NASA Technical Reports Server (NTRS)
Eckert, E R G; Diaguila, A J
1955-01-01
Report presents the results of an investigation conducted to study free-convection heat transfer in a stationary vertical tube closed at the bottom. The walls of the tube were heated, and heated air in the tube was continuously replaced by fresh cool air at the top. The tube was designed to provide a gravitational field with Grashof numbers of a magnitude comparable with those generated by the centrifugal field in rotating-blade coolant passages (10(8) to 10(13)). Local heat-transfer coefficients in the turbulent-flow range and the temperature field within the fluid were obtained.
Mark Kannapel; Sam Lowry; Anantha Krishnan; Ivan O. Clark; Paul V. Hyer; Edward J. Johnson
1997-01-01
The combined effect of Grashof and Reynolds numbers on the flow and heat transfer in a metal organic chemical vapor deposition (MOCVD) reactor is investigated both experimentally and numerically. Experimental data for pure hydrogen, helium, and nitrogen with induction heating are obtained at the Chemical Vapor Deposition Facility for Reactor Characterization at NASA Langley Research Center (LaRC). The test facility
NASA Astrophysics Data System (ADS)
Ooi, Seng-Keat
2005-11-01
Lock-exchange gravity current flows produced by the instantaneous release of a heavy fluid are investigated using 3-D well resolved Large Eddy Simulation simulations at Grashof numbers up to 8*10^9. It is found the 3-D simulations correctly predict a constant front velocity over the initial slumping phase and a front speed decrease proportional to t-1/3 (the time t is measured from the release) over the inviscid phase, in agreement with theory. The evolution of the current in the simulations is found to be similar to that observed experimentally by Hacker et al. (1996). The effect of the dynamic LES model on the solutions is discussed. The energy budget of the current is discussed and the contribution of the turbulent dissipation to the total dissipation is analyzed. The limitations of less expensive 2D simulations are discussed; in particular their failure to correctly predict the spatio-temporal distributions of the bed shear stresses which is important in determining the amount of sediment the gravity current can entrain in the case in advances of a loose bed.
NASA Technical Reports Server (NTRS)
Eckert, E R G; Diaguila, A J
1952-01-01
Local free-convection heat-transfer coefficients and temperature fields in the turbulent flow range were obtained within a vertical, stationary tube closed at the boom, heated along its walls, and having a length-to-diameter ratio of 5. Convective heat-transfer coefficients were correlated by the general relations for free-convection heat transfer. These coefficients, converted to dimensionless Nusselt numbers were 35 percent below known relations for vertical flat plates. Air temperature measurements within the tube indicated a thin boundary layer along the heated wall surface and unstable conditions in the air flow.
NSDL National Science Digital Library
2013-06-14
The purpose of this video tutorial is to review a couple ways in which we think about numbers. Thinking in terms of street numbers, money in bank accounts, and quantum particles (e.g. Bose-Einstein condensate) is contrasted with focusing on associating numbers with distinguishable manipulatives, as is more familiar in K-8 courses. This video concludes with a reminder that the symbol "infinity" is not, itself, a number.
NSDL National Science Digital Library
Jo Edkins
2006-01-01
This engaging web site contains information and interactive applets related to various number systems: Egyptian, Babylonian, Chinese, Greek, Roman, Mayan, and Arabic. Users learn the history and structure of each system as well as how to count and write numbers. The site also allows users to explore finger systems, calculating machines, other number bases, and "interesting numbers." A series of pages on data and graphs includes information and activities on gathering, analyzing, graphing and sorting data. (Because the section on the Arabic number system is so extensive, it is cataloged separately as a related resource.)
NSDL National Science Digital Library
Clarity Innovations, Inc.
2013-11-22
This iOS app helps students to visualize number sentences and create models for addition, subtractions, multiplication, and division. The number line can be adjusted to represent multiples of numbers from one to one hundred.
NSDL National Science Digital Library
TERC
2010-01-01
Combine logic and numbers in this game for all ages. Players start with a 10x10 grid of the numbers 1 to 100. One person chooses a secret number and announces the range in which it falls. Other players ask yes or no questions to identify the number. They cross out the numbers on the board that are no longer possibilities. The player who identifies the secret number wins. Available as a downloadable pdf and in Spanish.
NSDL National Science Digital Library
Michiel Doorman
2003-01-01
This interactive game develops fluency and flexibility with whole number operations. In each round the player is given 4 single-digit whole numbers, presented in the context of a factory. The player uses each number exactly once with the interactive calculator to arrive as close as possible to a given target number.
NSDL National Science Digital Library
Mitchell Mark
2013-03-10
This iOS app helps students make the transition from counting to number recognition by thinking of a number of objects in relation to five and ten. The app displays a set number of items from one to twenty in ten frames then flashes away after the preset number of seconds. The user must identify the number that was shown on the ten frames.
NSDL National Science Digital Library
Miss.Cochran
2008-03-26
You will be working with numbers in all sorts of ways. First, you will play cop by picking numbers based on their divisibility. Then you will be adding and subtracting fractions in two fun and exciting games. First, as a cop, you will catch numbers that are divisible by which ever number you pick, avoinding crashing into non-divisible numbers. Number Cop-Divisibility Now, play Fishy Fractions! and help feed the seagull by practicing adding fractions. Make sure you read the instructions before getting started! Make sure to simplify your answers! After you ...
ERIC Educational Resources Information Center
Rich, Andrew
2008-01-01
The leftist number system consists of numbers with decimal digits arranged in strings to the left, instead of to the right. This system fails to be a field only because it contains zerodivisors. The same construction with prime base yields the p-adic numbers.
M. R. Schroeder
1989-01-01
Number theory, an abstract branch of mathematics that deals with relationships between whole numbers, has provided highly useful answers to numerous real-world problems. The author briefly reviews earlier uses of number theory and then examines recent applications to music, cryptography, and error-correction codes
NSDL National Science Digital Library
Mrs. Black
2007-10-03
Students will practice counting to 100 and making numbers with base ten blocks Let\\'s have some fun with math! First, practice counting to 100. Listen to the instructions on this website. Count to 100 Now that you have worked on counting to 100, let\\'s make some numbers! Use the base ten blocks to make the numbers shown on the screen! Base Ten Blocks Great work! The next ...
Number Grids and Number Triangles
NSDL National Science Digital Library
Quincy Brown
Practice counting, counting by tens, place value, and fact families by entering your answers into the blank boxes; click the big blue and green buttons to check your work. Each of the five levels of Number Grid activities displays a section of a matrix containing a set of of consecutive whole numbers. A move from one number to the next within a row corresponds to a change of one; a move from one number to the next within a column refers to a change of ten. The three levels of Number Triangle activities provide practice with fact families and inverse relationships through flash cards. An addition/subtraction Number Triangle has two addends and a sum; a multiplication/division Number Triangle has two factors and a product.
NSDL National Science Digital Library
2012-06-26
In this online puzzle game, learners need to choose a path from a starting number to a goal number. Along the path are simple operations (e.g. add 1, subtract 2, multiply by 2) to change the current number to a new number. This is a good challenge for young learners. When learners set up a free account at Kinetic City, they can answer bonus questions at the end of the activity as a quick assessment. As a larger assessment, learners can complete the Bug Blaster game after they've completed several activities.
NSDL National Science Digital Library
2014-01-01
This interactive Flash version of the familiar game Concentration helps students develop number sense by matching various symbolic and pictorial representations of single digit numbers. The scoring rewards a systematic strategy over random guessing. The resource includes teacher notes with suggestions for implementation and differentiation, discussion questions, and printable sets of cards (pdf).
NSDL National Science Digital Library
John Brignell, Professor Emeritus from the Department of Electronics & Computer Science at the University of Southampton, is the author of this informal website "devoted to the monitoring of the misleading numbers that rain down on us via the media." Brignell says he aims to "nail" a few of the "Single Issue Fanatics (SIFs), politicians, bureaucrats, quasi-scientists (junk, pseudo- or just bad)," who use misleading numbers to write catchy articles or who try to keep numbers away from public notice. Since April 2000, he has been posting a "number of the month" as well as a "number for the year," which offer his commentary on media usage of misleading numbers and explanations for why the numbers are misleading. He also posts book reviews and an extensive list of online resources on statistics and statistics education. The FAQ section includes answers to some interesting questions, such as "Is there such a thing as average global temperature?" and some more basic questions such as "What is the Normal Distribution and what is so normal about it?" The Bits and Pieces section includes a variety of short articles on statistics and his definitions for some terms he uses on the website. Visitors are also invited to join the discussion forum (complete with a few advertisements) and view comments by others who want to discuss "wrong numbers in science, politics and the media." A few comments sent to Brignell and his responses are also posted online. This site is also reviewed in the February 11, 2005_NSDL MET Report_.
... tooth on the lower right would be T. Palmer Notation Method Adults In this system, the mouth ... the upper right quadrant. Children In children, the Palmer Notation System uses uppercase letters instead of numbers. ...
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…
NSDL National Science Digital Library
Ms. Painter
2006-10-27
Perform operations with whole numbers, simple fractions, and decimals. 1. Begin your work at the Comparing Fractions website. Complete 10 problems. 2. When you are finished Comparing Fractions, I\\'m sure you will hunger for more! Click on the website, Who Wants Pizza? These activities are sure to fill your brain with nutritious information. 3. Explore Egyptian ...
Enclosed Gas and Liquid with Nonuniform Heating from Above
NASA Technical Reports Server (NTRS)
Aggarwal, S. K.; Iyengar, J.; Sirignano, W. A.
1986-01-01
Buoyancy-driven flows of gases above liquids in a common enclosure with nonuniform heating from above are studied via finite-difference solutions of the governing equations. Unsteady solutions are calculated, and steady-state solutions are sought as asymptotes. Grashof numbers between 10 to the 3rd and 10 to the 8th are examined, and multicellular circulatory flow structure is found at the higher Grashof numbers. Convective transport dominates for higher Grashof numbers, while conductive transport is the primary mechanism at the lower Grashof numbers. Surface tension has a major effect upon the gas flow field only at lower Grashof numbers but, since conduction dominates there, it does not significantly affect transport.
COMPLEX NUMBERS 1. Definition of complex numbers
La Rosa, Andres H.
COMPLEX NUMBERS 1. Definition of complex numbers Complex conjugate, Magnitude Operations Addition, multiplication, reciprocal number 2. Representation of complex numbers in polar complex variable #12;2.2.A Complex numbers #12;#12;3 #12;4 #12;In short, Anytime we write Ae j we
3. Complex Numbers 17 3 Complex Numbers
Givental, Alexander
3. Complex Numbers 17 3 Complex Numbers Law and Order Life is unfair: The quadratic equation x2 - 1 solutions to the equation. This is how complex numbers could have been invented. More formally, complex numbers a and b are called respectively the real part and imagi- nary part of the complex number z
ERIC Educational Resources Information Center
Griffin, Sharon
2004-01-01
Educators define number sense as a set of conceptual relationships between quantities and numerical symbols. The instructional principals of teaching number sense and number worlds program are mentioned.
Applications of Fibonacci Numbers
Benjamin, Arthur T.
Applications of Fibonacci Numbers Volume 9 KLUWERACADEMIC PUBLISHERS #12;Applications of Fibonacci Numbers I Volume 9 Proceedingsof The Tenth International Research Conference on Fibonacci Numbers the presence of both Fibonacci numbers and binomial coefficients demands a combinatorial explanation. Beginning
Complex numbers Quaternions Imaginary numbers and Quaternions Katrin Leschke University of Leicester June 29, 2010 Katrin Leschke Imaginary numbers and Quaternions #12;Complex numbers Quaternions Imaginary numbers and Quaternions #12;Complex numbers Quaternions Vectors in 2dspace A vector in 2d
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…
NASA Astrophysics Data System (ADS)
Moestam, Robert; Davidson, Lars
2005-07-01
Direct numerical simulations of pressure-driven flow between two infinite horizontal plates with a stabilizing temperature difference imposed on the plates are presented, for different Grashof numbers. A thermocline-like solution is obtained. The thermocline decorrelates velocity fluctuations which results in a high mean flow velocity. Temperature fluctuations decorrelate from the vertical velocity fluctuations and it is found that although ?T'2? and ??'2? increase with Grashof number, ??'T'? decreases. It is argued from the simulations that this behavior is due to internal gravity waves. It is also found that the demands on the size of the computational box increase with Grashof number.
NSDL National Science Digital Library
2012-01-01
This activity for the interactive white board (free access with registration) allows the learner to practice comparing numbers. Two numbers are given and students identify those numbers inbetween the numbers by dragging them from below into the shaded window. A number line is provide as a means for the learner to check their choices.
NSDL National Science Digital Library
Mrs. Estes
2007-11-02
Let\\'s learn about numbers! How many Fish? Count the Fish Let\\'s count! How many... Matching is fun! Match the number How well do I really know these numbers? Getting to know the numbers Counting the kids Kids on the bus We love Ants! Count the ants Flying into the univerise of numbers Rocket ...
MARIA SABITOVA
2004-01-01
We generalize a theorem of D. Rohrlich concerning root numbers of elliptic curves over the field of rational numbers. Our result applies to curves of all higher genera over number fields. Namely, under certain conditions which naturally extend the conditions used by D. Rohrlich, we show that the root number associated to a smooth projective curve over a number field
Number Systems Introduction & Objectives
Bouhraoua, Abdelhafid
number system that was in common use is the decimal number system ( ) which has a total of 10 digits (0 to the more familiar decimal system Â· In this lesson, you will learn: What is meant by a weighted number system. Basic features of weighted number systems. Commonly used number systems, e.g. decimal, binary
Occupancy Numbers in Testing Random Number Generators
A. Figotin; A. Gordon; J. Quinn; N. Stavrakas; S. Molchanov
2002-01-01
Abstract. The classical occupancy,problem,where n balls are placed in N cells is used for testing of random,number generators. We show that the statistics of appropriately chosen occupancy numbers,are incompatible with the statistics of many,pseudorandom,number,generators (PRNGs) evenif they are trun cated. More thanthat, the in compatibility shows up onrelatively small samples long before the period of the PRNG is reached. We
Representing decimal numbers on the number line
NSDL National Science Digital Library
National Library of Virtual Manipulatives
2010-03-02
The user can choose decimals with explore, practice, assess on the screen. Using explore, the student drags the point to the number line and the decimal value of that point is given. Using practice, the student drags the point to the location of the designated decimal number. Zooming in produces lines representing whole numbers, tenths, hundredths, and thousandths in succession. The zooming allows the student to choose the correct point, rather than the approximate location. The series of lines with successively smaller place values is a visual model for extending the base ten system to decimal numbers.
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,…
Number Sense Series: Developing Early Number Sense
NSDL National Science Digital Library
Jenni Way
The author of this one-page article discusses early number sense and how it develops. She provides research background and suggests teaching strategies that promote early number sense, including instructions for simple games using dot cards. The article includes a list of references and a link to a follow-up article, "A Sense of 'ten' and Place Value" (cataloged separately).
Lim, Chjan C.
Generation. The problem. Essential to a Monte Carlo algorithm is a good random number generator randomly selected numbers are multiplied together, and the faulty random number generator produced only by four. Unfortunately, there do not exist any known truly random number generators; despite
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…
DIDIER DUBOIS; HENRI PRADE
1978-01-01
A fuzzy number is a fuzzy subset of the real line whose highest membership values are clustered around a given real number called the mean value ; the membership function is monotonia on both sides of this mean value. In this paper, the usual algebraic operations on real numbers are extended to fuzzy numbers by the use of a fuzzification
Spooky Sequences- Square Numbers
NSDL National Science Digital Library
Mark Cogan
2002-01-01
This interactive Flash game helps students recognize and generate the sequence of square numbers, and also to discover the pattern of differences between them. The applet displays a sequence of six consecutive square numbers with one number missing. The player provides the missing number to "send the ghosts back to the haunted house." Each game consists of five sequences to complete.
NSDL National Science Digital Library
Mrs. Williams
2008-04-03
Numbers, Matching and Addition Let\\'s count How many chicks are there? Great! Now lets try Number Match Let\\'s try Seahorse Counting Now Concentrate on Concentration Number Match Addition Practice Quick Adding and Robot Addition Make the number with Base 10 ...
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…
Jailton C. Ferreira
2002-02-14
The infinite numbers of the set M of finite and infinite natural numbers are defined starting from the sequence 0\\Phi, where 0 is the first natural number, \\Phi is a succession of symbols S and xS is the successor of the natural number x. The concept of limit of the natural number n, when n tends to infinite, is examined. Definitions and theorems about operations with elements of M, equivalence and equality of natural numbers, distance between elements of M and the order of the elements are presented.
Harbour, Daniel, 1975-
2003-01-01
The dissertation argues for the necessity of a morphosemantic theory of number, that is, a theory of number serviceable both to semantics and morphology. The basis for this position, and the empirical core of the dissertation, ...
Calgary, University of
UCGE Reports Number 20378 Department of Geomatics Engineering Integration of UWB Ranging and GPS OF GEOMATICS ENGINEERING CALGARY, ALBERTA DECEMBER 2012 © Yuhang Jiang 2012 #12;UCGE Reports Number 20378
NSDL National Science Digital Library
TERC
2010-01-01
In this activity, learners will ask yes-no questions to identify a secret number (similar to Twenty Questions). Combine logic and numbers in this game for all ages. One person chooses a secret number and announces the range in which it falls, for instance: “I’m thinking of a number between 1 and 50.” Other players ask yes or no questions to identify the number. The player who identifies the secret number wins. This game is easy to adapt to different ages: young children can ask and reason about “more than” and “less than” (Is it less than 7? Is there a 1 in the 10’s place)? and older ones can ask about multiples, factors, or number relationships (Is it a multiple of 3? Is it a square number?). Available as a web page and downloadable pdf.
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.
NSDL National Science Digital Library
This problem offers a simple context to begin an exploration of the properties of numbers and to make conjectures about those properties. Learners explore the sums of consecutive numbers and whether all positive numbers from 1-30 can be written as the sum of two or more consecutive numbers. The Teachers' Notes page offers suggestions for implementation, key discussion questions, ideas for extension and support.
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…
NSDL National Science Digital Library
ROBIN MARMITT
2012-09-03
The students will receive explicit instruction from the teacher on the definition of decomposing a number and how to represent a decomposition with manipulatives, drawings, and equations. The students will use linking cubes to reflect numbers from 11-19, and to show their understanding of how to decompose a number. Students will record decompositions as an equation.
NSDL National Science Digital Library
Olsson, Martin
This course provides an introduction to number theory, including topics such as prime numbers, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions and elliptic curves. The materials include lecture notes, exams and assignments with solutions. MIT presents OpenCourseWare as free educational material online. No registration or enrollment is required to use the materials.
NSDL National Science Digital Library
Jo Edkins
2010-01-01
This is a collection of simple interactive activities to help young children practice early number skills. They use visual representations to develop counting and subitizing skills, number sense, place value concepts, and basic whole number operations (addition, subtraction, doubling). A teacher page summarizes the purpose and functions of each activity.
Donald E. Knuth
1960-01-01
For centuries the decimal number system reigned supreme, except, perhaps, among the Mayan Indians, until the advent of digital computers brought the binary and octal systems into the limelight. This paper introduces another number system which may prove useful for manipulating complex numbers on machines.
Approximating the domatic number
Uriel Feige; Magnús M. Halldórsson; Guy Kortsarz
2000-01-01
Abstract. A set of vertices in a graph is a dominating set if every vertex outside the set has a neighbor in the set. The domatic number,problem is that of partitioning the vertices of a graph into the maximum number of disjoint dominating sets. Let n denote the number of vertices, ? the minimum degree, and ? the maximum degree.
Approximating the Domatic Number
Uriel Feige; Magnús M. Halldórsson; Guy Kortsarz; Aravind Srinivasan
2002-01-01
A set of vertices in a graph is a dominating set if every vertex outside the set has a neighbor in the set. The domatic number problem is that of partitioning the vertices of a graph into the maximum number of disjoint dominating sets. Let n denote the number of vertices, ? the minimum degree, and ? the maximum degree.
NSDL National Science Digital Library
David Joiner
The process of creating numbers that simulate randomness on a computer is known as pseudorandom number generation. The "pseudo" in pseudo random refers to the fact that if you use a rule to generate a number, it is by definition not random, though it may appear so, and be close enough to random for all practical purposes.
Convoluted convolved Fibonacci numbers
Pieter Moree
2003-01-01
The convolved Fibonacci numbers F_j^(r) are defined by\\u000a (1-z-z^2)^{-r}=\\\\sum_{j>=0}F_{j+1}^(r)z^j. In this note some related numbers\\u000athat can be expressed in terms of convolved Fibonacci numbers are considered.\\u000aThese numbers appear in the numerical evaluation of a certain number\\u000atheoretical constant.\\u000a This note is a case study of the transform {1\\/n}\\\\sum_{d|n}mu(d)f(z^d)^{n\\/d},\\u000awith f any formal series and mu the Moebius function),
Curvature and Tachibana numbers
Stepanov, Sergey E [Finance Academy under the Government of the Russian Federation, Moscow (Russian Federation)
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.
NSDL National Science Digital Library
This problem provides an opportunity to introduce a visual way of representing operations on unknown numbers to help lead students to using a symbolic representation. Learners are asked to think of a number and then through an interactivity are given a sequence of operational instructions to follow which leads all students to the same final number. The Teachers' Notes page offers suggestions for implementation, key discussion questions, ideas for extension and support.
NSDL National Science Digital Library
This problem provides an opportunity to introduce the concept of representing operations on unknown numbers algebraically and leads to work on inverse operations. Students are asked to think of a number, follow a sequence of computational instructions and finally to enter the result into the "machine." Students explore how the "machine" works out the starting number. The Teachers' Notes page offers rationale, suggestions for implementation, discussion questions, ideas for extension and support.
Complex Numbers and Trigonometry
NSDL National Science Digital Library
Alexanderson, Gerald L.
Complex numbers have applications in many applied sciences. This online text begins with an introduction to trigonometry, which serves as a starting point for additional discussion about complex numbers (also known as imaginary numbers). The drawings and figures are the only notable downside to this excellent resource, because many of them are somewhat crude; however, they are still fairly easy to follow. The book can be read online or downloaded for offline viewing.
Interactive Fraction Number Lines
NSDL National Science Digital Library
Michael Green
2012-05-25
In this lesson students make models of fractions, including a human number line. Using a number line, students develop conceptual understanding of fractions. Students use the number line to represent and compare fractions less than one. The activities are engaging and include full participation/engagement of all students. The fractions are limited to positive fractions less than one with a denominator of 2 or 4 including 0 and 1 whole.
Estimating quantum chromatic numbers
Vern I. Paulsen; Simone Severini; Daniel Stahlke; Ivan G. Todorov; Andreas Winter
2014-07-25
We develop further the new versions of quantum chromatic numbers of graphs introduced by the first and fourth authors. We prove that the problem of computation of the commuting quantum chromatic number of a graph is solvable by an SDP and describe an hierarchy of variants of the commuting quantum chromatic number which converge to it. We introduce the tracial rank of a graph, a parameter that gives a lower bound for the commuting quantum chromatic number and parallels the projective rank, and prove that it is multiplicative. We describe the tracial rank, the projective rank and the fractional chromatic numbers in a unified manner that clarifies their connection with the commuting quantum chromatic number, the quantum chromatic number and the classical chromatic number, respectively. Finally, we present a new SDP that yields a parameter larger than the Lov\\'asz number and is yet a lower bound for the tracial rank of the graph. We determine the precise value of the tracial rank of an odd cycle.
Honors problem 1: Complex numbers. Arithmetic of complex numbers
Leininger, Christopher J.
