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.
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
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…
Cornel, Veronica M
2007-07-06
Reviews are listed in order of appearance in the sources indicated. In multidisciplinary review journals, only those reviews which fall within the scope of this Journal are included. Sources are listed alphabetically in three categories: regularly issued review journals and series volumes, contributed volumes, and other monographs. Titles are numbered serially, and these numbers are used for reference in the index. Major English-language sources of critical reviews are covered. Encyclopedic treatises, annual surveys such as Specialist Periodical Reports, and compilations of symposia proceedings are omitted. This installment of Recent Reviews covers principally the early part of the 2007 literature. Previous installment: J. Org. Chem. 2007, 72 (7), 2699-706.
Cornel, Veronica M
2007-03-30
Reviews are listed in order of appearance in the sources indicated. In multidisciplinary review journals, only those reviews which fall within the scope of this Journal are included. Sources are listed alphabetically in three categories: regularly issued review journals and series volumes, contributed volumes, and other monographs. Titles are numbered serially, and these numbers are used for reference in the index. Major English-language sources of critical reviews are covered. Encyclopedic treatises, annual surveys such as Specialist Periodical Reports, and compilations of symposia proceedings are omitted. This installment of Recent Reviews covers principally the latter part of the 2006 literature. Previous installment: J. Org. Chem. 2007, 72(1), 303-12.
Cornel, Veronica M
2007-01-05
Reviews are listed in order of appearance in the sources indicated. In multidisciplinary review journals, only those reviews which fall within the scope of this Journal are included. Sources are listed alphabetically in three categories: regularly issued review journals and series volumes, contributed volumes, and other monographs. Titles are numbered serially, and these numbers are used for reference in the index. Major English-language sources of critical reviews are covered. Encyclopedic treatises, annual surveys such as Specialist Periodical Reports, and compilations of symposia proceedings are omitted. This installment of Recent Reviews covers principally the middle part of the 2006 literature. Previous installment: J. Org. Chem. 2006, 71(20), 7923-30.
Cornel, Veronica M
2005-01-07
Reviews are listed in order of appearance in the sources indicated. In multidisciplinary review journals, only those reviews which fall within the scope of this Journal are included. Sources are listed alphabetically in three categories: regularly issued review journals and series volumes, contributed volumes, and other monographs. Titles are numbered serially, and these numbers are used for reference in the index. Major English-language sources of critical reviews are covered. Encyclopedic treatises, annual surveys such as Specialist Periodical Reports, and compilations of symposia proceedings are omitted. This installment of Recent Reviews covers principally the middle part of the 2004 literature. Previous installment: J. Org. Chem. 2004, 69(20), 6957-66.
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
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
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
Buscemi, William I.
1997-01-01
Suggests that political apathy among young people is the result of not having the conceptual tools necessary to comprehend present issues. Argues that to grasp many issues, students need to be mathematically literate, which many are not. Suggests that instructors should expose students to comparative numbers more often. (DSK)
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)
NASA Technical Reports Server (NTRS)
2006-01-01
29 January 2006 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows a spotted, high latitude plain, south of the Argyre basin. When the image was received from Mars by the MOC operations team, they noticed -- with a sense of humor -- the number '8' on this martian surface. The '8' is located at the center-right and is formed by the rims of two old impact craters that have been eroded and partly-filled and partly-buried beneath the surface.
Location near: 68.6oS, 38.4oW Image width: 3 km (1.9 mi) Illumination from: upper left Season: Southern Summer
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…
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,…
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
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…
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
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…
Somers, E.
1987-03-01
Regulatory agencies require numbers to provide health protection. The manner in which these numbers are derived from animal experiments and human epidemiology is considered together with the limitations and inadequacies of these numbers. Some recent examples of risk assessment in Canada are given including asbestos, drinking water, and indoor air quality. The value of these numbers in providing a measure of the hazard in a wider perspective is stressed, although they can never be the sole determinant of public policy.
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
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…
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
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…
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
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
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…
Landy, David; Silbert, Noah; Goldin, Aleah
2013-07-01
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 predict a log-to-linear shift: People will either place numbers linearly or will place numbers according to a compressive logarithmic or power-shaped function (Barth & Paladino, ; Siegler & Opfer, ). While about half of people did estimate numbers linearly over this range, nearly all the remaining participants placed 1 million approximately halfway between 1 thousand and 1 billion, but placed numbers linearly across each half, as though they believed that the number words "thousand, million, billion, trillion" constitute a uniformly spaced count list. Participants in this group also tended to be optimistic in evaluations of largely ineffective political strategies, relative to linear number-line placers. The results indicate that the surface structure of number words can heavily influence processes for dealing with numbers in this range, and it can amplify the possibility that analogous surface regularities are partially responsible for parallel phenomena in children. In addition, these results have direct implications for lawmakers and scientists hoping to communicate effectively with the public. Copyright © 2013 Cognitive Science Society, Inc.
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
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
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)
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)
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…
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…
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)
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…
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)
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.
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
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)
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.
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.
Computer Corner: Growing Numbers.
ERIC Educational Resources Information Center
Shumway, Richard J.
1983-01-01
Exponential growth provides an interesting setting for exploration. A sequence of activities and questions which will help students become better acquainted with large numbers and scientific notation, as well as computer notions, is given. (MNS)
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)
... genome is larger than any other known species. Credit: Open Cage That's how many base pairs—or ... of chromosomes, which are made up of DNA. Credit: NHGRI That's the approximate number of genes in ...
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.
ERIC Educational Resources Information Center
Lustick, David
1997-01-01
Describes a simple activity that explores and reveals the principles of significant figures and scientific notation using a 500 gram bag of unpopped popcorn. Students must devise a method for determining the number of kernels in the bag. (DDR)
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…
1985-02-01
numbers. At high altitudes aircraft gas turbine engine fan, compressor, and turbine blades with their small chords encounter Reynolds numhers...light man-carrying/man-powered aircraft , minl-RPVs at low altitude, and wind turbines . Since the airfoil section forms the basic element in the...Wind turbine blades also require high aerodynamic efficiency and all-weather capabilities. The need for efficient low Reynolds number airfoils which
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…
[Projection of prisoner numbers].
Metz, Rainer; Sohn, Werner
2015-01-01
The past and future development of occupancy rates in prisons is of crucial importance for the judicial administration of every country. Basic factors for planning the required penal facilities are seasonal fluctuations, minimum, maximum and average occupancy as well as the present situation and potential development of certain imprisonment categories. As the prisoner number of a country is determined by a complex set of interdependent conditions, it has turned out to be difficult to provide any theoretical explanations. The idea accepted in criminology for a long time that prisoner numbers are interdependent with criminal policy must be regarded as having failed. Statistical and time series analyses may help, however, to identify the factors having influenced the development of prisoner numbers in the past. The analyses presented here, first describe such influencing factors from a criminological perspective and then deal with their statistical identification and modelling. Using the development of prisoner numbers in Hesse as an example, it has been found that modelling methods in which the independent variables predict the dependent variable with a time lag are particularly helpful. A potential complication is, however, that for predicting the number of prisoners the different dynamics in German and foreign prisoners require the development of further models.
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.
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
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
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.
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
Earthquake number forecasts testing
NASA Astrophysics Data System (ADS)
Kagan, Yan Y.
2017-10-01
We study the distributions of earthquake numbers in two global earthquake catalogues: Global Centroid-Moment Tensor and Preliminary Determinations of Epicenters. The properties of these distributions are especially required to develop the number test for our forecasts of future seismic activity rate, tested by the Collaboratory for Study of Earthquake Predictability (CSEP). A common assumption, as used in the CSEP tests, is that the numbers are described by the Poisson distribution. It is clear, however, that the Poisson assumption for the earthquake number distribution is incorrect, especially for the catalogues with a lower magnitude threshold. In contrast to the one-parameter Poisson distribution so widely used to describe earthquake occurrences, the negative-binomial distribution (NBD) has two parameters. The second parameter can be used to characterize the clustering or overdispersion of a process. We also introduce and study a more complex three-parameter beta negative-binomial distribution. We investigate the dependence of parameters for both Poisson and NBD distributions on the catalogue magnitude threshold and on temporal subdivision of catalogue duration. First, we study whether the Poisson law can be statistically rejected for various catalogue subdivisions. We find that for most cases of interest, the Poisson distribution can be shown to be rejected statistically at a high significance level in favour of the NBD. Thereafter, we investigate whether these distributions fit the observed distributions of seismicity. For this purpose, we study upper statistical moments of earthquake numbers (skewness and kurtosis) and compare them to the theoretical values for both distributions. Empirical values for the skewness and the kurtosis increase for the smaller magnitude threshold and increase with even greater intensity for small temporal subdivision of catalogues. The Poisson distribution for large rate values approaches the Gaussian law, therefore its skewness
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
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
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…
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
Moomaw, Sally; Carr, Victoria; Boat, Mary; Barnett, David
2010-01-01
A child's demonstration of his conceptual understanding of number bodes well for his future success in school mathematics. As youngsters' thinking becomes more logical, they apply one-to-one correspondence relationships to quantification. Yet, reliable assessment of young children's mathematical ability is difficult because of social and emotional…
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'…
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'…
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…
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…
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…
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…
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…
NASA Astrophysics Data System (ADS)
Bryant, J. A.; Drage, N. A.; Richmond, S.
2012-04-01
The accuracy of CT number plots has been found lacking in several medical applications. This is of concern since the ability to compare and evaluate results on a reproducible and standard basis is essential to long term development. Apart from the technical limitations arising from the CT scanner and the data treatment, there are fundamental issues with the definition of the Hounsfield number, namely the absence of a standard photon energy and the need to specify the attenuation mechanism for standard measurements. This paper presents calculations to demonstrate the shortcomings of the present definition with a brief discussion. The remedy is straightforward, but probably of long duration as it would require an international agreement.
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.
NASA Astrophysics Data System (ADS)
Holik, Federico
2014-03-01
Since its origins, quantum mechanics has presented problems with the concept of individuality. It is argued that quantum particles do not have individuality, and so, one can speak about "entities without identity". On the contrary, we claim that the problem of quantum non individuality goes deeper, and that one of its most important features is the fact that there are quantum systems for which particle number is not well defined. In this work, we continue this discussion in relation to the problem about the one and the many.
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
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.
7 CFR 29.9205 - Identification number (farm serial number).
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 2 2014-01-01 2014-01-01 false Identification number (farm serial number). 29.9205 Section 29.9205 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE... number (farm serial number). The serial number assigned to an individual farm by the appropriate office...
7 CFR 29.9205 - Identification number (farm serial number).
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 2 2012-01-01 2012-01-01 false Identification number (farm serial number). 29.9205 Section 29.9205 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE... number (farm serial number). The serial number assigned to an individual farm by the appropriate office...
7 CFR 29.9205 - Identification number (farm serial number).
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 2 2013-01-01 2013-01-01 false Identification number (farm serial number). 29.9205 Section 29.9205 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE... number (farm serial number). The serial number assigned to an individual farm by the appropriate office...
7 CFR 29.9205 - Identification number (farm serial number).
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 2 2011-01-01 2011-01-01 false Identification number (farm serial number). 29.9205 Section 29.9205 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE... number (farm serial number). The serial number assigned to an individual farm by the appropriate office...
7 CFR 29.9205 - Identification number (farm serial number).
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Identification number (farm serial number). 29.9205 Section 29.9205 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE... number (farm serial number). The serial number assigned to an individual farm by the appropriate office...
