NASA Astrophysics Data System (ADS)
Ooi, Seng-Keat
2005-11-01
Lock-exchange gravity current flows produced by the instantaneous release of a heavy fluid are investigated using 3-D well resolved Large Eddy Simulation simulations at Grashof numbers up to 8*10^9. It is found the 3-D simulations correctly predict a constant front velocity over the initial slumping phase and a front speed decrease proportional to t-1/3 (the time t is measured from the release) over the inviscid phase, in agreement with theory. The evolution of the current in the simulations is found to be similar to that observed experimentally by Hacker et al. (1996). The effect of the dynamic LES model on the solutions is discussed. The energy budget of the current is discussed and the contribution of the turbulent dissipation to the total dissipation is analyzed. The limitations of less expensive 2D simulations are discussed; in particular their failure to correctly predict the spatio-temporal distributions of the bed shear stresses which is important in determining the amount of sediment the gravity current can entrain in the case in advances of a loose bed.
NASA 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.
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.
NASA Astrophysics Data System (ADS)
Miroshnichenko, E.; Kit, E.; Gelfgat, A. Yu.
2016-11-01
Effect of the capillary meniscus on the instability of large Prandtl number Czochralski melt flow is studied experimentally. The measurements are conducted in two experimental facilities by two independent non-intrusive optical techniques. The quantitative results are presented as dependencies of the critical Grashof number (critical temperature difference) on the meniscus height for different Prandtl numbers, radii and aspect ratios. The results show that with increase of the meniscus height the critical temperature difference noticeably grows and sometimes doubles. Recently reported parametric relations for the critical Grashof number and oscillations frequency are extended to include parameters of the meniscus.
Buoyant convection of low Prandtl number melts in horizontal boat configuration
NASA Astrophysics Data System (ADS)
Kuhl, R.; Wilke, H.
Results of experimental investigations and numerical simulations of buoyant convection in metal and semiconductor melt layers with an applied horizontal temperature gradient are presented. Stability diagrams characterize the transition from steady to unsteady convection in terms of Grashof number, aspect ratio and Prandtl number. Periodic temperature oscillations of the melt are analysed and the oscillatory convection mechanism is discussed by numerical results. In order to grow striation-free crystals by means of the horizontal Bridgman method, the necessary conditions can be concluded by the results obtained.
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.
Transitions in Convection of a Low Prandtl Number Fluid Driven by a Horizontal Temperature Gradient
NASA Astrophysics Data System (ADS)
Hung, Ming-Cheng
The transitions in convection of a low Prandtl number fluid (mercury) contained in enclosed rectangular cavities driven by horizontal temperature gradients were investigated. These cavities have insulating top, bottom and side boundaries. The other two end walls are highly conducting. The temperatures on the conducting walls were varied to control the temperature gradient inside. Both the temperature and the velocity of the fluid inside the cavity were measured. A traversing system allowed the probe position to be changed with the cavity always sealed. The temperature gradient, controlled by a computer, was ramped very slowly. At every 0.2 or 0.12 degree the ramping was held and a data file of several hours was taken. The Prandtl number of the fluid was varied from 0.025 to 0.035 by changing the average temperature. The cavity size effect on the transitions was investigated. The primary (large) cavity had aspect ratio (length:height:width) of 17.8:1:17.8 (height = 0.9 cm). The other cavities for size effect investigation were shorter and narrower. Fourier transform was used to analyze the time series. Phase portraits were constructed in 3d using time delay method and correlation dimensions were computed for some trajectories. For the large cavity, the observed onset of the longitudinal oscillatory state at Grashof number Gr = 18490 was far above the predicted value of 10610 for an infinite long cavity (height/length = 0). At low Grashof numbers, the flow was time independent. As Gr was increased, it changed to a noisy state with a periodic component and then became purely chaotic. Finally the longitudinal oscillatory state appeared with two frequencies and noise. The longitudinal oscillatory state was observed to be a standing wave with a wavelength of about 3 cm. The critical Gr was affected by the cavity width and length. The narrower the cavity, the more stable the flow. The critical Gr for oscillation decreased as the length was increased. An unusual
ERIC Educational Resources Information Center
Herrera, Terese A.
2004-01-01
This article features Number Time, a site developed by the British Broadcasting Corporation (BBC) for young mathematics learners, located at www.bbc.co.uk/schools/numbertime. The site uses interactive animation to help children in pre-K through grade 2 understand and practice number basics. Users will find online games, videos that tell number…
ERIC Educational Resources Information Center
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…
ERIC Educational Resources Information Center
Thelin, John R.
