Science.gov

Sample records for grashof number

  1. Numerical calculation of the drag force induced by natural convection of spheres at low Grashof numbers

    SciTech Connect

    Dudek, D.; Fletcher, T.H.

    1987-02-01

    When a heated solid sphere is introduced into an ambient fluid, a natural convective flow occurs which results in a drag force on the sphere. This study involves the numerical calculation of both the steady-state and the transient natural convective drag force around spheres at low Grashof numbers. Numerical techniques are taken from Geoola and Cornish. An empirical expression is suggested for the total drag coefficient for Grashof numbers ranging from 4 x 10/sup -4/ to 0.5 and Prandtl number = 0.72: log C/sub DT/ = 1.25 + 0.31 log Gr - 0.097(log Gr)/sup 2/. The dimensionless time required to reach 90% of the steady-state drag force can be approximated by the second-order polynomial: log t/sub 90%/ = 1.32 - log Gr - 0.11(Gr)/sup 2/.

  2. 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.

  3. Natural convection in power-law fluids from two square cylinders in tandem arrangement at moderate Grashof numbers

    NASA Astrophysics Data System (ADS)

    Shyam, Radhe; Chhabra, R. P.

    2013-06-01

    In this work, free convective flow and heat transfer in power-law fluids from two heated square cylinders in tandem arrangement is studied. The governing differential equations have been solved numerically over wide ranges of Grashof number, 10 ≤ Gr ≤ 1,000, Prandtl number, 0.71 ≤ Pr ≤ 50 and power-law index, 0.4 ≤ n ≤ 1.8. In order to elucidate the extent of inter-cylinder interaction, the non-dimensional inter-cylinder spacing, L/d is varied in the range, 2 ≤ L/d ≤ 6. The results are interpreted in terms of streamline and isotherm contours in the proximity of two cylinders to gain physical insights into the nature of flow. At the next level, the distribution of the local Nusselt number along the surface of the cylinders is presented. At the minimum inter-cylinder spacing due to the intense interference, the downstream cylinder contributes much less to the overall heat transfer whereas it experiences much higher hydrodynamic drag than the upstream cylinder. Broadly, the local and average Nusselt number for both cylinders show a positive dependence on both Grashof and Prandtl numbers. Also, all else being equal, shear-thinning fluid behaviour promotes the rate of heat transfer and shear-thickening fluid behaviour impedes it. Finally, the present numerical results have been correlated by using simple forms of equations thereby enabling the estimation of Nusselt number in a new application.

  4. 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.

  5. Effect of Reynolds and Grashof numbers on mixed convection inside a lid-driven square cavity filled with water-Al2O3 nanofluid

    NASA Astrophysics Data System (ADS)

    Jaman, Md. Shah; Islam, Showmic; Saha, Sumon; Hasan, Mohammad Nasim; Islam, Md. Quamrul

    2016-07-01

    A numerical analysis is carried out to study the performance of steady laminar mixed convection flow inside a square lid-driven cavity filled with water-Al2O3 nanofluid. The top wall of the cavity is moving at a constant velocity and is heated by an isothermal heat source. Two-dimensional Navier-stokes equations along with the energy equations are solved using Galerkin finite element method. Results are obtained for a range of Reynolds and Grashof numbers by considering with and without the presence of nanoparticles. The parametric studies for a wide range of governing parameters in case of pure mixed convective flow show significant features of the present problem in terms of streamline and isotherm contours, average Nusselt number and average temperature profiles. The computational results indicate that the heat transfer coeffcient is strongly influenced by the above governing parameters at the pure mixed convection regime.

  6. 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.

  7. Multicellular natural convection of a low Prandlt number fluid between horizontal concentric cylinders

    SciTech Connect

    Joosik Yoo; Jun Young Choi; Moonuhn Kim . Dept. of Mechanical Engineering)

    1994-01-01

    Two-dimensional natural convection of a fluid of low Prandtl number (Pr = 0.02) in an annulus between two concentric horizontal cylinders is numerically investigated in a wide range of gap widths. For low Grashof numbers, a steady unicellular convection is obtained. Above a transition Grashof number that depends on the gap width, a steady bicellular flow occurs. With further increase of the Grashof number, steady or time-periodic multicellular convection occurs, and finally, complex unsteady convective flow appears. A plot is presented that predicts the type of flow patterns for various combination of gap widths and Grashof numbers.

  8. Experimental study of cold plume instability in large Prandtl number Czochralski melt: Parametric dependences and scaling laws

    NASA Astrophysics Data System (ADS)

    Miroshnichenko, E.; Kit, E.; Gelfgat, A. Yu.

    2016-03-01

    A parametric experimental study of the cold plume instability that appears in the large-Prandtl-number Czochralski melt flows is reported. The critical temperature difference (the critical Grashof number) and the frequency of appearing oscillations were measured for varying Prandtl numbers, aspect ratios of the melt, and crystal/crucible radii ratio. The measurements were carried out by two independent and fully non-intrusive experimental techniques. The results are reported as dimensional and dimensionless parametric dependences, and then are joined into relatively simple empirical relations showing how the critical Grashof number and the frequency of emerging oscillations depend on other parameters.

  9. Story Numbers.

    ERIC Educational Resources Information Center

    Swafford, Jane; McGinty, Robert

    1978-01-01

    A concrete approach to prime numbers is presented using rectangles and triangles to construct a building for each number so that each story represents a pair of factors and the triangular-shaped roof represents the number. (MP)

  10. Number relativity

    NASA Astrophysics Data System (ADS)

    Shin, Philip

    Number relativity 1.Every equation of the relativity is just the way to understand through to solve one question of the math problem. We just add the hypothesis into the number. 2. Sequence of number is the machine physics for software(computer) as the number order is program equation as calculator. 3. When zero is denominator, it is not existing as it is doing something by nothing. So nothing means time as we put zero denominator into time. My personal physics imagine.

  11. 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.

  12. Superharmonic numbers

    NASA Astrophysics Data System (ADS)

    Cohen, Graeme L.

    2009-03-01

    Let tau(n) denote the number of positive divisors of a natural number n>1 and let sigma(n) denote their sum. Then n is superharmonic if sigma(n)mid n^ktau(n) for some positive integer k . We deduce numerous properties of superharmonic numbers and show in particular that the set of all superharmonic numbers is the first nontrivial example that has been given of an infinite set that contains all perfect numbers but for which it is difficult to determine whether there is an odd member.

  13. Number Time

    ERIC Educational Resources Information Center

    Herrera, Terese A.

    2004-01-01

    This article features Number Time, a site developed by the British Broadcasting Corporation (BBC) for young mathematics learners, located at www.bbc.co.uk/schools/numbertime. The site uses interactive animation to help children in pre-K through grade 2 understand and practice number basics. Users will find online games, videos that tell number…

  14. Numbers Sense

    ERIC Educational Resources Information Center

    Kathotia, Vinay

    2009-01-01

    This article reports on work undertaken by schools as part of Qualifications and Curriculum Authority's (QCA's) "Engaging mathematics for all learners" project. The goal was to use in the classroom, materials and approaches from a Royal Institution (Ri) Year 10 master-class, "Number Sense", which was inspired by examples from Michael Blastland and…

  15. 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…

  16. Number Guessing

    ERIC Educational Resources Information Center

    Sezin, Fatin

    2009-01-01

    It is instructive and interesting to find hidden numbers by using different positional numeration systems. Most of the present guessing techniques use the binary system expressed as less-than, greater-than or present-absent type information. This article describes how, by employing four cards having integers 1-64 written in different colours, one…

  17. Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids

    PubMed Central

    Schumacher, Jörg; Götzfried, Paul; Scheel, Janet D.

    2015-01-01

    Turbulent convection is often present in liquids with a kinematic viscosity much smaller than the diffusivity of the temperature. Here we reveal why these convection flows obey a much stronger level of fluid turbulence than those in which kinematic viscosity and thermal diffusivity are the same; i.e., the Prandtl number Pr is unity. We compare turbulent convection in air at Pr=0.7 and in liquid mercury at Pr=0.021. In this comparison the Prandtl number at constant Grashof number Gr is varied, rather than at constant Rayleigh number Ra as usually done. Our simulations demonstrate that the turbulent Kolmogorov-like cascade is extended both at the large- and small-scale ends with decreasing Pr. The kinetic energy injection into the flow takes place over the whole cascade range. In contrast to convection in air, the kinetic energy injection rate is particularly enhanced for liquid mercury for all scales larger than the characteristic width of thermal plumes. As a consequence, mean values and fluctuations of the local strain rates are increased, which in turn results in significantly enhanced enstrophy production by vortex stretching. The normalized distributions of enstrophy production in the bulk and the ratio of the principal strain rates are found to agree for both Prs. Despite the different energy injection mechanisms, the principal strain rates also agree with those in homogeneous isotropic turbulence conducted at the same Reynolds numbers as for the convection flows. Our results have thus interesting implications for small-scale turbulence modeling of liquid metal convection in astrophysical and technological applications. PMID:26195793

  18. Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids.

    PubMed

    Schumacher, Jörg; Götzfried, Paul; Scheel, Janet D

    2015-08-01

    Turbulent convection is often present in liquids with a kinematic viscosity much smaller than the diffusivity of the temperature. Here we reveal why these convection flows obey a much stronger level of fluid turbulence than those in which kinematic viscosity and thermal diffusivity are the same; i.e., the Prandtl number Pr is unity. We compare turbulent convection in air at Pr=0.7 and in liquid mercury at Pr=0.021. In this comparison the Prandtl number at constant Grashof number Gr is varied, rather than at constant Rayleigh number Ra as usually done. Our simulations demonstrate that the turbulent Kolmogorov-like cascade is extended both at the large- and small-scale ends with decreasing Pr. The kinetic energy injection into the flow takes place over the whole cascade range. In contrast to convection in air, the kinetic energy injection rate is particularly enhanced for liquid mercury for all scales larger than the characteristic width of thermal plumes. As a consequence, mean values and fluctuations of the local strain rates are increased, which in turn results in significantly enhanced enstrophy production by vortex stretching. The normalized distributions of enstrophy production in the bulk and the ratio of the principal strain rates are found to agree for both Prs. Despite the different energy injection mechanisms, the principal strain rates also agree with those in homogeneous isotropic turbulence conducted at the same Reynolds numbers as for the convection flows. Our results have thus interesting implications for small-scale turbulence modeling of liquid metal convection in astrophysical and technological applications. PMID:26195793

  19. Topics in Number Theory: The Number Game.

    ERIC Educational Resources Information Center

    Batra, Laj, Ed.; And Others

    This teacher's guide contains nine topics in number theory. Suggested questions for the teacher, short investigations, and possible exercises for the student are included. Chapter 1 is an introduction to sequences and series using geoboard activities involving triangular numbers, square numbers, rectangular numbers, and pentagonal numbers. The…

  20. 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…

  1. Promote Number Sense

    ERIC Educational Resources Information Center

    Gurganus, Susan

    2004-01-01

    "Number sense" is "an intuition about numbers that is drawn from all varied meanings of number" (NCTM, 1989, p. 39). Students with number sense understand that numbers are representative of objects, magnitudes, relationships, and other attributes; that numbers can be operated on, compared, and used for communication. It is fundamental knowledge…

  2. Star Numbers and Constellations.

    ERIC Educational Resources Information Center

    Francis, Richard L.

    1993-01-01

    A number for which the number of digits categorizes the number is called a star number. A set of star numbers having a designated property is called a constellation. Discusses nature and cardinality of constellations made up of star square, star prime, star abundant, and star deficient numbers. Presents five related problems for exploration. (MDH)

  3. All Square Chiliagonal Numbers

    ERIC Educational Resources Information Center

    A?iru, Muniru A.

    2016-01-01

    A square chiliagonal number is a number which is simultaneously a chiliagonal number and a perfect square (just as the well-known square triangular number is both triangular and square). In this work, we determine which of the chiliagonal numbers are perfect squares and provide the indices of the corresponding chiliagonal numbers and square…

  4. 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,…

  5. Numbers and Numerals.

    ERIC Educational Resources Information Center

    Smith, David Eugene; Ginsburg, Jekuthiel

    Counting, naming numbers, numerals, computation, and fractions are the topics covered in this pamphlet. Number lore and interesting number properties are noted; the derivation of some arithmetic terms is briefly discussed. (DT)

  6. Factorialsum Number Chains.

    ERIC Educational Resources Information Center

    Lamb, John, Jr.

