Sample records for grashof number

  1. Experimental Investigation of Free-Convection Heat Transfer in Vertical Tube at Large Grashof Numbers

    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.

  2. Preliminary study of the influence of Grashof and Reynolds numbers on the flow and heat transfer in an MOCVD reactor

    Microsoft Academic Search

    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

  3. Large Eddy Simulation study of the development of finite-channel lock-release currents at high Grashof numbers

    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.

  4. Experimental investigation of free-convection heat transfer in vertical tube at large Grashof numbers / E. R. G. Eckert, A. J. Diaguila

    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.

  5. Numbers

    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.

  6. Numbers

    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.)

  7. Number Line

    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.

  8. Mystery Number

    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.

  9. Number Factory

    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.

  10. Number Flash

    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.

  11. Nifty Numbers!

    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 ...

  12. Leftist Numbers

    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.

  13. Number theory

    Microsoft Academic Search

    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

  14. Number Sense

    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 ...

  15. 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.

  16. Number Cruncher

    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.

  17. Matching Numbers

    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).

  18. Number Watch

    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_.

  19. Tooth Numbering

    MedlinePLUS

    ... 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. ...

  20. Numbers, Please!

    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…

  1. Number Sense!

    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 ...

  2. 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.

  3. COMPLEX NUMBERS 1. Definition of complex numbers

    E-print Network

    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

  4. 3. Complex Numbers 17 3 Complex Numbers

    E-print Network

    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

  5. Teaching Number Sense

    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.

  6. Applications of Fibonacci Numbers

    E-print Network

    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

  7. Complex numbers Quaternions

    E-print Network

    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

  8. 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…

  9. Numerical simulations of a thermocline in a pressure-driven flow between two infinite horizontal plates

    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.

  10. Comparing Numbers-Between

    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.

  11. Kindergarten Number Sense

    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 ...

  12. Root numbers of curves

    Microsoft Academic Search

    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

  13. Number Systems Introduction & Objectives

    E-print Network

    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 · 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

  14. Occupancy Numbers in Testing Random Number Generators

    Microsoft Academic Search

    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

  15. 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.

  16. 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,…

  17. 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).

  18. 1 Random Number Generation.

    E-print Network

    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

  19. Building Numbers from Primes

    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…

  20. Operations on fuzzy numbers

    Microsoft Academic Search

    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

  1. 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.

  2. Numbers and Operations

    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 ...

  3. Sum-Difference Numbers

    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

  4. Infinite and natural numbers

    E-print Network

    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.

  5. Elements of number theory

    E-print Network

    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, ...

  6. UCGE Reports Number 20378

    E-print Network

    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

  7. Narrow it Down: Numbers

    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.

  8. PET: [number sign]1 is number one

    SciTech Connect

    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.

  9. Summing Consecutive Numbers

    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.

  10. Discovery: Prime Numbers

    ERIC Educational Resources Information Center

    de Mestre, Neville

    2008-01-01

    Prime numbers are important as the building blocks for the set of all natural numbers, because prime factorisation is an important and useful property of all natural numbers. Students can discover them by using the method known as the Sieve of Eratosthenes, named after the Greek geographer and astronomer who lived from c. 276-194 BC. Eratosthenes…

  11. Decompose That Teen Number!

    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.

  12. Theory of Numbers

    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.

  13. Simple Number Skills

    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.

  14. A imaginary number system

    Microsoft Academic Search

    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.

  15. Approximating the domatic number

    Microsoft Academic Search

    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.

  16. Approximating the Domatic Number

    Microsoft Academic Search

    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.

  17. Random Number Generation

    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.

  18. Convoluted convolved Fibonacci numbers

    Microsoft Academic Search

    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),

  19. Curvature and Tachibana numbers

    SciTech Connect

    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.

  20. Your Number Is...

    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.

  1. Your Number Was

    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.

  2. 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.

  3. 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.

  4. Estimating quantum chromatic numbers

    E-print Network

    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.

  5. Honors problem 1: Complex numbers. Arithmetic of complex numbers

    E-print Network

    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

  6. Numbers Are Not Everything

    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…

  7. Law of Large Numbers

    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.

  8. Hyperquarks and generation number

    SciTech Connect

    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.

  9. Counting whole numbers

    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 ...

  10. Participant number in this

    E-print Network

    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

  11. Number Base Clocks

    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.

