This article examines a familiar approach to thinking about negative numbers, that is an…
ERIC Educational Resources Information Center
McMurdo, George
1996-01-01
The expansion of the commercial Internet has encouraged the interpretation of the Internet and its uses as a potential marketing medium. Examines statistical and demographic information about the Internet including number of Internet hosts and World Wide Web servers, and estimates of Internet users; and raises questions about definitions and…
Khan, T.A.; Baum, J.W.; Beckman, M.C.
1993-10-01
This document contains information dealing with the lessons learned from the experience of nuclear plants. In this issue the authors tried to avoid the `tyranny` of numbers and concentrated on the main lessons learned. Topics include: filtration devices for air pollution abatement, crack repair and inspection, and remote handling equipment.
ERIC Educational Resources Information Center
Hahn, Nic
2012-01-01
Remember paint by numbers? This revived trend was a perfect solution to teaching geometric shapes to the author's first-grade students. Geometric shapes are identified and used in early elementary art classrooms, but this lesson gives students a deeper understanding of shape, encourages problem-solving, and makes a strong correlation between math…
ERIC Educational Resources Information Center
Cech, Scott J.
2008-01-01
This article discusses College Summit, a nonprofit effort centered around the premise that there is a sizable number of students who are more capable of college academics than their test scores and grade point averages suggest. Its four-day summer sessions are focused not on ramping up students' academic performance but in mining students'…
Number in Classifier Languages
ERIC Educational Resources Information Center
Nomoto, Hiroki
2013-01-01
Classifier languages are often described as lacking genuine number morphology and treating all common nouns, including those conceptually count, as an unindividuated mass. This study argues that neither of these popular assumptions is true, and presents new generalizations and analyses gained by abandoning them. I claim that no difference exists…
Analogies for Avogadro's Number.
ERIC Educational Resources Information Center
Poskozim, Paul S.; And Others
1986-01-01
Reviews analogies used to try to capture the concept of the magnitude of Avogadro's number, including analogies related to small/tiny objects, counting, people, water, and money. Also presents several new ones which are based on modern computers and printers. (JN)
ERIC Educational Resources Information Center
Doyle, William R.
2010-01-01
Some say that the educators now have a gender-stratified system of higher education, with nearly 60 percent of all undergraduates being women and fewer men attending each year. The battle for gender equity for women in higher education has been a long and contentious one. In the decades since, increasing numbers of women have gone to college, to…
ERIC Educational Resources Information Center
Girard, Suzanne; Willing, Kathlene R.
Intended for young children just becoming familiar with computers, this counting book introduces and reinforces new computer vocabulary and concepts. The numbers, from one to twelve, are presented along with words and illustrations from the world of computers, allowing for different activities in which children can count or match and name the…
NASA Astrophysics Data System (ADS)
Allen, G. Donald
2014-09-01
In human history, the origin of the numbers came from definite practical needs. Indeed, there is strong evidence that numbers were created before writing. The number "1", dating back at least 20,000 years, was found as a counting symbol on a bone. The famous statement by the German mathematician Leopold Kronecker (1823-1891), "God made the integers; all else is the work of man," has spawned a lively modern philosophical discussion, and this discussion begins by trying to get a philosophical handle on "1." This approach remains under heavy discussion, and is more-or-less unresolved (Frege in Die Grundlagen der Arithmetik (English: The foundations of arithmetic). Polhman, 1884). In this note, we consider the many facets of "one" in it many guises and applications. Nonetheless, "one" has multiple meanings, from the very practical to the abstract, from mathematics to science to basically everything. We examine here a mere slice of mathematical history with a focus on the most basic and applicable concept therein. It troubles many, particularly students, even today.
High Reynolds Number Turbulence
2007-03-27
wall relation of McKeon et al. (2005), and the results for the smallest sandgrain roughness used by Nikuradse (1933). 3 57xI03 "eI : uhp - 2 8 1 6 8 x l 0...Reynolds Number Turbulent Pipe Flow," ASME International Mechanical Engineering Conference and Exposition, Washington, D.C., November 16-21, 2003... Engineering Sciences, Vol. 365 (1852) pp. 699-714, 2007. 14 ’Pipe flow roughness Allen, J.J., Shockling, M.A. and Smits, A.J. "Effects of a machined rough
NASA Astrophysics Data System (ADS)
Pati, Jogesh C.; Salam, Abdus
We suggest that baryon-number conservation may not be absolute and that an integrally charged quark may disintegrate into two leptons and an antilepton with a coupling strength G Bmp2≲ 10-9. On the other hand, if quarks are much heavier than low-lying hadrons, the decay of a three-quark system like the proton is highly forbidden (proton lifetime ≳ 1028 y). Motivation for these ideas appears to arise within a unified theory of hadrons and leptons and their gauge interactions. We emphasize the consequences of such a possibility for real quark searches.
Grozeva, Detelina; Kirov, George; Ivanov, Dobril; Jones, Ian R.; Jones, Lisa; Green, Elaine K.; St Clair, David M.; Young, Allan H.; Ferrier, Nicol; Farmer, Anne E.; McGuffin, Peter; Holmans, Peter A.; Owen, Michael J.; O’Donovan, Michael C.; Craddock, Nick
2015-01-01
Context Recent studies suggest that copy number variation in the human genome is extensive and may play an important role in susceptibility to disease, including neuropsychiatric disorders such as schizophrenia and autism. The possible involvement of copy number variants (CNVs) in bipolar disorder has received little attention to date. Objectives To determine whether large (>100 000 base pairs) and rare (found in <1% of the population) CNVs are associated with susceptibility to bipolar disorder and to compare with findings in schizophrenia. Design A genome-wide survey of large, rare CNVs in a case-control sample using a high-density microarray. Setting The Wellcome Trust Case Control Consortium. Participants There were 1697 cases of bipolar disorder and 2806 nonpsychiatric controls. All participants were white UK residents. Main Outcome Measures Overall load of CNVs and presence of rare CNVs. Results The burden of CNVs in bipolar disorder was not increased compared with controls and was significantly less than in schizophrenia cases. The CNVs previously implicated in the etiology of schizophrenia were not more common in cases with bipolar disorder. Conclusions Schizophrenia and bipolar disorder differ with respect to CNV burden in general and association with specific CNVs in particular. Our data are consistent with the possibility that possession of large, rare deletions may modify the phenotype in those at risk of psychosis: those possessing such events are more likely to be diagnosed as having schizophrenia, and those without them are more likely to be diagnosed as having bipolar disorder. PMID:20368508
An introduction to hyperharmonic numbers
NASA Astrophysics Data System (ADS)
Cereceda, José Luis
2015-04-01
In this note, we deal with a generalization of the harmonic numbers proposed by Conway and Guy in their Book of Numbers, namely, the so-called hyperharmonic numbers. Our main aim is to prove, by mathematical induction, the formula defining the hyperharmonic numbers in terms of ordinary harmonic numbers. Moreover, we calculate the hyperharmonic numbers as the derivative of a certain binomial coefficient.
Beyond natural numbers: negative number representation in parietal cortex.
Blair, Kristen P; Rosenberg-Lee, Miriam; Tsang, Jessica M; Schwartz, Daniel L; Menon, Vinod
2012-01-01
Unlike natural numbers, negative numbers do not have natural physical referents. How does the brain represent such abstract mathematical concepts? Two competing hypotheses regarding representational systems for negative numbers are a rule-based model, in which symbolic rules are applied to negative numbers to translate them into positive numbers when assessing magnitudes, and an expanded magnitude model, in which negative numbers have a distinct magnitude representation. Using an event-related functional magnetic resonance imaging design, we examined brain responses in 22 adults while they performed magnitude comparisons of negative and positive numbers that were quantitatively near (difference <4) or far apart (difference >6). Reaction times (RTs) for negative numbers were slower than positive numbers, and both showed a distance effect whereby near pairs took longer to compare. A network of parietal, frontal, and occipital regions were differentially engaged by negative numbers. Specifically, compared to positive numbers, negative number processing resulted in greater activation bilaterally in intraparietal sulcus (IPS), middle frontal gyrus, and inferior lateral occipital cortex. Representational similarity analysis revealed that neural responses in the IPS were more differentiated among positive numbers than among negative numbers, and greater differentiation among negative numbers was associated with faster RTs. Our findings indicate that despite negative numbers engaging the IPS more strongly, the underlying neural representation are less distinct than that of positive numbers. We discuss our findings in the context of the two theoretical models of negative number processing and demonstrate how multivariate approaches can provide novel insights into abstract number representation.
Percents Are Not Natural Numbers
ERIC Educational Resources Information Center
Jacobs, Jennifer A.
2013-01-01
Adults are prone to treating percents, one representational format of rational numbers, as novel cases of natural number. This suggests that percent values are not differentiated from natural numbers; a conceptual shift from the natural numbers to the rational numbers has not yet occurred. This is most surprising, considering people are inundated…
Series of Reciprocal Triangular Numbers
ERIC Educational Resources Information Center
Bruckman, Paul; Dence, Joseph B.; Dence, Thomas P.; Young, Justin
2013-01-01
Reciprocal triangular numbers have appeared in series since the very first infinite series were summed. Here we attack a number of subseries of the reciprocal triangular numbers by methodically expressing them as integrals.
Number Sense in the Transition from Natural to Rational Numbers
ERIC Educational Resources Information Center
Van Hoof, Jo; Verschaffel, Lieven; Van Dooren, Wim
2017-01-01
Background: Rational numbers are of critical importance both in mathematics and in other fields of science. However, they form a stumbling block for learners. One widely known source of the difficulty learners have with rational numbers is the natural number bias, that is the tendency to (inappropriately) apply natural number properties in…
Representing Numbers: Prime and Irrational
ERIC Educational Resources Information Center
Zazkis, Rina
2005-01-01
This article draws an analogy between prime and irrational numbers with respect to how these numbers are defined and how they are perceived by learners. Excerpts are presented from two research studies: a study on understanding prime numbers by pre-service elementary school teachers and a study on understanding irrational numbers by pre-service…
15. Stress Sheet, Truss number 2, span number 6, Superior ...
15. Stress Sheet, Truss number 2, span number 6, Superior Avenue viaduct. Drawing courtesy Engineering Dept., City of Cleveland. - Superior Avenue Viaduct, Cleveland East & West side, Cuyahoga Valley Vicinity, Cleveland, Cuyahoga County, OH
Toddlers' Spontaneous Attention to Number and Verbal Number Quantification
ERIC Educational Resources Information Center
Li, Xia
2009-01-01
"S"pontaneous "a"ttention to "n"umber (SAN) is the tendency to notice the relatively abstract attribute of number despite the presence of other attributes. According to nativists, an innate concept of one to three directs young children's attention to these "intuitive numbers" in everyday situations--even before they acquire language. According to…
Natural Number Bias in Operations with Missing Numbers
ERIC Educational Resources Information Center
Christou, Konstantinos P.
2015-01-01
This study investigates the hypothesis that there is a natural number bias that influences how students understand the effects of arithmetical operations involving both Arabic numerals and numbers that are represented by symbols for missing numbers. It also investigates whether this bias correlates with other aspects of students' understanding of…
Introducing Number and Arithmetic Concepts with Number Sticks.
ERIC Educational Resources Information Center
Baroody, Arthur J.
1993-01-01
This article compares the relative merits of using Cuisenaire rods (unsegmented, unnumbered, and representing continuous quantities) and number sticks (segmented, numbered, and representing discrete quantities) to introduce number and arithmetic concepts to beginning students or students with learning difficulties or mental disabilities. (DB)
Number Tracks, Number Lines, Number Strips Are They All the Same?
ERIC Educational Resources Information Center
Iannone, Paola
2006-01-01
In this article, the author argues that there is a big conceptual difference between number lines and number strips and that number lines should be consistently used as early as Y1. Her interest in the use of the number line as a powerful image of the real numbers, and how this is introduced in the early years, comes from her own experience as a…
Relating Mason number to Bingham number in magnetorheological fluids
NASA Astrophysics Data System (ADS)
Sherman, Stephen G.; Becnel, Andrew C.; Wereley, Norman M.
2015-04-01
Magnetorheological (MR) fluids are described using two nondimensional numbers, the Bingham and Mason numbers. The Mason number is the ratio of particle magnetic forces to viscous forces and describes the behavior of MR fluids at the microscopic, particle level scale. At the macroscopic, continuum scale, Bingham number is the ratio of yield stress to viscous stress, and describes the bulk motion of the fluid. If these two nondimensional numbers can be related, then microscopic models can be directly compared to macroscopic results. We show that if microscopic and macroscopic forces are linearly related, then Bingham and Mason number are inversely related, or, alternatively, that the product of the Bingham number and the Mason number is a constant. This relationship is experimentally validated based on measurements of apparent viscosity on a high shear rate, γ ˙ ≈ 10 000s-1, Searle cell rheometer. This relationship between Mason number and Bingham number is then used to analyze a Mason number based result, and is also used to inform the MR fluid device design process.
Number games, magnitude representation, and basic number skills in preschoolers.
Whyte, Jemma Catherine; Bull, Rebecca
2008-03-01
The effect of 3 intervention board games (linear number, linear color, and nonlinear number) on young children's (mean age = 3.8 years) counting abilities, number naming, magnitude comprehension, accuracy in number-to-position estimation tasks, and best-fit numerical magnitude representations was examined. Pre- and posttest performance was compared following four 25-min intervention sessions. The linear number board game significantly improved children's performance in all posttest measures and facilitated a shift from a logarithmic to a linear representation of numerical magnitude, emphasizing the importance of spatial cues in estimation. Exposure to the number card games involving nonsymbolic magnitude judgments and association of symbolic and nonsymbolic quantities, but without any linear spatial cues, improved some aspects of children's basic number skills but not numerical estimation precision.
Identifying Fractions on Number Lines.
ERIC Educational Resources Information Center
Bright, George W.; And Others
1988-01-01
This study investigated the ways students represented fractions on number lines and the effects of instruction on those representations. The instruction primarily concerned representing fractions and ordering fractions on number lines. (Author/PK)
The Mental Number Line in Dyscalculia: Impaired Number Sense or Access From Symbolic Numbers?
Lafay, Anne; St-Pierre, Marie-Catherine; Macoir, Joël
2016-03-25
Numbers may be manipulated and represented mentally over a compressible number line oriented from left to right. According to numerous studies, one of the primary reasons for dyscalculia is related to improper understanding of the mental number line. Children with dyscalculia usually show difficulty when they have to place Arabic numbers on a physical number line. However, it remains unclear whether they have a deficit with the mental number line per se or a deficit with accessing it from nonsymbolic and/or symbolic numbers. Quebec French-speaking 8- to 9-year-old children with (24) and without (37) dyscalculia were assessed with transcoding tasks (number-to-positionandposition-to-number) designed to assess the acuity of the mental number line with Arabic and spoken numbers as well as with analogic numerosities. Results showed that children with dyscalculia produced a larger percentage absolute error than children without mathematics difficulties in every task except the number-to-position transcoding task with analogic numerosities. Hence, these results suggested that children with dyscalculia do not have a general deficit of the mental number line but rather a deficit with accessing it from symbolic numbers.
ERIC Educational Resources Information Center
Jue, Brian
2010-01-01
Separate a three-digit number into its component digits. After raising each digit to the third power and computing the sum of the cubes, determine how often the original number reappears. Modular arithmetic is used to reduce the number of potential solutions to a more manageable quantity. (Contains 4 tables.)
Random Numbers and Quantum Computers
ERIC Educational Resources Information Center
McCartney, Mark; Glass, David
2002-01-01
The topic of random numbers is investigated in such a way as to illustrate links between mathematics, physics and computer science. First, the generation of random numbers by a classical computer using the linear congruential generator and logistic map is considered. It is noted that these procedures yield only pseudo-random numbers since…
ERIC Educational Resources Information Center
Fletcher, Rodney
2008-01-01
This article presents a guided investigation into the spacial relationships between the centres of the squares in a Fibonacci tiling. It is essentially a lesson in number pattern, but includes work with surds, coordinate geometry, and some elementary use of complex numbers. The investigation could be presented to students in a number of ways…
Linear or Exponential Number Lines
ERIC Educational Resources Information Center
Stafford, Pat
2011-01-01
Having decided to spend some time looking at one's understanding of numbers, the author was inspired by "Alex's Adventures in Numberland," by Alex Bellos to look at one's innate appreciation of number. Bellos quotes research studies suggesting that an individual's natural appreciation of numbers is more likely to be exponential rather…
Numbers and Math. Beginnings Workshop.
ERIC Educational Resources Information Center
Gross, Fred E.; Elkind, CavidEpstein, Ann S.; Copley, Juanita V.; Haugen, Ginny; Haugen, Kirsten
2003-01-01
Presents five articles addressing numbers and math instruction for young children: "Math Talk with Young Children: One Parent's Experience" (Fred E. Gross); "How Children Build Their Understanding of Numbers" (David Elkind); "Early Math: It's More than Numbers" (Ann S. Epstein); "Assessing Mathematical Learning: Observing and Listening to…
ERIC Educational Resources Information Center
Huang, Yi Ting; Spelke, Elizabeth; Snedeker, Jesse
2013-01-01
Number words are generally used to refer to the exact cardinal value of a set, but cognitive scientists disagree about their meanings. Although most psychological analyses presuppose that numbers have exact semantics ("two" means exactly two), many linguistic accounts propose that numbers have lower-bounded semantics (at least two), and…
Cognitive representation of negative numbers.
Fischer, Martin H
2003-05-01
To understand negative numbers, must we refer to positive number representations (the phylogenetic hypothesis), or do we acquire a negative mental number line (the ontogenetic hypothesis)? In the experiment reported here, participants made lateralized button responses to indicate the larger of two digits from the range -9 to 9. Digit pairs were displayed spatially congruent or incongruent with either a phylogenetic or an ontogenetic mental number line. The pattern of decision latencies suggests that negative numbers become associated with left space, thus supporting the ontogenetic view.
Generalized Bernoulli-Hurwitz numbers and the universal Bernoulli numbers
NASA Astrophysics Data System (ADS)
Ônishi, Yoshihiro
2011-10-01
The three fundamental properties of the Bernoulli numbers, namely, the von Staudt-Clausen theorem, von Staudt's second theorem, and Kummer's original congruence, are generalized to new numbers that we call generalized Bernoulli-Hurwitz numbers. These are coefficients in the power series expansion of a higher-genus algebraic function with respect to a suitable variable. Our generalization differs strongly from previous works. Indeed, the order of the power of the modulus prime in our Kummer-type congruences is exactly the same as in the trigonometric function case (namely, Kummer's own congruence for the original Bernoulli numbers), and as in the elliptic function case (namely, H. Lang's extension for the Hurwitz numbers). However, in other past results on higher-genus algebraic functions, the modulus was at most half of its value in these classical cases. This contrast is clarified by investigating the analogue of the three properties above for the universal Bernoulli numbers. Bibliography: 34 titles.
Quantum random number generator using photon-number path entanglement
NASA Astrophysics Data System (ADS)
Kwon, Osung; Cho, Young-Wook; Kim, Yoon-Ho
2010-08-01
We report an experimental implementation of quantum random number generator based on the photon-number-path entangled state. The photon-number-path entangled state is prepared by means of two-photon Hong-Ou-Mandel quantum interference at a beam splitter. The randomness in our scheme is of truly quantum mechanical origin as it comes from the projection measurement of the entangled two-photon state. The generated bit sequences satisfy the standard randomness test.
Catalan Numbers, the Hankel Transform, and Fibonacci Numbers
NASA Astrophysics Data System (ADS)
Cvetkovic, Aleksandar; Rajkovic, Predrag; Ivkovic, Milos
2002-05-01
We prove that the Hankel transformation of a sequence whose elements are the sums of two adjacent Catalan numbers is a subsequence of the Fibonacci numbers. This is done by finding the explicit form for the coefficients in the three-term recurrence relation that the corresponding orthogonal polynomials satisfy.
On Fibonacci Numbers Which Are Elliptic Korselt Numbers
2014-11-17
On Fibonacci numbers which are elliptic Korselt numbers Florian Luca School of Mathematics University of the Witwatersrand P. O. Box Wits 2050, South... Witwatersrand . This author thanks this institution for hospitality. 6 References [1] W. R. Alford, A. Granville and C. Pomerance, “There are infinitely
Huang, Yi Ting; Spelke, Elizabeth; Snedeker, Jesse
2014-01-01
Number words are generally used to refer to the exact cardinal value of a set, but cognitive scientists disagree about their meanings. Although most psychological analyses presuppose that numbers have exact semantics (two means EXACTLY TWO), many linguistic accounts propose that numbers have lower-bounded semantics (AT LEAST TWO), and that speakers restrict their reference through a pragmatic inference (scalar implicature). We address this debate through studies of children who are in the process of acquiring the meanings of numbers. Adults and 2- and 3-year-olds were tested in a novel paradigm that teases apart semantic and pragmatic aspects of interpretation (the covered box task). Our findings establish that when scalar implicatures are cancelled in the critical trials of this task, both adults and children consistently give exact interpretations for number words. These results, in concert with recent work on real-time processing, provide the first unambiguous evidence that number words have exact semantics. PMID:25285053
Dynamic Virtual Credit Card Numbers
NASA Astrophysics Data System (ADS)
Molloy, Ian; Li, Jiangtao; Li, Ninghui
Theft of stored credit card information is an increasing threat to e-commerce. We propose a dynamic virtual credit card number scheme that reduces the damage caused by stolen credit card numbers. A user can use an existing credit card account to generate multiple virtual credit card numbers that are either usable for a single transaction or are tied with a particular merchant. We call the scheme dynamic because the virtual credit card numbers can be generated without online contact with the credit card issuers. These numbers can be processed without changing any of the infrastructure currently in place; the only changes will be at the end points, namely, the card users and the card issuers. We analyze the security requirements for dynamic virtual credit card numbers, discuss the design space, propose a scheme using HMAC, and prove its security under the assumption the underlying function is a PRF.
Refactorable Numbers - A Machine Invention
NASA Astrophysics Data System (ADS)
Colton, Simon
1999-02-01
The HR (or Hardy-Ramanujan) program invents and analyses definitions in areas of pure mathematics, including finite algebras, graph theory and number theory. While working in number theory, HR recently invented a new integer sequence, the refactorable numbers, which are defined and developed here. A discussion of how HR works, along with details of well known sequences reinvented by HR and other new sequences invented by HR is also given.
Compendium of Experimental Cetane Numbers
Yanowitz, J.; Ratcliff, M. A.; McCormick, R. L.; Taylor, J. D.; Murphy, M. J.
2014-08-01
This report is an updated version of the 2004 Compendium of Experimental Cetane Number Data and presents a compilation of measured cetane numbers for pure chemical compounds. It includes all available single compound cetane number data found in the scientific literature up until March 2014 as well as a number of unpublished values, most measured over the past decade at the National Renewable Energy Laboratory. This Compendium contains cetane values for 389 pure compounds, including 189 hydrocarbons and 201 oxygenates. More than 250 individual measurements are new to this version of the Compendium. For many compounds, numerous measurements are included, often collected by different researchers using different methods. Cetane number is a relative ranking of a fuel's autoignition characteristics for use in compression ignition engines; it is based on the amount of time between fuel injection and ignition, also known as ignition delay. The cetane number is typically measured either in a single-cylinder engine or a constant volume combustion chamber. Values in the previous Compendium derived from octane numbers have been removed, and replaced with a brief analysis of the correlation between cetane numbers and octane numbers. The discussion on the accuracy and precision of the most commonly used methods for measuring cetane has been expanded and the data has been annotated extensively to provide additional information that will help the reader judge the relative reliability of individual results.
BKP and projective Hurwitz numbers
NASA Astrophysics Data System (ADS)
Natanzon, Sergey M.; Orlov, Aleksandr Yu.
2017-02-01
We consider d-fold branched coverings of the projective plane RP^2 and show that the hypergeometric tau function of the BKP hierarchy of Kac and van de Leur is the generating function for weighted sums of the related Hurwitz numbers. In particular, we get the RP^2 analogues of the CP^1 generating functions proposed by Okounkov and by Goulden and Jackson. Other examples are Hurwitz numbers weighted by the Hall-Littlewood and by the Macdonald polynomials. We also consider integrals of tau functions which generate Hurwitz numbers related to base surfaces with arbitrary Euler characteristics e, in particular projective Hurwitz numbers e=1.
Brain representations of negative numbers.
Parnes, Michael; Berger, Andrea; Tzelgov, Joseph
2012-12-01
Participants performed a physical comparison task of pairs of positive and pairs of negative one-digit numbers while their electrophysiological brain activity was measured. The numerical value of the presented digits was either congruent or incongruent with the physical size of the digits. Analysis has shown that the earliest event-related potential (ERP) difference between positive and negative numbers was found in the P300 ERP component peak, where there was an inverse effect of congruity in the negative pairs, compared with the positive ones. This pattern of results supports the idea that natural numbers serve as primitives of the human cognitive system, whereas negative numbers are apparently generated if needed.
Measuring Distance of Fuzzy Numbers by Trapezoidal Fuzzy Numbers
NASA Astrophysics Data System (ADS)
Hajjari, Tayebeh
2010-11-01
Fuzzy numbers and more generally linguistic values are approximate assessments, given by experts and accepted by decision-makers when obtaining value that is more accurate is impossible or unnecessary. Distance between two fuzzy numbers plays an important role in linguistic decision-making. It is reasonable to define a fuzzy distance between fuzzy objects. To achieve this aim, the researcher presents a new distance measure for fuzzy numbers by means of improved centroid distance method. The metric properties are also studied. The advantage is the calculation of the proposed method is far simple than previous approaches.
Building Buildings with Triangular Numbers
ERIC Educational Resources Information Center
Pagni, David L.
2006-01-01
Triangular numbers are used to unravel a new sequence of natural numbers here-to-fore not appearing on the Encyclopedia of Integer Sequences website. Insight is provided on the construction of the sequence using "buildings" as a viewable model of the sequence entries. A step-by-step analysis of the sequence pattern reveals a method for generating…
ERIC Educational Resources Information Center
Pomerance, Carl
1982-01-01
Until recently the testing of a 100-digit number to determine whether it is prime or composite could have taken a century. However, in the past two years a method has been developed enabling a computer to determine the primality of an arbitrary number in about 40 seconds of running time. (Author/JN)
Regular Numbers and Mathematical Worlds
ERIC Educational Resources Information Center
Whitacre, Ian; Bouhjar, Khalid; Bishop, Jessica Pierson; Philipp, Randolph; Schappelle, Bonnie P.
2016-01-01
Rather than describing the challenges of integer learning in terms of a transition from positive to negative numbers, we have arrived at a different perspective: We view students as inhabiting distinct mathematical worlds consisting of particular types of numbers (as construed by the students). These worlds distinguish and illuminate students'…
Identifying Fractions on Number Lines.
ERIC Educational Resources Information Center
Behr, Merlyn J.; Bright, George W.
A two-year study was conducted with fourth-grade children in the context of extensive teaching experiments concerned with the learning of rational number concepts. Representational difficulties in using the number line model were investigated. While instruction in the second year attempted to resolve observed learning difficulties, the results of…
Counting copy number and calories.
White, Stefan
2015-08-01
Copy number variation (CNV) at several genomic loci has been associated with different human traits and diseases, but in many cases the findings could not be replicated. A new study provides insights into the degree of variation present at the amylase locus and calls into question a previous association between amylase copy number and body mass index.
Number Talks Build Numerical Reasoning
ERIC Educational Resources Information Center
Parrish, Sherry D.
2011-01-01
"Classroom number talks," five- to fifteen-minute conversations around purposefully crafted computation problems, are a productive tool that can be incorporated into classroom instruction to combine the essential processes and habits of mind of doing math. During number talks, students are asked to communicate their thinking when presenting and…
Investigating the Randomness of Numbers
ERIC Educational Resources Information Center
Pendleton, Kenn L.
2009-01-01
The use of random numbers is pervasive in today's world. Random numbers have practical applications in such far-flung arenas as computer simulations, cryptography, gambling, the legal system, statistical sampling, and even the war on terrorism. Evaluating the randomness of extremely large samples is a complex, intricate process. However, the…
Toddlers' Spontaneous Attention to Number
ERIC Educational Resources Information Center
Baroody, Arthur J.; Li, Xia; Lai, Meng-lung
2008-01-01
Hannula and Lehtinen (2001, 2005) defined spontaneous focusing on numerosity (SFON) as the tendency to notice the relatively abstract attribute of number despite the presence of other attributes. According to nativists, an innate concept of one to three directs young children's attention to these "intuitive numbers" in everyday situations--even…
Spontaneous Number Representation in Mosquitofish
ERIC Educational Resources Information Center
Dadda, Marco; Piffer, Laura; Agrillo, Christian; Bisazza, Angelo
2009-01-01
While there is convincing evidence that preverbal human infants and non-human primates can spontaneously represent number, considerable debate surrounds the possibility that such capacity is also present in other animals. Fish show a remarkable ability to discriminate between different numbers of social companions. Previous work has demonstrated…
The Algebra of Complex Numbers.
ERIC Educational Resources Information Center
LePage, Wilbur R.
This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…
Some Ideas About Number Theory.
ERIC Educational Resources Information Center
Barnett, I. A.
The material in this booklet is designed for non-professional mathematicians who have an interest in the theory of numbers. The author presents some elementary results of number theory without involving detailed proofs. Much of the material has direct application for secondary school mathematics teachers. A brief account of the nature of number…
Talmi, Igal
2008-11-11
The discovery of magic numbers led to the shell model. They indicated closure of major shells and are robust: proton magic numbers are rather independent of the occupation of neutron orbits and vice versa. Recently the magic property became less stringent and we hear a lot about the discovery of new magic numbers. These, however, indicate sub-shell closures and strongly depend on occupation numbers and hence, may be called quasi-magic numbers. Some of these have been known for many years and the mechanism for their appearance as well as disappearance, was well understood within the simple shell model. The situation will be illustrated by a few examples which demonstrate the simple features of the shell model. Will this simplicity emerge from the complex computations of nuclear many-body theory?.
SOME CHROMOSOME NUMBERS OF DRAPARNALDIA.
Carroll, J W; Deason, T R
1969-03-01
The variability exhibited by Draparnaldia both in nature and in the laboratory makes it difficult to identify the species. The natural variability of Draparnaldia was amplified by the environmental conditions and the media used in this study. With the hope that chromosome studies would aid in taxonomic characterization by providing additional differentiating criteria, special attention was devoted to adapting techniques which could be used to determine chromosome numbers of Draparnaldia isolates. The chromosome numbers reported herein are as follows: (1) Draparnaldia glomerata, Isolate #1, isolated from Davis Falls, Montevallo, Alabama, was found to have a chromosome number of 13. (2) Draparnaldia Isolate #2, an unidentified species obtained from Anniston, Alabama, was found to have a chromosome number of 13. (3) Draparnaldia acuta, Isolate #3 from Northwood Lake, Northport, Alabama, exhibited 26 chromosomes. (4) Draparnaldia plumosa strain 423 (Indiana Culture Collection), 418/a (Cambridge) was observed to have a chromosome number of 13.
Reynolds number influences in aeronautics
NASA Technical Reports Server (NTRS)
Bushnell, Dennis M.; Yip, Long P.; Yao, Chung-Sheng; Lin, John C.; Lawing, Pierce L.; Batina, John T.; Hardin, Jay C.; Horvath, Thomas J.; Fenbert, James W.; Domack, Christopher S.
1993-01-01
Reynolds number, a measure of the ratio of inertia to viscous forces, is a fundamental similarity parameter for fluid flows and therefore, would be expected to have a major influence in aerodynamics and aeronautics. Reynolds number influences are generally large, but monatomic, for attached laminar (continuum) flow; however, laminar flows are easily separated, inducing even stronger, non-monatomic, Reynolds number sensitivities. Probably the strongest Reynolds number influences occur in connection with transitional flow behavior. Transition can take place over a tremendous Reynolds number range, from the order of 20 x 10(exp 3) for 2-D free shear layers up to the order of 100 x 10(exp 6) for hypersonic boundary layers. This variability in transition behavior is especially important for complex configurations where various vehicle and flow field elements can undergo transition at various Reynolds numbers, causing often surprising changes in aerodynamics characteristics over wide ranges in Reynolds number. This is further compounded by the vast parameterization associated with transition, in that any parameter which influences mean viscous flow development (e.g., pressure gradient, flow curvature, wall temperature, Mach number, sweep, roughness, flow chemistry, shock interactions, etc.), and incident disturbance fields (acoustics, vorticity, particulates, temperature spottiness, even electro static discharges) can alter transition locations to first order. The usual method of dealing with the transition problem is to trip the flow in the generally lower Reynolds number wind tunnel to simulate the flight turbulent behavior. However, this is not wholly satisfactory as it results in incorrectly scaled viscous region thicknesses and cannot be utilized at all for applications such as turbine blades and helicopter rotors, nacelles, leading edge and nose regions, and High Altitude Long Endurance and hypersonic airbreathers where the transitional flow is an innately critical
Poison control center - emergency number
For a POISON EMERGENCY call: 1-800-222-1222 ANYWHERE IN THE UNITED STATES This national hotline number will let you ... is a free and confidential service. All local poison control centers in the United States use this ...
Atomic Structure - A Numbers Game
ERIC Educational Resources Information Center
George, W. O.; Vincent, A.