    1989-01-01

    Describes several phenomena in which interesting properties of numbers are demonstrated. Includes discussions of amicable, perfect, and sociable numbers. Presents computer programs for conducting a number chain search. (RT)

  7. 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…

  8. Enriching Number Knowledge

    ERIC Educational Resources Information Center

    Mack, Nancy K.

    2011-01-01

    Exploring number systems of other cultures can be an enjoyable learning experience that enriches students' knowledge of numbers and number systems in important ways. It helps students deepen mental computation fluency, knowledge of place value, and equivalent representations for numbers. This article describes how the author designed her…

  9. Are Numbers Gendered?

    ERIC Educational Resources Information Center

    Wilkie, James E. B.; Bodenhausen, Galen V.

    2012-01-01

    We examined the possibility that nonsocial, highly generic concepts are gendered. Specifically, we investigated the gender connotations of Arabic numerals. Across several experiments, we show that the number 1 and other odd numbers are associated with masculinity, whereas the number 2 and other even numbers are associated with femininity, in ways…

  10. Number Sense Made Simple Using Number Patterns

    ERIC Educational Resources Information Center

    Su, Hui Fang Huang; Marinas, Carol; Furner, Joseph

    2011-01-01

    This article highlights investigating intriguing number patterns utilising an emerging technology called the Square Tool. Mathematics teachers of grades K-12 will find the Square Tool useful in making connections and bridging the gap from the concrete to the abstract. Pattern recognition helps students discover various mathematical concepts. With…

  11. 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…

  12. 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…

  13. The Remarkable Number "1"

    ERIC Educational Resources Information Center

    Allen, G. Donald

    2014-01-01

    In human history, the origin of the numbers came from definite practical needs. Indeed, there is strong evidence that numbers were created before writing. The number "1", dating back at least 20,000 years, was found as a counting symbol on a bone. The famous statement by the German mathematician Leopold Kronecker (1823-1891), "God…

  14. Number Relationships in Preschool

    ERIC Educational Resources Information Center

    Jung, Myoungwhon

    2011-01-01

    When a child understands number relationships, he or she comprehends the meaning of numbers by developing multiple, flexible ways of representing them. The importance of developing number relationships in the early years has been highlighted because it helps children build a good foundation for developing a more sophisticated understanding of…

  15. Estimating Large Numbers

    ERIC Educational Resources Information Center

    Landy, David; Silbert, Noah; Goldin, Aleah

    2013-01-01

    Despite their importance in public discourse, numbers in the range of 1 million to 1 trillion are notoriously difficult to understand. We examine magnitude estimation by adult Americans when placing large numbers on a number line and when qualitatively evaluating descriptions of imaginary geopolitical scenarios. Prior theoretical conceptions…

  16. Curvature and Tachibana numbers

    SciTech Connect

    Stepanov, Sergey E

    2011-07-31

    The aim of this paper is to define the rth Tachibana number t{sub r} of an n-dimensional compact oriented Riemannian manifold as the dimension of the space of conformally Killing r-forms, for r=1,2,...,n-1. We also describe properties of these numbers, by analogy with properties of the Betti numbers b{sub r} of a compact oriented Riemannian manifold. Bibliography: 25 titles.

  17. High Reynolds Number Research

    NASA Technical Reports Server (NTRS)

    Baals, D. D. (Editor)

    1977-01-01

    Fundamental aerodynamic questions for which high Reynolds number experimental capability is required are discussed. The operational characteristics and design features of the National Transonic Facility are reviewed.

  18. The Number Story.

    ERIC Educational Resources Information Center

    Freitag, Herta Taussig; Freitag, Arthur H.

    The development of number concepts from prehistoric time to the present day are presented. Section 1 presents the historical development, logical development, and the infinitude of numbers. Section 2 focuses on non-positional and positional numeration systems. Section 3 compares historical and modern techniques and devices for computation. Section…

  19. First Graders' Number Knowledge

    ERIC Educational Resources Information Center

    Thomas, Jonathan N.; Tabor, Pamela D.; Wright, Robert J.

    2010-01-01

    As young children make sense of mathematics, they begin to see with new eyes. What once was uncertain may now be determined. Objects become countable; fingers become tools; and numbers become more than just names. Educators revel in such developments--which mark significant progress toward more sophisticated understanding of number--and work…

  20. Templates, Numbers & Watercolors.

    ERIC Educational Resources Information Center

    Clemesha, David J.

    1990-01-01

    Describes how a second-grade class used large templates to draw and paint five-digit numbers. The lesson integrated artistic knowledge and vocabulary with their mathematics lesson in place value. Students learned how draftspeople use templates, and they studied number paintings by Charles Demuth and Jasper Johns. (KM)

  1. Genetics by the Numbers

    MedlinePlus

    ... Life Science > Genetics by the Numbers Inside Life Science View All Articles | Inside Life Science Home Page Genetics by the Numbers By Chelsea ... Genetics NIH's National DNA Day This Inside Life Science article also appears on LiveScience . Learn about related ...

  2. 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)

  3. Avogadro's Number Ferromagnetically

    ERIC Educational Resources Information Center

    Houari, Ahmed

    2010-01-01

    Avogadro's number, usually denoted by N[subscript A], plays a fundamental role in both physics and chemistry. It defines the extremely useful concept of the mole, which is the base unit of the amount of matter in the international system of units. The fundamental character of this number can also be illustrated by its appearance in the definitions…

  4. Numbers in Action

    PubMed Central

    Rugani, Rosa; Sartori, Luisa

    2016-01-01

    Humans show a remarkable tendency to describe and think of numbers as being placed on a mental number line (MNL), with smaller numbers located on the left and larger ones on the right. Faster responses to small numbers are indeed performed on the left side of space, while responses to large numbers are facilitated on the right side of space (spatial-numerical association of response codes, SNARC effect). This phenomenon is considered the experimental demonstration of the MNL and has been extensively replicated throughout a variety of paradigms. Nevertheless, the majority of previous literature has mainly investigated this effect by means of response times and accuracy, whereas studies considering more subtle and automatic measures such as kinematic parameters are rare (e.g., in a reaching-to-grasp movement, the grip aperture is enlarged in responding to larger numbers than in responding to small numbers). In this brief review we suggest that numerical magnitude can also affect the what and how of action execution (i.e., temporal and spatial components of movement). This evidence could have large implications in the strongly debated issue concerning the effect of experience and culture on the orientation of MNL. PMID:27524965

  5. 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)

  6. Logo and Negative Numbers.

    ERIC Educational Resources Information Center

    Strawn, Candace A.

    1998-01-01

    Describes LOGO's turtle graphics capabilities based on a sixth-grade classroom's activities with negative numbers and Logo programming. A sidebar explains LOGO and offers suggestions to teachers for using LOGO effectively. (LRW)

  7. Nursing by numbers.

    PubMed

    Hurst, Keith

    In the face of NHS budget cuts, nurses are being asked to justify their workforce numbers. Keith Hurst reviews some of the tools available for calculating staffing levels, examines their pros and cons, and discusses their application. PMID:17087410

  8. Quantum random number generator

    DOEpatents

    Pooser, Raphael C.

    2016-05-10

    A quantum random number generator (QRNG) and a photon generator for a QRNG are provided. The photon generator may be operated in a spontaneous mode below a lasing threshold to emit photons. Photons emitted from the photon generator may have at least one random characteristic, which may be monitored by the QRNG to generate a random number. In one embodiment, the photon generator may include a photon emitter and an amplifier coupled to the photon emitter. The amplifier may enable the photon generator to be used in the QRNG without introducing significant bias in the random number and may enable multiplexing of multiple random numbers. The amplifier may also desensitize the photon generator to fluctuations in power supplied thereto while operating in the spontaneous mode. In one embodiment, the photon emitter and amplifier may be a tapered diode amplifier.

  9. 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…

  10. 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.

  11. Report number codes

    SciTech Connect

    Nelson, R.N.

    1985-05-01

    This publication lists all report number codes processed by the Office of Scientific and Technical Information. The report codes are substantially based on the American National Standards Institute, Standard Technical Report Number (STRN)-Format and Creation Z39.23-1983. The Standard Technical Report Number (STRN) provides one of the primary methods of identifying a specific technical report. The STRN consists of two parts: The report code and the sequential number. The report code identifies the issuing organization, a specific program, or a type of document. The sequential number, which is assigned in sequence by each report issuing entity, is not included in this publication. Part I of this compilation is alphabetized by report codes followed by issuing installations. Part II lists the issuing organization followed by the assigned report code(s). In both Parts I and II, the names of issuing organizations appear for the most part in the form used at the time the reports were issued. However, for some of the more prolific installations which have had name changes, all entries have been merged under the current name.

  12. Beyond the Number Domain

    PubMed Central

    Cantlon, Jessica F.; Platt, Michael L.; Brannon, Elizabeth M.

    2009-01-01

    In a world without numbers, we would be unable to build a skyscraper, hold a national election, plan a wedding, or pay for a chicken at the market. The numerical symbols used in all these behaviors build on the approximate number system (ANS) which represents the number of discrete objects or events as a continuous mental magnitude. In this review, we first discuss evidence that the ANS bears a set of behavioral and brain signatures that are universally displayed across animal species, human cultures, and development. We then turn to the question of whether the ANS constitutes a specialized cognitive and neural domain--a question central to understanding how this system works, the nature of its evolutionary and developmental trajectory, and its physical instantiation in the brain. PMID:19131268

  13. Quantum random number generation

    DOE PAGESBeta

    Ma, Xiongfeng; Yuan, Xiao; Cao, Zhu; Zhang, Zhen; Qi, Bing

    2016-06-28

    Here, quantum physics can be exploited to generate true random numbers, which play important roles in many applications, especially in cryptography. Genuine randomness from the measurement of a quantum system reveals the inherent nature of quantumness -- coherence, an important feature that differentiates quantum mechanics from classical physics. The generation of genuine randomness is generally considered impossible with only classical means. Based on the degree of trustworthiness on devices, quantum random number generators (QRNGs) can be grouped into three categories. The first category, practical QRNG, is built on fully trusted and calibrated devices and typically can generate randomness at amore » high speed by properly modeling the devices. The second category is self-testing QRNG, where verifiable randomness can be generated without trusting the actual implementation. The third category, semi-self-testing QRNG, is an intermediate category which provides a tradeoff between the trustworthiness on the device and the random number generation speed.« less

  14. Quantum random number generation

    SciTech Connect

    Ma, Xiongfeng; Yuan, Xiao; Cao, Zhu; Zhang, Zhen; Qi, Bing

    2016-01-01

    Here, quantum physics can be exploited to generate true random numbers, which play important roles in many applications, especially in cryptography. Genuine randomness from the measurement of a quantum system reveals the inherent nature of quantumness — coherence, an important feature that differentiates quantum mechanics from classical physics. The generation of genuine randomness is generally considered impossible with only classical means. Based on the degree of trustworthiness on devices, quantum random number generators (QRNGs) can be grouped into three categories. The first category, practical QRNG, is built on fully trusted and calibrated devices and typically can generate randomness at a high speed by properly modeling the devices. The second category is self-testing QRNG, where verifiable randomness can be generated without trusting the actual implementation. The third category, semi-self-testing QRNG, is an intermediate category which provides a tradeoff between the trustworthiness on the device and the random number generation speed.

  15. Introducing Complex Numbers

    ERIC Educational Resources Information Center

    Trudgian, Timothy

    2009-01-01

    One of the difficulties in any teaching of mathematics is to bridge the divide between the abstract and the intuitive. Throughout school one encounters increasingly abstract notions, which are more and more difficult to relate to everyday experiences. This article examines a familiar approach to thinking about negative numbers, that is an…

  16. Uniform random number generators

    NASA Technical Reports Server (NTRS)

    Farr, W. R.

    1971-01-01

    Methods are presented for the generation of random numbers with uniform and normal distributions. Subprogram listings of Fortran generators for the Univac 1108, SDS 930, and CDC 3200 digital computers are also included. The generators are of the mixed multiplicative type, and the mathematical method employed is that of Marsaglia and Bray.

  17. ALARA notes, Number 8

    SciTech Connect

    Khan, T.A.; Baum, J.W.; Beckman, M.C.

    1993-10-01

    This document contains information dealing with the lessons learned from the experience of nuclear plants. In this issue the authors tried to avoid the `tyranny` of numbers and concentrated on the main lessons learned. Topics include: filtration devices for air pollution abatement, crack repair and inspection, and remote handling equipment.