  12. The Fibonacci Numbers.

    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)

  13. Fraction Number Line

    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.

  14. Education by the Numbers

    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…

  15. Generalized binary number systems

    Microsoft Academic Search

    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

  16. Numbers, taxonomy, and judgment

    Microsoft Academic Search

    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,

  17. Unrecognizable Sets of Numbers

    E-print Network

    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 ...

  18. Teachers Name Contact Number

    E-print Network

    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;

  19. Hypercomplex numbers Johanna Ramo

    E-print Network

    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

  20. Honors problem 1: Complex numbers. Arithmetic of complex numbers

    E-print Network

    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

  1. Conversion Between Different Number Systems Positional number systems

    E-print Network

    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

  2. 1.NBT Ordering Numbers

    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...

  3. 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.

  4. Number Conveyor Belt

    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.

  5. The magical Fibonacci number

    Microsoft Academic Search

    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

  6. The Numbers Game.

    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)

  7. Zero: A "None" Number?

    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.

  8. 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.

  9. History of Complex Numbers

    Microsoft Academic Search

    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),

  10. Fibonacci's Forgotten Number

    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…

  11. The number of \\

    Microsoft Academic Search

    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

  12. Definitions Algebra of complex numbers

    E-print Network

    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

  13. 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)....

  14. 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)....

  15. Erdos Number Project

    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.

  16. Expansion of rational numbers in Mobius number systems Petr Kurka

    E-print Network

    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

  17. 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.

  18. Generalized van der Waerden numbers

    Microsoft Academic Search

    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.

  19. Activated Immunoaffinity Catalog Numbers

    E-print Network

    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

  20. Instruction Catalog Number

    E-print Network

    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

  1. Playing the Numbers

    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…

  2. Review Article Number 138

    Microsoft Academic Search

    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.

  3. Teaching Denominate Numbers

    Microsoft Academic Search

    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

  4. Numbers, Groups Cryptography

    E-print Network

    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

  5. Numbers, Groups Cryptography

    E-print Network

    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

  6. IN NUMBERS: Biostatistics Faculty

    E-print Network

    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

  7. Proposal Number: Competition title

    E-print Network

    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

  8. Fibonacci numbers and words

    Microsoft Academic Search

    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,

  9. Number and Operation Games

    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! ...

  10. Poissonian copy numbers

    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.

  11. A Highly Random Number

    Microsoft Academic Search

    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

  12. UCGE Reports Number 20162

    E-print Network

    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

  13. Number2.com

    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.

  14. Houses with Height Numbers

    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.

  15. Quasar number density evolution

    Microsoft Academic Search

    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

  16. UCGE Reports Number 20176

    E-print Network

    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

  17. UCGE Reports Number 20042

    E-print Network

    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

  18. UCGE Reports Number 20277

    E-print Network

    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

  19. Create an Address Number

    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.

  20. Detecting squarefree numbers

    E-print Network

    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.

  1. "Better than Their Numbers"

    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'…

  2. Origami and Constructible Numbers

    E-print Network

    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

  3. Developing Early Number Sense

    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.

  4. Paint by Numbers Revived!

    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…

  5. Roundoff and Number Representation

    E-print Network

    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

  6. Honors question 3: Complex numbers (revisited). Arithmetic of complex numbers

    E-print Network

    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

  7. Number Theory Elliptic curves BSD Research : Number Theory group

    E-print Network

    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

  8. CT number definition

    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.

  9. Nature by Numbers

    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.

  10. Maths Doctor: Number

    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.

  11. Variable Number of \\

    Microsoft Academic Search

    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,

  12. The Remarkable Number "1"

    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.

  13. Paint by Number

    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.

  14. Beyond Natural Numbers: Negative Number Representation in Parietal Cortex

    PubMed Central

    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

  15. q Numbers of quantum groups, Fibonacci numbers, and orthogonal polynomials

    Microsoft Academic Search

    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

  16. Complex Numbers First: Define i

    E-print Network

    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

  17. Crossing Numbers and Parameterized Complexity

    Microsoft Academic Search

    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

  18. Elliptic Pseudoprimes Elliptic Carmichael Numbers

    E-print Network

    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

  19. Conway Numbers and Iteration Theory

    Microsoft Academic Search

    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

  20. Quasar number density evolution

    SciTech Connect

    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.