1975-01-01
Emphasizes the simplicity and elegance of early discoveries related to the hydrogen spectrum and provides an elementary experimental basis of quantum theory based on a "numbers game" which can be played by students. (Author/GS)
Integral Presentations of Catalan Numbers
ERIC Educational Resources Information Center
Dana-Picard, Thierry
2010-01-01
We compute in three different ways the same definite parametric integral. By-products are the derivation of a combinatorial identity and two integral presentations of Catalan numbers. One of them leads to a presentation using the [gamma] function.
Avogadro's Number and Avogadro's Constant
ERIC Educational Resources Information Center
Davies, R. O.
1973-01-01
Discusses three possible methods of thinking about the implications of the definitions of the Avogadro constant and number. Indicates that there is only one way to arrive at a simple and standard conclusion. (CC)
Fibonacci Numbers and the Spreadsheet.
ERIC Educational Resources Information Center
Verderber, Nadine L.
1991-01-01
Described is a classroom activity incorporating a computer spreadsheet to study number patterns generated by the Fibonacci sequence. Included are examples and suggestions for the use of the spreadsheet in other recursive relationships. (JJK)
Graspable Objects Shape Number Processing
Ranzini, Mariagrazia; Lugli, Luisa; Anelli, Filomena; Carbone, Rossella; Nicoletti, Roberto; Borghi, Anna M.
2011-01-01
The field of numerical cognition represents an interesting case for action-based theories of cognition, since number is a special kind of abstract concept. Several studies have shown that within the parietal lobes adjacent neural regions code numerical magnitude and grasping-related information. This anatomical proximity between brain areas involved in number and sensorimotor processes may account for interactions between numerical magnitude and action. In particular, recent studies have demonstrated a causal role of action perception on numerical magnitude processing. If objects are represented in terms of actions (affordances), the causal role of action on number processing should extend to the case of objects affordances. This study investigates the relationship between numbers and objects affordances in two experiments, without (Experiment 1) or with (Experiment 2) the requirement of an action (i.e., participants were asked to hold an object in their hands during the task). The task consisted in repeating aloud the odd or even digit within a pair depending on the type of the preceding or following object. Order of presentation (object–number vs. number–object), Object type (graspable vs. ungraspable), Object size (small vs. large), and Numerical magnitude (small vs. large) were manipulated for each experiment. Experiment 1 showed a facilitation – in terms of quicker responses – for graspable over ungraspable objects preceded by numbers, and an effect of numerical magnitude after the presentation of graspable objects. Experiment 2 demonstrated that the action execution enhanced overall the sensitivity to numerical magnitude, and that at the same time it interfered with the effects of objects affordances on number processing. Overall, these findings demonstrate that numbers and graspable objects are strongly interrelated, supporting the view that abstract concepts may be grounded in the motor experience. PMID:22164141
Entropy estimation and Fibonacci numbers
NASA Astrophysics Data System (ADS)
Timofeev, Evgeniy A.; Kaltchenko, Alexei
2013-05-01
We introduce a new metric on a space of right-sided infinite sequences drawn from a finite alphabet. Emerging from a problem of entropy estimation of a discrete stationary ergodic process, the metric is important on its own part and exhibits some interesting properties. Notably, the number of distinct metric values for a set of sequences of length m is equal to Fm+3 - 1, where Fm is a Fibonacci number.
Random numbers from vacuum fluctuations
NASA Astrophysics Data System (ADS)
Shi, Yicheng; Chng, Brenda; Kurtsiefer, Christian
2016-07-01
We implement a quantum random number generator based on a balanced homodyne measurement of vacuum fluctuations of the electromagnetic field. The digitized signal is directly processed with a fast randomness extraction scheme based on a linear feedback shift register. The random bit stream is continuously read in a computer at a rate of about 480 Mbit/s and passes an extended test suite for random numbers.
Dimensionless numbers in additive manufacturing
NASA Astrophysics Data System (ADS)
Mukherjee, T.; Manvatkar, V.; De, A.; DebRoy, T.
2017-02-01
The effects of many process variables and alloy properties on the structure and properties of additively manufactured parts are examined using four dimensionless numbers. The structure and properties of components made from 316 Stainless steel, Ti-6Al-4V, and Inconel 718 powders for various dimensionless heat inputs, Peclet numbers, Marangoni numbers, and Fourier numbers are studied. Temperature fields, cooling rates, solidification parameters, lack of fusion defects, and thermal strains are examined using a well-tested three-dimensional transient heat transfer and fluid flow model. The results show that lack of fusion defects in the fabricated parts can be minimized by strengthening interlayer bonding using high values of dimensionless heat input. The formation of harmful intermetallics such as laves phases in Inconel 718 can be suppressed using low heat input that results in a small molten pool, a steep temperature gradient, and a fast cooling rate. Improved interlayer bonding can be achieved at high Marangoni numbers, which results in vigorous circulation of liquid metal, larger pool dimensions, and greater depth of penetration. A high Fourier number ensures rapid cooling, low thermal distortion, and a high ratio of temperature gradient to the solidification growth rate with a greater tendency of plane front solidification.
Number matters: control of mammalian mitochondrial DNA copy number.
Clay Montier, Laura L; Deng, Janice J; Bai, Yidong
2009-03-01
Regulation of mitochondrial biogenesis is essential for proper cellular functioning. Mitochondrial DNA (mtDNA) depletion and the resulting mitochondrial malfunction have been implicated in cancer, neurodegeneration, diabetes, aging, and many other human diseases. Although it is known that the dynamics of the mammalian mitochondrial genome are not linked with that of the nuclear genome, very little is known about the mechanism of mtDNA propagation. Nevertheless, our understanding of the mode of mtDNA replication has advanced in recent years, though not without some controversies. This review summarizes our current knowledge of mtDNA copy number control in mammalian cells, while focusing on both mtDNA replication and turnover. Although mtDNA copy number is seemingly in excess, we reason that mtDNA copy number control is an important aspect of mitochondrial genetics and biogenesis and is essential for normal cellular function.
Number Meaning and Number Grammar in English and Spanish
ERIC Educational Resources Information Center
Bock, Kathryn; Carreiras, Manuel; Meseguer, Enrique
2012-01-01
Grammatical agreement makes different demands on speakers of different languages. Being widespread in the languages of the world, the features of agreement systems offer valuable tests of how language affects deep-seated domains of human cognition and categorization. Number agreement is one such domain, with intriguing evidence that typological…
The MIXMAX random number generator
NASA Astrophysics Data System (ADS)
Savvidy, Konstantin G.
2015-11-01
In this paper, we study the randomness properties of unimodular matrix random number generators. Under well-known conditions, these discrete-time dynamical systems have the highly desirable K-mixing properties which guarantee high quality random numbers. It is found that some widely used random number generators have poor Kolmogorov entropy and consequently fail in empirical tests of randomness. These tests show that the lowest acceptable value of the Kolmogorov entropy is around 50. Next, we provide a solution to the problem of determining the maximal period of unimodular matrix generators of pseudo-random numbers. We formulate the necessary and sufficient condition to attain the maximum period and present a family of specific generators in the MIXMAX family with superior performance and excellent statistical properties. Finally, we construct three efficient algorithms for operations with the MIXMAX matrix which is a multi-dimensional generalization of the famous cat-map. First, allowing to compute the multiplication by the MIXMAX matrix with O(N) operations. Second, to recursively compute its characteristic polynomial with O(N2) operations, and third, to apply skips of large number of steps S to the sequence in O(N2 log(S)) operations.
Negative Numbers and Antimatter Particles
NASA Astrophysics Data System (ADS)
Tsan, Ung Chan
Dirac's equation states that an electron implies the existence of an antielectron with the same mass (more generally same arithmetic properties) and opposite charge (more generally opposite algebraic properties). Subsequent observation of antielectron validated this concept. This statement can be extended to all matter particles; observation of antiproton, antineutron, antideuton … is in complete agreement with this view. Recently antihypertriton was observed and 38 atoms of antihydrogen were trapped. This opens the path for use in precise testing of nature's fundamental symmetries. The symmetric properties of a matter particle and its mirror antimatter particle seem to be well established. Interactions operate on matter particles and antimatter particles as well. Conservation of matter parallels addition operating on positive and negative numbers. Without antimatter particles, interactions of the Standard Model (electromagnetism, strong interaction and weak interaction) cannot have the structure of group. Antimatter particles are characterized by negative baryonic number A or/and negative leptonic number L. Materialization and annihilation obey conservation of A and L (associated to all known interactions), explaining why from pure energy (A = 0, L = 0) one can only obtain a pair of matter particle antimatter particle — electron antielectron, proton and antiproton — via materialization where the mass of a pair of particle antiparticle gives back to pure energy with annihilation. These two mechanisms cannot change the difference in the number of matter particles and antimatter particles. Thus from pure energy only a perfectly symmetric (in number) universe could be generated as proposed by Dirac but observation showed that our universe is not symmetric, it is a matter universe which is nevertheless neutral. Fall of reflection symmetries shattered the prejudice that there is no way to define in an absolute way right and left or matter and antimatter
On the three primordial numbers
Gobbetti, Roberto; Pajer, Enrico; Roest, Diederik E-mail: enrico.pajer@gmail.com
2015-09-01
Cosmological observations have provided us with the measurement of just three numbers that characterize the very early universe: 1−n{sub s} , N and ln Δ{sub R}{sup 2}. Although each of the three numbers individually carries limited information about the physics of inflation, one may hope to extract non-trivial information from relations among them. Invoking minimality, namely the absence of ad hoc large numbers, we find two viable and mutually exclusive inflationary scenarios. The first is the well-known inverse relation between 1− n{sub s} and N. The second implies a new relation between 1−n{sub s} and ln Δ{sub R}{sup 2}, which might provide us with a handle on the beginning of inflation and predicts the intriguing lower bound on the tensor-to-scalar ratio r > 0.006 (95% CL)
Negative numbers in simple arithmetic.
Das, Runa; LeFevre, Jo-Anne; Penner-Wilger, Marcie
2010-10-01
Are negative numbers processed differently from positive numbers in arithmetic problems? In two experiments, adults (N = 66) solved standard addition and subtraction problems such as 3 + 4 and 7 - 4 and recasted versions that included explicit negative signs-that is, 3 - (-4), 7 + (-4), and (-4) + 7. Solution times on the recasted problems were slower than those on standard problems, but the effect was much larger for addition than subtraction. The negative sign may prime subtraction in both kinds of recasted problem. Problem size effects were the same or smaller in recasted than in standard problems, suggesting that the recasted formats did not interfere with mental calculation. These results suggest that the underlying conceptual structure of the problem (i.e., addition vs. subtraction) is more important for solution processes than the presence of negative numbers.
Experimental Determination of Ramsey Numbers
NASA Astrophysics Data System (ADS)
Bian, Zhengbing; Chudak, Fabian; Macready, William G.; Clark, Lane; Gaitan, Frank
2013-09-01
Ramsey theory is a highly active research area in mathematics that studies the emergence of order in large disordered structures. Ramsey numbers mark the threshold at which order first appears and are extremely difficult to calculate due to their explosive rate of growth. Recently, an algorithm that can be implemented using adiabatic quantum evolution has been proposed that calculates the two-color Ramsey numbers R(m,n). Here we present results of an experimental implementation of this algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(m,2) for 4≤m≤8. The R(8,2) computation used 84 qubits of which 28 were computational qubits. This computation is the largest experimental implementation of a scientifically meaningful adiabatic evolution algorithm that has been done to date.
Experimental determination of Ramsey numbers.
Bian, Zhengbing; Chudak, Fabian; Macready, William G; Clark, Lane; Gaitan, Frank
2013-09-27
Ramsey theory is a highly active research area in mathematics that studies the emergence of order in large disordered structures. Ramsey numbers mark the threshold at which order first appears and are extremely difficult to calculate due to their explosive rate of growth. Recently, an algorithm that can be implemented using adiabatic quantum evolution has been proposed that calculates the two-color Ramsey numbers R(m,n). Here we present results of an experimental implementation of this algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(m,2) for 4≤m≤8. The R(8,2) computation used 84 qubits of which 28 were computational qubits. This computation is the largest experimental implementation of a scientifically meaningful adiabatic evolution algorithm that has been done to date.
Newborn infants perceive abstract numbers.
Izard, Véronique; Sann, Coralie; Spelke, Elizabeth S; Streri, Arlette
2009-06-23
Although infants and animals respond to the approximate number of elements in visual, auditory, and tactile arrays, only human children and adults have been shown to possess abstract numerical representations that apply to entities of all kinds (e.g., 7 samurai, seas, or sins). Do abstract numerical concepts depend on language or culture, or do they form a part of humans' innate, core knowledge? Here we show that newborn infants spontaneously associate stationary, visual-spatial arrays of 4-18 objects with auditory sequences of events on the basis of number. Their performance provides evidence for abstract numerical representations at the start of postnatal experience.
Biotechnology at low Reynolds numbers.
Brody, J P; Yager, P; Goldstein, R E; Austin, R H
1996-01-01
The shrinking of liquid handling systems to the micron and submicron size range entails moving into the area of small Reynolds numbers. The fluid dynamics in this regime are very different from the macroscale. We present an intuitive explanation of how the different physics of small Reynolds numbers flow, along with microscopic sizes, can influence device design, and give examples from our own work using fluid flow in microfabricated devices designed for biological processing. Images FIGURE 1 FIGURE 9 FIGURE 10 FIGURE 11 FIGURE 12 FIGURE 13 PMID:8968612
Adjuncts Build Strength in Numbers
ERIC Educational Resources Information Center
June, Audrey Williams
2012-01-01
When professors in positions that offer no chance of earning tenure begin to stack the faculty, campus dynamics start to change. Growing numbers of adjuncts make themselves more visible. They push for roles in governance, better pay and working conditions, and recognition for work well done. And they do so at institutions where tenured faculty,…
ERIC Educational Resources Information Center
Materiales, 1997
1997-01-01
These three journals of contemporary cultural, historical, and social interest contain activities designed to enhance the awareness of students of Spanish as a foreign language regarding the entire panorama of daily life in Spain. Number 21 focuses on the role of modern Spanish women; their career status; female authors; and the changing place of…
Residual number processing in dyscalculia.
Cappelletti, Marinella; Price, Cathy J
2014-01-01
Developmental dyscalculia - a congenital learning disability in understanding numerical concepts - is typically associated with parietal lobe abnormality. However, people with dyscalculia often retain some residual numerical abilities, reported in studies that otherwise focused on abnormalities in the dyscalculic brain. Here we took a different perspective by focusing on brain regions that support residual number processing in dyscalculia. All participants accurately performed semantic and categorical colour-decision tasks with numerical and non-numerical stimuli, with adults with dyscalculia performing slower than controls in the number semantic tasks only. Structural imaging showed less grey-matter volume in the right parietal cortex in people with dyscalculia relative to controls. Functional MRI showed that accurate number semantic judgements were maintained by parietal and inferior frontal activations that were common to adults with dyscalculia and controls, with higher activation for participants with dyscalculia than controls in the right superior frontal cortex and the left inferior frontal sulcus. Enhanced activation in these frontal areas was driven by people with dyscalculia who made faster rather than slower numerical decisions; however, activation could not be accounted for by response times per se, because it was greater for fast relative to slow dyscalculics but not greater for fast controls relative to slow dyscalculics. In conclusion, our results reveal two frontal brain regions that support efficient number processing in dyscalculia.
Arrighi, Roberto; Togoli, Irene; Burr, David C.
2014-01-01
Much evidence has accumulated to suggest that many animals, including young human infants, possess an abstract sense of approximate quantity, a number sense. Most research has concentrated on apparent numerosity of spatial arrays of dots or other objects, but a truly abstract sense of number should be capable of encoding the numerosity of any set of discrete elements, however displayed and in whatever sensory modality. Here, we use the psychophysical technique of adaptation to study the sense of number for serially presented items. We show that numerosity of both auditory and visual sequences is greatly affected by prior adaptation to slow or rapid sequences of events. The adaptation to visual stimuli was spatially selective (in external, not retinal coordinates), pointing to a sensory rather than cognitive process. However, adaptation generalized across modalities, from auditory to visual and vice versa. Adaptation also generalized across formats: adapting to sequential streams of flashes affected the perceived numerosity of spatial arrays. All these results point to a perceptual system that transcends vision and audition to encode an abstract sense of number in space and in time. PMID:25377454
Strouhal number for free swimming
NASA Astrophysics Data System (ADS)
Saadat, Mehdi; van Buren, Tyler; Floryan, Daniel; Smits, Alexander; Haj-Hariri, Hossein
2015-11-01
In this work, we present experimental results to explore the implications of free swimming for Strouhal number (as an outcome) in the context of a simple model for a fish that consists of a 2D virtual body (source of drag) and a 2D pitching foil (source of thrust) representing cruising with thunniform locomotion. The results validate the findings of Saadat and Haj-Hariri (2012): for pitching foils thrust coefficient is a function of Strouhal number for all gaits having amplitude less than a certain critical value. Equivalently, given the balance of thrust and drag forces at cruise, Strouhal number is only a function of the shape, i.e. drag coefficient and area, and essentially a constant for high enough swimming speeds for which the mild dependence of drag coefficient on the speed vanishes. Furthermore, a dimensional analysis generalizes the findings. A scaling analysis shows that the variation of Strouhal number with cruising speed is functionally related to the variation of body drag coefficient with speed. Supported by ONR MURI Grant N00014-14-1-0533.
Winding number constrained contour detection.
Ming, Yansheng; Li, Hongdong; He, Xuming
2015-01-01
Salient contour detection can benefit from the integration of both contour cues and region cues. However, this task is difficult due to different nature of region representations and contour representations. To solve this problem, this paper proposes an energy minimization framework based on winding number constraints. In this framework, both region cues, such as color/texture homogeneity, and contour cues, such as local contrast and continuity, are represented in a joint objective function, which has both region and contour labels. The key problem is how to design constraints that ensure the topological consistency of the two kinds of labels. Our technique is based on the topological concept of winding number. Using a fast method for winding number computation, a small number of linear constraints are derived to ensure label consistency. Our method is instantiated by ratio-based energy functions. By successfully integrating both region and contour cues, our method shows advantages over competitive methods. Our method is extended to incorporate user interaction, which leads to further improvements.
ERIC Educational Resources Information Center
Surrena, Michelle
2011-01-01
In order to inspire her students to work in mixed media, the author chose to highlight the art of Jasper Johns and Robert Indiana, both of whom used numbers and letters as a main focus in their art. In this article, the author describes a mixed-media printmaking project. (Contains 2 online resources.)
Number Crunching: A Sheep's Tale
ERIC Educational Resources Information Center
Sam, Chris Lam
2005-01-01
In this article, the author talks about an allegorical tale which he has written as a message for teachers of mathematics. The story is about Gordon, who led a flock of small sheep. Gordon was a mathematics genius; however, his flock criticized his teaching of numbers and his boring lectures. His furry-god-farmer advised him to share his…
Whole Number Subtraction -- An Analysis.
ERIC Educational Resources Information Center
Gilpin, John B.
This document is intended as a resource for persons using, designing, or evaluating instructional materials in whole number subtraction. Its purpose is to provide conceptual machinery: (1) for describing/specifying subtraction tests and exercises and (2) for formulating related questions and conjectures. It is mainly a logical analysis subject to…
ERIC Educational Resources Information Center
Henderson, Nancy
2008-01-01
In the Essex, Cincinnati retirement center where they both worked as nurses, Holly Doherty and Michele Schavoir often heard aides complain about one longtime resident in particular. The patient kicks and screams and nurses can not stand to be around her. After a year of playing detective, Doherty found a number of the patient's relatives in…
An Estimate of Avogadro's Number.
ERIC Educational Resources Information Center
Stauffer, Frederic R.
1991-01-01
Calculates an approximation to Avagadro's number for one mole of water by assuming the mole to be in cubical form and then halving the cube three times, thereby doubling the surface area of the original cube. The calculations are derived from the work necessary to perform these divisions. Presents calculated values for several liquids. (MDH)
High Reynolds number research - 1980
NASA Technical Reports Server (NTRS)
Mckinney, L. W. (Editor); Baals, D. D. (Editor)
1981-01-01
The fundamental aerodynamic questions for which high Reynolds number experimental capability is required were examined. Potential experiments which maximize the research returns from the use of the National Transonic Facility (NTF) were outlined. Calibration plans were reviewed and the following topics were discussed: fluid dynamics; high lit; configuration aerodynamics; aeroelasticity and unsteady aerodynamics; wind tunnel/flight correlation; space vehicles; and theoretical aerodynamics
ERIC Educational Resources Information Center
Materiales, 1995
1995-01-01
Four booklets present articles on Spanish language and culture aimed at teachers of Spanish in the United States for student use in their classes. Number 17, "Los Jovenes Espanoles" (Spanish Youth), includes articles on Spanish youth sports, music, gangs, thoughts, and t-shirt slogans: (1) "Young Spanish Athletes"; (2)…
Solar System Number-Crunching.
ERIC Educational Resources Information Center
Albrecht, Bob; Firedrake, George
1997-01-01
Defines terrestrial and Jovian planets and provides directions to obtain planetary data from the National Space Science Data Center Web sites. Provides "number-crunching" activities for the terrestrial planets using Texas Instruments TI-83 graphing calculators: computing volumetric mean radius and volume, density, ellipticity, speed,…
Questioning Zero and Negative Numbers
ERIC Educational Resources Information Center
Wilcox, Virginia B.
2008-01-01
After experiencing a Developing Mathematical Ideas (DMI) class on the construction of algebraic concepts surrounding zero and negative numbers, the author conducted an interview with a first grader to determine the youngster's existing level of understanding about these topics. Uncovering young students' existing understanding can provide focus…
A generalized sense of number.
Arrighi, Roberto; Togoli, Irene; Burr, David C
2014-12-22
Much evidence has accumulated to suggest that many animals, including young human infants, possess an abstract sense of approximate quantity, a number sense. Most research has concentrated on apparent numerosity of spatial arrays of dots or other objects, but a truly abstract sense of number should be capable of encoding the numerosity of any set of discrete elements, however displayed and in whatever sensory modality. Here, we use the psychophysical technique of adaptation to study the sense of number for serially presented items. We show that numerosity of both auditory and visual sequences is greatly affected by prior adaptation to slow or rapid sequences of events. The adaptation to visual stimuli was spatially selective (in external, not retinal coordinates), pointing to a sensory rather than cognitive process. However, adaptation generalized across modalities, from auditory to visual and vice versa. Adaptation also generalized across formats: adapting to sequential streams of flashes affected the perceived numerosity of spatial arrays. All these results point to a perceptual system that transcends vision and audition to encode an abstract sense of number in space and in time.
Oxidation Numbers and Their Limitations.
ERIC Educational Resources Information Center
Woolf, A. A.
1988-01-01
Reviews a method for determining oxidation numbers in covalent compounds and balancing mixed organic-inorganic or purely organic systems. Points out ambiguities presented when adjacent atoms have small or zero electronegativity differences. Presents other limitations that arise when using electronegativity values. (CW)
Upper bounds on Nusselt number at finite Prandtl number
NASA Astrophysics Data System (ADS)
Choffrut, Antoine; Nobili, Camilla; Otto, Felix
2016-02-01
We study Rayleigh-Bénard convection based on the Boussinesq approximation. We are interested in upper bounds on the Nusselt number Nu, the upwards heat transport, in terms of the Rayleigh number Ra, that characterizes the relative strength of the driving mechanism and the Prandtl number Pr, that characterizes the strength of the inertial effects. We show that, up to logarithmic corrections, the upper bound Nu ≲Ra1/3 from [1] persists as long as Pr ≳Ra1/3 and then crosses over to Nu ≲Pr-1/2Ra1/2. This result improves the one of Wang [2] by going beyond the perturbative regime Pr ≫ Ra . The proof uses a new way to estimate the transport nonlinearity in the Navier-Stokes equations capitalizing on the no-slip boundary condition. It relies on a new Calderón-Zygmund estimate for the non-stationary Stokes equations in L1 with a borderline Muckenhoupt weight.
Energy: Selected Facts and Numbers
2008-08-08
air quality by reducing emissions led utilities to convert a number of coal-fired powerplants to burn oil, and many new plants were designed to burn...years were recently submitted, but no new plants are currently under construction or on order. Construction of major hydroelectric projects has also...5.1 and 5.13a-d. Percentages calculated by CRS. Industrial consumption of petroleum, which includes such large consumers as refineries and
2011-12-01
person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number...points, and other population- control measures imposed as part of the counterinsurgency cam- paign. While these may seem repressive, specific case...structures and forces that share one’s agenda, either in part or in full, does not represent an abdication of control or loss of ini- tiative; it is in
Complex numbers in quantum theory
NASA Astrophysics Data System (ADS)
Maynard, Glenn
In 1927, Nobel prize winning physicist, E. Schrodinger, in correspondence with Ehrenfest, wrote the following about the new theory: "What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers. Psi is surely fundamentally a real function." This seemingly simple issue remains unexplained almost ninety years later. In this dissertation I elucidate the physical and theoretical origins of the complex requirement. (Abstract shortened by ProQuest.).
Sasanguie, Delphine; Göbel, Silke M; Moll, Kristina; Smets, Karolien; Reynvoet, Bert
2013-03-01
In this study, the performance of typically developing 6- to 8-year-old children on an approximate number discrimination task, a symbolic comparison task, and a symbolic and nonsymbolic number line estimation task was examined. For the first time, children's performances on these basic cognitive number processing tasks were explicitly contrasted to investigate which of them is the best predictor of their future mathematical abilities. Math achievement was measured with a timed arithmetic test and with a general curriculum-based math test to address the additional question of whether the predictive association between the basic numerical abilities and mathematics achievement is dependent on which math test is used. Results revealed that performance on both mathematics achievement tests was best predicted by how well childrencompared digits. In addition, an association between performance on the symbolic number line estimation task and math achievement scores for the general curriculum-based math test measuring a broader spectrum of skills was found. Together, these results emphasize the importance of learning experiences with symbols for later math abilities.
Quasiperpendicular High Mach Number Shocks
NASA Astrophysics Data System (ADS)
Sulaiman, A. H.; Masters, A.; Dougherty, M. K.; Burgess, D.; Fujimoto, M.; Hospodarsky, G. B.
2015-09-01
Shock waves exist throughout the Universe and are fundamental to understanding the nature of collisionless plasmas. Reformation is a process, driven by microphysics, which typically occurs at high Mach number supercritical shocks. While ongoing studies have investigated this process extensively both theoretically and via simulations, their observations remain few and far between. In this Letter we present a study of very high Mach number shocks in a parameter space that has been poorly explored and we identify reformation using in situ magnetic field observations from the Cassini spacecraft at 10 AU. This has given us an insight into quasiperpendicular shocks across 2 orders of magnitude in Alfvén Mach number (MA ) which could potentially bridge the gap between modest terrestrial shocks and more exotic astrophysical shocks. For the first time, we show evidence for cyclic reformation controlled by specular ion reflection occurring at the predicted time scale of ˜0.3 τc , where τc is the ion gyroperiod. In addition, we experimentally reveal the relationship between reformation and MA and focus on the magnetic structure of such shocks to further show that for the same MA , a reforming shock exhibits stronger magnetic field amplification than a shock that is not reforming.
Simple low Reynolds number microswimmers
NASA Astrophysics Data System (ADS)
Cheang, U. Kei; Kim, Min Jun
2016-11-01
An extremely simple low Reynolds number microswimmer had been observed to swim in bulk fluid. The development of microscopic swimmers had been hindered by technical limitations in micro- and nanofabrication. To address this practical problem, the minimal geometrical requirements for swimming in low Reynolds number has been investigated. Micro- and nanofabrication of complex shapes with specialized materials, such as helices or flexible bodies, on a massive scale requires sophisticated state of the art technologies which have size limitations. In contrast, simple shaped structures, such as spherical particles, can be synthesized massively using chemical methods with relative ease at low costs. In this work, simple microswimmers were fabricated by conjugating two microbeads with debris attached to their surface. The debris allow the 2-bead structures to have two or more planes of symmetry, thus, allowing them to swim in bulk fluid at low Reynolds number. The microswimmers are magnetically actuated and controlled via a rotating magnetic field generated by an electromagnetic coil system. The microswimmers' velocity profiles had been characterized with respect to increasing rotating frequency. Furthermore, the motion of the microswimmers were analyzed using image processing. Finally, their swimming capability had been shown through experiments by steering the microswimmers in any desired direction.
A Pseudo-Random Number Generator Based on Normal Numbers
Bailey, David H.
2004-12-31
In a recent paper, Richard Crandall and the present author established that each of a certain class of explicitly given real constants, uncountably infinite in number, is b-normal, for an integer that appears in the formula defining the constant. A b-normal constant is one where every string of m digits appears in the base-b expansion of the constant with limiting frequency b{sup -m}. This paper shows how this result can be used to fashion an efficient and effective pseudo-random number generator, which generates successive strings of binary digits from one of the constants in this class. The resulting generator, which tests slightly faster than a conventional linear congruential generator, avoids difficulties with large power-of-two data access strides that may occur when using conventional generators. It is also well suited for parallel processing--each processor can quickly and independently compute its starting value, with the collective sequence generated by all processors being the same as that generated by a single processor.
The conceptual representation of number.
Patson, Nikole D; George, Gerret; Warren, Tessa
2014-01-01
The experiments reported here investigated the format of plural conceptual representations using a picture-matching paradigm. In Experiment 1, participants read sentences that ended with a singular noun phrase (NP), a two-quantified plural NP, or a plural definite description [The parents handed the child the (two) crayon/s] and then saw a picture of one or multiple referents for the NP. Judgement times to confirm that there was overlap between the pictured object(s) and a noun in the sentence showed an interaction between the NP's number and NP-picture match. For singular NPs and two-quantified NPs, participants were reliably faster to respond "yes" to a picture that had the exact number of objects specified by the NP, but for plural definite descriptions, the effect of the number of pictured items was not reliable. Experiment 2 extended this finding to conceptual plurals. Participants read sentences biased toward either a collective (Together the men carried a box-box is interpreted as singular) or distributed (Each of the men carried a box-box is likely interpreted as plural) reading. Experiment 2 showed the same interaction between NP conceptual plurality and NP-picture match as that in Experiment 1. These results suggest that: (a) our default conceptual representations for plural definite descriptions are no more similar to images of small sets of multiple items than to images of singular items; and (b) the difference between singular and plural conceptual representations is unlikely to be simply the presence or absence of a plural feature. The results are consistent with theories in which plurality is unmarked, such that some plural NPs can refer to singular referents [e.g., Sauerland, U., Anderssen, J., & Yatsushiro, J. (2005). The plural is semantically unmarked. In S. Kepser & M. Reis (Eds.), Linguistic evidence (pp. 413-434). Berlin: de Gruyter].
Formation number for vortex dipoles
NASA Astrophysics Data System (ADS)
Sadri, Vahid; Krueger, Paul S.
2016-11-01
This investigation considers the axisymmetric formation of two opposite sign concentric vortex rings from jet ejection between concentric cylinders. This arrangement is similar to planar flow in that the vortex rings will travel together when the gap between the cylinders is small, similar to a vortex dipole, but it has the advantage that the vortex motion is less constrained than the planar case (vortex stretching and vortex line curvature is allowed). The flow was simulated numerically at a jet Reynolds number of 1,000 (based on ΔR and the jet velocity), jet pulse length-to-gap ratio (L / ΔR) in the range 10-20, and gap-to-outer radius ratio (ΔR /Ro) in the range 0.01-0.1. Small gap ratios were chosen for comparison with 2D results. In contrast with 2D results, the closely paired vortices in this study exhibited pinch-off from the generating flow and finite formation numbers. The more complex flow evolution afforded by the axisymmetric model and its influence on the pinch-off process will be discussed. This material is based on work supported by the National Science Foundation under Grant No. 1133876 and SMU. This supports are gratefully acknowledged.
Indexing the approximate number system.
Inglis, Matthew; Gilmore, Camilla
2014-01-01
Much recent research attention has focused on understanding individual differences in the approximate number system, a cognitive system believed to underlie human mathematical competence. To date researchers have used four main indices of ANS acuity, and have typically assumed that they measure similar properties. Here we report a study which questions this assumption. We demonstrate that the numerical ratio effect has poor test-retest reliability and that it does not relate to either Weber fractions or accuracy on nonsymbolic comparison tasks. Furthermore, we show that Weber fractions follow a strongly skewed distribution and that they have lower test-retest reliability than a simple accuracy measure. We conclude by arguing that in the future researchers interested in indexing individual differences in ANS acuity should use accuracy figures, not Weber fractions or numerical ratio effects.
Redundant Multiple-Valued Number Systems
1997-07-01
Fibonacci ou de nombres de Lucas ,” Bull. Soc. Royale Sci. Liege 41, 1972, pp. 179-182. 14-1 ABSTRACT We survey number systems in which the...Figure 5. The 4-Bit One’s Complement Number System. E. FIBONACCI NUMBER SYSTEM The Fibonacci number system is the second example of a redundant number ...instead of powers of 2 or -2, Fibonacci numbers are used as the base. In such a number system, there are many redundant representatives. Fig.
Random Number Generation for High Performance Computing
2015-01-01
REPORT TYPE 17. LIMITATION OF ABSTRACT 15. NUMBER OF PAGES 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 5c. PROGRAM ELEMENT NUMBER...of Distinct Pseudorandom Number Streams Based on Program Context," and "A Statistical Test Method to Quantify Inter-Streams Based on Program Context...regarding the development and implementation of the context aware pseudorandom number generator test program . Provide subject matter expertise (testing
Verification Challenges at Low Numbers
Benz, Jacob M.; Booker, Paul M.; McDonald, Benjamin S.