  18. 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…

  19. The Net by Numbers.

    ERIC Educational Resources Information Center

    McMurdo, George

    1996-01-01

    The expansion of the commercial Internet has encouraged the interpretation of the Internet and its uses as a potential marketing medium. Examines statistical and demographic information about the Internet including number of Internet hosts and World Wide Web servers, and estimates of Internet users; and raises questions about definitions and…

  20. 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…

  1. Counting and Number Conservation.

    ERIC Educational Resources Information Center

    Tollefsrud-Anderson, Linda

    This study assessed estimation skills on both static and transformation (conservation) tasks on numerosities ranging from 3 to 16, and included addition and subtraction trials to control for response bias. A total of 148 four- and five-year-old children estimated the number of balls of yarn sewn on elastic straps, and participated in 1 addition, 1…

  2. "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'…

  3. Number in Classifier Languages

    ERIC Educational Resources Information Center

    Nomoto, Hiroki

    2013-01-01

    Classifier languages are often described as lacking genuine number morphology and treating all common nouns, including those conceptually count, as an unindividuated mass. This study argues that neither of these popular assumptions is true, and presents new generalizations and analyses gained by abandoning them. I claim that no difference exists…

  4. Fun with Safronov Numbers

    NASA Astrophysics Data System (ADS)

    Christian, Damian Joseph; Lund, M. B.

    2010-10-01

    A growing number (over 100!) of extra-solar planets (ESPs) have been discovered by transit photometry, and these systems are important because the transit strongly constrains their orbital inclination and allows accurate physical parameters for the planet to be derived, especially their radii. Their mass-radius relation allows us to probe their internal structure. In the present work we calculate Safronov numbers for the current sample of ESP and compare their masses and radii to current models with the goal of obtaining better constrains on their formation processes. Our calculation of Safronov numbers for the current TESP sample does show 2 classes, although about 20% lie above the formal Class I definition. These trends and recent results that argue against a useful distinction between Safronov classes are under further investigation. Mass-radius relations for the current sample of TESP are inconsistent with ESP models with very large core masses (> 100 M_Earth). Most TESP with radii near 1R_J are consistent with models with no core mass or core masses of 10 M_Earth. The inflated planets, with radii >1.2 R_J are not consistent with current ESP models, but may lie along the lower end of models for brown dwarfs. Although such models are nascent, it is important to establish trends for the current sample of ESP, which will further the understanding of their formation and evolution.

  5. Leading by numbers.

    PubMed

    Kerfoot, Karlene

    2005-01-01

    We measure to determine where we stand financially or in our quality outcomes. As people see the connection of measures and the success of the company, everything makes more sense. Izzo (2005) writes that profits/net margins are important to an organization and are like oxygen to a person. If we have oxygen, we can focus on the important things in life; if we don't we are preoccupied with gasping for air. Organizations are the same way. With the oxygen of profits, organizations can focus on those things that matter most to the staff and the customer. But when the search for profits becomes obsessive because of greed for excess profits or impending financial doom, everybody loses. Izzo (2005) reminds us that organizations shouldn't exist for only profit, just as people don't exist for only oxygen. Oxygen is merely an enabler for us to do the work of living. Measurement and numbers are the oxygen needed to achieve excellence. As people in organizations use numbers as their servants rather than being slaves to numbers, everyone will succeed. If the use of measurement is seen as punitive, and not a system of serving people to attain that zest for business and a higher mission, we will not achieve the level of excellence our people, patients, and communities deserve. PMID:16033147

  6. 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.

  7. 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

  8. Nomogram for sunspot numbers.

    NASA Astrophysics Data System (ADS)

    Upreti, U. C.

    1997-12-01

    Nomogram construction using the parabolic relationship f0F2 = a0+a1R12+a2R122 between monthly median f0F2 and running average sunspot number (RASSN) R12 values has been described; here a0, a1 and a2 are the best fit coefficients. The nomogram can give the required local effective sunspot number (LESSN) values corresponding to any observed value of f0F2. Transforming the f0F2-RASSN relation to the form R122+pR12+q = 0 [where p = a1/a2 and q = (a0-f0F2)/a2], a practical method for the preparation of a single nomogram for f0F2-RASSN has been described and the problem of very high and very low values of the variables has also been dealt with successfully. A single nomogram for a large range of variables, namely, f0F2, a0, a1, and a2 has been obtained so that one can easily find LESSN values at any location, season, and time. The nomogram tends to minimize the errors in LESSN calculations at all levels of solar activity.

  9. An introduction to hyperharmonic numbers

    NASA Astrophysics Data System (ADS)

    Cereceda, José Luis

    2015-04-01

    In this note, we deal with a generalization of the harmonic numbers proposed by Conway and Guy in their Book of Numbers, namely, the so-called hyperharmonic numbers. Our main aim is to prove, by mathematical induction, the formula defining the hyperharmonic numbers in terms of ordinary harmonic numbers. Moreover, we calculate the hyperharmonic numbers as the derivative of a certain binomial coefficient.

  10. 7 CFR 29.9205 - Identification number (farm serial number).

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 7 Agriculture 2 2014-01-01 2014-01-01 false Identification number (farm serial number). 29.9205 Section 29.9205 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE... number (farm serial number). The serial number assigned to an individual farm by the appropriate...

  11. 7 CFR 29.9205 - Identification number (farm serial number).

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 7 Agriculture 2 2012-01-01 2012-01-01 false Identification number (farm serial number). 29.9205 Section 29.9205 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE... number (farm serial number). The serial number assigned to an individual farm by the appropriate...

  12. 7 CFR 29.9205 - Identification number (farm serial number).

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 7 Agriculture 2 2013-01-01 2013-01-01 false Identification number (farm serial number). 29.9205 Section 29.9205 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE... number (farm serial number). The serial number assigned to an individual farm by the appropriate...

  13. 7 CFR 29.9205 - Identification number (farm serial number).

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 7 Agriculture 2 2011-01-01 2011-01-01 false Identification number (farm serial number). 29.9205 Section 29.9205 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE... number (farm serial number). The serial number assigned to an individual farm by the appropriate...

  14. 7 CFR 29.9205 - Identification number (farm serial number).

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 7 Agriculture 2 2010-01-01 2010-01-01 false Identification number (farm serial number). 29.9205 Section 29.9205 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE... number (farm serial number). The serial number assigned to an individual farm by the appropriate...

  15. Percents Are Not Natural Numbers

    ERIC Educational Resources Information Center

    Jacobs, Jennifer A.

    2013-01-01

    Adults are prone to treating percents, one representational format of rational numbers, as novel cases of natural number. This suggests that percent values are not differentiated from natural numbers; a conceptual shift from the natural numbers to the rational numbers has not yet occurred. This is most surprising, considering people are inundated…

  16. Series of Reciprocal Triangular Numbers

    ERIC Educational Resources Information Center

    Bruckman, Paul; Dence, Joseph B.; Dence, Thomas P.; Young, Justin

    2013-01-01

    Reciprocal triangular numbers have appeared in series since the very first infinite series were summed. Here we attack a number of subseries of the reciprocal triangular numbers by methodically expressing them as integrals.

  17. Even Perfect Numbers: (Update)2.

    ERIC Educational Resources Information Center

    Bezuszka, Stanley J.; Kenney, Margaret J.

    1997-01-01

    Presents an assignment given to students to produce a report on perfect numbers and their properties. Summarizes the history of perfect numbers and their features. Recommends spreadsheet, theoretical, and programming activities on perfect numbers. (ASK)

  18. 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…

  19. Representing Numbers: Prime and Irrational

    ERIC Educational Resources Information Center

    Zazkis, Rina

    2005-01-01

    This article draws an analogy between prime and irrational numbers with respect to how these numbers are defined and how they are perceived by learners. Excerpts are presented from two research studies: a study on understanding prime numbers by pre-service elementary school teachers and a study on understanding irrational numbers by pre-service…

  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. 96. RECTIFIER NUMBER 1 AND RECTIFIER NUMBER 2 ON EAST ...

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

    96. RECTIFIER NUMBER 1 AND RECTIFIER NUMBER 2 ON EAST WALL OF LANDLINE INSTRUMENTATION ROOM (106), LSB (BLDG. 770) - Vandenberg Air Force Base, Space Launch Complex 3, Launch Pad 3 West, Napa & Alden Roads, Lompoc, Santa Barbara County, CA

  2. How Spencer Made Number: First Uses of the Number Words

    ERIC Educational Resources Information Center

    Mix, Kelly S.

    2009-01-01

    This article describes the development of number concepts between infancy and early childhood. It is based on a diary study that tracked number word use in a child from 12 to 38 months of age. Number words appeared early in the child's vocabulary, but accurate reference to specific numerosities evolved gradually over the entire 27-month period.…

  3. Feeling Number: Grounding Number Sense in a Sense of Quantity

    ERIC Educational Resources Information Center

    Wagner, David; Davis, Brent

    2010-01-01

    Drawing on results from psychology and from cultural and linguistic studies, we argue for an increased focus on developing quantity sense in school mathematics. We explore the notion of "feeling number", a phrase that we offer in a twofold sense--resisting tendencies to feel numb-er (more numb) by developing a feeling for numbers and the…

  4. Natural Number Bias in Operations with Missing Numbers

    ERIC Educational Resources Information Center

    Christou, Konstantinos P.

    2015-01-01

    This study investigates the hypothesis that there is a natural number bias that influences how students understand the effects of arithmetical operations involving both Arabic numerals and numbers that are represented by symbols for missing numbers. It also investigates whether this bias correlates with other aspects of students' understanding of…

  5. 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…

  6. Number Tracks, Number Lines, Number Strips Are They All the Same?

    ERIC Educational Resources Information Center

    Iannone, Paola

    2006-01-01

    In this article, the author argues that there is a big conceptual difference between number lines and number strips and that number lines should be consistently used as early as Y1. Her interest in the use of the number line as a powerful image of the real numbers, and how this is introduced in the early years, comes from her own experience as a…

  7. Relating Mason number to Bingham number in magnetorheological fluids

    NASA Astrophysics Data System (ADS)

    Sherman, Stephen G.; Becnel, Andrew C.; Wereley, Norman M.

    2015-04-01

    Magnetorheological (MR) fluids are described using two nondimensional numbers, the Bingham and Mason numbers. The Mason number is the ratio of particle magnetic forces to viscous forces and describes the behavior of MR fluids at the microscopic, particle level scale. At the macroscopic, continuum scale, Bingham number is the ratio of yield stress to viscous stress, and describes the bulk motion of the fluid. If these two nondimensional numbers can be related, then microscopic models can be directly compared to macroscopic results. We show that if microscopic and macroscopic forces are linearly related, then Bingham and Mason number are inversely related, or, alternatively, that the product of the Bingham number and the Mason number is a constant. This relationship is experimentally validated based on measurements of apparent viscosity on a high shear rate, γ ˙ ≈ 10 000s-1, Searle cell rheometer. This relationship between Mason number and Bingham number is then used to analyze a Mason number based result, and is also used to inform the MR fluid device design process.

  8. Number games, magnitude representation, and basic number skills in preschoolers.

    PubMed

    Whyte, Jemma Catherine; Bull, Rebecca

    2008-03-01

    The effect of 3 intervention board games (linear number, linear color, and nonlinear number) on young children's (mean age = 3.8 years) counting abilities, number naming, magnitude comprehension, accuracy in number-to-position estimation tasks, and best-fit numerical magnitude representations was examined. Pre- and posttest performance was compared following four 25-min intervention sessions. The linear number board game significantly improved children's performance in all posttest measures and facilitated a shift from a logarithmic to a linear representation of numerical magnitude, emphasizing the importance of spatial cues in estimation. Exposure to the number card games involving nonsymbolic magnitude judgments and association of symbolic and nonsymbolic quantities, but without any linear spatial cues, improved some aspects of children's basic number skills but not numerical estimation precision. PMID:18331146

  9. Poison control center - emergency number

    MedlinePlus

    ... ANYWHERE IN THE UNITED STATES This national hotline number will let you talk to experts in poisoning. ... centers in the United States use this national number. You should call if you have any questions ...