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. PMID:22363276
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.
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...is a CM elliptic curve with CM field Q( √ −d), then the set of n for which the nth Fibonacci number Fn satisfies an elliptic Korselt criterion for Q...SUBTITLE On Fibonacci Numbers Which Are Elliptic Korselt Numbers 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d
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…
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…
Number sense in the transition from natural to rational numbers.
Van Hoof, Jo; Verschaffel, Lieven; Van Dooren, Wim
2017-03-01
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 rational number tasks. Still, it has been shown that a good understanding of natural numbers is highly predictive for mathematics achievement in general, and for performance on rational number tasks in particular. In this study, we further investigated the relation between learners' natural and rational number knowledge, specifically in cases where a natural number bias may lead to errors. Participants were 140 sixth graders from six different primary schools. Participants completed a symbolic and a non-symbolic natural number comparison task, a number line estimation task, and a rational number sense test. Learners' natural number knowledge was found to be a good predictor of their rational number knowledge. However, after first controlling for learners' general mathematics achievement, their natural number knowledge only predicted the subaspect of operations with rational numbers. The results of this study suggest that the relation between learners' natural and rational number knowledge can largely be explained by their relation with learners' general mathematics achievement. © 2016 The British Psychological Society.
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.
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…
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…
Number Games, Magnitude Representation, and Basic Number Skills in Preschoolers
ERIC Educational Resources Information Center
Whyte, Jemma Catherine; Bull, Rebecca
2008-01-01
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…
[Intel random number generator-based true random number generator].
Huang, Feng; Shen, Hong
2004-09-01
To establish a true random number generator on the basis of certain Intel chips. The random numbers were acquired by programming using Microsoft Visual C++ 6.0 via register reading from the random number generator (RNG) unit of an Intel 815 chipset-based computer with Intel Security Driver (ISD). We tested the generator with 500 random numbers in NIST FIPS 140-1 and X(2) R-Squared test, and the result showed that the random number it generated satisfied the demand of independence and uniform distribution. We also compared the random numbers generated by Intel RNG-based true random number generator and those from the random number table statistically, by using the same amount of 7500 random numbers in the same value domain, which showed that the SD, SE and CV of Intel RNG-based random number generator were less than those of the random number table. The result of u test of two CVs revealed no significant difference between the two methods. Intel RNG-based random number generator can produce high-quality random numbers with good independence and uniform distribution, and solves some problems with random number table in acquisition of the random numbers.
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…
Turbulent Skin Friction at High Mach Numbers and Reynolds Numbers
NASA Technical Reports Server (NTRS)
Matting, Fred W.; Chapman, Dean R.
1958-01-01
For a number of years now, experimenters have been making measurements of skin friction. Formerly, the main interest was at low Mach numbers; later, measurements were made at supersonic Mach numbers. However, almost all of these measurements were over a limited range of Reynolds numbers. On the other hand, these measurements fairly well determined the effects of Mach number and heat transfer on skin friction. The purpose of this paper is to give the results of skin-friction measurements in turbulent boundary layers at high Mach numbers and high Reynolds numbers where data have not previously existed. The equipment used was expressly designed to provide these conditions. As is well known, it is difficult to obtain high Mach numbers and high Reynolds numbers simultaneously with air in a wind tunnel. In order to avoid condensation, it is necessary to heat the air, with a resulting loss in density and Reynolds number. It is desirable, then, to use a gas that does not condense at high Mach numbers. This suggested helium, which was used as a working fluid in some of the tests. At high Mach numbers in a given wind tunnel, higher Reynolds numbers can be obtained with helium than with air, principally because no heating of the helium is required. The different ratios of specific heats also contribute to the increase. In using helium as a working fluid, it is, of course, necessary to determine the equivalence of air and helium in the turbulent boundary layer.
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
NASA Astrophysics Data System (ADS)
Mohamad, Daud; Shaharani, Saidatull Akma; Kamis, Nor Hanimah
2017-08-01
The concept of Z-number which was introduced by Zadeh in 2010 has captured attention by many due to its enormous applications in the area of Computing with Words (CWW). A Z-number is an ordered pair of fuzzy numbers, (A, R), where A essentially plays the role of fuzzy restriction which is a real-valued uncertain variable and R is a measure of reliability of the first component. Besides its theoretical development, Z-numbers have been successfully applied to decision making problems under uncertain environment. In any decision making evaluation using Z-number, ideally the final outcome of the calculation should also be in Z-number. A question will arise: how do we order the Z-numbers so that the preference of the alternatives can be ranked appropriately? In this paper, we propose a method of ordering the Z-number via the transformation of the Z-numbers to fuzzy numbers. The Z-number will then be ranked using a ranking fuzzy number method. The proposed method will be tested in several combinations of Z-numbers to investigate its effectiveness. The effect of different values of A and R towards the ordering of Z-numbers is analyzed and discussed.
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…
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…
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…
Irrational Numbers on the Number Line--Where Are They?
ERIC Educational Resources Information Center
Sirotic, N.; Zazkis, R.
2007-01-01
This paper reports part of an ongoing investigation into the understanding of irrational numbers by prospective secondary school teachers. It focuses on the representation of irrational numbers as points on a number line. In a written questionnaire, followed by a clinical interview, participants were asked to indicate the exact location of the…
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. © Hammill Institute on Disabilities 2016.
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…
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…
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…
Simple Remarks on Carmichael Numbers
NASA Astrophysics Data System (ADS)
Uchiyama, Shigenori
An odd composite number n for which an-1 ≡ 1 (mod n) for all integers a coprime to n is called a Carmichael number. This paper shows that some class of Carmichael numbers which have relatively large prime factors can be recognized in deterministic polynomial time under the assumption of the Extended Riemann Hypothesis (ERH). Also some related problems are discussed.
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
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
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…
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…
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.
ERIC Educational Resources Information Center
Sasanguie, Delphine; Gobel, Silke M.; Moll, Kristina; Smets, Karolien; Reynvoet, Bert
2013-01-01
In this study, the performance of typically developing 6- to 8-year-old children on an approximate number discrimination task, a symbolic comparison task, and a symbolic and nonsymbolic number line estimation task was examined. For the first time, children's performances on these basic cognitive number processing tasks were explicitly contrasted…
Betti Numbers of Gaussian Fields
NASA Astrophysics Data System (ADS)
Park, Changbom; Pranav, Pratyush; Chingangbam, Pravabati; van de Weygaert, Rien; Jones, Bernard; Vegter, Gert; Kim, Inkang; Hidding, Johan; Hellwing, Wojciech A.
2013-06-01
We present the relation between the genus in cosmology and the Betti numbers for excursion sets of three- and two-dimensional smooth Gaussian random fields, and numerically investigate the Betti numbers as a function of threshold level. Betti numbers are topological invariants of figures that can be used to distinguish topological spaces. In the case of the excursion sets of a three-dimensional field there are three possibly non-zero Betti numbers; β_0 is the number of connected regions, β_1 is the number of circular holes (i.e., complement of solid tori), and β_2 is the number of three-dimensional voids (i.e., complement of three-dimensional excursion regions). Their sum with alternating signs is the genus of the surface of excursion regions. It is found that each Betti number has a dominant contribution to the genus in a specific threshold range. β_0 dominates the high-threshold part of the genus curve measuring the abundance of high density regions (clusters). β_1 dominates the genus near the median thresholds which measures the topology of negatively curved iso-density surfaces, and β_2 corresponds to the low-threshold part measuring the void abundance. We average the Betti number curves (the Betti numbers as a function of the threshold level) over many realizations of Gaussian fields and find that both the amplitude and shape of the Betti number curves depend on the slope of the power spectrum n in such a way that their shape becomes broader and their amplitude drops less steeply than the genus as n decreases. This behaviour contrasts with the fact that the shape of the genus curve is fixed for all Gaussian fields regardless of the power spectrum. Even though the Gaussian Betti number curves should be calculated for each given power spectrum, we propose to use the Betti numbers for better specification of the topology of large scale structures in the universe.
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.
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.
Nonliteral understanding of number words.
Kao, Justine T; Wu, Jean Y; Bergen, Leon; Goodman, Noah D
2014-08-19
One of the most puzzling and important facts about communication is that people do not always mean what they say; speakers often use imprecise, exaggerated, or otherwise literally false descriptions to communicate experiences and attitudes. Here, we focus on the nonliteral interpretation of number words, in particular hyperbole (interpreting unlikely numbers as exaggerated and conveying affect) and pragmatic halo (interpreting round numbers imprecisely). We provide a computational model of number interpretation as social inference regarding the communicative goal, meaning, and affective subtext of an utterance. We show that our model predicts humans' interpretation of number words with high accuracy. Our model is the first to our knowledge to incorporate principles of communication and empirically measured background knowledge to quantitatively predict hyperbolic and pragmatic halo effects in number interpretation. This modeling framework provides a unified approach to nonliteral language understanding more generally.
Nonliteral understanding of number words
Kao, Justine T.; Wu, Jean Y.; Bergen, Leon; Goodman, Noah D.
2014-01-01
One of the most puzzling and important facts about communication is that people do not always mean what they say; speakers often use imprecise, exaggerated, or otherwise literally false descriptions to communicate experiences and attitudes. Here, we focus on the nonliteral interpretation of number words, in particular hyperbole (interpreting unlikely numbers as exaggerated and conveying affect) and pragmatic halo (interpreting round numbers imprecisely). We provide a computational model of number interpretation as social inference regarding the communicative goal, meaning, and affective subtext of an utterance. We show that our model predicts humans’ interpretation of number words with high accuracy. Our model is the first to our knowledge to incorporate principles of communication and empirically measured background knowledge to quantitatively predict hyperbolic and pragmatic halo effects in number interpretation. This modeling framework provides a unified approach to nonliteral language understanding more generally. PMID:25092304
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.
Random number generation and creativity.
Bains, William
2008-01-01
A previous paper suggested that humans can generate genuinely random numbers. I tested this hypothesis by repeating the experiment with a larger number of highly numerate subjects, asking them to call out a sequence of digits selected from 0 through 9. The resulting sequences were substantially non-random, with an excess of sequential pairs of numbers and a deficit of repeats of the same number, in line with previous literature. However, the previous literature suggests that humans generate random numbers with substantial conscious effort, and distractions which reduce that effort reduce the randomness of the numbers. I reduced my subjects' concentration by asking them to call out in another language, and with alcohol - neither affected the randomness of their responses. This suggests that the ability to generate random numbers is a 'basic' function of the human mind, even if those numbers are not mathematically 'random'. I hypothesise that there is a 'creativity' mechanism, while not truly random, provides novelty as part of the mind's defence against closed programming loops, and that testing for the effects seen here in people more or less familiar with numbers or with spontaneous creativity could identify more features of this process. It is possible that training to perform better at simple random generation tasks could help to increase creativity, through training people to reduce the conscious mind's suppression of the 'spontaneous', creative response to new questions.
BKP and projective Hurwitz numbers
NASA Astrophysics Data System (ADS)
Natanzon, Sergey M.; Orlov, Aleksandr Yu.
2017-06-01
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 sc {e}, in particular projective Hurwitz numbers sc {e}=1.
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.
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.
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.
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.
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…
Core Knowledge, Language, and Number
ERIC Educational Resources Information Center
Spelke, Elizabeth S.