  1. By the Numbers

    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.

  2. 1.NBT Comparing Numbers

    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...

  3. Relative Sunspot Number (RSN)

    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.

  4. History of Prime Numbers

    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.

  5. Generalized Maxwell Love numbers

    E-print Network

    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.

  6. Rare Copy Number Variants

    PubMed Central

    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

  7. 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…

  8. Abstract. Geometry and Complex Numbers GEOMETRY AND COMPLEX NUMBERS

    E-print Network

    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

  9. Pauli Pascal Pyramids, Pauli Fibonacci Numbers, and Pauli Jacobsthal Numbers

    E-print Network

    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?

  10. Generalized Lucas Numbers and Relations with Generalized Fibonacci Numbers

    E-print Network

    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.

  11. Section 5.6 Complex Numbers1 Section 5.Section 5.Section 5.Section 5.6666 Complex NumbersComplex NumbersComplex NumbersComplex Numbers

    E-print Network

    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

  12. 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.

  13. Deterministic Random Number Generator Benchmarks

    E-print Network

    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

  14. Stirling Numbers for Complex Arguments

    Microsoft Academic Search

    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

  15. Number of applied research projects

    E-print Network

    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

  16. ALGEBRAIC NUMBER THEORY Romyar Sharifi

    E-print Network

    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

  17. 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 ...

  18. 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.

  19. Lepton family number violation

    SciTech Connect

    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.

  20. 15. Stress Sheet, Truss number 2, span number 6, Superior ...

    Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

    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

  1. Account Name Account Number Spending Distribution Account Number (if applicable)

    E-print Network

    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

  2. On the number of ordered factorizations of natural numbers

    Microsoft Academic Search

    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

  3. Concatenated Fibonacci and Lucas numbers do not form normal numbers

    E-print Network

    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.

  4. 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…

  5. The Kissing Numbers of Tetrahedra

    Microsoft Academic Search

    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.

  6. Graphs, partitions and Fibonacci numbers

    Microsoft Academic Search

    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.

  7. True & Deterministic Random Number Generators

    E-print Network

    True & Deterministic Random Number Generators C¸etin Kaya Ko¸c http://cs.ucsb.edu/~koc koc. This characterizes an ideal random number generator Ko¸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

  8. Sequence Analysis by Numbers: Proteins

    Microsoft Academic Search

    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

  9. Chromatic number of Euclidean plane

    E-print Network

    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.

  10. A Lesson in Number Pattern

    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…

  11. Ecological reading of random numbers

    Microsoft Academic Search

    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

  12. PLURIDICTA, Numbers 28-35.

    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"…

  13. 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…

  14. Program Number: Company (if applicable)

    E-print Network

    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

  15. The complex binary number system

    Microsoft Academic Search

    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

  16. Data Compression with Prime Numbers

    E-print Network

    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.

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

    ERIC Educational Resources Information Center

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

    2013-01-01

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

  18. 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.

  19. 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.

  20. 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.

  1. What exactly do numbers mean?

    PubMed Central

    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

  2. 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…

  3. Topology (Forskerprosjekt) Application Number: ES431408 Project Number: 0

    E-print Network

    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

  4. Catalan Numbers, the Hankel Transform, and Fibonacci Numbers

    Microsoft Academic Search

    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.

  5. Towards implementation of a binary number system for complex numbers

    Microsoft Academic Search

    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

  6. Finite Prandtl number 2-D convection at high Rayleigh numbers

    Microsoft Academic Search

    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

  7. 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)

  8. Familial Sinistrals Avoid Exact Numbers

    PubMed Central

    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

  9. Higher-order Fibonacci numbers

    Microsoft Academic Search

    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

  10. On quasi-number algebras

    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].

  11. 2.NBT Number Line Comparisons

    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...

  12. Familial sinistrals avoid exact numbers.

    PubMed

    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

  13. Explicit Methods in Number Theory

    Microsoft Academic Search

    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.

  14. 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).

  15. Wave Packets can Factorize Numbers

    E-print Network

    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.

  16. Whole Numbers - When in Rome

    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.

  17. On normal numbers Veronica Becher

    E-print Network

    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

  18. 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.