2013-07-16
This paper will explore the difficulties of deep reductions by examining the technical verification challenges. At each step on the road to low numbers, the verification required to ensure compliance of all parties will increase significantly. Looking post New START, the next step will likely include warhead limits in the neighborhood of 1000 (Pifer 2010). Further reductions will include stepping stones at 100’s of warheads, and then 10’s of warheads before final elimination could be considered of the last few remaining warheads and weapons. This paper will focus on these three threshold reduction levels, 1000, 100’s, 10’s. For each, the issues and challenges will be discussed, potential solutions will be identified, and the verification technologies and chain of custody measures that address these solutions will be surveyed. It is important to note that many of the issues that need to be addressed have no current solution. In these cases, the paper will explore new or novel technologies that could be applied. These technologies will draw from the research and development that is ongoing throughout the national lab complex, and will look at technologies utilized in other areas of industry for their application to arms control verification.
Verification Challenges at Low Numbers
Benz, Jacob M.; Booker, Paul M.; McDonald, Benjamin S.
2013-06-01
Many papers have dealt with the political difficulties and ramifications of deep nuclear arms reductions, and the issues of “Going to Zero”. Political issues include extended deterrence, conventional weapons, ballistic missile defense, and regional and geo-political security issues. At each step on the road to low numbers, the verification required to ensure compliance of all parties will increase significantly. Looking post New START, the next step will likely include warhead limits in the neighborhood of 1000 . Further reductions will include stepping stones at1000 warheads, 100’s of warheads, and then 10’s of warheads before final elimination could be considered of the last few remaining warheads and weapons. This paper will focus on these three threshold reduction levels, 1000, 100’s, 10’s. For each, the issues and challenges will be discussed, potential solutions will be identified, and the verification technologies and chain of custody measures that address these solutions will be surveyed. It is important to note that many of the issues that need to be addressed have no current solution. In these cases, the paper will explore new or novel technologies that could be applied. These technologies will draw from the research and development that is ongoing throughout the national laboratory complex, and will look at technologies utilized in other areas of industry for their application to arms control verification.
Access to emergency number services.
Harkins, Judith E; Strauss, Karen Peltz
2008-01-01
Access to emergency services is mandated by Title II of the Americans with Disabilities Act (ADA). The Department of Justice oversees the accessibility of public safety answering points (PSAPs), popularly called 9-1-1 centers. The Federal Communications Commission (FCC) has at least two roles in emergency number access: (1) as regulator of the ADA's Title IV on telecommunications access, and (2) as regulator of communications companies with regard to support of and interconnection with PSAPs. The rules of both agencies contributed significantly to the improvement during the 1990s of access to 9-1-1 for people who are deaf, hard of hearing, or speech disabled. However, as new technologies for text wireless communications and relay services have moved quickly to Internet protocol (IP)-based technologies over the past 5-8 years, the use of traditional wireline telephones and text telephones among deaf, hard of hearing, and speech-disabled people has declined. PSAPs cannot be contacted via the newer forms of telecommunications, such as e-mail, instant messaging, and IP-based forms of relay services, including video relay services. The gap between the technology supported by policy and the technologies currently being used by deaf and hard of hearing people has become a serious problem that is difficult to solve because of the separate jurisdictions of the two agencies, the need for coordination within the FCC, technological challenges, and funding issues. In this article, the key policy and technology challenges will be analyzed and recommendations made for short-and long-term solutions to this dilemma.
Numbers, Counting, and Infinity in Middle Schools.
ERIC Educational Resources Information Center
Meconi, L. J.
1992-01-01
Discusses the use of middle-school students' natural understanding of large numbers to introduce the concept of infinity. Presents activities that investigate infinite sets by demonstrating a one-to-one correspondence between the counting numbers and the given set. Examples include prime numbers, Fibonacci numbers, fractions, even and odd numbers,…
14 CFR 47.15 - Registration number.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 14 Aeronautics and Space 1 2013-01-01 2013-01-01 false Registration number. 47.15 Section 47.15... REGISTRATION General § 47.15 Registration number. (a) Number required. An applicant for aircraft registration must place a U.S. registration number (registration mark) on the Aircraft Registration Application,...
14 CFR 47.15 - Registration number.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 14 Aeronautics and Space 1 2012-01-01 2012-01-01 false Registration number. 47.15 Section 47.15... REGISTRATION General § 47.15 Registration number. (a) Number required. An applicant for aircraft registration must place a U.S. registration number (registration mark) on the Aircraft Registration Application,...
14 CFR 47.15 - Registration number.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 14 Aeronautics and Space 1 2011-01-01 2011-01-01 false Registration number. 47.15 Section 47.15... REGISTRATION General § 47.15 Registration number. (a) Number required. An applicant for aircraft registration must place a U.S. registration number (registration mark) on the Aircraft Registration Application,...
Orbital elements of numbered minor planets.
NASA Astrophysics Data System (ADS)
Williams, G. V.; Marsden, B. G.; Asher, D. J.; Nakano, S.
2000-06-01
This list is a continuation of Abstr. 098.023. The numbered minor planets are listed according to their definitive number. Newly numbered objects are indicated by an asterisk. The names of the orbit computers are given behind the respective M.P.C. (or MPO) numbers:
Contextual Effects on Number-Time Interaction
ERIC Educational Resources Information Center
Lu, Aitao; Hodges, Bert; Zhang, Jijia; Zhang, John X.
2009-01-01
Time perception has long been known to be affected by numerical representations. Recent studies further demonstrate that when participants estimate the duration of Arabic numbers, number magnitude, though task-irrelevant, biases duration judgment to produce underestimation for smaller numbers and overestimation for larger numbers. Such effects…
The Decimal Number System and Young Children
ERIC Educational Resources Information Center
Harrison, John
2006-01-01
In this article, the author believes that a visual image of the number system is helpful to everyone, especially children, in understanding what is, after all, an abstract idea. The simplest model is the number line, a row of equally spaced numbers, starting at zero. This illustrates the continuous progression of the natural numbers, moving to the…
Avogadro Number and Mole: A Royal Confusion.
ERIC Educational Resources Information Center
Emiliani, Cesare
1991-01-01
There is a great deal of confusion in physics and chemistry textbooks, dictionaries, manuals, and handbooks about the definition of Avogadro's number and the term "mole." Avogadro's number is defined simply as the number of atomic mass units in one gram. Mole is defined as the mass of one Avogadro number of identical items. (Author/PR)
Code of Federal Regulations, 2011 CFR
2011-01-01
... Receivers § 46.20 Lot numbers. An identifying lot number shall be assigned to each shipment of produce to be sold on consignment or joint account or for the account of another person or firm. A lot number should... lot number shall be assigned to each purchased shipment of similar produce on hand at that time...
Code of Federal Regulations, 2014 CFR
2014-01-01
... Receivers § 46.20 Lot numbers. An identifying lot number shall be assigned to each shipment of produce to be sold on consignment or joint account or for the account of another person or firm. A lot number should... lot number shall be assigned to each purchased shipment of similar produce on hand at that time...
Code of Federal Regulations, 2013 CFR
2013-01-01
... Receivers § 46.20 Lot numbers. An identifying lot number shall be assigned to each shipment of produce to be sold on consignment or joint account or for the account of another person or firm. A lot number should... lot number shall be assigned to each purchased shipment of similar produce on hand at that time...
Code of Federal Regulations, 2012 CFR
2012-01-01
... Receivers § 46.20 Lot numbers. An identifying lot number shall be assigned to each shipment of produce to be sold on consignment or joint account or for the account of another person or firm. A lot number should... lot number shall be assigned to each purchased shipment of similar produce on hand at that time...
Integrated-Circuit Pseudorandom-Number Generator
NASA Technical Reports Server (NTRS)
Steelman, James E.; Beasley, Jeff; Aragon, Michael; Ramirez, Francisco; Summers, Kenneth L.; Knoebel, Arthur
1992-01-01
Integrated circuit produces 8-bit pseudorandom numbers from specified probability distribution, at rate of 10 MHz. Use of Boolean logic, circuit implements pseudorandom-number-generating algorithm. Circuit includes eight 12-bit pseudorandom-number generators, outputs are uniformly distributed. 8-bit pseudorandom numbers satisfying specified nonuniform probability distribution are generated by processing uniformly distributed outputs of eight 12-bit pseudorandom-number generators through "pipeline" of D flip-flops, comparators, and memories implementing conditional probabilities on zeros and ones.
The Translated Dowling Polynomials and Numbers
Mangontarum, Mahid M.; Macodi-Ringia, Amila P.; Abdulcarim, Normalah S.
2014-01-01
More properties for the translated Whitney numbers of the second kind such as horizontal generating function, explicit formula, and exponential generating function are proposed. Using the translated Whitney numbers of the second kind, we will define the translated Dowling polynomials and numbers. Basic properties such as exponential generating functions and explicit formula for the translated Dowling polynomials and numbers are obtained. Convexity, integral representation, and other interesting identities are also investigated and presented. We show that the properties obtained are generalizations of some of the known results involving the classical Bell polynomials and numbers. Lastly, we established the Hankel transform of the translated Dowling numbers. PMID:27433494
Number Theory in the High School Classroom.
ERIC Educational Resources Information Center
Dence, Thomas
1999-01-01
Demonstrates some of the usefulness of number theory to students on the high school setting in four areas: Fibonacci numbers, Diophantine equations, continued fractions, and algorithms for computing pi. (ASK)
Measurement Corner Mass, Moles and Avogadro's Number
ERIC Educational Resources Information Center
Todd, Robert M.
1977-01-01
Discusses and clarifies the confusion arising from the use of the terms "mass,""volume,""matter,""mole," and "Avogadro's number." Suggests three laboratory activities concerning mass, volume, and number of particles in a given volume. (CS)
47 CFR 95.671 - Serial number.
Code of Federal Regulations, 2010 CFR
2010-10-01
... SERVICES Technical Regulations Additional Certification Requirements for Cb Transmitters § 95.671 Serial number. The serial number of each CB transmitter must be engraved on the transmitter chassis....
Quantity Cognition: Numbers, Numerosity, Zero and Mathematics.
Harvey, Ben M
2016-05-23
Physical quantities differ from abstract numbers and mathematics, but recent results are revealing the neural representation of both: a new study demonstrates how an absence of quantity is transformed into a representation of zero as a number.
Using Number Theory to Reinforce Elementary Algebra.
ERIC Educational Resources Information Center
Covillion, Jane D.
1995-01-01
Demonstrates that using the elementary number theory in algebra classes helps students to use acquired algebraic skills as well as helping them to more clearly understand concepts that are presented. Discusses factoring, divisibility rules, and number patterns. (AIM)
Negative numbers are generated in the mind.
Ganor-Stern, Dana; Tzelgov, Joseph
2008-01-01
The goal of the present study was to disentangle two possible representations of negative numbers--the holistic representation, where absolute magnitude is integrated with polarity; and the components representation, where absolute magnitude is stored separately from polarity. Participants' performance was examined in two tasks involving numbers from--100 to 100. In the numerical comparison task, participants had to decide which number of a pair was numerically larger/smaller. In the number line task, participants were presented with a spatial number line on which they had to place a number. The results of both tasks support the components representation of negative numbers. The findings suggest that processing of negative numbers does not involve retrieval of their meaning from memory, but rather the integration of the polarity sign with the digits' magnitudes.
NASA Astrophysics Data System (ADS)
M"Uller, Tom
2007-09-01
An odd prime number p is called anti-elite if only finitely many Fermat numbers are quadratic non-residues to p. This concept is the exact opposite to that of elite prime numbers. We study some fundamental properties of anti-elites and show that there are infinitely many of them. A computational search among all the numbers up to 100 billion yielded 84 anti-elite primes.
14 CFR 47.15 - Registration number.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 14 Aeronautics and Space 1 2014-01-01 2014-01-01 false Registration number. 47.15 Section 47.15 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION AIRCRAFT AIRCRAFT REGISTRATION General § 47.15 Registration number. (a) Number required. An applicant for aircraft...
46 CFR Sec. 7 - Job order numbering.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 46 Shipping 8 2013-10-01 2013-10-01 false Job order numbering. Sec. 7 Section 7 Shipping MARITIME... REPAIRS UNDER NATIONAL SHIPPING AUTHORITY MASTER LUMP SUM REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP Contract number shall be inserted in every job order and supplemental...
46 CFR Sec. 7 - Job order numbering.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 46 Shipping 8 2010-10-01 2010-10-01 false Job order numbering. Sec. 7 Section 7 Shipping MARITIME... REPAIRS UNDER NATIONAL SHIPPING AUTHORITY MASTER LUMP SUM REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP Contract number shall be inserted in every job order and supplemental...
46 CFR Sec. 7 - Job order numbering.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 46 Shipping 8 2012-10-01 2012-10-01 false Job order numbering. Sec. 7 Section 7 Shipping MARITIME... REPAIRS UNDER NATIONAL SHIPPING AUTHORITY MASTER LUMP SUM REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP Contract number shall be inserted in every job order and supplemental...
46 CFR Sec. 7 - Job order numbering.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 46 Shipping 8 2011-10-01 2011-10-01 false Job order numbering. Sec. 7 Section 7 Shipping MARITIME... REPAIRS UNDER NATIONAL SHIPPING AUTHORITY MASTER LUMP SUM REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP Contract number shall be inserted in every job order and supplemental...
46 CFR Sec. 7 - Job order numbering.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 46 Shipping 8 2014-10-01 2014-10-01 false Job order numbering. Sec. 7 Section 7 Shipping MARITIME... REPAIRS UNDER NATIONAL SHIPPING AUTHORITY MASTER LUMP SUM REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP Contract number shall be inserted in every job order and supplemental...
7 CFR 29.32 - Identification number.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Identification number. 29.32 Section 29.32 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... INSPECTION Regulations Definitions § 29.32 Identification number. A number or a combination of letters...
Evaluating Number Sense in Workforce Students
ERIC Educational Resources Information Center
Steinke, Dorothea A.
2015-01-01
Earlier institution-sponsored research revealed that about 20% of students in community college basic math and pre-algebra programs lacked a sense of part-whole relationships with whole numbers. Using the same tool with a group of 86 workforce students, about 75% placed five whole numbers on an empty number line in a way that indicated lack of…
47 CFR 32.20 - Numbering convention.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 47 Telecommunication 2 2010-10-01 2010-10-01 false Numbering convention. 32.20 Section 32.20 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES UNIFORM SYSTEM OF ACCOUNTS FOR TELECOMMUNICATIONS COMPANIES General Instructions § 32.20 Numbering convention. (a) The number...
Developmental Changes in the Whole Number Bias
ERIC Educational Resources Information Center
Braithwaite, David W.; Siegler, Robert S.
2017-01-01
Many students' knowledge of fractions is adversely affected by whole number bias, the tendency to focus on the separate whole number components (numerator and denominator) of a fraction rather than on the fraction's integrated magnitude (ratio of numerator to denominator). Although whole number bias appears early in the fraction learning process…
49 CFR 230.47 - Boiler number.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 49 Transportation 4 2011-10-01 2011-10-01 false Boiler number. 230.47 Section 230.47..., DEPARTMENT OF TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges § 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known,...
49 CFR 230.47 - Boiler number.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 49 Transportation 4 2010-10-01 2010-10-01 false Boiler number. 230.47 Section 230.47..., DEPARTMENT OF TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges § 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known,...
49 CFR 230.47 - Boiler number.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 49 Transportation 4 2013-10-01 2013-10-01 false Boiler number. 230.47 Section 230.47..., DEPARTMENT OF TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges § 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known,...
49 CFR 230.47 - Boiler number.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 49 Transportation 4 2012-10-01 2012-10-01 false Boiler number. 230.47 Section 230.47..., DEPARTMENT OF TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges § 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known,...
49 CFR 230.47 - Boiler number.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 49 Transportation 4 2014-10-01 2014-10-01 false Boiler number. 230.47 Section 230.47..., DEPARTMENT OF TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges § 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known,...
47 CFR 32.20 - Numbering convention.
Code of Federal Regulations, 2014 CFR
2014-10-01
...” (appearing to the left of the first decimal point) indicates the part number. (b) The numbers immediately following to the right of the decimal point indicate, respectively, the section or account. All Part 32 Account numbers contain 4 digits to-the-right-of the decimal point. (c) Cross references to accounts...
47 CFR 32.20 - Numbering convention.
Code of Federal Regulations, 2011 CFR
2011-10-01
...” (appearing to the left of the first decimal point) indicates the part number. (b) The numbers immediately following to the right of the decimal point indicate, respectively, the section or account. All Part 32 Account numbers contain 4 digits to-the-right-of the decimal point. (c) Cross references to accounts...
47 CFR 32.20 - Numbering convention.
Code of Federal Regulations, 2013 CFR
2013-10-01
...” (appearing to the left of the first decimal point) indicates the part number. (b) The numbers immediately following to the right of the decimal point indicate, respectively, the section or account. All Part 32 Account numbers contain 4 digits to-the-right-of the decimal point. (c) Cross references to accounts...
47 CFR 32.20 - Numbering convention.
Code of Federal Regulations, 2012 CFR
2012-10-01
...” (appearing to the left of the first decimal point) indicates the part number. (b) The numbers immediately following to the right of the decimal point indicate, respectively, the section or account. All Part 32 Account numbers contain 4 digits to-the-right-of the decimal point. (c) Cross references to accounts...
Identifying Fractions on a Number Line
ERIC Educational Resources Information Center
Wong, Monica
2013-01-01
Fractions are generally introduced to students using the part--whole model. Yet the number line is another important representation which can be used to build fraction concepts (Australian Curriculum Assessment and Reporting Authority [ACARA], 2012). Number lines are recognised as key in students' number development not only of fractions, but…
Graphing Powers and Roots of Complex Numbers.
ERIC Educational Resources Information Center
Embse, Charles Vonder
1993-01-01
Using De Moivre's theorem and a parametric graphing utility, examines powers and roots of complex numbers and allows students to establish connections between the visual and numerical representations of complex numbers. Provides a program to numerically verify the roots of complex numbers. (MDH)
Fascinating Fibonaccis: Mystery and Magic in Numbers.
ERIC Educational Resources Information Center
Garland, Trudi Hammel
This document presents activities and information related to Fibonacci numbers, which are based upon the Golden Ratio, in areas of the arts, sciences, and mathematics. The work is organized into eight chapters: (1) "Origins and Definitions"; (2) "Fibonacci Numbers in Nature"; (3) "Fibonacci Numbers in Art and…
Reading the World through Very Large Numbers
ERIC Educational Resources Information Center
Greer, Brian; Mukhopadhyay, Swapna
2010-01-01
One original, and continuing, source of interest in large numbers is observation of the natural world, such as trying to count the stars on a clear night or contemplation of the number of grains of sand on the seashore. Indeed, a search of the internet quickly reveals many discussions of the relative numbers of stars and grains of sand. Big…
27 CFR 24.115 - Registry number.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Registry number. 24.115... OF THE TREASURY LIQUORS WINE Establishment and Operations Application § 24.115 Registry number. Upon approval of the application, the appropriate TTB officer will assign a registry number to the bonded...
27 CFR 24.115 - Registry number.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2014-04-01 2014-04-01 false Registry number. 24.115... OF THE TREASURY ALCOHOL WINE Establishment and Operations Application § 24.115 Registry number. Upon approval of the application, the appropriate TTB officer will assign a registry number to the bonded...
27 CFR 24.115 - Registry number.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Registry number. 24.115... OF THE TREASURY LIQUORS WINE Establishment and Operations Application § 24.115 Registry number. Upon approval of the application, the appropriate TTB officer will assign a registry number to the bonded...
27 CFR 24.115 - Registry number.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2012-04-01 2012-04-01 false Registry number. 24.115... OF THE TREASURY LIQUORS WINE Establishment and Operations Application § 24.115 Registry number. Upon approval of the application, the appropriate TTB officer will assign a registry number to the bonded...
27 CFR 24.115 - Registry number.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2013-04-01 2013-04-01 false Registry number. 24.115... OF THE TREASURY ALCOHOL WINE Establishment and Operations Application § 24.115 Registry number. Upon approval of the application, the appropriate TTB officer will assign a registry number to the bonded...
Code of Federal Regulations, 2012 CFR
2012-07-01
... 32 National Defense 6 2012-07-01 2012-07-01 false Numbers. 1602.19 Section 1602.19 National Defense Other Regulations Relating to National Defense SELECTIVE SERVICE SYSTEM DEFINITIONS § 1602.19 Numbers. Cardinal numbers may be expressed by Arabic or Roman symbols....
Code of Federal Regulations, 2014 CFR
2014-07-01
... 32 National Defense 6 2014-07-01 2014-07-01 false Numbers. 1602.19 Section 1602.19 National Defense Other Regulations Relating to National Defense SELECTIVE SERVICE SYSTEM DEFINITIONS § 1602.19 Numbers. Cardinal numbers may be expressed by Arabic or Roman symbols....
Code of Federal Regulations, 2010 CFR
2010-07-01
... 32 National Defense 6 2010-07-01 2010-07-01 false Numbers. 1602.19 Section 1602.19 National Defense Other Regulations Relating to National Defense SELECTIVE SERVICE SYSTEM DEFINITIONS § 1602.19 Numbers. Cardinal numbers may be expressed by Arabic or Roman symbols....
Code of Federal Regulations, 2011 CFR
2011-07-01
... 32 National Defense 6 2011-07-01 2011-07-01 false Numbers. 1602.19 Section 1602.19 National Defense Other Regulations Relating to National Defense SELECTIVE SERVICE SYSTEM DEFINITIONS § 1602.19 Numbers. Cardinal numbers may be expressed by Arabic or Roman symbols....
Code of Federal Regulations, 2013 CFR
2013-07-01
... 32 National Defense 6 2013-07-01 2013-07-01 false Numbers. 1602.19 Section 1602.19 National Defense Other Regulations Relating to National Defense SELECTIVE SERVICE SYSTEM DEFINITIONS § 1602.19 Numbers. Cardinal numbers may be expressed by Arabic or Roman symbols....
Cycles and Universality in Sunspot Number Fluctuations
NASA Astrophysics Data System (ADS)
Gonçalves, R.; Pinto, A. A.; Stollenwerk, N.
2009-02-01
We analyze the famous Wolf's sunspot numbers. Surprisingly, we discovered that the distribution of the sunspot number fluctuations for both the ascending and descending phases is close to the universal nonparametric Bramwell-Holdsworth-Pinton (BHP) distribution. Since the BHP probability density function appears in several other physical phenomena, our result reveals a universal feature of the Wolf's sunspot numbers.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 47 Telecommunication 1 2010-10-01 2010-10-01 false File numbers. 1.1405 Section 1.1405... Procedures § 1.1405 File numbers. Each complaint which appears to be essentially complete under § 1.1404 will be accepted and assigned a file number. Such assignment is for administrative purposes only and...
Insights into Our Understandings of Large Numbers
ERIC Educational Resources Information Center
Kastberg, Signe E.; Walker, Vicki
2008-01-01
This article explores prospective teachers' understandings of one million to gain insights into the development of adult understanding of large numbers. Themes in the prospective teachers' work included number associated with a quantity of objects, number as an abstraction, and additive and multiplicative approaches. The authors suggest that the…
Technology Transfer Automated Retrieval System (TEKTRAN)
Number of functional teats is an important trait in commercial swine production. As litter size continues to increase, the number of teats must also increase to supply nutrition to all piglets. The pig displays considerable variation for number of teats; therefore, a genome-wide association (GWA) an...
The Decimal Representation of Real Numbers
ERIC Educational Resources Information Center
Kalapodi, A.
2010-01-01
The representation of natural numbers in decimal form is an unequivocal procedure while for the representation of real numbers some ambiguities concerning the existence of infinitely many digits equal to 9 still emerge. One of the most frequently confronted misunderstandings is whether 0.999...equals 1 or not, and if not what number does this…
Developing Young Children's Multidigit Number Sense.
ERIC Educational Resources Information Center
Diezmann, Carmel M.; English, Lyn D.
2001-01-01
This article describes a series of enrichment experiences designed to develop young (ages 5 to 8) gifted children's understanding of large numbers, central to their investigation of space travel. It describes activities designed to teach reading of large numbers and exploring numbers to a thousand and then a million. (Contains ten references.) (DB)
An Evaluation of App-Based and Paper-Based Number Lines for Teaching Number Comparison
ERIC Educational Resources Information Center
Weng, Pei-Lin; Bouck, Emily C.
2016-01-01
Number comparison is a fundamental skill required for academic and functional mathematics (e.g., time, money, purchasing) for students with disabilities. The most commonly used method to teach number comparison is number lines. Although historically paper number lines are used, app-based number lines may offer greater flexibility. This study…
On the binary expansions of algebraic numbers
Bailey, David H.; Borwein, Jonathan M.; Crandall, Richard E.; Pomerance, Carl
2003-07-01
Employing concepts from additive number theory, together with results on binary evaluations and partial series, we establish bounds on the density of 1's in the binary expansions of real algebraic numbers. A central result is that if a real y has algebraic degree D > 1, then the number {number_sign}(|y|, N) of 1-bits in the expansion of |y| through bit position N satisfies {number_sign}(|y|, N) > CN{sup 1/D} for a positive number C (depending on y) and sufficiently large N. This in itself establishes the transcendency of a class of reals {summation}{sub n{ge}0} 1/2{sup f(n)} where the integer-valued function f grows sufficiently fast; say, faster than any fixed power of n. By these methods we re-establish the transcendency of the Kempner--Mahler number {summation}{sub n{ge}0}1/2{sup 2{sup n}}, yet we can also handle numbers with a substantially denser occurrence of 1's. Though the number z = {summation}{sub n{ge}0}1/2{sup n{sup 2}} has too high a 1's density for application of our central result, we are able to invoke some rather intricate number-theoretical analysis and extended computations to reveal aspects of the binary structure of z{sup 2}.
47 CFR 52.20 - Thousands-block number pooling.
Code of Federal Regulations, 2011 CFR
2011-10-01
... (CONTINUED) NUMBERING Number Portability § 52.20 Thousands-block number pooling. (a) Definition. Thousands... number pooling as a mandatory nationwide numbering resource optimization strategy, all carriers,...
47 CFR 52.20 - Thousands-block number pooling.
Code of Federal Regulations, 2010 CFR
2010-10-01
... (CONTINUED) NUMBERING Number Portability § 52.20 Thousands-block number pooling. (a) Definition. Thousands... number pooling as a mandatory nationwide numbering resource optimization strategy, all carriers,...
47 CFR 52.20 - Thousands-block number pooling.
Code of Federal Regulations, 2013 CFR
2013-10-01
... (CONTINUED) NUMBERING Number Portability § 52.20 Thousands-block number pooling. (a) Definition. Thousands... number pooling as a mandatory nationwide numbering resource optimization strategy, all carriers,...
47 CFR 52.20 - Thousands-block number pooling.
Code of Federal Regulations, 2012 CFR
2012-10-01
... (CONTINUED) NUMBERING Number Portability § 52.20 Thousands-block number pooling. (a) Definition. Thousands... number pooling as a mandatory nationwide numbering resource optimization strategy, all carriers,...
47 CFR 52.20 - Thousands-block number pooling.
Code of Federal Regulations, 2014 CFR
2014-10-01
... (CONTINUED) NUMBERING Number Portability § 52.20 Thousands-block number pooling. (a) Definition. Thousands... number pooling as a mandatory nationwide numbering resource optimization strategy, all carriers,...
Deafness for the meanings of number words.
Caño, Agnès; Rapp, Brenda; Costa, Albert; Juncadella, Montserrat
2008-01-15
We describe the performance of an aphasic individual who showed a selective impairment affecting his comprehension of auditorily presented number words and not other word categories. His difficulty in number word comprehension was restricted to the auditory modality, given that with visual stimuli (written words, Arabic numerals and pictures) his comprehension of number and non-number words was intact. While there have been previous reports of selective difficulty or sparing of number words at the semantic and post-semantic levels, this is the first reported case of a pre-semantic deficit that is specific to the category of number words. This constitutes evidence that lexical semantic distinctions are respected by modality-specific neural mechanisms responsible for providing access to the meanings of words.
Relativistic theory of tidal Love numbers
Binnington, Taylor; Poisson, Eric
2009-10-15
In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neutron star can be measured by Earth-based gravitational-wave detectors. We consider a spherical body deformed by an external tidal field, and provide precise and meaningful definitions for electric-type and magnetic-type Love numbers; and these are computed for polytropic equations of state. The theory applies to black holes as well, and we find that the relativistic Love numbers of a nonrotating black hole are all zero.
Deafness for the meanings of number words
Caño, Agnès; Rapp, Brenda; Costa, Albert; Juncadella, Montserrat
2008-01-01
We describe the performance of an aphasic individual who showed a selective impairment affecting his comprehension of auditorily presented number words and not other word categories. His difficulty in number word comprehension was restricted to the auditory modality, given that with visual stimuli (written words, Arabic numerals and pictures) his comprehension of number and non-number words was intact. While there have been previous reports of selective difficulty or sparing of number words at the semantic and post-semantic levels, this is the first reported case of a pre-semantic deficit that is specific to the category of number words. This constitutes evidence that lexical semantic distinctions are respected by modality-specific neural mechanisms responsible for providing access to the meanings of words. PMID:17915265
Self-correcting random number generator
Humble, Travis S.; Pooser, Raphael C.
2016-09-06
A system and method for generating random numbers. The system may include a random number generator (RNG), such as a quantum random number generator (QRNG) configured to self-correct or adapt in order to substantially achieve randomness from the output of the RNG. By adapting, the RNG may generate a random number that may be considered random regardless of whether the random number itself is tested as such. As an example, the RNG may include components to monitor one or more characteristics of the RNG during operation, and may use the monitored characteristics as a basis for adapting, or self-correcting, to provide a random number according to one or more performance criteria.
European Scientific Notes. Volume 36, Number 4,
1982-04-30
primarily for the information of L ’ S. Government scientific personnel and contractors. It i-, not coli- c sidered part of the scientific literature...Stjbtiti.) S YEO EOT&PRO OEE EUROPEAN SCIENTIFIC NOTES April_____________ S. PERFORMING ORG. REPORT NUMBER 7. AUTHOR(*) S. CONTRACT OR GRANT NUMBER(#) 9... PERFORMING ORGANI1ZATION NAME AND ADDRESS 10, PROGRAM ELEMENT PROJECT, TASK( AREA & WORK UNIT NUMBERS US OFFICE OF NAVAL RESEARCH BRANCH OFFICE
Quasi-Fibonacci Numbers of Order 11
NASA Astrophysics Data System (ADS)
Wituła, Roman; Słota, Damian
2007-08-01
In this paper we introduce and investigate the so-called quasi-Fibonacci numbers of order 11 . These numbers are defined by five conjugate recurrence equations of order five. We study some relations and identities concerning these numbers. We present some applications to the decomposition of some polynomials. Many of the identities presented here are the generalizations of the identities characteristic for general recurrence sequences of order three given by Rabinowitz.
Studies in Intelligence. Volume 57, Number 3
2013-09-01
Studies in Intelligence Journal of the American Intelligence Professional Unclassified articles from Studies in Intelligence Volume 57, Number 3...1908 to 1914 Intelligence Officer’s Bookshelf Report Documentation Page Form ApprovedOMB No. 0704-0188 Public reporting burden for the collection of...ACRONYM(S) 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for public release; distribution unlimited 13
Demonstrations of the Enormity of Avogadro's Number.
ERIC Educational Resources Information Center
Diemente, Damon
1998-01-01
Describes three calculations used to make students aware of the size of Avogadro's number: (1) the new size of a 6-inch diameter ball with volume increased by a factor of Avogadro's number; (2) the number of moles of sand grains in the Sahara Desert; and (3) the dimensions and length of a mole of hydrogen atoms shaped into a cube, a square, and a…
High speed optical quantum random number generation.
Fürst, Martin; Weier, Henning; Nauerth, Sebastian; Marangon, Davide G; Kurtsiefer, Christian; Weinfurter, Harald
2010-06-07
We present a fully integrated, ready-for-use quantum random number generator (QRNG) whose stochastic model is based on the randomness of detecting single photons in attenuated light. We show that often annoying deadtime effects associated with photomultiplier tubes (PMT) can be utilized to avoid postprocessing for bias or correlations. The random numbers directly delivered to a PC, generated at a rate of up to 50 Mbit/s, clearly pass all tests relevant for (physical) random number generators.
CRC octane number requirement survey 1992
Not Available
1993-08-01
An annual statistical survey of octane number requirements of current model vehicles is conducted by the Coordinating Research Council, Inc. Test data have been obtained by ten companies on 184 1992 vehicles including passenger cars and light-duty trucks and vans, of which 88 were equipped with knock sensors. Octane number requirements were determined by testing at maximum-throttle conditions, as well as at part-throttle, with four unleaded fuel series of varying sensitivities, one containing 15 percent methyl tertiary butyl ether. Requirements are expressed as the (R+M)/2 octane number, Research octane number, and Motor octane number of the reference fuel producing knock which was recurrent and repeatable at the lowest audible level. Estimated octane number requirements for the total vehicles are weighted in proportion to the 1992 vehicle model production and/or sales figures. The octane number requirements of 1992 models with average sensitivity unleaded fuels were 85.1 (R+M)/2 octane numbers at the 50 percent satisfaction level, and 92.0 (R+M)/2 octane numbers at the 90 percent satisfaction level. In order to make a more powerful test of statistical significance of the FBRUM fuel series, the 1991 ONRS was pooled with the 1992 ONRS and compared with the pooled data for the FBRU fuel series. There was no significant difference between the two fuel series up to about 90 percent satisfaction. Beyond 90 percent satisfaction, the variability in the data is high.