2017-01-01
The natural numbers may be our simplest, most useful, and best-studied abstract concepts, but their origins are debated. I consider this debate in the context of the proposal, by Gallistel and Gelman, that natural number system is a product of cognitive evolution and the proposal, by Carey, that it is a product of human cultural history. I offer a…
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…
SICs and Algebraic Number Theory
NASA Astrophysics Data System (ADS)
Appleby, Marcus; Flammia, Steven; McConnell, Gary; Yard, Jon
2017-08-01
We give an overview of some remarkable connections between symmetric informationally complete measurements (SIC-POVMs, or SICs) and algebraic number theory, in particular, a connection with Hilbert's 12th problem. The paper is meant to be intelligible to a physicist who has no prior knowledge of either Galois theory or algebraic number theory.
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…
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…
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…
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…
Photon-number resolving detectors
NASA Astrophysics Data System (ADS)
Haderka, O.; Peřina, J., Jr.; Hamar, M.; Michálek, V.; Černoch, A.; Soubusta, J.
2010-12-01
An overview of current commercial and emerging approaches to single-photon-sensitive detection is given. Special attention is devoted to the detectors providing photon-number resolution with respect to their application in quantum optics and quantum information. Besides detectors offering photon-number resolution intrinsically, also multiplexing detectors are treated. A comparison of the detector technologies is presented.
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)
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…
Organizing, Concerns and Control Numbers.
ERIC Educational Resources Information Center
Washington, Gene
A heuristic procedure can be used to teach organizational skills to students of technical writing. Designed to allow students on their own to explore ways that numbers can be used to give a definite shape to technical information, its central feature is a matrix composed of a series of control numbers (horizontal axis) and organizing concerns…
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…
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'…
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…
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…
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.
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 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.
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?.
Seasonal Regulation of Petal Number.
McKim, Sarah M; Routier-Kierzkowska, Anne-Lise; Monniaux, Marie; Kierzkowski, Daniel; Pieper, Bjorn; Smith, Richard S; Tsiantis, Miltos; Hay, Angela
2017-10-01
Four petals characterize the flowers of most species in the Brassicaceae family, and this phenotype is generally robust to genetic and environmental variation. A variable petal number distinguishes the flowers of Cardamine hirsuta from those of its close relative Arabidopsis (Arabidopsis thaliana), and allelic variation at many loci contribute to this trait. However, it is less clear whether C. hirsuta petal number varies in response to seasonal changes in environment. To address this question, we assessed whether petal number responds to a suite of environmental and endogenous cues that regulate flowering time in C. hirsuta We found that petal number showed seasonal variation in C. hirsuta, such that spring flowering plants developed more petals than those flowering in summer. Conditions associated with spring flowering, including cool ambient temperature, short photoperiod, and vernalization, all increased petal number in C. hirsuta Cool temperature caused the strongest increase in petal number and lengthened the time interval over which floral meristems matured. We performed live imaging of early flower development and showed that floral buds developed more slowly at 15°C versus 20°C. This extended phase of floral meristem formation, coupled with slower growth of sepals at 15°C, produced larger intersepal regions with more space available for petal initiation. In summary, the growth and maturation of floral buds is associated with variable petal number in C. hirsuta and responds to seasonal changes in ambient temperature. © 2017 American Society of Plant Biologists. All Rights Reserved.
Number without a language model.
Spaepen, Elizabet; Coppola, Marie; Spelke, Elizabeth S; Carey, Susan E; Goldin-Meadow, Susan
2011-02-22
Cross-cultural studies suggest that access to a conventional language containing words that can be used for counting is essential to develop representations of large exact numbers. However, cultures that lack a conventional counting system typically differ from cultures that have such systems, not only in language but also in many other ways. As a result, it is difficult to isolate the effects of language on the development of number representations. Here we examine the numerical abilities of individuals who lack conventional language for number (deaf individuals who do not have access to a usable model for language, spoken or signed) but who live in a numerate culture (Nicaragua) and thus have access to other aspects of culture that might foster the development of number. These deaf individuals develop their own gestures, called homesigns, to communicate. We show that homesigners use gestures to communicate about number. However, they do not consistently extend the correct number of fingers when communicating about sets greater than three, nor do they always correctly match the number of items in one set to a target set when that target set is greater than three. Thus, even when integrated into a numerate society, individuals who lack input from a conventional language do not spontaneously develop representations of large exact numerosities.
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
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.
Numbered nasal discs for waterfowl
Bartonek, J.C.; Dane, C.W.
1964-01-01
Numbered nasal discs were successfully used in studies requiring large numbers of individually marked waterfowl. The procedure for constructing these discs is outlined. Blue-winged teal (Anas discors) with 5/8-inch discs, and canvasback (Aythya valisineria) and redhead (A. americana) with 3/4-inch discs can be individually identified up to 50 and 80 yards, respectively, with a gunstock-mounted, 20-power spotting scope. The particular value of these markers is their durability, the number of combinations possible, and the apparent absence of behavioral or mortality influence among such species as the blue-winged teal.
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)
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)
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.
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.
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)
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 ...
Young Students Investigate Number Cubes.
ERIC Educational Resources Information Center
Friedlander, Alex
1997-01-01
Describes a series of learning activities built around number cubes. Sample activities introduce elementary properties of the cube, the magic rule of seven, and basic concepts related to graphs in the plane coordinate system. (PVD)
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.
Covering Numbers for Semicontinuous Functions
2016-04-29
Covering Numbers for Semicontinuous Functions Johannes O. Royset Operations Research Department Naval Postgraduate School joroyset@nps.edu Abstract...Considering the metric space of extended real-valued lower semicontinuous functions under the epi-distance, the paper gives an upper bound on the...covering numbers of bounded subsets of such functions . No assumptions about continuity, smoothness, variation, and even finiteness of the functions are
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
1982-12-01
partitions, the restriction being that the first r elements must be in distinct cycles and respectively distinct subsets. The combinatorial and algebraic ...the first r elements must be in distinct cycles and respectively distinct subsets. The combinatorial and algebraic properties of these numbers, which in...the minimum number within each cycle (called the cycle leader) as the first element of the cycle, and list all cycles (including singletons) in
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.
Random numbers from vacuum fluctuations
Shi, Yicheng; Kurtsiefer, Christian; Chng, Brenda
2016-07-25
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.
Thermodynamics of random number generation
NASA Astrophysics Data System (ADS)
Aghamohammadi, Cina; Crutchfield, James P.
2017-06-01
We analyze the thermodynamic costs of the three main approaches to generating random numbers via the recently introduced Information Processing Second Law. Given access to a specified source of randomness, a random number generator (RNG) produces samples from a desired target probability distribution. This differs from pseudorandom number generators (PRNGs) that use wholly deterministic algorithms and from true random number generators (TRNGs) in which the randomness source is a physical system. For each class, we analyze the thermodynamics of generators based on algorithms implemented as finite-state machines, as these allow for direct bounds on the required physical resources. This establishes bounds on heat dissipation and work consumption during the operation of three main classes of RNG algorithms—including those of von Neumann, Knuth, and Yao and Roche and Hoshi—and for PRNG methods. We introduce a general TRNG and determine its thermodynamic costs exactly for arbitrary target distributions. The results highlight the significant differences between the three main approaches to random number generation: One is work producing, one is work consuming, and the other is potentially dissipation neutral. Notably, TRNGs can both generate random numbers and convert thermal energy to stored work. These thermodynamic costs on information creation complement Landauer's limit on the irreducible costs of information destruction.
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.
Are Number Gestures Easier than Number Words for Preschoolers?
ERIC Educational Resources Information Center
Nicoladis, Elena; Pika, Simone; Marentette, Paula
2010-01-01
Some researchers have argued that children's earliest symbols are based on their sensorimotor experience and that arbitrary symbol-referent mapping poses a challenge for them. If so, exposure to iconic symbols (such as one-finger-for-one-object manual gestures) might help children in a difficult domain such as number. We assessed 44 preschoolers'…
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…
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.
Low magnetic Prandtl number dynamos
NASA Astrophysics Data System (ADS)
Montgomery, David; Mininni, Pablo
2005-11-01
Dynamo amplification by velocity fields in conducting fluids can be highly varied. Here [1] we study dynamos numerically in one of the most efficient flows found for exciting dynamo fields at low magnetic Reynolds numbers: ``Roberts flow,'' in which the large scales are driven helically in 3D periodic boundary conditions. Three qualitatively distinct regimes are identified, depending upon mechanical Reynolds number: steady-state laminar flow, mildly unstable periodic hydrodynamic flow, and fully turbulent hydrodynamic flow. A critical magnetic Reynolds number for dynamo amplification can be identified in all three regimes, and it plateaus as the inverse magnetic Prandtl number increases (paralleling earlier results for the ``Taylor-Green vortex'' flow). It is over five times higher in the turbulent velocity field regime than it is for the time-averaged flow for that turbulent velocity field. Explorations are carried out both in the linear (``kinematic dynamo'') and nonlinear regimes of incompressible MHD. Periodic boundary conditions appear as an undesirable limitation and we are attempting to dispense with them by a spectral method in which the fields are expanded in Chandrasekhar-Kendall spherical eigenfunctions of the curl. [1] P.D. Mininni and D.C. Montgomery, ``Low magnetic Prandtl number dynamos with helical forcing,'' submitted to Phys. Rev. E (2005). Arxiv: physics/0505192.
Number theoretical foundations in cryptography
NASA Astrophysics Data System (ADS)
Atan, Kamel Ariffin Mohd
2017-08-01
In recent times the hazards in relationships among entities in different establishments worldwide have generated exciting developments in cryptography. Central to this is the theory of numbers. This area of mathematics provides very rich source of fundamental materials for constructing secret codes. Some number theoretical concepts that have been very actively used in designing crypto systems will be highlighted in this presentation. This paper will begin with introduction to basic number theoretical concepts which for many years have been thought to have no practical applications. This will include several theoretical assertions that were discovered much earlier in the historical development of number theory. This will be followed by discussion on the "hidden" properties of these assertions that were later exploited by designers of cryptosystems in their quest for developing secret codes. This paper also highlights some earlier and existing cryptosystems and the role played by number theoretical concepts in their constructions. The role played by cryptanalysts in detecting weaknesses in the systems developed by cryptographers concludes this presentation.
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 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
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.
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.
JOC Recent Reviews, Number 81.
Cornel, Veronica M
2006-07-07
Reviews are listed in order of appearance in the sources indicated. In multidisciplinary review journals, only those reviews which fall within the scope of this Journal are included. Sources are listed alphabetically in three categories: regularly issued review journals and series volumes, contributed volumes, and other monographs. Titles are numbered serially, and these numbers are used for reference in the index. Major English-language sources of critical reviews are covered. Encyclopedic treatises, annual surveys such as Specialist Periodical Reports, and compilations of symposia proceedings are omitted. This installment of Recent Reviews covers principally the early part of the 2006 literature. Previous installment: J. Org. Chem. 2006, 71(7), 2926-34.
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
Number of medications or number of diseases: what influences underprescribing?