  19. Account Number Citation Reappeal Form

    E-print Network

    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

  20. Particle number in kinetic theory

    Microsoft Academic Search

    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

  1. numbers and SAT Oliver Kullmann

    E-print Network

    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

  2. numbers and SAT Oliver Kullmann

    E-print Network

    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

  3. On residue number system decoding

    Microsoft Academic Search

    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

  4. 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…

  5. 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…

  6. "JUST THE MATHS" UNIT NUMBER

    E-print Network

    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

  7. 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.

  8. Number Three Comes to See.

    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)

  9. Beyond complex numbers Johanna Ramo

    E-print Network

    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

  10. 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…

  11. 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...

  12. A Novel Redundant Binary Number to Natural Binary Number Converter

    Microsoft Academic Search

    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

  13. Hurwitz numbers and BKP hierarchy

    E-print Network

    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.

  14. Graspable Objects Shape Number Processing

    PubMed Central

    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

  15. 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.

  16. Incomplete Fibonacci and Lucas numbers

    Microsoft Academic Search

    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

  17. 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.

  18. The Plane of Complex Numbers In this chapter we'll introduce the complex numbers as a plane of numbers.

    E-print Network

    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

  19. Motion at low Reynolds number

    E-print Network

    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 ...

  20. 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.

  1. 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)

  2. OFFICE USE ONLY Reference number

    E-print Network

    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

  3. 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.

  4. 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...

  5. Poison control center - emergency number

    MedlinePLUS

    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 ...

  6. Bass Numbers and Semidualizing Complexes

    Microsoft Academic Search

    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

  7. 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.

  8. Neural Addition and Fibonacci Numbers

    Microsoft Academic Search

    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

  9. Use of Number by Fish

    Microsoft Academic Search

    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

  10. 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.

  11. 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.

  12. 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.

  13. Experimental investigation of mixed convection from an array of discrete heat sources at the bottom of a horizontal channel

    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.

  14. 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.

  15. Transport Numbers in Transdermal Iontophoresis

    PubMed Central

    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

  16. RECORDS RETENTION & DISPOSITION SCHEDULE AGENCY NUMBER SCHEDULE NUMBER

    E-print Network

    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

  17. Finite Prandtl Number 2-D Convection at High Rayleigh Number

    Microsoft Academic Search

    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 \\

  18. Betti numbers and injectivity radii

    E-print Network

    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.

  19. 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...

  20. 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.

  1. Newborn infants perceive abstract numbers

    PubMed Central

    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

  2. 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.

  3. Linear stability and bifurcation of natural convection flows in narrow-gap, concentric spherical annulus enclosures

    SciTech Connect

    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.

  4. Random Numbers a quick and dirty guide

    E-print Network

    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

  5. Real numbers. Constants, variables, and mathematical modeling.

    E-print Network

    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

  6. Student Learning Centre Review of Number

    E-print Network

    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

  7. Note on the Theory of Perfect Numbers

    E-print Network

    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.

  8. Two Problems of Number Theory Manindra Agarwal

    E-print Network

    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

  9. Not Just a Number Anymore

    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…

  10. Materiales. Numbers 21-23.

    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…

  11. Mitosis and Meiosis Chromosome number

    E-print Network

    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

  12. 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

  13. these numbers located on the

    E-print Network

    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

  14. 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…

  15. Re ferences llne numbers of

    E-print Network

    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

  16. On the number of factors

    Microsoft Academic Search

    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

  17. Fibonacci numbers and trigonometric identities

    Microsoft Academic Search

    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.

  18. Access to Emergency Number Services

    Microsoft Academic Search

    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)

  19. MOTOR POOL RESERVATIONS Reservation Number:_______________

    E-print Network

    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

  20. 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)

  1. Materiales. Numbers 17-20.

    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…

  2. Residual number processing in dyscalculia.

    PubMed

    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

  3. volume 41 number 1 agroborealis

    E-print Network

    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

  4. 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)

  5. Europe Note Europe note number

    E-print Network

    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

  6. Europe Note Europe note number

    E-print Network

    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

  7. Europe Note Europe note number

    E-print Network

    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

  8. "JUST THE MATHS" UNIT NUMBER

    E-print Network

    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

  9. Random number generators for microcomputers.

    PubMed

    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

  10. "JUST THE MATHS" UNIT NUMBER

    E-print Network

    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

  11. Down to Earth: Binary Numbers

    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.