CRC octane-number-requirement survey, 1990
Not Available
1991-07-01
An annual statistical survey of octane number requirements of current model vehicles is conducted by the Coordinating Research Council, Inc. Test data have been obtained by seventeen companies on 356 1990 vehicles including passenger cars and light-duty trucks and vans, of which 169 were equipped with knock sensors. Octane number requirements were determined by testing at maximum-throttle conditions, as well as at part-throttle, with three unleaded fuel series of varying sensitivities. Requirements are expressed as the (R+M)/2 octane number, Research octane number, and Motor octane number of the reference fuel producing knock which was recurrent and repeatable at the lowest audible level. Estimated octane number requirements for the total vehicles are weighted in proportion to the 1990 vehicle model production and/or sales figures. The octane number requirements of 1990 models with average sensitivity unleaded fuels were 85.4 (R+M)/2 octane numbers at the 50 percent satisfaction level, and 89.2 (R+M)/2 octane numbers at the 90 percent satisfaction level.
CRC octane number requirement survey for 1989
Not Available
1990-08-01
An annual statistical survey of octane number requirements of current model vehicles is conducted by the Coordinating Research Council, Inc. Test data have been obtained by eighteen companies on 391 1989 vehicles including passenger cars and light-duty trucks and vans, of which 179 were equipped with knock sensors. Maximum octane number requirements were determined by testing at maximum-throttle conditions, as well as at part-throttle, with three unleaded fuel series of varying sensitivities. Requirements are expressed as the (R+M)/2 octane number, Research octane number, and Motor octane number of the reference fuel producing knock which was recurrent and repeatable at the lowest audible level. Estimated octane number requirements for the total vehicles are weighted in proportion to the 1989 vehicle model production and/or sales figures. The maximum octane number requirements of 1989 models with average sensitivity unleaded fuels were 85.1 (R+M)/2 octane numbers at the 50 percent satisfaction level, and 89.2 (R+M)/2 octane numbers at the 90 percent satisfaction level. Comparison with previous Surveys are made in this report.
47 CFR 32.6622 - Number services.
Code of Federal Regulations, 2013 CFR
2013-10-01
... account shall include costs incurred in providing customer number and classified listings. This includes preparing or purchasing, compiling, and disseminating those listings through directory assistance or...
47 CFR 32.6622 - Number services.
Code of Federal Regulations, 2014 CFR
2014-10-01
... account shall include costs incurred in providing customer number and classified listings. This includes preparing or purchasing, compiling, and disseminating those listings through directory assistance or...
47 CFR 32.6622 - Number services.
Code of Federal Regulations, 2011 CFR
2011-10-01
... account shall include costs incurred in providing customer number and classified listings. This includes preparing or purchasing, compiling, and disseminating those listings through directory assistance or...
47 CFR 32.6622 - Number services.
Code of Federal Regulations, 2012 CFR
2012-10-01
... account shall include costs incurred in providing customer number and classified listings. This includes preparing or purchasing, compiling, and disseminating those listings through directory assistance or...
Graceful label numbering in optical MPLS networks
NASA Astrophysics Data System (ADS)
Arkut, Ibrahim C.; Arkut, Refik C.; Ghani, Nasir
2000-09-01
This paper explores the positive effects of the new multi protocol label switching (MPLS) routing platform in IP networks. In particular, novel node numbering algorithms based upon graceful numbering of trees are presented. The first part presents the application of the well-known graceful numbering of spanning caterpillars to the MPLS multicast routing problem. In the second part of the paper, the numbering algorithm is adjusted for the case of unicast routing in the framework of IP-over-WDM optical networks using MPLS, e.g., particularly lambda-labeling and multi protocol lambda switching.
Generalized Ramsey numbers through adiabatic quantum optimization
NASA Astrophysics Data System (ADS)
Ranjbar, Mani; Macready, William G.; Clark, Lane; Gaitan, Frank
2016-09-01
Ramsey theory is an active research area in combinatorics whose central theme is the emergence of order in large disordered structures, with Ramsey numbers marking the threshold at which this order first appears. For generalized Ramsey numbers r( G, H), the emergent order is characterized by graphs G and H. In this paper we: (i) present a quantum algorithm for computing generalized Ramsey numbers by reformulating the computation as a combinatorial optimization problem which is solved using adiabatic quantum optimization; and (ii) determine the Ramsey numbers r({{T}}m,{{T}}n) for trees of order m,n = 6,7,8, most of which were previously unknown.
Continental anthropogenic primary particle number emissions
NASA Astrophysics Data System (ADS)
Paasonen, Pauli; Kupiainen, Kaarle; Klimont, Zbigniew; Visschedijk, Antoon; Denier van der Gon, Hugo A. C.; Amann, Markus
2016-06-01
Atmospheric aerosol particle number concentrations impact our climate and health in ways different from those of aerosol mass concentrations. However, the global, current and future anthropogenic particle number emissions and their size distributions are so far poorly known. In this article, we present the implementation of particle number emission factors and the related size distributions in the GAINS (Greenhouse Gas-Air Pollution Interactions and Synergies) model. This implementation allows for global estimates of particle number emissions under different future scenarios, consistent with emissions of other pollutants and greenhouse gases. In addition to determining the general particulate number emissions, we also describe a method to estimate the number size distributions of the emitted black carbon particles. The first results show that the sources dominating the particle number emissions are different to those dominating the mass emissions. The major global number source is road traffic, followed by residential combustion of biofuels and coal (especially in China, India and Africa), coke production (Russia and China), and industrial combustion and processes. The size distributions of emitted particles differ across the world, depending on the main sources: in regions dominated by traffic and industry, the number size distribution of emissions peaks in diameters range from 20 to 50 nm, whereas in regions with intensive biofuel combustion and/or agricultural waste burning, the emissions of particles with diameters around 100 nm are dominant. In the baseline (current legislation) scenario, the particle number emissions in Europe, Northern and Southern Americas, Australia, and China decrease until 2030, whereas especially for India, a strong increase is estimated. The results of this study provide input for modelling of the future changes in aerosol-cloud interactions as well as particle number related adverse health effects, e.g. in response to tightening
Kong, Feng; Zhao, Jingjing; You, Xuqun
2012-01-01
Past research suggested that negative numbers could be represented in terms of their components in the visual modality. The present study examined the processing of negative numbers in the auditory modality and whether it is affected by context. Experiment 1 employed a stimuli detection task where only negative numbers were presented binaurally. Experiment 2 employed the same task, but both positive and negative numbers were mixed as cues. A reverse attentional spatial-numerical association of response codes (SNARC) effect for negative numbers was obtained in these two experiments. Experiment 3 employed a number classification task where only negative numbers were presented binaurally. Experiment 4 employed the same task, but both positive and negative numbers were mixed. A reverse SNARC effect for negative numbers was obtained in these two experiments. These findings suggest that negative numbers in the auditory modality are generated from the set of positive numbers, thus supporting a components representation.
Inhibition, Conflict Detection, and Number Conservation
ERIC Educational Resources Information Center
Lubin, Amélie; Simon, Grégory; Houdé, Olivier; De Neys, Wim
2015-01-01
The acquisition of number conservation is a critical step in children's numerical and mathematical development. Classic developmental studies have established that children's number conservation is often biased by misleading intuitions. However, the precise nature of these conservation errors is not clear. A key question is whether conservation…
Families of Linear Recurrences for Catalan Numbers
ERIC Educational Resources Information Center
Gauthier, N.
2011-01-01
Four different families of linear recurrences are derived for Catalan numbers. The derivations rest on John Riordan's 1973 generalization of Catalan numbers to a set of polynomials. Elementary differential and integral calculus techniques are used and the results should be of interest to teachers and students of introductory courses in calculus…
Fostering At-Risk Preschoolers' Number Sense
ERIC Educational Resources Information Center
Baroody, Arthur; Eiland, Michael; Thompson, Bradley
2009-01-01
Research Findings: A 9-month study served to evaluate the effectiveness of a pre-kindergarten number sense curriculum. Phase 1 of the intervention involved manipulative-, game-based number sense instruction; Phase 2, computer-aided mental-arithmetic training with the simplest sums. Eighty 4- and 5-year-olds at risk for school failure were randomly…
Language Influence on Children's Cognitive Number Representation
ERIC Educational Resources Information Center
Alsawaie, Othman N.
2004-01-01
This study examined the effect of language on children's cognitive representation of number. The sample for the study consisted of 90 Arabic speaking children with a mean age of 80 months. Children were interviewed individually and asked to represent written two-digit numbers using base-10 blocks. A new approach for testing the linguistic…
Good Morning, Numbers Day: Motivating for Mathematics
ERIC Educational Resources Information Center
Ramentol, Salvador Vidal
2011-01-01
The aversion that many girls and boys experience towards mathematics has been one of the author's major concerns since he started teaching. In this article, he describes a project called "Numbers Day" that was designed to improve students' attitudes toward mathematics. There are many features of Numbers Day that teachers might…
40 CFR 86.1204 - Section numbering.
Code of Federal Regulations, 2013 CFR
2013-07-01
...) CONTROL OF EMISSIONS FROM NEW AND IN-USE HIGHWAY VEHICLES AND ENGINES (CONTINUED) Evaporative Emission Test Procedures for New Gasoline-Fueled, Natural Gas-Fueled, Liquefied Petroleum Gas-Fueled and Methanol-Fueled Heavy-Duty Vehicles § 86.1204 Section numbering. The section numbering system set forth...
40 CFR 86.1204 - Section numbering.
Code of Federal Regulations, 2011 CFR
2011-07-01
...) CONTROL OF EMISSIONS FROM NEW AND IN-USE HIGHWAY VEHICLES AND ENGINES (CONTINUED) Evaporative Emission Test Procedures for New Gasoline-Fueled, Natural Gas-Fueled, Liquefied Petroleum Gas-Fueled and Methanol-Fueled Heavy-Duty Vehicles § 86.1204 Section numbering. The section numbering system set forth...
40 CFR 86.1204 - Section numbering.
Code of Federal Regulations, 2010 CFR
2010-07-01
...) CONTROL OF EMISSIONS FROM NEW AND IN-USE HIGHWAY VEHICLES AND ENGINES (CONTINUED) Evaporative Emission Test Procedures for New Gasoline-Fueled, Natural Gas-Fueled, Liquefied Petroleum Gas-Fueled and Methanol-Fueled Heavy-Duty Vehicles § 86.1204 Section numbering. The section numbering system set forth...
40 CFR 86.1204 - Section numbering.
Code of Federal Regulations, 2012 CFR
2012-07-01
...) CONTROL OF EMISSIONS FROM NEW AND IN-USE HIGHWAY VEHICLES AND ENGINES (CONTINUED) Evaporative Emission Test Procedures for New Gasoline-Fueled, Natural Gas-Fueled, Liquefied Petroleum Gas-Fueled and Methanol-Fueled Heavy-Duty Vehicles § 86.1204 Section numbering. The section numbering system set forth...
A Partition Formula for Fibonacci Numbers
NASA Astrophysics Data System (ADS)
Fahr, Philipp; Ringerl, Claus Michael
2008-02-01
We present a partition formula for the even index Fibonacci numbers. The formula is motivated by the appearance of these Fibonacci numbers in the representation theory of the socalled 3-Kronecker quiver, i.e., the oriented graph with two vertices and three arrows in the same direction.
Learning Disabled: Number Concepts, Primary Grades.
ERIC Educational Resources Information Center
National Center on Educational Media and Materials for the Handicapped, Columbus, OH.
Selected from the National Instructional Materials Information System (NIMIS)--a computer based on-line interactive retrieval system on special education materials--the bibliography covers 62 materials for teaching number concepts to learning disabled students at the primary grades. Entries are presented in order of NIMIS accession number and…
From Whole Numbers to Invert and Multiply
ERIC Educational Resources Information Center
Cavey, Laurie O.; Kinzel, Margaret T.
2014-01-01
Teachers report that engaging students in solving contextual problems is an important part of supporting student understanding of algorithms for fraction division. Meaning for whole-number operations is a crucial part of making sense of contextual problems involving rational numbers. The authors present a developed instructional sequence to…
Locating Fractions on a Number Line
ERIC Educational Resources Information Center
Wong, Monica
2013-01-01
Understanding fractions remains problematic for many students. The use of the number line aids in this understanding, but requires students to recognise that a fraction represents the distance from zero to a dot or arrow marked on a number line which is a linear scale. This article continues the discussion from "Identifying Fractions on a…
On the Concept Image of Complex Numbers
ERIC Educational Resources Information Center
Nordlander, Maria Cortas; Nordlander, Edvard
2012-01-01
A study of how Swedish students understand the concept of complex numbers was performed. A questionnaire was issued reflecting the student view of own perception. Obtained answers show a variety of concept images describing how students adopt the concept of complex numbers. These concept images are classified into four categories in order to…
Neural correlates of merging number words.
Hung, Yi-Hui; Pallier, Christophe; Dehaene, Stanislas; Lin, Yi-Chen; Chang, Acer; Tzeng, Ovid J-L; Wu, Denise H
2015-11-15
Complex number words (e.g., "twenty two") are formed by merging together several simple number words (e.g., "twenty" and "two"). In the present study, we explored the neural correlates of this operation and investigated to what extent it engages brain areas involved processing numerical quantity and linguistic syntactic structure. Participants speaking two typologically distinct languages, French and Chinese, were required to read aloud sequences of simple number words while their cerebral activity was recorded by functional magnetic resonance imaging. Each number word could either be merged with the previous ones (e.g., 'twenty three') or not (e.g., 'three twenty'), thus forming four levels ranging from lists of number words to complex numerals. When a number word could be merged with the preceding ones, it was named faster than when it could not. Neuroimaging results showed that the number of merges correlated with activation in the left inferior frontal gyrus and in the left inferior parietal lobule. Consistent findings across Chinese and French participants suggest that these regions serve as the neural bases for forming complex number words in different languages.
Home Schooling. ERIC Digest, Number 95.
ERIC Educational Resources Information Center
Lines, Patricia M.
A small but increasing number of school-aged children are engaging in home schooling--pursuing learning at home or elsewhere in the community. This digest summarizes research findings on and issues around home schooling. It describes the historical roots of home schooling, the estimated number of participants, the constitutionality and legal…
Infinite Sums of M-Bonacci Numbers
ERIC Educational Resources Information Center
A-iru, Muniru A.
2009-01-01
In this note, we construct infinite series using M-bonacci numbers in a manner similar to that used in previous studies and investigate the convergence of the series to an integer. Our results generalize the ones obtained for Fibonacci numbers.
The Second Strong Law of Small Numbers.
ERIC Educational Resources Information Center
Guy, Richard K.
1990-01-01
Presented are 44 examples in which students are invited to guess what pattern of numbers is emerging and to decide whether the pattern will persist. Topics of examples include Pascal's triangle, integers, vertices, Fibonacci numbers, power series, partition functions, and Euler's theorem. The answers to all problems are included. (KR)
Hello, I am not an NHS number.
Bates, Jane
2016-09-14
I was handed a request to return a patient's call and given a name, signs and symptoms and a number with ten digits, starting with a seven. There was no preceding zero, and assuming it must be a mistake I stuck one on, and dialled. The number was unobtainable.
National Resources [and] National Toll Free Numbers.
ERIC Educational Resources Information Center
National Information Center for Children and Youth with Disabilities, Washington, DC.
This resource list provides names, addresses, and telephone numbers of 13 information clearinghouses and 42 organizations providing information on children and youth with disabilities. Telephone numbers are designated as either voice or text telephone. Spanish-language resources are also indicated. A list of organizations that have national…
When Symbolic Spatial Cues Go before Numbers
ERIC Educational Resources Information Center
Herrera, Amparo; Macizo, Pedro
2011-01-01
This work explores the effect of spatial cueing on number processing. Participants performed a parity judgment task. However, shortly before the target number, a cue (arrow pointing to left, arrow pointing to right or a cross) was centrally presented. In Experiment 1, in which responses were lateralized, the cue direction modulated the interaction…
Code of Federal Regulations, 2010 CFR
2010-01-01
... of Sourcing Area Applications and Formal Review of Sourcing Areas Pursuant to the Forest Resources... proceeding shall be referred to by such number. The Hearing Clerk shall notify the sourcing area applicant... number and the name of the Judge to whom the case has been assigned. In a formal review of a...
Hodge numbers for all CICY quotients
NASA Astrophysics Data System (ADS)
Constantin, Andrei; Gray, James; Lukas, Andre
2017-01-01
We present a general method for computing Hodge numbers for Calabi-Yau manifolds realised as discrete quotients of complete intersections in products of projective spaces. The method relies on the computation of equivariant cohomologies and is illustrated for several explicit examples. In this way, we compute the Hodge numbers for all discrete quotients obtained in Braun's classification [1].
Historical Objections against the Number Line
ERIC Educational Resources Information Center
Heeffer, Albrecht
2011-01-01
Historical studies on the development of mathematical concepts will help mathematics teachers to relate their students' difficulties in understanding to conceptual problems in the history of mathematics. We argue that one popular tool for teaching about numbers, the number line, may not be fit for early teaching of operations involving negative…
Number Theory in the Elementary School.
ERIC Educational Resources Information Center
Beougher, Elton E.
The paper presents reasons for teaching topics from number theory to elementary school students: (1) it can help reveal why numbers "act" in a certain way when added, multiplied, etc., (2) it offers drill material in new areas of mathematics, (3) it can develop interest - as mathematical enrichment, (4) it offers opportunities for students to…
Keypad Geometry and Divisibility of Numbers
ERIC Educational Resources Information Center
Van Dyke, Frances; Keynes, Michael
2010-01-01
In this article, the authors show how students can form familiar geometric figures on the calculator keypad and generate numbers that are all divisible by a common number. Students are intrigued by the results and want to know "why it works". The activities can be presented and students given an extended amount of time to think about…
ERIC Educational Resources Information Center
Goldenhersh, Barbara, Ed.
This document consists of three issues of the journal "Seedbed," an outcome of the Teachers' Center Project at Southern Illinois University at Edwardsville (SIUE). Issue Number 29 contains 67 articles on teachers' ideas that they thought worth sharing with other teachers. Issue Number 30 consists of a single paper, "Children and…
Nonclassicality in phase-number uncertainty relations
Matia-Hernando, Paloma; Luis, Alfredo
2011-12-15
We show that there are nonclassical states with lesser joint fluctuations of phase and number than any classical state. This is rather paradoxical since one would expect classical coherent states to be always of minimum uncertainty. The same result is obtained when we replace phase by a phase-dependent field quadrature. Number and phase uncertainties are assessed using variance and Holevo relation.
Number of Oxidations Relative to Methylene.
ERIC Educational Resources Information Center
Kjonaas, Richard A.
1986-01-01
Describes a new way of quantifying organic oxidation-reduction reactions that extends the traditional method of assigning oxidation numbers by replacing them with NORM's (Number of Oxidations Relative to Methylene). This modification allows the system to be applied to more complex examples without the cumbersomeness inherent in the original…
Teach Kids about Numbers All around Us
ERIC Educational Resources Information Center
Hudson, Hannah Trierweiler
2011-01-01
Recognizing the role numbers play in people's everyday lives is crucial to students' math understanding now and down the road. That's why Bob Krech, a curriculum specialist in New Jersey's West Windsor-Plainsboro district, likes to teach a lesson he calls "Numbers All Around Us." This lesson uses real-world examples to show that numbers…
Math Sense: Whole Numbers and Money.
ERIC Educational Resources Information Center
Phillips, Jan
This book is designed to help students gain the range of math skills they need to succeed in life, work, and on standardized tests; overcome math anxiety; discover math as interesting and purposeful; and develop good number sense. Topics covered in this book include whole numbers and addition, subtraction, multiplication, and division. Lessons are…
LEAN: laser-etched aqua number
NASA Astrophysics Data System (ADS)
Schell, Karel J.
1998-04-01
A security device on a banknote has to be recognized immediately by the general public and has to enable the general public to establish the genuineness of the banknote. This is the so-called first line of defense. Recently the development of the ability to establish the genuiness has gained momentum and is called 'self authenticating.' Comparing the banknote number with a 'watermark number' can do authenticating. The watermark number is engraved by a laser beam in the paper and is -- as the printed number -- different for each note. Recent progress in the material processing by laser enables the engraving of the individual watermark number for each banknote in line with the production process.
Ramsey numbers and adiabatic quantum computing.
Gaitan, Frank; Clark, Lane
2012-01-06
The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers R(m,n) with m, n≥3, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers R(m,n). We show how the computation of R(m,n) can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for 5≤s≤7. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class quantum Merlin Arthur.
Low Mach Number Modeling of Stratified Flows
NASA Astrophysics Data System (ADS)
Almgren, A. S.; Bell, J. B.; Nonaka, A.; Zingale, M.
2015-06-01
Low Mach number equation sets approximate the equations of motion of a compressible fluid by filtering out the sound waves, which allows the system to evolve on the advective rather than the acoustic time scale. Depending on the degree of approximation, low Mach number models retain some sub set of possible compressible effects. In this paper we give an overview of low Mach number methods for modeling stratified flows arising in astrophysics and atmospheric science as well as low Mach number reacting flows. We discuss how elements from the different fields are combined to form MAESTRO, a code for modeling low Mach number stratified flows with general equations of state, reactions and time-varying stratification.
Low Reynolds number airfoil survey, volume 1
NASA Technical Reports Server (NTRS)
Carmichael, B. H.
1981-01-01
The differences in flow behavior two dimensional airfoils in the critical chordlength Reynolds number compared with lower and higher Reynolds number are discussed. The large laminar separation bubble is discussed in view of its important influence on critical Reynolds number airfoil behavior. The shortcomings of application of theoretical boundary layer computations which are successful at higher Reynolds numbers to the critical regime are discussed. The large variation in experimental aerodynamic characteristic measurement due to small changes in ambient turbulence, vibration, and sound level is illustrated. The difficulties in obtaining accurate detailed measurements in free flight and dramatic performance improvements at critical Reynolds number, achieved with various types of boundary layer tripping devices are discussed.
Compendium of Experimental Cetane Number Data
Murphy, M. J.; Taylor, J. D.; McCormick, R. L.
2004-09-01
In this report, we present a compilation of reported cetane numbers for pure chemical compounds. The compiled database contains cetane values for 299 pure compounds, including 156 hydrocarbons and 143 oxygenates. Cetane number is a relative ranking of fuels based on the amount of time between fuel injection and ignition. The cetane number is typically measured either in a combustion bomb or in a single-cylinder research engine. This report includes cetane values from several different measurement techniques - each of which has associated uncertainties. Additionally, many of the reported values are determined by measuring blending cetane numbers, which introduces significant error. In many cases, the measurement technique is not reported nor is there any discussion about the purity of the compounds. Nonetheless, the data in this report represent the best pure compound cetane number values available from the literature as of August 2004.
Random numbers spring from alpha decay
Frigerio, N.A.; Sanathanan, L.P.; Morley, M.; Clark, N.A.; Tyler, S.A.
1980-05-01
Congruential random number generators, which are widely used in Monte Carlo simulations, are deficient in that the number they generate are concentrated in a relatively small number of hyperplanes. While this deficiency may not be a limitation in small Monte Carlo studies involving a few variables, it introduces a significant bias in large simulations requiring high resolution. This bias was recognized and assessed during preparations for an accident analysis study of nuclear power plants. This report describes a random number device based on the radioactive decay of alpha particles from a /sup 235/U source in a high-resolution gas proportional counter. The signals were fed to a 4096-channel analyzer and for each channel the frequency of signals registered in a 20,000-microsecond interval was recorded. The parity bits of these frequency counts (0 for an even count and 1 for an odd count) were then assembled in sequence to form 31-bit binary random numbers and transcribed to a magnetic tape. This cycle was repeated as many times as were necessary to create 3 million random numbers. The frequency distribution of counts from the present device conforms to the Brockwell-Moyal distribution, which takes into account the dead time of the counter (both the dead time and decay constant of the underlying Poisson process were estimated). Analysis of the count data and tests of randomness on a sample set of the 31-bit binary numbers indicate that this random number device is a highly reliable source of truly random numbers. Its use is, therefore, recommended in Monte Carlo simulations for which the congruential pseudorandom number generators are found to be inadequate. 6 figures, 5 tables.
Number Worlds: Visual and Experimental Access to Elementary Number Theory Concepts
ERIC Educational Resources Information Center
Sinclair, Nathalie; Zazkis, Rina; Liljedahl, Peter
2004-01-01
Recent research demonstrates that many issues related to the structure of natural numbers and the relationship among numbers are not well grasped by students. In this article, we describe a computer-based learning environment called "Number Worlds" that was designed to support the exploration of elementary number theory concepts by…
Theory of analogous force on number sets
NASA Astrophysics Data System (ADS)
Canessa, Enrique
2003-10-01
A general statistical thermodynamic theory that considers given sequences of x-integers to play the role of particles of known type in an isolated elastic system is proposed. By also considering some explicit discrete probability distributions px for natural numbers, we claim that they lead to a better understanding of probabilistic laws associated with number theory. Sequences of numbers are treated as the size measure of finite sets. By considering px to describe complex phenomena, the theory leads to derive a distinct analogous force fx on number sets proportional to (∂ px/∂ x) T at an analogous system temperature T. In particular, this leads to an understanding of the uneven distribution of integers of random sets in terms of analogous scale invariance and a screened inverse square force acting on the significant digits. The theory also allows to establish recursion relations to predict sequences of Fibonacci numbers and to give an answer to the interesting theoretical question of the appearance of the Benford's law in Fibonacci numbers. A possible relevance to prime numbers is also analyzed.
Estimating shorebird numbers at migration stopover sites
Farmer, A.; Durbian, F.
2006-01-01
We describe a method for estimating the total number of shorebirds that use a migration stopover site during spring and fall migration. We combined weekly shorebird counts with parameter estimates for detection probability, sampled proportion, and length of stay on the Squaw Creek National Wildlife Refuge. Double sampling was used to determine detection probability and estimated values varied among wetland units from a low of 0.07 to a high of 0.82. The sampled proportion of most wetland units was 100% but was lower in some of the larger units. Length of stay (measured for Pectoral [Calidris melanotos] and Least Sandpipers [C. minutilla] combined) averaged 10.0 days in spring and 3.7 days in fall. Spring shorebird numbers were approximately five times greater than fall numbers on the Refuge. Annual shorebird numbers varied among years from an estimated low in 2003 of 15 734 to a high in 2002 of 69 570. Peak daily counts during study years averaged only 12% of estimated spring totals and 4% of fall totals. An estimate of shorebird numbers based on summing weekly counts, not corrected for detection probability or sampled proportion, would have been only 21% (spring) to 31% (fall) of the total number of birds. These results reveal that peak counts and nonadjusted counts can significantly underestimate the number of shorebirds that use migration stopover sites in the midcontinent of North America. ?? The Cooper Ornithological Society 2006.
Stochastic variation in Cardamine hirsuta petal number
Monniaux, Marie; Pieper, Bjorn; Hay, Angela
2016-01-01
Background and Aims Floral development is remarkably robust in terms of the identity and number of floral organs in each whorl, whereas vegetative development can be quite plastic. This canalization of flower development prevents the phenotypic expression of cryptic genetic variation, even in fluctuating environments. A cruciform perianth with four petals is a hallmark of the Brassicaceae family, typified in the model species Arabidopsis thaliana. However, variable petal loss is found in Cardamine hirsuta, a genetically tractable relative of A. thaliana. Cardamine hirsuta petal number varies in response to stochastic, genetic and environmental perturbations, which makes it an interesting model to study mechanisms of decanalization and the expression of cryptic variation. Methods Multitrait quantitative trait locus (QTL) analysis in recombinant inbred lines (RILs) was used to identify whether the stochastic variation found in C. hirsuta petal number had a genetic basis. Key Results Stochastic variation (standard error of the average petal number) was found to be a heritable phenotype, and four QTL that influenced this trait were identified. The sensitivity to detect these QTL effects was increased by accounting for the effect of ageing on petal number variation. All QTL had significant effects on both average petal number and its standard error, indicating that these two traits share a common genetic basis. However, for some QTL, a degree of independence was found between the age of the flowers where allelic effects were significant for each trait. Conclusions Stochastic variation in C. hirsuta petal number has a genetic basis, and common QTL influence both average petal number and its standard error. Allelic variation at these QTL can, therefore, modify petal number in an age-specific manner via effects on the phenotypic mean and stochastic variation. These results are discussed in the context of trait evolution via a loss of robustness. PMID:26346720
Viscous thermocapillary convection at high Marangoni number
NASA Technical Reports Server (NTRS)
Cowley, S. J.; Davis, S. H.
1983-01-01
A liquid, contained in a quarter plane, undergoes steady motion due to thermocapillary forcing on its upper boundary, a free surface separating the liquid from a passive gas. The rigid vertical sidewall has a strip whose temperature is elevated compared with the liquid at infinity. A boudnary-layer analysis is performed that is valid for large Marangoni numbers M and Prandtl numbers P. It is found that the Nusselt number N for the horizontal heat transport satisfies N proportional to min (M to the 1 2/7/power, M to the 1 1/5/power, M to the 1 1/10/power) Generalizations are discussed.
Hyperimmunity and A-computable universal numberings
NASA Astrophysics Data System (ADS)
Issakhov, Assylbek
2016-08-01
Whether there exists a computable universal numbering for a computable family is the key question in theory of numberings. In a very general setting, this problem was explored in [Yu. L. Ershov, Theory of Numberings, Handbook of Computability Theory, North-Holland; Amsterdam: Stud. Log. Found. Math., Vol. 140, pp. 473-503, 1999]. For sets A that are Turing jumps of the empty set, the problem was treated in [S. A. Badaev, S. S. Goncharov, and A. Sorbi, Computability and Models, 11-44 (2003)] and other papers. In this work, we investigate families of total functions computable relative to hyperimmune and hyperimmune-free oracles.
Animal cognition. Number-space mapping in the newborn chick resembles humans' mental number line.
Rugani, Rosa; Vallortigara, Giorgio; Priftis, Konstantinos; Regolin, Lucia
2015-01-30
Humans represent numbers along a mental number line (MNL), where smaller values are located on the left and larger on the right. The origin of the MNL and its connections with cultural experience are unclear: Pre-verbal infants and nonhuman species master a variety of numerical abilities, supporting the existence of evolutionary ancient precursor systems. In our experiments, 3-day-old domestic chicks, once familiarized with a target number (5), spontaneously associated a smaller number (2) with the left space and a larger number (8) with the right space. The same number (8), though, was associated with the left space when the target number was 20. Similarly to humans, chicks associate smaller numbers with the left space and larger numbers with the right space.
Opening the Door on Triangular Numbers
ERIC Educational Resources Information Center
McMartin, Kimberley; McMaster, Heather
2016-01-01
As an alternative to looking solely at linear functions, a three-lesson learning progression developed for Year 6 students that incorporates triangular numbers to develop children's algebraic thinking is described and evaluated.
Generalized Fibonacci Numbers and Dimer Statistics
NASA Astrophysics Data System (ADS)
Lu, W. T.; Wu, F. Y.
2003-04-01
We establish new product identities involving the q-analogue of the Fibonacci numbers. We show that the identities lead to alternate expressions of generating functions for close-packed dimers on non-orientable surfaces.
Generalized Fibonacci Numbers and Dimer Statistics
NASA Astrophysics Data System (ADS)
Lu, W. T.; Wu, F. Y.
We establish new product identities involving the q-analogue of the Fibonacci numbers. We show that the identities lead to alternate expressions of generating functions for close-packed dimers on non-orientable surfaces.
Ideal photon number amplifier and duplicator
NASA Technical Reports Server (NTRS)
Dariano, G. M.
1992-01-01
The photon number-amplification and number-duplication mechanism are analyzed in the ideal case. The search for unitary evolutions leads to consider also a number-deamplification mechanism, the symmetry between amplification and deamplification being broken by the integer-value nature of the number operator. Both transformations, amplification and duplication, need an auxiliary field which, in the case of amplification, turns out to be amplified in the inverse way. Input-output energy conservation is accounted for using a classical pump or through frequency-conversion of the fields. Ignoring one of the fields is equivalent to considering the amplifier as an open system involving entropy production. The Hamiltonians of the ideal devices are given and compared with those of realistic systems.
Chaotic behaviour of high Mach number flows
NASA Technical Reports Server (NTRS)
Varvoglis, H.; Ghosh, S.
1985-01-01
The stability of the super-Alfvenic flow of a two-fluid plasma model with respect to the Mach number and the angle between the flow direction and the magnetic field is investigated. It is found that, in general, a large scale chaotic region develops around the initial equilibrium of the laminar flow when the Mach number exceeds a certain threshold value. After reaching a maximum the size of this region begins shrinking and goes to zero as the Mach number tends to infinity. As a result high Mach number flows in time independent astrophysical plasmas may lead to the formation of 'quasi-shocks' in the presence of little or no dissipation.
Thermal convection at infinite Prandtl number
NASA Technical Reports Server (NTRS)
Herring, J. R.