Honors problem 1: Complex numbers. Arithmetic of complex numbers Recall that the complex numbers identify the complex numbers with the set of linear polynomials with real coefficients). The numbers as a subset of the complex numbers by identifying the real number a with a+0i. The imaginary numbers
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…
NSDL National Science Digital Library
Grinstead, Charles M.
Created by Charles M. Grinstead and J. Laurie Snell of Dartmouth College, this website is part of an online statistics textbook. Topics include: (1) Law of Large Numbers for Discrete Random Variables, (2) Chebyshev Inequality, (3) Law of Averages, (4) Law of Large Numbers for Continuous Random Variables, (5) Monte Carlo Method. There are several examples and exercises that accompany the material.
Hyperquarks and generation number
Buchmann, Alfons J.; Schmid, Michael L. [Institut fuer Theoretische Physik, Universitaet Tuebingen, Auf der Morgenstelle 14, D-72076 Tuebingen (Germany)
2005-03-01
In a model in which quarks and leptons are built up from two spin-(1/2) preons as fundamental entities, a new class of fermionic bound states (hyperquarks) arises. It turns out that these hyperquarks are necessary to fulfill the 't Hooft anomaly constraint, which then links the number of fermionic generations to the number of colors and hypercolors.
NSDL National Science Digital Library
Ms. Hirst
2007-10-12
Identify and use whole numbers up to 100 Here are some links to help you learn more about counting Teach R Kids Math counting and number activity themes Here are some games to help you practice your counting counting cherrios Bunny Count Connect the Dots Game ...
Hoffmeister, Thomas S.
to sign the grant agreement or to commit the organisation for this project Family name First name(s) Title/technological aspects in this project Family name First name(s) Title 34 Gender 35 (Female F / Male M) PositionA2.1: Who we are Project number 1 Project acronym 2 Participant number in this project 10
NSDL National Science Digital Library
Visually explore counting and place value with different number bases, from base 2 to base 16, and up to the hundreds place using a clock like interface. The activity also allows you to look at the numbers on the clock in base 10 or in your other chosen base to explore the relationship between those values.
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)
NSDL National Science Digital Library
2010-01-01
Using this interactive fraction number line, students can identify and locate equivalent fractions as well as compare fractions. They can move the mouse to the left or right and "mark" fractions on the number line. A section called "Which is Larger?" provides examples of fraction pairs to compare.
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…
Generalized binary number systems
Attila Kovacs
The object of this note is to analyze canonical radix expansions in algebraic number fields, especially using 0 and 1 as digits. We shall prove that infinitely many such binary number system exist and we enumerate all of them up to degree 8, where degree means the degree of the defining polynomial. In general, we prove that there are infinitely
Numbers, taxonomy, and judgment
W. T. Williams
1967-01-01
From the earliest times man has endowed numbers with magical properties. We all know that misfortunes come in threes, that the seventh son of a seventh son has remarkable gifts, and that it is unlucky to sit down thirteen at table. Even in more erudite spheres the tendency is discernible: how else can we explain the interest in perfect numbers,
Unrecognizable Sets of Numbers
Minsky, Marvin
1964-11-01
When is a set A of positive integers, represented as binary numbers, "regular" in the sense that it is a set of sequences that can be recognized by a finite-state machine? Let pie A(n) be the number of members of A less ...
South Australia, University of
Teachers Name Contact Number Email School Year Level of Students Number of students attending Lakes on Thursday 19 September 2013, 1.00--3.30pm. Workshops are between 1.00 and 3.00pm, with a free Lakes campus Switch On: Mawson Lakes--Registration Form #12;
Hypercomplex numbers Johanna Ramo
Wright, Francis
ordinary numbers. You can add, subtract, multiply and divide them, and on top of that, do some nice things but kept them secret. They made their living by challenging each other to public contests of 1 #12;problem kept secret. The mathematicians of the time did not like negative numbers because to them they had
Honors problem 1: Complex numbers. Arithmetic of complex numbers
Leininger, Christopher J.
Honors problem 1: Complex numbers. Arithmetic of complex numbers Recall that the complex numbers we can identify the complex numbers with the set of linear polynomials with real coefficients as a subset of the complex numbers by identifying the real number a with a + 0i. The imaginary numbers
Conversion Between Different Number Systems Positional number systems
Simonson, Shai
Conversion Between Different Number Systems Positional number systems Our decimal number system digits are used in both numbers. (Although we are accustomed to our decimal number system, which of each position correspond to powers of the base of the number system. So for our decimal number system
NSDL National Science Digital Library
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Malik is given a list of numbers: 1 \\ \\ 5 \\ \\ 10 \\ \\ 50 \\ \\ 100 He wants to include the following numbers so all numbers will be listed in order from l...
Introduction to Negative Numbers
NSDL National Science Digital Library
WNET.org
2006-01-01
This lesson plan based on a Cyberchase activity, first addresses a common misconception: starting measurement from 1 instead of 0. Then, it introduces negative numbers by extending a number line beyond 0 in the negative (left) direction. It is motivated by the Cyber Squad’s mission to find the captured Cyberchase Council on a particular floor of a tall building as seen in two quicktime videos: “Importance of the Origin" and "Inventing Negative Numbers" (each are cataloged separately). In addition to the learning activity, other support materials are included: handouts, assessments and answer keys.
NSDL National Science Digital Library
2012-01-01
This activity for the interactive white board (free access with registration) allows a teacher to create an arithmetic sequence for students to watch being built as the sequence of numbers moves along a conveyor. Learners must determine the pattern being used so when the belt randomly stops, the missing number in the sequence can be dragged/ dropped into its place. The teacher sets the start number (0-19), the interval or common difference (1-10) and if the sequence will count up or down. This last option provides an opportunity to display patterns with integers.
D. R. Mack
1990-01-01
Fibonacci numbers are explained, and some of the many manifestations of the Fibonacci series in nature are described. These range from the so-called golden spiral to the Penrose tiling patterns that describe the structure of quasicrystals
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
Anthony, Glenda J.; Walshaw, Margaret A.
2004-01-01
This article discusses the challenges students face in making sense of zero as a number. A range of different student responses to a computation problem involving zero reveal students' different understandings of zero.
Fluctuations in recoil numbers
NASA Astrophysics Data System (ADS)
Winterbon, K. B.
The variance of the number of high-energy recoils produced in a cascade is calculated in the power-cross-section approximation. These' recoils have initial energy greater than some specified threshold value, which in turn is greater than a displacement energy. Displacement energy is neglected in this calculation. This distribution of high-energy-recoil number is wider than the Kinchin-Pease distribution but narrower than a Poisson distribution: the variance is (asymptotically) proportional to the number of recoils for all three, and the proportionality constant for the recoil number is greater than the Kinchin-Pease constant but less than unity. Both the asymptotic value of the variance and the energy dependence are obtained. These quantities should be of interest in the study of recoil implantation.
Ravi P. Agarwal; Kanishka Perera; Sandra Pinelas
\\u000a The problem of complex numbers dates back to the 1st century, when Heron of Alexandria (about 75 AD) attempted to find the\\u000a volume of a frustum of a pyramid, which required computing the square root of 81-144 (though negative numbers were not conceived in the Hellenistic world). We also have the following quotation from Bhaskara\\u000a Acharya (working in 486 AD),
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…
Matthias Beck; Moshe Cohen; Jessica Cuomo; Paul Gribelyuk
2002-01-01
We define a magic square to be a square matrix whose entries are nonnegative\\u000aintegers and whose rows, columns, and main diagonals sum up to the same number.\\u000aWe prove structural results for the number of such squares as a function of the\\u000asize of the matrix and the line sum. We give examples for small sizes and show\\u000asimilar
Definitions Algebra of complex numbers
Lega, Joceline
Definitions Algebra of complex numbers Polar coordinates form of complex numbers Check your knowledge Review of Complex Numbers Definitions, Algebra of complex numbers, Polar coordinates Review of Complex Numbers #12;Definitions Algebra of complex numbers Polar coordinates form of complex numbers Check
7 CFR 29.9205 - Identification number (farm serial number).
Code of Federal Regulations, 2011 CFR
2011-01-01
...2011-01-01 2011-01-01 false Identification number (farm serial number). ...Statement and Regulations Governing the Identification and Certification of Nonquota Tobacco...Area Definitions § 29.9205 Identification number (farm serial number)....
7 CFR 29.9205 - Identification number (farm serial number).
Code of Federal Regulations, 2010 CFR
2010-01-01
...2010-01-01 2010-01-01 false Identification number (farm serial number). ...Statement and Regulations Governing the Identification and Certification of Nonquota Tobacco...Area Definitions § 29.9205 Identification number (farm serial number)....
NSDL National Science Digital Library
Have you ever wondered about the mathematics behind the idea of "six degrees of separation?" The Erd's Number Project offers several fairly comprehensive lists of co-author relationships to elaborate (with a bit of humor) studies of the dynamics involved in "the collaboration graph," which the website says is "a 'real-life' fairly large graph for combinatorialists to study." The co-author relationship list begins with the Hungarian mathematician Paul Erd's and branches outward, so that anyone who co-authored with Erd's is assigned Erd's number 1 and anyone who co-authored with an Erd's number 1 is assigned the Erd's number 2, and so on. The website offers some suggestions for how the lists might be used, including finding your own Erd's number, testing algorithms, or just getting a sense of the different areas of mathematics represented by Erd's' co-authors. Visitors can also learn more about Erd's, read articles about collaboration in mathematics, or browse through the websites which are linked from the co-author data lists.
Expansion of rational numbers in Mobius number systems Petr Kurka
Kurka, Petr
Expansion of rational numbers in M¨obius number systems Petr K°urka Center for Theoretical Study- tions. We say that a M¨obius number system is rational, if it represents rational numbers by periodic. In the present paper we study expansions of rational numbers in the integer M¨obius number systems, whose
Multiplying Whole Numbers & Fractions
NSDL National Science Digital Library
2013-01-01
In this 9-minute video, Amy Spies shows her 4th grade class working through a problem multiplying a fraction by a whole number. During the lesson Amy realized that the students were not pulling out the knowledge that she had intended. She then revised the lesson and gave them examples and non-examples and through discussion had them make the connection between repeated addition and multiplying a fraction by a whole number. Students also gained a deeper understanding of the meaning of the numerator and denominator in these repeated addition problems.
Generalized van der Waerden numbers
Bruce M. Landman
1986-01-01
Certain generalizations of arithmetic progressions are used to define numbers analogous to the van der Waerden numbers. Several exact values of the new numbers are given, and upper bounds for these numbers are obtained. In addition, a comparison is made between the number of different arithmetic progressions and the number of different generalized arithmetic progressions.
Activated Immunoaffinity Catalog Numbers
Lebendiker, Mario
Activated Immunoaffinity Supports Catalog Numbers 153-6046 Affi-Gel® 10 Gel 153-6052 Affi-Gel 15 Gel 153-6098 Affi-Gel 10 and 15 Gel #12;Table of Contents Section 1 Introduction ................................. 19 Section 6 Monitoring For Protein Coupling .. 22 Section 7 Troubleshooting
Lebendiker, Mario
Affi-Gel® Protein A MAPS® II Kit Instruction Manual Catalog Number 153-6159 For Technical Service;Introduction The Affi-Gel protein A MAPS II (Monoclonal Antibody Purification System) kit provides a dramatic improvement in protein A-agarose methods for purification of mouse IgG1 from ascites fluid. When Affi-Gel
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…
Virinder S Parmar; Amitabh Jha; Kirpal S Bisht; Poonam Taneja; Sanjay K Singh; Ajay Kumar; Denmarkpp; Rajni Jain; Carl E Olsen
1999-01-01
Yew trees, taxonomically classified under the genus Taxus, are sources of a number of physiologically active compounds of different classes. Taxane derivatives with various carbon skeletons, lignans, flavonoids, steroids and sugar derivatives have been isolated from different Taxus species. Compounds isolated from the genus Taxus between 1908 and December 1997 have been comprehensively reviewed.
Isidore Springer
1915-01-01
A topic rarely mentioned in experiments on Arithmetic is that of the teaching of denominate numbers. This topic usually appears about the sixth year of the child's school life, receives very little attention from the makers of text books, and up to the present time has been hardly noticed in the ever increasing volume of arithmetical investigations. The following is
Singh, Anurag
Numbers, Groups and Cryptography Gordan Savin #12;#12;Contents Chapter 1. Euclidean Algorithm 5 1. Euclidean Algorithm 5 2. Fundamental Theorem of Arithmetic 9 3. Uniqueness of Factorization 14 4. Efficiency of the Euclidean Algorithm 16 Chapter 2. Groups and Arithmetic 21 1. Groups 21 2. Congruences 25 3. Modular
Hacon, Christopher
Numbers, Groups and Cryptography Gordan Savin #12;#12;Contents Chapter 1. Euclidean Algorithm 5 1. Euclidean Algorithm 5 2. Fundamental Theorem of Arithmetic 9 3. Uniqueness of Factorization 13 4. Efficiency of the Euclidean Algorithm 16 Chapter 2. Groups and Arithmetic 19 1. Groups 19 2. Congruences 23 3. Modular
IN NUMBERS: Biostatistics Faculty
Grether, Gregory
STRENGTH IN NUMBERS: Biostatistics Faculty Are in Great Demand in the SPH and Beyond of the school's Department of Biostatistics faculty (clockwise starting from lower left): Drs. Catherine Sugar specialize in other aspects of clinical trials design. With this expertise, the Department of Biostatistics
Proposal Number: Competition title
Proposal Number: Competition title: Year: PROPOSAL - TITLE PAGE PROJECT TITLE: Program: TitleName Init LastName Co-Project Leader: FirstName Init LastName Fax: Email: Position/Title: FirstName Init, State, Zip: Phone: Fax: Email: Position/Title: FINANCIAL SUMMARY: Project Duration: Federal Funds: (e
Giuseppe Pirillo
1997-01-01
Let ? be the golden ratio (?5 + 1)\\/2, fn the nth Fibonacci finite word and f the Fibonacci infinite word. Let r be a rational number greater than (2 + ?)\\/2 and u a nondashempty word. If ur is a factor of f, then there exists n ? 1 such that u is a conjugate of fn and, moreover,
NSDL National Science Digital Library
Ms. Allen
2010-10-09
Play the counting games below. First, help Curious George juggle the fruit in the Curious George Juggling game. Next, count the fish in the Fish Counting game. Then, try to catch the correct number of fish in the net. Go Fishing! ...
NSDL National Science Digital Library
David Liao
Why do quantitative biologists sometimes claim that mRNA copy numbers are Poisson distributed in simple models of gene transcription? The first video segment addresses this question under the simplifying assumption that mRNA degradation occurs after a well-defined, deterministic lifetime, and the second segment illustrates the same basic concept for the more realistic situation in which degradation is stochastic.
Facultad De Ciencias Exactas; Gregory Chaitin; Sergio Daicz I; Vernica Becher
2001-01-01
In his celebrated 1936 paper Turing defined a machine to becircular iff it performs an infinite computation outputting only finitelymany symbols. We define ( as the probability that an arbitrary machinebe circular and we prove that is a random number that goes beyond$2, the probability that a universal self alelimiting machine halts. Thealgorithmic complexity of c is strictly greater than
Calgary, University of
together. To compute the remaining errors, the receiver clock error must be removed, which is possibleUCGE Reports Number 20162 Department of Geomatics Engineering Temporal Characteristics of GPS Error://www.geomatics.ucalgary.ca/links/GradTheses.html) by Michael C. Olynik July 2002 #12;THE UNIVERSITY OF CALGARY TEMPORAL CHARACTERISTICS OF GPS ERROR SOURCES
NSDL National Science Digital Library
Free online SAT, ACT, and GRE test preparation courses. Register for tutorials and practice sessions that dynamically adapt to performance, providing customized feedback for every response and monitoring overall student progress in the coaching system. Number2.com also offers a vocabulary builder, question of the day, and word of the day; and links to financial aid, college application, and career planning resources.
NSDL National Science Digital Library
2010-09-21
This applet allows students to freely build shapes by stacking cubes and "explore the relation between a building (house) consisting of cubes and the height numbers representing the height of the different parts of the building." This exercise helps students visualize and understand the concepts of volume and three-dimensional, measurable space.
Quasar number density evolution
J. T. Stocke; S. C. Perrenod
1981-01-01
A simple model of quasar number density evolution is presented based on the occurrence of quasar-like radio galaxies (i.e., strong optical emission lines and type 2 radio morphology) exclusively in regions of low galaxy and intergalactic medium (IGM) density. This suggests a limit for the IGM density of 10 to the -4th (+ or - 1) per cu cm below
Calgary, University of
sensitivity GPS receiver involved hard- ware simulations and extensive field testing in a forest, urbanUCGE Reports Number 20176 Department of Geomatics Engineering High Sensitivity GPS Performance://www.geomatics.ucalgary.ca/links/GradTheses.html) by Glenn D. MacGougan June 2003 #12;THE UNIVERSITY OF CALGARY High Sensitivity GPS Performance Analysis
Calgary, University of
-time statistical testing and implementation procedure for use in kinematic GPS positioning is given basedUCGE Reports Number 20042 Quality Control for Differential Kinematic GPS Positioning (URL: http OF CALGARY QUALITY CONTROL FOR DIFFERENTIAL KINEMATIC GPS POSITIONING BY GANG LU A THESIS SUBMITTED
Calgary, University of
testing UWB-GPS integration in numerous scenarios, this thesis proves that UWB is a feasible solutionUCGE Reports Number 20277 Department of Geomatics Engineering Ultra Wideband Augmented GPS (URL;UNIVERSITY OF CALGARY Ultra Wideband Augmented GPS by David Sung-Tat Chiu A THESIS SUBMITTED TO THE FACULTY
NSDL National Science Digital Library
2014-01-01
This place value and problem solving lesson focuses on forming 3-digit address numbers to meet specific requirement. The lesson provides an opportunity for learners to use the problem-solving strategies of looking for patterns and establishing an organized list. Students also learn that careful reading of information and understanding of mathematical language are important to finding appropriate solutions.
Andrew R. Booker; Ghaith A. Hiary; Jon P. Keating
2015-01-05
We present an algorithm, based on the explicit formula for $L$-functions and conditional on GRH, for proving that a given integer is squarefree with little or no knowledge of its factorization. We analyze the algorithm both theoretically and practically, and use it to prove that several RSA challenge numbers are not squarefull.
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'…
Origami and Constructible Numbers
Hull, Thomas C.
Origami and Constructible Numbers (and some other stuff) Tom Hull, Merrimack College thull of Origami? #12;What are the Basic Operations of Origami? Given two points P1 and P2, we can fold the crease important move in origami (probably) #12;Origami angle trisection L3 2 3 L1 L1 L2 p1 p2 #12;Origami angle
NSDL National Science Digital Library
Laura Domalik
2010-01-01
In this 5-minute video Laura Domalik defines number sense and provides instructional strategies for counting and vocabulary, including counting on, counting back, one more than (+1), one less than (-1), basic fact concepts of +1 and -1, and missing addends. She demonstrates a game called Garbage, which can be played alone or with a partner.
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…
Roundoff and Number Representation
Schörghofer, Norbert
illustrated in figure 2-1). In the decimal system this corresponds to a maximum/minimum exponent of ±38 and approximately 7 decimal dig- its (at least 6 and at most 9). For a 64-bit number (8 bytes) there are 11 bits for the exponent (±308) and 52 bits for the mantissa, which gives around 16 decimal digits of precision (at least
Honors question 3: Complex numbers (revisited). Arithmetic of complex numbers
Leininger, Christopher J.
Honors question 3: Complex numbers (revisited). Arithmetic of complex numbers Recall that the complex numbers are formally defined as C = {a + bi} where a and b can be any real numbers and i is treated as a variable (so we can identify the complex numbers with the set of linear polynomials with real
Number Theory Elliptic curves BSD Research : Number Theory group
Wuthrich, Christian
Number Theory Elliptic curves BSD Research : Number Theory group Christian Wuthrich 14 Dec 2011 Christian Wuthrich #12;Number Theory Elliptic curves BSD Number theory is the Queen of Mathematics. Christian Wuthrich #12;Number Theory Elliptic curves BSD Sometimes our research looks like this
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.
NSDL National Science Digital Library
This 4-minute computer animation highlights three forms in nature that have connections with numbers and geometry. The Fibonacci sequence and the golden ratio are shown relating to the chambered nautilus shell and the sunflower seed pattern. The Delaunay triangulation and Voronoi tessellation are shown to simulate the capillary distribution on a dragonfly wing. Included are descriptions of the mathematics and stills from the production.
NSDL National Science Digital Library
The Maths Doctor website from Macmillan Publishers contains more than 250 lessons that are free for anyone. Each lesson includes a three to five minute video tutorial on the topic and a related worksheet for the student to complete. Each worksheet has a convenient QR code that a student can scan to access the video. The Number section contains numerous lessons ranging from Conversion of Units to Dividing Fractions to Subtracting Negative Integers.
Yu Huang; Joan Llach
2007-01-01
Particle filter is a sequential Monte Carlo method for object tracking in a recursive Bayesian filtering framework. The efficiency and accuracy of the particle filter depends on two key factors: how many particles are used and how these particles are re-located. In this paper, we estimate the number of required particles using the Kullback-Leibler distance (KLD), which is called KLD-sampling,
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.
NSDL National Science Digital Library
Only in America, one might say, would artistic self-expression be so successfully mass produced, commodified, and regimented. Nevertheless, in a brave attempt at recuperation, the Smithsonian Institution's National Museum of American History offers this new Website on the popular 1950s' hobby of painting by number from the perspective of "the artists and entrepreneurs who created the popular paint kits, the cultural critics who reviled them, and the hobbyists who happily completed them and hung them in their homes." Taking a decidedly cultural studies approach, the Website stresses the pleasures derived from the activity as well as the modifications to the kits made by many participants. It also places the phenomenon in the context of the culture of the 1950s, particularly its expansion of leisure time. There are plenty of images here of the creation of the numbers kits as well as representations of the finished product. A bibliography and a bulletin board for posting reminiscences about painting by number are also provided. The authors claim the hobby, which pretty much died out in the 1960s, had the "peculiarly American virtue" of inviting people "who never held a brush before to enter a world of art and creativity." The editors invite our readers to be the judge of that.
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
q Numbers of quantum groups, Fibonacci numbers, and orthogonal polynomials
I. I. Kachurik
1998-01-01
We obtain algebraic relations (identities) for q-numbers that do not contain q\\u000a ?-factors. We derive a formula that expresses any q-number [x] in terms of the q-number [2]. We establish the relationship between the q-numbers [n] and the Fibonacci numbers, Chebyshev polynomials, and other special functions. The sums of combinations of q-numbers, in particular, the sums of their powers, are
Complex Numbers First: Define i
Sands, Jonathan W.
Complex Numbers First: Define i Solve the quadratic: Ryan Tarring Max Van Over Mike Diamond Mentor therefore, #12;The set of complex numbers is when we add real numbers to real multiples of this imaginary unit Complex numbers are written in the form: a +bi for real numbers a&b if b is not equal to 0 #12
Crossing Numbers and Parameterized Complexity
Michael J. Pelsmajer; Marcus Schaefer
2007-01-01
The odd crossing number of G is the smallest number of pairs of edges that cross an odd number of times in any drawing of G. We show that there always is a drawing realizing the odd crossing number of G that uses at most 9k crossings, where k is the odd crossing number of G. As a consequence of
Elliptic Pseudoprimes Elliptic Carmichael Numbers
Silverman, Joseph H.