  12. Time to Make the Numbers

    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.)

  13. Symmetry in Numbers David Marshall

    E-print Network

    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 ­ Typeset by FoilTEX ­ #12;Symmetry One of the guiding principles group of symmetries. -Paul Yale, in Geometry and Symmetry 2. Due or just proportion; harmony of parts

  14. IDENTIFICATION NUMBER REQUIREMENTS SOCIAL SECURITY NUMBER (SSN) OR INDIVIDUAL TAXPAYER IDENTIFICATION NUMBER (ITIN)

    E-print Network

    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

  15. 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.

  16. Remarks On General Fibonacci Numbers

    E-print Network

    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.

  17. 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.

  18. Complex Numbers A complex number is a number of the form a + bi, where a and b are real numbers and i =

    E-print Network

    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

  19. In Defense of Quantum Numbers

    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.

  20. Large Number Discrimination by Mosquitofish

    PubMed Central

    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

  1. Random Numbers from Astronomical Imaging

    E-print Network

    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.

  2. Diophantine approximations with Fibonacci numbers

    E-print Network

    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.

  3. Fibonacci numbers and orthogonal polynomials

    Microsoft Academic Search

    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

  4. Lozenge tilings and Hurwitz numbers

    E-print Network

    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.

  5. Happy Numbers: K-2 Numeracy

    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.

  6. Upper bounds for Ramsey numbers

    Microsoft Academic Search

    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

  7. Descendant invariants and characteristic numbers

    Microsoft Academic Search

    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

  8. Ultrafilters and combinatorial number theory

    Microsoft Academic Search

    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

  9. Algorithms in algebraic number theory

    Microsoft Academic Search

    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

  10. 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.

  11. A Pseudo-Random Number Generator Based on Normal Numbers

    SciTech Connect

    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.

  12. Numbers in English and Chinese language use

    Microsoft Academic Search

    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.

  13. Permutations, Parenthesis Words, and Schroder Numbers

    E-print Network

    Harju, Tero

    Permutations, Parenthesis Words, and Schr¨oder Numbers A. Ehrenfeucht1 T. Harju2 P. ten Pas3 G due to J. West is given: the Schr¨oder number sn-1 equals the number of permutations on {1, 2, Schr¨oder numbers, Catalan numbers, parenthe- sis words 1 Introduction We give here a different

  14. 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,…

  15. KISSING NUMBERS FOR SURFACES Hugo Parlier

    E-print Network

    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

  16. Tafelbild zum Einstieg Das Kissing Number Problem

    E-print Network

    69 Tafelbild zum Einstieg #12;70 Das Kissing Number Problem Definition: Kissing Number __________________________________________________________________________________________________ __________________________________________________________________________________________________ Figur / Körper Kreise Quadrate gleichseitige Dreiecke Kugeln Kissing Number Skizze der Anordnung Name: ________________________ Symbol: Stammgruppenfarbe: __________ #12;71 Definition: Kissing Number Als Kissing Number einer Figur

  17. ON -GREEDY EXPANSIONS OF NUMBERS CLEMENS HEUBERGER

    E-print Network

    Heuberger, Clemens

    a redundant binary number system that was recently introduced by Sz´ekely and Wang. For a natural number n´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

  18. hp calculators HP 50g Complex numbers

    E-print Network

    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

  19. 4.NBT What's My Number?

    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...

  20. 7 CFR 987.102 - Lot number.

    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...

  1. 7 CFR 987.102 - Lot number.

    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...

  2. 7 CFR 987.102 - Lot number.

    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...

  3. 7 CFR 987.102 - Lot number.

    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...

  4. Expansion of algebraic numbers Complexity of words

    E-print Network

    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

  5. Braess's Paradox, Fibonacci Numbers, and Exponential Inapproximability

    E-print Network

    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

  6. REGULAR ARTICLE Reproductive Numbers for Nonautonomous Spatially

    E-print Network

    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

  7. 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...

  8. 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...

  9. Use of Number by Fish

    PubMed Central

    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

  10. Natural convection in unsteady Couette motion

    Microsoft Academic Search

    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

  11. Estimation of convective mass transfer in solar distillation systems

    Microsoft Academic Search

    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

  12. Life at high Deborah number

    E-print Network

    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.