Gorup, Eva Cedilnik; Šter, Marija Petek
2017-09-17
An increasing number of older adults suffer from multimorbidity and receive multiple medications. Despite that, underprescribing of potentially beneficial medications is widespread in this population. Our aim was to examine influence of polypharmacy and multimorbidity on the presence of prescribing omissions (PO) in general practice attenders. We conducted a cross-sectional study of older adults attending general practices in Slovenia who were regularly prescribed at least one medication. Patients' data was entered into a computer application evaluating the presence of START (Screening Tool to Alert doctors to Right Treatment) criteria for PO. Demographic data, CIRS-G (Cumulative Illness Rating Scale for geriatric patients) questionnaire, number of medications, and healthcare utilization data were also collected. We defined polypharmacy as five or more concurrent medications. Five hundred three patients were enrolled, 258 (56.7%) female. The average age was 74.9 and average value of CIRS-G index 1.48 (± 0.6). Patients took on average 5.6 medications and 216 (42.9%) patients had at least one PO according to START criteria. In bivariate analysis, there was a significant association between age, number of medications, polypharmacy and CIRS-G index measures, and presence of PO. In multivariate analysis, only age and number of affected CIRS-G categories significantly predicted PO (p < 0.05). Older patients with more affected CIRS-G categories were at higher risk for PO. Polypharmacy was not an independent risk factor for the presence of PO. A possible reason is that in multimorbid older people, physicians and patients set individual priorities to treatment instead of treating all diseases and conditions.
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
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)
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…
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,…
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,…
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.)
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)
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
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)…
Herculano-Houzel, Suzana; Avelino-de-Souza, Kamilla; Neves, Kleber; Porfírio, Jairo; Messeder, Débora; Mattos Feijó, Larissa; Maldonado, José; Manger, Paul R.
2014-01-01
What explains the superior cognitive abilities of the human brain compared to other, larger brains? Here we investigate the possibility that the human brain has a larger number of neurons than even larger brains by determining the cellular composition of the brain of the African elephant. We find that the African elephant brain, which is about three times larger than the human brain, contains 257 billion (109) neurons, three times more than the average human brain; however, 97.5% of the neurons in the elephant brain (251 billion) are found in the cerebellum. This makes the elephant an outlier in regard to the number of cerebellar neurons compared to other mammals, which might be related to sensorimotor specializations. In contrast, the elephant cerebral cortex, which has twice the mass of the human cerebral cortex, holds only 5.6 billion neurons, about one third of the number of neurons found in the human cerebral cortex. This finding supports the hypothesis that the larger absolute number of neurons in the human cerebral cortex (but not in the whole brain) is correlated with the superior cognitive abilities of humans compared to elephants and other large-brained mammals. PMID:24971054
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…
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…
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…
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.
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,…
Particle number and random phases
Kandrup, H.E.
1988-09-15
This paper focuses on the particle content of some scalar field as defined with respect to two sets of modes connected via a well-behaved (and unitarily implementable) Bogoliubov transformation. The principal conclusion impacts on the special role of ''random phase'' states, for which the relative phases associated with the projection of the quantum state into two different numbers eigenstates are treated as ''random'' and averaged over in a density matrix. Specifically, it is demonstrated that if, with respect to one set of modes, the field is in a ''random phase'' state, then any other mode decomposition related via a nontrivial Bogoliubov transformation will yield a larger expectation value for the total particle number. This special role of ''random phase'' states is also related to a recently discussed measure of entropy S/sub N/ which assesses the ''spread'' or ''uncertainty'' in particle number. One specific example of all this is the relative particle content in Minkowski space as defined with respect to the modes natural for inertial and uniformly accelerated observers. Another is the initial and final particle numbers detected by two observers in a ''statically bounded'' universe of the form examined by Parker and Zel'dovich.
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)
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.)
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,…
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
Squirming At Finite Reynolds Number
NASA Astrophysics Data System (ADS)
Chisholm, Nicholas; Zhu, Ziyi; Khair, Aditya
2013-11-01
The dynamics of swimming microorganisms at zero Reynolds number (Re = 0) has been the subject of extensive theoretical and experimental investigation over the past decade, and the study of locomotion at high Reynolds number (Re >> 1), where inertial forces are dominant, has a venerable history. In this talk, we consider swimming between these limits, i.e. at finite Reynolds numbers, using the popular ``squirmer'' model of self-propulsion, wherein locomotion is achieved through surface distortions. We first utilize matched asymptotic expansions to derive an analytical expression for the swimming velocity of a squirmer through O (Re2) , which highlights that inertia affects so-called ``pusher'' and ``puller'' swimmers in fundamentally different manners. (The equivalent of Whitehead's paradox for a self-propelled object is elucidated in the process.) Next, we employ numerical methods to compute the swimming velocity of pushers and pullers for higher Reynolds numbers. Finally, we demonstrate that inertia causes squirmers (which are non-chiral) to drift across the streamlines of an imposed shear flow.
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…
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…
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)
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.
Residual number processing in dyscalculia☆
Cappelletti, Marinella; Price, Cathy J.
2013-01-01
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. PMID:24266008
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
Energy: Selected Facts and Numbers
2006-11-29
emissions led utilities to convert a number of coal-fired powerplants to burn oil, and many new plants were designed to burn oil or natural gas. Utilities...Tables 5.13a-d. Industrial consumption of petroleum, which includes such large consumers as refineries and petrochemical industries, has remained about...1960s because it resulted in lower emissions of air pollutants, and consumption continued in the 1970s despite the price surge because natural gas was
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.).
2017-09-08
Expedition 52, as simple as 1-2-3: the first International Space Station science officer who was also the second woman to serve as a station crewmember has now finished her third long-duration mission…and that’s just for starters. Last week’s crew return to Earth puts Expedition 52 in the record books; we peeked inside and pulled out some of the best numbers to sum up the flight.
Sasanguie, Delphine; Göbel, Silke M; Moll, Kristina; Smets, Karolien; Reynvoet, Bert
2013-03-01
In this study, the performance of typically developing 6- to 8-year-old children on an approximate number discrimination task, a symbolic comparison task, and a symbolic and nonsymbolic number line estimation task was examined. For the first time, children's performances on these basic cognitive number processing tasks were explicitly contrasted to investigate which of them is the best predictor of their future mathematical abilities. Math achievement was measured with a timed arithmetic test and with a general curriculum-based math test to address the additional question of whether the predictive association between the basic numerical abilities and mathematics achievement is dependent on which math test is used. Results revealed that performance on both mathematics achievement tests was best predicted by how well childrencompared digits. In addition, an association between performance on the symbolic number line estimation task and math achievement scores for the general curriculum-based math test measuring a broader spectrum of skills was found. Together, these results emphasize the importance of learning experiences with symbols for later math abilities. Copyright © 2012 Elsevier Inc. All rights reserved.
Vertebral numbers and human evolution.
Williams, Scott A; Middleton, Emily R; Villamil, Catalina I; Shattuck, Milena R
2016-01-01
Ever since Tyson (1699), anatomists have noted and compared differences in the regional numbers of vertebrae among humans and other hominoids. Subsequent workers interpreted these differences in phylogenetic, functional, and behavioral frameworks and speculated on the history of vertebral numbers during human evolution. Even in a modern phylogenetic framework and with greatly expanded sample sizes of hominoid species, researchers' conclusions vary drastically, positing that hominins evolved from either a "long-backed" (numerically long lumbar column) or a "short-backed" (numerically short lumbar column) ancestor. We show that these disparate interpretations are due in part to the use of different criteria for what defines a lumbar vertebra, but argue that, regardless of which lumbar definition is used, hominins are similar to their great ape relatives in possessing a short trunk, a rare occurrence in mammals and one that defines the clade Hominoidea. Furthermore, we address the recent claim that the early hominin thoracolumbar configuration is not distinct from that of modern humans and conclude that early hominins show evidence of "cranial shifting," which might explain the anomalous morphology of several early hominin fossils. Finally, we evaluate the competing hypotheses on numbers of vertebrae and argue that the current data support a hominin ancestor with an African ape-like short trunk and lower back. © 2016 Wiley Periodicals, Inc.
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.
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.
Quasiperpendicular High Mach Number Shocks.
Sulaiman, A H; Masters, A; Dougherty, M K; Burgess, D; Fujimoto, M; Hospodarsky, G B
2015-09-18
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 (M_{A}) 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 ~0.3τ_{c}, where τ_{c} is the ion gyroperiod. In addition, we experimentally reveal the relationship between reformation and M_{A} and focus on the magnetic structure of such shocks to further show that for the same M_{A}, a reforming shock exhibits stronger magnetic field amplification than a shock that is not reforming.
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].
Propulsion at low Reynolds number
NASA Astrophysics Data System (ADS)
Najafi, Ali; Golestanian, Ramin
2005-04-01
We study the propulsion of two model swimmers at low Reynolds number. Inspired by Purcell's model, we propose a very simple one-dimensional swimmer consisting of three spheres that are connected by two arms whose lengths can change between two values. The proposed swimmer can swim with a special type of motion, which breaks the time-reversal symmetry. We also show that an ellipsoidal membrane with tangential travelling wave on it can also propel itself in the direction preferred by the travelling wave. This system resembles the realistic biological animals like Paramecium.
Turbulence at Finite Reynolds Number
NASA Astrophysics Data System (ADS)
George, William K.
2003-11-01
Some of the unique features and challenges of turbulence at modest Reynolds number will be discussed and illustrated by example. Almost all laboratory and DNS turbulent flows fall into this class of flows, as do all turbulent wall-bounded flows within at least a few hundred viscous lengths from the surface. Particularly important is absence of an inertial subrange in the energy spectrum, which precludes the applicability of most turbulence theories to-date. Also interesting is the apparent tendency of at least free (no boundary) turbulent flows (e.g., decaying homogeneous turbulence, jets, wakes, etc.) to preserve asymptotically remnants of their initial (or upstream) conditions. These dependencies create great difficulties for the turbulence modellers and theoreticians alike. Equilibrium similarity and near-asymptotics provide useful theoretical tools for analyzing these flows, but troublesome questions remain. These anomalies challenge both the new ideas and the classical high Reynolds number ones as well. Will they vanish as our experiments, computations and theories improve, or are they harbingers of a paradigm shift? Regardless, we must acknowledge the problems and learn to ask the right questions to find out.
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.
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.
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.
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,…
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...
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... IDENTIFICATION AS TO CLASS, QUALITY, QUANTITY, AND CONDITION Inauguration of Inspection § 355.8 Official number. To each plant granted inspection an official number shall be assigned. Such number shall be preceded...
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 8 2013-01-01 2013-01-01 false Docket number. 900.5 Section 900.5 Agriculture... Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter the proceeding may be referred to by such number. ...
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, AC...
7 CFR 75.48 - Identification number.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 3 2012-01-01 2012-01-01 false Identification number. 75.48 Section 75.48 Agriculture... number. The Director may require the use of official identification numbers in connection with seed certificated or sampled under the Act. When identification numbers are required, they shall be specified by the...
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 8 2014-01-01 2014-01-01 false Docket number. 900.5 Section 900.5 Agriculture... Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter the proceeding may be referred to by such number. ...
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 8 2014-01-01 2014-01-01 false Lot number. 987.102 Section 987.102 Agriculture... RIVERSIDE COUNTY, CALIFORNIA Administrative Rules Definitions § 987.102 Lot number. Lot number is synonymous with code and means a combination of letters or numbers, or both, acceptable to the Committee, showing...
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 8 2012-01-01 2012-01-01 false Lot number. 987.102 Section 987.102 Agriculture... RIVERSIDE COUNTY, CALIFORNIA Administrative Rules Definitions § 987.102 Lot number. Lot number is synonymous with code and means a combination of letters or numbers, or both, acceptable to the Committee, showing...