1969-01-01
Numerical solutions are developed for the full scaled three dimensional thermal convection problem, at infinite Prandtl number, and for rigid boundaries. The procedure is designed to give an approximate account of horizontally homogeneous and isotropic flow situations. Results, which included a maximum of 36 horizontal wave number vectors and 20 vertical wave numbers, appear to adequately describe the flow fill up to R = 100,000; beyond this R the results appear to show horizontal wave number truncation error. This error seems to affect the boundary slope of the mean temperature field more than other mean quantities. Despite some numerical uncertainities, certain of the qualitative features of the flow fill are predicted with reasonable confidence.
Predicting unknown species numbers using discovery curves
Bebber, Daniel P; Marriott, Francis H.C; Gaston, Kevin J; Harris, Stephen A; Scotland, Robert W
2007-01-01
A common approach to estimating the total number of extant species in a taxonomic group is to extrapolate from the temporal pattern of known species descriptions. A formal statistical approach to this problem is provided. The approach is applied to a number of global datasets for birds, ants, mosses, lycophytes, monilophytes (ferns and horsetails), gymnosperms and also to New World grasses and UK flowering plants. Overall, our results suggest that unless the inventory of a group is nearly complete, estimating the total number of species is associated with very large margins of error. The strong influence of unpredictable variations in the discovery process on species accumulation curves makes these data unreliable in estimating total species numbers. PMID:17456460
Small Atwood number Rayleigh-Taylor experiments.
Andrews, Malcolm J; Dalziel, Stuart B
2010-04-13
Consideration is given to small Atwood number (non-dimensional density difference) experiments to investigate mixing driven by Rayleigh-Taylor (R-T) instability. The past 20 years have seen the development of novel experiments to investigate R-T mixing and, simultaneously, the advent of high-fidelity diagnostics. Indeed, the developments of experiments and diagnostics have gone hand in hand, and as a result modern R-T experiments rival the capabilities and research scope of shear-driven mixing experiments. Thus, research into the small Atwood number limit has made significant progress over the past 20 years, and has offered important insights into natural mixing processes as well as the general R-T problem. This review of small Atwood number experiments serves as an opportunity to discuss progress, and also to provoke thoughts about future high Atwood number designs and difficulties.
Rhizobial gibberellin negatively regulates host nodule number
Tatsukami, Yohei; Ueda, Mitsuyoshi
2016-01-01
In legume–rhizobia symbiosis, the nodule number is controlled to ensure optimal growth of the host. In Lotus japonicus, the nodule number has been considered to be tightly regulated by host-derived phytohormones and glycopeptides. However, we have discovered a symbiont-derived phytohormonal regulation of nodule number in Mesorhizobium loti. In this study, we found that M. loti synthesized gibberellic acid (GA) under symbiosis. Hosts inoculated with a GA-synthesis-deficient M. loti mutant formed more nodules than those inoculated with the wild-type form at four weeks post inoculation, indicating that GA from already-incorporated rhizobia prevents new nodule formation. Interestingly, the genes for GA synthesis are only found in rhizobial species that inhabit determinate nodules. Our findings suggest that the already-incorporated rhizobia perform GA-associated negative regulation of nodule number to prevent delayed infection by other rhizobia. PMID:27307029
Fractions but not negative numbers are represented on the mental number line.
Ganor-Stern, Dana
2012-02-01
The present study is the first to directly compare numerical representations of positive numbers, negative numbers and unit fractions. The results show that negative numbers and unit fractions were not represented in the same way. Distance effects were found when positive numbers were compared with fractions but not when they were compared with negative numbers, thus suggesting that unit fractions but not negative numbers were represented on the number line with positive numbers. As indicated by the semantic congruity effect, negative numbers were perceived to be small, positive numbers were perceived as large, while unit fractions were perceived neither as large nor small. Comparisons between negative numbers were faster than between unit fractions, possibly due to the smaller differences between the holistic magnitudes of the unit fractions. Finally, comparing unit fractions to 1 was faster than comparing them to 0, consistent with the idea that unit fractions are perceived as entities smaller than 1 (Kallai & Tzelgov, 2009). The results are consistent with the idea of a mental division between numbers that represent a quantity (positive numbers and unit fractions) and those that do not (negative numbers).
Predicting apparent Sherwood numbers for fluidized beds
Groenewold, H.; Tsotsas, E.
1999-09-01
Mass transfer data of bubbling fluidized beds have been reevaluated with a new model which is completely predictive. The model is based on a two-phase approach with active bypass, formally plug flow for the suspension gas and a consideration of backmixing in the main kinetic coefficient, i.e. in the apparent particle-to-fluid Sherwood number. A good agreement with experimental results of various authors with a broad range of Reynolds numbers and particle diameters is demonstrated.
Genetic Algorithms, Floating Point Numbers and Applications
NASA Astrophysics Data System (ADS)
Hardy, Yorick; Steeb, Willi-Hans; Stoop, Ruedi
The core in most genetic algorithms is the bitwise manipulations of bit strings. We show that one can directly manipulate the bits in floating point numbers. This means the main bitwise operations in genetic algorithm mutations and crossings are directly done inside the floating point number. Thus the interval under consideration does not need to be known in advance. For applications, we consider the roots of polynomials and finding solutions of linear equations.
All-optical fast random number generator.
Li, Pu; Wang, Yun-Cai; Zhang, Jian-Zhong
2010-09-13
We propose a scheme of all-optical random number generator (RNG), which consists of an ultra-wide bandwidth (UWB) chaotic laser, an all-optical sampler and an all-optical comparator. Free from the electric-device bandwidth, it can generate 10Gbit/s random numbers in our simulation. The high-speed bit sequences can pass standard statistical tests for randomness after all-optical exclusive-or (XOR) operation.
Analysis and prediction of sunspot numbers
Paul, A.K.
1985-12-01
An extension of anharmonic frequency analysis (AFA) is used to analyze and extrapolate the sunspot numbers. The higher resolution possible with this new approach in principle permits a better accuracy of the prediction for a given extrapolation range, provided the time series is stationary. The results indicate that the extremas of the sunspot numbers of the next three solar cycles will not exceed a magnitude of 100 significantly.
Analysis and prediction of sunspot numbers
NASA Astrophysics Data System (ADS)
Paul, A. K.
1985-12-01
An extension of anharmonic frequency analysis (AFA) is used to analyze and extrapolate the sunspot numbers. The higher resolution possible with this new approach in principle permits a better accuracy of the prediction for a given exrapolation range, provided the time series is stationary. The results indicate that the extremas of the sunspot numbers of the next three solar cycles will not exceed a magnitude of 100 significantly.
Computing the isoperimetric number of a graph
Golovach, P.A.
1995-01-01
Let G be a finite graph. Denote by {partial_derivative}X, where X {contained_in} VG, the set of edges of the graph G with one end in X and the other end in the set VG{backslash}X. The ratio i(G) = min {vert_bar}{vert_bar}X{vert_bar}/{vert_bar}X{vert_bar}, where the minimum is over all nonempty subsets X of the set VG such that {vert_bar}X{vert_bar} {le} {vert_bar} VG {vert_bar}/2, is called the isoperimetric number of the graph G. It is easy to see that the isoperimetric number may be used as a {open_quotes}measure of connectivity{close_quotes} of the graph. The problem of determining the isoperimetric number is clearly linked with graph partition problems, which often arise in various applications. The isoperimetric number is also important for studying Riemann surfaces. These and other applications of the isoperimetric number justify the analysis of graphs of this kind. The properties of the isoperimetric number are presented in more detail elsewhere. It is shown elsewhere that the computation of the isoperimetric number is an NP-hard problem for graphs with multiple edges. We will show that the decision problem {open_quotes}given the graph G and two integers s and t decide if i(G) {le} s/t{close_quotes} is NP-complete even for simple graphs with vertex degrees not exceeding 3. Note that the isoperimetric number of a tree can be computed by a known polynomial-time algorithm.
SESAME equation of state number 7740: Polycarbonate
Boettger, J.C.
1991-06-01
An equation of state (EOS) for polycarbonate (a widely used polymer) has been generated with the computer code GRIZZLY and will be added to the SESAME library as material number 7740. Although a number of the input parameter used in the calculations are based on rough estimates. 7740 provides a good match to experimental Hugoniot data and should be reliable on or near the principal Hugoniot. 6 refs., 1 fig.
Analysis of Additive Random Number Generators.
1977-03-01
linear congruential generators yn*\\* ayn+bmo,iPa- The simplest example of a sequence satisfying (1.1) with *> I is the Fibonacci sequence with p - 2...However, the Fibonacci sequence is not a suitable random number generator because successive triples are very poorly distributed in three...number generator should have small discrepancy. Definition 2.1 can be extended naturally to define discrepancy for sequences of points yn lying in
Theoretical basis for the Beale number
West, C.D.
1981-08-01
Th Beale number is an empirically derived figure relating the power output of a Stirling engine to working gas pressure, operating frequency, and piston displacement. It is widely used to make preliminary estimates of performance of new designs and to compare the performance of existing engines. Two separate areas of investigation are combined to give a theoretical value for the Beale number and a straightforward explanation of its physical significance. 5 refs.
Binet's formula for generalized tribonacci numbers
NASA Astrophysics Data System (ADS)
Cereceda, José Luis
2015-11-01
In this note, we derive Binet's formula for the general term ? of the generalized tribonacci sequence. This formula gives ? explicitly as a function of the index n, the roots of the associated characteristic equation, and the initial terms ?, ?, and ?. By way of illustration, we obtain Binet's formula for the Cordonnier, Perrin, and Van der Laan numbers. In addition, we establish a double identity that can be regarded as a parent of Binet's formula for generalized tribonacci numbers.
Number Rigidity in Superhomogeneous Random Point Fields
NASA Astrophysics Data System (ADS)
Ghosh, Subhro; Lebowitz, Joel
2017-02-01
We give sufficient conditions for the number rigidity of a large class of point processes in dimension d=1 and 2, based on the decay of correlations. Number rigidity implies that the probability distribution of the number of particles in a bounded domain Λ subset R^d, conditional on the configuration on Λ ^\\complement , is concentrated on a single integer N_Λ . Our conditions are: (a) ρ _1(x)= - int _{R^d} ρ _tr^{(2)}(x,y) dy for all x, where ρ _1 and ρ _tr^{(2)} are the intensity and the truncated pair correlation function resp., and (b)|ρ _tr^{(2)}(x,y)| is bounded by C_1[|x-y|+1]^{-2} in d=1 and by C_2[|x-y|+1]^{-(4+ɛ)} in d=2. Condition (a) covers a wide class of processes, including translation invariant or periodic point process on R^d, d=1,2, that are superhomogeneous or hyperuniform (that is the variance of the number of particles in a bounded domain Ω subset R^d grows slower than the volume of Ω ). It also covers determinantal point processes having a projection kernel. Our conditions for number rigidity are satisfied by all known processes with number rigidity in d=1,2. We also observe, in the light of the results of [26], that no such criteria exist in d>2.
Ion Stopping Powers and CT Numbers
Moyers, Michael F.; Sardesai, Milind; Sun, Sean; Miller, Daniel W.
2010-10-01
One of the advantages of ion beam therapy is the steep dose gradient produced near the ion's range. Use of this advantage makes knowledge of the stopping powers for all materials through which the beam passes critical. Most treatment planning systems calculate dose distributions using depth dose data measured in water and an algorithm that converts the kilovoltage X-ray computed tomography (CT) number of a given material to its linear stopping power relative to water. Some materials present in kilovoltage scans of patients and simulation phantoms do not lie on the standard tissue conversion curve. The relative linear stopping powers (RLSPs) of 21 different tissue substitutes and positioning, registration, immobilization, and beamline materials were measured in beams of protons accelerated to energies of 155, 200, and 250 MeV; carbon ions accelerated to 290 MeV/n; and iron ions accelerated to 970 MeV/n. These same materials were scanned with both kilovoltage and megavoltage CT scanners to obtain their CT numbers. Measured RLSPs and CT numbers were compared with calculated and/or literature values. Relationships of RLSPs to physical densities, electronic densities, kilovoltage CT numbers, megavoltage CT numbers, and water equivalence values converted by a treatment planning system are given. Usage of CT numbers and substitution of measured values into treatment plans to provide accurate patient and phantom simulations are discussed.
Courant number and unsteady flow computation
Lai, Chintu; ,
1993-01-01
The Courant number C, the key to unsteady flow computation, is a ratio of physical wave velocity, ??, to computational signal-transmission velocity, ??, i.e., C = ??/??. In this way, it uniquely relates a physical quantity to a mathematical quantity. Because most unsteady open-channel flows are describable by a set of n characteristic equations along n characteristic paths, each represented by velocity ??i, i = 1,2,....,n, there exist as many as n components for the numerator of C. To develop a numerical model, a numerical integration must be made on each characteristic curve from an earlier point to a later point on the curve. Different numerical methods are available in unsteady flow computation due to the different paths along which the numerical integration is actually performed. For the denominator of C, the ?? defined as ?? = ?? 0 = ??x/??t has been customarily used; thus, the Courant number has the familiar form of C?? = ??/??0. This form will be referred to as ???common Courant number??? in this paper. The commonly used numerical criteria C?? for stability, neutral stability and instability, are imprecise or not universal in the sense that r0 does not always reflect the true maximum computational data-transmission speed of the scheme at hand, i.e., Ctau is no indication for the Courant constraint. In view of this , a new Courant number, called the ???natural Courant number???, Cn, that truly reflects the Courant constraint, has been defined. However, considering the numerous advantages inherent in the traditional C??, a useful and meaningful composite Courant number, denoted by C??* has been formulated from C??. It is hoped that the new aspects of the Courant number discussed herein afford the hydraulician a broader perspective, consistent criteria, and unified guidelines, with which to model various unsteady flows.
Physical model of the dependence of the Nusselt number on the Rayleigh number
NASA Astrophysics Data System (ADS)
Patochkina, O. L.; Kazarinov, Yu. G.; Tkachenko, V. I.
2016-11-01
The dependence of the Nusselt number on the Rayleigh number at the stage preceding the turbulent regime of convection is substantiated and obtained in analytic form. At this stage, the Nusselt number can be described by the power dependence on the Rayleigh number, which contains five constants. One of these constants is the same for all liquids and is the critical Rayleigh number Racr = 1700 ± 51. The remaining four constants are strictly individual for each type of liquid. For liquid helium, the critical Rayleigh number Racr = 35000 ± 4000 has the threshold value (Ra1 mix)th = 37 085.75. This value is determined by the small ratio of the diameter of the vessel to its height, as well as the formation of a cylindrical convection cell at the bottom of the vessel with a mode number of 2 and a radial number determined by the fourth root of the firstorder Bessel function of the first kind.
Extending the mental number line--how do negative numbers contribute?
Zhang, Yu; You, Xuqun
2012-01-01
Previous studies suggest that there is an association between positive numbers and space; however, there is less agreement for negative numbers. The main purpose of the present study was to investigate the nature of the processing and representation of negative numbers, and the association between negative numbers and space. Results of the two experiments show that low-level processing (perception) of negative numbers can induce spatial shifts of attention. Whether this is caused by their numerical value or absolute value depends on the numerical context and task requirements, indicating that there are both components and holistic processing, and representation for negative numbers. The representation is automatically associated with leftward space; the coding and representation of the mental number line is adaptable to the specific numerical context and task requirements. The mental number line, therefore, can extend to the left side of zero, thus supporting the context-dependent view.
[International migration: small numbers, large challenges].
Garcia Y Griego, M
1988-01-01
Mexican immigration into the United States during the period of 1850-1980 is analyzed relying on census data. In the late 1800's immigrants worked on railway construction and on farms in the central and northern plains, but they numbered only 68,000 in 1880. Between 1900-1930 their numbers exploded from 103,000 to close to 1 million due to the demand for agricultural laborers in California and Texas. The Great Depression saw en masse repatriation, by 1940 their numbers dwindled to 377,000, and it was not until the 60's that a resurgence started. By 1970 their number was 789,000, and the corrected 1980 census figure puts their number at 2,531,000 of which 1.1 million were illegals. Most were males 15-44 years old. Mexicans born outside Mexico were only 269,000 in 1980, a figure slightly higher than Mexicans registered in the U.S. in 1910. North Americans and Spanish have been the most numerous immigrants into Mexico since the 19th century, but in recent years a massive immigration from Central America has occurred as a result of political turmoil and war. Mexican immigration into the U.S. served as a safety valve for the economy and it has been compared to other demographic phenomena such as births and deaths. The legalization of immigrants in 1986 under a U.S. law has significantly dissipated a constant source of friction with the U.S.
The New Sunspot Number: Assembling All Corrections
NASA Astrophysics Data System (ADS)
Clette, Frédéric; Lefèvre, Laure
2016-11-01
Based on various diagnostics and corrections established in the framework of several Sunspot Number Workshops and described by Clette et al. ( Space Sci. Rev. 186, 35, 2014), we now assembled all separately derived corrections to produce a new standard version of the reference sunspot-number time series. We explain here the three main corrections and the criteria used to choose a final optimal version of each correction factor or function, given the available information and published analyses. We then discuss the differences between the new corrected series and the original sunspot number, including the disappearance of any significant rising secular trend in the solar-cycle amplitudes after this recalibration. We also introduce the new version management scheme now implemented at the World Data Center Sunspot Index and Long-term Solar Observations (WDC-SILSO), which reflects a major conceptual transition: beyond the rescaled numbers, this first revision of the sunspot number also transforms the former static data archive into a living observational series open to future improvements.
Froude number corrections in anthropological studies.
Steudel-Numbers, Karen; Weaver, Timothy D
2006-09-01
The Froude number has been widely used in anthropology to adjust for size differences when comparing gait parameters or other nonmorphological locomotor variables (such as optimal walking speed or speed at gait transitions) among humans, nonhuman primates, and fossil hominins. However, the dynamic similarity hypothesis, which is the theoretical basis for Froude number corrections, was originally developed and tested at much higher taxonomic levels, for which the ranges of variation are much greater than in the intraspecific or intrageneric comparisons typical of anthropological studies. Here we present new experimental data on optimal walking speed and the mass-specific cost of transport at that speed from 19 adult humans walking on a treadmill, and evaluate the predictive power of the dynamic similarity hypothesis in this sample. Contrary to the predictions of the dynamic similarity hypothesis, we found that the mass-specific cost of transport at experimentally measured optimal walking speed and Froude number were not equal across individuals, but retained a significant correlation with body mass. Overall, the effect of lower limb length on optimal walking speed was weak. These results suggest that the Froude number may not be an effective way for anthropologists to correct for size differences across individuals, but more studies are needed. We suggest that researchers first determine whether geometric similarity characterizes their data before making inferences based on the dynamic similarity hypothesis, and then check the consistency of their results with and without Froude number corrections before drawing any firm conclusions.
Experimental study of low Reynolds number nozzles
NASA Technical Reports Server (NTRS)
Grisnik, Stanley P.; Smith, Tamara A.; Saltz, Larry E.
1987-01-01
High-performance electrothermal thrusters operate in a low nozzle-throat Reynolds number regime. Under these conditions, the flow boundary layer occupies a large volume inside the nozzle, contributing to large viscous losses. Four nozzles (conical, bell, trumpet, and modified trumpet) and a sharp-edged orifice were evaluated over a Reynolds number range of 500 to 9000 with unheated nitrogen and hydrogen. The nozzles showed significant decreases in specific impulse efficiency with decreasing Reynolds number. At Reynolds numbers less than 1000, all four nozzles were probably filled with a large boundary layer. The discharge coefficient decreased with Reynolds number in the same manner as the specific impulse efficiency. The bell and modified trumpet nozzles had discharge coefficients 4 to 8 percent higher than those of the cone or trumpet nozzles. The Two-Dimensional Kinetics (TDK) nozzle analysis computer program was used to predict nozzle performance. The results were then compared to the experimental results in order to determine the accuracy of the program within this flow regime.
Unpredictability and the transmission of numbers
NASA Astrophysics Data System (ADS)
Myers, John M.; Madjid, F. Hadi
2016-03-01
Curiously overlooked in physics is its dependence on the transmission of numbers. For example, the transmission of numerical clock readings is implicit in the concept of a coordinate system. The transmission of numbers and other logical distinctions is often achieved over a computer-mediated communications network in the face of an unpredictable environment. By unpredictable we mean something stronger than the spread of probabilities over given possible outcomes, namely an opening to unforeseeable possibilities. Unpredictability, until now overlooked in theoretical physics, makes the transmission of numbers interesting. Based on recent proofs within quantum theory that provide a theoretical foundation to unpredictability, here we show how regularities in physics rest on a background of channels over which numbers are transmitted. As is known to engineers of digital communications, numerical transmissions depend on coordination reminiscent of the cycle of throwing and catching by players tossing a ball back and forth. In digital communications, the players are computers, and the required coordination involves unpredictably adjusting "live clocks" that step these computers through phases of a cycle. We show how this phasing, which we call logical synchronization, constrains number-carrying networks, and, if a spacetime manifold in invoked, put "stripes" on spacetime. Via its logically synchronized channels, a network of live clocks serves as a reference against which to locate events. Such a network in any case underpins a coordinate frame, and in some cases the direct use of a network can be tailored to investigate an unpredictable environment. Examples include explorations of gravitational variations near Earth.
Nonlinear dynamos at infinite magnetic Prandtl number.
Alexakis, Alexandros
2011-03-01
The dynamo instability is investigated in the limit of infinite magnetic Prandtl number. In this limit the fluid is assumed to be very viscous so that the inertial terms can be neglected and the flow is enslaved to the forcing. The forcing consist of an external forcing function that drives the dynamo flow and the resulting Lorentz force caused by the back reaction of the magnetic field. The flows under investigation are the Archontis flow and the ABC flow forced at two different scales. The investigation covers roughly 3 orders of magnitude of the magnetic Reynolds number above onset. All flows show a weak increase of the averaged magnetic energy as the magnetic Reynolds number is increased. Most of the magnetic energy is concentrated in flat elongated structures that produce a Lorentz force with small solenoidal projection so that the resulting magnetic field configuration is almost force free. Although the examined system has zero kinetic Reynolds number at sufficiently large magnetic Reynolds number the structures are unstable to small scale fluctuations that result in a chaotic temporal behavior.
True random numbers from amplified quantum vacuum.
Jofre, M; Curty, M; Steinlechner, F; Anzolin, G; Torres, J P; Mitchell, M W; Pruneri, V
2011-10-10
Random numbers are essential for applications ranging from secure communications to numerical simulation and quantitative finance. Algorithms can rapidly produce pseudo-random outcomes, series of numbers that mimic most properties of true random numbers while quantum random number generators (QRNGs) exploit intrinsic quantum randomness to produce true random numbers. Single-photon QRNGs are conceptually simple but produce few random bits per detection. In contrast, vacuum fluctuations are a vast resource for QRNGs: they are broad-band and thus can encode many random bits per second. Direct recording of vacuum fluctuations is possible, but requires shot-noise-limited detectors, at the cost of bandwidth. We demonstrate efficient conversion of vacuum fluctuations to true random bits using optical amplification of vacuum and interferometry. Using commercially-available optical components we demonstrate a QRNG at a bit rate of 1.11 Gbps. The proposed scheme has the potential to be extended to 10 Gbps and even up to 100 Gbps by taking advantage of high speed modulation sources and detectors for optical fiber telecommunication devices.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 21 Food and Drugs 4 2011-04-01 2011-04-01 false Notification of registrant; drug establishment registration number and drug listing number. 207.35 Section 207.35 Food and Drugs FOOD AND DRUG ADMINISTRATION... top third of the label, the NDC number may appear as part of and contiguous to any bar-code symbol...
Code of Federal Regulations, 2012 CFR
2012-04-01
... 21 Food and Drugs 4 2012-04-01 2012-04-01 false Notification of registrant; drug establishment registration number and drug listing number. 207.35 Section 207.35 Food and Drugs FOOD AND DRUG ADMINISTRATION... top third of the label, the NDC number may appear as part of and contiguous to any bar-code symbol...
Code of Federal Regulations, 2014 CFR
2014-04-01
... 21 Food and Drugs 4 2014-04-01 2014-04-01 false Notification of registrant; drug establishment registration number and drug listing number. 207.35 Section 207.35 Food and Drugs FOOD AND DRUG ADMINISTRATION... top third of the label, the NDC number may appear as part of and contiguous to any bar-code symbol...
An Exploratory Study of a Number Sense Program to Develop Kindergarten Students' Number Proficiency
ERIC Educational Resources Information Center
Sood, Sheetal; Jitendra, Asha K.
2013-01-01
This study examined the effectiveness of a number sense program on kindergarten students' number proficiency and responsiveness to treatment as a function of students' risk for mathematics difficulties. The program targeted development of relationships among numbers (e.g., spatial, more and less). A total of 101 kindergarten students (not at risk:…
48 CFR 52.204-6 - Data Universal Numbering System Number.
Code of Federal Regulations, 2014 CFR
2014-10-01
... provision: Data Universal Numbering System Number (JUL 2013) (a) Definition. Data Universal Numbering System... one. (1) An offeror may obtain a DUNS number— (i) Via the Internet at http://fedgov.dnb.com/webform or if the offeror does not have internet access, it may call Dun and Bradstreet at 1-866-705-5711...
Federal Register 2010, 2011, 2012, 2013, 2014
2013-06-19
... multiple devices. See Nathan Ingram, iOS 6 unifies your Apple ID and phone number for improved iMessage and...-unified-apple-id-phone-number (``Now, if someone calls your phone number for Facetime, you'll be able to... and not your Apple ID email.''). 25. In light of these changes, in this Notice we seek comment on...
The Numbers Game: Phasing in Generated ID Numbers at the University of Oregon
ERIC Educational Resources Information Center
Eveland, Sue
2005-01-01
With all the recent headlines about security breaches and information loss at financial and educational institutions, the higher education community needs to address the issue of using social security numbers as ID numbers. The University of Oregon undertook a change process to assign generated ID numbers to all records in their information…
High Reynolds Number Thermal Stability Experiments
NASA Technical Reports Server (NTRS)
Emens, Jessica M.; Brown, Sarah P.; Frederick Robert A., Jr.; Wood, A. John
2004-01-01
This work represents preliminary thermal stability results for liquid hydrocarbon fuels. High Reynolds Number Thermal Stability experiments with Jet A and RP-1 resulted in a quantitative measurement of the thermal stability. Each fuel flowed through a heated capillary tube that held the outlet temperature at 290 C. An optical pyrometer measured the surface temperature of the tube at 12 locations as a function of time. The High Reynolds Number Thermal Stability number was then determined using standards published by the American Society for Testing and Materials. The results for Jet A showed lower thermal stability than similar tests conducted at another facility. The RP-1 results are the first reported using this technique. Because the temperature rise on the capillary tube during testing for the RP-1 fuels was not significant, a new standard for the testing conditions should be developed for these types of fuels.
Control of segment number in vertebrate embryos.
Gomez, Céline; Ozbudak, Ertuğrul M; Wunderlich, Joshua; Baumann, Diana; Lewis, Julian; Pourquié, Olivier
2008-07-17
The vertebrate body axis is subdivided into repeated segments, best exemplified by the vertebrae that derive from embryonic somites. The number of somites is precisely defined for any given species but varies widely from one species to another. To determine the mechanism controlling somite number, we have compared somitogenesis in zebrafish, chicken, mouse and corn snake embryos. Here we present evidence that in all of these species a similar 'clock-and-wavefront' mechanism operates to control somitogenesis; in all of them, somitogenesis is brought to an end through a process in which the presomitic mesoderm, having first increased in size, gradually shrinks until it is exhausted, terminating somite formation. In snake embryos, however, the segmentation clock rate is much faster relative to developmental rate than in other amniotes, leading to a greatly increased number of smaller-sized somites.
Optimal Strouhal number for swimming animals
NASA Astrophysics Data System (ADS)
Eloy, Christophe
2012-04-01
To evaluate the swimming performances of aquatic animals, an important dimensionless quantity is the Strouhal number, St=fA/U, with f the tail-beat frequency, A the peak-to-peak tail amplitude, and U the swimming velocity. Experiments with flapping foils have exhibited maximum propulsive efficiency in the interval 0.25
National transonic facility Mach number system
NASA Technical Reports Server (NTRS)
Kern, F. A.; Knight, C. W.; Zasimowich, R. F.
1985-01-01
The Mach number system for the Langley Research Center's National Transonic Facility was designed to measure pressures to determine Mach number to within + or - 0.002. Nine calibration laboratory type fused quartz gages, four different range gages for the total pressure measurement, and five different range gages for the static pressure measurement were used to satisfy the accuracy requirement over the 103,000-890,000 Pa total pressure range of the tunnel. The system which has been in operation for over 1 year is controlled by a programmable data process controller to select, through the operation of solenoid valves, the proper range fused quartz gage to maximize the measurement accuracy. The pressure gage's analog outputs are digitized by the process controller and transmitted to the main computer for Mach number computation. An automatic two-point on-line calibration of the nine quartz gages is provided using a high accuracy mercury manometer.
Mechanisms of change in gene copy number.
Hastings, P J; Lupski, James R; Rosenberg, Susan M; Ira, Grzegorz
2009-08-01
Deletions and duplications of chromosomal segments (copy number variants, CNVs) are a major source of variation between individual humans and are an underlying factor in human evolution and in many diseases, including mental illness, developmental disorders and cancer. CNVs form at a faster rate than other types of mutation, and seem to do so by similar mechanisms in bacteria, yeast and humans. Here we review current models of the mechanisms that cause copy number variation. Non-homologous end-joining mechanisms are well known, but recent models focus on perturbation of DNA replication and replication of non-contiguous DNA segments. For example, cellular stress might induce repair of broken replication forks to switch from high-fidelity homologous recombination to non-homologous repair, thus promoting copy number change.
Nusselt number scaling in tokamak plasma turbulence
Takeda, K.; Benkadda, S.; Hamaguchi, S.; Wakatani, M.
2005-05-15
Anomalous heat transport caused by ion temperature gradient (ITG) driven turbulence in tokamak plasmas is evaluated from numerical simulations of the two-dimensional (2D) partial-differential equations of the ITG model and of a reduced 1D version derived from a quasilinear approximation. In the strongly turbulent state, intermittent bursts of thermal transport are observed in both cases. In the strongly turbulent regime, the reduced model as well as the direct numerical simulation show that the Nusselt number Nu (normalized heat flux) scales with the normalized ion pressure gradient K{sub i} as Nu{proportional_to}K{sub i}{sup 1/3}. Since the Rayleigh number for ITG turbulence is proportional to K{sub i}, the Nusselt number scaling for ITG turbulence is thus similar to the classical thermal transport scaling for Rayleigh-Benard convections in neutral fluids.
Random Numbers from a Delay Equation
NASA Astrophysics Data System (ADS)
Self, Julian; Mackey, Michael C.
2016-10-01
Delay differential equations can have "chaotic" solutions that can be used to mimic Brownian motion. Since a Brownian motion is random in its velocity, it is reasonable to think that a random number generator might be constructed from such a model. In this preliminary study, we consider one specific example of this and show that it satisfies criteria commonly employed in the testing of random number generators (from TestU01's very stringent "Big Crush" battery of tests). A technique termed digit discarding, commonly used in both this generator and physical RNGs using laser feedback systems, is discussed with regard to the maximal Lyapunov exponent. Also, we benchmark the generator to a contemporary common method: the multiple recursive generator, MRG32k3a. Although our method is about 7 times slower than MRG32k3a, there is in principle no apparent limit on the number of possible values that can be generated from the scheme we present here.
Particle number fluctuations in the microcanonical ensemble
NASA Astrophysics Data System (ADS)
Begun, V. V.; Gorenstein, M. I.; Kostyuk, A. P.; Zozulya, O. S.
2005-05-01
Particle number fluctuations are studied in the microcanonical ensemble. For the Boltzmann statistics we deduce exact analytical formulas for the microcanonical partition functions in the case of noninteracting massless neutral particles and charged particles with zero net charge. The particle number fluctuations are calculated and we find that in the microcanonical ensemble they are suppressed in comparison to the fluctuations in the canonical and grand canonical ensembles. This remains valid in the thermodynamic limit too, so that the well-known equivalence of all statistical ensembles refers to average quantities, but does not apply to fluctuations. In the thermodynamic limit we are able to calculate the particle number fluctuations in the system of massive bosons and fermions when the exact conservation laws of both the energy and charge are taken into account.
Large numbers hypothesis. II - Electromagnetic radiation
NASA Technical Reports Server (NTRS)
Adams, P. J.
1983-01-01
This paper develops the theory of electromagnetic radiation in the units covariant formalism incorporating Dirac's large numbers hypothesis (LNH). A direct field-to-particle technique is used to obtain the photon propagation equation which explicitly involves the photon replication rate. This replication rate is fixed uniquely by requiring that the form of a free-photon distribution function be preserved, as required by the 2.7 K cosmic radiation. One finds that with this particular photon replication rate the units covariant formalism developed in Paper I actually predicts that the ratio of photon number to proton number in the universe varies as t to the 1/4, precisely in accord with LNH. The cosmological red-shift law is also derived and it is shown to differ considerably from the standard form of (nu)(R) - const.
Droplet Number Concentration Value-Added Product
Riihimaki, L.; McFarlane, S.; Sivaraman, C.