  13. Indexing the approximate number system.

    PubMed

    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

  14. DENORMAL NUMBERS IN FLOATING POINT SIGNAL PROCESSING APPLICATIONS Denormal numbers in floating point signal

    E-print Network

    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

  15. Analysis of Random Number Generators Parijat Naik

    E-print Network

    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

  16. 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…

  17. 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…

  18. 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)

  19. A Kilobit Special Number Field Sieve Factorization

    E-print Network

    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

  20. Fun With Complex Numbers Algebra 5/Trig

    E-print Network

    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

  1. The Kolmogorov Complexity of Liouville Numbers \\Lambda

    E-print Network

    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

  2. On the Betti Numbers of Chessboard Complexes

    Microsoft Academic Search

    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

  3. 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

  4. NOTES ON COMPLEX NUMBERS DAVID M. MCCLENDON

    E-print Network

    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

  5. 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…

  6. 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)

  7. Logic Design Chapter 1: Binary Numbers

    E-print Network

    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

  8. h-analogue of Fibonacci Numbers

    E-print Network

    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.

  9. The Magic of a Number System

    Microsoft Academic Search

    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

  10. On the number of prime factors of an odd perfect number

    E-print Network

    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

  11. Department for Analysis and Computational Number Theory Non-normal numbers

    E-print Network

    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

  12. 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.

  13. Prime number generation and factor elimination

    E-print Network

    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.

  14. The Euclidean Algorithm in Cubic Number Fields

    E-print Network

    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.

  15. A determinant of generalized Fibonacci numbers

    E-print Network

    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.

  16. 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)

  17. 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.

  18. 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.

  19. 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...

  20. 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...

  1. 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...

  2. 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...

  3. 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...

  4. 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...

  5. 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...

  6. 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...

  7. 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...

  8. 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...

  9. A System of Names for Binary Numbers

    Microsoft Academic Search

    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.

  10. 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)

  11. 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.

  12. Symmetry numbers and chemical reaction rates

    Microsoft Academic Search

    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

  13. Approximation of complex algebraic numbers by algebraic numbers of bounded degree

    E-print Network

    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

  14. Approximation of complex algebraic numbers by algebraic numbers of bounded degree

    E-print Network

    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

  15. Department for Analysis and Computational Number Theory Additive functions and number systems

    E-print Network

    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

  16. 7 CFR 46.20 - Lot numbers.

    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...

  17. 7 CFR 46.20 - Lot numbers.

    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...

  18. 7 CFR 46.20 - Lot numbers.

    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...

  19. 7 CFR 46.20 - Lot numbers.

    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...

  20. Cryptanalysis of the Windows Random Number Generator

    E-print Network

    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

  1. High speed optical quantum random number generation

    E-print Network

    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

  2. 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.

  3. 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.

  4. A Kilobit Special Number Field Sieve Factorization

    Microsoft Academic Search

    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

  5. Determining the number of interpretable factors

    Microsoft Academic Search

    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,

  6. Whence the complex numbers? Hans Halvorson

    E-print Network

    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

  7. 182 MATHEMATICS MAGAZINE The Fibonacci Numbers--

    E-print Network

    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

  8. When is a number Fibonacci? Phillip James

    E-print Network

    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

  9. Time series analysis for bug number prediction

    Microsoft Academic Search

    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

  10. 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…

  11. 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.

  12. 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...

  13. 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...

  14. 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...

  15. 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...

  16. 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...

  17. THE CONGRUENT NUMBER PROBLEM KEITH CONRAD

    E-print Network

    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

  18. Vector Rational Number Reconstruction Curtis Bright

    E-print Network

    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

  19. Vector Rational Number Reconstruction Curtis Bright

    E-print Network

    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

  20. THE CONGRUENT NUMBER PROBLEM KEITH CONRAD

    E-print Network

    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

  1. Convergence 1. Convergence of Sequence of numbers

    E-print Network

    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

  2. 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)

  3. ON -GREEDY EXPANSIONS OF NUMBERS CLEMENS HEUBERGER

    E-print Network

    Wagner, Stephan

    a redundant binary number system that was recently introduced by Sz´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

  4. VLSI binary multiplier using residue number systems

    Microsoft Academic Search

    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

  5. On the Number of Triangulation Simplexes

    Microsoft Academic Search

    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

  6. Algebraic Number Theory, a Computational Approach

    E-print Network

    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

  7. Number Theory I: Tools and Diophantine Equations

    E-print Network

    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

  8. Number Theory group in Nottingham Current members

    E-print Network

    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

  9. Lethbridge Number Theory and Combinatorics Seminar

    E-print Network

    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

  10. Random Numbers in Scientific Computing: An Introduction

    E-print Network

    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.