2013-01-01
What topic would you choose if you had the luxury of writing forever? In this article, John Thelin provides his response: He would opt to write about the history of higher education in a way that relies on quantitative data. "Numbers, please!" is his research request in taking on a longitudinal study of colleges and universities over…
ERIC Educational Resources Information Center
Sezin, Fatin
2009-01-01
It is instructive and interesting to find hidden numbers by using different positional numeration systems. Most of the present guessing techniques use the binary system expressed as less-than, greater-than or present-absent type information. This article describes how, by employing four cards having integers 1-64 written in different colours, one…
Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids
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
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…
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…
Expansion of real numbers by algebraic numbers
NASA Astrophysics Data System (ADS)
Hajime, Kaneko
2008-01-01
In this paper we represent the fractional part of ξαn, where ξ is a nonzero real number and α is an algebraic number. By using this representation, we give new lower bounds for the distance from ξαn to the nearest integer.
Numbers Defy the Law of Large Numbers
ERIC Educational Resources Information Center
Falk, Ruma; Lann, Avital Lavie
2015-01-01
As the number of independent tosses of a fair coin grows, the rates of heads and tails tend to equality. This is misinterpreted by many students as being true also for the absolute numbers of the two outcomes, which, conversely, depart unboundedly from each other in the process. Eradicating that misconception, as by coin-tossing experiments,…
ERIC Educational Resources Information Center
Wilkie, James E. B.; Bodenhausen, Galen V.
2012-01-01
We examined the possibility that nonsocial, highly generic concepts are gendered. Specifically, we investigated the gender connotations of Arabic numerals. Across several experiments, we show that the number 1 and other odd numbers are associated with masculinity, whereas the number 2 and other even numbers are associated with femininity, in ways…
ERIC Educational Resources Information Center
Burkhart, Jerry
2009-01-01
Prime numbers are often described as the "building blocks" of natural numbers. This article shows how the author and his students took this idea literally by using prime factorizations to build numbers with blocks. In this activity, students explore many concepts of number theory, including the relationship between greatest common factors and…
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…
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…
All square chiliagonal numbers
NASA Astrophysics Data System (ADS)
Aṣiru, Muniru A.
2016-10-01
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 numbers. The study revealed that the determination of square chiliagonal numbers naturally leads to a generalized Pell equation x2 - Dy2 = N with D = 1996 and N = 9962, and has six fundamental solutions out of which only three yielded integer values for use as indices of chiliagonal numbers. The crossing/independent recurrence relations satisfied by each class of indices of the corresponding chiliagonal numbers and square numbers are obtained. Finally, the generating functions serve as a clothesline to hang up the indices of the corresponding chiliagonal numbers and square numbers for easy display and this was used to obtain the first few sequence of square chiliagonal numbers.
Kaneko, K.
1987-02-01
A relationship between the number projection and the shell model methods is investigated in the case of a single-j shell. We can find a one-to-one correspondence between the number projected and the shell model states.
Somers, E.
1987-03-01
Regulatory agencies require numbers to provide health protection. The manner in which these numbers are derived from animal experiments and human epidemiology is considered together with the limitations and inadequacies of these numbers. Some recent examples of risk assessment in Canada are given including asbestos, drinking water, and indoor air quality. The value of these numbers in providing a measure of the hazard in a wider perspective is stressed, although they can never be the sole determinant of public policy.
ERIC Educational Resources Information Center
Allen, G. Donald
2014-01-01
In human history, the origin of the numbers came from definite practical needs. Indeed, there is strong evidence that numbers were created before writing. The number "1", dating back at least 20,000 years, was found as a counting symbol on a bone. The famous statement by the German mathematician Leopold Kronecker (1823-1891), "God…
ERIC Educational Resources Information Center
Shi, Yixun
2010-01-01
Starting with an interesting number game sometimes used by school teachers to demonstrate the factorization of integers, "sum-difference numbers" are defined. A positive integer n is a "sum-difference number" if there exist positive integers "x, y, w, z" such that n = xy = wz and x ? y = w + z. This paper characterizes all sum-difference numbers…
ERIC Educational Resources Information Center
de Mestre, Neville
2008-01-01
Prime numbers are important as the building blocks for the set of all natural numbers, because prime factorisation is an important and useful property of all natural numbers. Students can discover them by using the method known as the Sieve of Eratosthenes, named after the Greek geographer and astronomer who lived from c. 276-194 BC. Eratosthenes…
ERIC Educational Resources Information Center
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…
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…
Hierarchical number estimation.