Elliptic Pseudoprimes and Elliptic Carmichael Numbers Joseph H. Silverman Brown University AMS January 6, 9:009:20am 0 #12;Elliptic Carmichael Numbers 1 Pseudoprimes and Carmichael Numbers Let a 2) There are infinitely many Carmichael numbers. #12;Elliptic Carmichael Numbers 2 Elliptic Pseudoprimes The reason
Conway Numbers and Iteration Theory
James D. Louck
1997-01-01
Conway (“On Numbers and Games,” Academic Press, New York, 1976) has given an inductive procedure for generating the real numbers that extends in a natural way to a new class of numbers called the surreals. The number 0 is defined at the first step in terms of a pair of empty sets. At step 1, the number 1 and its
Quasar number density evolution
Stocke, J.T.; Perrenod, S.C.
1981-04-15
We present a simple model of quasar number density evolution, based upon the occurrence of quasar-like radio galaxies (i.e., strong optical emission lines and type 2 radio morphology) exclusively in regions of low galaxy and intergalactic medium (IGM) density. This suggests a limit for the IGM density of 10/sup -4plus-or-minus1/ cm/sup -3/ below which quasars are allowed to form and above which they are not allowed. In the recent past (z< or approx. =1), the inferred quasar environments are the outskirts of clusters and near the centers of groups of galaxies. However, models of rich cluster evolution consistent with current X-ray observations predict gas densities <10/sup -4/ cm/sup -3/ in cluster cores in the more distant past (1< or approx. =z< or approx. =5). This suggests that quasars were allowed to form in the cores of rich clusters at those epochs, which explains both the rich absorption spectra of high-redshift quasars and the absence of clusters surrounding quasars at lower redshift. The rapid increase in core gas density of clusters and groups in the recent past decreases the number of available quasar sites with time, although not nearly as rapidly as observed. Thus, our model explains some, but probably not all, of the number density evolution of quasars, requiring additional evolution with is independent of environment. At very high redshifts (z>5) the universe has not expanded sufficiently to allow any quasar formation in our model. Such a cutoff is suggested by recent observations.
NSDL National Science Digital Library
2012-01-10
Learners describe objects in a room using only numbers and shapes. They can measure the object (like a desk) and make a list of facts about it (e.g. 21 inches tall, 42 inches wide, 3 different colors). Then other learners try to identify the objects described. When learners set up a free account at Kinetic City, they can answer bonus questions at the end of the activity as a quick assessment. As a larger assessment, learners can complete the Bug Blaster game after they've completed several activities.
NSDL National Science Digital Library
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Materials A spinner with the numbers 0, 1, 2, ... 9 A spinner with the decades 00, 10, 20, ... 90 Math journal or teacher-made worksheet Pencil Actions...
NSDL National Science Digital Library
This is an activity about assessing magnetic activity on the Sun as astronomers do. Learners will select and compare five visible light solar images and identify and label each individual sunspot group. Then, learners will count all possible sunspots from each group and use both counts in a standard equation to calculate the Relative Sunspot Number for each respective solar image. This activity requires access to the internet to obtain images from the SOHO image archive. This is Activity 8 of the Space Weather Forecast curriculum.
NSDL National Science Digital Library
The School of Mathematics and Statistics at the University of St Andrews, Scotland has developed an extensive collection of articles on the history of mathematics (See also NSDL Scout Report for Math, Engineering, and Technology, June 4, 2004). This article, written by J J O'Connor and E F Robertson, reviews the history of Prime Numbers. The article includes hyperlinks to topics addressed further in other sections of the website. For example, from this website visitors can also find articles on Pythagoras and Euclid.
Generalized Maxwell Love numbers
Giorgio Spada
2009-11-04
By elementary methods, I study the Love numbers of a homogeneous, incompressible, self-gravitating sphere characterized by a generalized Maxwell rheology, whose mechanical analogue is represented by a finite or infinite system of classical Maxwell elements disposed in parallel. Analytical, previously unknown forms of the complex shear modulus for the generalized Maxwell body are found by algebraic manipulation, and studied in the particular case of systems of springs and dashpots whose strength follows a power-law distribution. We show that the sphere is asymptotically stable for any choice of the mechanical parameters that define the generalized Maxwell body and analytical forms of the Love numbers are always available for generalized bodies composed by less than five classical Maxwell bodies. For the homogeneous sphere, real Laplace inversion methods based on the Post-Widder formula can be applied without performing a numerical discretization of the n-th derivative, which can be computed in a "closed-form" with the aid of the Faa di Bruno formula.
Grozeva, Detelina; Kirov, George; Ivanov, Dobril; Jones, Ian R.; Jones, Lisa; Green, Elaine K.; St Clair, David M.; Young, Allan H.; Ferrier, Nicol; Farmer, Anne E.; McGuffin, Peter; Holmans, Peter A.; Owen, Michael J.; O’Donovan, Michael C.; Craddock, Nick
2015-01-01
Context Recent studies suggest that copy number variation in the human genome is extensive and may play an important role in susceptibility to disease, including neuropsychiatric disorders such as schizophrenia and autism. The possible involvement of copy number variants (CNVs) in bipolar disorder has received little attention to date. Objectives To determine whether large (>100 000 base pairs) and rare (found in <1% of the population) CNVs are associated with susceptibility to bipolar disorder and to compare with findings in schizophrenia. Design A genome-wide survey of large, rare CNVs in a case-control sample using a high-density microarray. Setting The Wellcome Trust Case Control Consortium. Participants There were 1697 cases of bipolar disorder and 2806 nonpsychiatric controls. All participants were white UK residents. Main Outcome Measures Overall load of CNVs and presence of rare CNVs. Results The burden of CNVs in bipolar disorder was not increased compared with controls and was significantly less than in schizophrenia cases. The CNVs previously implicated in the etiology of schizophrenia were not more common in cases with bipolar disorder. Conclusions Schizophrenia and bipolar disorder differ with respect to CNV burden in general and association with specific CNVs in particular. Our data are consistent with the possibility that possession of large, rare deletions may modify the phenotype in those at risk of psychosis: those possessing such events are more likely to be diagnosed as having schizophrenia, and those without them are more likely to be diagnosed as having bipolar disorder. PMID:20368508
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…
Abstract. Geometry and Complex Numbers GEOMETRY AND COMPLEX NUMBERS
Lee, Carl
Abstract. Geometry and Complex Numbers GEOMETRY AND COMPLEX NUMBERS JERZY DYDAK Contents 1. Introduction 2 2. Solving equations 10 3. Geometric proofs 20 Key words and phrases. Complex numbers. 1 #12-Euclidean, Projective, and Discrete' by Michael Henle (2nd edition, Prentice Hall). (2) `Complex numbers and geometry
Pauli Pascal Pyramids, Pauli Fibonacci Numbers, and Pauli Jacobsthal Numbers
Martin Erik Horn
2007-11-26
The three anti-commutative two-dimensional Pauli Pascal triangles can be generalized into multi-dimensional Pauli Pascal hyperpyramids. Fibonacci and Jacobsthal numbers are then generalized into Pauli Fibonacci numbers, Pauli Jacobsthal numbers, and Pauli Fibonacci numbers of higher order. And the question is: are Pauli rabbits killer rabbits?
Generalized Lucas Numbers and Relations with Generalized Fibonacci Numbers
Kaygisiz, Kenan
2011-01-01
In this paper, we present a new generalization of the Lucas numbers by matrix representation using Genaralized Lucas Polynomials. We give some properties of this new generalization and some relations between the generalized order-k Lucas numbers and generalized order-k Fibonacci numbers. In addition, we obtain Binet formula and combinatorial representation for generalized order-k Lucas numbers by using properties of generalized Fibonacci numbers.
Farlow, Jerry
Section 5.6 Complex Numbers1 Section 5.Section 5.Section 5.Section 5.6666 Complex NumbersComplex NumbersComplex NumbersComplex Numbers Purpose of SectionPurpose of SectionPurpose of SectionPurpose of Section To introduce the field ( ), ,+ ×» of complex numbers and their Cartesian
Transient natural convection heat and mass transfer in crystal growth
NASA Technical Reports Server (NTRS)
Han, Samuel S.
1988-01-01
A numerical analysis of transient combined heat and mass transfer across a rectangular cavity is performed by a numerical method based on the SIMPLE algorithm. The physical parameters are selected to represent a range of possible crystal growth in solutions. Numerical results are compared with available experimental data to confirm the accuracy of the results. Good qualitative agreements are obtained for the average mass transfer rate across the cavity. Also, qualitative agreements are observed for the global development of thermal and solute fields. It is found that the thermal and solute fields become highly oscillatory when the thermal and solute Grashof numbers are large. Oscillations are probably caused by a number of different instability mechanisms. By reducing the gravity some of these instabilities were made to disappear at the lower Grashof numbers. Transient temperature and solute distribution near the crystal growing surface are highly non-uniform at the higher Grashof numbers. These non-uniformities are less severe in the reduced gravity environments but still exist. The effects of convection on the rate of average mass transfer are more than one order of magnitude higher than those of conduction in the range of Grashof numbers studied. Dependency of mass transfer rate on the Grashof number indicates that the convection effects many not be negligible even in the microgravity environments for the range of parameters investigated.
Deterministic Random Number Generator Benchmarks
Deterministic Random Number Generator Benchmarks By Karl Lopker Introduction Deterministic Random to generate its numbers. The DevRandom class is also secure. It gets its numbers from the Linux /dev/random Number Generators (DRNGs) are important for a wide variety of applications. However, all languages
Stirling Numbers for Complex Arguments
L. Bruce Richmond; Donatella Merlini
1997-01-01
We define the Stirling numbers for complex values and obtain extensions of certain identities involving these numbers. We also show that the generalization is a natural one for proving unimodality and monotonicity results for these numbers. The definition is based on the Cauchy integral formula and can be used for many other combinatorial numbers. PII. S0895480195284329 1. Introduction. In this
Number of applied research projects
Bates, Rebecca A.
through assistantships and fellowships ·Number of graduate programs ·Number of graduate students enrolled programs developed in response to an industry or social need ·Dollar amount of graduate student support ·Number of presentations at the Graduate Research Conference ·Number of graduate students participating
ALGEBRAIC NUMBER THEORY Romyar Sharifi
Sharifi, Romyar
ALGEBRAIC NUMBER THEORY Romyar Sharifi #12;#12;Contents Introduction 5 Chapter 1. Abstract algebra At its core, the ancient subject of number theory is concerned with the arithmetic of the integers numbers. Over the centuries, number theory grew immensely as a subject, and techniques were developed
Divisibility - Prime and Composite Numbers
NSDL National Science Digital Library
Mrs. Harris
2007-11-05
Learn how to tell if a number is divisible by 2, 3, 5, 6, 9, or 10. Learn about prime and composite numbers This is a PowerPoint teaching Divisibility rules PowerPoint on Divisibility Have fun practicing divisibility! Divisibility Rules Practice Prime Factorization with this Factor Tree. Factor Tree You can be a Prime Number Cop while you play this game. Catch those prime numbers! Number Cop ...
Quasar number density evolution
NASA Technical Reports Server (NTRS)
Stocke, J. T.; Perrenod, S. C.
1981-01-01
A simple model of quasar number density evolution is presented based on the occurrence of quasar-like radio galaxies (i.e., strong optical emission lines and type 2 radio morphology) exclusively in regions of low galaxy and intergalactic medium (IGM) density. This suggests a limit for the IGM density of 10 to the -4th (+ or - 1) per cu cm below which quasars are allowed to form and above which they are not allowed. In the recent past (z not greater than 1), the inferred quasar environments are the outskirts of clusters and near the centers of groups of galaxies. However, models of rich cluster evolution consistent with current X-ray observations predict gas densities of less than 10 to the -4th per cu cm in cluster cores in the more distant past (z between 1 and 5). This suggests that quasars were allowed to form in the cores of rich clusters at those epochs, which explains both the rich absorption spectra of high-redshift quasars and the absence of clusters surrounding quasars at lower redshift.
Lepton family number violation
Herczeg, P.
1999-03-01
At present there is evidence from neutrino oscillation searches that the neutrinos are in fact massive particles and that they mix. If confirmed, this would imply that the conservation of LFN is not exact. Lepton family number violation (LFNV) has been searched for with impressive sensitivities in many processes involving charged leptons. The present experimental limits on some of them (those which the author shall consider here) are shown in Table 1. These stringent limits are not inconsistent with the neutrino oscillation results since, given the experimental bounds on the masses of the known neutrinos and the neutrino mass squared differences required by the oscillation results, the effects of LFNV from neutrino mixing would be too small to be seen elsewhere (see Section 2). The purpose of experiments searching for LFNV involving the charged leptons is to probe the existence of other sources of LFNV. Such sources are present in many extensions of the SM. In this lecture the author shall discuss some of the possibilities, focusing on processes that require muon beams. Other LFNV processes, such as the decays of the kaons and of the {tau}, provide complementary information. In the next Section he shall consider some sources of LFNV that do not require an extension of the gauge group of the SM (the added leptons or Higgs bosons may of course originate from models with extended gauge groups). In Section 3 he discusses LFNV in left-right symmetric models. In Section 4 he considers LFNV in supersymmetric models, first in R-parity conserving supersymmetric grand unified models, and then in the minimal supersymmetric standard model with R-parity violation. The last section is a brief summary of the author`s conclusions.
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
Account Name Account Number Spending Distribution Account Number (if applicable)
de Lijser, Peter
Account Name Account Number Spending Distribution Account Number (if applicable) College with CSFPF is required Name: CSUF email: signature Secondary Signatories Name: CSUF email: signature Third Signatories/ Fourth Signatories Name: /Name: /CSUF email: /CSUF email: signature signature Fifth Signatories
On the number of ordered factorizations of natural numbers
Benny Chor; Paul Lemke; Ziv Mador
2000-01-01
Abstract We study the number of ways to factor a natural number n into an ordered product of integers, each factor greater than one, denoted by H(n). This counting function from number theory was shown by Newberg and Naor (Adv. Appl. Math. 14 (1993) 172{183) to be a lower bound on the number of solutions to the so-called probed partial
Concatenated Fibonacci and Lucas numbers do not form normal numbers
Mendonça, J Ricardo G
2011-01-01
We show that the infinite decimal numbers $\\mathcal{F} = 0.F_{1}F_{2}F_{3}...$ and $\\mathcal{L} = 0.L_{1}L_{2}L_{3}...$ obtained by concatenating respectively the Fibonacci and the Lucas numbers for their fractional parts are not normal numbers to base 10.
The Case of Blake: Number-Word and Number Development.
ERIC Educational Resources Information Center
Benson, Alexis P.; Baroody, Arthur J.
Noting that current research on childrens mathematical development does not adequately detail how toddlers represent small numbers and the role that number words play in the development of number understanding, this study used a combination of methods to examine mathematical development in one toddler. Underlying the study was an Integrated Model…
The Kissing Numbers of Tetrahedra
Chuanming Zong
1996-01-01
We determine the lattice kissing numbers of tetrahedra, by which we disprove a conjecture by Grünbaum. At the same time, we\\u000a present a strange phenomenon concerning kissing numbers and packing densities of tetrahedra.
Graphs, partitions and Fibonacci numbers
Arnold Knopfmacher; Robert F. Tichy; Stephan Wagner; Volker Ziegler
2007-01-01
Abstract The Fibonacci number of a graph is the number of independent vertex subsets. In this paper, we investigate trees with large Fibonacci number. In particular, we show that all trees with n edges and Fibonacci number,> 2,\\/4 for constants A,B as n ! 1. This is proved by using a natural correspondence between partitions of integers and star-like trees.
True & Deterministic Random Number Generators
True & Deterministic Random Number Generators CÂ¸etin Kaya KoÂ¸c http://cs.ucsb.edu/~koc koc. This characterizes an ideal random number generator KoÂ¸c (http://cs.ucsb.edu/~koc) HRL RNG April 11, 2013 3 / 47 #12, 2013 5 / 47 #12;Random Number Generators in Cryptography Deterministic RNGs are also known
Sequence Analysis by Numbers: Proteins
JOHNSON F. Yan
1996-01-01
As a number code to the protein sequence language, the amino acid numbers (z) derived previously (1, 25, 45, and 17 prime numbers smaller than 64) are used to characterize oligopeptide motifs. The grammatical rule of this language is expressed with two theorems governing the collective properties of oligopeptides. This numeric representation contrasts particular sequence patterns. The language's equivalent forms
Chromatic number of Euclidean plane
Kai-Rui Wang
2015-07-01
If the chromatic number of Euclidean plane is larger than four, but it is known that the chromatic number of planar graphs is equal to four, then how does one explain it? In my opinion, they are contradictory to each other. This idea leads to confirm the chromatic number of the plane about its exact value.
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…
Ecological reading of random numbers
B. Vilenkin
2006-01-01
Numerical simulation of species assemblages is presented. When the level of the external disturbance is below the species tolerance, the size of every population changes by addition of positive or negative random number to the previous number. In the opposite case, the number of individuals in a population converges to zero. External disturbances change randomly between time steps for each
ERIC Educational Resources Information Center
Wagner, Johannes, Ed.
1998-01-01
The eight titles in this document include the following: "Comprehension and Input Processing as Useful Terms in the Field of SLA" (number 28) (Teresa Cadierno); "On the Role of Instruction in SLA: Research Results and Theoretical Explanations" (number 29) (Teresa Cadierno); "Can Writing Be Taught" (number 30) (Stuart Greene); "Academic Listening"…
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…
Program Number: Company (if applicable)
Hutcheon, James M.
: ZIP: Daytime Phone Number: Cell Phone: Evening Phone Number: FAX Number: E-mail (Required for e, GA 30460-8124 ONLINE: GeorgiaSouthern.edu/conted FAX: 912.478.0847 PHONE: Call toll free 1 to that effect signed by a faculty member. Faculty signature for full-time graduate students required. Signature
The complex binary number system
Tariq Jamil
2001-01-01
Conversion algorithms and arithmetic procedures for a (-1 + j)-base binary number allow a given complex number to be represented as one unit. This should simplify the operations involving complex numbers in today's microprocessors. With the division process secure, we can implement the usual algorithms for calculating functions and processes such as logarithms, exponentials and trigonometric functions Currently, work is
Data Compression with Prime Numbers
Gordon Chalmers
2005-11-16
A compression algorithm is presented that uses the set of prime numbers. Sequences of numbers are correlated with the prime numbers, and labeled with the integers. The algorithm can be iterated on data sets, generating factors of doubles on the compression.
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…
Prandtl number dependence of Nusselt number in DNS
NASA Astrophysics Data System (ADS)
Kerr, R. M.; Herring, Jackson R.
1997-11-01
Simulation results on the Prandtl and Rayleigh number dependence of the Nussult number for Pr=0.07 to 7 are reported. Ra up to 10^7 is used for Pr>1, but for Pr=0.07 the largest Ra is 2×10^6 due to the vigorous turbulent motion and high Reynolds number. Initial results support experimental work for a strong dependence on Prandtl number for Pr<1 and nearly no dependence for Pr>1. Statistical errors are still too large to determine the exact trend for Pr>1.
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.
Chaotic Nonlinear Prime Number Function
NASA Astrophysics Data System (ADS)
Mateos, Luis A.
2011-06-01
Dynamical systems in nature, such as heartbeat patterns, DNA sequence pattern, prime number distribution, etc., exhibit nonlinear (chaotic) space-time fluctuations and exact quantification of the fluctuation pattern for predictability purposes has not yet been achieved [1]. In this paper a chaotic-nonlinear prime number function P(s) is developed, from which prime numbers are generated and decoded while composite numbers are encoded over time following the Euler product methodology, which works on sequences progressively culled from multiples of the preceding primes. By relating this P(s) to a virtually closed 2D number line manifold, it is possible to represent the evolving in time of nonlinear (chaotic) systems to a final value where the system becomes stable, becomes linear. This nonlinear prime number function is proposed as a chaotic model system able to describe chaotic systems.
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
Extending the Number Line to Make Connections with Number Theory.
ERIC Educational Resources Information Center
Graviss, Tom; Greaver, Joanne
1992-01-01
Shares a coded version of the number line to provide concrete experiences for learning abstract concepts. Using the fundamental theorem of arithmetic, appropriate coded symbols are determined for the prime factorization of each natural number and used to study the concepts of greatest common divisor, least common multiple, square roots, and…
Topology (Forskerprosjekt) Application Number: ES431408 Project Number: 0
Dundas, Bjørn Ian
Administration Project administrator First name Stein Arild Last name Strømme Position/title Professor Bokmål Phone +47 55582827 E-mail dundas@math.uib.no Project info Project title Topology PrimaryTopology (Forskerprosjekt) Application Number: ES431408 Project Number: 0 Page: 1 Applicant Project
Catalan Numbers, the Hankel Transform, and Fibonacci Numbers
Aleksandar Cvetkovic; Predrag Rajkovic; Milos Ivkovic
2002-01-01
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.
Towards implementation of a binary number system for complex numbers
Tariq Jamil; N. Holmes; D. Blest
2000-01-01
These days computer operations involving complex numbers are most commonly performed by dealing with the real and imaginary parts separately and then accumulating their individual results to get the final result of the operation. This divide-and-conquer technique forsakes the advantages of using complex numbers in computer arithmetic and there exists a need, at least for some problems, to treat a
Finite Prandtl number 2-D convection at high Rayleigh numbers
Catherine A. Hier Majumder; David A. Yuen; Erik O. Sevre; John M. Boggs; Stephen Y. Bergeron
2002-01-01
Finite Prandtl number thermal convection is important to the dynamics of planetary bodies in the solar system. For example, the complex geology on the surface of the Jovian moon Europa is caused by a convecting, brine-rich global ocean that deforms the overlying icy “lithosphere”. We have conducted a systematic study on the variations of the convection style, as Prandtl numbers
Reprint Series: Prime Numbers and Perfect Numbers. RS-2.
ERIC Educational Resources Information Center
Schaaf, William L., Ed.
This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series makes available expository articles which appeared in a variety of mathematical periodicals. Topics covered include: (1) the prime numbers; (2) mathematical sieves; (3) the factorgram; and (4) perfect numbers. (MP)
Familial Sinistrals Avoid Exact Numbers
Sauerland, Uli; Gotzner, Nicole
2013-01-01
We report data from an internet questionnaire of sixty number trivia. Participants were asked for the number of cups in their house, the number of cities they know and 58 other quantities. We compare the answers of familial sinistrals – individuals who are left-handed themselves or have a left-handed close blood-relative – with those of pure familial dextrals – right-handed individuals who reported only having right-handed close blood-relatives. We show that familial sinistrals use rounder numbers than pure familial dextrals in the survey responses. Round numbers in the decimal system are those that are multiples of powers of 10 or of half or a quarter of a power of 10. Roundness is a gradient concept, e.g. 100 is rounder than 50 or 200. We show that very round number like 100 and 1000 are used with 25% greater likelihood by familial sinistrals than by pure familial dextrals, while pure familial dextrals are more likely to use less round numbers such as 25, 60, and 200. We then use Sigurd’s (1988, Language in Society) index of the roundness of a number and report that familial sinistrals’ responses are significantly rounder on average than those of pure familial dextrals. To explain the difference, we propose that the cognitive effort of using exact numbers is greater for the familial sinistral group because their language and number systems tend to be more distributed over both hemispheres of the brain. Our data support the view that exact and approximate quantities are processed by two separate cognitive systems. Specifically, our behavioral data corroborates the view that the evolutionarily older, approximate number system is present in both hemispheres of the brain, while the exact number system tends to be localized in only one hemisphere. PMID:23544052
Higher-order Fibonacci numbers
Milan Randi?; Daniel A. Morales; Oswaldo Araujo
1996-01-01
We consider a generalization of Fibonacci numbers that was motivated by the relationship of the HosoyaZ topological index to the Fibonacci numbers. In the case of the linear chain structures the new higher order Fibonacci numbershFn are directly related to the higher order Hosoya-typeZ numbers. We investigate the limitsFn\\/Fn-1 and the corresponding equations, the roots of which allow one to
NASA Astrophysics Data System (ADS)
Kwa?niewski, A. K.; Czech, R.