  10. Linear or Exponential Number Lines

    ERIC Educational Resources Information Center

    Stafford, Pat

    2011-01-01

    Having decided to spend some time looking at one's understanding of numbers, the author was inspired by "Alex's Adventures in Numberland," by Alex Bellos to look at one's innate appreciation of number. Bellos quotes research studies suggesting that an individual's natural appreciation of numbers is more likely to be exponential rather than linear,…

  11. 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"…

  12. Random Numbers and Quantum Computers

    ERIC Educational Resources Information Center

    McCartney, Mark; Glass, David

    2002-01-01

    The topic of random numbers is investigated in such a way as to illustrate links between mathematics, physics and computer science. First, the generation of random numbers by a classical computer using the linear congruential generator and logistic map is considered. It is noted that these procedures yield only pseudo-random numbers since…

  13. What Exactly Do Numbers Mean?

    ERIC Educational Resources Information Center

    Huang, Yi Ting; Spelke, Elizabeth; Snedeker, Jesse

    2013-01-01

    Number words are generally used to refer to the exact cardinal value of a set, but cognitive scientists disagree about their meanings. Although most psychological analyses presuppose that numbers have exact semantics ("two" means exactly two), many linguistic accounts propose that numbers have lower-bounded semantics (at least two), and…

  14. 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…

  15. 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…

  16. Three Cubes in One Number

    ERIC Educational Resources Information Center

    Jue, Brian

    2010-01-01

    Separate a three-digit number into its component digits. After raising each digit to the third power and computing the sum of the cubes, determine how often the original number reappears. Modular arithmetic is used to reduce the number of potential solutions to a more manageable quantity. (Contains 4 tables.)

  17. Calibrating the Mental Number Line

    ERIC Educational Resources Information Center

    Izard, Veronique; Dehaene, Stanislas

    2008-01-01

    Human adults are thought to possess two dissociable systems to represent numbers: an approximate quantity system akin to a mental number line, and a verbal system capable of representing numbers exactly. Here, we study the interface between these two systems using an estimation task. Observers were asked to estimate the approximate numerosity of…

  18. Generalized Bernoulli-Hurwitz numbers and the universal Bernoulli numbers

    NASA Astrophysics Data System (ADS)

    Ônishi, Yoshihiro

    2011-10-01

    The three fundamental properties of the Bernoulli numbers, namely, the von Staudt-Clausen theorem, von Staudt's second theorem, and Kummer's original congruence, are generalized to new numbers that we call generalized Bernoulli-Hurwitz numbers. These are coefficients in the power series expansion of a higher-genus algebraic function with respect to a suitable variable. Our generalization differs strongly from previous works. Indeed, the order of the power of the modulus prime in our Kummer-type congruences is exactly the same as in the trigonometric function case (namely, Kummer's own congruence for the original Bernoulli numbers), and as in the elliptic function case (namely, H. Lang's extension for the Hurwitz numbers). However, in other past results on higher-genus algebraic functions, the modulus was at most half of its value in these classical cases. This contrast is clarified by investigating the analogue of the three properties above for the universal Bernoulli numbers. Bibliography: 34 titles.

  19. Children's mappings between number words and the approximate number system.

    PubMed

    Odic, Darko; Le Corre, Mathieu; Halberda, Justin

    2015-05-01

    Humans can represent number either exactly--using their knowledge of exact numbers as supported by language, or approximately--using their approximate number system (ANS). Adults can map between these two systems--they can both translate from an approximate sense of the number of items in a brief visual display to a discrete number word estimate (i.e., ANS-to-Word), and can generate an approximation, for example by rapidly tapping, when provided with an exact verbal number (i.e., Word-to-ANS). Here we ask how these mappings are initially formed and whether one mapping direction may become functional before the other during development. In two experiments, we gave 2-5 year old children both an ANS-to-Word task, where they had to give a verbal number response to an approximate presentation (i.e., after seeing rapidly flashed dots, or watching rapid hand taps), and a Word-to-ANS task, where they had to generate an approximate response to a verbal number request (i.e., rapidly tapping after hearing a number word). Replicating previous results, children did not successfully generate numerically appropriate verbal responses in the ANS-to-Word task until after 4 years of age--well after they had acquired the Cardinality Principle of verbal counting. In contrast, children successfully generated numerically appropriate tapping sequences in the Word-to-ANS task before 4 years of age--well before many understood the Cardinality Principle. We further found that the accuracy of the mapping between the ANS and number words, as captured by error rates, continues to develop after this initial formation of the interface. These results suggest that the mapping between the ANS and verbal number representations is not functionally bidirectional in early development, and that the mapping direction from number representations to the ANS is established before the reverse. PMID:25721021

  20. 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…

  1. 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)

  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. Nonliteral understanding of number words

    PubMed Central

    Kao, Justine T.; Wu, Jean Y.; Bergen, Leon; Goodman, Noah D.

    2014-01-01

    One of the most puzzling and important facts about communication is that people do not always mean what they say; speakers often use imprecise, exaggerated, or otherwise literally false descriptions to communicate experiences and attitudes. Here, we focus on the nonliteral interpretation of number words, in particular hyperbole (interpreting unlikely numbers as exaggerated and conveying affect) and pragmatic halo (interpreting round numbers imprecisely). We provide a computational model of number interpretation as social inference regarding the communicative goal, meaning, and affective subtext of an utterance. We show that our model predicts humans’ interpretation of number words with high accuracy. Our model is the first to our knowledge to incorporate principles of communication and empirically measured background knowledge to quantitatively predict hyperbolic and pragmatic halo effects in number interpretation. This modeling framework provides a unified approach to nonliteral language understanding more generally. PMID:25092304

  4. The neuronal code for number.

    PubMed

    Nieder, Andreas

    2016-06-01

    Humans and non-human primates share an elemental quantification system that resides in a dedicated neural network in the parietal and frontal lobes. In this cortical network, 'number neurons' encode the number of elements in a set, its cardinality or numerosity, irrespective of stimulus appearance across sensory motor systems, and from both spatial and temporal presentation arrays. After numbers have been extracted from sensory input, they need to be processed to support goal-directed behaviour. Studying number neurons provides insights into how information is maintained in working memory and transformed in tasks that require rule-based decisions. Beyond an understanding of how cardinal numbers are encoded, number processing provides a window into the neuronal mechanisms of high-level brain functions. PMID:27150407

  5. 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.

  6. 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.

  7. Refactorable Numbers - A Machine Invention

    NASA Astrophysics Data System (ADS)

    Colton, Simon

    1999-02-01

    The HR (or Hardy-Ramanujan) program invents and analyses definitions in areas of pure mathematics, including finite algebras, graph theory and number theory. While working in number theory, HR recently invented a new integer sequence, the refactorable numbers, which are defined and developed here. A discussion of how HR works, along with details of well known sequences reinvented by HR and other new sequences invented by HR is also given.

  8. 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

  9. Compendium of Experimental Cetane Numbers

    SciTech Connect

    Yanowitz, J.; Ratcliff, M. A.; McCormick, R. L.; Taylor, J. D.; Murphy, M. J.

    2014-08-01

    This report is an updated version of the 2004 Compendium of Experimental Cetane Number Data and presents a compilation of measured cetane numbers for pure chemical compounds. It includes all available single compound cetane number data found in the scientific literature up until March 2014 as well as a number of unpublished values, most measured over the past decade at the National Renewable Energy Laboratory. This Compendium contains cetane values for 389 pure compounds, including 189 hydrocarbons and 201 oxygenates. More than 250 individual measurements are new to this version of the Compendium. For many compounds, numerous measurements are included, often collected by different researchers using different methods. Cetane number is a relative ranking of a fuel's autoignition characteristics for use in compression ignition engines; it is based on the amount of time between fuel injection and ignition, also known as ignition delay. The cetane number is typically measured either in a single-cylinder engine or a constant volume combustion chamber. Values in the previous Compendium derived from octane numbers have been removed, and replaced with a brief analysis of the correlation between cetane numbers and octane numbers. The discussion on the accuracy and precision of the most commonly used methods for measuring cetane has been expanded and the data has been annotated extensively to provide additional information that will help the reader judge the relative reliability of individual results.

  10. Number development and developmental dyscalculia.

    PubMed

    von Aster, Michael G; Shalev, Ruth S

    2007-11-01

    There is a growing consensus that the neuropsychological underpinnings of developmental dyscalculia (DD) are a genetically determined disorder of 'number sense', a term denoting the ability to represent and manipulate numerical magnitude nonverbally on an internal number line. However, this spatially-oriented number line develops during elementary school and requires additional cognitive components including working memory and number symbolization (language). Thus, there may be children with familial-genetic DD with deficits limited to number sense and others with DD and comorbidities such as language delay, dyslexia, or attention-deficit-hyperactivity disorder. This duality is supported by epidemiological data indicating that two-thirds of children with DD have comorbid conditions while one-third have pure DD. Clinically, they differ according to their profile of arithmetic difficulties. fMRI studies indicate that parietal areas (important for number functions), and frontal regions (dominant for executive working memory and attention functions), are under-activated in children with DD. A four-step developmental model that allows prediction of different pathways for DD is presented. The core-system representation of numerical magnitude (cardinality; step 1) provides the meaning of 'number', a precondition to acquiring linguistic (step 2), and Arabic (step 3) number symbols, while a growing working memory enables neuroplastic development of an expanding mental number line during school years (step 4). Therapeutic and educational interventions can be drawn from this model. PMID:17979867

  11. 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…

  12. Spontaneous Number Representation in Mosquitofish

    ERIC Educational Resources Information Center

    Dadda, Marco; Piffer, Laura; Agrillo, Christian; Bisazza, Angelo

    2009-01-01

    While there is convincing evidence that preverbal human infants and non-human primates can spontaneously represent number, considerable debate surrounds the possibility that such capacity is also present in other animals. Fish show a remarkable ability to discriminate between different numbers of social companions. Previous work has demonstrated…

  13. 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.

  14. The Search for Prime Numbers.

    ERIC Educational Resources Information Center

    Pomerance, Carl

    1982-01-01

    Until recently the testing of a 100-digit number to determine whether it is prime or composite could have taken a century. However, in the past two years a method has been developed enabling a computer to determine the primality of an arbitrary number in about 40 seconds of running time. (Author/JN)

  15. Number Talks Build Numerical Reasoning

    ERIC Educational Resources Information Center

    Parrish, Sherry D.

    2011-01-01

    "Classroom number talks," five- to fifteen-minute conversations around purposefully crafted computation problems, are a productive tool that can be incorporated into classroom instruction to combine the essential processes and habits of mind of doing math. During number talks, students are asked to communicate their thinking when presenting and…

  16. Toddlers' Spontaneous Attention to Number

    ERIC Educational Resources Information Center

    Baroody, Arthur J.; Li, Xia; Lai, Meng-lung

    2008-01-01

    Hannula and Lehtinen (2001, 2005) defined spontaneous focusing on numerosity (SFON) as the tendency to notice the relatively abstract attribute of number despite the presence of other attributes. According to nativists, an innate concept of one to three directs young children's attention to these "intuitive numbers" in everyday situations--even…

  17. The Algebra of Complex Numbers.

    ERIC Educational Resources Information Center

    LePage, Wilbur R.

    This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…

  18. Counting copy number and calories.

    PubMed

    White, Stefan

    2015-08-01

    Copy number variation (CNV) at several genomic loci has been associated with different human traits and diseases, but in many cases the findings could not be replicated. A new study provides insights into the degree of variation present at the amylase locus and calls into question a previous association between amylase copy number and body mass index. PMID:26220133

  19. On Counting the Rational Numbers

    ERIC Educational Resources Information Center

    Almada, Carlos

    2010-01-01

    In this study, we show how to construct a function from the set N of natural numbers that explicitly counts the set Q[superscript +] of all positive rational numbers using a very intuitive approach. The function has the appeal of Cantor's function and it has the advantage that any high school student can understand the main idea at a glance…

  20. Some Ideas About Number Theory.

    ERIC Educational Resources Information Center

    Barnett, I. A.

    The material in this booklet is designed for non-professional mathematicians who have an interest in the theory of numbers. The author presents some elementary results of number theory without involving detailed proofs. Much of the material has direct application for secondary school mathematics teachers. A brief account of the nature of number…

  1. 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…

  2. Computation of Most Probable Numbers

    PubMed Central

    Russek, Estelle; Colwell, Rita R.

    1983-01-01

    A rapid computational method for maximum likelihood estimation of most-probable-number values, incorporating a modified Newton-Raphson method, is presented. The method offers a much greater reliability for the most-probable-number estimate of total viable bacteria, i.e., those capable of growth in laboratory media. PMID:6870242

  3. Old and New Magic Numbers

    SciTech Connect

    Talmi, Igal

    2008-11-11

    The discovery of magic numbers led to the shell model. They indicated closure of major shells and are robust: proton magic numbers are rather independent of the occupation of neutron orbits and vice versa. Recently the magic property became less stringent and we hear a lot about the discovery of new magic numbers. These, however, indicate sub-shell closures and strongly depend on occupation numbers and hence, may be called quasi-magic numbers. Some of these have been known for many years and the mechanism for their appearance as well as disappearance, was well understood within the simple shell model. The situation will be illustrated by a few examples which demonstrate the simple features of the shell model. Will this simplicity emerge from the complex computations of nuclear many-body theory?.