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, AC...
7 CFR 29.32 - Identification number.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 2 2013-01-01 2013-01-01 false Identification number. 29.32 Section 29.32 Agriculture... INSPECTION Regulations Definitions § 29.32 Identification number. A number or a combination of letters and numbers in a design or mark approved by the Director, stamped, printed, or stenciled on a lot of tobacco...
7 CFR 29.32 - Identification number.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 2 2012-01-01 2012-01-01 false Identification number. 29.32 Section 29.32 Agriculture... INSPECTION Regulations Definitions § 29.32 Identification number. A number or a combination of letters and numbers in a design or mark approved by the Director, stamped, printed, or stenciled on a lot of tobacco...
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 8 2013-01-01 2013-01-01 false Lot number. 987.102 Section 987.102 Agriculture... RIVERSIDE COUNTY, CALIFORNIA Administrative Rules Definitions § 987.102 Lot number. Lot number is synonymous with code and means a combination of letters or numbers, or both, acceptable to the Committee, showing...
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 8 2012-01-01 2012-01-01 false Docket number. 900.5 Section 900.5 Agriculture... Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter the proceeding may be referred to by such number. ...
7 CFR 75.48 - Identification number.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 3 2014-01-01 2014-01-01 false Identification number. 75.48 Section 75.48 Agriculture... number. The Director may require the use of official identification numbers in connection with seed certificated or sampled under the Act. When identification numbers are required, they shall be specified by the...
7 CFR 75.48 - Identification number.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 3 2013-01-01 2013-01-01 false Identification number. 75.48 Section 75.48 Agriculture... number. The Director may require the use of official identification numbers in connection with seed certificated or sampled under the Act. When identification numbers are required, they shall be specified by 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)
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…
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:
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,...
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…
7 CFR 75.48 - Identification number.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 3 2010-01-01 2010-01-01 false Identification number. 75.48 Section 75.48 Agriculture... number. The Director may require the use of official identification numbers in connection with seed certificated or sampled under the Act. When identification numbers are required, they shall be specified by the...
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Lot numbers. 46.20 Section 46.20 Agriculture... 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...
7 CFR 29.32 - Identification number.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 2 2011-01-01 2011-01-01 false Identification number. 29.32 Section 29.32 Agriculture... INSPECTION Regulations Definitions § 29.32 Identification number. A number or a combination of letters and numbers in a design or mark approved by the Director, stamped, printed, or stenciled on a lot of tobacco...
7 CFR 75.48 - Identification number.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 3 2011-01-01 2011-01-01 false Identification number. 75.48 Section 75.48 Agriculture... number. The Director may require the use of official identification numbers in connection with seed certificated or sampled under the Act. When identification numbers are required, they shall be specified by the...
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 8 2011-01-01 2011-01-01 false Docket number. 900.5 Section 900.5 Agriculture... Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter the proceeding may be referred to by such number. ...
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 8 2010-01-01 2010-01-01 false Lot number. 987.102 Section 987.102 Agriculture... RIVERSIDE COUNTY, CALIFORNIA Administrative Rules Definitions § 987.102 Lot number. Lot number is synonymous with code and means a combination of letters or numbers, or both, acceptable to the Committee, showing...
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... INSPECTION Regulations Definitions § 29.32 Identification number. A number or a combination of letters and numbers in a design or mark approved by the Director, stamped, printed, or stenciled on a lot of tobacco...
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 8 2011-01-01 2011-01-01 false Lot number. 987.102 Section 987.102 Agriculture... RIVERSIDE COUNTY, CALIFORNIA Administrative Rules Definitions § 987.102 Lot number. Lot number is synonymous with code and means a combination of letters or numbers, or both, acceptable to the Committee, showing...
14 CFR 47.15 - Identification number.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Identification number. 47.15 Section 47.15... REGISTRATION General § 47.15 Identification number. (a) Number required. An applicant for Aircraft Registration must place a U.S. identification number (registration mark) on his Aircraft Registration Application...
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…
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.
Group Sunspot Numbers: Sunspot Cycle Characteristics
NASA Technical Reports Server (NTRS)
Hathaway, D. H.; Wilson, R. M.; Reichmann, E. J.; Six, N. Frank (Technical Monitor)
2002-01-01
We examine the "Group" sunspot numbers constructed by Hoyt and Schatten to determine their utility in characterizing the solar activity cycle. We compare smoothed monthly Group Sunspot Numbers to Zurich (International) Sunspot Numbers, 10.7-cm radio flux, and total sunspot area. We find that the Zurich numbers follow the 10.7-cm radio flux and total sunspot area measurements slightly better than the Group numbers. We examine several significant characteristics of the sunspot cycle using both Group numbers and Zurich numbers. We find that the "Waldmeier Effect" - the anti-correlation between cycle amplitude and the elapsed time between minimum and maximum of a cycle - is much more apparent in the Zurich numbers. The "Amplitude-Period Effect" the anti-correlation between cycle amplitude and the length of the previous cycle from minimum to minimum - is also much more apparent in the Zurich numbers. The "Amplitude-Minimum Effect" - the correlation between cycle amplitude and the activity level at the previous (onset) minimum is equally apparent in both the Zurich numbers and the Group numbers. The "Even-Odd Effect" - in which odd-numbered cycles are larger than their even-numbered precursors - is somewhat stronger in the Group numbers but with a tighter relationship in the Zurich numbers. The "Secular Trend" - the increase in cycle amplitudes since the Maunder Minimum - is much stronger in Group numbers. After removing this trend we find little evidence for multi-cycle periodicities like the 80 year Gleissberg cycle or the two- and three-cycle periodicities. We also find little evidence for a correlation between the amplitude of a cycle and its period or for a bimodal distribution of cycle periods. We conclude that the Group numbers are most useful for extending the sunspot cycle data further back in time and thereby adding more cycles and improving the statistics. However, the Zurich numbers are more useful for characterizing the on-going levels of solar activity.
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
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.
Stochastic Blockmodels with Growing Number of Classes
2011-01-01
NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 5c. PROGRAM ELEMENT NUMBER 5b. GRANT NUMBER 5a. CONTRACT NUMBER W911NF-11-1-0036 611103 Form Approved...blockmodel in work by Holland et al. (1983) and Fienberg et al. (1985). The model 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72...this work we provide a finite-sample confidence bound that can be used when estimating network structure from data modeled by independent Bernoulli
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)
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....
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)
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)
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)
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.
World well numbering standard to be developed
Not Available
1992-08-31
This paper reports that an industry subcommittee has formulated a proposal for a worldwide well number standard and has issued a request for quote to develop the proposal. The American Association of Petroleum Geologists database standards subcommittee reviewed comments on the standard Aug. 6 in Houston. The subcommittee reached consensus that a worldwide well number standard be proposed, that the number should provide a minimum amount of data, and that one vendor should assign the numbers.
18 CFR 367.4 - Numbering system.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 18 Conservation of Power and Water Resources 1 2013-04-01 2013-04-01 false Numbering system. 367.4... NATURAL GAS ACT UNIFORM SYSTEM OF ACCOUNTS FOR CENTRALIZED SERVICE COMPANIES SUBJECT TO THE PROVISIONS OF... Instructions § 367.4 Numbering system. (a) The account numbering plan used in this part consists of a system of...
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…
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.
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…
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....
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...
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…
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 10 2012-01-01 2012-01-01 false Docket number. 1200.6 Section 1200.6 Agriculture... Governing Proceedings To Formulate and Amend an Order § 1200.6 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter the...
47 CFR 51.203 - Number portability.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 47 Telecommunication 3 2012-10-01 2012-10-01 false Number portability. 51.203 Section 51.203 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES (CONTINUED) INTERCONNECTION Obligations of All Local Exchange Carriers § 51.203 Number portability. The rules governing number portability...
46 CFR 169.515 - Number required.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 46 Shipping 7 2014-10-01 2014-10-01 false Number required. 169.515 Section 169.515 Shipping COAST... and Firefighting Equipment Primary Lifesaving Equipment § 169.515 Number required. (a) Except as... additional inflatable liferafts to accommodate 25% of the persons on board or the number of persons...
21 CFR 1210.21 - Permit number.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 21 Food and Drugs 8 2012-04-01 2012-04-01 false Permit number. 1210.21 Section 1210.21 Food and... IMPORT MILK ACT Permit Control § 1210.21 Permit number. Each permit issued under the Federal Import Milk Act, including each temporary permit, shall bear an individual number. The right to the use of such...
46 CFR 169.515 - Number required.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 46 Shipping 7 2013-10-01 2013-10-01 false Number required. 169.515 Section 169.515 Shipping COAST... and Firefighting Equipment Primary Lifesaving Equipment § 169.515 Number required. (a) Except as... additional inflatable liferafts to accommodate 25% of the persons on board or the number of persons...
46 CFR 10.207 - Identification number.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 46 Shipping 1 2014-10-01 2014-10-01 false Identification number. 10.207 Section 10.207 Shipping... CREDENTIAL General Requirements for All Merchant Mariner Credentials § 10.207 Identification number. For recordkeeping purposes only, a mariner's official MMC identification number is the individual's social security...
40 CFR 265.11 - Identification number.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 40 Protection of Environment 27 2012-07-01 2012-07-01 false Identification number. 265.11 Section... FACILITIES General Facility Standards § 265.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR...
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 1 2014-01-01 2014-01-01 false Docket number. 1.414 Section 1.414 Agriculture Office... Conservation and Shortage Relief Act of 1990 (16 U.S.C. 620 et seq.) § 1.414 Docket number. Each proceeding, following its institution, shall be assigned a docket number by the Hearing Clerk, and thereafter the...
47 CFR 51.203 - Number portability.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 47 Telecommunication 3 2013-10-01 2013-10-01 false Number portability. 51.203 Section 51.203 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES (CONTINUED) INTERCONNECTION Obligations of All Local Exchange Carriers § 51.203 Number portability. The rules governing number portability...
Code of Federal Regulations, 2012 CFR
2012-10-01
... 47 Telecommunication 1 2012-10-01 2012-10-01 false File numbers. 1.1405 Section 1.1405... Attachment Complaint 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...
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 1 2013-01-01 2013-01-01 false Docket number. 1.134 Section 1.134 Agriculture Office... Adjudicatory Proceedings Instituted by the Secretary Under Various Statutes § 1.134 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the Hearing Clerk...
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 8 2012-01-01 2012-01-01 false Docket number. 900.54 Section 900.54 Agriculture... Governing Proceedings on Petitions To Modify or To Be Exempted From Marketing Orders § 900.54 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the...
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 1 2012-01-01 2012-01-01 false Docket number. 1.414 Section 1.414 Agriculture Office... Conservation and Shortage Relief Act of 1990 (16 U.S.C. 620 et seq.) § 1.414 Docket number. Each proceeding, following its institution, shall be assigned a docket number by the Hearing Clerk, and thereafter the...
24 CFR 3280.6 - Serial number.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 24 Housing and Urban Development 5 2012-04-01 2012-04-01 false Serial number. 3280.6 Section 3280... DEVELOPMENT MANUFACTURED HOME CONSTRUCTION AND SAFETY STANDARDS General § 3280.6 Serial number. (a) A manufactured home serial number which will identify the manufacturer and the state in which the manufactured...