1992-06-01
Generalizations of complex numbers suggested by Weierstrass, Bruwier, Mikusi?ski et al. are investigated in detail. These generalizations are intrinsincly related to hyperbolic and elliptic mappings via polar representation of "quasi-numbers" proposed by Fleury et al. Relevance of these quasi-number systems to Potts-like models, fractals and Weyl's finite quantum mechanics with discrete configuration space is indicated. The note is based on [0].
NSDL National Science Digital Library
2014-04-04
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Plot the following numbers on the number line. 456 \\ \\ 983\\ \\ 938 \\ \\ 425 \\ \\ 220 \\ \\ 202\\ \\ 799 Choose eight pairs of numbers from those you plotted o...
Familial sinistrals avoid exact numbers.
Sauerland, Uli; Gotzner, Nicole
2013-01-01
We report data from an internet questionnaire of sixty number trivia. Participants were asked for the number of cups in their house, the number of cities they know and 58 other quantities. We compare the answers of familial sinistrals--individuals who are left-handed themselves or have a left-handed close blood-relative--with those of pure familial dextrals--right-handed individuals who reported only having right-handed close blood-relatives. We show that familial sinistrals use rounder numbers than pure familial dextrals in the survey responses. Round numbers in the decimal system are those that are multiples of powers of 10 or of half or a quarter of a power of 10. Roundness is a gradient concept, e.g. 100 is rounder than 50 or 200. We show that very round number like 100 and 1000 are used with 25% greater likelihood by familial sinistrals than by pure familial dextrals, while pure familial dextrals are more likely to use less round numbers such as 25, 60, and 200. We then use Sigurd's (1988, Language in Society) index of the roundness of a number and report that familial sinistrals' responses are significantly rounder on average than those of pure familial dextrals. To explain the difference, we propose that the cognitive effort of using exact numbers is greater for the familial sinistral group because their language and number systems tend to be more distributed over both hemispheres of the brain. Our data support the view that exact and approximate quantities are processed by two separate cognitive systems. Specifically, our behavioral data corroborates the view that the evolutionarily older, approximate number system is present in both hemispheres of the brain, while the exact number system tends to be localized in only one hemisphere. PMID:23544052
Explicit Methods in Number Theory
Karim Belabas; Leiden Don
2007-01-01
These notes contain extended abstracts on the topic of explicit methods in number theory. The range of topics includes asymptotics for field extensions and class numbers, random matrices and L-functions, rational points on curves and higher-dimensional varieties, and aspects of lattice basis reduction.
Quick Images: Visualizing Number Combinations
NSDL National Science Digital Library
2012-01-01
In this 6-minute video kindergarten teacher Stephanie Latimer describes and models techniques for developing children's number sense and visual recognition of number combinations. After quickly displaying groups of objects on a ten frame, she asks her students to describe the ways that they see the objects grouped. The resource includes reflection questions for viewers and a transcript of the video (doc).
Wave Packets can Factorize Numbers
Holger Mack; Marc Bienert; Florian Haug; Matthias Freyberger; Wolfgang P. Schleich
2002-08-30
We draw attention to various aspects of number theory emerging in the time evolution of elementary quantum systems with quadratic phases. Such model systems can be realized in actual experiments. Our analysis paves the way to a new, promising and effective method to factorize numbers.
NSDL National Science Digital Library
2010-01-01
The students perform the Sieve of Eratosthenes in class to find the prime number between 1 and 100. They also look for patterns such as where the multiples of 2 or 5 appear in the sieve. At home or in a computer lab they then research the Fibonacci Sequence and other number systems.
On normal numbers Veronica Becher
Becher, Verónica
American Symposium on Mathematical Logic July 2014 Ver´onica Becher On normal numbers 0 / 22 #12;Normal normal. Problem (Borel 1909) Give one example. Conjecture (Borel 1950) Irrational algebraic numbers independence there is between normality to different bases? We gave a logical analysis of normality
Quantum Computing and Number Theory
NASA Astrophysics Data System (ADS)
Sasaki, Yoshitaka
2013-09-01
The prime factorization can be efficiently solved on a quantum computer. This result was given by Shor in 1994. In the first half of this article, a review of Shor's algorithm with mathematical setups is given. In the second half of this article, the prime number theorem which is an essential tool to understand the distribution of prime numbers is given.
Account Number Citation Reappeal Form
Massachusetts at Amherst, University of
Account Number Citation Reappeal Form Parking Services, University of Massachusetts, Amherst 51://parking.umass.edu Email: parking@admin.umass.edu Appeals must be received within 14 days of citation issuance and may. ________________________________________________________________________________________________________ Citation #:___________________________ Date Issued: _____ / _____ / ____________ State/Plate Number
Particle number in kinetic theory
Bjorn Garbrecht; Tomislav Prokopec; Michael G. Schmidt
2004-01-01
We provide a derivation for the particle number densities on phase space for scalar and fermionic fields in terms of Wigner functions. Our expressions satisfy the desired properties: for bosons the particle number is positive, for fermions it lies in the interval between zero and one, and both are consistent with thermal field theory. As applications we consider the Bunch-Davies
numbers and SAT Oliver Kullmann
Martin, Ralph R.
, 7, 11, 13, 17, 19, 23} into two parts such that no part contains an arithmetic progression of size 3 by the OKlibrary: c 2 parts, arithmetic progressions of size 3, and 9 prime numbers. c Variables and associated numbers, there exists some i {1, . . . , m} such that f-1(i) contains an arithmetic progression of size
numbers and SAT Oliver Kullmann
Martin, Ralph R.
(diagonal form), created by the OKlibrary: c 2 parts, arithmetic progressions of size 3, and 9 prime numbers extensions The generic boolean translation On the history of the Green-Tao theorem Arithmetic progressions n prime numbers contain an arithmetic progression of length k. Trivially grt1(1) = 1 and grt1(2) = 2
On residue number system decoding
RUDOLF E. THUN
1986-01-01
The use of a residue number system (RNS) in digital systems and especially filter designs is facilitated by efficient algorithms for the conversion from RNS to binary numbers. The conversion is generally based on the Chinese remainder theorem or the mixed radix conversion. This correspondence describes another conversion algorithm which employs the direct pairwise solution of the Diophantine equations defining
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…
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…
Davies, Christopher
) Rounding to a specified number of significant figures The first significant figure of a decimal quantity to a specified number of significant figures, we use the same principle as in (a), but starting from the first significant figure, then working to the right. EXAMPLES 1. 362.5863 = 362.59 to 5 significant figures; 362
Pseudo-Random Number Generators
NASA Technical Reports Server (NTRS)
Howell, L. W.; Rheinfurth, M. H.
1984-01-01
Package features comprehensive selection of probabilistic distributions. Monte Carlo simulations resorted to whenever systems studied not amenable to deterministic analyses or when direct experimentation not feasible. Random numbers having certain specified distribution characteristic integral part of simulations. Package consists of collector of "pseudorandom" number generators for use in Monte Carlo simulations.
ERIC Educational Resources Information Center
Avital, Shmuel; Grinblat, Uri
1983-01-01
The material focuses on the power and usefulness of the number three and is presented as though the number was being interviewed. Among the issues covered in the presentation is the impossibility of dividing an angle into three equal parts using just a straight edge and a compass. (Author/MP)
Beyond complex numbers Johanna Ramo
Wright, Francis
, multiply and divide them, and on top of that, do things which you cannot do with real numbers. Today their results but kept them secret. They made their living by challenging each other to public contests, was first kept secret. The mathematicians of the time did not like negative numbers because to them they had
Acceptance of Others (Number Form).
ERIC Educational Resources Information Center
Masters, James R.; Laverty, Grace E.
As part of the instrumentation to assess the effectiveness of the Schools Without Failure (SWF) program in 10 elementary schools in the New Castle, Pa. School District, the Acceptance of Others (Number Form) was prepared to determine pupil's attitudes toward classmates. Given a list of all class members, pupils are asked to circle a number from 1…
8.NS Irrational Numbers on the Number Line
NSDL National Science Digital Library
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Without using your calculator, label approximate locations for the following numbers on the number line. $\\pi$ $-(\\frac12 \\times \\pi)$ $2\\sqrt2$ $\\sqrt...
A Novel Redundant Binary Number to Natural Binary Number Converter
S. K. Sahoo; Anu Gupta; Abhijit R. Asati; Chandra Shekhar
2010-01-01
Redundant binary number appears to be appropriate for high-speed arithmetic operation, but the delay and hardware cost associated\\u000a with the conversion from redundant binary (RB) to natural binary (NB) number is still a challenging task. In the present investigation\\u000a a simple approach has been adopted to achieve high speed with lesser hardware and power saving. A circuit level approach has
Hurwitz numbers and BKP hierarchy
S. M. Natanzon; A. Yu. Orlov
2014-10-29
We consider special series in ratios of the Schur functions which are defined by integers $\\textsc{f}\\ge 0$ and $\\textsc{e} \\le 2$, and also by the set of $3k$ parameters $n_i,q_i,t_i,\\,i=1,..., k$. These series may be presented in form of matrix integrals. In case $k=0$ these series generates Hurwitz numbers for the $d$-fold branched covering of connected surfaces with a given Euler characteristic $\\textsc{e}$ and arbitrary profiles at $\\textsc{f}$ ramification points. If $k>0$ they generate weighted sums of the Hurwitz numbers with additional ramification points which are distributed between color groups indexed by $i=1,...,k$, the weights being written in terms of parameters $n_i,q_i,t_i$. By specifying the parameters we get sums of all Hurwitz numbers with $\\textsc{f}$ arbitrary fixed profiles and the additional profiles provided the following condition: both, the sum of profile lengths and the number of ramification points in each color group are given numbers. In case $\\textsc{e}=\\textsc{f}=1,2$ the series may be identified with BKP tau functions of Kac and van de Leur of a special type called hypergeometric tau functions. Sums of Hurwitz numbers for $d$-fold branched coverings of ${\\mathbb{RP}}^2$ are related to the one-component BKP hierarchy. We also present links between sums of Hurwitz numbers and one-matrix model of the fat graphs.
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
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 portion of the problem.
Incomplete Fibonacci and Lucas numbers
Piero Filipponi
1996-01-01
A particular use of well-known combinatorial expressions for Fibonacci and Lucas numbers gives rise to two interesting classes\\u000a of integers (namely, the numbersF\\u000a n(k) andL\\u000a n(k)) governed by the integral parametersn andk. After establishing the main properties of these numbers and their interrelationship, we study some congruence properties\\u000a ofL\\u000a n(k), one of which leads to a supposedly new characterisation of
Objective Calibration of Sunspot Numbers
NASA Astrophysics Data System (ADS)
Svalgaard, L.
2010-12-01
Waldmeier [1971] found a very tight relationship between the F10.7 solar radio flux and the sunspot number and suggested using the flux for an objective calibration of the sunspot number. He suggested that if this relationship changed later on, the sunspot number should be re-calibrated, assuming that the calibration must have drifted with time. I repeat his analysis using data up to the present and it is, indeed, clear that the relationship has changed significantly. This could be due to a drift of the calibration or to a secular change in the visibility of sunspots, or both.
Wortman, Kevin
The Plane of Complex Numbers In this chapter we'll introduce the complex numbers as a plane of numbers. Each complex number will be identified by a number on a "real axis" and a number on an "imaginary axis". This description of the complex numbers is analogous to the description of R2 using cartesian
Tam, Daniel See Wai, 1980-
2008-01-01
The work described in this thesis centers on inertialess motion at low Reynolds numbers at the crossroad between biofluids and microfluids. Here we address questions regarding locomotion of micro-swimmers, transport of ...
1 and prime numbers - Numberphile
NSDL National Science Digital Library
James Grime
2012-02-03
In this 5.5 minute video Dr James Grime (Cambridge University, UK) explains why mathematicians don't classify the number 1 as a prime. He includes historical background and an explanation of the Fundamental Theorem of Arithmetic.
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)
OFFICE USE ONLY Reference number
Dixon, Peter
-exempt 501(c)(3) organization and your donation is tax deductible to the extent allowed by law. Thank youAlumni Fund Donation Form. OFFICE USE ONLY Reference number: Thank you for supporting Sheffield
Pinning of Fermionic Occupation Numbers
NASA Astrophysics Data System (ADS)
Schilling, Christian; Gross, David; Christandl, Matthias
2013-01-01
The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states. It has been suspected since at least the 1970s, and only proved very recently, that there is a multitude of further constraints on these numbers, generalizing the Pauli principle. Here, we provide the first analytic analysis of the physical relevance of these constraints. We compute the natural occupation numbers for the ground states of a family of interacting fermions in a harmonic potential. Intriguingly, we find that the occupation numbers are almost, but not exactly, pinned to the boundary of the allowed region (quasipinned). The result suggests that the physics behind the phenomenon is richer than previously appreciated. In particular, it shows that for some models, the generalized Pauli constraints play a role for the ground state, even though they do not limit the ground-state energy. Our findings suggest a generalization of the Hartree-Fock approximation.
Compendium of Experimental Cetane Numbers
National Renewable Energy Laboratory (NREL)
start with difficulty and run poorly. This report presents the results of an exhaustive literature search for available experimental cetane number data for pure compounds as of...
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 ...
Bass Numbers and Semidualizing Complexes
Sean Sather-Wagstaff
2008-01-01
Let R be a commutative local noetherian ring. We prove that the existence of a chain of semidualizing R-complexes of length (d+1) yields a degree-d polynomial lower bound for the Bass numbers of R. We also show how information about certain Bass numbers of R provide restrictions on the lengths of chains of semidualizing R-complexes. To make this article somewhat
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.
Neural Addition and Fibonacci Numbers
Valeriu Beiu
1999-01-01
This paper presents an intriguing relation between neural networks having as weights the Fibonacci numbers and the Addition of (two) binary numbers. The practical application of interest is that such ‘Fibonacci’ networks are VLSI-optimal with respect\\u000a to the area of the circuit. We shortly present the state-of-the-art, and detail a class of multilayer solutions for Addition. For this class we
Christian Agrillo; Marco Dadda; Giovanna Serena; Angelo Bisazza; Georges Chapouthier
2009-01-01
BackgroundResearch on human infants, mammals, birds and fish has demonstrated that rudimentary numerical abilities pre-date the evolution of human language. Yet there is controversy as to whether animals represent numbers mentally or rather base their judgments on non-numerical perceptual variables that co-vary with numerosity. To date, mental representation of number has been convincingly documented only for a few mammals.Methodology\\/Principal FindingsHere
Digital random-number generator
NASA Technical Reports Server (NTRS)
Brocker, D. H.
1973-01-01
For binary digit array of N bits, use N noise sources to feed N nonlinear operators; each flip-flop in digit array is set by nonlinear operator to reflect whether amplitude of generator which feeds it is above or below mean value of generated noise. Fixed-point uniform distribution random number generation method can also be used to generate random numbers with other than uniform distribution.
Particle number in kinetic theory
NASA Astrophysics Data System (ADS)
Garbrecht, B.; Prokopec, T.; Schmidt, M. G.
2004-12-01
We provide a derivation for the particle number densities on phase space for scalar and fermionic fields in terms of Wigner functions. Our expressions satisfy the desired properties: for bosons the particle number is positive, for fermions it lies in the interval between zero and one, and both are consistent with thermal field theory. As applications we consider the Bunch-Davies vacuum and fermionic preheating after inflation.
Prandtl number dependence of Nusselt number in direct numerical simulations
NASA Astrophysics Data System (ADS)
Kerr, Robert M.; Herring, Jackson R.
2000-09-01
The dependence of the Nusselt number Nu on the Rayleigh Ra and Prandtl Pr number is determined for 104 < Ra < 107 and 0.07 < Pr < 7 using DNS with no-slip upper and lower boundaries and free-slip sidewalls in a 8 × 8 × 2 box. Nusselt numbers, velocity scales and boundary layer thicknesses are calculated. For Nu there are good comparisons with experimental data and scaling laws for all the cases, including Ra2/7 laws at Pr = 0.7 and Pr = 7 and at low Pr, a Ra1/4 regime. Calculations at Pr = 0.3 predict a new Nu [similar] Ra2/7 regime at slightly higher Ra than the Pr = 0.07 calculations reported here and the mercury Pr = 0.025 experiments.
NASA Astrophysics Data System (ADS)
Baskaya, S.; Erturhan, U.; Sivrioglu, M.
2005-11-01
Mixed convection heat transfer from an array of discrete heat sources inside a rectangular channel has been investigated experimentally under various operating conditions for air. The lower surface of the channel was equipped with 8 × 4 flush-mounted heat sources subjected to uniform heat flux, sidewalls and the upper wall are insulated and adiabatic. The experimental parametric study was made for an aspect ratio of AR = 10, Reynolds numbers 241 ? ReDh ? 980, and modified Grashof numbers Gr* = 9.53 × 105 to 1.53 × 107 . From the experimental measurements, surface temperature distributions of the discrete heat sources were obtained and effects of Reynolds and Grashof numbers on these temperatures were investigated. Furthermore, Nusselt number distributions were calculated for different Reynolds and Grashof numbers, with emphasis on changes obtained for different discrete heat source locations. From these results, the buoyancy affected secondary flow and the onset of instability have been discussed. Results show that surface temperatures increase with increasing Grashof number and decrease with increasing Reynolds number. However, with the increase in the buoyancy affected secondary flow and the onset of instability, temperatures level off and even drop as a result of heat transfer enhancement. This outcome can also be observed from the variation of the row-averaged Nusselt number showing an increase towards the exit, especially for low Reynolds numbers.
Dependence of the Nusselt number on the Rayleigh number for Prandtl numbers near 0.7
NASA Astrophysics Data System (ADS)
Hogg, James; Ahlers, Guenter
2010-11-01
We report Nusselt-number measurements for a cylindrical Rayleigh-B'enard sample of height L = 49.6 cm and aspect ratio ?= 0.497 that were made using three pure gases: helium (Prandtl number Pr=0.67), nitrogen (Pr=0.73), and argon (Pr=0.67-0.70) at pressures up to 47 bars. They cover the Rayleigh number range 9x10^6 < Ra < 2x10^11. The uncorrected results are not well fit by the standard power law Nu Ra^?eff and the results for different gases disagree more than can be attributed to any expected Prandtl-number dependence. We find that a correction to the Nusselt number using a model for the non-linear temperature gradient in the side wall brings the results for different gases into agreement in their region of overlap. After the side-wall correction, the Nusselt number results are consistent with a power law, with ?eff 0.32 for relatively large Ra and ?eff 0.27 for relatively small Ra.
Transport Numbers in Transdermal Iontophoresis
Mudry, Blaise; Guy, Richard H.; Delgado-Charro, M. Begoña
2006-01-01
Parameters determining ionic transport numbers in transdermal iontophoresis have been characterized. The transport number of an ion (its ability to carry charge) is key to its iontophoretic delivery or extraction across the skin. Using small inorganic ions, the roles of molar fraction and mobility of the co- and counterions present have been demonstrated. A direct, constant current was applied across mammalian skin in vitro. Cations were anodally delivered from either simple M+Cl? solutions (single-ion case, M+ = sodium, lithium, ammonium, potassium), or binary and quaternary mixtures thereof. Transport numbers were deduced from ion fluxes. In the single-ion case, maximum cationic fluxes directly related to the corresponding ionic aqueous mobilities were found. Addition of co-ions decreased the transport numbers of all cations relative to the single-ion case, the degree of effect depending upon the molar fraction and mobility of the species involved. With chloride as the principal counterion competing to carry current across the skin (the in vivo situation), a maximum limit on the single or collective cation transport number was 0.6–0.8. Overall, these results demonstrate how current flowing across the skin during transdermal iontophoresis is distributed between competing ions, and establish simple rules with which to optimize transdermal iontophoretic transport. PMID:16443654
RECORDS RETENTION & DISPOSITION SCHEDULE AGENCY NUMBER SCHEDULE NUMBER
Rusu, Adrian
, upon expiration of their retention periods, will be deemed to have no continuing value to the State. It is in accordance with state college, state government, and federal government codes, statutes and regulations. All NUMBER SCHEDULE APPROVAL: Unless in litigation, the records covered by this schedule, upon expiration
Finite Prandtl Number 2-D Convection at High Rayleigh Number
Catherine Hier Majumder; David A. Yuen; Erik O. Sevre; John M. Boggs; Stephen Y. Bergeron
Finite Prandtl number thermal convection is important to the dynamics of planetary bodies in the solar system. For example, the complex geology on the surface of the Jovian moon Europa is caused by a convecting, brine-rich global ocean that deforms the overlying icy \\
Betti numbers and injectivity radii
Culler, Marc
2009-01-01
We give lower bounds on the maximal injectivity radius for a closed orientable hyperbolic 3-manifold M with first Betti number 2, under some additional topological hypotheses. A corollary of the main result is that if M has first Betti number 2 and contains no fibroid surface then its maximal injectivity radius exceeds 0.32798. For comparison, Andrew Przeworski showed, with no topological restrictions, that the maximal injectivity radius exceeds arcsinh(1/4) = 0.247..., while the authors showed that if M has first Betti number at least 3 then the maximal injectivity exceeds log(3)/2 = 0.549.... The proof combines a result due to Przeworski with techniques developed by the authors in the 1990s.
14 CFR 47.15 - Identification number.
Code of Federal Regulations, 2010 CFR
2010-01-01
...2010-01-01 2010-01-01 false Identification number. 47.15 Section 47...REGISTRATION General § 47.15 Identification number. (a) Number required...Aircraft Registration must place a U.S. identification number (registration...
Euler's number, a first introduction
NSDL National Science Digital Library
David Liao
In the first video segment, we introduce Euler's number by considering the problem of interest compounded continuously. After we obtain the power-series representation for exp(x), we explore its properties, in the next four video segments, to convince ourselves that exp(x) is literally an exponential function, meaning a number, approximately 2.71828, taken to the power x. In the final two segments, we present the natural logarithm and demonstrate that it is the anti-derivative of 1/x.
Newborn infants perceive abstract numbers
Izard, Véronique; Sann, Coralie; Spelke, Elizabeth S.; Streri, Arlette
2009-01-01
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. PMID:19520833
Learning math: Number and operations
NSDL National Science Digital Library
Carol R. Findell
2007-12-12
This online workshop for elementary and middle school teachers covers the real number system, place value, the behavior of zero and infinity, the meanings and models of basic operations, percentages, and modeling operations with fractions, often with the aid of concrete, physical models that enhance understanding. It also examines basic number theory topics, such as factors and multiples, as well as divisibility tests. Each of its ten sessions contains video programming, problem-solving activities provided online and in a print guide, and interactive activities and demonstrations on the Web.
Gardner, D.R.
1988-01-01
Natural convection in a fluid filling the narrow gap between two isothermal, concentric spheres at different temperatures is strongly dependent on radius ration, Prandtl number, and Grashof number. The gravitational acceleration vector is not everywhere parallel to the temperature gradient, and so the base flow is non-quiescent. Hence, this problem is different from the spherical analog of Rayleigh-Benard problem. For fixed values of radius ratio and Prandtl number, the flow is steady and axisymmetric for sufficiently small Grashof number, or quasi-periodic and axisymmetric for Grashof numbers greater than a critical values. The hypothesis that the transition is a flow bifurcation is tested by solving an appropriate eigenvalue problem for infinitesimal disturbances to the base flow in a Boussinesq fluid. The numerical solution of the eigenvalue problem involves the use of poloidal and toroidal potentials; and a new spectral method, called the modified tau method, which eliminates spurious eigenvalues. The critical Grashof number, critical eigenvalues, and corresponding eigenvectors are obtained as functions of the radius ratio, Prandtl number, and longitudinal wave number.