  4. Quantum random number generator using photon-number path entanglement.

    PubMed

    Kwon, Osung; Cho, Young-Wook; Kim, Yoon-Ho

    2009-03-20

    We report a quantum random number generator based on the photon-number-path entangled state that is prepared by means of two-photon quantum interference at a beam splitter. The randomness in our scheme is truly quantum mechanical in origin since it results from the projection measurement of the entangled two-photon state. The generated bit sequences satisfy the standard randomness test. PMID:19305476

  5. 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

  6. Laryngology and the numbers game.

    PubMed

    Lucente, F E

    1980-01-01

    Numbers play a great role in our practice of laryngology, and when used appropriately can be extremely valuable. However, careless or uncritical use may cause them to be an impediment of detriment to clinical practice and teaching. Examples of problems which arise with numbers are readily found in the areas of tumor staging (TNM system), the scientific literature, resident training and communications with third-party agencies. Consideration of these examples reminds us of the need to evaluate our use of numbers frequently. PMID:7458142

  7. Numbered nasal discs for waterfowl

    USGS Publications Warehouse

    Bartonek, J.C.; Dane, C.W.

    1964-01-01

    Numbered nasal discs were successfully used in studies requiring large numbers of individually marked waterfowl. The procedure for constructing these discs is outlined. Blue-winged teal (Anas discors) with 5/8-inch discs, and canvasback (Aythya valisineria) and redhead (A. americana) with 3/4-inch discs can be individually identified up to 50 and 80 yards, respectively, with a gunstock-mounted, 20-power spotting scope. The particular value of these markers is their durability, the number of combinations possible, and the apparent absence of behavioral or mortality influence among such species as the blue-winged teal.

  8. Efficient computation of root numbers and class numbers of parametrized families of real abelian number fields

    NASA Astrophysics Data System (ADS)

    Louboutin, Stephane R.

    2007-03-01

    Let \\{K_m\\} be a parametrized family of simplest real cyclic cubic, quartic, quintic or sextic number fields of known regulators, e.g., the so-called simplest cubic and quartic fields associated with the polynomials P_m(x) Dx^3 -mx^2-(m+3)x+1 and P_m(x) Dx^4 -mx^3-6x^2+mx+1 . We give explicit formulas for powers of the Gaussian sums attached to the characters associated with these simplest number fields. We deduce a method for computing the exact values of these Gaussian sums. These values are then used to efficiently compute class numbers of simplest fields. Finally, such class number computations yield many examples of real cyclotomic fields Q(zeta_p)^+ of prime conductors pge 3 and class numbers h_p^+ greater than or equal to p . However, in accordance with Vandiver's conjecture, we found no example of p for which p divides h_p^+ .

  9. Atomic Structure - A Numbers Game

    ERIC Educational Resources Information Center

    George, W. O.; Vincent, A.

    1975-01-01

    Emphasizes the simplicity and elegance of early discoveries related to the hydrogen spectrum and provides an elementary experimental basis of quantum theory based on a "numbers game" which can be played by students. (Author/GS)

  10. Young Students Investigate Number Cubes.

    ERIC Educational Resources Information Center

    Friedlander, Alex

    1997-01-01

    Describes a series of learning activities built around number cubes. Sample activities introduce elementary properties of the cube, the magic rule of seven, and basic concepts related to graphs in the plane coordinate system. (PVD)

  11. 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)

  12. Heptagonal Numbers: A Neglected Set.

    ERIC Educational Resources Information Center

    O'Donnell, William J.

    1979-01-01

    An investigation of these numbers is shown to give students an opportunity to make use of such mathematical skills as algebraic substitution, modular arithmetic, counting arguments, and mathematical induction. (MP)

  13. Integral Presentations of Catalan Numbers

    ERIC Educational Resources Information Center

    Dana-Picard, Thierry

    2010-01-01

    We compute in three different ways the same definite parametric integral. By-products are the derivation of a combinatorial identity and two integral presentations of Catalan numbers. One of them leads to a presentation using the [gamma] function.

  14. 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.

  15. 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.

  16. Random numbers from vacuum fluctuations

    NASA Astrophysics Data System (ADS)

    Shi, Yicheng; Chng, Brenda; Kurtsiefer, Christian

    2016-07-01

    We implement a quantum random number generator based on a balanced homodyne measurement of vacuum fluctuations of the electromagnetic field. The digitized signal is directly processed with a fast randomness extraction scheme based on a linear feedback shift register. The random bit stream is continuously read in a computer at a rate of about 480 Mbit/s and passes an extended test suite for random numbers.

  17. Copy number variation and mutation

    NASA Astrophysics Data System (ADS)

    Clark, Brian; Weidner, Jacob; Wabick, Kevin

    2009-11-01

    Until very recently, the standard model of DNA included two genes for each trait. This dated model has given way to a model that includes copies of some genes well in excess of the canonical two. Copy number variations in the human genome play critical roles in causing or aggravating a number of syndromes and diseases while providing increased resistance to others. We explore the role of mutation, crossover, inversion, and reproduction in determining copy number variations in a numerical simulation of a population. The numerical model consists of a population of individuals, where each individual is represented by a single strand of DNA with the same number of genes. Each gene is initially assigned to one of two traits. Fitness of the individual is determined by the two most fit genes for trait one, and trait two genetic material is treated as a reservoir of junk DNA. After a sufficient number of generations, during which the genetic distribution is allowed to reach a steady-state, the mean numberof genes per trait and the copy number variation are recorded. Here, we focus on the role of mutation and compare simulation results to theory.

  18. Number Meaning and Number Grammar in English and Spanish

    ERIC Educational Resources Information Center

    Bock, Kathryn; Carreiras, Manuel; Meseguer, Enrique

    2012-01-01

    Grammatical agreement makes different demands on speakers of different languages. Being widespread in the languages of the world, the features of agreement systems offer valuable tests of how language affects deep-seated domains of human cognition and categorization. Number agreement is one such domain, with intriguing evidence that typological…

  19. Are Number Gestures Easier than Number Words for Preschoolers?

    ERIC Educational Resources Information Center

    Nicoladis, Elena; Pika, Simone; Marentette, Paula

    2010-01-01

    Some researchers have argued that children's earliest symbols are based on their sensorimotor experience and that arbitrary symbol-referent mapping poses a challenge for them. If so, exposure to iconic symbols (such as one-finger-for-one-object manual gestures) might help children in a difficult domain such as number. We assessed 44 preschoolers'…

  20. Nanoplasmonics of prime number arrays.

    PubMed

    Forestiere, Carlo; Walsh, Gary F; Miano, Giovanni; Dal Negro, Luca

    2009-12-21

    In this paper, we investigate the plasmonic near-field localization and the far-field scattering properties of non-periodic arrays of Ag nanoparticles generated by prime number sequences in two spatial dimensions. In particular, we demonstrate that the engineering of plasmonic arrays with large spectral flatness and particle density is necessary to achieve a high density of electromagnetic hot spots over a broader frequency range and a larger area compared to strongly coupled periodic and quasi-periodic structures. Finally, we study the far-field scattering properties of prime number arrays illuminated by plane waves and we discuss their angular scattering properties. The study of prime number arrays of metal nanoparticles provides a novel strategy to achieve broadband enhancement and localization of plasmonic fields for the engineering of nanoscale nano-antenna arrays and active plasmonic structures. PMID:20052140

  1. Biotechnology at low Reynolds numbers.

    PubMed Central

    Brody, J P; Yager, P; Goldstein, R E; Austin, R H

    1996-01-01

    The shrinking of liquid handling systems to the micron and submicron size range entails moving into the area of small Reynolds numbers. The fluid dynamics in this regime are very different from the macroscale. We present an intuitive explanation of how the different physics of small Reynolds numbers flow, along with microscopic sizes, can influence device design, and give examples from our own work using fluid flow in microfabricated devices designed for biological processing. Images FIGURE 1 FIGURE 9 FIGURE 10 FIGURE 11 FIGURE 12 FIGURE 13 PMID:8968612

  2. A generalized sense of number

    PubMed Central

    Arrighi, Roberto; Togoli, Irene; Burr, David C.

    2014-01-01

    Much evidence has accumulated to suggest that many animals, including young human infants, possess an abstract sense of approximate quantity, a number sense. Most research has concentrated on apparent numerosity of spatial arrays of dots or other objects, but a truly abstract sense of number should be capable of encoding the numerosity of any set of discrete elements, however displayed and in whatever sensory modality. Here, we use the psychophysical technique of adaptation to study the sense of number for serially presented items. We show that numerosity of both auditory and visual sequences is greatly affected by prior adaptation to slow or rapid sequences of events. The adaptation to visual stimuli was spatially selective (in external, not retinal coordinates), pointing to a sensory rather than cognitive process. However, adaptation generalized across modalities, from auditory to visual and vice versa. Adaptation also generalized across formats: adapting to sequential streams of flashes affected the perceived numerosity of spatial arrays. All these results point to a perceptual system that transcends vision and audition to encode an abstract sense of number in space and in time. PMID:25377454

  3. 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…

  4. 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…

  5. Number Crunching: A Sheep's Tale

    ERIC Educational Resources Information Center

    Sam, Chris Lam

    2005-01-01

    In this article, the author talks about an allegorical tale which he has written as a message for teachers of mathematics. The story is about Gordon, who led a flock of small sheep. Gordon was a mathematics genius; however, his flock criticized his teaching of numbers and his boring lectures. His furry-god-farmer advised him to share his…

  6. Dual numbers and supersymmetric mechanics

    NASA Astrophysics Data System (ADS)

    Frydryszak, Andrzej M.

    2005-11-01

    We show that dual numbers, apart from the known practical applications to the description of a rigid body movements in three dimensional space and natural presence in abstract differential algebra, play a role in field theory and are related to supersymmetry as well. Relevant models are considered.

  7. 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.)

  8. The elephant brain in numbers

    PubMed Central

    Herculano-Houzel, Suzana; Avelino-de-Souza, Kamilla; Neves, Kleber; Porfírio, Jairo; Messeder, Débora; Mattos Feijó, Larissa; Maldonado, José; Manger, Paul R.

    2014-01-01

    What explains the superior cognitive abilities of the human brain compared to other, larger brains? Here we investigate the possibility that the human brain has a larger number of neurons than even larger brains by determining the cellular composition of the brain of the African elephant. We find that the African elephant brain, which is about three times larger than the human brain, contains 257 billion (109) neurons, three times more than the average human brain; however, 97.5% of the neurons in the elephant brain (251 billion) are found in the cerebellum. This makes the elephant an outlier in regard to the number of cerebellar neurons compared to other mammals, which might be related to sensorimotor specializations. In contrast, the elephant cerebral cortex, which has twice the mass of the human cerebral cortex, holds only 5.6 billion neurons, about one third of the number of neurons found in the human cerebral cortex. This finding supports the hypothesis that the larger absolute number of neurons in the human cerebral cortex (but not in the whole brain) is correlated with the superior cognitive abilities of humans compared to elephants and other large-brained mammals. PMID:24971054

  9. 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

  10. An Estimate of Avogadro's Number.

    ERIC Educational Resources Information Center

    Stauffer, Frederic R.

    1991-01-01

    Calculates an approximation to Avagadro's number for one mole of water by assuming the mole to be in cubical form and then halving the cube three times, thereby doubling the surface area of the original cube. The calculations are derived from the work necessary to perform these divisions. Presents calculated values for several liquids. (MDH)

  11. Know Your Blood Sugar Numbers

    MedlinePlus

    ... John’s A1C and blood sugar numbers are too high. John and his health care team talk about what he can do to get closer to his A1C and blood sugar goals. John decides he will be more active. He ...

  12. 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…

  13. Number Program for Primary Schoolers.

    ERIC Educational Resources Information Center

    Moser, James M.