46 CFR 10.207 - Identification number.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 46 Shipping 1 2012-10-01 2012-10-01 false Identification number. 10.207 Section 10.207 Shipping... CREDENTIAL General Requirements for All Merchant Mariner Credentials § 10.207 Identification number. For recordkeeping purposes only, a mariner's official MMC identification number is the individual's social security...
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 8 2014-01-01 2014-01-01 false Docket number. 900.54 Section 900.54 Agriculture... Governing Proceedings on Petitions To Modify or To Be Exempted From Marketing Orders § 900.54 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the...
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 1 2013-01-01 2013-01-01 false Docket number. 1.414 Section 1.414 Agriculture Office... Conservation and Shortage Relief Act of 1990 (16 U.S.C. 620 et seq.) § 1.414 Docket number. Each proceeding, following its institution, shall be assigned a docket number by the Hearing Clerk, and thereafter the...
46 CFR 169.515 - Number required.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 46 Shipping 7 2012-10-01 2012-10-01 false Number required. 169.515 Section 169.515 Shipping COAST... and Firefighting Equipment Primary Lifesaving Equipment § 169.515 Number required. (a) Except as... additional inflatable liferafts to accommodate 25% of the persons on board or the number of persons...
47 CFR 64.1506 - Number designation.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 47 Telecommunication 3 2012-10-01 2012-10-01 false Number designation. 64.1506 Section 64.1506... Number designation. Any interstate service described in § 64.1501(a)(1)-(2), and not subject to the exclusions contained in § 64.1501(a)(4), shall be offered only through telephone numbers beginning with a 900...
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 10 2013-01-01 2013-01-01 false Docket number. 1200.6 Section 1200.6 Agriculture... Governing Proceedings To Formulate and Amend an Order § 1200.6 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter the...
24 CFR 3280.6 - Serial number.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 24 Housing and Urban Development 5 2014-04-01 2014-04-01 false Serial number. 3280.6 Section 3280... DEVELOPMENT MANUFACTURED HOME CONSTRUCTION AND SAFETY STANDARDS General § 3280.6 Serial number. (a) A manufactured home serial number which will identify the manufacturer and the state in which the manufactured...
20 CFR 404.1220 - Identification numbers.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 20 Employees' Benefits 2 2013-04-01 2013-04-01 false Identification numbers. 404.1220 Section 404... § 404.1220 Identification numbers. (a) State and local governments. When a State submits a modification... will assign a special identification number to each political subdivision included in that modification...
Code of Federal Regulations, 2013 CFR
2013-10-01
... 47 Telecommunication 1 2013-10-01 2013-10-01 false File numbers. 1.1405 Section 1.1405... Attachment Complaint 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...
7 CFR 29.133 - Identification number.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 2 2012-01-01 2012-01-01 false Identification number. 29.133 Section 29.133... REGULATIONS TOBACCO INSPECTION Regulations Miscellaneous § 29.133 Identification number. The Director may require the use of official identification numbers in connection with tobacco certificated or sampled...
20 CFR 404.1220 - Identification numbers.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 20 Employees' Benefits 2 2014-04-01 2014-04-01 false Identification numbers. 404.1220 Section 404... § 404.1220 Identification numbers. (a) State and local governments. When a State submits a modification... will assign a special identification number to each political subdivision included in that modification...
47 CFR 64.1506 - Number designation.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 47 Telecommunication 3 2013-10-01 2013-10-01 false Number designation. 64.1506 Section 64.1506... Number designation. Any interstate service described in § 64.1501(a)(1)-(2), and not subject to the exclusions contained in § 64.1501(a)(4), shall be offered only through telephone numbers beginning with a 900...
40 CFR 264.11 - Identification number.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 40 Protection of Environment 27 2012-07-01 2012-07-01 false Identification number. 264.11 Section... Facility Standards § 264.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR 12746). ...
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 10 2014-01-01 2014-01-01 false Docket number. 1200.6 Section 1200.6 Agriculture... Governing Proceedings To Formulate and Amend an Order § 1200.6 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter the...
20 CFR 404.1220 - Identification numbers.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 20 Employees' Benefits 2 2012-04-01 2012-04-01 false Identification numbers. 404.1220 Section 404... § 404.1220 Identification numbers. (a) State and local governments. When a State submits a modification... will assign a special identification number to each political subdivision included in that modification...
7 CFR 29.133 - Identification number.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 2 2014-01-01 2014-01-01 false Identification number. 29.133 Section 29.133... REGULATIONS TOBACCO INSPECTION Regulations Miscellaneous § 29.133 Identification number. The Director may require the use of official identification numbers in connection with tobacco certificated or sampled...
47 CFR 95.671 - Serial number.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 47 Telecommunication 5 2013-10-01 2013-10-01 false Serial number. 95.671 Section 95.671 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES PERSONAL RADIO... number. The serial number of each CB transmitter must be engraved on the transmitter chassis. ...
40 CFR 265.11 - Identification number.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 40 Protection of Environment 26 2014-07-01 2014-07-01 false Identification number. 265.11 Section... FACILITIES General Facility Standards § 265.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR...
40 CFR 264.11 - Identification number.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 27 2013-07-01 2013-07-01 false Identification number. 264.11 Section... Facility Standards § 264.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR 12746). ...
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 winery...
47 CFR 95.671 - Serial number.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 47 Telecommunication 5 2014-10-01 2014-10-01 false Serial number. 95.671 Section 95.671 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES PERSONAL RADIO... number. The serial number of each CB transmitter must be engraved on the transmitter chassis. ...
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 1 2012-01-01 2012-01-01 false Docket number. 1.134 Section 1.134 Agriculture Office... Adjudicatory Proceedings Instituted by the Secretary Under Various Statutes § 1.134 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the Hearing Clerk...
7 CFR 29.133 - Identification number.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 2 2013-01-01 2013-01-01 false Identification number. 29.133 Section 29.133... REGULATIONS TOBACCO INSPECTION Regulations Miscellaneous § 29.133 Identification number. The Director may require the use of official identification numbers in connection with tobacco certificated or sampled...
47 CFR 64.1506 - Number designation.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 47 Telecommunication 3 2014-10-01 2014-10-01 false Number designation. 64.1506 Section 64.1506... Number designation. Any interstate service described in § 64.1501(a)(1)-(2), and not subject to the exclusions contained in § 64.1501(a)(4), shall be offered only through telephone numbers beginning with a 900...
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 1 2014-01-01 2014-01-01 false Docket number. 1.134 Section 1.134 Agriculture Office... Adjudicatory Proceedings Instituted by the Secretary Under Various Statutes § 1.134 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the Hearing Clerk...
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 8 2013-01-01 2013-01-01 false Docket number. 900.54 Section 900.54 Agriculture... Governing Proceedings on Petitions To Modify or To Be Exempted From Marketing Orders § 900.54 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the...
40 CFR 264.11 - Identification number.
Code of Federal Regulations, 2014 CFR
2014-07-01
... 40 Protection of Environment 26 2014-07-01 2014-07-01 false Identification number. 264.11 Section... Facility Standards § 264.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR 12746). ...
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 winery...
Code of Federal Regulations, 2014 CFR
2014-10-01
... 47 Telecommunication 1 2014-10-01 2014-10-01 false File numbers. 1.1405 Section 1.1405... Attachment Complaint 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...
21 CFR 1210.21 - Permit number.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 21 Food and Drugs 8 2013-04-01 2013-04-01 false Permit number. 1210.21 Section 1210.21 Food and... IMPORT MILK ACT Permit Control § 1210.21 Permit number. Each permit issued under the Federal Import Milk Act, including each temporary permit, shall bear an individual number. The right to the use of such...
47 CFR 51.203 - Number portability.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 47 Telecommunication 3 2014-10-01 2014-10-01 false Number portability. 51.203 Section 51.203 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES (CONTINUED) INTERCONNECTION Obligations of All Local Exchange Carriers § 51.203 Number portability. The rules governing number portability...
46 CFR 10.207 - Identification number.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 46 Shipping 1 2013-10-01 2013-10-01 false Identification number. 10.207 Section 10.207 Shipping... CREDENTIAL General Requirements for All Merchant Mariner Credentials § 10.207 Identification number. For recordkeeping purposes only, a mariner's official MMC identification number is the individual's social security...
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…
24 CFR 3280.6 - Serial number.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 24 Housing and Urban Development 5 2013-04-01 2013-04-01 false Serial number. 3280.6 Section 3280... DEVELOPMENT MANUFACTURED HOME CONSTRUCTION AND SAFETY STANDARDS General § 3280.6 Serial number. (a) A manufactured home serial number which will identify the manufacturer and the state in which the manufactured...
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 winery...
40 CFR 265.11 - Identification number.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 27 2013-07-01 2013-07-01 false Identification number. 265.11 Section... FACILITIES General Facility Standards § 265.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR...
47 CFR 95.671 - Serial number.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 47 Telecommunication 5 2012-10-01 2012-10-01 false Serial number. 95.671 Section 95.671 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES PERSONAL RADIO... number. The serial number of each CB transmitter must be engraved on the transmitter chassis. ...
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…
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…
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...
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)
18 CFR 367.4 - Numbering system.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 18 Conservation of Power and Water Resources 1 2012-04-01 2012-04-01 false Numbering system. 367.4... NATURAL GAS ACT UNIFORM SYSTEM OF ACCOUNTS FOR CENTRALIZED SERVICE COMPANIES SUBJECT TO THE PROVISIONS OF... Instructions § 367.4 Numbering system. (a) The account numbering plan used in this part consists of a system of...
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...
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)
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, 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,...
24 CFR 3280.6 - Serial number.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 24 Housing and Urban Development 5 2011-04-01 2011-04-01 false Serial number. 3280.6 Section 3280... DEVELOPMENT MANUFACTURED HOME CONSTRUCTION AND SAFETY STANDARDS General § 3280.6 Serial number. (a) A manufactured home serial number which will identify the manufacturer and the state in which the manufactured...
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 winery...
40 CFR 265.11 - Identification number.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 40 Protection of Environment 25 2010-07-01 2010-07-01 false Identification number. 265.11 Section... FACILITIES General Facility Standards § 265.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR...
7 CFR 29.133 - Identification number.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Identification number. 29.133 Section 29.133... REGULATIONS TOBACCO INSPECTION Regulations Miscellaneous § 29.133 Identification number. The Director may require the use of official identification numbers in connection with tobacco certificated or sampled...
47 CFR 51.203 - Number portability.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 47 Telecommunication 3 2010-10-01 2010-10-01 false Number portability. 51.203 Section 51.203 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES (CONTINUED) INTERCONNECTION Obligations of All Local Exchange Carriers § 51.203 Number portability. The rules governing number portability...
40 CFR 264.11 - Identification number.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 40 Protection of Environment 26 2011-07-01 2011-07-01 false Identification number. 264.11 Section... Facility Standards § 264.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR 12746). ...
24 CFR 3280.6 - Serial number.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 24 Housing and Urban Development 5 2010-04-01 2010-04-01 false Serial number. 3280.6 Section 3280... DEVELOPMENT MANUFACTURED HOME CONSTRUCTION AND SAFETY STANDARDS General § 3280.6 Serial number. (a) A manufactured home serial number which will identify the manufacturer and the state in which the manufactured...
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 1 2011-01-01 2011-01-01 false Docket number. 1.414 Section 1.414 Agriculture Office... Conservation and Shortage Relief Act of 1990 (16 U.S.C. 620 et seq.) § 1.414 Docket number. Each proceeding, following its institution, shall be assigned a docket number by the Hearing Clerk, and thereafter the...