Random Numbers a quick and dirty guide
A simple PRNG Measuring random number quality Random number generators as dynamical systems RANLUX "Bad" random numbers in tmLQCD Conclusions #12;Introduction True random numbers + truly random number generator deterministic algorithm to produce numbers that "look random" Figures of merit period
Real numbers. Constants, variables, and mathematical modeling.
Alekseenko, Alexander
with their multiplicative inverses we get Rational numbers, or numbers of the form m n , where m and n are integer numbers. It can be verified that all addition and multiplication properties make sense for the rational numbers and multiplicative inverses to m n ? The Irrational numbers is the next stage after the Rational numbers
Student Learning Centre Review of Number
directions, { ... , -4 , -3 , -2 , -1 , 0 , 1, 2 , 3 , 4 , 5, ...} is the set of integers. Rational numbers are all the numbers on the real number line that are not rational, e.g. 2, -10, ,5 /2 Every real number) integers (d) negative real numbers (e) rational (f) irrational (g) prime (h) composite 2. Use a number line
Note on the Theory of Perfect Numbers
N. A. Carella
2011-03-03
A perfect number is a number whose divisors add up to twice the number itself. The existence of odd perfect numbers is a millennia-old unsolved problem. This note proposes a proof of the nonexistence of odd perfect numbers. More generally, the same analysis seems to generalize to a proof of the nonexistence of odd multiperfect numbers.
Two Problems of Number Theory Manindra Agarwal
Agrawal, Manindra
Two Problems of Number Theory Manindra Agarwal IIT Kanpur LSR Delhi, September 18, 2009 Manindra Theory Number Theory is the study of properties of numbers. Here, by numbers, we mean integers Kanpur) Two Problems of NT LSR, 09/2009 3 / 43 #12;Number Theory Number Theory is the study of properties
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…
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…
Mitosis and Meiosis Chromosome number
Dellaire, Graham
Lecture 5 Mitosis and Meiosis #12;Chromosome number Early improvements in our ability to look look at normal chromosomes as they go through mitosis and meiosis #12; Mitosis The biologic function is to produce 2 identical cells Mitotic cell cycle #12;#12;Mitosis #12;Difference between a cell entering
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
McGaughey, Alan
at Giant Eagle. Clear Green Brown Blue Steel Tin Aluminum Please rinse before recycling. Batteries - UCLook for these numbers located on the bottom or sides of the container Plastic bags can be recycled info desk, Mellon 3rd floor, or sent by campus mail to FMS recycling CDs - UC recycling center or sent
Florida Statewide Course Numbering System.
ERIC Educational Resources Information Center
Florida State Dept. of Education, Tallahassee. Office of Postsecondary Education Coordination.
In an effort to fulfill state policies on higher education articulation and student transfers, the Florida state legislature encouraged establishment of a common Statewide Course Numbering System (SCNS) which is presented in this document. Early sections describe the establishment and development of the SCNS and logistics of its maintenance. Also…
Hogendijk, Jan P.
the language of the Nuzhah and that of llrc Persian version are paralIeI, but with some divergence. Irr give the folio and the Persian manuscript. Numbers enclosed in are references to the bibliography which medieval ïslamic scientific books. fn contrast to the bald unadorned language of the text proper
Quinn McNemar
1942-01-01
A proposed criterion for the number of factors is developed on the basis of the similarity between a factorial residual and the partial correlation coefficient; something is known concerning the sampling error of the latter. Instead of computing the residuals as partials, a formula is presented for adjusting the standard deviation of the distribution of residuals so as to approximate
Fibonacci numbers and trigonometric identities
N. Garnier; O. Ramare
2006-01-01
Webb & Parberry proved in 1969 a startling trigonometric iden- tity involving Fibonacci numbers. This identity has remained isolated up to now, despite the amount of work on related polynomials. We provide a wide generalization of this identity together with what we believe (and hope!) to be its proper understanding.
Access to Emergency Number Services
Judith E. Harkins; Karen Peltz Strauss
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)
MOTOR POOL RESERVATIONS Reservation Number:_______________
Shahriar, Selim
: __________________________ Vehicle Type: ____________________________ Number of Passengers: ______________________ Pick Up Date: ____________________________ Pick Up Time: ______________________________ Return Date: _____________________________ Return Time.m. to 5:00 p.m., Monday to Friday Hours: 8:00 a.m. to 5:00 p.m., Monday to Friday Date of Request
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)
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) "Youth Music"; (3) "Urban…
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. PMID:24266008
volume 41 number 1 agroborealis
Wagner, Diane
volume 41 number 1 2010 agroborealis School of Natural Resources and Agricultural Sciences, is dependent upon Outside sources. ...By Thomas F. Paragi, S. Craig Gerlach, and Alison M. Meadow natural, and purple. See story on p. 23. --photos by Glenn oliver Eggs dyed with birch bark dye, one of dozens
900 Numbers: A Controversial Industry.
ERIC Educational Resources Information Center
Galvez, Nancy D.
1992-01-01
Pay-per-call telephone services through 900 numbers have given rise to criticism of their content and complaints of consumer fraud. The Federal Communications Commission, legislative initiatives, industry self-regulation, and consumer educators are attempting to protect consumers. (SK)
Europe Note Europe note number
Müller, Jens-Dominik
1 Europe Note Europe note number: E/2012/03 Date 15 April 2012 Distribution Vice degrees and collaborative degrees; · recognition of UK qualifications elsewhere in Europe; · institutional by the European Commission, the Council of Europe and UNESCO/CEPES. This compares with 87% in 2009 and 81% in 2007
Europe Note Europe note number
Müller, Jens-Dominik
1 Europe Note Europe note number: E/2012/05 Date 23 April 2012 Distribution Vice qualifications elsewhere in Europe; · institutional strategies and responsibility for the Bologna Process (or 60%) use the standard format developed by the European Commission, the Council of Europe
Europe Note Europe note number
Müller, Jens-Dominik
Europe Note Europe note number: E/2012/04 Date 23 April 2012 Distribution Vice of UK qualifications elsewhere in Europe; · institutional strategies and responsibility for the Bologna by the European Commission, the Council of Europe and UNESCO/CEPES. This contrasts with the 2009 results, when
Davies, Christopher
is z. 6 ? z Surface P Ignoring atmospheric pressure, the pressure, p, at P is measured as the thrust"JUST THE MATHS" UNIT NUMBER 13.16 INTEGRATION APPLICATIONS 16 (Centres of pressure) by A.J.Hobson 13.16.1 The pressure at a point in a liquid 13.16.2 The pressure on an immersed plate 13
Random number generators for microcomputers.
Rosenbaum, W; Syrotuik, J; Gordon, R
1983-06-01
The feasibility of random number generation using microcomputers is discussed and the appropriateness of alternative algorithms is evaluated on the basis of several criteria of statistical randomness. The relative deficiencies of each algorithm are cited and a modified Fibonacci generator is recommended for use in the microcomputer environment. PMID:6688575
Davies, Christopher
.1.1 Arithmetic progressions 2.1.2 Arithmetic series 2.1.3 Geometric progressions 2.1.4 Geometric series 2 - ELEMENTARY PROGRESSIONS AND SERIES 2.1.1 ARITHMETIC PROGRESSIONS The "sequence" of numbers, a, a + d, a + 2d, a + 3d, ... is said to form an "arithmetic progression". The symbol a represents the "first term
NSDL National Science Digital Library
2012-08-03
In this activity, students use the binary number system to transmit messages. Two flashlights are used to demonstrate how astronomy spacecraft to transmit images and other scientific data to Earth. This activity is part of Unit 4 in the Space Based Astronomy guide that contains background information, worksheets, assessments, extensions, and standards.
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.)
Symmetry in Numbers David Marshall
Marshall, David
Symmetry in Numbers David Marshall Monmouth University April 13, 2005 808 -2 3 + 3 -169 54 + 1007 18 + 3 -169 54 - 1007 18 Â Typeset by FoilTEX Â #12;Symmetry One of the guiding principles group of symmetries. -Paul Yale, in Geometry and Symmetry 2. Due or just proportion; harmony of parts
Wisconsin at Madison, University of
-2 with EAD SSN (Social Security Number) Research Assistant Student Assistant Y41NN Any Visa Type UW-in-Training X30NN Graduate Intern/Trainee Employee-in-Training X75NN Fellow Student Assistant Y21NN Scholar Student Assistant Y22NN Trainee Student Assistant Y23NN Adv. Opportunity Fellow Student Assistant Y26NN J
Cosmic Rays and Sunspot Numbers
NSDL National Science Digital Library
Susan Higley
In this activity students analyze and compare two or more graphs to determine if there is a correlation between sunspot number and the variation of cosmic ray flux. They discover that cosmic rays are very energetic particles, mostly protons and electrons, that enter the solar system from the depths of interstellar space and that although the Earth's magnetic field partially shields us from these particles, so too does the much more extended solar wind with its own magnetic field. This is a three-part lesson in which students will construct line graphs displaying the cosmic ray flux and sunspot numbers for a period of time, and then determine if there is a correlation. In order to compare these two sets of data, students will need to scale the data in order to visualize the results. Teacher and student notes for the graphing calculator are included.
Remarks On General Fibonacci Numbers
Masum Billal
2015-02-22
We dedicate this paper to investigate the most generalized form of Fibonacci Sequence, one of the most studied sections of the mathematical literature. One can notice that, we have discussed even a more general form of the conventional one. Although it seems the topic in the first section has already been covered before, but we present a different proof here. Later I found out that, the auxiliary theorem used in the first section was proven and even generalized further by F. T. Howard. Thanks to Curtis Cooper for pointing out the fact that this has already been studied and providing me with references. the At first, we prove that, only the common general Fibonacci Sequence can be a divisible sequence under some restrictions. In the latter part, we find some properties of the sequence, prove that there are infinite alternating bisquable Fibonacci sequence(defined later) and provide a lower bound on the number of divisors of Fibonacci numbers.
Women in Politics: Beyond Numbers
NSDL National Science Digital Library
Developed by the International Institute for Democracy and Electoral Assistance (IDEA), Women in Politics: Beyond Numbers is an initiative devoted to researching, evaluating, and promoting the role and impact of women in the advancement of sustainable democracy and electoral processes worldwide. This Website functions as an international resource providing information about IDEA's research projects and publications related to women's political involvement. The site features an extensive report, "Women in Parliament: Beyond Numbers," that examines such issues as obstacles to women's political participation and the impact of women in international politics, as well as compares the involvement of women within various electoral systems. The site also includes links to relevant resources and maintains several interactive forums for discussing IDEA's projects to enhance women's political participation.
Ikenaga, Bruce
3-30-2008 Complex Numbers A complex number is a number of the form a + bi, where a and b are real numbers and i = -1 (so i2 = -1). For example, here are some complex numbers: 2 + 3i, -77.5i, 13 7, -54, 1 + i 2 . Notice that real numbers are special kinds of complex numbers -- namely, those that don
NASA Astrophysics Data System (ADS)
Richman, Robert M.
1998-05-01
A recent paper has argued that the derivation of the periodic table using quantum numbers is a topic that should be eliminated from introductory chemistry courses because it is too abstract, mysterious, and esoteric. A rebuttal is offered based on the claim that it would be wrong to omit discussions of the inductive approach of Mendeleev and the deductive approach initiated by Schroedinger, because they compose the consummate example of that interaction of empirical and rational epistemologies that defines how chemists think.
Large Number Discrimination by Mosquitofish
Agrillo, Christian; Piffer, Laura; Bisazza, Angelo
2010-01-01
Background Recent studies have demonstrated that fish display rudimentary numerical abilities similar to those observed in mammals and birds. The mechanisms underlying the discrimination of small quantities (<4) were recently investigated while, to date, no study has examined the discrimination of large numerosities in fish. Methodology/Principal Findings Subjects were trained to discriminate between two sets of small geometric figures using social reinforcement. In the first experiment mosquitofish were required to discriminate 4 from 8 objects with or without experimental control of the continuous variables that co-vary with number (area, space, density, total luminance). Results showed that fish can use the sole numerical information to compare quantities but that they preferentially use cumulative surface area as a proxy of the number when this information is available. A second experiment investigated the influence of the total number of elements to discriminate large quantities. Fish proved to be able to discriminate up to 100 vs. 200 objects, without showing any significant decrease in accuracy compared with the 4 vs. 8 discrimination. The third experiment investigated the influence of the ratio between the numerosities. Performance was found to decrease when decreasing the numerical distance. Fish were able to discriminate numbers when ratios were 1?2 or 2?3 but not when the ratio was 3?4. The performance of a sample of undergraduate students, tested non-verbally using the same sets of stimuli, largely overlapped that of fish. Conclusions/Significance Fish are able to use pure numerical information when discriminating between quantities larger than 4 units. As observed in human and non-human primates, the numerical system of fish appears to have virtually no upper limit while the numerical ratio has a clear effect on performance. These similarities further reinforce the view of a common origin of non-verbal numerical systems in all vertebrates. PMID:21203508
Random Numbers from Astronomical Imaging
Kevin A. Pimbblet; Michael Bulmer
2004-08-16
This article describes a method to turn astronomical imaging into a random number generator by using the positions of incident cosmic rays and hot pixels to generate bit streams. We subject the resultant bit streams to a battery of standard benchmark statistical tests for randomness and show that these bit streams are statistically the same as a perfect random bit stream. Strategies for improving and building upon this method are outlined.
Diophantine approximations with Fibonacci numbers
Zhuravleva, Victoria
2011-01-01
Let $F_{n}$ be the $n$-th Fibonacci number. Put $\\varphi=\\frac{1+\\sqrt5}{2}$. We prove that the following inequalities hold for any real $\\alpha$: 1) $\\inf_{n \\in \\mathbb N} ||F_n\\alpha||\\le\\frac{\\varphi-1}{\\varphi+2}$, 2) $\\liminf_{n\\to \\infty}||F_n\\alpha||\\le 1/5$, 3) $\\liminf_{n \\to \\infty}||\\varphi^n \\alpha||\\le 1/5$. These results are the best possible.
Fibonacci numbers and orthogonal polynomials
Christian Berg
2006-01-01
We prove that the sequence $(1\\/F_{n+2})_{n\\\\ge 0}$ of reciprocals of the Fibonacci numbers is a moment sequence of a certain discrete probability, and we identify the orthogonal polynomials as little $q$-Jacobi polynomials with $q=(1-\\\\sqrt{5})\\/(1+\\\\sqrt{5})$. We prove that the corresponding kernel polynomials have integer coefficients, and from this we deduce that the inverse of the corresponding Hankel matrices $(1\\/F_{i+j+2})$ have integer
Lozenge tilings and Hurwitz numbers
Jonathan Novak
2014-12-27
We give a new proof of the fact that, near a turning point of the frozen boundary, the vertical tiles in a uniformly random lozenge tiling of a large sawtooth domain are distributed like the eigenvalues of a GUE random matrix. Our argument uses none of the standard tools of integrable probability. In their place, it uses a combinatorial interpretation of the Harish-Chandra/Itzykson-Zuber integral as a generating function for desymmetrized Hurwitz numbers.
NSDL National Science Digital Library
2014-01-01
This website, devoted to early numeracy skills, includes links to Happy Numbers teacher accounts, student accounts, and blog. A free teacher account provides access to applets that develop conceptual understanding and procedural fluency. The applets are compatible with interactive whiteboards and tablets. With a subscription teachers can create student accounts and individualize assignments. The blog posts further explain how to utilize these applets in the classroom.
Upper bounds for Ramsey numbers
Lingsheng Shi
2003-01-01
The Ramsey number R(G1,G2,…,Gk) is the least integer p so that for any k-edge coloring of the complete graph Kp, there is a monochromatic copy of Gi of color i. In this paper, we derive upper bounds of R(G1,G2,…,Gk) for certain graphs Gi. In particular, these bounds show that R(9,9)?6588 and R(10,10)?23556 improving the previous best bounds of 6625 and
Descendant invariants and characteristic numbers
Thomas Benjamin Graber; Joachim Kock; Rahul Pandharipande
2002-01-01
On a stack of stable maps, the psi classes are modified by subtracting\\u000acertain boundary divisors. These modified psi classes are compatible with\\u000aforgetful morphisms, and are well-suited to enumerative geometry: tangency\\u000aconditions allow simple expressions in terms of modified psi classes.\\u000aTopological recursion relations are established among their top products in\\u000agenus zero, yielding effective recursions for characteristic numbers
Ultrafilters and combinatorial number theory
Neil Hindman; Los Amgeles
Our concern is with two areas of mathematics and a, possibly surprising, intimate connection between them. One is the branch\\u000a of combinatorial number theory which deals with the ability, given a finite partition of ?, to find sums or products of certain\\u000a descriptions lying in one cell of that partition. The other is the branch of set theoretic topology dealing
Algorithms in algebraic number theory
Hendrik W. Lenstra Jr.
1992-01-01
In this paper we discuss the basic problems of algorithmic algebraic number\\u000atheory. The emphasis is on aspects that are of interest from a purely\\u000amathematical point of view, and practical issues are largely disregarded. We\\u000adescribe what has been done and, more importantly, what remains to be done in\\u000athe area. We hope to show that the study of
Accurate Nusselt-number measurements at high Rayleigh numbers
NASA Astrophysics Data System (ADS)
Xu, Xiaochao; Bajaj, Kapil M. S.; Ahlers, Guenter
2000-03-01
Measurements by others(See, e.g., X. Wu and A. Libchaber, Phys. Rev. A 45), 842 (1992); and J.J. Niemela, L. Skrbek, K.R. Sreenivasan, and R.J. Donnelly, preprint. of the Nusselt number N as a function of the Rayleigh number R, when fitted to N = N0 R ^ ?, yielded ? in the range 0.28 to 0.31. Theoretical values based on different models cover a similar range, making it difficult to distinguish between them on the basis of experiment. We made new measurements in a cylindrical cell of aspect ratio ? = d/h = 1 with a diameter d and height h of 87 mm, using acetone. The cell top was optically flat sapphire, and the bottom diamond-machined aluminum. We measured the heat currents which do not pass through the fluid with an evacuated cell. The fluid properties are known extremely well. Thus we hope to have eliminated most systematic errors. The Prandtl number was 4.0 at the mean temperature of 32.0^oC. The heat currents were measured with an accuracy of 0.1%. The temperature differences were from 0.080^circC to 34.00^circC, corresponding to 2.2× 10^7 <= R <= 9.1× 10^9. A preliminary analysis over the range 10^8 < R < 10^10 yielded ?=0.291±0.004 and N_0=0.16. Further experiments over a larger range of R and ? are under way.
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.
Numbers in English and Chinese language use
ZHANG Wu-ping
2007-01-01
The cultural connotations of numbers in English and Chinese languages are demonstrated to discuss the grammatical functions of the numbers and their rhetoric usages. For a foreign language learner, it is essential that they know not only the denotation of the numbers, but also the connotation of the numbers. Numbers frequently play an important role in daily communication.
Permutations, Parenthesis Words, and Schroder Numbers
Harju, Tero
Permutations, Parenthesis Words, and SchrÂ¨oder Numbers A. Ehrenfeucht1 T. Harju2 P. ten Pas3 G due to J. West is given: the SchrÂ¨oder number sn-1 equals the number of permutations on {1, 2, SchrÂ¨oder numbers, Catalan numbers, parenthe- sis words 1 Introduction We give here a different
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,…
KISSING NUMBERS FOR SURFACES Hugo Parlier
Parlier, Hugo
KISSING NUMBERS FOR SURFACES Hugo Parlier Abstract. The so-called kissing number for hyperbolic. INTRODUCTION The classical kissing number problem for sphere packings is the search for an optimal upper bound be tangent to a fixed unit sphere. Exact values for these numbers, commonly called kissing numbers
Tafelbild zum Einstieg Das Kissing Number Problem
69 Tafelbild zum Einstieg #12;70 Das Kissing Number Problem Definition: Kissing Number __________________________________________________________________________________________________ __________________________________________________________________________________________________ Figur / KÃ¶rper Kreise Quadrate gleichseitige Dreiecke Kugeln Kissing Number Skizze der Anordnung Name: ________________________ Symbol: Stammgruppenfarbe: __________ #12;71 Definition: Kissing Number Als Kissing Number einer Figur
ON -GREEDY EXPANSIONS OF NUMBERS CLEMENS HEUBERGER
Heuberger, Clemens
a redundant binary number system that was recently introduced by SzÂ´ekely and Wang. For a natural number nÂ´ekely and Wang [21, 22] invented a novel binary number system when study- ing trees with a large number/ instead of just ). Clearly, = 1 just produces the traditional binary number system. We study
hp calculators HP 50g Complex numbers
Vetter, Frederick J.
hp calculators HP 50g Complex numbers The MTH (MATH) menu The CMPLX (COMPLEX) menu Complex numbers Practice working problems involving complex numbers #12;hp calculators HP 50g Complex numbers hp calculators - 2 - HP 50g Complex numbers The MTH (MATH) menu The Math menu is accessed from the WHITE shifted
NSDL National Science Digital Library
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Find a number greater than 0 and less than 1,000 that: Is closer to 500 than 0, and Is closer to 200 than 500. There are many correct answers to this p...
Code of Federal Regulations, 2012 CFR
2012-01-01
...Agriculture 8 2012-01-01 2012-01-01 false Lot number. 987.102 Section 987.102 Agriculture...CALIFORNIA Administrative Rules Definitions § 987.102 Lot number. Lot number is synonymous with code and means a...
Code of Federal Regulations, 2013 CFR
2013-01-01
...Agriculture 8 2013-01-01 2013-01-01 false Lot number. 987.102 Section 987.102 Agriculture...CALIFORNIA Administrative Rules Definitions § 987.102 Lot number. Lot number is synonymous with code and means a...
Code of Federal Regulations, 2014 CFR
2014-01-01
...Agriculture 8 2014-01-01 2014-01-01 false Lot number. 987.102 Section 987.102 Agriculture...CALIFORNIA Administrative Rules Definitions § 987.102 Lot number. Lot number is synonymous with code and means a...
Code of Federal Regulations, 2011 CFR
2011-01-01
...Agriculture 8 2011-01-01 2011-01-01 false Lot number. 987.102 Section 987.102 Agriculture...CALIFORNIA Administrative Rules Definitions § 987.102 Lot number. Lot number is synonymous with code and means a...
Expansion of algebraic numbers Complexity of words
Waldschmidt, Michel
Expansion of algebraic numbers Complexity of words Words and transcendence Continued fractions Survey of some recent results on the complexity of expansions of algebraic numbers Michel Waldschmidt Expansion of algebraic numbers Complexity of words Words and transcendence Continued fractions Diophantine
Braess's Paradox, Fibonacci Numbers, and Exponential Inapproximability
Lin, Henry
Braess's Paradox, Fibonacci Numbers, and Exponential Inapproximability Henry Lin # , Tim of twocommodity networks, related to the Fibonacci numbers, in which both of these quantities grow commodity networks is arguably quite unexpected, given the negligible dependence on the number
REGULAR ARTICLE Reproductive Numbers for Nonautonomous Spatially
Bravo de la Parra, Rafael
, aggregated, system. We derive global reproduction numbers governing the general spatially distributed through the reproduction numbers of the corresponding averaged systems (the autonomous systems obtainedREGULAR ARTICLE Reproductive Numbers for Nonautonomous Spatially Distributed Periodic SIS Models
47 CFR 32.20 - Numbering convention.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 2 2010-10-01 2010-10-01 false Numbering convention. 32.20 Section 32.20 Telecommunication FEDERAL...TELECOMMUNICATIONS COMPANIES General Instructions § 32.20 Numbering convention. (a) The number “32” (appearing to the left of...
47 CFR 32.20 - Numbering convention.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 2 2011-10-01 2011-10-01 false Numbering convention. 32.20 Section 32.20 Telecommunication FEDERAL...TELECOMMUNICATIONS COMPANIES General Instructions § 32.20 Numbering convention. (a) The number “32” (appearing to the left of...