    The arithmetic portion of the Developing Mathematical Processes (DMP) program, as it applies to children of ages 5 to 8, is described in some detail. The terminal objective of the number program of the primary segment of DMP is the ability of the child to correctly write, read and validate mathematical sentences of the form A = B plus or minus X.…

  14. Solar System Number-Crunching.

    ERIC Educational Resources Information Center

    Albrecht, Bob; Firedrake, George

    1997-01-01

    Defines terrestrial and Jovian planets and provides directions to obtain planetary data from the National Space Science Data Center Web sites. Provides "number-crunching" activities for the terrestrial planets using Texas Instruments TI-83 graphing calculators: computing volumetric mean radius and volume, density, ellipticity, speed, surface…

  15. Distance Effects in Number Agreement

    ERIC Educational Resources Information Center

    Schweppe, Judith

    2013-01-01

    One pronoun production experiment and one pronoun comprehension experiment were performed to investigate the role of grammatical number information in long-distance anaphora, with referent and pronoun either in adjacent sentences or separated by an intervening sentence. The experiments tested the assumption that the influence of grammatical number…

  16. On Milne's quantum number function

    NASA Astrophysics Data System (ADS)

    Korsch, H. Jürgen

    1985-06-01

    The quantum number function N( E) introduced by Milne is studied in detail. It is shown that N( E) is not uniquely defined for energies different from the bound state values. The density of states {dN }/{dE } is nowhere unique and not necessarily positive.

  17. 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

  18. 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)

  19. 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 talk to ... ncbi.nlm.nih.gov/pubmed/12630734 . Shannon MW. Emergency management of poisoning. In: Shannon MW, Borron SW, ...

  20. Number-theory dark matter

    NASA Astrophysics Data System (ADS)

    Nakayama, Kazunori; Takahashi, Fuminobu; Yanagida, Tsutomu T.

    2011-05-01

    We propose that the stability of dark matter is ensured by a discrete subgroup of the U(1)B-L gauge symmetry, Z(B-L). We introduce a set of chiral fermions charged under the U(1)B-L in addition to the right-handed neutrinos, and require the anomaly-cancellation conditions associated with the U(1)B-L gauge symmetry. We find that the possible number of fermions and their charges are tightly constrained, and that non-trivial solutions appear when at least five additional chiral fermions are introduced. The Fermat theorem in the number theory plays an important role in this argument. Focusing on one of the solutions, we show that there is indeed a good candidate for dark matter, whose stability is guaranteed by Z(B-L).

  1. How to Differentiate a Number

    NASA Astrophysics Data System (ADS)

    Ufnarovski, Victor; Ahlander, Bo

    2003-09-01

    We define the derivative of an integer to be the map sending every prime to 1 and satisfying the Leibnitz rule. The aim of the article is to consider the basic properties of this map and to show how to generalize the notion to the case of rational and arbitrary real numbers. We make some conjectures and find some connections with Goldbach's Conjecture and the Twin Prime Conjecture. Finally, we solve the easiest associated differential equations and calculate the generating function.

  2. Determination of the Schmidt number

    SciTech Connect

    Sperling, J.; Vogel, W.

    2011-04-15

    Optimized, necessary, and sufficient conditions for the identification of the Schmidt number will be derived in terms of general Hermitian operators. These conditions apply to arbitrary mixed quantum states. The optimization procedure delivers equations similar to the eigenvalue problem of an operator. The properties of the solution of these equations will be studied. We solve these equations for classes of operators. The solutions will be applied to phase randomized two-mode squeezed-vacuum states in continuous variable systems.

  3. Lozenge Tilings and Hurwitz Numbers

    NASA Astrophysics Data System (ADS)

    Novak, Jonathan

    2015-10-01

    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.

  4. Automatic Assignment of EC Numbers

    PubMed Central

    Egelhofer, Volker; Schomburg, Ida; Schomburg, Dietmar

    2010-01-01

    A wide range of research areas in molecular biology and medical biochemistry require a reliable enzyme classification system, e.g., drug design, metabolic network reconstruction and system biology. When research scientists in the above mentioned areas wish to unambiguously refer to an enzyme and its function, the EC number introduced by the Nomenclature Committee of the International Union of Biochemistry and Molecular Biology (IUBMB) is used. However, each and every one of these applications is critically dependent upon the consistency and reliability of the underlying data for success. We have developed tools for the validation of the EC number classification scheme. In this paper, we present validated data of 3788 enzymatic reactions including 229 sub-subclasses of the EC classification system. Over 80% agreement was found between our assignment and the EC classification. For 61 (i.e., only 2.5%) reactions we found that their assignment was inconsistent with the rules of the nomenclature committee; they have to be transferred to other sub-subclasses. We demonstrate that our validation results can be used to initiate corrections and improvements to the EC number classification scheme. PMID:20126531

  5. Quasiperpendicular High Mach Number Shocks.

    PubMed

    Sulaiman, A H; Masters, A; Dougherty, M K; Burgess, D; Fujimoto, M; Hospodarsky, G B

    2015-09-18

    Shock waves exist throughout the Universe and are fundamental to understanding the nature of collisionless plasmas. Reformation is a process, driven by microphysics, which typically occurs at high Mach number supercritical shocks. While ongoing studies have investigated this process extensively both theoretically and via simulations, their observations remain few and far between. In this Letter we present a study of very high Mach number shocks in a parameter space that has been poorly explored and we identify reformation using in situ magnetic field observations from the Cassini spacecraft at 10 AU. This has given us an insight into quasiperpendicular shocks across 2 orders of magnitude in Alfvén Mach number (M_{A}) which could potentially bridge the gap between modest terrestrial shocks and more exotic astrophysical shocks. For the first time, we show evidence for cyclic reformation controlled by specular ion reflection occurring at the predicted time scale of ~0.3τ_{c}, where τ_{c} is the ion gyroperiod. In addition, we experimentally reveal the relationship between reformation and M_{A} and focus on the magnetic structure of such shocks to further show that for the same M_{A}, a reforming shock exhibits stronger magnetic field amplification than a shock that is not reforming. PMID:26430997

  6. Quasiperpendicular High Mach Number Shocks

    NASA Astrophysics Data System (ADS)

    Sulaiman, A. H.; Masters, A.; Dougherty, M. K.; Burgess, D.; Fujimoto, M.; Hospodarsky, G. B.

    2015-09-01

    Shock waves exist throughout the Universe and are fundamental to understanding the nature of collisionless plasmas. Reformation is a process, driven by microphysics, which typically occurs at high Mach number supercritical shocks. While ongoing studies have investigated this process extensively both theoretically and via simulations, their observations remain few and far between. In this Letter we present a study of very high Mach number shocks in a parameter space that has been poorly explored and we identify reformation using in situ magnetic field observations from the Cassini spacecraft at 10 AU. This has given us an insight into quasiperpendicular shocks across 2 orders of magnitude in Alfvén Mach number (MA ) which could potentially bridge the gap between modest terrestrial shocks and more exotic astrophysical shocks. For the first time, we show evidence for cyclic reformation controlled by specular ion reflection occurring at the predicted time scale of ˜0.3 τc , where τc is the ion gyroperiod. In addition, we experimentally reveal the relationship between reformation and MA and focus on the magnetic structure of such shocks to further show that for the same MA , a reforming shock exhibits stronger magnetic field amplification than a shock that is not reforming.

  7. 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.

  8. Propulsion at low Reynolds number

    NASA Astrophysics Data System (ADS)

    Najafi, Ali; Golestanian, Ramin

    2005-04-01

    We study the propulsion of two model swimmers at low Reynolds number. Inspired by Purcell's model, we propose a very simple one-dimensional swimmer consisting of three spheres that are connected by two arms whose lengths can change between two values. The proposed swimmer can swim with a special type of motion, which breaks the time-reversal symmetry. We also show that an ellipsoidal membrane with tangential travelling wave on it can also propel itself in the direction preferred by the travelling wave. This system resembles the realistic biological animals like Paramecium.

  9. Topological number of edge states

    NASA Astrophysics Data System (ADS)

    Hashimoto, Koji; Kimura, Taro

    2016-05-01

    We show that the edge states of the four-dimensional class A system can have topological charges, which are characterized by Abelian/non-Abelian monopoles. The edge topological charges are a new feature of relations among theories with different dimensions. From this novel viewpoint, we provide a non-Abelian analog of the TKNN number as an edge topological charge, which is defined by an SU(2) 't Hooft-Polyakov BPS monopole through an equivalence to Nahm construction. Furthermore, putting a constant magnetic field yields an edge monopole in a noncommutative momentum space, where D-brane methods in string theory facilitate study of edge fermions.

  10. Buoyancy-aided convection flow in a heated straight pipe: comparing different asymptotic models

    NASA Astrophysics Data System (ADS)

    Arfaoui, Walid; Safi, Mohamed Jomaa; Lagrée, Pierre-Yves

    2016-08-01

    A vertical straight circular adiabatic vertical long tube, open at its lower and upper ends, is heated at its base on a short portion. The flow is studied with the hypothesis of no pressure drop between the entrance and the exit. Direct resolution of Navier Stokes equations is done by finite volumes. The numerical solutions are then compared to a one dimensional model and to two asymptotic models. The first asymptotic model is inspired from boundary layer approximations whereas the second one is more a linear perturbation of the Navier Stokes Boussinesq equations. For moderate values of the Grashof number, pressure, starting from zero decreases over the heated part to a minimum and increases on the adiabatic tube to zero. For larger values of Grashof, a local maximum in pressure appears, this pressure hump may even be positive. The four model agree, for moderate Grashof. When increasing the Grashof, only the two asymptotic models recover the behavior obtained from the numerical simulations.

  11. Verification Challenges at Low Numbers

    SciTech Connect

    Benz, Jacob M.; Booker, Paul M.; McDonald, Benjamin S.

    2013-07-16

    This paper will explore the difficulties of deep reductions by examining the technical verification challenges. At each step on the road to low numbers, the verification required to ensure compliance of all parties will increase significantly. Looking post New START, the next step will likely include warhead limits in the neighborhood of 1000 (Pifer 2010). Further reductions will include stepping stones at 100’s of warheads, and then 10’s of warheads before final elimination could be considered of the last few remaining warheads and weapons. This paper will focus on these three threshold reduction levels, 1000, 100’s, 10’s. For each, the issues and challenges will be discussed, potential solutions will be identified, and the verification technologies and chain of custody measures that address these solutions will be surveyed. It is important to note that many of the issues that need to be addressed have no current solution. In these cases, the paper will explore new or novel technologies that could be applied. These technologies will draw from the research and development that is ongoing throughout the national lab complex, and will look at technologies utilized in other areas of industry for their application to arms control verification.

  12. Verification Challenges at Low Numbers

    SciTech Connect

    Benz, Jacob M.; Booker, Paul M.; McDonald, Benjamin S.

    2013-06-01

    Many papers have dealt with the political difficulties and ramifications of deep nuclear arms reductions, and the issues of “Going to Zero”. Political issues include extended deterrence, conventional weapons, ballistic missile defense, and regional and geo-political security issues. At each step on the road to low numbers, the verification required to ensure compliance of all parties will increase significantly. Looking post New START, the next step will likely include warhead limits in the neighborhood of 1000 . Further reductions will include stepping stones at1000 warheads, 100’s of warheads, and then 10’s of warheads before final elimination could be considered of the last few remaining warheads and weapons. This paper will focus on these three threshold reduction levels, 1000, 100’s, 10’s. For each, the issues and challenges will be discussed, potential solutions will be identified, and the verification technologies and chain of custody measures that address these solutions will be surveyed. It is important to note that many of the issues that need to be addressed have no current solution. In these cases, the paper will explore new or novel technologies that could be applied. These technologies will draw from the research and development that is ongoing throughout the national laboratory complex, and will look at technologies utilized in other areas of industry for their application to arms control verification.

  13. Numbers, Counting, and Infinity in Middle Schools.

    ERIC Educational Resources Information Center

    Meconi, L. J.

    1992-01-01

    Discusses the use of middle-school students' natural understanding of large numbers to introduce the concept of infinity. Presents activities that investigate infinite sets by demonstrating a one-to-one correspondence between the counting numbers and the given set. Examples include prime numbers, Fibonacci numbers, fractions, even and odd numbers,…

  14. 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)

  15. 14 CFR 47.15 - Identification number.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 100AB). The letters “I” and “O” may not be used. The first zero in a number must always be preceded by... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Identification number. 47.15 Section 47.15... REGISTRATION General § 47.15 Identification number. (a) Number required. An applicant for Aircraft...