Friedenberg, Jay; Limratana, William
2005-01-01
We investigated number estimation using dot patterns grouped by proximity into larger clusters. Participants estimated the number of dots and clusters in separate trials. Estimation was most accurate when the numbers of elements on both scales were the same. When the number of elements on the unattended scale was higher, overestimation occurred. Conversely, when the number of elements on the unattended scale was lower, underestimation occurred. In Experiment 2, response cues were blocked to reduce any tendency toward attending the irrelevant level. The results were essentially unchanged, indicating response confusion alone cannot account for the effect. The data support the existence of an opposite scale effect in which the number of elements at the unattended level influence the processing of number.
Curvature and Tachibana numbers
Stepanov, Sergey E
2011-07-31
The aim of this paper is to define the rth Tachibana number t{sub r} of an n-dimensional compact oriented Riemannian manifold as the dimension of the space of conformally Killing r-forms, for r=1,2,...,n-1. We also describe properties of these numbers, by analogy with properties of the Betti numbers b{sub r} of a compact oriented Riemannian manifold. Bibliography: 25 titles.
NASA Technical Reports Server (NTRS)
Baals, D. D. (Editor)
1977-01-01
Fundamental aerodynamic questions for which high Reynolds number experimental capability is required are discussed. The operational characteristics and design features of the National Transonic Facility are reviewed.
... 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 ...
ERIC Educational Resources Information Center
Onstad, Torgeir
1991-01-01
After a brief historical account of Leonardo Pisano Fibonacci, some basic results concerning the Fibonacci numbers are developed and proved, and entertaining examples are described. Connections are made between the Fibonacci numbers and the Golden Ratio, biological nature, and other combinatorics examples. (MDH)
Templates, Numbers & Watercolors.
ERIC Educational Resources Information Center
Clemesha, David J.
1990-01-01
Describes how a second-grade class used large templates to draw and paint five-digit numbers. The lesson integrated artistic knowledge and vocabulary with their mathematics lesson in place value. Students learned how draftspeople use templates, and they studied number paintings by Charles Demuth and Jasper Johns. (KM)
Avogadro's Number Ferromagnetically
ERIC Educational Resources Information Center
Houari, Ahmed
2010-01-01
Avogadro's number, usually denoted by N[subscript A], plays a fundamental role in both physics and chemistry. It defines the extremely useful concept of the mole, which is the base unit of the amount of matter in the international system of units. The fundamental character of this number can also be illustrated by its appearance in the definitions…
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
ERIC Educational Resources Information Center
Strawn, Candace A.
1998-01-01
Describes LOGO's turtle graphics capabilities based on a sixth-grade classroom's activities with negative numbers and Logo programming. A sidebar explains LOGO and offers suggestions to teachers for using LOGO effectively. (LRW)
ERIC Educational Resources Information Center
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)
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
Quantum random number generator
Pooser, Raphael C.
2016-05-10
A quantum random number generator (QRNG) and a photon generator for a QRNG are provided. The photon generator may be operated in a spontaneous mode below a lasing threshold to emit photons. Photons emitted from the photon generator may have at least one random characteristic, which may be monitored by the QRNG to generate a random number. In one embodiment, the photon generator may include a photon emitter and an amplifier coupled to the photon emitter. The amplifier may enable the photon generator to be used in the QRNG without introducing significant bias in the random number and may enable multiplexing of multiple random numbers. The amplifier may also desensitize the photon generator to fluctuations in power supplied thereto while operating in the spontaneous mode. In one embodiment, the photon emitter and amplifier may be a tapered diode amplifier.
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…
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.
[Projection of prisoner numbers].
Metz, Rainer; Sohn, Werner
2015-01-01
The past and future development of occupancy rates in prisons is of crucial importance for the judicial administration of every country. Basic factors for planning the required penal facilities are seasonal fluctuations, minimum, maximum and average occupancy as well as the present situation and potential development of certain imprisonment categories. As the prisoner number of a country is determined by a complex set of interdependent conditions, it has turned out to be difficult to provide any theoretical explanations. The idea accepted in criminology for a long time that prisoner numbers are interdependent with criminal policy must be regarded as having failed. Statistical and time series analyses may help, however, to identify the factors having influenced the development of prisoner numbers in the past. The analyses presented here, first describe such influencing factors from a criminological perspective and then deal with their statistical identification and modelling. Using the development of prisoner numbers in Hesse as an example, it has been found that modelling methods in which the independent variables predict the dependent variable with a time lag are particularly helpful. A potential complication is, however, that for predicting the number of prisoners the different dynamics in German and foreign prisoners require the development of further models. PMID:26419083
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.