Agrillo, Christian; Dadda, Marco; Serena, Giovanna; Bisazza, Angelo
2009-01-01
Background Research on human infants, mammals, birds and fish has demonstrated that rudimentary numerical abilities pre-date the evolution of human language. Yet there is controversy as to whether animals represent numbers mentally or rather base their judgments on non-numerical perceptual variables that co-vary with numerosity. To date, mental representation of number has been convincingly documented only for a few mammals. Methodology/Principal Findings Here we used a training procedure to investigate whether mosquitofish could learn to discriminate between two and three objects even when denied access to non-numerical information. In the first experiment, fish were trained to discriminate between two sets of geometric figures. These varied in shape, size, brightness and distance, but no control for non-numerical variables was made. Subjects were then re-tested while controlling for one non-numerical variable at a time. Total luminance of the stimuli and the sum of perimeter of figures appeared irrelevant, but performance dropped to chance level when stimuli were matched for the cumulative surface area or for the overall space occupied by the arrays, indicating that these latter cues had been spontaneously used by the fish during the learning process. In a second experiment, where the task consisted of discriminating 2 vs 3 elements with all non-numerical variables simultaneously controlled for, all subjects proved able to learn the discrimination, and interestingly they did not make more errors than the fish in Experiment 1 that could access non-numerical information in order to accomplish the task. Conclusions/Significance Mosquitofish can learn to discriminate small quantities, even when non-numerical indicators of quantity are unavailable, hence providing the first evidence that fish, like primates, can use numbers. As in humans and non-human primates, genuine counting appears to be a ‘last resort’ strategy in fish, when no other perceptual mechanism may suggest the quantity of the elements. However, our data suggest that, at least in fish, the priority of perceptual over numerical information is not related to a greater cognitive load imposed by direct numerical computation. PMID:19274079
Natural convection in unsteady Couette motion
A. K. Singh
1988-01-01
Unsteady free convective flow of an incompressible viscous fluid between two vertical parallel plates is considered for impulsive start of one of the plates. Expressions for velocity and temperature fields and their related quantities are obtained by the Laplace transform technique. The effect of Grashof number is to increase the velocity of both air and water and to decrease the
Estimation of convective mass transfer in solar distillation systems
Sanjay Kumar; G. N. Tiwari
1996-01-01
In this article a thermal model has been developed to determine the convective mass transfer for different Grashof Number range in solar distillatiOn process. The model is based on simple regression analysis. Based on the experimental data obtained from the rigorous outdoor experimentation on passive and active distillation systems for summer climatic conditions, the values of C and n have
Eric Lauga
2009-04-28
In many biological systems, microorganisms swim through complex polymeric fluids, and usually deform the medium at a rate faster than the inverse fluid relaxation time. We address the basic properties of such life at high Deborah number analytically by considering the small-amplitude swimming of a body in an arbitrary complex fluid. Using asymptotic analysis and differential geometry, we show that for a given swimming gait, the time-averaged leading-order swimming kinematics of the body can be expressed as an integral equation on the solution to a series of simpler Newtonian problems. We then use our results to demonstrate that Purcell's scallop theorem, which states that time-reversible body motion cannot be used for locomotion in a Newtonian fluid, breaks down in polymeric fluid environments.
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. PMID:24361686
Mascarenhas, Walter Figueiredo
DENORMAL NUMBERS IN FLOATING POINT SIGNAL PROCESSING APPLICATIONS Denormal numbers in floating Signal Processing, CPU Copyright 2002-2005 Laurent de Soras Page 1/10 #12;DENORMAL NUMBERS IN FLOATING.............................................................................................................. 2 1. FLOATING POINT NUMBER CODING OVERVIEW...................................................... 3 1
Analysis of Random Number Generators Parijat Naik
generators can produce incorrect results. A. True Random Number Generators Security protocols heavily depend1 Analysis of Random Number Generators Parijat Naik Department of Computer Science Oregon State Random number generators are used for generating an array of numbers that have a random distribution
Producing Number Agreement: How Pronouns Equal Verbs
ERIC Educational Resources Information Center
Bock, Kathryn; Eberhard, Kathleen M.; Cutting, J. Cooper
2004-01-01
The major targets of number agreement in English are pronouns and verbs. To examine the factors that control pronoun number and to test pronouns against a psycholinguistic account of how verb number arises during language production, we varied the meaningful and grammatical number properties of agreement controllers and examined the impact of…
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…
Girotondo dei Numeri (A Ring of Numbers).
ERIC Educational Resources Information Center
Palandra, Maria; And Others
This workbook in Italian for learning the numbers from one to ten is intended for use in a bilingual education setting. It is introduced and concluded by a song about playing "ring around the rosy" with numbers. Each paqe has a pen and ink drawing illustrating the number and a sentence about the picture and the number. (AMH)
A Kilobit Special Number Field Sieve Factorization
Lenstra, Arjen K.
A Kilobit Special Number Field Sieve Factorization Kazumaro Aoki1 , Jens Franke2 , Thorsten special number field sieve factorization of a number having more than 1024 bits, namely the Mersenne number 21039 - 1. Although this factorization is orders of magnitude `easier' than a fac- torization
Fun With Complex Numbers Algebra 5/Trig
Lega, Joceline
Fun With Complex Numbers Algebra 5/Trig Spring 2010 Instructions: There are none! This contains questions by these subsections. 1 Background Recall that the complex number system C is the set of all complex numbers in section 1.5 of your textbook. You should be accustomed to thinking of the real numbers
The Kolmogorov Complexity of Liouville Numbers \\Lambda
The Kolmogorov Complexity of Liouville Numbers \\Lambda Ludwig Staiger Institut für Informatik The complexity of real numbers 8 3.1 Random reals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 The Kolmogorov complexity of Liouville numbers . . . . . . . . 9 3.3 The Hausdorff dimension of Liouville numbers
On the Betti Numbers of Chessboard Complexes
Joel Friedman; Phil Hanlony
1998-01-01
In this paper we study the Betti numbers of a type of simplicial complex known as a chessboard complex. We obtain a formula for their Betti numbers as a sum of terms involving partitions. This formula allows us to determine which is the first nonvanishing Betti number (aside from the 0-th Betti number). We can therefore settle certain cases 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 Architecture"; (4) "Fibonacci Numbers…
NOTES ON COMPLEX NUMBERS DAVID M. MCCLENDON
McClendon, David M.
which solves the equation 2x = 3. 1.3. Rational numbers. To fix this, we consider the rational numbers divisors, and q = 0. What is great about the rational numbers is that you get all the pros of the integers and you can also divide one rational number by another (as long as the divisor is not zero) and get
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…
Semiperfect and Integer-Perfect Numbers.
ERIC Educational Resources Information Center
Costello, Patrick
1991-01-01
The number theory concepts of perfect, deficient, and abundant numbers are subdivided and then utilized to discuss propositions concerning semiperfect, weird, and integer-perfect numbers. Conjectures about relationships among these latter numbers are suggested as avenues for further investigation. (JJK)
Logic Design Chapter 1: Binary Numbers
Wu, Xiaolin
· Decimal number system As a digit has 10 possible values (human hands!), decimal numbers are said with decimal numbers consisting of digits of 10 possible values, 0, 1, ..., 9 Decimal vs. Binary Numbers of four bits: nibble · A group of eight bits: byte Conversion between Decimal and Binary · Converting
h-analogue of Fibonacci Numbers
H. B. Benaoum
2009-09-30
In this paper, we introduce the h-analogue of Fibonacci numbers for non-commutative h-plane. For h h'= 1 and h = 0, these are just the usual Fibonacci numbers as it should be. We also derive a collection of identities for these numbers. Furthermore, h-Binet's formula for the h-Fibonacci numbers is found and the generating function that generates these numbers is obtained.
Amr Elmasry; Claus Jensen; Jyrki Katajainen
2010-01-01
\\u000a We introduce a new number system that supports increments with a constant number of digit changes. We also give a simple method\\u000a that extends any number system supporting increments to support decrements using the same number of digit changes. In the\\u000a new number system the weight of the ith digit is 2\\u000a i\\u000a ??1, and hence we can implement a
On the number of prime factors of an odd perfect number
Ochem, Pascal
On the number of prime factors of an odd perfect number Pascal Ochem CNRS, LIRMM, Universit) and (n) denote respectively the total number of prime factors and the number of distinct prime factors the total number of prime factors and the number of dis- tinct prime factors of the integer n. Euler proved
Department for Analysis and Computational Number Theory Non-normal numbers
Liège, Université de
Department for Analysis and Computational Number Theory Non-normal numbers The interplay Number Theory Graz University of Technology madritsch@math.tugraz.at Combinatorics, Automata and Number-normal numbers CANT, 21 may 2012 1 / 29 #12;Department for Analysis and Computational Number Theory Outline
Number systems, ?-splines and refinement
NASA Astrophysics Data System (ADS)
Zube, Severinas
2004-12-01
This paper is concerned with the smooth refinable function on a plane relative with complex scaling factor . Characteristic functions of certain self-affine tiles related to a given scaling factor are the simplest examples of such refinable function. We study the smooth refinable functions obtained by a convolution power of such charactericstic functions. Dahlke, Dahmen, and Latour obtained some explicit estimates for the smoothness of the resulting convolution products. In the case ?=1+i, we prove better results. We introduce ?-splines in two variables which are the linear combination of shifted basic functions. We derive basic properties of ?-splines and proceed with a detailed presentation of refinement methods. We illustrate the application of ?-splines to subdivision with several examples. It turns out that ?-splines produce well-known subdivision algorithms which are based on box splines: Doo-Sabin, Catmull-Clark, Loop, Midedge and some -subdivision schemes with good continuity. The main geometric ingredient in the definition of ?-splines is the fundamental domain (a fractal set or a self-affine tile). The properties of the fractal obtained in number theory are important and necessary in order to determine two basic properties of ?-splines: partition of unity and the refinement equation.
Prime number generation and factor elimination
Vineet Kumar
2014-10-06
We have presented a multivariate polynomial function termed as factor elimination function,by which, we can generate prime numbers. This function's mapping behavior can explain the irregularities in the occurrence of prime numbers on the number line. Generally the different categories of prime numbers found till date, satisfy the form of this function. We present some absolute and probabilistic conditions for the primality of the number generated by this method. This function is capable of leading to highly efficient algorithms for generating prime numbers.
The Euclidean Algorithm in Cubic Number Fields
Cavallar, Stefania
2012-01-01
In this note we present algorithms for computing Euclidean minima of cubic number fields; in particular, we were able to find all norm-Euclidean cubic number fields with discriminants -999 < d < 10000.
A determinant of generalized Fibonacci numbers
Krattenthaler, Christian
2012-01-01
We evaluate a determinant of generalized Fibonacci numbers, thus providing a common generalization of several determinant evaluation results that have previously appeared in the literature, all of them extending Cassini's identity for Fibonacci numbers.
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)
ChemTeacher Resource: Oxidation Number Exercise
NSDL National Science Digital Library
2012-08-02
This is an exercise in determining the oxidation numbers in ions and compounds. Calculate the oxidation numbers of all the elements using the standard assignment rules, then mouse over the formula to reveal the answers.
Rockin' Round the Number Line: Lesson Two
NSDL National Science Digital Library
Andreas Howell
2012-07-23
After completing the formative assessments for proficiency with place value, the concept of "half-way", and estimation using a real world context, students will complete the lesson which uses their prior knowledge to support them in drawing conclusions about number patterns used in estimation and rounding numbers. Students will identify which "ten" or "hundred" the whole number falls closest to based on whether the number falls before or after a "half-way" number. Finally students will conclude that there are number patterns that guide estimation when one does not have a specific context that determines a need. Specifically we can use "half-way" numbers that are multiples of 5 to guide whether we "round up" or "round down" when estimating stand alone numbers.
48 CFR 304.7001 - Numbering acquisitions.
Code of Federal Regulations, 2010 CFR
2010-10-01
...Officer shall also assign the letter contract number to the superseding definitized contract.) (2) Basic ordering agreements (BOAs) and BPAs. (3) Requests for proposals and invitations for bids. (4) Requests for quotations. (b) Numbering...
48 CFR 304.7001 - Numbering acquisitions.
Code of Federal Regulations, 2014 CFR
2014-10-01
...Officer shall also assign the letter contract number to the superseding definitized contract.) (2) Basic ordering agreements (BOAs) and BPAs. (3) Requests for proposals and invitations for bids. (4) Requests for quotations. (b) Numbering...
48 CFR 304.7001 - Numbering acquisitions.
Code of Federal Regulations, 2013 CFR
2013-10-01
...Officer shall also assign the letter contract number to the superseding definitized contract.) (2) Basic ordering agreements (BOAs) and BPAs. (3) Requests for proposals and invitations for bids. (4) Requests for quotations. (b) Numbering...
48 CFR 304.7001 - Numbering acquisitions.
Code of Federal Regulations, 2011 CFR
2011-10-01
...Officer shall also assign the letter contract number to the superseding definitized contract.) (2) Basic ordering agreements (BOAs) and BPAs. (3) Requests for proposals and invitations for bids. (4) Requests for quotations. (b) Numbering...
48 CFR 304.7001 - Numbering acquisitions.
Code of Federal Regulations, 2012 CFR
2012-10-01
...Officer shall also assign the letter contract number to the superseding definitized contract.) (2) Basic ordering agreements (BOAs) and BPAs. (3) Requests for proposals and invitations for bids. (4) Requests for quotations. (b) Numbering...
46 CFR Sec. 2 - Voyage numbers.
Code of Federal Regulations, 2012 CFR
2012-10-01
...with 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 berth...
46 CFR Sec. 2 - Voyage numbers.
Code of Federal Regulations, 2010 CFR
2010-10-01
...with 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 berth...
46 CFR Sec. 2 - Voyage numbers.
Code of Federal Regulations, 2011 CFR
2011-10-01
...with 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 berth...
46 CFR Sec. 2 - Voyage numbers.
Code of Federal Regulations, 2014 CFR
2014-10-01
...with 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 berth...
46 CFR Sec. 2 - Voyage numbers.
Code of Federal Regulations, 2013 CFR
2013-10-01
...with 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 berth...
A System of Names for Binary Numbers
Joshua Stern
1958-01-01
A nomenclature is proposed for the binary number system to permit expression of binary numbers in words and to encourage visualization of magnitudes expressed in binary notation without recourse to decimal translation.
Number Systems. Popular Lectures in Mathematics.
ERIC Educational Resources Information Center
Fomin, S. V.
The origin, properties, and applications of various number systems are discussed. Among the 15 topics discussed are: tests for divisibility, the binary system, the game of Nim, computers, and infinite number representations. (MK)
Pearl Diver: A number line math game
NSDL National Science Digital Library
NM State Learning Games Lab
2013-01-01
In this Java application students must identify several points on a number line. The number line positions may include integers, fractional values, decimal values, and whole numbers. In the more advanced levels the number line does not begin with a 0 in all cases. Between levels students are asked to cut the eel into fractional parts and given points for their accuracy. This game is also available as an iOS app for a fee.
Symmetry numbers and chemical reaction rates
Antonio Fernández-Ramos; Benjamin A. Ellingson; Rubén Meana-Pañeda; Jorge M. C. Marques; Donald G. Truhlar
2007-01-01
This article shows how to evaluate rotational symmetry numbers for different molecular configurations and how to apply them\\u000a to transition state theory. In general, the symmetry number is given by the ratio of the reactant and transition state rotational\\u000a symmetry numbers. However, special care is advised in the evaluation of symmetry numbers in the following situations: (i)\\u000a if the reaction
Approximation of complex algebraic numbers by algebraic numbers of bounded degree
Evertse, Jan-Hendrik
Approximation of complex algebraic numbers by algebraic numbers of bounded degree YANN BUGEAUD (Strasbourg) & JAN-HENDRIK EVERTSE (Leiden) Abstract. To measure how well a given complex number can be ap numbers , but up to now not for complex, non-real algebraic numbers . In this paper we compute wn(), w n
Approximation of complex algebraic numbers by algebraic numbers of bounded degree
Evertse, Jan-Hendrik
Approximation of complex algebraic numbers by algebraic numbers of bounded degree YANN BUGEAUD (Strasbourg) & JANHENDRIK EVERTSE (Leiden) Abstract. To measure how well a given complex number # can be ap for real al gebraic numbers #, but up to now not for complex, nonreal algebraic numbers #. In this paper
Department for Analysis and Computational Number Theory Additive functions and number systems
Department for Analysis and Computational Number Theory Additive functions and number systems Manfred Madritsch Department for Analysis and Computational Number Theory Graz University of Technology systems April 7, 2010 1 / 35 #12;Department for Analysis and Computational Number Theory Outline Number
Code of Federal Regulations, 2014 CFR
2014-01-01
...Agriculture 2 2014-01-01 2014-01-01 false Lot numbers. 46.20 Section 46.20 Agriculture...1930 Records of Market Receivers § 46.20 Lot numbers. An identifying lot number shall be assigned to each shipment of...
Code of Federal Regulations, 2013 CFR
2013-01-01
...Agriculture 2 2013-01-01 2013-01-01 false Lot numbers. 46.20 Section 46.20 Agriculture...1930 Records of Market Receivers § 46.20 Lot numbers. An identifying lot number shall be assigned to each shipment of...
Code of Federal Regulations, 2012 CFR
2012-01-01
...Agriculture 2 2012-01-01 2012-01-01 false Lot numbers. 46.20 Section 46.20 Agriculture...1930 Records of Market Receivers § 46.20 Lot numbers. An identifying lot number shall be assigned to each shipment of...
Code of Federal Regulations, 2011 CFR
2011-01-01
...Agriculture 2 2011-01-01 2011-01-01 false Lot numbers. 46.20 Section 46.20 Agriculture...1930 Records of Market Receivers § 46.20 Lot numbers. An identifying lot number shall be assigned to each shipment of...
Cryptanalysis of the Windows Random Number Generator
Dolev, Danny
. . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3.1 True Random Number Generators . . . . . . . . . . . . . . . . . . 12 2.3.2 Pseudo RandomCryptanalysis of the Windows Random Number Generator A thesis submitted in partial fulfillment protocol. The quality of a sys- tem's random number generator (RNG) is therefore vital to its security
High speed optical quantum random number generation
Weinfurter, Harald
High speed optical quantum random number generation Martin F¨urst1,2,, Henning Weier1,2, Sebastian, ready-for-use quantum random number generator (QRNG) whose stochastic model is based on the ran- domness for (physical) random number generators. © 2010 Optical Society of America OCIS codes: (270.5568) Quantum
Generalized Catalan Numbers and Generalized Hankel Transformations
NASA Astrophysics Data System (ADS)
Chamberland, Marc; French, Christopher
2007-01-01
Cvetkovic, Rajkovic and Ivkovic proved that the Hankel transformation of the sequence of sums of adjacent Catalan numbers is a sequence of every other Fibonacci number. In this paper, an elementary proof is given and a generalization to sequences of generalized Catalan numbers.
Calculating Mach Numbers Using Ratios and Fractions
NSDL National Science Digital Library
2004-01-01
A mach number represents how many times the speed of sound a vehicle is traveling. NASA uses mach numbers to describe the speed of their planes. This video shows you how algebra can be used to determine the mach number of a NASA plane.
A Kilobit Special Number Field Sieve Factorization
Kazumaro Aoki; Jens Franke; Thorsten Kleinjung; Arjen K. Lenstra; Dag Arne Osvik
2007-01-01
We describe how we reached a new factoring milestone by completing the first special number field sieve factorization of a number having more than 1024 bits, namely the Mersenne number 21039 1. Although this factorization is orders of magnitude 'easier' than a factorization of a 1024-bit RSA modulus is believed to be, the methods we used to obtain our result
Determining the number of interpretable factors
Charles B. Crawford
1975-01-01
Argues that a major weakness of current methods of determining the number of factors is that they require this decision to be made before rotation; therefore, information on the possible interpretability of factors cannot be considered in determining the appropriate number. An objective, noninferential index for determining the number of interpretable factors is described. The effects of type of rotation,
Whence the complex numbers? Hans Halvorson
Halvorson, Hans
Whence the complex numbers? Hans Halvorson April 25, 2003 After all these years, we still do not fully understand why the complex numbers C play such a central role in our best theories of physical content with cataloging reasons why the real numbers R will not suffice. One of the reasons that R
182 MATHEMATICS MAGAZINE The Fibonacci Numbers--
Benjamin, Arthur T.
182 MATHEMATICS MAGAZINE The Fibonacci Numbers-- Exposed More Discretely ARTHUR T. BENJAMIN Harvey generalize Fibonacci and Lucas numbers: Given nonnegative integers a and b, the generalized Fibonacci: The Art of Combinatorial Proof, published by the MAA. #12;VOL. 76, NO. 3, JUNE 2003 183 Fibonacci numbers
When is a number Fibonacci? Phillip James
Berger, Ulrich
When is a number Fibonacci? Phillip James Department of Computer Science, Swansea University January 25, 2009 Abstract This article looks into the importance of the Fibonacci numbers within Computer Science, commenting on how to compute a Fibonacci number. It introduces an efficient test as to whether
Time series analysis for bug number prediction
Wenjin Wu; Wen Zhang; Ye Yang; Qing Wang
2010-01-01
Monitoring and predicting the increasing or decreasing trend of bug number in a software system is of great importance to both software project managers and software end-users. For software managers, accurate prediction of bug number of a software system will assist them in making timely decisions, such as effort investment and resource allocation. For software end-users, knowing possible bug number
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…
Let's Count! Learning Numbers in Multiple Ways
NSDL National Science Digital Library
2013-01-01
In this 5-minute video Pre-K teacher Rosemary Kungu demonstrates a variety of activities that develop early number skills, including number recognition, counting and ordering numbers. The activities involve active participation and incorporate multiple senses and learning styles, music, and collaboration. A downloadable transcript of the video (doc) is included along with reflection questions for viewers.
46 CFR Sec. 7 - Job order numbering.
Code of Federal Regulations, 2013 CFR
2013-10-01
...2013-10-01 2013-10-01 false Job order numbering. Sec. 7 Section 7...REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP...Contract number shall be inserted in every job order and supplemental job order...
46 CFR Sec. 7 - Job order numbering.
Code of Federal Regulations, 2014 CFR
2014-10-01
...2014-10-01 2014-10-01 false Job order numbering. Sec. 7 Section 7...REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP...Contract number shall be inserted in every job order and supplemental job order...
46 CFR Sec. 7 - Job order numbering.
Code of Federal Regulations, 2012 CFR
2012-10-01
...2012-10-01 2012-10-01 false Job order numbering. Sec. 7 Section 7...REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP...Contract number shall be inserted in every job order and supplemental job order...
46 CFR Sec. 7 - Job order numbering.
Code of Federal Regulations, 2010 CFR
2010-10-01
...2010-10-01 2010-10-01 false Job order numbering. Sec. 7 Section 7...REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP...Contract number shall be inserted in every job order and supplemental job order...
46 CFR Sec. 7 - Job order numbering.
Code of Federal Regulations, 2011 CFR
2011-10-01
...2011-10-01 2011-10-01 false Job order numbering. Sec. 7 Section 7...REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP...Contract number shall be inserted in every job order and supplemental job order...