  16. Visuospatial Priming of the Mental Number Line

    ERIC Educational Resources Information Center

    Stoianov, Ivilin; Kramer, Peter; Umilta, Carlo; Zorzi, Marco

    2008-01-01

    It has been argued that numbers are spatially organized along a "mental number line" that facilitates left-hand responses to small numbers, and right-hand responses to large numbers. We hypothesized that whenever the representations of visual and numerical space are concurrently activated, interactions can occur between them, before response…

  17. 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)

  18. Avogadro Number and Mole: A Royal Confusion.

    ERIC Educational Resources Information Center

    Emiliani, Cesare

    1991-01-01

    There is a great deal of confusion in physics and chemistry textbooks, dictionaries, manuals, and handbooks about the definition of Avogadro's number and the term "mole." Avogadro's number is defined simply as the number of atomic mass units in one gram. Mole is defined as the mass of one Avogadro number of identical items. (Author/PR)

  19. 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…

  20. 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…

  1. 7 CFR 46.20 - Lot numbers.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 7 Agriculture 2 2013-01-01 2013-01-01 false Lot numbers. 46.20 Section 46.20 Agriculture... Receivers § 46.20 Lot numbers. An identifying lot number shall be assigned to each shipment of produce to be sold on consignment or joint account or for the account of another person or firm. A lot number...

  2. 14 CFR 47.15 - Registration number.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 14 Aeronautics and Space 1 2011-01-01 2011-01-01 false Registration number. 47.15 Section 47.15... REGISTRATION General § 47.15 Registration number. (a) Number required. An applicant for aircraft registration must place a U.S. registration number (registration mark) on the Aircraft Registration Application,...

  3. 9 CFR 355.8 - Official number.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 9 Animals and Animal Products 2 2014-01-01 2014-01-01 false Official number. 355.8 Section 355.8... IDENTIFICATION AS TO CLASS, QUALITY, QUANTITY, AND CONDITION Inauguration of Inspection § 355.8 Official number. To each plant granted inspection an official number shall be assigned. Such number shall be...

  4. 7 CFR 75.48 - Identification number.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 7 Agriculture 3 2011-01-01 2011-01-01 false Identification number. 75.48 Section 75.48 Agriculture... number. The Director may require the use of official identification numbers in connection with seed certificated or sampled under the Act. When identification numbers are required, they shall be specified by...

  5. 7 CFR 900.5 - Docket number.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 7 Agriculture 8 2013-01-01 2013-01-01 false Docket number. 900.5 Section 900.5 Agriculture... Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter the proceeding may be referred to by such number....

  6. 7 CFR 900.5 - Docket number.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 7 Agriculture 8 2014-01-01 2014-01-01 false Docket number. 900.5 Section 900.5 Agriculture... Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter the proceeding may be referred to by such number....

  7. 9 CFR 355.8 - Official number.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 9 Animals and Animal Products 2 2011-01-01 2011-01-01 false Official number. 355.8 Section 355.8... IDENTIFICATION AS TO CLASS, QUALITY, QUANTITY, AND CONDITION Inauguration of Inspection § 355.8 Official number. To each plant granted inspection an official number shall be assigned. Such number shall be...

  8. 7 CFR 900.5 - Docket number.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 7 Agriculture 8 2010-01-01 2010-01-01 false Docket number. 900.5 Section 900.5 Agriculture... Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter the proceeding may be referred to by such number....

  9. 7 CFR 987.102 - Lot number.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 7 Agriculture 8 2011-01-01 2011-01-01 false Lot number. 987.102 Section 987.102 Agriculture... RIVERSIDE COUNTY, CALIFORNIA Administrative Rules Definitions § 987.102 Lot number. Lot number is synonymous with code and means a combination of letters or numbers, or both, acceptable to the Committee,...

  10. 7 CFR 75.48 - Identification number.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 7 Agriculture 3 2012-01-01 2012-01-01 false Identification number. 75.48 Section 75.48 Agriculture... number. The Director may require the use of official identification numbers in connection with seed certificated or sampled under the Act. When identification numbers are required, they shall be specified by...

  11. 7 CFR 29.32 - Identification number.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 7 Agriculture 2 2012-01-01 2012-01-01 false Identification number. 29.32 Section 29.32 Agriculture... INSPECTION Regulations Definitions § 29.32 Identification number. A number or a combination of letters and numbers in a design or mark approved by the Director, stamped, printed, or stenciled on a lot of...

  12. 7 CFR 29.32 - Identification number.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 7 Agriculture 2 2013-01-01 2013-01-01 false Identification number. 29.32 Section 29.32 Agriculture... INSPECTION Regulations Definitions § 29.32 Identification number. A number or a combination of letters and numbers in a design or mark approved by the Director, stamped, printed, or stenciled on a lot of...

  13. 7 CFR 987.102 - Lot number.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 7 Agriculture 8 2012-01-01 2012-01-01 false Lot number. 987.102 Section 987.102 Agriculture... RIVERSIDE COUNTY, CALIFORNIA Administrative Rules Definitions § 987.102 Lot number. Lot number is synonymous with code and means a combination of letters or numbers, or both, acceptable to the Committee,...

  14. 7 CFR 29.32 - Identification number.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 7 Agriculture 2 2010-01-01 2010-01-01 false Identification number. 29.32 Section 29.32 Agriculture... INSPECTION Regulations Definitions § 29.32 Identification number. A number or a combination of letters and numbers in a design or mark approved by the Director, stamped, printed, or stenciled on a lot of...

  15. 7 CFR 46.20 - Lot numbers.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 7 Agriculture 2 2014-01-01 2014-01-01 false Lot numbers. 46.20 Section 46.20 Agriculture... Receivers § 46.20 Lot numbers. An identifying lot number shall be assigned to each shipment of produce to be sold on consignment or joint account or for the account of another person or firm. A lot number...

  16. 9 CFR 355.8 - Official number.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 9 Animals and Animal Products 2 2013-01-01 2013-01-01 false Official number. 355.8 Section 355.8... IDENTIFICATION AS TO CLASS, QUALITY, QUANTITY, AND CONDITION Inauguration of Inspection § 355.8 Official number. To each plant granted inspection an official number shall be assigned. Such number shall be...

  17. 7 CFR 29.32 - Identification number.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 7 Agriculture 2 2014-01-01 2014-01-01 false Identification number. 29.32 Section 29.32 Agriculture... INSPECTION Regulations Definitions § 29.32 Identification number. A number or a combination of letters and numbers in a design or mark approved by the Director, stamped, printed, or stenciled on a lot of...

  18. 7 CFR 987.102 - Lot number.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 7 Agriculture 8 2014-01-01 2014-01-01 false Lot number. 987.102 Section 987.102 Agriculture... RIVERSIDE COUNTY, CALIFORNIA Administrative Rules Definitions § 987.102 Lot number. Lot number is synonymous with code and means a combination of letters or numbers, or both, acceptable to the Committee,...

  19. 7 CFR 46.20 - Lot numbers.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 7 Agriculture 2 2011-01-01 2011-01-01 false Lot numbers. 46.20 Section 46.20 Agriculture... Receivers § 46.20 Lot numbers. An identifying lot number shall be assigned to each shipment of produce to be sold on consignment or joint account or for the account of another person or firm. A lot number...

  20. 14 CFR 47.15 - Registration number.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 14 Aeronautics and Space 1 2012-01-01 2012-01-01 false Registration number. 47.15 Section 47.15... REGISTRATION General § 47.15 Registration number. (a) Number required. An applicant for aircraft registration must place a U.S. registration number (registration mark) on the Aircraft Registration Application,...

  1. 14 CFR 47.15 - Registration number.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 14 Aeronautics and Space 1 2013-01-01 2013-01-01 false Registration number. 47.15 Section 47.15... REGISTRATION General § 47.15 Registration number. (a) Number required. An applicant for aircraft registration must place a U.S. registration number (registration mark) on the Aircraft Registration Application,...

  2. How is the ERBE region number determined?

    Atmospheric Science Data Center

    2014-12-08

    The ERBE region number can be easily determined with the following: 2.5-degree Data: Region number = int(colat / 2.5) * 144 + (lon / 2.5) 5-degree Data: Region number = int(colat / 5) * 72 + (lon / 5) 10-degree Data: Region number ...

  3. 7 CFR 75.48 - Identification number.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 7 Agriculture 3 2013-01-01 2013-01-01 false Identification number. 75.48 Section 75.48 Agriculture... number. The Director may require the use of official identification numbers in connection with seed certificated or sampled under the Act. When identification numbers are required, they shall be specified by...

  4. 7 CFR 75.48 - Identification number.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 7 Agriculture 3 2010-01-01 2010-01-01 false Identification number. 75.48 Section 75.48 Agriculture... number. The Director may require the use of official identification numbers in connection with seed certificated or sampled under the Act. When identification numbers are required, they shall be specified by...

  5. 7 CFR 900.5 - Docket number.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 7 Agriculture 8 2011-01-01 2011-01-01 false Docket number. 900.5 Section 900.5 Agriculture... Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter the proceeding may be referred to by such number....

  6. 7 CFR 46.20 - Lot numbers.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 7 Agriculture 2 2012-01-01 2012-01-01 false Lot numbers. 46.20 Section 46.20 Agriculture... Receivers § 46.20 Lot numbers. An identifying lot number shall be assigned to each shipment of produce to be sold on consignment or joint account or for the account of another person or firm. A lot number...

  7. 7 CFR 987.102 - Lot number.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 7 Agriculture 8 2010-01-01 2010-01-01 false Lot number. 987.102 Section 987.102 Agriculture... RIVERSIDE COUNTY, CALIFORNIA Administrative Rules Definitions § 987.102 Lot number. Lot number is synonymous with code and means a combination of letters or numbers, or both, acceptable to the Committee,...

  8. 7 CFR 46.20 - Lot numbers.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 7 Agriculture 2 2010-01-01 2010-01-01 false Lot numbers. 46.20 Section 46.20 Agriculture... Receivers § 46.20 Lot numbers. An identifying lot number shall be assigned to each shipment of produce to be sold on consignment or joint account or for the account of another person or firm. A lot number...

  9. 7 CFR 900.5 - Docket number.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 7 Agriculture 8 2012-01-01 2012-01-01 false Docket number. 900.5 Section 900.5 Agriculture... Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter the proceeding may be referred to by such number....

  10. 7 CFR 987.102 - Lot number.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 7 Agriculture 8 2013-01-01 2013-01-01 false Lot number. 987.102 Section 987.102 Agriculture... RIVERSIDE COUNTY, CALIFORNIA Administrative Rules Definitions § 987.102 Lot number. Lot number is synonymous with code and means a combination of letters or numbers, or both, acceptable to the Committee,...

  11. 9 CFR 355.8 - Official number.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 9 Animals and Animal Products 2 2012-01-01 2012-01-01 false Official number. 355.8 Section 355.8... IDENTIFICATION AS TO CLASS, QUALITY, QUANTITY, AND CONDITION Inauguration of Inspection § 355.8 Official number. To each plant granted inspection an official number shall be assigned. Such number shall be...

  12. 7 CFR 29.32 - Identification number.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 7 Agriculture 2 2011-01-01 2011-01-01 false Identification number. 29.32 Section 29.32 Agriculture... INSPECTION Regulations Definitions § 29.32 Identification number. A number or a combination of letters and numbers in a design or mark approved by the Director, stamped, printed, or stenciled on a lot of...

  13. 7 CFR 75.48 - Identification number.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 7 Agriculture 3 2014-01-01 2014-01-01 false Identification number. 75.48 Section 75.48 Agriculture... number. The Director may require the use of official identification numbers in connection with seed certificated or sampled under the Act. When identification numbers are required, they shall be specified by...

  14. Some Remarks on Numbers and their Cognition

    NASA Astrophysics Data System (ADS)

    Divakaran, P. P.

    2014-07-01

    Humans perceive numbers (positive integers) through counting, i.e., by establishing a correspondence between the cardinality of a set of objects and a structured set of number symbols or number names. The structure requires the choice of a base -- `succession' structure alone is not enough. The point is made that for numbers below the base, cognition involves the learning and recalling of this association, fixed once and for all, while for larger numbers it results from learning the rules of construction of based numbers. Experiments on number cognition which do not take into account this essential distinction are likely to remain inconclusive.

  15. Integrated-Circuit Pseudorandom-Number Generator

    NASA Technical Reports Server (NTRS)

    Steelman, James E.; Beasley, Jeff; Aragon, Michael; Ramirez, Francisco; Summers, Kenneth L.; Knoebel, Arthur

    1992-01-01

    Integrated circuit produces 8-bit pseudorandom numbers from specified probability distribution, at rate of 10 MHz. Use of Boolean logic, circuit implements pseudorandom-number-generating algorithm. Circuit includes eight 12-bit pseudorandom-number generators, outputs are uniformly distributed. 8-bit pseudorandom numbers satisfying specified nonuniform probability distribution are generated by processing uniformly distributed outputs of eight 12-bit pseudorandom-number generators through "pipeline" of D flip-flops, comparators, and memories implementing conditional probabilities on zeros and ones.