2014-06-01
The ndrop_mfrsr value-added product (VAP) provides an estimate of the cloud droplet number concentration of overcast water clouds retrieved from cloud optical depth from the multi-filter rotating shadowband radiometer (MFRSR) instrument and liquid water path (LWP) retrieved from the microwave radiometer (MWR). When cloud layer information is available from vertically pointing lidar and radars in the Active Remote Sensing of Clouds (ARSCL) product, the VAP also provides estimates of the adiabatic LWP and an adiabatic parameter (beta) that indicates how divergent the LWP is from the adiabatic case. quality control (QC) flags (qc_drop_number_conc), an uncertainty estimate (drop_number_conc_toterr), and a cloud layer type flag (cloud_base_type) are useful indicators of the quality and accuracy of any given value of the retrieval. Examples of these major input and output variables are given in sample plots in section 6.0.
Seniority Number in Valence Bond Theory.
Chen, Zhenhua; Zhou, Chen; Wu, Wei
2015-09-08
In this work, a hierarchy of valence bond (VB) methods based on the concept of seniority number, defined as the number of singly occupied orbitals in a determinant or an orbital configuration, is proposed and applied to the studies of the potential energy curves (PECs) of H8, N2, and C2 molecules. It is found that the seniority-based VB expansion converges more rapidly toward the full configuration interaction (FCI) or complete active space self-consistent field (CASSCF) limit and produces more accurate PECs with smaller nonparallelity errors than its molecular orbital (MO) theory-based analogue. Test results reveal that the nonorthogonal orbital-based VB theory provides a reverse but more efficient way to truncate the complete active Hilbert space by seniority numbers.
Theoretical basis for the Beale number
NASA Astrophysics Data System (ADS)
West, C. D.
The Beale number is an important, empirically derived figure relating the power output of a Stirling engine to working gas pressure, operating frequency, and piston displacement. It is widely used to make preliminary estimates of performance of new designs and to compare the performance of existing engines. Two separate areas of investigation (the simplified formula for power output of an ideal machine first derived by Cooke-Yarborough, and the actual performance ratings of several real engines collected by Martini) are combined to give a theoretical value for the Beale number and a straightforward explanation of its physical significance. The derived value is in good agreement with the empirical figure and is consistent with Walker's estimates of the temperature dependence of the Beale number.
Lepton number violation in 331 models
NASA Astrophysics Data System (ADS)
Fonseca, Renato M.; Hirsch, Martin
2016-12-01
Different models based on the extended S U (3 )C×S U (3 )L×U (1 )X (331) gauge group have been proposed over the past four decades. Yet, despite being an active research topic, the status of lepton number in 331 models has not been fully addressed in the literature, and furthermore many of the original proposals can not explain the observed neutrino masses. In this paper we review the basic features of various 331 models, focusing on potential sources of lepton number violation. We then describe different modifications which can be made to the original models in order to accommodate neutrino (and charged lepton) masses.
Gene copy number and malaria biology
Anderson, Tim J.C.; Patel, Jigar; Ferdig, Michael T.
2010-01-01
Alteration in gene copy number provides a simple way to change expression levels and alter phenotype. This was fully appreciated by bacteriologists more than 25 years ago, but the extent and implications of copy number polymorphism (CNP) have only recently become apparent in other organisms. New methods demonstrate the ubiquity of CNPs in eukaryotes and their medical importance in humans. CNP is also widespread in the Plasmodium falciparum genome and has an important and underappreciated role in determining phenotype. In this review, we summarize the distribution of CNP, its evolutionary dynamics within populations, its functional importance and its mode of evolution. PMID:19559648
Number Theoretic Methods in Parameter Estimation
2007-11-02
Washington, DC 20503. 1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 5 /29/98 3. REPORT TYPE AND DATES COVERED Final- 1 April 97- 31 May 98 4. TITLE AND...American University Department of Mathematics and Statistics 4400 Massachusetts Ave., N.W. Washington, D.C. 20016- 8050 9. SPONSORING / MONITORING...AGENCY NAMES(S) AND ADDRESS(ES) Office of Naval Research 800 North Quincy Street Arlington, VA 22217-5660 5 . FUNDING NUMBERS (g) ONR Grant Number
Cantor-Type Sets in Hyperbolic Numbers
NASA Astrophysics Data System (ADS)
Balankin, A. S.; Bory-Reyes, J.; Luna-Elizarrarás, M. E.; Shapiro, M.
2016-12-01
The construction of the ternary Cantor set is generalized into the context of hyperbolic numbers. The partial order structure of hyperbolic numbers is revealed and the notion of hyperbolic interval is defined. This allows us to define a general framework of the fractal geometry on the hyperbolic plane. Three types of the hyperbolic analogues of the real Cantor set are identified. The complementary nature of the real Cantor dust and the real Sierpinski carpet on the hyperbolic plane are outlined. The relevance of these findings in the context of modern physics are briefly discussed.
The vegetative index number and crop identification
NASA Technical Reports Server (NTRS)
Ashburn, P. (Principal Investigator)
1979-01-01
A vegetative index number of numerical value was calculated from the digital values of the LANDSAT system to provide some measure of green growing vegetation. The usefulness of the green numbers for schemes in crop identification and acreage estimation is investigated and the Ashburn vegetation index (AVI) is compared with the Kauth-Thomas vegetation index (KVI) for crop identification schemes. Results of wheat acreage estimation using LACIE Procedure 1 and the AVI for eight sample segments are given. Tables show comparisons between the AVI and the KVI as well as visual results of the AVI.
Searches for violation of muon number conservation
Redwine, R.P.
1981-01-01
The question of violation of muon number conservation is one which has occupied considerable attention and resources in recent years. The first generation of experiments at the medium energy accelerators has now been completed and the next generation of experiments is ready to begin. The history of muon number conservation is reviewed, including the reasons for the present belief that the conservation law may not be exact. The experiments that have been completed in the last few years are discussed. The new experiments that are being mounted and planned at several laboratories are discussed, and the relationship of these types of experiments to other studies, such as searches for neutrino oscillations, are considered.
Simulations of motor unit number estimation techniques
NASA Astrophysics Data System (ADS)
Major, Lora A.; Jones, Kelvin E.
2005-06-01
Motor unit number estimation (MUNE) is an electrodiagnostic procedure used to evaluate the number of motor axons connected to a muscle. All MUNE techniques rely on assumptions that must be fulfilled to produce a valid estimate. As there is no gold standard to compare the MUNE techniques against, we have developed a model of the relevant neuromuscular physiology and have used this model to simulate various MUNE techniques. The model allows for a quantitative analysis of candidate MUNE techniques that will hopefully contribute to consensus regarding a standard procedure for performing MUNE.
Parametric number covariance in quantum chaotic spectra.
Vinayak; Kumar, Sandeep; Pandey, Akhilesh
2016-03-01
We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation method and obtain compact expressions for the covariance. We illustrate the universality of this measure by presenting the spectral analysis of the quantum kicked rotors for the time-reversal invariant and time-reversal noninvariant cases. A local version of the parametric number variance introduced earlier is also investigated.
Navy Plastics Dialogue, Modification Number 2
1993-09-28
the Navy Washington, D.C. 20350-2000 703-602-2562 Fax: 703-602-4642 Tom Ledvina Navy Deputy Assistant General Counsel (I&E) 5 Room 368 Crystal Plaza #5...a whistleblower number. The Navy staff responded that the Naval Inspector does have such a mechanism with its 800 number hotline. Captain Tom Ledvina ...Dialogue has accomplished from both Navy and non-Navy members. The first item on the agenda was the Navy’s Report to Congress. Tom Ledvina , Navy Deputy
The WSTIAC Quarterly. Volume 9, Number 3
2010-01-25
Technical Information Center, Ft Belvoir, VA 10 . SPONSOR/MONITOR’S ACRONYM(S) 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 12. DISTRIBUTION...WSTIAC) revealed the “WSTIAC 10 ” – ten strategic areas critical to the Department of Defense (DoD) in which WSTIAC provides focused support. Since this...blocks in a static environment, with Table 4. 160 x 120 MPEG4, bitrate = 150ks. Frame Rate kBps kbps Comments 1 fps 5- 10 40-80 Still images appear better
Statistical Analysis of Random Number Generators
NASA Astrophysics Data System (ADS)
Accardi, Luigi; Gäbler, Markus
2011-01-01
In many applications, for example cryptography and Monte Carlo simulation, there is need for random numbers. Any procedure, algorithm or device which is intended to produce such is called a random number generator (RNG). What makes a good RNG? This paper gives an overview on empirical testing of the statistical properties of the sequences produced by RNGs and special software packages designed for that purpose. We also present the results of applying a particular test suite--TestU01-- to a family of RNGs currently being developed at the Centro Interdipartimentale Vito Volterra (CIVV), Roma, Italy.
Equations with Arithmetic Functions of Pell Numbers
2014-01-01
2Pantelimon Stănică Abstract Here, we prove some diophantine results about the Euler function of Pell numbers and their Pell–Lucas companion sequence . For...the quadratic equation x2 − 2x − 1 = 0. Let (Pn)n≥0 and (Qn)n≥0 be the Pell sequence and its companion of general terms Pn = αn − βn α− β and Qn = α n...we prove some diophantine results about the Euler function of Pell numbers and their Pell{Lucas companion sequence . For example, if the Euler
Approximate resolution of hard numbering problems
Bailleux, O.; Chabrier, J.J.
1996-12-31
We present a new method for estimating the number of solutions of constraint satisfaction problems. We use a stochastic forward checking algorithm for drawing a sample of paths from a search tree. With this sample, we compute two values related to the number of solutions of a CSP instance. First, an unbiased estimate, second, a lower bound with an arbitrary low error probability. We will describe applications to the Boolean Satisfiability problem and the Queens problem. We shall give some experimental results for these problems.
Number theory meets high energy physics
NASA Astrophysics Data System (ADS)
Todorov, Ivan
2017-03-01
Feynman amplitudes in perturbative quantum field theory are being expressed in terms of an algebra of functions, extending the familiar logarithms, and associated numbers— periods. The study of these functions (including hyperlogarithms) and numbers (like the multiple zeta values), that dates back to Leibniz and Euler, has attracted anew the interest of algebraic geometers and number theorists during the last decades. The two originally independent developments are recently coming together in an unlikely collaboration between particle physics and what were regarded as the most abstruse branches of mathematics.
High Prandtl number effect on Rayleigh-Bénard convection heat transfer at high Rayleigh number
NASA Astrophysics Data System (ADS)
Ma, Li; Li, Jing; Ji, Shui; Chang, Huajian
2017-02-01
This paper represents results of the Rayleigh-Bénard convection heat transfer in silicon oil confined by two horizontal plates, heated from below, and cooled from above. The Prandtl numbers considered as 100-10,000 corresponding to three types of silicon oil. The experiments covered a range of Rayleigh numbers from 2.14·109 to 2.27·1013. The data points that the Nusselt number dependents on the Rayleigh number, which is asymptotic to a 0.248 power. Furthermore, the experiment results can fit the data in low Rayleigh number well.
Two-bit quantum random number generator based on photon-number-resolving detection
NASA Astrophysics Data System (ADS)
Jian, Yi; Ren, Min; Wu, E.; Wu, Guang; Zeng, Heping
2011-07-01
Here we present a new fast two-bit quantum random number generator based on the intrinsic randomness of the quantum physical phenomenon of photon statistics of coherent light source. Two-bit random numbers were generated according to the number of detected photons in each light pulse by a photon-number-resolving detector. Poissonian photon statistics of the coherent light source guaranteed the complete randomness of the bit sequences. Multi-bit true random numbers were generated for the first time based on the multi-photon events from a coherent light source.
NASA Astrophysics Data System (ADS)
Lockwood, M.; Owens, M. J.; Barnard, L.
2016-11-01
We use five test data series to search for, and quantify, putative discontinuities around 1946 in five different annual-mean sunspot-number or sunspot-group-number data sequences. The data series tested are the original and new versions of the Wolf/Zürich/International sunspot number composite [R_{{ISNv1}} and R_{{ISNv2}}] (respectively Clette et al. in Adv. Space Res. 40, 919, 2007 and Clette et al. in The Solar Activity Cycle 35, Springer, New York, 2015); the corrected version of R ISNv1 proposed by Lockwood, Owens, and Barnard ( J. Geophys. Res. 119, 5193, 2014a) [R C]; the new "backbone" group-number composite proposed by Svalgaard and Schatten ( Solar Phys. 291, 2016) [R_{{BB}}]; and the new group-number composite derived by Usoskin et al. ( Solar Phys. 291, 2016) [R_{{UEA}}]. The test data series used are the group-number [NG] and total sunspot area [A G] from the Royal Observatory, Greenwich/Royal Greenwich Observatory (RGO) photoheliographic data; the Ca K index from the recent re-analysis of Mount Wilson Observatory (MWO) spectroheliograms in the Calcium ii K ion line; the sunspot-group-number from the MWO sunspot drawings [N_{{MWO}}]; and the dayside ionospheric F2-region critical frequencies measured by the Slough ionosonde [foF2]. These test data all vary in close association with sunspot numbers, in some cases non-linearly. The tests are carried out using both the before-and-after fit-residual comparison method and the correlation method of Lockwood, Owens, and Barnard, applied to annual mean data for intervals iterated to minimise errors and to eliminate uncertainties associated with the precise date of the putative discontinuity. It is not assumed that the correction required is by a constant factor, nor even linear in sunspot number. It is shown that a non-linear correction is required by RC, R_{BB}, and R_{{ISNv1}}, but not by R_{{ISNv2}} or R_{{UEA}}. The five test datasets give very similar results in all cases. By multiplying the probability
Hyde, Daniel C.; Spelke, Elizabeth S.
2009-01-01
Behavioral and brain imaging research indicates that human infants, humans adults, and many non-human animals represent large non-symbolic numbers approximately, discriminating between sets with a ratio limit on accuracy. Some behavioral evidence, especially with human infants, suggests that these representations differ from representations of small numbers of objects. To investigate neural signatures of this distinction, event-related potentials (ERPs) were recorded as adult humans passively viewed the sequential presentation of dot arrays in an adaptation paradigm. In two studies, subjects viewed successive arrays of a single number of dots interspersed with test arrays presenting the same or a different number; numerical range (small numerical quantities 1-3 vs. large numerical quantities 8-24) and ratio difference varied across blocks as continuous variables were controlled. An early-evoked component (N1), observed over widespread posterior scalp locations, was modulated by absolute number with small but not large number arrays. In contrast, a later component (P2p), observed over the same scalp locations, was modulated by the ratio difference between arrays for large but not small numbers. Despite many years of experience with symbolic systems that apply equally to all numbers, adults spontaneously process small and large numbers differently. They appear to treat small-number arrays as individual objects to be tracked through space and time, and large-number arrays as cardinal values to be compared and manipulated. PMID:18752403
Zougkou, Konstantina; Temple, Christine M
2016-01-01
The arithmetical skills in two children with Turner's syndrome (TS), each the focus of a case study, were analysed in whole numbers and other number scales that have not been systematically explored previously, fractions, decimals, percentages, and negative numbers. The intention was to identify the fractionation of arithmetical skills. The two girls with TS showed dissociations of arithmetical skill in the calculation system of whole numbers that support its modular organization. Fractionation of skills was observed in some components of the other number scales, suggesting an analogous organization within these scales. The operational specificity of impairment within number scales but not others argued against a unitary arithmetical system but rather for autonomous operational scales within distinct number scales. A general model of arithmetic is proposed.
Particle Test Fluence: What's the Right Number?
NASA Technical Reports Server (NTRS)
LaBel, Kenneth A.
2014-01-01
While we have been utilizing standard fluence levels such as those listed in the JESD57 document, we have begun revisiting what an appropriate test fluence is when it comes to qualifying a device for single events. Instead of a fixed fluence level or until a specific number of events occurs, a different thought process is required.
English Teachers' Journal (Israel), Number 25.
ERIC Educational Resources Information Center
English Teachers' Journal (Israel), 1981
1981-01-01
This number of a journal devoted to ideas for teachers of English as a second language (ESL) contains the following articles: (1) "Teaching Grammar as Part of Meaningful Communication" by Raphael Gefen, (2) "Does the School Have a Role to Play in Teaching Environmental Awareness?" by Ora Herzog, (3) "Identifying with…
21 CFR 1210.21 - Permit number.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 21 Food and Drugs 8 2014-04-01 2014-04-01 false Permit number. 1210.21 Section 1210.21 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) REGULATIONS UNDER CERTAIN OTHER ACTS ADMINISTERED BY THE FOOD AND DRUG ADMINISTRATION REGULATIONS UNDER THE...
Sustaining Student Numbers in the Competitive Marketplace
ERIC Educational Resources Information Center
Szekeres, Judy
2010-01-01
The climate of competition for students in the higher education sector makes it imperative that institutions increase their marketing efforts, both domestically and internationally, to help sustain student numbers. In Australia, the Bradley Report and the government response, which will do away with quotas, allows for a much freer market than…
Workjobs II: Number Activities for Early Childhood.
ERIC Educational Resources Information Center
Baratta-Lorton, Mary
This curriculum guide presents a program of 20 open-ended math activities to be used to supplement the math programs in kindergarten, first, or second grade classrooms. The program consists of child-oriented counters and gameboards used to explore the concept of number from counting to making up and solving addition and subtraction equations. Each…
Arithmetic for First Graders Lacking Number Concepts
ERIC Educational Resources Information Center
Kamii, Constance; Rummelsburg, Judith
2008-01-01
To build cognitive foundation for number, twenty-six low-performing, low-SES first graders did mathematical physical-knowledge activities, such as "bowling," during the first half of the year. As their arithmetic readiness developed, they tried more word problems and games. At the end of the year, these children did better in mental arithmetic and…
Computation of Semantic Number from Morphological Information
ERIC Educational Resources Information Center
Berent, Iris; Pinker, Steven; Tzelgov, Joseph; Bibi, Uri; Goldfarb, Liat
2005-01-01
The distinction between singular and plural enters into linguistic phenomena such as morphology, lexical semantics, and agreement and also must interface with perceptual and conceptual systems that assess numerosity in the world. Three experiments examine the computation of semantic number for singulars and plurals from the morphological…
The Development of Semantic Components of Number.
ERIC Educational Resources Information Center
Walker, Alice A.
In this paper the author reviews and synthesizes the research literature concerning the developmental relationships between conservation of number and linguistic capability in handling of quantitative and relational terms. Several models for the development of these competencies are discussed. On the basis of this review the author concludes that…
High Reynolds number oscillating contact lines
NASA Astrophysics Data System (ADS)
Liu, Ziyuan; Schultz, William W.; Perlin, Marc
1999-11-01
Stainless steel, instead of Ting and Perlin's (1995) glass, is used in vertically oscillating plate experiments for a large range of Reynolds numbers. We used the non-wetting stainless steel to minimize the static meniscus that we ignore in our analysis. Except for the different static contact angle serving as an initial condition, the dynamic features in both cases are similar. In low Reynolds number oscillation, a pinned-edge condition can appropriately describe the contact line motion. In high Reynolds number oscillation, contact-line behavior becomes nonlinear and very complicated. The periodic, non-sinusoidal motion exhibits three types of motion: stick (associated with contact angle hysteresis), partial stick, and total slip. Increasing the Reynolds number, reduces the hysteresis phenomenon that still cannot be ignored. An edge condition allowing both the static range and dynamic interface behavior uses a slip coefficient mode that varies with time, stroke amplitude and frequency by introducing additional harmonic modes. Using this edge condition, we calculate the dynamic contact angle and the contact-line position for both stick and slip motion and compare them to our experimental data. Results show that the inviscid, linearized boundary-value problem combined with our slip coefficient model provides an improved prediction of the contact-line behavior.
Poison control center - Emergency number (image)
For a poison emergency call 1-800-222-1222 anywhere in the United States. This national hotline number will let you ... is a free and confidential service. All local poison control centers in the U.S. use this national ...
The New Element Curium (Atomic Number 96)
DOE R&D Accomplishments Database
Seaborg, G. T.; James, R. A.; Ghiorso, A.
1948-01-01
Two isotopes of the element with atomic number 96 have been produced by the helium-ion bombardment of plutonium. The name curium, symbol Cm, is proposed for element 96. The chemical experiments indicate that the most stable oxidation state of curium is the III state.
Critical Number of Fields in Stochastic Inflation.
Vennin, Vincent; Assadullahi, Hooshyar; Firouzjahi, Hassan; Noorbala, Mahdiyar; Wands, David
2017-01-20
Stochastic effects in generic scenarios of inflation with multiple fields are investigated. First passage time techniques are employed to calculate the statistical moments of the number of inflationary e-folds, which give rise to all correlation functions of primordial curvature perturbations through the stochastic δN formalism. The number of fields is a critical parameter. The probability of exploring arbitrarily large-field regions of the potential becomes nonvanishing when more than two fields are driving inflation. The mean number of e-folds can be infinite, depending on the number of fields; for plateau potentials, this occurs even with one field. In such cases, correlation functions of curvature perturbations are infinite. They can, however, be regularized if a reflecting (or absorbing) wall is added at large energy or field value. The results are found to be independent of the exact location of the wall and this procedure is, therefore, well defined for a wide range of cutoffs, above or below the Planck scale. Finally, we show that, contrary to single-field setups, multifield models can yield large stochastic corrections even at sub-Planckian energy, opening interesting prospects for probing quantum effects on cosmological fluctuations.
Chinese Number Words, Culture, and Mathematics Learning
ERIC Educational Resources Information Center
Ng, Sharon Sui Ngan; Rao, Nirmala
2010-01-01
This review evaluates the role of language--specifically, the Chinese-based system of number words and the simplicity of Chinese mathematical terms--in explaining the relatively superior performance of Chinese and other East Asian students in cross-national studies of mathematics achievement. Relevant research is critically reviewed focusing on…
Zero Tolerance Policies. ERIC Digest Number 146.
ERIC Educational Resources Information Center
McAndrews, Tobin
State legislatures and school boards are adopting a growing number of zero-tolerance polices toward weapons, guns, and violence. Zero-tolerance polices are rules intended to address specific school-safety issues. They have arisen in part as a response to the threat of the withdrawal of federal funds under the 1994 Gun-Free Schools Act, and…
EXPERIMENTAL RETRIEVAL SYSTEMS STUDIES, REPORT NUMBER 3.
ERIC Educational Resources Information Center
ANDERSON, RONALD R.; AND OTHERS
CONTENTS--(1) AN ASSOCIATIVITY TECHNIQUE FOR AUTOMATICALLY OPTIMIZING RETRIEVAL RESULTS BY RONALD R. ANDERSON. AN ASSOCIATIVE TECHNIQUE BY WHICH IT IS POSSIBLE TO AUTOMATICALLY EXPAND AND NARROW THE NUMBER OF DOCUMENTS RETRIEVED AND TO RETRIEVE DOCUMENTS RELATED TO A REQUEST EVEN THOUGH THEY MAY NOT BE INDEXED BY THE EXACT TERMS OF THE REQUEST IS…
Counting on Using a Number Game
ERIC Educational Resources Information Center
Betts, Paul
2015-01-01
Counting all and counting on are distinct counting strategies that can be used to compute such quantities as the total number of objects in two sets (Wright, Martland, and Stafford 2010). Given five objects and three more objects, for example, children who use counting all to determine quantity will count both collections; that is, they count…
Science Books & Films, Volume XIII, Number 3.
ERIC Educational Resources Information Center
Finch, Shari, Ed.
This document provides annotated bibliographies of 205 books, 61 children's books, and 87 films all of which are science related. Each annotation includes author, publisher, title, number of pages, cost, an appraisal from highly recommended to not recommended, and level of difficulty from preschool to professional. Entries are grouped by topics…
46 CFR 169.541 - Number required.
Code of Federal Regulations, 2012 CFR
2012-10-01
... and Firefighting Equipment Personal Flotation Devices § 169.541 Number required. Each vessel must be provided with an approved adult personal flotation device of an appropriate size for each person carried... approved personal flotation device of a suitable size for each child carried....
46 CFR 169.541 - Number required.
Code of Federal Regulations, 2014 CFR
2014-10-01
... and Firefighting Equipment Personal Flotation Devices § 169.541 Number required. Each vessel must be provided with an approved adult personal flotation device of an appropriate size for each person carried... approved personal flotation device of a suitable size for each child carried....
46 CFR 169.541 - Number required.
Code of Federal Regulations, 2011 CFR
2011-10-01
... and Firefighting Equipment Personal Flotation Devices § 169.541 Number required. Each vessel must be provided with an approved adult personal flotation device of an appropriate size for each person carried... approved personal flotation device of a suitable size for each child carried....
46 CFR 169.541 - Number required.
Code of Federal Regulations, 2013 CFR
2013-10-01
... and Firefighting Equipment Personal Flotation Devices § 169.541 Number required. Each vessel must be provided with an approved adult personal flotation device of an appropriate size for each person carried... approved personal flotation device of a suitable size for each child carried....
The aerodynamics of small Reynolds numbers
NASA Technical Reports Server (NTRS)
Schmitz, F. W.
1980-01-01
Aerodynamic characteristics of wing model gliders and bird wings in particular are discussed. Wind tunnel measurements and aerodynamics of small Reynolds numbers are enumerated. Airfoil behavior in the critical transition from laminar to turbulent boundary layer, which is more important to bird wing models than to large airplanes, was observed. Experimental results are provided, and an artificial bird wing is described.
Visualizing the Arithmetic of Complex Numbers
ERIC Educational Resources Information Center
Soto-Johnson, Hortensia
2014-01-01
The Common Core State Standards Initiative stresses the importance of developing a geometric and algebraic understanding of complex numbers in their different forms (i.e., Cartesian, polar and exponential). Unfortunately, most high school textbooks do not offer such explanations much less exercises that encourage students to bridge geometric and…
Mass-induced transition in fermion number
Aragao de Carvalho, C.; Pureza, J. M.
1989-05-15
We show that if we increase the mass of fermions in interaction with a topological (kink) scalar background in 1+1 dimensions, the fractional fermion number of the system will eventually vanish. The transition is sharp and corresponds to the disappearance of localized states from the spectrum of a Dirac operator which is exactly solvable. Possible applications to different physical systems are discussed.
On Fibonacci Numbers Which Are Elliptic Carmichael
2014-12-27
On Fibonacci numbers which are elliptic Carmichael Florian Luca School of Mathematics University of the Witwatersrand P. O. Box Wits 2050, South...was written during a visit of P. S. to the School of Mathematics of the University of the Witwatersrand in 2014. This author thanks the institution for
Maple Explorations, Perfect Numbers, and Mersenne Primes
ERIC Educational Resources Information Center
Ghusayni, B.
2005-01-01
Some examples from different areas of mathematics are explored to give a working knowledge of the computer algebra system Maple. Perfect numbers and Mersenne primes, which have fascinated people for a very long time and continue to do so, are studied using Maple and some questions are posed that still await answers.
How Do Students Misunderstand Number Representations?
ERIC Educational Resources Information Center
Herman, Geoffrey L.; Zilles, Craig; Loui, Michael C.
2011-01-01
We used both student interviews and diagnostic testing to reveal students' misconceptions about number representations in computing systems. This article reveals that students who have passed an undergraduate level computer organization course still possess surprising misconceptions about positional notations, two's complement representation, and…
Authenticating "Number the Stars" Using Nonfiction Resources
ERIC Educational Resources Information Center
Groce, Robin D.
2009-01-01
"Number the Stars" by Lois Lowry is a popular historical novel for adolescent readers about the Nazi occupation of Copenhagen, Denmark during World War II and the efforts of Danish resisters who successfully rescued 98% of that nation's Jewish population. While this 1998 book is considered to be a fictional account, most of the events in…
The 17 GHz active region number
Selhorst, C. L.; Pacini, A. A.; Costa, J. E. R.; Giménez de Castro, C. G.; Valio, A.; Shibasaki, K.
2014-08-01
We report the statistics of the number of active regions (NAR) observed at 17 GHz with the Nobeyama Radioheliograph between 1992, near the maximum of cycle 22, and 2013, which also includes the maximum of cycle 24, and we compare with other activity indexes. We find that NAR minima are shorter than those of the sunspot number (SSN) and radio flux at 10.7 cm (F10.7). This shorter NAR minima could reflect the presence of active regions generated by faint magnetic fields or spotless regions, which were a considerable fraction of the counted active regions. The ratio between the solar radio indexes F10.7/NAR shows a similar reduction during the two minima analyzed, which contrasts with the increase of the ratio of both radio indexes in relation to the SSN during the minimum of cycle 23-24. These results indicate that the radio indexes are more sensitive to weaker magnetic fields than those necessary to form sunspots, of the order of 1500 G. The analysis of the monthly averages of the active region brightness temperatures shows that its long-term variation mimics the solar cycle; however, due to the gyro-resonance emission, a great number of intense spikes are observed in the maximum temperature study. The decrease in the number of these spikes is also evident during the current cycle 24, a consequence of the sunspot magnetic field weakening in the last few years.
Satellite situation report, volume 31, number 1
NASA Technical Reports Server (NTRS)
1991-01-01
Data computed at GSFC, NORAD, or provided by satellite owners is reported. A space objects box score is presented of objects in orbit and decayed objects. Data of objects in orbit is presented in tabular form and the table headings include name of the object, catalog number, source, launch date, period minutes, inclination, apogee KM., perigee KM., and transmitting frequency.
Semantics and the Number of English Sentences.
ERIC Educational Resources Information Center
Bjurlof, Thomas; Jamieson, Dale
It has long been said that there are an infinite number of English sentences. "This is the cat that caught the rat" is an Enqlish sentence. So is "This is the cat that caught the rat that stole the cheese.""This is the cat with white paws that caught the rat that stole the cheese" is unobjectionable as well. Since a…
A Fresh Approach to Prime Numbers.
ERIC Educational Resources Information Center
Hampton, Homer F.
1979-01-01
The introduction of prime numbers in the intermediate grades should be handled with care or the concept will appear arbitrary, artificial, and unreal to the pupils. The approach suggested here is in the form of a game-like activity. A knowledge of multiplication and factors is a prerequisite. (BB)
The LSS Review. Volume 3, Number 1
ERIC Educational Resources Information Center
Hoag, Lydia, Ed.
2004-01-01
A growing number of American students are nonnative English speakers. These students are vulnerable to early school exit and schools are facing more and more such students each year. Presently, about 56% of all public school teachers in the United States have at least one English language learner (ELL) student in their class, but less than 20% of…
7 CFR 29.32 - Identification number.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 2 2014-01-01 2014-01-01 false Identification number. 29.32 Section 29.32 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing Practices), DEPARTMENT OF AGRICULTURE COMMODITY STANDARDS AND STANDARD CONTAINER REGULATIONS...
The Emperor's Perfect Map: Leadership by Numbers
ERIC Educational Resources Information Center
Heffernan, Amanda
2016-01-01
This paper establishes that system-generated data profiles are influencing the work of principals in three Queensland state schools. Drawing upon Foucault's notions of governance, as well as research emphasising performative cultures and the importance placed upon numbers and data in education, this paper uses the tale of the Emperor's map as a…
Understanding Quantum Numbers in General Chemistry Textbooks
ERIC Educational Resources Information Center
Niaz, Mansoor; Fernandez, Ramon
2008-01-01
Quantum numbers and electron configurations form an important part of the general chemistry curriculum and textbooks. The objectives of this study are: (1) Elaboration of a framework based on the following aspects: (a) Origin of the quantum hypothesis, (b) Alternative interpretations of quantum mechanics, (c) Differentiation between an orbital and…
NASA Astrophysics Data System (ADS)
Brekke, Lee; Freund, Peter G. O.
1993-10-01
The boundary of the ordinary open string world sheet is the real line. Along with the usual open string, one can consider p-adic open strings whose world sheet has as boundary the p-adic line instead (the points on this boundary are labelled by p-adic numbers rather than real numbers). The world sheet itself is then no longer a continous manifold but becomes a discrete homogeneous Bethe lattice, or Bruhat-Tits tree of incidence number p + 1. The p-adic strings thus correspond to specific discretizations of the world sheet. Studying all these discretizations (one for each prime p) together, as suggested by number theory, sheds new light on the ordinary string, via adelic product formulae. One is also led this way to a new type of string, the adelic string. These issues and their generalization to closed strings are discussed after a self-contained mathematical introduction. Other physical systems with natural p-adic counterparts are considered and in their context the connection between p-adic theories and quantum groups is explored.
How Can Syntax Support Number Word Acquisition?
ERIC Educational Resources Information Center
Syrett, Kristen; Musolino, Julien; Gelman, Rochel
2012-01-01
We expand upon a previous proposal by Bloom and Wynn (1997) that young children learn about the meaning of number words by tracking their occurrence in particular syntactic environments, in combination with the discourse context in which they are used. An analysis of the Childes database (MacWhinney, 2000) reveals that the environments studied by…
Synesthesia and Number Cognition in Children
ERIC Educational Resources Information Center
Green, Jennifer A. K.; Goswami, Usha
2008-01-01
Grapheme-color synesthesia, when achromatic digits evoke an experience of a specific color (photisms), has been shown to be consistent, involuntary, and linked with number concept in adults, yet there have been no comparable investigations with children. We present a systematic study of grapheme-color synesthesia in children aged between 7 and 15…
A Framework for Remediating Number Combination Deficits
ERIC Educational Resources Information Center
Fuchs, Lynn S.; Powell, Sarah R.; Seethaler, Pamela M.; Fuchs, Douglas; Hamlett, Carol L.; Cirino, Paul T.; Fletcher, Jack M.