THE CONGRUENT NUMBER PROBLEM KEITH CONRAD
Lozano-Robledo, Alvaro
THE CONGRUENT NUMBER PROBLEM KEITH CONRAD 1. Introduction A right triangle is called rational when its legs and hypotenuse are all rational numbers. Examples of rational right triangles include) ratio- nal numbers can occur as the area of a rational right triangle. For instance, no rational right
Vector Rational Number Reconstruction Curtis Bright
Storjohann, Arne
Vector Rational Number Reconstruction By Curtis Bright A research paper presented to the University Bright 2009 #12;Vector Rational Number Reconstruction August 26, 2009 Abstract The final step of some algebraic algorithms is to reconstruct the common denominator d of a collection of rational numbers (ni/d)1
Vector Rational Number Reconstruction Curtis Bright
Storjohann, Arne
Vector Rational Number Reconstruction Curtis Bright cbright@uwaterloo.ca Arne Storjohann astorjoh and |ni| N for a given magnitude bound N. Applying elementwise rational number reconstruction requires. INTRODUCTION A rational number reconstruction of an integer a Z with respect to a positive modulus M Z>0
THE CONGRUENT NUMBER PROBLEM KEITH CONRAD
Lozano-Robledo, Alvaro
THE CONGRUENT NUMBER PROBLEM KEITH CONRAD 1. Introduction A right triangle is called rational when its legs and hypotenuse are all rational numbers. Examples of rational right triangles include) rational numbers can occur as the area of a rational right triangle. For instance, no rational right
Convergence 1. Convergence of Sequence of numbers
Wu, Dapeng Oliver
Convergence 1. Convergence of Sequence of numbers 1) Definition ( ): A sequence of numbers converges to the number ( r), iff 0, , . . , | r| 2) Cauchy sequence: The sequence is Cauchy iff 0 of points in M has a limit that is also in M, or alternatively if every Cauchy sequence in M converges in M
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)
ON -GREEDY EXPANSIONS OF NUMBERS CLEMENS HEUBERGER
Wagner, Stephan
a redundant binary number system that was recently introduced by SzÂ´ekely and Wang. It works recursively is for convenience that we use 1/ instead of just ). Clearly, = 1 just produces the traditional binary number system, and the expansion continues. It stops, when a power of 2 is reached. For this and more general number systems, where
VLSI binary multiplier using residue number systems
F. Barsi; A. Di Cola
1982-01-01
The idea of performing multiplication of n-bit binary numbers using a hardware based on residue number systems is considered. This paper develops the design of a VLSI chip deriving area and time upper bounds of a n-bit multiplier. To perform multiplication using residue arithmetic, numbers are converted from binary to residue representation and, after residue multiplication, the result is reconverted
On the Number of Triangulation Simplexes
M. Kh Gizatullin
1995-01-01
We consider generating functions for the number of triangulation simplexes. We show that the binomial generating function is multiplicative. Certain exponential generating functions turn out to be solutions of evolutionary differential equations. We get congruences for the number of internal simplexes of certain triangulations generalizing the Staudt congruences for Bernoulli numbers. Bibtex entry for this abstract Preferred format for this
Algebraic Number Theory, a Computational Approach
Stein, William
Algebraic Number Theory, a Computational Approach William is based on notes the author created for a one-semester undergraduate course on Algebraic Number Theory number theory o Basic Galois theory of fields o Point set topology o Basic of topological
Number Theory I: Tools and Diophantine Equations
Cohen, Henri
i Number Theory I: Tools and Diophantine Equations II: Analytic and Modern Methods by Henri COHEN "explicit number theory," not including the essential algorithmic aspects, which are for the most part of the reader that he or she is familiar with the standard basic theory of number fields, up to and including
Number Theory group in Nottingham Current members
Wuthrich, Christian
Number Theory group in Nottingham Current members Prof. Ivan Fesenko Dr. Konstantin Ardakov Dr Ricotta (12/2007 8/2008) Dr. Masatoshi Suzuki (until 2/2008) Six Ph.D. students #12;Number Theory group in Nottingham What do we do ? #12;Number Theory group in Nottingham What do we do ? Analytic : Algebraic
Lethbridge Number Theory and Combinatorics Seminar
Seldin, Jonathan P.
Lethbridge Number Theory and Combinatorics Seminar Monday -- March 3, 2014 Room: B650 Time: 12:00 to 12:50 p.m. Daniel Fiorilli (University of Michigan) Nuclear physics and number theory Abstract: While on the number theory side. This amazing connection came to life during a meeting between Freeman Dyson and Hugh
Random Numbers in Scientific Computing: An Introduction
Katzgraber, Helmut G
2010-01-01
Random numbers play a crucial role in science and industry. Many numerical methods require the use of random numbers, in particular the Monte Carlo method. Therefore it is of paramount importance to have efficient random number generators. The differences, advantages and disadvantages of true and pseudo random number generators are discussed with an emphasis on the intrinsic details of modern and fast pseudo random number generators. Furthermore, standard tests to verify the quality of the random numbers produced by a given generator are outlined. Finally, standard scientific libraries with built-in generators are presented, as well as different approaches to generate nonuniform random numbers. Potential problems that one might encounter when using large parallel machines are discussed.
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}.
Relativistic theory of tidal Love numbers
Taylor Binnington; Eric Poisson
2009-09-16
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.
Generalized Schroder Numbers and the Rotation Principle
NASA Astrophysics Data System (ADS)
Schr"Oder, Joachim
2007-07-01
Given a point-lattice (m+1)times (n+1) subseteq N times N and l in N, we determine the number of royal paths from (0,0) to (m,n) with unit steps (1,0), (0,1) and (1,1), which never go below the line y = l*x, by means of the rotation principle. Compared to the method of "penetrating analysis", this principle has here the advantage of greater clarity and enables us to find meaningful additive decompositions of Schroder numbers. It also enables us to establish a connection to coordination numbers and the crystal ball in the cubic lattice Z^d. As a by-product we derive a recursion for the number of North-East turns of rectangular lattice paths and construct a WZ-pair involving coordination numbers and Delannoy numbers.
Riemann equation for prime number diffusion
NASA Astrophysics Data System (ADS)
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.
From Taub Numbers to the Bondi Mass
E. N. Glass
1997-12-17
Taub numbers are studied on asymptotically flat backgrounds with Killing symmetries. When the field equations are solved for a background spacetime and higher order functional derivatives (higher order variational derivatives of the Hilbert Lagrangean) are solved for perturbations from the background, such perturbed space-times admit zeroth, first, and second order Taub numbers. Zeroth order Taub numbers are Komar constants (upto numerical factors) or Penrose-Goldberg constants of the background. For a Killing symmetry of the background, first order Taub numbers give the contribution of the linearized perturbation to the associated backgound quantity, such as the perturbing mass. Second order Taub numbers give the contribution of second order perturbations to the background quantity. The Bondi mass is a sum of first and second order Taubs numbers on a Minkowski background.
Quasi-Fibonacci Numbers of Order 11
NASA Astrophysics Data System (ADS)
Witu?a, Roman; S?ota, 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.
Factoring numbers with a single interferogram
Vincenzo Tamma; Heyi Zhang; Xuehua He; Augusto Garuccio; Wolfgang P. Schleich; Yanhua Shih
2015-06-09
We construct an analog computer based on light interference to encode the hyperbolic function f({\\zeta}) = 1/{\\zeta} into a sequence of skewed curlicue functions. The resulting interferogram when scaled appropriately allows us to find the prime number decompositions of integers. We implement this idea exploiting polychromatic optical interference in a multipath interferometer and factor seven-digit numbers. We give an estimate for the largest number that can be factored by this scheme.
Help With Fractions: Seeing Them As Numbers
NSDL National Science Digital Library
Roger
2011-01-01
In this informative webpage, teachers are given ideas on how to test what their students know about fractions on a number line, as well as some easy ideas to get students comfortable with placing fractions on a number line. There is a 2:50 minute video explaining how to place fractions on a number line. Two printable practice sheets are available in PDF format.
HotBits: Genuine Random Numbers
NSDL National Science Digital Library
Walker, John
HotBits is a genuine random number generator powered by radioactive decay. Simply click the "Request HotBits" link, and specify how many bytes you would like (up to 2048) and in what form you prefer them. Hexadecimal returns numbers and letters, while C language returns integers. Then click the "Get HotBits" button, and your random numbers will appear on the screen.
Zooming in and out from the Mental Number Line: Evidence for a Number Range Effect
ERIC Educational Resources Information Center
Pinhas, Michal; Pothos, Emmanuel M.; Tzelgov, Joseph
2013-01-01
The representation of numbers is commonly viewed as an ordered continuum of magnitudes, referred to as the "mental number line." Previous work has repeatedly shown that number representations evoked by a given task can be easily altered, yielding an ongoing discussion about the basic properties of the mental number line and how malleable…
GEOMETRY AND COMPLEX NUMBERS (February 4, 2004) 7 6. Basic proofs for complex numbers
Lee, Carl
GEOMETRY AND COMPLEX NUMBERS (February 4, 2004) 7 6. Basic proofs for complex numbers Problem 6;GEOMETRY AND COMPLEX NUMBERS (February 4, 2004) 9 Problem 6.3. Prove that tan(arg(z)) = Im(z)/Re(z). #12;10 JERZY DYDAK Problem 6.4. Prove that z · ¯z = |z|2 . #12;GEOMETRY AND COMPLEX NUMBERS (February 4, 2004
On the domination number and the 2-packing number of Fibonacci cubes and Lucas cubes
Paris-Sud XI, Université de
On the domination number and the 2-packing number of Fibonacci cubes and Lucas cubes Aline Castro, respectively. The domination number of Fibonacci cubes and Lucas cubes is studied. In particular it is proved of these graphs in Section 2. In Section 3 we study the domination number of Fibonacci cubes as initiated in [12
Fibonacci Numbers. You may have heard about the Fibonacci sequence of numbers. It
Brand, Neal
Fibonacci Numbers. You may have heard about the Fibonacci sequence of numbers. It starts previous numbers. This gives an easy way to write out the Fibonacci sequence as far as you wish. Suppose with the numbers 1; 1; 2; 3; 5; 8; 13; 21; 34; 55; 89; \\Delta \\Delta \\Delta Even if you haven't seen them before
Young Children's Number-Word Knowledge Predicts Their Performance on a Nonlinguistic Number Task
Stanford, Kyle
Young Children's Number-Word Knowledge Predicts Their Performance on a Nonlinguistic Number Task-word learning and changes in the child's attention and memory for implicit number information. 71 children (ages 2-2 to 4-9) were asked, without number words, to replicate sets of 1 to 4 objects. Children
Name: U of M ID number: Social Security number: Date of birth
Amin, S. Massoud
is private. Except for social security number, which is voluntary, all information requested on this formName: U of M ID number: Social Security number: Date of birth: Phone (home): Phone (other-Manitoba reciprocity fee status will be granted. Failure to provide your social security number will have no effect
Deriving the number of jobs in proximity services from the number of inhabitants in French rural
Paris-Sud XI, Université de
Deriving the number of jobs in proximity services from the number of inhabitants in French rural a minimum requirement approach to derive the number of jobs of proximity services per inhabitant observe that the minimum number of service jobs per inhabitant (interpreted as jobs of proximity services
27 CFR 20.179 - Package identification number or serial number.
Code of Federal Regulations, 2013 CFR
2013-04-01
...Continuation of numbering series. If a change in proprietorship...numbering system in use at the time of the change may be continued...serial numbers are used at the time of a change, the numbering series in use at the time of the change may be...
27 CFR 20.179 - Package identification number or serial number.
Code of Federal Regulations, 2012 CFR
2012-04-01
...Continuation of numbering series. If a change in proprietorship...numbering system in use at the time of the change may be continued...serial numbers are used at the time of a change, the numbering series in use at the time of the change may be...
27 CFR 20.179 - Package identification number or serial number.
Code of Federal Regulations, 2011 CFR
2011-04-01
...Continuation of numbering series. If a change in proprietorship...numbering system in use at the time of the change may be continued...serial numbers are used at the time of a change, the numbering series in use at the time of the change may be...
27 CFR 20.179 - Package identification number or serial number.
Code of Federal Regulations, 2014 CFR
2014-04-01
...Continuation of numbering series. If a change in proprietorship...numbering system in use at the time of the change may be continued...serial numbers are used at the time of a change, the numbering series in use at the time of the change may be...
27 CFR 20.179 - Package identification number or serial number.
Code of Federal Regulations, 2010 CFR
2010-04-01
...first three lots filled into packages on November 19, 1983, would be identified...number shall be marked on each package, beginning with the number...but similar number series for packages containing specially denatured...name occurs, the numbering system in use at the time of...
Predicting landfalling hurricane numbers from basin hurricane numbers: basic statistical analysis
Laepple, T; Penzer, J; Bellone, E; Nzerem, K; Laepple, Thomas; Jewson, Stephen; Penzer, Jeremy; Bellone, Enrica; Nzerem, Kechi
2007-01-01
One possible method for predicting landfalling hurricane numbers is to first predict the number of hurricanes in the basin and then convert that prediction to a prediction of landfalling hurricane numbers using an estimated proportion. Should this work better than just predicting landfalling hurricane numbers directly? We perform a basic statistical analysis of this question in the context of a simple abstract model.
Number Worlds: Visual and Experimental Access to Elementary Number Theory Concepts
ERIC Educational Resources Information Center
Sinclair, Nathalie; Zazkis, Rina; Liljedahl, Peter
2004-01-01
Recent research demonstrates that many issues related to the structure of natural numbers and the relationship among numbers are not well grasped by students. In this article, we describe a computer-based learning environment called "Number Worlds" that was designed to support the exploration of elementary number theory concepts by making the…
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
7.NS Operations on the number line
NSDL National Science Digital Library
This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: A number line is shown below. The numbers $0$ and $1$ are marked on the line, as are two other numbers $a$ and $b$. Which of the following numbers is n...
Texas Rice, Volume IV, Number 5
2004-01-01
visits increased by 79% in 2004. The number of unique visi- tors, which refers to the number of people who visited the web site one or more times, increased by 95%, or almost double the number from last year. Both the num- ber of files downloaded (46...%) and the bytes of down- loaded data (59%) also increased over last year, even though the number of files downloaded per visitor de- creased by 18%. Probably one of the best statistics for determining Internet website access and growth is the cumulative hours...
FPGA Vendor Agnostic True Random Number Generator
Dries Schellekens; Bart Preneel; Ingrid Verbauwhede
2006-01-01
This paper describes a solution for the generation of true random numbers in a purely digital fashion; making it suit- able for any FPGA type, because no FPGA vendor spe- cic features (e.g., like phase-locked loop) or external ana- log components are required. Our solution is based on a framework for a provable secure true random number gen- erator recently
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…
Teaching Number in the Early Elementary Years
ERIC Educational Resources Information Center
Cain, Chris R.; Faulkner, Valerie N.
2011-01-01
The widely adopted Common Core State Standards for Mathematics (CCSSM) are designed to deepen instruction of number sense and will demand that elementary school teachers have a strong understanding of number. These changes arrive at a time when it is still understood that teachers and the curriculum in the United States have not been fundamentally…
TEACHING THE NATURAL NUMBERS AS OPERATORS
Kapelou Katerina
Children can construct the concept of the natural number sufficiently, if they are engaged in activities concerning additive as well as multiplicative structures. Kindergarten children's engagement with activities concerning the number as operator has a special research interest, as there is not a lot of work on it. In this workshop the activities discussed were part of a broader research
Brandeis University Philosophy current number of majors
Fraden, Seth
of philosophy, logic, metaphysics, philosophy of mind and language, political philosophy Popular second majorsBrandeis University Philosophy fast facts current number of majors and minors: 84 Number of faculty.edu/departments/ philosophy aBoUt thE Program Why be good? What is thinking? What is knowledge, and do we have any? Is free
enter part number BNC / RP-BNC
Berns, Hans-Gerd
enter part number Products 7/16 1.0/2.3 1.6/5.6 AFI AMC BNC / RP-BNC C FAKRA SMB FME HN MCX Mini ------- Product Search ------- Inventory Search Search Results for: 31-10152-RFX Results: 1 - 1 of 1 Part Number. All rights reserved. Copyright | Terms & Conditions | RF E-Mail Client | Contact Us | Amphenol
Carmichael numbers and a new primality test
J. C. L. da Silva; Leandro da Silva
2010-01-01
A new algorithm which correctly identifies every positive integer tested as being either prime or composite is considered. In fact, the first one hundred Carmichael numbers were tested and each one resulted composite as expected. It is well known that other primality tests exist that can also identify Carmichael numbers as composites, but the given algorithm seems to work without
Measures of Planarity: Crossing Number Stephanie Jones
Laison, Josh
Measures of Planarity: Crossing Number Stephanie Jones Willamette University April 17, 2012 Stephanie Jones (Willamette University) Measures of Planarity: Crossing Number April 17, 2012 1 / 17 #12 distinct edges have at most one crossing. Stephanie Jones (Willamette University) Measures of Planarity
Paul Peach
1961-01-01
Some congruential pseudo-random number generators are shown to be subject to sub-periods or harmonics whose effect is to constrain the variability of the numbers generated. An experiment with such a generator produced a long sequence whose variance was significantly less than the theoretical value.
NEUTRON NUMBERS 98, 108 AND 116
L. H. AHRENS
1963-01-01
In a discussion of neutron capture processes and theories of element ; origin, Malkiel has suggested that the neutron numbers 98, 108. and 116 may be ; favored. The probability is considered that these neutron numbers are favored, ; using as evidence a systematic study of the principal isotopes of the elements. ; An N-- Z, Z diagram is presented
Class numbers of complex quadratic fields
Ezra Brown
1974-01-01
Congruence conditions on the class numbers of complex quadratic fields have recently been studied by various investigators, including Barrucand and Cohn, Hasse, and the author. In this paper, we study the class number of Q([radical sign] - pq), where p [reverse not equivalent] q (mod 4) are distinct primes.
Algorithmic Number Theory-The Complexity Contribution
Leonard M. Adleman
1994-01-01
Though algorithmic number theory is one of man's oldest intellectual pursuits, its current vitality is perhaps unrivalled in history. This is due in part to the injection of new ideas from computational complexity. In this paper, a brief history of the symbiotic relationship between number theory and complexity theory will be presented. In addition, some of the technical aspects underlying
The Fibonacci Numbers and the Golden Section
NSDL National Science Digital Library
Ron Knott, Ph.D.
2007-12-12
This award-winning site explores not only who Fibonacci was, but also the Fibonacci number properties, where they occur in nature, and much, much more. Puzzles with answers, illustrations, diagrams, and graphs are included. The Golden Ratio and Lucas numbers are addressed here as well. This site contains over 200 pages of information.
The Second Strong Law of Small Numbers.
ERIC Educational Resources Information Center
Guy, Richard K.
1990-01-01
Presented are 44 examples in which students are invited to guess what pattern of numbers is emerging and to decide whether the pattern will persist. Topics of examples include Pascal's triangle, integers, vertices, Fibonacci numbers, power series, partition functions, and Euler's theorem. The answers to all problems are included. (KR)
A Partition Formula for Fibonacci Numbers
Philipp Fahr; Claus Michael Ringerl
2008-01-01
We present a partition formula for the even index Fibonacci numbers. The formula is motivated by the appearance of these Fibonacci numbers in the representation theory of the socalled 3-Kronecker quiver, i.e., the oriented graph with two vertices and three arrows in the same direction.
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.
Terms You Need to Know Course Numbering
Gallo, Linda C.
division (juniors and seniors). Grade Point Average (GPA) To compute your GPA, divide the total number of grade points by the total number of units attempted. Four averages, each 2.0 or higher, are required Probation Academic probation occurs when your overall cumulative grade point average and/or your SDSU grade
Fostering At-Risk Preschoolers' Number Sense
ERIC Educational Resources Information Center
Baroody, Arthur; Eiland, Michael; Thompson, Bradley
2009-01-01
Research Findings: A 9-month study served to evaluate the effectiveness of a pre-kindergarten number sense curriculum. Phase 1 of the intervention involved manipulative-, game-based number sense instruction; Phase 2, computer-aided mental-arithmetic training with the simplest sums. Eighty 4- and 5-year-olds at risk for school failure were randomly…
Correlation of capillary number relationships for sandstone
I. Chatzis; N. R. Morrow
1981-01-01
Capillary number relationships are presented for displacement of residual oil, and for displacement of oil which is initially continuous from water-wet sandstone having permeabilities which varied over about two orders of magnitude. It was found that the onset of mobilization could be correlated with sample permeability. Relationships between normalized reduced residual oil saturation and capillary number were correlated satisfactorily for
Code of Federal Regulations, 2013 CFR
2013-01-01
...Formal Review of Sourcing Areas Pursuant to the Forest Resources 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...
Code of Federal Regulations, 2010 CFR
2010-01-01
...Formal Review of Sourcing Areas Pursuant to the Forest Resources 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...
Code of Federal Regulations, 2014 CFR
2014-01-01
...Formal Review of Sourcing Areas Pursuant to the Forest Resources 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...
Code of Federal Regulations, 2012 CFR
2012-01-01
...Formal Review of Sourcing Areas Pursuant to the Forest Resources 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...
Code of Federal Regulations, 2011 CFR
2011-01-01
...Formal Review of Sourcing Areas Pursuant to the Forest Resources 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...
Search for lepton-family-number nonconservation
Hoffman, C.M.
1986-01-01
A review of the status of lepton-family-number nonconservation is given. After a brief historical and theoretical discussion, a description of how experimental searches for lepton-family-number nonconservation are performed is presented. Finally, a summary of the results from past experiments and prospects for future experiments is given.
Promoting Number Sense in the Middle Grades.
ERIC Educational Resources Information Center
Reys, Barbara J.
1994-01-01
Defines number sense and gives suggestions and activities for teachers to use in helping students develop number sense, including using process questions, using writing assignments, encouraging invented methods, using appropriate calculation tools, helping students establish benchmarks, and promoting internal questioning. (MKR)
Library Collections 74 Number of Loans 75
Sun, Yu
,293 Stand-Alone PC's 78 DIGITAL LIBRARY E-RESOURCES LICENSED* PUBLIC** TOTAL Article Databases and Text by anyone. ** These items are available on the Internet for use by anyone. For current figures, see http://main.libraryPart H Library Library Collections 74 Number of Loans 75 Number of Computers in the Library 75
Writing about Numbers We Should Know
NSDL National Science Digital Library
Neil Lutsky
This opening assignment for an introductory quantitative reasoning course asks students to write about "Numbers We Should Know." Its goal is to help students begin to think quantitatively, evaluate the sources of quantitative information critically, and write using numbers precisely and thoughtfully.
Requisition Number Requisition for Vehicle and Driver
Kirschner, Denise
Requisition Number Requisition for Vehicle and Driver For information, please contact Parking.763.1470 · 1213 Kipke Drive, Ann Arbor, MI 48109-2002 CONTACT INFORMATION TODAY'S DATE DEPARTMENT CHARTER PHONE NUMBER AUTHORIZED SIGNATURE FOR SHORTCODE CHARTER INFORMATION IF ANY OF THE FOLLOWING
Good Morning, Numbers Day: Motivating for Mathematics
ERIC Educational Resources Information Center
Ramentol, Salvador Vidal
2011-01-01
The aversion that many girls and boys experience towards mathematics has been one of the author's major concerns since he started teaching. In this article, he describes a project called "Numbers Day" that was designed to improve students' attitudes toward mathematics. There are many features of Numbers Day that teachers might incorporate into…
-P and T number -Residence Permit
- P and T number - Residence Permit - Banking Information - Insurance - Other... #12;P and T number service options when opening bank account #12;Swedish Migration Board - Migrationsverket 2012 or online. When you apply for an extension by post, you must use the form Application for residence permit
Veterinary Seizure Detector Report Number 1
Levi, Anthony F. J.