  16. Group Sunspot Numbers: Sunspot Cycle Characteristics

    NASA Technical Reports Server (NTRS)

    Hathaway, D. H.; Wilson, R. M.; Reichmann, E. J.; Six, N. Frank (Technical Monitor)

    2002-01-01

    We examine the "Group" sunspot numbers constructed by Hoyt and Schatten to determine their utility in characterizing the solar activity cycle. We compare smoothed monthly Group Sunspot Numbers to Zurich (International) Sunspot Numbers, 10.7-cm radio flux, and total sunspot area. We find that the Zurich numbers follow the 10.7-cm radio flux and total sunspot area measurements slightly better than the Group numbers. We examine several significant characteristics of the sunspot cycle using both Group numbers and Zurich numbers. We find that the "Waldmeier Effect" - the anti-correlation between cycle amplitude and the elapsed time between minimum and maximum of a cycle - is much more apparent in the Zurich numbers. The "Amplitude-Period Effect" the anti-correlation between cycle amplitude and the length of the previous cycle from minimum to minimum - is also much more apparent in the Zurich numbers. The "Amplitude-Minimum Effect" - the correlation between cycle amplitude and the activity level at the previous (onset) minimum is equally apparent in both the Zurich numbers and the Group numbers. The "Even-Odd Effect" - in which odd-numbered cycles are larger than their even-numbered precursors - is somewhat stronger in the Group numbers but with a tighter relationship in the Zurich numbers. The "Secular Trend" - the increase in cycle amplitudes since the Maunder Minimum - is much stronger in Group numbers. After removing this trend we find little evidence for multi-cycle periodicities like the 80 year Gleissberg cycle or the two- and three-cycle periodicities. We also find little evidence for a correlation between the amplitude of a cycle and its period or for a bimodal distribution of cycle periods. We conclude that the Group numbers are most useful for extending the sunspot cycle data further back in time and thereby adding more cycles and improving the statistics. However, the Zurich numbers are more useful for characterizing the on-going levels of solar activity.

  17. The Translated Dowling Polynomials and Numbers

    PubMed Central

    Mangontarum, Mahid M.; Macodi-Ringia, Amila P.; Abdulcarim, Normalah S.

    2014-01-01

    More properties for the translated Whitney numbers of the second kind such as horizontal generating function, explicit formula, and exponential generating function are proposed. Using the translated Whitney numbers of the second kind, we will define the translated Dowling polynomials and numbers. Basic properties such as exponential generating functions and explicit formula for the translated Dowling polynomials and numbers are obtained. Convexity, integral representation, and other interesting identities are also investigated and presented. We show that the properties obtained are generalizations of some of the known results involving the classical Bell polynomials and numbers. Lastly, we established the Hankel transform of the translated Dowling numbers.

  18. The Many Pearls of Number Theory

    ERIC Educational Resources Information Center

    Prielipp, Robert W.

    1970-01-01

    Presents information about prime numbers which the elementary or junior high school teacher might introduce to students. Gives five definition statements followed by at least one theorem and its proof. Introduces some historical aspects to prime numbers. (RR)

  19. 40 CFR 86.1204 - Section numbering.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... Test Procedures for New Gasoline-Fueled, Natural Gas-Fueled, Liquefied Petroleum Gas-Fueled and Methanol-Fueled Heavy-Duty Vehicles § 86.1204 Section numbering. The section numbering system set forth...

  20. Quantity Cognition: Numbers, Numerosity, Zero and Mathematics.

    PubMed

    Harvey, Ben M

    2016-05-23

    Physical quantities differ from abstract numbers and mathematics, but recent results are revealing the neural representation of both: a new study demonstrates how an absence of quantity is transformed into a representation of zero as a number. PMID:27218850

  1. 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)

  2. Poison control center - Emergency number (image)

    MedlinePlus

    ... anywhere in the United States. This national hotline number will let you talk to experts in poisoning. ... control centers in the U.S. use this national number. You should call if you have any questions ...

  3. On Anti-Elite Prime Numbers

    NASA Astrophysics Data System (ADS)

    M"Uller, Tom

    2007-09-01

    An odd prime number p is called anti-elite if only finitely many Fermat numbers are quadratic non-residues to p. This concept is the exact opposite to that of elite prime numbers. We study some fundamental properties of anti-elites and show that there are infinitely many of them. A computational search among all the numbers up to 100 billion yielded 84 anti-elite primes.

  4. 14 CFR 47.15 - Registration number.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 14 Aeronautics and Space 1 2014-01-01 2014-01-01 false Registration number. 47.15 Section 47.15 Aeronautics and Space FEDERAL AVIATION ADMINISTRATION, DEPARTMENT OF TRANSPORTATION AIRCRAFT AIRCRAFT REGISTRATION General § 47.15 Registration number. (a) Number required. An applicant for aircraft...

  5. 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)

  6. Teach Kids about Numbers All around Us

    ERIC Educational Resources Information Center

    Hudson, Hannah Trierweiler

    2011-01-01

    Recognizing the role numbers play in people's everyday lives is crucial to students' math understanding now and down the road. That's why Bob Krech, a curriculum specialist in New Jersey's West Windsor-Plainsboro district, likes to teach a lesson he calls "Numbers All Around Us." This lesson uses real-world examples to show that numbers help…

  7. The Decimal Representation of Real Numbers

    ERIC Educational Resources Information Center

    Kalapodi, A.

    2010-01-01

    The representation of natural numbers in decimal form is an unequivocal procedure while for the representation of real numbers some ambiguities concerning the existence of infinitely many digits equal to 9 still emerge. One of the most frequently confronted misunderstandings is whether 0.999...equals 1 or not, and if not what number does this…

  8. Children's Use of Number Line Estimation Strategies

    ERIC Educational Resources Information Center

    Peeters, Dominique; Degrande, Tine; Ebersbach, Mirjam; Verschaffel, Lieven; Luwel, Koen

    2016-01-01

    This study tested whether second graders use benchmark-based strategies when solving a number line estimation (NLE) task. Participants were assigned to one of three conditions based on the availability of benchmarks provided on the number line. In the bounded condition, number lines were only bounded at both sides by 0 and 200, while the midpoint…

  9. Identifying Fractions on a Number Line

    ERIC Educational Resources Information Center

    Wong, Monica

    2013-01-01

    Fractions are generally introduced to students using the part--whole model. Yet the number line is another important representation which can be used to build fraction concepts (Australian Curriculum Assessment and Reporting Authority [ACARA], 2012). Number lines are recognised as key in students' number development not only of fractions, but…

  10. 46 CFR Sec. 7 - Job order numbering.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 46 Shipping 8 2012-10-01 2012-10-01 false Job order numbering. Sec. 7 Section 7 Shipping MARITIME... REPAIRS UNDER NATIONAL SHIPPING AUTHORITY MASTER LUMP SUM REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP Contract number shall be inserted in every job order and supplemental...

  11. 46 CFR Sec. 7 - Job order numbering.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... 46 Shipping 8 2013-10-01 2013-10-01 false Job order numbering. Sec. 7 Section 7 Shipping MARITIME... REPAIRS UNDER NATIONAL SHIPPING AUTHORITY MASTER LUMP SUM REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP Contract number shall be inserted in every job order and supplemental...

  12. 46 CFR Sec. 7 - Job order numbering.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 46 Shipping 8 2014-10-01 2014-10-01 false Job order numbering. Sec. 7 Section 7 Shipping MARITIME... REPAIRS UNDER NATIONAL SHIPPING AUTHORITY MASTER LUMP SUM REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP Contract number shall be inserted in every job order and supplemental...

  13. 46 CFR Sec. 7 - Job order numbering.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 46 Shipping 8 2010-10-01 2010-10-01 false Job order numbering. Sec. 7 Section 7 Shipping MARITIME... REPAIRS UNDER NATIONAL SHIPPING AUTHORITY MASTER LUMP SUM REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP Contract number shall be inserted in every job order and supplemental...

  14. 46 CFR Sec. 7 - Job order numbering.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... 46 Shipping 8 2011-10-01 2011-10-01 false Job order numbering. Sec. 7 Section 7 Shipping MARITIME... REPAIRS UNDER NATIONAL SHIPPING AUTHORITY MASTER LUMP SUM REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP Contract number shall be inserted in every job order and supplemental...

  15. 48 CFR 304.7001 - Numbering acquisitions.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 48 Federal Acquisition Regulations System 4 2014-10-01 2014-10-01 false Numbering acquisitions. 304.7001 Section 304.7001 Federal Acquisition Regulations System HEALTH AND HUMAN SERVICES GENERAL ADMINISTRATIVE MATTERS Acquisition Instrument Identification Numbering System 304.7001 Numbering acquisitions....

  16. 48 CFR 304.7001 - Numbering acquisitions.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... 48 Federal Acquisition Regulations System 4 2011-10-01 2011-10-01 false Numbering acquisitions. 304.7001 Section 304.7001 Federal Acquisition Regulations System HEALTH AND HUMAN SERVICES GENERAL ADMINISTRATIVE MATTERS Acquisition Instrument Identification Numbering System 304.7001 Numbering acquisitions....

  17. 48 CFR 304.7001 - Numbering acquisitions.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 48 Federal Acquisition Regulations System 4 2012-10-01 2012-10-01 false Numbering acquisitions. 304.7001 Section 304.7001 Federal Acquisition Regulations System HEALTH AND HUMAN SERVICES GENERAL ADMINISTRATIVE MATTERS Acquisition Instrument Identification Numbering System 304.7001 Numbering acquisitions....

  18. 48 CFR 304.7001 - Numbering acquisitions.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 48 Federal Acquisition Regulations System 4 2010-10-01 2010-10-01 false Numbering acquisitions. 304.7001 Section 304.7001 Federal Acquisition Regulations System HEALTH AND HUMAN SERVICES GENERAL ADMINISTRATIVE MATTERS Acquisition Instrument Identification Numbering System 304.7001 Numbering acquisitions....

  19. 48 CFR 304.7001 - Numbering acquisitions.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... 48 Federal Acquisition Regulations System 4 2013-10-01 2013-10-01 false Numbering acquisitions. 304.7001 Section 304.7001 Federal Acquisition Regulations System HEALTH AND HUMAN SERVICES GENERAL ADMINISTRATIVE MATTERS Acquisition Instrument Identification Numbering System 304.7001 Numbering acquisitions....

  20. Insights into Our Understandings of Large Numbers

    ERIC Educational Resources Information Center

    Kastberg, Signe E.; Walker, Vicki

    2008-01-01

    This article explores prospective teachers' understandings of one million to gain insights into the development of adult understanding of large numbers. Themes in the prospective teachers' work included number associated with a quantity of objects, number as an abstraction, and additive and multiplicative approaches. The authors suggest that the…

  1. 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…

  2. 46 CFR Sec. 2 - Voyage numbers.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with... General Agent shall affix his abbreviated designation and initial voyage numbers, as NSA-13/XYZ-1....

  3. 46 CFR Sec. 2 - Voyage numbers.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with... General Agent shall affix his abbreviated designation and initial voyage numbers, as NSA-13/XYZ-1....

  4. 46 CFR Sec. 2 - Voyage numbers.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with... General Agent shall affix his abbreviated designation and initial voyage numbers, as NSA-13/XYZ-1....

  5. 46 CFR Sec. 2 - Voyage numbers.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with... General Agent shall affix his abbreviated designation and initial voyage numbers, as NSA-13/XYZ-1....

  6. 46 CFR Sec. 2 - Voyage numbers.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with... General Agent shall affix his abbreviated designation and initial voyage numbers, as NSA-13/XYZ-1....

  7. 47 CFR 1.1405 - File numbers.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 47 Telecommunication 1 2010-10-01 2010-10-01 false File numbers. 1.1405 Section 1.1405... Procedures § 1.1405 File numbers. Each complaint which appears to be essentially complete under § 1.1404 will be accepted and assigned a file number. Such assignment is for administrative purposes only and...

  8. 32 CFR 1602.19 - Numbers.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 32 National Defense 6 2010-07-01 2010-07-01 false Numbers. 1602.19 Section 1602.19 National Defense Other Regulations Relating to National Defense SELECTIVE SERVICE SYSTEM DEFINITIONS § 1602.19 Numbers. Cardinal numbers may be expressed by Arabic or Roman symbols....

  9. 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…

  10. 49 CFR 230.47 - Boiler number.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 49 Transportation 4 2012-10-01 2012-10-01 false Boiler number. 230.47 Section 230.47..., DEPARTMENT OF TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges § 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known,...