  11. On the binary expansions of algebraic numbers

    SciTech Connect

    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}.

  12. Relativistic theory of tidal Love numbers

    E-print Network

    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.

  13. 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.

  14. 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.

  15. From Taub Numbers to the Bondi Mass

    E-print Network

    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.

  16. 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.

  17. Factoring numbers with a single interferogram

    E-print Network

    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.

  18. 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.

  19. 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.

  20. 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…

  1. GEOMETRY AND COMPLEX NUMBERS (February 4, 2004) 7 6. Basic proofs for complex numbers

    E-print Network

    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

  2. On the domination number and the 2-packing number of Fibonacci cubes and Lucas cubes

    E-print Network

    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

  3. Fibonacci Numbers. You may have heard about the Fibonacci sequence of numbers. It

    E-print Network

    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

  4. Young Children's Number-Word Knowledge Predicts Their Performance on a Nonlinguistic Number Task

    E-print Network

    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

  5. Name: U of M ID number: Social Security number: Date of birth

    E-print Network

    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

  6. Deriving the number of jobs in proximity services from the number of inhabitants in French rural

    E-print Network

    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

  7. 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...

  8. 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...

  9. 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...

  10. 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...

  11. 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...

  12. Predicting landfalling hurricane numbers from basin hurricane numbers: basic statistical analysis

    E-print Network

    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.

  13. 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…

  14. THE DISCOUNTED REPRODUCTIVE NUMBER FOR EPIDEMIOLOGY

    PubMed Central

    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

  15. 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...

  16. Texas Rice, Volume IV, Number

    E-print Network

    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...

  17. FPGA Vendor Agnostic True Random Number Generator

    Microsoft Academic Search

    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

  18. 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…

  19. 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…

  20. TEACHING THE NATURAL NUMBERS AS OPERATORS

    Microsoft Academic Search

    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

  1. Brandeis University Philosophy current number of majors

    E-print Network

    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

  2. enter part number BNC / RP-BNC

    E-print Network

    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

  3. Carmichael numbers and a new primality test

    Microsoft Academic Search

    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

  4. Measures of Planarity: Crossing Number Stephanie Jones

    E-print Network

    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

  5. Bias in PseudoRandom Numbers

    Microsoft Academic Search

    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.

  6. NEUTRON NUMBERS 98, 108 AND 116

    Microsoft Academic Search

    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

  7. Class numbers of complex quadratic fields

    Microsoft Academic Search

    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.

  8. Algorithmic Number Theory-The Complexity Contribution

    Microsoft Academic Search

    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

  9. 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.

  10. 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)

  11. A Partition Formula for Fibonacci Numbers

    Microsoft Academic Search

    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.

  12. 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.

  13. Terms You Need to Know Course Numbering

    E-print Network

    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

  14. 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…

  15. Correlation of capillary number relationships for sandstone

    Microsoft Academic Search

    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

  16. 7 CFR 1.414 - Docket number.

    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...

  17. 7 CFR 1.414 - Docket number.

    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...

  18. 7 CFR 1.414 - Docket number.

    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...

  19. 7 CFR 1.414 - Docket number.

    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...

  20. 7 CFR 1.414 - Docket number.

    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...

  1. Search for lepton-family-number nonconservation

    SciTech Connect

    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.

  2. 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)

  3. Library Collections 74 Number of Loans 75

    E-print Network

    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

  4. 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.