Veterinary Seizure Detector Report Number 1 Page 1 of 20 DISTRIBUTION STATEMENT: Distribution authorized to all. Veterinary Seizure Detector Report Number 1 Submitted by Nicolas Roy University) 393 8351 Email nroy@usc.edu Date: April 27, 2010 Work performed at USC #12;Veterinary Seizure Detector
Session Number Session Title Approved CM
Minnesota, University of
Session Number Session Title Number of Approved CM Credits Morning Plenary The End of Car Culture? Socio-Demographic Trends and Travel Demand 1.50 Session 1 Local Road Safety: Data Collection and Lessons Resilience 1.00 Session 6 Intersection Safety Strategies 1.25 Session 8 Understanding the Relationship
HANDBOOK FOR PARENTS 20132014 USEFUL TELEPHONE NUMBERS
Royer, Dana
HANDBOOK FOR PARENTS 20132014 #12;ii USEFUL TELEPHONE NUMBERS The telephone number. We have prepared this handbook because we thought it would be helpful for you, as parents-685-3756 or send an e-mail to parents@wesleyan.edu. This handbook is provided to parents for their general guidance
Recognising zero among implicitly defined elementary numbers
Richardson, Daniel
Recognising zero among implicitly defined elementary numbers Daniel Richardson Department which have been given previously to solve related problems, depending essentially on the zero problem for implicitly defined algebraic numbers. Key words: Exp-Log constants, zero test, Schanuel conjecture, interval
On Carmichael numbers in arithmetic progressions
Pomerance, Carl
On Carmichael numbers in arithmetic progressions William D. Banks Department of Mathematics an analogue of Dirichlet's theorem on primes in an arithmetic progression holds for the set of Carmichael Carmichael numbers in the arithmetic progression 1 mod m, we use a straightforward variant of the Alford
High Weissenberg Number Asymptotics Who? Sebastian Hannes
Hanke-Bourgeois, Martin
Similarity Solution #12;Physical motivation analyzation of flow properties around objects in hydro. Reynolds number represents the ration of kinetic energy and friction energy for small Reynolds number.g. in constructing water pipes #12;Euler Equations For ideal fluids we have = 0 and hence Re = , in the Navier
Quadratic dynamics in binary number systems
Paul E. Fishback
2005-01-01
We describe the quadratic dynamics in certain two-component number systems, which like the complex numbers, can be expressed as rings of two by two real matrices. This description is accomplished using the properties of the real quadratic family and its derivative. We also demonstrate that the Mandelbrot set for any of these systems may be defined in two equivalent ways
Serious toys: teaching the binary number system
Yvon Feaster; Farha Ali; Jason O. Hallstrom
2012-01-01
The binary number system is the lingua franca of computing, requisite to myriad areas, from hardware architecture and data storage to wireless communication and algorithm design. Given its significance to such a broad range of computing topics, it is not surprising that the binary number system plays a prominent role in K-12 outreach efforts. It is even less surprising that
Computer arithmetic architectures with redundant number systems
Hosahalli R. Srinivas; Keshab K. Parhi
1994-01-01
Redundant arithmetic number systems are gaining popularity in computationally intensive environments particularly because of the carry-free addition\\/subtraction properties they possess. This property has enabled arithmetic operations such as addition, multiplication, division, square root, etc., to be performed much faster than with conventional binary number systems. In this paper, some of the recent contributions to the area of design of redundant
Number Theory in Cryptography ! and its Application"
Waldschmidt, Michel
Number Theory in Cryptography ! and its Application" http://www.math.jussieu.fr/~miw/! Michel, Kirtipur, Nepal ! Introduction to cryptography! 2! !Theoretical research in number theory has a long remain open. ! http://www.math.jussieu.fr/~miw/! Data transmission, Cryptography ! and Arithmetic! 3
The covering number in learning theory
Ding-xuan Zhou
2002-01-01
The covering number of a ball of a reproducing kernel Hilbert space as a subset of the continuous function space plays an important role in Learning Theory.We give estimates for this covering number by means of the regularity of the Mercer kernel K: For convolution type kernels Kðx; t Þ¼ kðxtÞ on ½0; 1? n; we provide estimates depending on
SESAME equation of state number 7740: Polycarbonate
Boettger
1991-01-01
An equation of state (EOS) for polycarbonate (a widely used polymer) has been generated with the computer code GRIZZLY and will be added to the SESAME library as material number 7740. Although a number of the input parameter used in the calculations are based on rough estimates. 7740 provides a good match to experimental Hugoniot data and should be reliable
GENERAL CHEMISTRY TEXTBOOK LIST ISBN Number
Jiang, Wen
FALL 2013 GENERAL CHEMISTRY TEXTBOOK LIST Course Number ISBN Number Title of Text and/or Material Edition Author Publishers 11100 978-1-2591-9687-4 Introduction to Chemistry, 3rd ed. (packaged w 978-1-2591-6192-6 Chemistry, The Molecular Nature of Matter and Change, 6e (packaged w
Understanding a Child's Development of Number Sense
NSDL National Science Digital Library
Marilyn Burns
2011-01-01
The brief video clips on this webpage illustrate the range of number sense exhibited by students in grades Pre K-2. In interviews, Cena and Jonathan, both age 7, and Rudy, age 9, demonstrate different levels of understanding number and place value concepts. The page includes discussion questions for each set of videos as well as concluding reflection questions.
Modifications to the Number Field Sieve
Don Coppersmith
1993-01-01
The Number Field Sieve, due to Lenstra et al. [LLMP] and Buhler et al. [BLP], is a new routine for factoring integers. We present here a modification of that sieve. We use the fact that certain smoothness computations can be reused, and thereby reduce the asymptotic running time of the Number Field Sieve. We also give a way to precompute
Company number 5857955 Wellcome Trust Finance plc
Rambaut, Andrew
holders and that the Company achieves sufficient return on its assets to be profitable, before anyCompany number 5857955 Wellcome Trust Finance plc Annual Report and Financial Statements Year ended 30 September 2013 #12;Company number 5857955 Wellcome Trust Finance plc Contents Page Directors
Computer Representation of Numbers and Computer Arithmetic
Sandu, Adrian
, 2008 1 Binary numbers In the decimal system, the number 107.625 means 107.625 = 1 · 102 + 7 · 100 + 6 power of 10} - we say that 10 is the basis of the decimal system. There are 10 digits (0,...,9). All-3 = (1101011.101)2 . Arithmetic operations in the binary system are performed similarly as in the decimal
A numerical approximation of the rotation number
R. Pavani
1995-01-01
The rotation number of a circle map is approximated by an efficient numerical method. The method works well for both irrational rotation numbers and rational ones. Moreover, it allows us to distinguish between the two cases. Numerical results are presented; they are mainly related to the standard circle map and the delayed logistic map.
New String Theories And Their Generation Number
Arel Genish; Doron Gepner
2014-04-30
New heterotic string theories in four dimensions are constructed by tensoring a nonstandard SCFT along with some minimal SCFT's. All such theories are identified and their particle generation number is found. We prove that from the infinite number of new heterotic string theories only the {6} theory predicts three generations as seen in nature which makes it an interesting candidate for further study.
Dividing Fraction by a Whole Number
NSDL National Science Digital Library
Mrs. West
2013-01-04
Everything you need to know about Dividing Fractions by a Whole Number. Learn the steps for dividing fractions by whole numbers in How to do it. Start out slow and divide with Fractions fun with soccer. Speed up the fun with Fraction Hoops. ...
Bit recycling for scaling random number generators
Mennucci, Andrea C G
2010-01-01
Many Random Number Generators (RNG) are available nowadays; they are divided in two categories, hardware RNG, that provide "true" random numbers, and algorithmic RNG, that generate pseudo random numbers (PRNG). Both types usually generate random numbers (X_n) as independent uniform samples in a range 0...2^b-1, with b = 8, 16, 32 or b = 64. In applications, it is instead sometimes desirable to draw random numbers as independent uniform samples (Y_n) in a range 1, . . . M, where moreover M may change between drawings. Transforming the sequence (X_n) to (Y_n) is sometimes known as scaling. We discuss different methods for scaling the RNG, both in term of mathematical efficiency and of computational speed.
Topological numbering of features on a mesh
NASA Technical Reports Server (NTRS)
Atallah, Mikhail J.; Hambrusch, Susanne E.; Tewinkel, Lynn E.
1988-01-01
Assume a nxn binary image is given containing horizontally convex features; i.e., for each feature, each of its row's pixels form an interval on that row. The problem of assigning topological numbers to such features is considered; i.e., assign a number to every feature f so that all features to the left of f have a smaller number assigned to them. This problem arises in solutions to the stereo matching problem. A parallel algorithm to solve the topological numbering problem in O(n) time on an nxn mesh of processors is presented. The key idea of the solution is to create a tree from which the topological numbers can be obtained even though the tree does not uniquely represent the to the left of relationship of the features.
Relativistic theory of surficial Love numbers
Philippe Landry; Eric Poisson
2014-04-27
A relativistic theory of surficial Love numbers, which characterize the surface deformation of a body subjected to tidal forces, was initiated by Damour and Nagar. We revisit this effort in order to extend it, clarify some of its aspects, and simplify its computational implementation. First, we refine the definition of surficial Love numbers proposed by Damour and Nagar, and formulate it directly in terms of the deformed curvature of the body's surface, a meaningful geometrical quantity. Second, we develop a unified theory of surficial Love numbers that applies equally well to material bodies and black holes. Third, we derive a compactness-dependent relation between the surficial and (electric-type) gravitational Love numbers of a perfect-fluid body, and show that it reduces to the familiar Newtonian relation when the compactness is small. And fourth, we simplify the tasks associated with the practical computation of the surficial and gravitational Love numbers for a material body.
Number-space mapping in human infants.
de Hevia, Maria Dolores; Spelke, Elizabeth S
2010-05-01
Mature representations of number are built on a core system of numerical representation that connects to spatial representations in the form of a mental number line. The core number system is functional in early infancy, but little is known about the origins of the mapping of numbers onto space. In this article, we show that preverbal infants transfer the discrimination of an ordered series of numerosities to the discrimination of an ordered series of line lengths. Moreover, infants construct relationships between numbers and line lengths when they are habituated to unordered pairings that vary positively, but not when they are habituated to unordered pairings that vary inversely. These findings provide evidence that a predisposition to relate representations of numerical magnitude to spatial length develops early in life. A central foundation of mathematics, science, and technology therefore emerges prior to experience with language, symbol systems, or measurement devices. PMID:20483843
LEAN: laser-etched aqua number
NASA Astrophysics Data System (ADS)
Schell, Karel J.
1998-04-01
A security device on a banknote has to be recognized immediately by the general public and has to enable the general public to establish the genuineness of the banknote. This is the so-called first line of defense. Recently the development of the ability to establish the genuiness has gained momentum and is called 'self authenticating.' Comparing the banknote number with a 'watermark number' can do authenticating. The watermark number is engraved by a laser beam in the paper and is -- as the printed number -- different for each note. Recent progress in the material processing by laser enables the engraving of the individual watermark number for each banknote in line with the production process.
True random numbers from amplified quantum vacuum
Jofre, M; Steinlechner, F; Anzolin, G; Torres, J P; Mitchell, M W; Pruneri, V; 10.1364/OE.19.020665
2011-01-01
Random numbers are essential for applications ranging from secure communications to numerical simulation and quantitative finance. Algorithms can rapidly produce pseudo-random outcomes, series of numbers that mimic most properties of true random numbers while quantum random number generators (QRNGs) exploit intrinsic quantum randomness to produce true random numbers. Single-photon QRNGs are conceptually simple but produce few random bits per detection. In contrast, vacuum fluctuations are a vast resource for QRNGs: they are broad-band and thus can encode many random bits per second. Direct recording of vacuum fluctuations is possible, but requires shot-noise-limited detectors, at the cost of bandwidth. We demonstrate efficient conversion of vacuum fluctuations to true random bits using optical amplification of vacuum and interferometry. Using commercially-available optical components we demonstrate a QRNG at a bit rate of 1.11 Gbps. The proposed scheme has the potential to be extended to 10 Gbps and even up t...
Random numbers spring from alpha decay
Frigerio, N.A.; Sanathanan, L.P.; Morley, M.; Clark, N.A.; Tyler, S.A.
1980-05-01
Congruential random number generators, which are widely used in Monte Carlo simulations, are deficient in that the number they generate are concentrated in a relatively small number of hyperplanes. While this deficiency may not be a limitation in small Monte Carlo studies involving a few variables, it introduces a significant bias in large simulations requiring high resolution. This bias was recognized and assessed during preparations for an accident analysis study of nuclear power plants. This report describes a random number device based on the radioactive decay of alpha particles from a /sup 235/U source in a high-resolution gas proportional counter. The signals were fed to a 4096-channel analyzer and for each channel the frequency of signals registered in a 20,000-microsecond interval was recorded. The parity bits of these frequency counts (0 for an even count and 1 for an odd count) were then assembled in sequence to form 31-bit binary random numbers and transcribed to a magnetic tape. This cycle was repeated as many times as were necessary to create 3 million random numbers. The frequency distribution of counts from the present device conforms to the Brockwell-Moyal distribution, which takes into account the dead time of the counter (both the dead time and decay constant of the underlying Poisson process were estimated). Analysis of the count data and tests of randomness on a sample set of the 31-bit binary numbers indicate that this random number device is a highly reliable source of truly random numbers. Its use is, therefore, recommended in Monte Carlo simulations for which the congruential pseudorandom number generators are found to be inadequate. 6 figures, 5 tables.
Mixed convection around a liquid sphere in an air stream
M. A. Antar; M. A. I. El-Shaarawi
2002-01-01
A linearized finite-difference scheme has been used to investigate the mixed convection boundary-layer flow about a liquid\\u000a sphere subjected to an air stream. For Prandtl number = 0.7, velocity and temperature profiles are obtained for a wide range\\u000a of the other controlling parameters: Reynolds number, interior-to-exterior (liquid- to-air) viscosity ratio and Grashof number.\\u000a Both aiding and opposing natural convections are
Mixed convection around a liquid sphere in an air stream
M. A. Antar; M. A. I. El-Shaarawi
2002-01-01
A linearized finite-difference scheme has been used to investigate the mixed convection boundary-layer flow about a liquid sphere subjected to an air stream. For Prandtl number = 0.7, velocity and temperature profiles are obtained for a wide range of the other controlling parameters: Reynolds number, interior-to-exterior (liquid- to-air) viscosity ratio and Grashof number. Both aiding and opposing natural convections are
26 CFR 301.6109-1 - Identifying numbers.
Code of Federal Regulations, 2012 CFR
2012-04-01
...security numbers, Internal Revenue Service (IRS) individual taxpayer identification numbers, IRS adoption taxpayer identification numbers...security numbers take the form 000-00-0000. IRS individual taxpayer identification numbers...
47 CFR 52.111 - Toll free number assignment.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 2010-10-01 2010-10-01 false Toll free number assignment. 52.111 Section 52.111...CARRIER SERVICES (CONTINUED) NUMBERING Toll Free Numbers § 52.111 Toll free number assignment. Toll free numbers...
47 CFR 52.111 - Toll free number assignment.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 2012-10-01 2012-10-01 false Toll free number assignment. 52.111 Section 52.111...CARRIER SERVICES (CONTINUED) NUMBERING Toll Free Numbers § 52.111 Toll free number assignment. Toll free numbers...
47 CFR 52.111 - Toll free number assignment.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 2014-10-01 2014-10-01 false Toll free number assignment. 52.111 Section 52.111...CARRIER SERVICES (CONTINUED) NUMBERING Toll Free Numbers § 52.111 Toll free number assignment. Toll free numbers...
47 CFR 52.111 - Toll free number assignment.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 2013-10-01 2013-10-01 false Toll free number assignment. 52.111 Section 52.111...CARRIER SERVICES (CONTINUED) NUMBERING Toll Free Numbers § 52.111 Toll free number assignment. Toll free numbers...
47 CFR 52.111 - Toll free number assignment.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 2011-10-01 2011-10-01 false Toll free number assignment. 52.111 Section 52.111...CARRIER SERVICES (CONTINUED) NUMBERING Toll Free Numbers § 52.111 Toll free number assignment. Toll free numbers...
Generating functions for weighted Hurwitz numbers
Mathieu Guay-Paquet; J. Harnad
2015-04-16
Double Hurwitz numbers enumerating weighted $n$-sheeted branched coverings of the Riemann sphere or, equivalently, weighted paths in the Cayley graph of $S_n$ generated by transpositions are determined by an associated weight generating function. A uniquely determined $1$-parameter family of 2D Toda $\\tau$-functions of hypergeometric type is shown to consist of generating functions for such weighted Hurwitz numbers. Four classical cases are detailed, in which the weighting is uniform: Okounkov's double Hurwitz numbers, for which the ramification is simple at all but two specified branch points; the case of Belyi curves, with three branch points, two with specified profiles; the general case, with a specified number of branch points, two with fixed profiles, the rest constrained only by the genus; and the signed enumeration case, with sign determined by the parity of the number of branch points. Using the exponentiated quantum dilogarithm function as weight generator, three new types of weighted enumerations are introduced. These determine {\\em quantum} Hurwitz numbers depending on a deformation parameter $q$. By suitable interpretation of $q$, the statistical mechanics of quantum weighted branched covers may be related to that of Bosonic gases. The standard double Hurwitz numbers are recovered in the classical limit.
Exploring number space by random digit generation.
Loetscher, Tobias; Brugger, Peter
2007-07-01
There is some evidence that human subjects preferentially select small numbers when asked to sample numbers from large intervals "at random". A retrospective analysis of single digit frequencies in 16 independent experiments with the Mental Dice Task (generation of digits 1-6 during 1 min) confirmed the occurrence of small-number biases (SNBs) in 488 healthy subjects. A subset of these experiments suggested a spatial nature of this bias in the sense of a "leftward" shift along the number line. First, individual SNBs were correlated with leftward deviations in a number line bisection task (but unrelated to the bisection of physical lines). Second, in 20 men, the magnitude of SNBs significantly correlated with leftward attentional biases in the judgment of chimeric faces. Finally, cognitive activation of the right hemisphere enhanced SNBs in 20 different men, while left hemisphere activation reduced them. Together, these findings provide support for a spatial component in random number generation. Specifically, they allow an interpretation of SNBs in terms of "pseudoneglect in number space." We recommend the use of random digit generation for future explorations of spatial-attentional asymmetries in numerical processing and discuss methodological issues relevant to prospective designs. PMID:17294177
Exponential Number of Shapes in Origami Metasheets
NASA Astrophysics Data System (ADS)
Dieleman, Peter; Waitukaitis, Scott; van Hecke, Martin
2015-03-01
The simplest possible fold pattern that allows for motion, the 4-vertex, has two distinct branches of motion. By deriving a local combinatorial rule, we show that the number of branches in a tessellated sheet of such 4-vertices grows exponentially with the number of vertices. We introduce energy in the system by approximating the folds as torsional springs and show that we can create an arbitrary number of well separated minima, i.e. shapes. With 3D printing, we bring these shape-shifting structures to life.
MSSM with gauged baryon and lepton numbers
Bartosz Fornal
2015-03-31
A simple extension of the minimal supersymmetric standard model in which baryon and lepton numbers are local gauge symmetries spontaneously broken at the supersymmetry scale is reported. This theory provides a natural explanation for proton stability. Despite violating R-parity, it contains a dark matter candidate carrying baryon number that can be searched for in direct detection experiments. The model accommodates a light active neutrino spectrum and predicts one heavy and two light sterile neutrinos. It also allows for lepton number violating processes testable at the Large Hadron Collider.
Viscous thermocapillary convection at high Marangoni number
NASA Technical Reports Server (NTRS)
Cowley, S. J.; Davis, S. H.
1983-01-01
A liquid, contained in a quarter plane, undergoes steady motion due to thermocapillary forcing on its upper boundary, a free surface separating the liquid from a passive gas. The rigid vertical sidewall has a strip whose temperature is elevated compared with the liquid at infinity. A boudnary-layer analysis is performed that is valid for large Marangoni numbers M and Prandtl numbers P. It is found that the Nusselt number N for the horizontal heat transport satisfies N proportional to min (M to the 1 2/7/power, M to the 1 1/5/power, M to the 1 1/10/power) Generalizations are discussed.
Patterns in Mathematics-Number Patterns
NSDL National Science Digital Library
2011-01-01
This set of two interactive challenges from the Annenberg Teachers' Lab helps learners develop reasoning skills with number patterns by looking systematically at specific examples, and then by making predictions and generalizations. In "How Many Valentines", students try to figure out the number of valentines sent by an entire class. In "Mystery Operation", solvers try to determine what the computer's mystery operation is by entering a pair of numbers and studying the outputs. Background discussion, a rationale, grade-level information, connections to standards, and solvers' comments are included for each activity.
Skyrmions up to baryon number 108
NASA Astrophysics Data System (ADS)
Feist, D. T. J.; Lau, P. H. C.; Manton, N. S.
2013-04-01
The Skyrme crystal is built up of repeating units similar to the cubic Skyrmion of baryon number 4. Using this as a guide, we construct new Skyrmion solutions in the massive-pion case, with various baryon numbers up to 108. Most of our solutions resemble chunks of the Skyrme crystal. They are constructed using a multilayer version of the rational map ansatz to create initial configurations, which are then relaxed numerically to find the energy minima. The coefficients of the rational maps are found by a geometrical construction related to the Skyrme crystal structure. We find some further solutions by numerical relaxation of clusters composed of baryon number 4 Skyrmions.
An Introduction to the Theory of Numbers
NSDL National Science Digital Library
Moser, Leo
Written by Leo Moser and presented by the Trillia Group, this virtual text introduces visitors to the theory of numbers. After agreeing to the terms and conditions of use, users will be able to download the full document as an 87-page pdf file in either large or regular print. The chapters include: "Compositions and Partitions," "Irrational Numbers," "Diophantine Equations," and "Geometry of Numbers." The terms limit this free download to students in mathematic self-study or for instructors to consider this text for use in their classrooms.
Federal Register 2010, 2011, 2012, 2013, 2014
2011-09-30
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VU Center Numbering Scheme All Center Numbers have ten digits. The digits are grouped to indicate
Bordenstein, Seth
VU Center Numbering Scheme All Center Numbers have ten digits. The digits are grouped to indicate Scholarships 562 -611 Associations 52 ITS 612 - 695 Foundations 53 VU Libraries 696 - 770 Corporations 58
Code of Federal Regulations, 2014 CFR
2014-04-01
21 Food and Drugs 4 2014-04-01 2014-04-01 false Notification of registrant; drug establishment registration number and drug listing number. 207.35 Section 207.35 Food and Drugs FOOD AND DRUG ADMINISTRATION,...
Code of Federal Regulations, 2010 CFR
2010-04-01
21 Food and Drugs 4 2010-04-01 2010-04-01 false Notification of registrant; drug establishment registration number and drug listing number. 207.35 Section 207.35 Food and Drugs FOOD AND DRUG ADMINISTRATION,...
Code of Federal Regulations, 2011 CFR
2011-04-01
21 Food and Drugs 4 2011-04-01 2011-04-01 false Notification of registrant; drug establishment registration number and drug listing number. 207.35 Section 207.35 Food and Drugs FOOD AND DRUG ADMINISTRATION,...
Code of Federal Regulations, 2012 CFR
2012-04-01
21 Food and Drugs 4 2012-04-01 2012-04-01 false Notification of registrant; drug establishment registration number and drug listing number. 207.35 Section 207.35 Food and Drugs FOOD AND DRUG ADMINISTRATION,...
We've Got Your Number Your life is filled with code numbers. Every commercial
Bowman,John C.
Serial Number). Open your wallet and check your student ID card. It likely has a code number on it. Your a fake S.I.N.? This "magic" is accomplished by using what is called an error- detecting code and
Code of Federal Regulations, 2013 CFR
2013-04-01
21 Food and Drugs 4 2013-04-01 2013-04-01 false Notification of registrant; drug establishment registration number and drug listing number. 207.35 Section 207.35 Food and Drugs FOOD AND DRUG ADMINISTRATION,...