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 8 2011-01-01 2011-01-01 false Docket number. 900.54 Section 900.54 Agriculture... Governing Proceedings on Petitions To Modify or To Be Exempted From Marketing Orders § 900.54 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the...
20 CFR 404.1220 - Identification numbers.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 20 Employees' Benefits 2 2010-04-01 2010-04-01 false Identification numbers. 404.1220 Section 404... § 404.1220 Identification numbers. (a) State and local governments. When a State submits a modification... will assign a special identification number to each political subdivision included in that modification...
40 CFR 265.11 - Identification number.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 40 Protection of Environment 26 2011-07-01 2011-07-01 false Identification number. 265.11 Section... FACILITIES General Facility Standards § 265.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR...
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 winery...
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 10 2010-01-01 2010-01-01 false Docket number. 1200.6 Section 1200.6 Agriculture... Governing Proceedings To Formulate and Amend an Order § 1200.6 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter the...
47 CFR 32.6622 - Number services.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 47 Telecommunication 2 2010-10-01 2010-10-01 false Number services. 32.6622 Section 32.6622... FOR TELECOMMUNICATIONS COMPANIES Instructions for Expense Accounts § 32.6622 Number services. This account shall include costs incurred in providing customer number and classified listings. This includes...
47 CFR 51.203 - Number portability.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 47 Telecommunication 3 2011-10-01 2011-10-01 false Number portability. 51.203 Section 51.203 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES (CONTINUED) INTERCONNECTION Obligations of All Local Exchange Carriers § 51.203 Number portability. The rules governing number portability...
20 CFR 404.1220 - Identification numbers.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 20 Employees' Benefits 2 2011-04-01 2011-04-01 false Identification numbers. 404.1220 Section 404... § 404.1220 Identification numbers. (a) State and local governments. When a State submits a modification... will assign a special identification number to each political subdivision included in that modification...
40 CFR 264.11 - Identification number.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 40 Protection of Environment 25 2010-07-01 2010-07-01 false Identification number. 264.11 Section... Facility Standards § 264.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR 12746). ...
21 CFR 1210.21 - Permit number.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 21 Food and Drugs 8 2011-04-01 2011-04-01 false Permit number. 1210.21 Section 1210.21 Food and... IMPORT MILK ACT Permit Control § 1210.21 Permit number. Each permit issued under the Federal Import Milk Act, including each temporary permit, shall bear an individual number. The right to the use of such...
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 10 2011-01-01 2011-01-01 false Docket number. 1200.6 Section 1200.6 Agriculture... Governing Proceedings To Formulate and Amend an Order § 1200.6 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter the...
21 CFR 1210.21 - Permit number.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Permit number. 1210.21 Section 1210.21 Food and... IMPORT MILK ACT Permit Control § 1210.21 Permit number. Each permit issued under the Federal Import Milk Act, including each temporary permit, shall bear an individual number. The right to the use of such...
47 CFR 95.671 - Serial number.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 47 Telecommunication 5 2011-10-01 2011-10-01 false Serial number. 95.671 Section 95.671 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES PERSONAL RADIO... number. The serial number of each CB transmitter must be engraved on the transmitter chassis. ...
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 1 2011-01-01 2011-01-01 false Docket number. 1.134 Section 1.134 Agriculture Office... Adjudicatory Proceedings Instituted by the Secretary Under Various Statutes § 1.134 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the Hearing Clerk...
47 CFR 64.1506 - Number designation.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 47 Telecommunication 3 2011-10-01 2011-10-01 false Number designation. 64.1506 Section 64.1506... Number designation. Any interstate service described in § 64.1501(a)(1)-(2), and not subject to the exclusions contained in § 64.1501(a)(4), shall be offered only through telephone numbers beginning with a 900...
46 CFR 10.207 - Identification number.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 46 Shipping 1 2010-10-01 2010-10-01 false Identification number. 10.207 Section 10.207 Shipping... CREDENTIAL General Requirements for All Merchant Mariner Credentials § 10.207 Identification number. For recordkeeping purposes only, a mariner's official MMC identification number is the individual's social security...
Code of Federal Regulations, 2011 CFR
2011-10-01
... 47 Telecommunication 1 2011-10-01 2011-10-01 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 does...
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 1 2010-01-01 2010-01-01 false Docket number. 1.134 Section 1.134 Agriculture Office... Adjudicatory Proceedings Instituted by the Secretary Under Various Statutes § 1.134 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the Hearing Clerk...
46 CFR 10.207 - Identification number.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 46 Shipping 1 2011-10-01 2011-10-01 false Identification number. 10.207 Section 10.207 Shipping... CREDENTIAL General Requirements for All Merchant Mariner Credentials § 10.207 Identification number. For recordkeeping purposes only, a mariner's official MMC identification number is the individual's social security...
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 8 2010-01-01 2010-01-01 false Docket number. 900.54 Section 900.54 Agriculture... Governing Proceedings on Petitions To Modify or To Be Exempted From Marketing Orders § 900.54 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the...
7 CFR 29.133 - Identification number.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 2 2011-01-01 2011-01-01 false Identification number. 29.133 Section 29.133... REGULATIONS TOBACCO INSPECTION Regulations Miscellaneous § 29.133 Identification number. The Director may require the use of official identification numbers in connection with tobacco certificated or sampled...
46 CFR Sec. 2 - Voyage numbers.
Code of Federal Regulations, 2010 CFR
2010-10-01
... voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with... General Agent shall affix his abbreviated designation and initial voyage numbers, as NSA-13/XYZ-1. ...
46 CFR Sec. 2 - Voyage numbers.
Code of Federal Regulations, 2012 CFR
2012-10-01
... voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with... General Agent shall affix his abbreviated designation and initial voyage numbers, as NSA-13/XYZ-1. ...
46 CFR Sec. 2 - Voyage numbers.
Code of Federal Regulations, 2011 CFR
2011-10-01
... voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with... General Agent shall affix his abbreviated designation and initial voyage numbers, as NSA-13/XYZ-1. ...
46 CFR Sec. 2 - Voyage numbers.
Code of Federal Regulations, 2013 CFR
2013-10-01
... voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with... General Agent shall affix his abbreviated designation and initial voyage numbers, as NSA-13/XYZ-1. ...
46 CFR Sec. 2 - Voyage numbers.
Code of Federal Regulations, 2014 CFR
2014-10-01
... voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with... General Agent shall affix his abbreviated designation and initial voyage numbers, as NSA-13/XYZ-1. ...
Children's Use of Number Line Estimation Strategies
ERIC Educational Resources Information Center
Peeters, Dominique; Degrande, Tine; Ebersbach, Mirjam; Verschaffel, Lieven; Luwel, Koen
2016-01-01
This study tested whether second graders use benchmark-based strategies when solving a number line estimation (NLE) task. Participants were assigned to one of three conditions based on the availability of benchmarks provided on the number line. In the bounded condition, number lines were only bounded at both sides by 0 and 200, while the midpoint…
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, 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...
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…
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...
Number-Theoretic Functions via Convolution Rings.
ERIC Educational Resources Information Center
Berberian, S. K.
1992-01-01
Demonstrates the number theory property that the number of divisors of an integer n times the number of positive integers k, less than or equal to and relatively prime to n, equals the sum of the divisors of n using theory developed about multiplicative functions, the units of a convolution ring, and the Mobius Function. (MDH)
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…
USDA-ARS?s Scientific Manuscript database
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...
49 CFR 230.47 - Boiler number.
Code of Federal Regulations, 2011 CFR
2011-10-01
..., 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, shall... known or the name of the steam locomotive owner if a new number is assigned. Safety Relief Valves ...
49 CFR 230.47 - Boiler number.
Code of Federal Regulations, 2010 CFR
2010-10-01
..., 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, shall... known or the name of the steam locomotive owner if a new number is assigned. Safety Relief Valves ...
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)
Ordinality and the nature of symbolic numbers.
Lyons, Ian M; Beilock, Sian L
2013-10-23
The view that representations of symbolic and nonsymbolic numbers are closely tied to one another is widespread. However, the link between symbolic and nonsymbolic numbers is almost always inferred from cardinal processing tasks. In the current work, we show that considering ordinality instead points to striking differences between symbolic and nonsymbolic numbers. Human behavioral and neural data show that ordinal processing of symbolic numbers (Are three Indo-Arabic numerals in numerical order?) is distinct from symbolic cardinal processing (Which of two numerals represents the greater quantity?) and nonsymbolic number processing (ordinal and cardinal judgments of dot-arrays). Behaviorally, distance-effects were reversed when assessing ordinality in symbolic numbers, but canonical distance-effects were observed for cardinal judgments of symbolic numbers and all nonsymbolic judgments. At the neural level, symbolic number-ordering was the only numerical task that did not show number-specific activity (greater than control) in the intraparietal sulcus. Only activity in left premotor cortex was specifically associated with symbolic number-ordering. For nonsymbolic numbers, activation in cognitive-control areas during ordinal processing and a high degree of overlap between ordinal and cardinal processing networks indicate that nonsymbolic ordinality is assessed via iterative cardinality judgments. This contrasts with a striking lack of neural overlap between ordinal and cardinal judgments anywhere in the brain for symbolic numbers, suggesting that symbolic number processing varies substantially with computational context. Ordinal processing sheds light on key differences between symbolic and nonsymbolic number processing both behaviorally and in the brain. Ordinality may prove important for understanding the power of representing numbers symbolically.
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…
27 CFR 20.179 - Package identification number or serial number.
Code of Federal Regulations, 2014 CFR
2014-04-01
... number or serial number. 20.179 Section 20.179 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO... Package identification number or serial number. (a) Requirement. A dealer who fills packages with specially denatured spirits shall mark each package with a package identification number, in accordance with...
27 CFR 20.179 - Package identification number or serial number.
Code of Federal Regulations, 2012 CFR
2012-04-01
... number or serial number. 20.179 Section 20.179 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO... Package identification number or serial number. (a) Requirement. A dealer who fills packages with specially denatured spirits shall mark each package with a package identification number, in accordance with...
27 CFR 20.179 - Package identification number or serial number.
Code of Federal Regulations, 2013 CFR
2013-04-01
... number or serial number. 20.179 Section 20.179 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO... Package identification number or serial number. (a) Requirement. A dealer who fills packages with specially denatured spirits shall mark each package with a package identification number, in accordance with...
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…
27 CFR 20.179 - Package identification number or serial number.
Code of Federal Regulations, 2011 CFR
2011-04-01
... number or serial number. 20.179 Section 20.179 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO... Package identification number or serial number. (a) Requirement. A dealer who fills packages with specially denatured spirits shall mark each package with a package identification number, in accordance with...
27 CFR 20.179 - Package identification number or serial number.
Code of Federal Regulations, 2010 CFR
2010-04-01
... number or serial number. 20.179 Section 20.179 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO... Package identification number or serial number. (a) Requirement. A dealer who fills packages with specially denatured spirits shall mark each package with a package identification number, in accordance with...
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}.
Cortical areas involved in Arabic number reading.