  5. Requisition Number Requisition for Vehicle and Driver

    E-print Network

    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

  6. 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…

  7. -P and T number -Residence Permit

    E-print Network

    - 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

  8. Veterinary Seizure Detector Report Number 1

    E-print Network

    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

  9. Session Number Session Title Approved CM

    E-print Network

    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

  10. HANDBOOK FOR PARENTS 20132014 USEFUL TELEPHONE NUMBERS

    E-print Network

    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

  11. Recognising zero among implicitly defined elementary numbers

    E-print Network

    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

  12. On Carmichael numbers in arithmetic progressions

    E-print Network

    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

  13. High Weissenberg Number Asymptotics Who? Sebastian Hannes

    E-print Network

    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

  14. Quadratic dynamics in binary number systems

    Microsoft Academic Search

    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

  15. Serious toys: teaching the binary number system

    Microsoft Academic Search

    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

  16. Computer arithmetic architectures with redundant number systems

    Microsoft Academic Search

    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

  17. Number Theory in Cryptography ! and its Application"

    E-print Network

    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

  18. The covering number in learning theory

    Microsoft Academic Search

    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

  19. SESAME equation of state number 7740: Polycarbonate

    Microsoft Academic Search

    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

  20. GENERAL CHEMISTRY TEXTBOOK LIST ISBN Number

    E-print Network

    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

  1. 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.

  2. Modifications to the Number Field Sieve

    Microsoft Academic Search

    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

  3. Company number 5857955 Wellcome Trust Finance plc

    E-print Network

    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

  4. Computer Representation of Numbers and Computer Arithmetic

    E-print Network

    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

  5. A numerical approximation of the rotation number

    Microsoft Academic Search

    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.

  6. New String Theories And Their Generation Number

    E-print Network

    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.

  7. 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. ...

  8. Bit recycling for scaling random number generators

    E-print Network

    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.

  9. 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.

  10. Relativistic theory of surficial Love numbers

    E-print Network

    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.

  11. Number-space mapping in human infants.

    PubMed

    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

  12. 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.

  13. True random numbers from amplified quantum vacuum

    E-print Network

    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...

  14. Random numbers spring from alpha decay

    SciTech Connect

    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.

  15. Mixed convection around a liquid sphere in an air stream

    Microsoft Academic Search

    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

  16. Mixed convection around a liquid sphere in an air stream

    Microsoft Academic Search

    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

  17. 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...

  18. 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...

  19. 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...

  20. 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...

  1. 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...

  2. 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...

  3. Generating functions for weighted Hurwitz numbers

    E-print Network

    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.

  4. Exploring number space by random digit generation.

    PubMed

    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

  5. 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.

  6. MSSM with gauged baryon and lepton numbers

    E-print Network

    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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 76 FR 60789 - Local Number Portability Porting Interval and Validation Requirements; Telephone Number Portability

    Federal Register 2010, 2011, 2012, 2013, 2014

    2011-09-30

    ...Part 52 [WC Docket No. 07-244, CC Docket No. 95-116; DA 11-1558] Local Number Portability Porting Interval and Validation Requirements; Telephone Number Portability AGENCY: Federal Communications Commission. ACTION: Proposed rule;...

  12. 75 FR 5013 - Local Number Portability Porting Interval and Validation Requirements; Telephone Number Portability

    Federal Register 2010, 2011, 2012, 2013, 2014

    2010-02-01

    ...COMMUNICATIONS COMMISSION 47 CFR Part 52 [WC Docket No. 07-244; DA 09-2569] Local Number Portability Porting Interval and Validation Requirements; Telephone Number Portability AGENCY: Federal Communications Commission. ACTION: Proposed...

  13. 75 FR 35305 - Local Number Portability Porting Interval and Validation Requirements; Telephone Number Portability

    Federal Register 2010, 2011, 2012, 2013, 2014

    2010-06-22

    ...COMMUNICATIONS COMMISSION 47 CFR Part 52 [WC Docket No. 07-244; FCC 10-85] Local Number Portability Porting Interval and Validation Requirements; Telephone Number Portability AGENCY: Federal Communications Commission. ACTION: Final...

  14. VU Center Numbering Scheme All Center Numbers have ten digits. The digits are grouped to indicate

    E-print Network

    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

  15. 21 CFR 207.35 - Notification of registrant; drug establishment registration number and drug listing number.

    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,...

  16. 21 CFR 207.35 - Notification of registrant; drug establishment registration number and drug listing number.

    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,...

  17. 21 CFR 207.35 - Notification of registrant; drug establishment registration number and drug listing number.

    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,...

  18. 21 CFR 207.35 - Notification of registrant; drug establishment registration number and drug listing number.

    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,...

  19. We've Got Your Number Your life is filled with code numbers. Every commercial

    E-print Network

    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

  20. 21 CFR 207.35 - Notification of registrant; drug establishment registration number and drug listing number.

    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,...