2010-01-01
This article introduces a framework for the remediation of number combination (NC) deficits. Research on the remediation of NC deficits is summarized, and research program studies are used to illustrate the 3 approaches to remediation. The Framework comprises a 2-stage system of remediation. The less intensive stage implementing 1 of 3…
Mirror Numbers and Wigner's ``Unreasonable Effectiveness''
NASA Astrophysics Data System (ADS)
Berezin, Alexander
2006-04-01
Wigner's ``unreasonable effectiveness of mathematics in physics'' can be augmented by concept of mirror number (MN). It is defined as digital string infinite in both directions. Example is ()5141327182() where first 5 digits is Pi ``spelled'' backward (``mirrored'') and last 5 digits is the beginning of decimal exp1 string. Let MN be constructed from two different transcendental (or algebraically irrational) numbers, set of such MNs is Cantor-uncountable. Most MNs have contain any finite digital sequence repeated infinitely many times. In spirit of ``Contact'' (C.Sagan) each normal MN contains ``Library of Babel'' of all possible texts and patterns (J.L.Borges). Infinite at both ends, MN do not have any numerical values and, contrary to numbers written in positional systems, all digits in MNs have equal weight -- sort of ``numerological democracy''. In Pythagorean-Platonic models (space-time and physical world originating from pure numbers) idea of MN resolves paradox of ``beginning'' (or ``end'') of time. Because in MNs all digits have equal status, (quantum) randomness leads to more uniform and fully ergodic phase trajectories (cf. F.Dyson, Infinite in All Directions) .
9 CFR 355.8 - Official number.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 9 Animals and Animal Products 2 2013-01-01 2013-01-01 false Official number. 355.8 Section 355.8 Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY... CERTIFICATION CERTIFIED PRODUCTS FOR DOGS, CATS, AND OTHER CARNIVORA; INSPECTION, CERTIFICATION,...
9 CFR 355.8 - Official number.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 9 Animals and Animal Products 2 2014-01-01 2014-01-01 false Official number. 355.8 Section 355.8 Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY... CERTIFICATION CERTIFIED PRODUCTS FOR DOGS, CATS, AND OTHER CARNIVORA; INSPECTION, CERTIFICATION,...
9 CFR 355.8 - Official number.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 9 Animals and Animal Products 2 2010-01-01 2010-01-01 false Official number. 355.8 Section 355.8 Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY... CERTIFICATION CERTIFIED PRODUCTS FOR DOGS, CATS, AND OTHER CARNIVORA; INSPECTION, CERTIFICATION,...
9 CFR 355.8 - Official number.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 9 Animals and Animal Products 2 2012-01-01 2012-01-01 false Official number. 355.8 Section 355.8 Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY... CERTIFICATION CERTIFIED PRODUCTS FOR DOGS, CATS, AND OTHER CARNIVORA; INSPECTION, CERTIFICATION,...
9 CFR 355.8 - Official number.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 9 Animals and Animal Products 2 2011-01-01 2011-01-01 false Official number. 355.8 Section 355.8 Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY... CERTIFICATION CERTIFIED PRODUCTS FOR DOGS, CATS, AND OTHER CARNIVORA; INSPECTION, CERTIFICATION,...
Tutoring Large Numbers: An Unmet Challenge
ERIC Educational Resources Information Center
Lentell, Helen; O'Rourke, Jennifer
2004-01-01
Open and distance learning (ODL) is increasingly being regarded as a viable policy option for developing countries with limited educational resources for buildings, books and trained teachers, seeking to increase accessibility for large numbers of learners in education and training opportunities. Advocates of ODL as an appropriate solution to…
9 CFR 351.6 - Official number.
Code of Federal Regulations, 2014 CFR
2014-01-01
... CERTIFICATION CERTIFICATION OF TECHNICAL ANIMAL FATS FOR EXPORT Procedure for Obtaining Service: Administration of Program § 351.6 Official number. The Administrator will assign a certified technical animal fat... to identify all certified technical animal fat prepared or stored by the plant....
9 CFR 351.6 - Official number.
Code of Federal Regulations, 2011 CFR
2011-01-01
... CERTIFICATION CERTIFICATION OF TECHNICAL ANIMAL FATS FOR EXPORT Procedure for Obtaining Service: Administration of Program § 351.6 Official number. The Administrator will assign a certified technical animal fat... to identify all certified technical animal fat prepared or stored by the plant....
9 CFR 351.6 - Official number.
Code of Federal Regulations, 2013 CFR
2013-01-01
... CERTIFICATION CERTIFICATION OF TECHNICAL ANIMAL FATS FOR EXPORT Procedure for Obtaining Service: Administration of Program § 351.6 Official number. The Administrator will assign a certified technical animal fat... to identify all certified technical animal fat prepared or stored by the plant....
9 CFR 351.6 - Official number.
Code of Federal Regulations, 2012 CFR
2012-01-01
... CERTIFICATION CERTIFICATION OF TECHNICAL ANIMAL FATS FOR EXPORT Procedure for Obtaining Service: Administration of Program § 351.6 Official number. The Administrator will assign a certified technical animal fat... to identify all certified technical animal fat prepared or stored by the plant....
9 CFR 351.6 - Official number.
Code of Federal Regulations, 2010 CFR
2010-01-01
... CERTIFICATION CERTIFICATION OF TECHNICAL ANIMAL FATS FOR EXPORT Procedure for Obtaining Service: Administration of Program § 351.6 Official number. The Administrator will assign a certified technical animal fat... to identify all certified technical animal fat prepared or stored by the plant....
46 CFR 169.515 - Number required.
Code of Federal Regulations, 2010 CFR
2010-10-01
... additional inflatable liferafts to accommodate 25% of the persons on board or the number of persons accommodated in the largest lifeboat or liferaft, whichever is greater. (c) Vessels certificated for protected... the lifeboats and inflatable liferafts required in paragraph (a) of this section....
46 CFR 169.515 - Number required.
Code of Federal Regulations, 2011 CFR
2011-10-01
... additional inflatable liferafts to accommodate 25% of the persons on board or the number of persons accommodated in the largest lifeboat or liferaft, whichever is greater. (c) Vessels certificated for protected... the lifeboats and inflatable liferafts required in paragraph (a) of this section....
Sequence Factorial of "g"-Gonal Numbers
ERIC Educational Resources Information Center
Asiru, Muniru A.
2013-01-01
The gamma function, which has the property to interpolate the factorial whenever the argument is an integer, is a special case (the case "g"?=?2) of the general term of the sequence factorial of "g"-gonal numbers. In relation to this special case, a formula for calculating the general term of the sequence factorial of any…
46 CFR 169.541 - Number required.
Code of Federal Regulations, 2010 CFR
2010-10-01
... and Firefighting Equipment Personal Flotation Devices § 169.541 Number required. Each vessel must be provided with an approved adult personal flotation device of an appropriate size for each person carried... approved personal flotation device of a suitable size for each child carried....
Demonstrations of the Enormity of Avogadro's Number
NASA Astrophysics Data System (ADS)
Diemente, Damon
1998-12-01
Most high-school students learn of Avogadro's number for the first time when they begin study of the mole concept. It is important to impress students with the enormity of Avogadro's number and the concomitant minuscularity of the atom, and papers addressing this need have regularly appeared in this Journal. The present article describes three new problems used annually at Trinity School to make the impression. The first two problems are suitable to be assigned as homework. The first of these uses Avogadro's number simply as a scaling factor; the second, requiring more attention to units, is a calculation of the number of moles of sand grains in the Sahara Desert. The third problem is a series of related calculations that requires some closer in-class mathematical analysis and culminates in an astonishing result. All calculations are done in familiar English units, because with them I have found the results to be more immediately impressive to American students. Conversion factors to metric units can be applied if teachers find that desirable.
A Geometrical Application of Number Theory
ERIC Educational Resources Information Center
Srinivasan, V. K.
2013-01-01
Any quadruple of natural numbers {a, b, c, d} is called a "Pythagorean quadruple" if it satisfies the relationship "a[superscript 2] + b[superscript 2] + c[superscript 2]". This "Pythagorean quadruple" can always be identified with a rectangular box of dimensions "a greater than 0," "b greater than…
Genomic characteristics of cattle copy number variations
Technology Transfer Automated Retrieval System (TEKTRAN)
We performed a systematic analysis of cattle copy number variations (CNVs) using the Bovine HapMap SNP genotyping data, including 539 animals of 21 modern cattle breeds and 6 outgroups. After correcting genomic waves and considering the trio information, we identified 682 candidate CNV regions (CNVR...
Early Concepts of Number and Counting
ERIC Educational Resources Information Center
Box, Katherine; Scott, Paul
2004-01-01
Before primitive man had grasped the concept of number, the written word or even speech, he was able to count. This was important for keeping track of food supplies, sending messages, trading between villages and even keeping track of how many animals were in their herd. Counting was done in various ways, but in all cases, the underlying principle…
Proofs in Number Theory: History and Heresy.
ERIC Educational Resources Information Center
Rowland, Tim
The domain of number theory lends itself particularly well to generic argument, presented with the intention of conveying the force and structure of a conventional generalized argument through the medium of a particular case. The potential of generic examples as a didactic tool is virtually unrecognized. Although the use of such examples has good…
Odd numbers of photons and teleportation
NASA Astrophysics Data System (ADS)
Enk, S. J.
2003-02-01
Several teleportation protocols, namely those using entangled coherent states, entangled squeezed states, and the single-photon Einstein-Podolsky-Rosen state, are all shown to be particular instances of a more general scheme that relies on the detection of an odd number of photons.
Golden Proportions for the Generalized Tribonacci Numbers
ERIC Educational Resources Information Center
Shah, Devbhadra V.; Mehta, Darshana A.
2009-01-01
It is known that the ratios of consecutive terms of Fibonacci and Tribonacci sequences converge to the fixed ratio. In this article, we consider the generalized form of Tribonacci numbers and derive the "golden proportion" for the whole family of this generalized sequence. (Contains 2 tables.)
A Knack for Numbers: Paquita Friday
ERIC Educational Resources Information Center
Yates, Eleanor Lee
2005-01-01
Back in middle school Dr. Paquita Friday began helping keep books at her grandmother's pharmacy during inventory. It was no chore, she recalls. It was fun. By then, of course, she already knew she had a knack for numbers. Today Friday is gaining recognition for her research in accounting stock market disclosures and winning awards for her teaching…
Random numbers certified by Bell's theorem.
Pironio, S; Acín, A; Massar, S; de la Giroday, A Boyer; Matsukevich, D N; Maunz, P; Olmschenk, S; Hayes, D; Luo, L; Manning, T A; Monroe, C
2010-04-15
Randomness is a fundamental feature of nature and a valuable resource for applications ranging from cryptography and gambling to numerical simulation of physical and biological systems. Random numbers, however, are difficult to characterize mathematically, and their generation must rely on an unpredictable physical process. Inaccuracies in the theoretical modelling of such processes or failures of the devices, possibly due to adversarial attacks, limit the reliability of random number generators in ways that are difficult to control and detect. Here, inspired by earlier work on non-locality-based and device-independent quantum information processing, we show that the non-local correlations of entangled quantum particles can be used to certify the presence of genuine randomness. It is thereby possible to design a cryptographically secure random number generator that does not require any assumption about the internal working of the device. Such a strong form of randomness generation is impossible classically and possible in quantum systems only if certified by a Bell inequality violation. We carry out a proof-of-concept demonstration of this proposal in a system of two entangled atoms separated by approximately one metre. The observed Bell inequality violation, featuring near perfect detection efficiency, guarantees that 42 new random numbers are generated with 99 per cent confidence. Our results lay the groundwork for future device-independent quantum information experiments and for addressing fundamental issues raised by the intrinsic randomness of quantum theory.
Ultra-fast Quantum Random Number Generator
NASA Astrophysics Data System (ADS)
Yicheng, Shi
We describe a series of Randomness Extractors for removing bias and residual correlations in random numbers generated from measurements on noisy physical systems. The structures of the randomness extractors are based on Linear Feedback Shift Registers (LFSR). This leads to a significant simplification in the implementation of randomness extractors.
Question Number Two: How Many Factors?
ERIC Educational Resources Information Center
Goodwyn, Fara
2012-01-01
Exploratory factor analysis involves five key decisions. The second decision, how many factors to retain, is the focus of the current paper. Extracting too many or too few factors often leads to devastating effects on study results. The advantages and disadvantages of the most effective and/or most utilized strategies to determine the number of…
Oxidation Numbers in the Study of Metabolism
ERIC Educational Resources Information Center
Bentley, Ronald; Franzen, James; Chasteen, Thomas G.
2002-01-01
The calculation and use of oxidation numbers in the study of metabolic reactions are discussed for normal oxidations (alcohol dehydrogenase and the NAD+/NADH couple, propanediol dehydratase) and for enzymatic reactions with a "hidden" redox component (transamination, the coupled conversion of ethylamine to ethanol, and the biomethylation of…
University Admissions. Policy Note. Number 3
ERIC Educational Resources Information Center
Group of Eight (NJ1), 2012
2012-01-01
University admissions, like many other aspects of the higher education sector, are going through a time of significant change. From 2012, universities will receive full funding under the Commonwealth Grants Scheme (CGS) for as many places as they offer. Previously, the Government limited the number of funded places, with a tolerance band for…
Toward a Coherent Treatment of Negative Numbers
ERIC Educational Resources Information Center
Kreith, Kurt; Mendle, Al
2013-01-01
The transition from whole numbers to integers involves challenges for both students and teachers. Leadership in mathematics education calls for an ability to translate depth of understanding into effective teaching methods, and this landscape includes alternative treatments of familiar topics. Noting the multiple meanings associated with the…
47 CFR 64.1506 - Number designation.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 47 Telecommunication 3 2010-10-01 2010-10-01 false Number designation. 64.1506 Section 64.1506 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES (CONTINUED) MISCELLANEOUS RULES RELATING TO COMMON CARRIERS Interstate Pay-Per-Call and Other Information Services §...
Critical Number of Fields in Stochastic Inflation
NASA Astrophysics Data System (ADS)
Vennin, Vincent; Assadullahi, Hooshyar; Firouzjahi, Hassan; Noorbala, Mahdiyar; Wands, David
2017-01-01
Stochastic effects in generic scenarios of inflation with multiple fields are investigated. First passage time techniques are employed to calculate the statistical moments of the number of inflationary e -folds, which give rise to all correlation functions of primordial curvature perturbations through the stochastic δ N formalism. The number of fields is a critical parameter. The probability of exploring arbitrarily large-field regions of the potential becomes nonvanishing when more than two fields are driving inflation. The mean number of e -folds can be infinite, depending on the number of fields; for plateau potentials, this occurs even with one field. In such cases, correlation functions of curvature perturbations are infinite. They can, however, be regularized if a reflecting (or absorbing) wall is added at large energy or field value. The results are found to be independent of the exact location of the wall and this procedure is, therefore, well defined for a wide range of cutoffs, above or below the Planck scale. Finally, we show that, contrary to single-field setups, multifield models can yield large stochastic corrections even at sub-Planckian energy, opening interesting prospects for probing quantum effects on cosmological fluctuations.
Magnetic Particle Recovery of Serial Numbers
D. Utrata; M.J. Johnson
2003-10-01
One method used by crime labs to recover obliterated serial numbers in steel firearms (ferrous samples) is the magnetic particle technique. The use of this method is predicated on the detection of metal deformation present under stamped serial numbers after the visible stamp has been removed. Equipment specialized for this detection is not used in these attempts; a portable magnetic yoke used typically for flaw detection on large weldments or structures, along with dry visible magnetic powders, have been the tools of criminologists working in this area. Crime labs have reported low success rates using these tools [1, 2]. This is not surprising when one considers that little formal development has apparently evolved for use in such investigations since the publication of seminal work in this area some time ago [3]. The aim of this project is to investigate specific aspects of magnetic particle inspection for serial number recovery. This includes attempts to understand the magnetic characteristics of different steels that affect their performance in the test, such as varying results for carbon steels and alloy steels after different thermal and forming treatments. Also investigated are the effects of the nature of the sample magnetization (AC, rectified DC, and true DC) and the use of various detection media, such as visible powders and fluorescent sprays, on test outcome. Additionally, some aspects of surface preparation of firearm samples prior to number recovery were included in this work. The scope of this report includes a brief overview of the magnetic particle inspection method in general and its applications to forensic serial number recovery. This is followed by a description of how such investigations were simulated on lab samples, including a look at how the microstructure of a given steel will affect its performance in the test. Investigations into the serial number recovery in a series of ferromagnetic firearms (both steel and certain stainless steels
Developmental control of segment numbers in vertebrates.
Gomez, Céline; Pourquié, Olivier
2009-09-15
Segmentation or metamery in vertebrates is best illustrated by the repetition of the vertebrae and ribs, their associated skeletal muscles and blood vessels, and the spinal nerves and ganglia. The segment number varies tremendously among the different vertebrate species, ranging from as few as six vertebrae in some frogs to as many as several hundred in some snakes and fish. In vertebrates, metameric segments or somites form sequentially during body axis formation. This results in the embryonic axis becoming entirely segmented into metameric units from the level of the otic vesicle almost to the very tip of the tail. The total segment number mostly depends on two parameters: (1) the control of the posterior growth of the body axis during somitogenesis-more same-size segments can be formed in a longer axis and (2) segment size--more smaller--size segments can be formed in a same-size body axis. During evolution, independent variations of these parameters could explain the huge diversity in segment numbers observed among vertebrate species. These variations in segment numbers are accompanied by diversity in the regionalization of the vertebral column. For example, amniotes can exhibit up to five different types of vertebrae: cervical, thoracic, lumbar, sacral and caudal, the number of which varies according to the species. This regionalization of the vertebral column is controlled by the Hox family of transcription factors. We propose that during development, dissociation of the Hox- and segmentation-clock-dependent vertebral patterning systems explains the enormous diversity of vertebral formulae observed in vertebrates.
Developmental control of segment numbers in vertebrates
Gomez, Céline; Pourquié, Olivier
2011-01-01
Segmentation or metamery in vertebrates is best illustrated by the repetition of the vertebrae and ribs, their associated skeletal muscles and blood vessels, and the spinal nerves and ganglia. The segment number varies tremendously among the different vertebrate species, ranging from as few as six vertebrae in some frogs to as many as several hundred in some snakes and fish. In vertebrates, metameric segments or somites form sequentially during body axis formation. This results in the embryonic axis becoming entirely segmented into metameric units from the level of the otic vesicle almost to the very tip of the tail. The total segment number mostly depends on two parameters: (1) the control of the posterior growth of the body axis during somitogenesis—more same-size segments can be formed in a longer axis and (2) segment size—more smaller-size segments can be formed in a same-size body axis. During evolution, independent variations of these parameters could explain the huge diversity in segment numbers observed among vertebrate species. These variations in segment numbers are accompanied by diversity in the regionalization of the vertebral column. For example, amniotes can exhibit up to five different types of vertebrae: cervical, thoracic, lumbar, sacral and caudal, the number of which varies according to the species. This regionalization of the vertebral column is controlled by the Hox family of transcription factors. We propose that during development, dissociation of the Hox- and segmentation-clock-dependent vertebral patterning systems explains the enormous diversity of vertebral formulae observed in vertebrates. PMID:19621429
Quantum abacus for counting and factorizing numbers
Suslov, M. V.; Lesovik, G. B.; Blatter, G.
2011-05-15
We generalize the binary quantum counting algorithm of Lesovik, Suslov, and Blatter [Phys. Rev. A 82, 012316 (2010)] to higher counting bases. The algorithm makes use of qubits, qutrits, and qudits to count numbers in a base-2, base-3, or base-d representation. In operating the algorithm, the number n
MHD Turbulence at Moderate Magnetic Reynolds Number
NASA Technical Reports Server (NTRS)
Knaepen, B.; Kassinos, S.; Carati, D.
2003-01-01
In the present article we will consider the decay of MHD turbulence under the influence of a strong external magnetic field at moderate magnetic Reynolds numbers. Typical values of R(sub m) that are considered here range from R(sub m) approx. 0.1 to R(sub m) approx. 20. As a comparison, the initial kinetic Reynolds number common to all our simulations is Re(sub L) = 199. This means that the range of Prandtl numbers explored is 5 x 10(exp -4) to 10(exp -1). Our motivation is mainly to exhibit how the transition from the QS approximation to FMHD occurs. At the lowest values of R(sub m) studied here, the QS approximation is shown to model the flow faithfully. However, for the higher values of R(sub m) considered, it is clearly inadequate but can be replaced by another approximation which will be referred to as the Quasi-Linear (QL) approximation. Another objective of the present study is to describe how variations in the magnetic Reynolds number (while maintaining all other parameters constant) affect the dynamics of the flow. This complements past studies where variations in either the strength of the external magnetic field or the kinetic Reynolds number were considered. This article is organized as follows. In section 2 we recall the definition of the quasi-static approximation. Section 3 is devoted to the description of the numerical experiments performed using the quasi-static approximation and full MHD. In section 4 we describe the quasi-linear approximation and test it numerically against full MHD. A concluding summary is given in section 5.
Courant Number and Mach Number Insensitive CE/SE Euler Solvers
NASA Technical Reports Server (NTRS)
Chang, Sin-Chung
2005-01-01
It has been known that the space-time CE/SE method can be used to obtain ID, 2D, and 3D steady and unsteady flow solutions with Mach numbers ranging from 0.0028 to 10. However, it is also known that a CE/SE solution may become overly dissipative when the Mach number is very small. As an initial attempt to remedy this weakness, new 1D Courant number and Mach number insensitive CE/SE Euler solvers are developed using several key concepts underlying the recent successful development of Courant number insensitive CE/SE schemes. Numerical results indicate that the new solvers are capable of resolving crisply a contact discontinuity embedded in a flow with the maximum Mach number = 0.01.
NASA Technical Reports Server (NTRS)
Wilson, Robert M.
2014-01-01
Examined are the yearly variations and ratios of sunspot number, the number of sunspot groups, and the total corrected sunspot area for the interval 1875-2013. While yearly sunspot number independently correlates strongly (r = 0.98) with the yearly number of sunspot groups (y = -2 + 11.99x) and the total corrected sunspot area (y = 5 + 0.059x), the strongest correlation (Ry12 = 0.99) is the one based on the bivariate fit of sunspot number against the combined variations of the number of sunspot groups and sunspot area (y = 1 + 5.88x1 + 0.031x2, where y refers to sunspot number, x1 refers to the number of sunspot groups, and x2 refers to the sunspot area). While all cycle minima based on the bivariate fit are concurrent with the observed minimum in sunspot number, cycle maxima are sometimes found to differ. For sunspot cycles 12, 19, 20, and 23, cycle maximum is inferred to have occurred in 1884, 1958, 1970, and 2002, respectively, rather than in 1883, 1957, 1968, and 2000, based on the observed sunspot number. Also, cycle 19's maximum amplitude based on observed sunspot number seems too high in comparison to that found using the bivariate fit. During the 139-year interval 1875-2013, the difference between the observed and predicted sunspot number based on the bivariate fit is <1 standard error of estimate (se) (<6.4) for 111 years, between 1 and <2 se (6.4 to <12.8) for 28 years, and =2 se (=12.8) for only 4 years, these years being 1957 (16.6), 1978 (-15.8), 1980 (23), and 1982 (-16.3). For sunspot cycle 24, the difference between observed and predicted values has been only -0.7 and 3.2 (=0.5 se).
Entanglement distillation protocols and number theory
NASA Astrophysics Data System (ADS)
Bombin, H.; Martin-Delgado, M. A.
2005-09-01
We show that the analysis of entanglement distillation protocols for qudits of arbitrary dimension D benefits from applying basic concepts from number theory, since the set ZDn associated with Bell diagonal states is a module rather than a vector space. We find that a partition of ZDn into divisor classes characterizes the invariant properties of mixed Bell diagonal states under local permutations. We construct a very general class of recursion protocols by means of unitary operations implementing these local permutations. We study these distillation protocols depending on whether we use twirling operations in the intermediate steps or not, and we study them both analytically and numerically with Monte Carlo methods. In the absence of twirling operations, we construct extensions of the quantum privacy algorithms valid for secure communications with qudits of any dimension D . When D is a prime number, we show that distillation protocols are optimal both qualitatively and quantitatively.
Secure Computation with Fixed-Point Numbers
NASA Astrophysics Data System (ADS)
Catrina, Octavian; Saxena, Amitabh
Secure computation is a promising approach to business problems in which several parties want to run a joint application and cannot reveal their inputs. Secure computation preserves the privacy of input data using cryptographic protocols, allowing the parties to obtain the benefits of data sharing and at the same time avoid the associated risks. These business applications need protocols that support all the primitive data types and allow secure protocol composition and efficient application development. Secure computation with rational numbers has been a challenging problem. We present in this paper a family of protocols for multiparty computation with rational numbers using fixed-point representation. This approach offers more efficient solutions for secure computation than other usual representations.
Automatic differentiation using vectorized hyper dual numbers
NASA Astrophysics Data System (ADS)
Swaroop, Kshitiz
Sensitivity analysis is a method to measure the change in a dependent variable with respect to one or more independent variables with uses including optimization, design analysis and risk modeling. Conventional methods like finite difference suffer from both truncation, subtraction errors and cannot be used to simultaneously calculate derivatives of an output with respect to multiple inputs (commonly seen in optimization problems). Automatic Differentiation tackles all these issues successfully allowing us to calculate derivatives of any variable with respect to the independent variables in a computer program up to machine precision without any significant user input. Vectorized Hyper Dual Numbers, an extension of Hyper Dual Numbers, which allows the user to automatically calculate both the Hessian and derivative along with the function evaluation is developed for this thesis. The method is then used for the sizing and layup of a composite wind turbine blade as a proof of concept.
Finite-particle-number approach to physics
Noyes, H.P.
1982-10-01
Starting from a discrete, self-generating and self-organizing, recursive model and self-consistent interpretive rules we construct: the scale constants of physics (3,10,137,1.7x10/sup 38/); 3+1 Minkowski space with a discrete metric and the algebraic bound ..delta.. is an element of ..delta.. tau is greater than or equal to 1; the Einstein-deBroglie relation; algebraic double slit interference; a single-time momentum-space scattering theory connected to laboratory experience; an approximation to wave functions; local phase severance and hence both distant correlations and separability; baryon number, lepton number, charge and helicity; m/sub p//m/sub e/; a cosmology not in disagreement with current observations.
Bridge Condition Assessment Using D Numbers
Hu, Yong
2014-01-01
Bridge condition assessment is a complex problem influenced by many factors. The uncertain environment increases more its complexity. Due to the uncertainty in the process of assessment, one of the key problems is the representation of assessment results. Though there exists many methods that can deal with uncertain information, however, they have more or less deficiencies. In this paper, a new representation of uncertain information, called D numbers, is presented. It extends the Dempster-Shafer theory. By using D numbers, a new method is developed for the bridge condition assessment. Compared to these existing methods, the proposed method is simpler and more effective. An illustrative case is given to show the effectiveness of the new method. PMID:24696639
Sensitivity in risk analyses with uncertain numbers.
Tucker, W. Troy; Ferson, Scott
2006-06-01
Sensitivity analysis is a study of how changes in the inputs to a model influence the results of the model. Many techniques have recently been proposed for use when the model is probabilistic. This report considers the related problem of sensitivity analysis when the model includes uncertain numbers that can involve both aleatory and epistemic uncertainty and the method of calculation is Dempster-Shafer evidence theory or probability bounds analysis. Some traditional methods for sensitivity analysis generalize directly for use with uncertain numbers, but, in some respects, sensitivity analysis for these analyses differs from traditional deterministic or probabilistic sensitivity analyses. A case study of a dike reliability assessment illustrates several methods of sensitivity analysis, including traditional probabilistic assessment, local derivatives, and a ''pinching'' strategy that hypothetically reduces the epistemic uncertainty or aleatory uncertainty, or both, in an input variable to estimate the reduction of uncertainty in the outputs. The prospects for applying the methods to black box models are also considered.
Noise suppression with high Mach number inlets
NASA Technical Reports Server (NTRS)
Lumsdaine, E.; Cherng, J. G.; Tag, I.
1976-01-01
Experimental results were obtained for two types of high Mach number inlets, one with a translating centerbody and a fixed geometry inlet (collapsing cowl) with no centerbody. The aerodynamic and acoustic performance of these inlets was examined. The effects of area ratio, length/diameter ratio, and lip geometry were among several parameters investigated. The translating centerbody type inlet was found to be superior to the collapsing cowl both acoustically and aerodynamically, particularly for area ratios greater than 1.5. Comparison of length/diameter ratio and area ratio effects on performance near choked flow showed the latter to be more significant. Also, greater high frequency noise attenuation was achieved by increasing Mach number from low to high subsonic values.
Self-Testing Quantum Random Number Generator
NASA Astrophysics Data System (ADS)
Lunghi, Tommaso; Brask, Jonatan Bohr; Lim, Charles Ci Wen; Lavigne, Quentin; Bowles, Joseph; Martin, Anthony; Zbinden, Hugo; Brunner, Nicolas
2015-04-01
The generation of random numbers is a task of paramount importance in modern science. A central problem for both classical and quantum randomness generation is to estimate the entropy of the data generated by a given device. Here we present a protocol for self-testing quantum random number generation, in which the user can monitor the entropy in real time. Based on a few general assumptions, our protocol guarantees continuous generation of high quality randomness, without the need for a detailed characterization of the devices. Using a fully optical setup, we implement our protocol and illustrate its self-testing capacity. Our work thus provides a practical approach to quantum randomness generation in a scenario of trusted but error-prone devices.
Operational conditions for random-number generation
NASA Astrophysics Data System (ADS)
Compagner, A.
1995-11-01
Ensemble theory is used to describe arbitrary sequences of integers, whether formed by the decimals of π or produced by a roulette or by any other means. Correlation coefficients of any range and order are defined as Fourier transforms of the ensemble weights. Competing definitions of random sequences are considered. Special attention is given to sequences of random numbers needed for Monte Carlo calculations. Different recipes for those sequences lead to correlations that vary in range and order, but the total amount of correlation is the same for all sequences of a given length (without internal periodicities). For maximum-length sequences produced by linear algorithms, most correlation coefficients are zero, but the remaining ones are of absolute value 1. In well-tempered sequences, these complete correlations are of high order or of very long range. General conditions to be obeyed by random-number generators are discussed and a qualitative method for comparing different recipes is given.
NASA Astrophysics Data System (ADS)
Maslov, V. P.
2016-10-01
We show how the abstract analytic number theory of Maier, Postnikov, and others can be extended to include negative numbers and apply this to thermodynamics, information theory, and human thermodynamics. In particular, we introduce a certain large number N 0 on the "zero level" with a high multiplicity number q i ≫ 1 related to the physical concept of gap in the spectrum. We introduce a general notion of "hole," similar to the Dirac hole in physics, in the theory. We also consider analogs of thermodynamical notions in human thermodynamics, in particular, in connection with the role of the individual in history.
Quantum random-number generator based on a photon-number-resolving detector
NASA Astrophysics Data System (ADS)
Ren, Min; Wu, E.; Liang, Yan; Jian, Yi; Wu, Guang; Zeng, Heping
2011-02-01
We demonstrated a high-efficiency quantum random number generator which takes inherent advantage of the photon number distribution randomness of a coherent light source. This scheme was realized by comparing the photon flux of consecutive pulses with a photon number resolving detector. The random bit generation rate could reach 2.4 MHz with a system clock of 6.0 MHz, corresponding to a random bit generation efficiency as high as 40%. The random number files passed all the stringent statistical tests.
Pharmacological Regulation of Peroxisome Number in Glia
2008-09-01
suggest a relationship between cholesterol homeostasis peroxisome abundance that may have relevance to therapies for Alzheimer’s disease and Neimann- Pick...FIGURE 4. Specialized Cholesterol Handling in the Brain FIGURE 5. LXR Control of Cholesterol Metabolism Chapter 2 FIGURE 1 . Differential Effects...Not Affect Levels of 4 Different Proteins That Potentially Could Participate in the Control of Peroxisome Number vi Chapter 3 FIGURE 1
iMAST Quarterly, Number 1, 2000
2000-01-01
this subject for Industrial Heating magazine. In this issue, our feature article has been written by Mr. Al Lemanski who presents the pericyclic ...reduced-parts, and pure rolling contact power transfer via kinematic/kinetic pericyclic technology is being addressed by the Applied Research Laboratory...to the number of high- precision, high-cost, high-weight components and the accompanying reliability challenges they bring. The pericyclic variable
48 CFR 304.7001 - Numbering acquisitions.
Code of Federal Regulations, 2012 CFR
2012-10-01
.... AHRQ: A ASPR/OAMCG: O CDC: D CMS: M FDA: F HRSA: H IHS: I NIH: N PSC: P SAMHSA: S (3) The three-digit... Institute, NIH, may number its first contract for fiscal year 2009 as HHSN261200900001C. (Note: When more... identification code of the servicing agency: AHRQ: A ASPR/OAMCG: O CDC: D CMS: M FDA: F HRSA: H IHS: I NIH: N...
48 CFR 304.7001 - Numbering acquisitions.
Code of Federal Regulations, 2014 CFR
2014-10-01
.... AHRQ: A ASPR/OAMCG: O CDC: D CMS: M FDA: F HRSA: H IHS: I NIH: N PSC: P SAMHSA: S (3) The three-digit... Institute, NIH, may number its first contract for fiscal year 2009 as HHSN261200900001C. (Note: When more... identification code of the servicing agency: AHRQ: A ASPR/OAMCG: O CDC: D CMS: M FDA: F HRSA: H IHS: I NIH: N...