Roux, F-E; Lubrano, V; Lauwers-Cances, V; Giussani, C; Démonet, J-F
2008-01-15
Distinct functional pathways for processing words and numbers have been hypothesized from the observation of dissociated impairments of these categories in brain-damaged patients. We aimed to identify the cortical areas involved in Arabic number reading process in patients operated on for various brain lesions. Direct cortical electrostimulation was prospectively used in 60 brain mappings. We used object naming and two reading tasks: alphabetic script (sentences and number words) and Arabic number reading. Cortical areas involved in Arabic number reading were identified according to location, type of interference, and distinctness from areas associated with other language tasks. Arabic number reading was sustained by small cortical areas, often extremely well localized (<1 cm(2)). Over 259 language sites detected, 43 (17%) were exclusively involved in Arabic number reading (no sentence or word number reading interference detected in these sites). Specific Arabic number reading interferences were mainly found in three regions: the Broca area (Brodmann area 45), the anterior part of the dominant supramarginal gyrus (Brodmann area 40; p < 0.0001), and the temporal-basal area (Brodmann area 37; p < 0.05). Diverse types of interferences were observed (reading arrest, phonemic or semantic paraphasia). Error patterns were fairly similar across temporal, parietal, and frontal stimulation sites, except for phonemic paraphasias, which were found only in supramarginal gyrus. Our findings strongly support the fact that the acquisition through education of specific symbolic entities, such as Arabic numbers, could result in the segregation and the specialization of anatomically distinct brain areas.
Object-based neglect in number processing.
Klein, Elise; Moeller, Korbinian; Zinsberger, Daniela; Zauner, Harald; Wood, Guilherme; Willmes, Klaus; Haider, Christine; Gassner, Alfred; Nuerk, Hans-Christoph
2013-01-23
Recent evidence suggests that neglect patients seem to have particular problems representing relatively smaller numbers corresponding to the left part of the mental number line. However, while this indicates space-based neglect for representational number space little is known about whether and --if so --how object-based neglect influences number processing.To evaluate influences of object-based neglect in numerical cognition, a group of neglect patients and two control groups had to compare two-digit numbers to an internally represented standard. Conceptualizing two-digit numbers as objects of which the left part (i.e., the tens digit should be specifically neglected) we were able to evaluate object-based neglect for number magnitude processing.Object-based neglect was indicated by a larger unit-decade compatibility effect actually reflecting impaired processing of the leftward tens digits. Additionally, faster processing of within- as compared to between-decade items provided further evidence suggesting particular difficulties in integrating tens and units into the place-value structure of the Arabic number system.In summary, the present study indicates that, in addition to the spatial representation of number magnitude, also the processing of place-value information of multi-digit numbers seems specifically impaired in neglect patients.
Number processing pathways in human parietal cortex.
Santens, Seppe; Roggeman, Chantal; Fias, Wim; Verguts, Tom
2010-01-01
Numerous studies have identified the intraparietal sulcus (IPS) as an area critically involved in numerical processing. IPS neurons in macaques are tuned to a preferred numerosity, hence neurally coding numerosity in a number-selective way. Neuroimaging studies in humans have demonstrated number-selective processing in the anterior parts of the IPS. Nevertheless, the processes that convert visual input into a number-selective neural code remain unknown. Computational studies have suggested that a neural coding stage that is sensitive, but not selective to number, precedes number-selective coding when processing nonsymbolic quantities but not when processing symbolic quantities. In Experiment 1, we used functional magnetic resonance imaging to localize number-sensitive areas in the human brain by searching for areas exhibiting increasing activation with increasing number, carefully controlling for nonnumerical parameters. An area in posterior superior parietal cortex was identified as a substrate for the intermediate number-sensitive steps required for processing nonsymbolic quantities. In Experiment 2, the interpretation of Experiment 1 was confirmed with a connectivity analysis showing that a shared number-selective representation in IPS is reached through different pathways for symbolic versus nonsymbolic quantities. The preferred pathway for processing nonsymbolic quantities included the number-sensitive area in superior parietal cortex, whereas the pathway for processing symbolic quantities did not.
Interaction of Number Magnitude and Auditory Localization.
Golob, Edward J; Lewald, Jörg; Jungilligens, Johannes; Getzmann, Stephan
2016-01-01
The interplay of perception and memory is very evident when we perceive and then recognize familiar stimuli. Conversely, information in long-term memory may also influence how a stimulus is perceived. Prior work on number cognition in the visual modality has shown that in Western number systems long-term memory for the magnitude of smaller numbers can influence performance involving the left side of space, while larger numbers have an influence toward the right. Here, we investigated in the auditory modality whether a related effect may bias the perception of sound location. Subjects (n = 28) used a swivel pointer to localize noise bursts presented from various azimuth positions. The noise bursts were preceded by a spoken number (1-9) or, as a nonsemantic control condition, numbers that were played in reverse. The relative constant error in noise localization (forward minus reversed speech) indicated a systematic shift in localization toward more central locations when the number was smaller and toward more peripheral positions when the preceding number magnitude was larger. These findings do not support the traditional left-right number mapping. Instead, the results may reflect an overlap between codes for number magnitude and codes for sound location as implemented by two channel models of sound localization, or possibly a categorical mapping stage of small versus large magnitudes. © The Author(s) 2015.
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.
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
2008-01-15
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.
Riemann equation for prime number diffusion.
Chen, Wen; Liang, Yingjie
2015-05-01
This study makes the first attempt to propose the Riemann diffusion equation to describe in a manner of partial differential equation and interpret in physics of diffusion the classical Riemann method for prime number distribution. The analytical solution of this equation is the well-known Riemann representation. The diffusion coefficient is dependent on natural number, a kind of position-dependent diffusivity diffusion. We find that the diffusion coefficient of the Riemann diffusion equation is nearly a straight line having a slope 0.99734 in the double-logarithmic axis. Consequently, an approximate solution of the Riemann diffusion equation is obtained, which agrees well with the Riemann representation in predicting the prime number distribution. Moreover, we interpret the scale-free property of prime number distribution via a power law function with 1.0169 the scale-free exponent in respect to logarithmic transform of the natural number, and then the fractal characteristic of prime number distribution is disclosed.
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
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…
Alternating sums of reciprocal generalized Fibonacci numbers.
Kuhapatanakul, Kantaphon
2014-01-01
Recently Holliday and Komatsu extended the results of Ohtsuka and Nakamura on reciprocal sums of Fibonacci numbers to reciprocal sums of generalized Fibonacci numbers. The aim of this work is to give similar results for the alternating sums of reciprocals of the generalized Fibonacci numbers with indices in arithmetic progression. Finally we note our generalizations of some results of Holliday and Komatsu. Primary 11B37; secondary 11B39.
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.
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.
Generation of large prime numbers from a sequence of previous prime numbers
NASA Astrophysics Data System (ADS)
Samir, Brahim Belhaouari; Rezk, Youssef A. Y.
2012-09-01
A prime number is co-prime with all the primes as well. This paper utilizes this fact by generating larger prime numbers based on a set of smaller prime numbers. The prime numbers are ordered and each two consecutive primes are coupled to generate their co-prime number formula extending this process larger prime sequence is established. Will the process help us produce larger prime numbers faster and more efficiently? This paper investigates the described process.
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.
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...CM elliptic curve with CM field different from Q( √ −1), then the set of n for which the nth Fibonacci number Fn is elliptic Carmichael for E is of...number. 1. REPORT DATE 27 DEC 2014 2. REPORT TYPE 3. DATES COVERED 00-00-2014 to 00-00-2014 4. TITLE AND SUBTITLE On Fibonacci Numbers Which Are
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.
THE DISCOUNTED REPRODUCTIVE NUMBER FOR EPIDEMIOLOGY
Reluga, Timothy C.; Medlock, Jan; Galvani, Alison
2013-01-01
The basic reproductive number, , and the effective reproductive number, , are commonly used in mathematical epidemiology as summary statistics for the size and controllability of epidemics. However, these commonly used reproductive numbers can be misleading when applied to predict pathogen evolution because they do not incorporate the impact of the timing of events in the life-history cycle of the pathogen. To study evolution problems where the host population size is changing, measures like the ultimate proliferation rate must be used. A third measure of reproductive success, which combines properties of both the basic reproductive number and the ultimate proliferation rate, is the discounted reproductive number . The discounted reproductive number is a measure of reproductive success that is an individual’s expected lifetime offspring production discounted by the background population growth rate. Here, we draw attention to the discounted reproductive number by providing an explicit definition and a systematic application framework. We describe how the discounted reproductive number overcomes the limitations of both the standard reproductive numbers and proliferation rates, and show that is closely connected to Fisher’s reproductive values for different life-history stages PMID:19364158
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.
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.
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, 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,...
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.
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…
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. Copyright © 2016 Elsevier Ltd. All rights reserved.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 41 Public Contracts and Property Management 3 2010-07-01 2010-07-01 false Numbering. 105-1.109 Section 105-1.109 Public Contracts and Property Management Federal Property Management Regulations System (Continued) GENERAL SERVICES ADMINISTRATION 1-INTRODUCTION 1.1-Regulations System § 105-1.109 Numbering. ...
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…
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.
Hacking DNA copy number for circuit engineering.
Wu, Feilun; You, Lingchong
2017-07-27
DNA copy number represents an essential parameter in the dynamics of synthetic gene circuits but typically is not explicitly considered. A new study demonstrates how dynamic control of DNA copy number can serve as an effective strategy to program robust oscillations in gene expression circuits.
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…
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.
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.
46 CFR 169.541 - Number required.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 46 Shipping 7 2014-10-01 2014-10-01 false Number required. 169.541 Section 169.541 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) NAUTICAL SCHOOLS SAILING SCHOOL VESSELS Lifesaving and Firefighting Equipment Personal Flotation Devices § 169.541 Number required. Each vessel must be...
46 CFR 169.541 - Number required.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 46 Shipping 7 2013-10-01 2013-10-01 false Number required. 169.541 Section 169.541 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) NAUTICAL SCHOOLS SAILING SCHOOL VESSELS Lifesaving and Firefighting Equipment Personal Flotation Devices § 169.541 Number required. Each vessel must be...
46 CFR 169.541 - Number required.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 46 Shipping 7 2012-10-01 2012-10-01 false Number required. 169.541 Section 169.541 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) NAUTICAL SCHOOLS SAILING SCHOOL VESSELS Lifesaving and Firefighting Equipment Personal Flotation Devices § 169.541 Number required. Each vessel must be...
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.
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…
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.
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…
Tell Your Students to Take a Number!
ERIC Educational Resources Information Center
Bloor, Phoebe H.
1995-01-01
By giving each student a number to keep throughout the school year, teachers can maintain efficient classrooms. The paper describes this classroom management system, in which students apply for classroom jobs. The numbers can be used for homework and classroom assignments, organizing attendance, choosing teams, drawing names, and teacher files.…
Predicting the required number of training samples
NASA Technical Reports Server (NTRS)
Kalayeh, H. M.; Landgrebe, D. A.
1982-01-01
A criterion which measures the quality of the estimate of the covariance matrix of a multivariate normal distribution is developed. Based on this criterion, the necessary number of training samples is predicted. Experimental results which are used as a guide for determining the number of training samples are included.
New Numbers in Mathematics in South Africa
ERIC Educational Resources Information Center
Engelbrecht, Johann; Harding, Ansie
2009-01-01
This article is a follow-up of a study conducted in 2000 by the same authors on trends in numbers of mathematics majors at South African universities. Data from 12 universities for the 2000-2007 period is investigated. The previously observed trend of general and dramatic decrease in numbers of mathematics majors appears to have been reversed and…
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…
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…
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…
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].
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…
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...