48 CFR 304.7001 - Numbering acquisitions.
Code of Federal Regulations, 2013 CFR
2013-10-01
.... AHRQ: A ASPR/OAMCG: O CDC: D CMS: M FDA: F HRSA: H IHS: I NIH: N PSC: P SAMHSA: S (3) The three-digit... Institute, NIH, may number its first contract for fiscal year 2009 as HHSN261200900001C. (Note: When more... identification code of the servicing agency: AHRQ: A ASPR/OAMCG: O CDC: D CMS: M FDA: F HRSA: H IHS: I NIH: N...
Locating Fraction on a Number Line
ERIC Educational Resources Information Center
Hannula, Markku S.
2003-01-01
Based on a survey of 3067 Finnish 5th and 7th graders and a task-based interview of 20 7th graders we examine student's understanding of fraction. Two tasks frame a specific fraction (3/4) in different contexts: as part of an eight-piece bar (area context) and as a location on a number line. The results suggest that students' understanding of…
Condition number estimation of preconditioned matrices.
Kushida, Noriyuki
2015-01-01
The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results. The Lanczos connection based method provides the condition numbers of coefficient matrices of systems of linear equations with information obtained through the preconditioned conjugate gradient method. Estimating the condition number of preconditioned matrices is sometimes important when describing the effectiveness of new preconditionerers or selecting adequate preconditioners. Operating a preconditioner on a coefficient matrix is the simplest method of estimation. However, this is not possible for large-scale computing, especially if computation is performed on distributed memory parallel computers. This is because, the preconditioned matrices become dense, even if the original matrices are sparse. Although the Lanczos connection method can be used to calculate the condition number of preconditioned matrices, it is not considered to be applicable to large-scale problems because of its weakness with respect to numerical errors. Therefore, we have developed a robust and parallelizable method based on Hager's method. The feasibility studies are curried out for the diagonal scaling preconditioner and the SSOR preconditioner with a diagonal matrix, a tri-daigonal matrix and Pei's matrix. As a result, the Lanczos connection method contains around 10% error in the results even with a simple problem. On the other hand, the new method contains negligible errors. In addition, the newly developed method returns reasonable solutions when the Lanczos connection method fails with Pei's matrix, and matrices generated with the finite element method.
Detecting Prime Numbers via Roots of Polynomials
ERIC Educational Resources Information Center
Dobbs, David E.
2012-01-01
It is proved that an integer n [greater than or equal] 2 is a prime (resp., composite) number if and only if there exists exactly one (resp., more than one) nth-degree monic polynomial f with coefficients in Z[subscript n], the ring of integers modulo n, such that each element of Z[subscript n] is a root of f. This classroom note could find use in…
On the Number of Entangled Clusters
NASA Astrophysics Data System (ADS)
Atapour, Mahshid; Madras, Neal
2010-04-01
We prove that the number of entangled clusters with N edges in the simple cubic lattice grows exponentially in N. This answers an open question posed by Grimmett and Holroyd (Proc. Lond. Math. Soc. 81:485-512, 2000). Our result has immediate implications for entanglement percolation: we obtain an improved rigorous lower bound on the critical probability, and we prove that the radius of the entangled component of the origin has exponentially decaying tail when p is small.
Joint Force Quarterly. Number 18, Spring 1998
1998-06-01
collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 1998 2. REPORT TYPE 3. DATES COVERED 00-00...We have implemented various initiatives to reduce risks and better manage readiness. They include better control of selected low density/high demand...training, tactics, and command and control . Exploiting the full potential of RMA requires linking emerging tech- nologies in a coherent framework of joint
Joint Force Quarterly. Number 4, Spring 1994
1994-05-01
subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE...primary needs of multinational peace operations arise in the areas of command and control , intelli- gence, training, logistics, and force mixes to forge...government for lying about the conduct of the war. Space versus Time Most images of war are linked to destroy- ing an enemy, controlling resources, main
Joint Force Quarterly. Number 21, Spring 1999
1999-03-01
information if it does not display a currently valid OMB control number. 1. REPORT DATE 1999 2. REPORT TYPE 3. DATES COVERED 00-00-1999 to 00...international regimes designed to control proliferation as well as national programs being pursued in this area. Finally, the United States fully supports ef...Eastern Europe fell further under communist control . Berlin re- mained exposed to Soviet pressure. Creation of the Warsaw Pact and the invasion of
Bronchogenic cysts with high CT numbers
Mendelson, D.S.; Rose, J.S.; Efremidis, S.C.; Kirschner, P.A.; Cohen, B.A.
1983-03-01
Four patients with mediastinal masses are described. CT examinations demonstrated masses of high attenuation, and solid masses were suspected. At thoracotomy each patient had a cystic mass containing a brownish, turbid, mucoid material. The pathologic diagnosis in each case was a bronchogenic cyst. The possibility of such a cyst should not be excluded because of a high CT number, which reflects the turbid contents of the cyst.
Linking numbers, spin, and statistics of solitons
NASA Technical Reports Server (NTRS)
Wilczek, F.; Zee, A.
1983-01-01
The spin and statistics of solitons in the (2 + 1)- and (3 + 1)-dimensional nonlinear sigma models is considered. For the (2 + 1)-dimensional case, there is the possibility of fractional spin and exotic statistics; for 3 + 1 dimensions, the usual spin-statistics relation is demonstrated. The linking-number interpretation of the Hopf invariant and the use of suspension considerably simplify the analysis.
Naval Research Reviews. Volume XXXIV. Number 4,
1982-01-01
AD-R123 226 NAVAL RESERH REVIEWS VOLUME XXXIV NUMBER 4(U) OFFICE i/i OF NAVAL RESEARCH ARLINGTON VA W J LESCURE 1982 UNCLASSIFIED F/ 5/ NL...circulation postage paid at Washington and additional mailing or- fices. The Enolneefin Siences In the case of the Matcrials Division, the research...almost axisymmetric, but quickly change to a more followed by a cloudy, spray-emitting jet from then irregular pattern . The wave spacing (wave-length) on
Laser interrogation of latent vehicle registration number
Russo, R.E. |; Pelkey, G.E.; Grant, P.; Whipple, R.E.; Andresen, B.D.
1994-09-01
A recent investigation involved automobile registration numbers as important evidentiary specimens. In California, as in most states, small, thin metallic decals are issued to owners of vehicles each year as the registration is renewed. The decals are applied directly to the license plate of the vehicle and typically on top of the previous year`s expired decal. To afford some degree of security, the individual registration decals have been designed to tear easily; they cannot be separated from each other, but can be carefully removed intact from the metal license plate by using a razor blade. In September 1993, the City of Livermore Police Department obtained a blue 1993 California decal that had been placed over an orange 1992 decal. The two decals were being investigated as possible evidence in a case involving vehicle registration fraud. To confirm the suspicion and implicate a suspect, the department needed to known the registration number on the bottom (completely covered) 1992 decal. The authors attempted to use intense and directed light to interrogate the colored stickers. Optical illumination using a filtered white-light source partially identified the latent number. However, the most successful technique used a tunable dye laser pumped by a pulsed Nd:YAG laser. By selectively tuning the wavelength and intensity of the dye laser, backlit illumination of the decals permitted visualization of the underlying registration number through the surface of the top sticker. With optimally-tuned wavelength and intensity, 100% accuracy was obtained in identifying the sequence of latent characters. The advantage of optical techniques is their completely nondestructive nature, thus preserving the evidence for further interrogation or courtroom presentation.
Condition Number Estimation of Preconditioned Matrices
Kushida, Noriyuki
2015-01-01
The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results. The Lanczos connection based method provides the condition numbers of coefficient matrices of systems of linear equations with information obtained through the preconditioned conjugate gradient method. Estimating the condition number of preconditioned matrices is sometimes important when describing the effectiveness of new preconditionerers or selecting adequate preconditioners. Operating a preconditioner on a coefficient matrix is the simplest method of estimation. However, this is not possible for large-scale computing, especially if computation is performed on distributed memory parallel computers. This is because, the preconditioned matrices become dense, even if the original matrices are sparse. Although the Lanczos connection method can be used to calculate the condition number of preconditioned matrices, it is not considered to be applicable to large-scale problems because of its weakness with respect to numerical errors. Therefore, we have developed a robust and parallelizable method based on Hager’s method. The feasibility studies are curried out for the diagonal scaling preconditioner and the SSOR preconditioner with a diagonal matrix, a tri-daigonal matrix and Pei’s matrix. As a result, the Lanczos connection method contains around 10% error in the results even with a simple problem. On the other hand, the new method contains negligible errors. In addition, the newly developed method returns reasonable solutions when the Lanczos connection method fails with Pei’s matrix, and matrices generated with the finite element method. PMID:25816331
European Scientific Notes. Volume 37, Number 4,
1983-04-30
Systems CDR M.G. Surdyk Command, Control and CommunicationsMr. M.N. Yoder Electronics ESV 37-4 (1983) I Immediate hard-copy scores fromBSOCIENCEA...The facility had long been an industrial obvious convenience of the system leader in electronic image devices, it probably means that such stations...complexes Sciences et Techniques du Laiguedoc of a number of transition metals. [USTLI, Montpellier) described some electron spin resonance (ESR
Large numbers hypothesis. I - Classical formalism
NASA Technical Reports Server (NTRS)
Adams, P. J.
1982-01-01
A self-consistent formulation of physics at the classical level embodying Dirac's large numbers hypothesis (LNH) is developed based on units covariance. A scalar 'field' phi(x) is introduced and some fundamental results are derived from the resultant equations. Some unusual properties of phi are noted such as the fact that phi cannot be the correspondence limit of a normal quantum scalar field.
Joint Force Quarterly. Number 15, Spring 1997
1997-06-01
the number of tasks or steps necessary to defeat an enemy grew dramati- cally. There is evidence of this in the rapid in- crease in the size of...have found it much more difficult to execute Desert Storm. Until alternatively powered vehicles and weapons are de- veloped, logistics will remain...over military operations. More - over, as General Joulwan notes in his ar- ticle, a new array of concepts such as the combined joint task force, Partner
Measurement of nonvolatile particle number size distribution
NASA Astrophysics Data System (ADS)
Gkatzelis, G. I.; Papanastasiou, D. K.; Florou, K.; Kaltsonoudis, C.; Louvaris, E.; Pandis, S. N.
2016-01-01
An experimental methodology was developed to measure the nonvolatile particle number concentration using a thermodenuder (TD). The TD was coupled with a high-resolution time-of-flight aerosol mass spectrometer, measuring the chemical composition and mass size distribution of the submicrometer aerosol and a scanning mobility particle sizer (SMPS) that provided the number size distribution of the aerosol in the range from 10 to 500 nm. The method was evaluated with a set of smog chamber experiments and achieved almost complete evaporation (> 98 %) of secondary organic as well as freshly nucleated particles, using a TD temperature of 400 °C and a centerline residence time of 15 s. This experimental approach was applied in a winter field campaign in Athens and provided a direct measurement of number concentration and size distribution for particles emitted from major pollution sources. During periods in which the contribution of biomass burning sources was dominant, more than 80 % of particle number concentration remained after passing through the thermodenuder, suggesting that nearly all biomass burning particles had a nonvolatile core. These remaining particles consisted mostly of black carbon (60 % mass contribution) and organic aerosol (OA; 40 %). Organics that had not evaporated through the TD were mostly biomass burning OA (BBOA) and oxygenated OA (OOA) as determined from AMS source apportionment analysis. For periods during which traffic contribution was dominant 50-60 % of the particles had a nonvolatile core while the rest evaporated at 400 °C. The remaining particle mass consisted mostly of black carbon with an 80 % contribution, while OA was responsible for another 15-20 %. Organics were mostly hydrocarbon-like OA (HOA) and OOA. These results suggest that even at 400 °C some fraction of the OA does not evaporate from particles emitted from common combustion processes, such as biomass burning and car engines, indicating that a fraction of this type of OA
European Scientific Notes, Volume 38, Number 9.
1984-09-01
France dealt with fractals--geometric structures which possess no characteristic size, but instead have features on many scales . Recent research...disclosure, and a number widespread among soldiers in the heat of of other factors. State-rating scales battle, and it can be made worse by poor...administered during time of danger or communications and loneliness ; after the its anticipation may be responded to Battle of Gettysburg, and in many later
Phalanx. Volume 48, Number 1. March 2015
2015-03-01
results from one of its annual wargames that resembled the actual Japanese status that naval intelligence was reporting to him (Caffrey, 2000). A...Volume 48, Number 1 In This Issue: • New MORS Website • 83rd Symposium • Analytic Wargaming Report Documentation Page Form ApprovedOMB No. 0704...0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing
Turbulent convection at very high Rayleigh numbers
Niemela; Skrbek; Sreenivasan; Donnelly
2000-04-20
Turbulent convection occurs when the Rayleigh number (Ra)--which quantifies the relative magnitude of thermal driving to dissipative forces in the fluid motion--becomes sufficiently high. Although many theoretical and experimental studies of turbulent convection exist, the basic properties of heat transport remain unclear. One important question concerns the existence of an asymptotic regime that is supposed to occur at very high Ra. Theory predicts that in such a state the Nusselt number (Nu), representing the global heat transport, should scale as Nu proportional to Ra(beta) with beta = 1/2. Here we investigate thermal transport over eleven orders of magnitude of the Rayleigh number (10(6) < or = Ra < or = 10(7)), using cryogenic helium gas as the working fluid. Our data, over the entire range of Ra, can be described to the lowest order by a single power-law with scaling exponent beta close to 0.31. In particular, we find no evidence for a transition to the Ra(1/2) regime. We also study the variation of internal temperature fluctuations with Ra, and probe velocity statistics indirectly.
Tidal Love Numbers of Neutron Stars
Hinderer, Tanja
2008-04-20
For a variety of fully relativistic polytropic neutron star models we calculate the star's tidal Love number k{sub 2}. Most realistic equations of state for neutron stars can be approximated as a polytrope with an effective index n {approx} 0.5-1.0. The equilibrium stellar model is obtained by numerical integration of the Tolman-Oppenheimer-Volkhov equations. We calculate the linear l = 2 static perturbations to the Schwarzschild spacetime following the method of Thorne and Campolattaro. Combining the perturbed Einstein equations into a single second-order differential equation for the perturbation to the metric coefficient g{sub tt} and matching the exterior solution to the asymptotic expansion of the metric in the star's local asymptotic rest frame gives the Love number. Our results agree well with the Newtonian results in the weak field limit. The fully relativistic values differ from the Newtonian values by up to {approx}24%. The Love number is potentially measurable in gravitational wave signals from inspiralling binary neutron stars.
Modeling genetic inheritance of copy number variations
Wang, Kai; Chen, Zhen; Tadesse, Mahlet G.; Glessner, Joseph; Grant, Struan F. A.; Hakonarson, Hakon; Bucan, Maja
2008-01-01
Copy number variations (CNVs) are being used as genetic markers or functional candidates in gene-mapping studies. However, unlike single nucleotide polymorphism or microsatellite genotyping techniques, most CNV detection methods are limited to detecting total copy numbers, rather than copy number in each of the two homologous chromosomes. To address this issue, we developed a statistical framework for intensity-based CNV detection platforms using family data. Our algorithm identifies CNVs for a family simultaneously, thus avoiding the generation of calls with Mendelian inconsistency while maintaining the ability to detect de novo CNVs. Applications to simulated data and real data indicate that our method significantly improves both call rates and accuracy of boundary inference, compared to existing approaches. We further illustrate the use of Mendelian inheritance to infer SNP allele compositions in each of the two homologous chromosomes in CNV regions using real data. Finally, we applied our method to a set of families genotyped using both the Illumina HumanHap550 and Affymetrix genome-wide 5.0 arrays to demonstrate its performance on both inherited and de novo CNVs. In conclusion, our method produces accurate CNV calls, gives probabilistic estimates of CNV transmission and builds a solid foundation for the development of linkage and association tests utilizing CNVs. PMID:18832372
Nowcasting sunshine number using logistic modeling
NASA Astrophysics Data System (ADS)
Brabec, Marek; Badescu, Viorel; Paulescu, Marius
2013-04-01
In this paper, we present a formalized approach to statistical modeling of the sunshine number, binary indicator of whether the Sun is covered by clouds introduced previously by Badescu (Theor Appl Climatol 72:127-136, 2002). Our statistical approach is based on Markov chain and logistic regression and yields fully specified probability models that are relatively easily identified (and their unknown parameters estimated) from a set of empirical data (observed sunshine number and sunshine stability number series). We discuss general structure of the model and its advantages, demonstrate its performance on real data and compare its results to classical ARIMA approach as to a competitor. Since the model parameters have clear interpretation, we also illustrate how, e.g., their inter-seasonal stability can be tested. We conclude with an outlook to future developments oriented to construction of models allowing for practically desirable smooth transition between data observed with different frequencies and with a short discussion of technical problems that such a goal brings.
Droplet Number Concentration Value Added Product
Chitra Sivaraman, PNNL
2015-08-06
Cloud droplet number concentration is an important factor in understanding aerosol-cloud interactions. As aerosol concentration increases, it is expected that droplet number concentration (Nd) will increase and droplet size will decrease, for a given liquid water path. This will greatly affect cloud albedo as smaller droplets reflect more shortwave radiation; however, the magnitude and variability of these processes under different environmental conditions is still uncertain.McComiskey et al. (2009) have implemented a method, based onBoers and Mitchell (1994), for calculating Nd from ground-based remote sensing measurements of optical depth and liquid water path. They show that the magnitude of the aerosol-cloud interactions (ACI) varies with a range of factors, including the relative value of the cloud liquid water path (LWP), the aerosol size distribution, and the cloud updraft velocity. Estimates of Nd under a range of cloud types and conditions and at a variety of sites are needed to further quantify the impacts of aerosol cloud interactions. In order to provide data sets for studying aerosol-cloud interactions, the McComiskey et al. (2009) method was implemented as the Droplet Number Concentration (NDROP) value-added product (VAP).
CONTRA: copy number analysis for targeted resequencing
Li, Jason; Lupat, Richard; Amarasinghe, Kaushalya C.; Thompson, Ella R.; Doyle, Maria A.; Ryland, Georgina L.; Tothill, Richard W.; Halgamuge, Saman K.; Campbell, Ian G.; Gorringe, Kylie L.
2012-01-01
Motivation: In light of the increasing adoption of targeted resequencing (TR) as a cost-effective strategy to identify disease-causing variants, a robust method for copy number variation (CNV) analysis is needed to maximize the value of this promising technology. Results: We present a method for CNV detection for TR data, including whole-exome capture data. Our method calls copy number gains and losses for each target region based on normalized depth of coverage. Our key strategies include the use of base-level log-ratios to remove GC-content bias, correction for an imbalanced library size effect on log-ratios, and the estimation of log-ratio variations via binning and interpolation. Our methods are made available via CONTRA (COpy Number Targeted Resequencing Analysis), a software package that takes standard alignment formats (BAM/SAM) and outputs in variant call format (VCF4.0), for easy integration with other next-generation sequencing analysis packages. We assessed our methods using samples from seven different target enrichment assays, and evaluated our results using simulated data and real germline data with known CNV genotypes. Availability and implementation: Source code and sample data are freely available under GNU license (GPLv3) at http://contra-cnv.sourceforge.net/ Contact: Jason.Li@petermac.org Supplementary information: Supplementary data are available at Bioinformatics online. PMID:22474122
Low-Reynolds-number swimming at pycnoclines.
Doostmohammadi, Amin; Stocker, Roman; Ardekani, Arezoo M
2012-03-06
Microorganisms play pivotal functions in the trophic dynamics and biogeochemistry of aquatic ecosystems. Their concentrations and activities often peak at localized hotspots, an important example of which are pycnoclines, where water density increases sharply with depth due to gradients in temperature or salinity. At pycnoclines organisms are exposed to different environmental conditions compared to the bulk water column, including reduced turbulence, slow mass transfer, and high particle and predator concentrations. Here we show that, at an even more fundamental level, the density stratification itself can affect microbial ecology at pycnoclines, by quenching the flow signature, increasing the energetic expenditure, and stifling the nutrient uptake of motile organisms. We demonstrate this through numerical simulations of an archetypal low-Reynolds-number swimmer, the "squirmer." We identify the Richardson number--the ratio of buoyancy forces to viscous forces--as the fundamental parameter that quantifies the effects of stratification. These results demonstrate an unexpected effect of buoyancy on low-Reynolds-number swimming, potentially affecting a broad range of abundant organisms living at pycnoclines in oceans and lakes.
Observer variability in estimating numbers: An experiment
Erwin, R.M.
1982-01-01
Census estimates of bird populations provide an essential framework for a host of research and management questions. However, with some exceptions, the reliability of numerical estimates and the factors influencing them have received insufficient attention. Independent of the problems associated with habitat type, weather conditions, cryptic coloration, ete., estimates may vary widely due only to intrinsic differences in observers? abilities to estimate numbers. Lessons learned in the field of perceptual psychology may be usefully applied to 'real world' problems in field ornithology. Based largely on dot discrimination tests in the laboratory, it was found that numerical abundance, density of objects, spatial configuration, color, background, and other variables influence individual accuracy in estimating numbers. The primary purpose of the present experiment was to assess the effects of observer, prior experience, and numerical range on accuracy in estimating numbers of waterfowl from black-and-white photographs. By using photographs of animals rather than black dots, I felt the results could be applied more meaningfully to field situations. Further, reinforcement was provided throughout some experiments to examine the influence of training on accuracy.
Source-Independent Quantum Random Number Generation
NASA Astrophysics Data System (ADS)
Cao, Zhu; Zhou, Hongyi; Yuan, Xiao; Ma, Xiongfeng
2016-01-01
Quantum random number generators can provide genuine randomness by appealing to the fundamental principles of quantum mechanics. In general, a physical generator contains two parts—a randomness source and its readout. The source is essential to the quality of the resulting random numbers; hence, it needs to be carefully calibrated and modeled to achieve information-theoretical provable randomness. However, in practice, the source is a complicated physical system, such as a light source or an atomic ensemble, and any deviations in the real-life implementation from the theoretical model may affect the randomness of the output. To close this gap, we propose a source-independent scheme for quantum random number generation in which output randomness can be certified, even when the source is uncharacterized and untrusted. In our randomness analysis, we make no assumptions about the dimension of the source. For instance, multiphoton emissions are allowed in optical implementations. Our analysis takes into account the finite-key effect with the composable security definition. In the limit of large data size, the length of the input random seed is exponentially small compared to that of the output random bit. In addition, by modifying a quantum key distribution system, we experimentally demonstrate our scheme and achieve a randomness generation rate of over 5 ×103 bit /s .
Variation of curve number with storm depth
NASA Astrophysics Data System (ADS)
Banasik, K.; Hejduk, L.
2012-04-01
The NRCS Curve Number (known also as SCS-CN) method is well known as a tool in predicting flood runoff depth from small ungauged catchment. The traditional way of determination the CNs, based on soil characteristics, land use and hydrological conditions, seemed to have tendency to overpredict the floods in some cases. Over 30 year rainfall-runoff data, collected in two small (A=23.4 & 82.4 km2), lowland, agricultural catchments in Center of Poland (Banasik & Woodward 2010), were used to determine runoff Curve Number and to check a tendency of changing. The observed CN declines with increasing storm size, which according recent views of Hawkins (1993) could be classified as a standard response of watershed. The analysis concluded, that using CN value according to the procedure described in USDA-SCS Handbook one receives representative value for estimating storm runoff from high rainfall depths in the analyzes catchments. This has been confirmed by applying "asymptotic approach" for estimating the watershed curve number from the rainfall-runoff data. Furthermore, the analysis indicated that CN, estimated from mean retention parameter S of recorded events with rainfall depth higher than initial abstraction, is also approaching the theoretical CN. The observed CN, ranging from 59.8 to 97.1 and from 52.3 to 95.5, in the smaller and the larger catchment respectively, declines with increasing storm size, which has been classified as a standard response of watershed. The investigation demonstrated also changeability of the CN during a year, with much lower values during the vegetation season. Banasik K. & D.E. Woodward (2010). "Empirical determination of curve number for a small agricultural watrshed in Poland". 2nd Joint Federal Interagency Conference, Las Vegas, NV, June 27 - July 1, 2010 (http://acwi.gov/sos/pubs/2ndJFIC/Contents/10E_Banasik_ 28_02_10. pdf). Hawkins R. H. (1993). "Asymptotic determination of curve numbers from data". Journal of Irrigation and Drainage
Preston Probe Calibrations at High Reynolds Number
NASA Technical Reports Server (NTRS)
Smits, Alexander J.
1998-01-01
The overall goal of the research effort is to study the performance of two Preston probes designed by NASA Langley Research Center across an unprecedented range of Reynolds number (based on friction velocity and probe diameter), and perform an accurate calibration over the same Reynolds number range. Using the Superpipe facility in Princeton, two rounds of experiments were performed. In each round of experiments for each Reynolds number, the pressure gradient, static pressure from the Preston probes and the total pressure from the Preston probes were measured. In the first round, 3 Preston probes having outer diameters of 0.058 inches, 0.083 inches and 0.203 inches were tested over a large range of pipe Reynolds numbers. Two data reduction methods were employed: first, the static pressure measured on the Preston probe was used to calculate P (modified Preston probe configuration), and secondly, the static pressure measured at the reference pressure tap was used to calculate P (un-modified Preston probe configuration). For both methods, the static pressure was adjusted to correspond with the static pressure at the Preston probe tip using the pressure gradient. The measurements for Preston probes with diameters of 0.058 inches, and 0.083 inches respectively were performed in the test pipe before it was polished a second time. Therefore, the measurements at high pipe Reynolds numbers may have been affected by roughness. In the second round of experiments the 0.058 inches and 0.083 inches diameter, un-modified probes were tested after the pipe was polished and prepared to ensure that the surface was smooth. The average velocity was estimated by assuming that the connection between the centerline velocity and the average velocity was known, and by using a Pitot tube to measure the centerline velocity. A preliminary error estimate suggests that it is possible to introduce a 1% to 2% error in estimating the average velocity using this approach. The evidence on the errors
2 CFR 25.315 - Data Universal Numbering System (DUNS) Number.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 2 Grants and Agreements 1 2012-01-01 2012-01-01 false Data Universal Numbering System (DUNS) Number. 25.315 Section 25.315 Grants and Agreements Office of Management and Budget Guidance for Grants... meaning given in paragraph C.2 of the award term in Appendix A to this part....
2 CFR 25.315 - Data Universal Numbering System (DUNS) Number.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 2 Grants and Agreements 1 2013-01-01 2013-01-01 false Data Universal Numbering System (DUNS) Number. 25.315 Section 25.315 Grants and Agreements Office of Management and Budget Guidance for Grants... meaning given in paragraph C.2 of the award term in Appendix A to this part....
2 CFR 25.315 - Data Universal Numbering System (DUNS) Number.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 2 Grants and Agreements 1 2014-01-01 2014-01-01 false Data Universal Numbering System (DUNS) Number. 25.315 Section 25.315 Grants and Agreements Office of Management and Budget Guidance for Grants... paragraph C.2 of the award term in Appendix A to this part....
48 CFR 52.204-12 - Data Universal Numbering System Number Maintenance.
Code of Federal Regulations, 2013 CFR
2013-10-01
...), insert the following clause: Data Universal Numbering System Number Maintenance (DEC 2012) (a) Definition... require a novation be accomplished. Dun & Bradstreet may be contacted— (1) Via the internet at http://fedgov.dnb.com/webform or if the Contractor does not have internet access, it may call Dun and...
48 CFR 52.204-12 - Data Universal Numbering System Number Maintenance.
Code of Federal Regulations, 2014 CFR
2014-10-01
...), insert the following clause: Data Universal Numbering System Number Maintenance (DEC 2012) (a) Definition... require a novation be accomplished. Dun & Bradstreet may be contacted— (1) Via the internet at http://fedgov.dnb.com/webform or if the Contractor does not have internet access, it may call Dun and...
2 CFR 25.315 - Data Universal Numbering System (DUNS) Number.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 2 Grants and Agreements 1 2011-01-01 2011-01-01 false Data Universal Numbering System (DUNS) Number. 25.315 Section 25.315 Grants and Agreements Office of Management and Budget Guidance for Grants... meaning given in paragraph C.2 of the award term in appendix A to this part....
48 CFR 52.204-6 - Data Universal Numbering System (DUNS) Number.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 48 Federal Acquisition Regulations System 2 2010-10-01 2010-10-01 false Data Universal Numbering System (DUNS) Number. 52.204-6 Section 52.204-6 Federal Acquisition Regulations System FEDERAL ACQUISITION REGULATION (CONTINUED) CLAUSES AND FORMS SOLICITATION PROVISIONS AND CONTRACT CLAUSES Text...
48 CFR 52.204-6 - Data Universal Numbering System (DUNS) Number.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 48 Federal Acquisition Regulations System 2 2012-10-01 2012-10-01 false Data Universal Numbering System (DUNS) Number. 52.204-6 Section 52.204-6 Federal Acquisition Regulations System FEDERAL ACQUISITION REGULATION (CONTINUED) CLAUSES AND FORMS SOLICITATION PROVISIONS AND CONTRACT CLAUSES Text...
Cosmological baryon and lepton number in the presence of electroweak fermion-number violation
NASA Technical Reports Server (NTRS)
Harvey, Jeffrey A.; Turner, Michael S.
1990-01-01
In the presence of rapid fermion-number violation due to nonperturbative electroweak effects certain relations between the baryon number of the Universe and the lepton numbers of the Universe are predicted. In some cases the electron-neutrino asymmetry is exactly specified in terms of the baryon asymmetry. Without introducing new particles, beyond the usual quarks and leptons, it is necessary that the Universe possess a nonzero value of B - L prior to the epoch of fermion-number violation if baryon and lepton asymmetries are to survive. Contrary to intuition, even though electroweak processes violate B + L, a nonzero value of B + L persists after the epoch of rapid fermion-number violation. If the standard model is extended to include lepton-number violation, for example through Majorana neutrino masses, then electroweak processes will reduce the baryon number to zero even in the presence of an initial B - L unless 20 M(sub L) approximately greater than the square root of (T(sub B - L) m(sub P1)) where M(sub L) sets the scale of lepton number violation and T(sub B - L) is the temperature at which a B - L asymmetry is produced. In many models this implies that neutrinos must be so light that they cannot contribute appreciably to the mass density of the Universe.
Number Sense and Number Nonsense: Understanding the Challenges of Learning Math
ERIC Educational Resources Information Center
Krasa, Nancy; Shunkwiler, Sara
2009-01-01
How do children learn math--and why do some children struggle with it? The answers are in "Number Sense and Number Nonsense," a straightforward, reader-friendly book for education professionals and an invaluable multidisciplinary resource for researchers. More than a first-ever research synthesis, this highly accessible book brings math…
Piaget, Children, and Number: Applying Piaget's Theory to the Teaching of Elementary Number.
ERIC Educational Resources Information Center
Kamii, Constance; DeVries, Rheta
This paper proposes a method for teaching number applying the conservation theory of Piaget in the classroom. It is suggested that number facts cannot be taught by social transmission, since there is a fundamental distinction between logico-mathematical and social knowledge. Conservation cannot be taught to non-conservers, but there are ways to…
Effect of Reynolds Number and Mach Number on flow angularity probe sensitivity
NASA Technical Reports Server (NTRS)
Smith, L. A.; Adcock, J. B.
1986-01-01
Preliminary calibrations were performed on nine flow angularity probes in the Langley 7- by 10-Foot High-Speed Tunnel (7 x 10 HST) and the Langley 0.3-Meter Transonic Cryogenic Tunnel (0.3-m TCT). These probes will be used in surveying the test section flows of the National Transonic Facility (NTF). The probes used in this study have a pyramid head with five pressure orifices. The calibrations consisted of both isolated probe measurements and rake-mounted multiprobe measurements that covered a range of subsonic Mach numbers up to 0.90 and Reynolds numbers per foot up to 40 X 10 to the 6th power. The preliminary calibration in the 7 x 10 HST included testing the probes both individually and in a rake. The 0.3-m TCT calibration tested two probes singly at varying Reynolds numbers. The results from these tests include Mach number, Reynolds number, and rake-mounting effects. The results of these tests showed probe sensitivity to be slightly affected by Mach number. At Reynolds numbers per foot above 10 x 10 to the 6th power, the probe did not exhibit a Reynolds number sensitivity.
New topological structures of Skyrme theory: baryon number and monopole number
NASA Astrophysics Data System (ADS)
Cho, Y. M.; Kimm, Kyoungtae; Yoon, J. H.; Zhang, Pengming
2017-02-01
Based on the observation that the skyrmion in Skyrme theory can be viewed as a dressed monopole, we show that the skyrmions have two independent topology, the baryon topology π _3(S^3) and the monopole topology π _2(S^2). With this we propose to classify the skyrmions by two topological numbers ( m, n), the monopole number m and the shell (radial) number n. In this scheme the popular (non spherically symmetric) skyrmions are classified as the ( m, 1) skyrmions but the spherically symmetric skyrmions are classified as the (1, n) skyrmions, and the baryon number B is given by B=mn. Moreover, we show that the vacuum of the Skyrme theory has the structure of the vacuum of the Sine-Gordon theory and QCD combined together, which can also be classified by two topological numbers ( p, q). This puts the Skyrme theory in a totally new perspective.