Cantlon, Jessica F.; Platt, Michael L.; Brannon, Elizabeth M.
2009-01-01
In a world without numbers, we would be unable to build a skyscraper, hold a national election, plan a wedding, or pay for a chicken at the market. The numerical symbols used in all these behaviors build on the approximate number system (ANS) which represents the number of discrete objects or events as a continuous mental magnitude. In this review, we first discuss evidence that the ANS bears a set of behavioral and brain signatures that are universally displayed across animal species, human cultures, and development. We then turn to the question of whether the ANS constitutes a specialized cognitive and neural domain--a question central to understanding how this system works, the nature of its evolutionary and developmental trajectory, and its physical instantiation in the brain. PMID:19131268
Quantum random number generation
Ma, Xiongfeng; Yuan, Xiao; Cao, Zhu; Zhang, Zhen; Qi, Bing
2016-06-28
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
Khan, T.A.; Baum, J.W.; Beckman, M.C.
1993-10-01
This document contains information dealing with the lessons learned from the experience of nuclear plants. In this issue the authors tried to avoid the `tyranny` of numbers and concentrated on the main lessons learned. Topics include: filtration devices for air pollution abatement, crack repair and inspection, and remote handling equipment.
ERIC Educational Resources Information Center
Hahn, Nic
2012-01-01
Remember paint by numbers? This revived trend was a perfect solution to teaching geometric shapes to the author's first-grade students. Geometric shapes are identified and used in early elementary art classrooms, but this lesson gives students a deeper understanding of shape, encourages problem-solving, and makes a strong correlation between math…
ERIC Educational Resources Information Center
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…
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.
ERIC Educational Resources Information Center
McMurdo, George
1996-01-01
The expansion of the commercial Internet has encouraged the interpretation of the Internet and its uses as a potential marketing medium. Examines statistical and demographic information about the Internet including number of Internet hosts and World Wide Web servers, and estimates of Internet users; and raises questions about definitions and…
ERIC Educational Resources Information Center
Cech, Scott J.
2008-01-01
This article discusses College Summit, a nonprofit effort centered around the premise that there is a sizable number of students who are more capable of college academics than their test scores and grade point averages suggest. Its four-day summer sessions are focused not on ramping up students' academic performance but in mining students'…
Number in Classifier Languages
ERIC Educational Resources Information Center
Nomoto, Hiroki
2013-01-01
Classifier languages are often described as lacking genuine number morphology and treating all common nouns, including those conceptually count, as an unindividuated mass. This study argues that neither of these popular assumptions is true, and presents new generalizations and analyses gained by abandoning them. I claim that no difference exists…
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.
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.
Grozeva, Detelina; Kirov, George; Ivanov, Dobril; Jones, Ian R.; Jones, Lisa; Green, Elaine K.; St Clair, David M.; Young, Allan H.; Ferrier, Nicol; Farmer, Anne E.; McGuffin, Peter; Holmans, Peter A.; Owen, Michael J.; O’Donovan, Michael C.; Craddock, Nick
2015-01-01
Context Recent studies suggest that copy number variation in the human genome is extensive and may play an important role in susceptibility to disease, including neuropsychiatric disorders such as schizophrenia and autism. The possible involvement of copy number variants (CNVs) in bipolar disorder has received little attention to date. Objectives To determine whether large (>100 000 base pairs) and rare (found in <1% of the population) CNVs are associated with susceptibility to bipolar disorder and to compare with findings in schizophrenia. Design A genome-wide survey of large, rare CNVs in a case-control sample using a high-density microarray. Setting The Wellcome Trust Case Control Consortium. Participants There were 1697 cases of bipolar disorder and 2806 nonpsychiatric controls. All participants were white UK residents. Main Outcome Measures Overall load of CNVs and presence of rare CNVs. Results The burden of CNVs in bipolar disorder was not increased compared with controls and was significantly less than in schizophrenia cases. The CNVs previously implicated in the etiology of schizophrenia were not more common in cases with bipolar disorder. Conclusions Schizophrenia and bipolar disorder differ with respect to CNV burden in general and association with specific CNVs in particular. Our data are consistent with the possibility that possession of large, rare deletions may modify the phenotype in those at risk of psychosis: those possessing such events are more likely to be diagnosed as having schizophrenia, and those without them are more likely to be diagnosed as having bipolar disorder. PMID:20368508
An introduction to hyperharmonic numbers
NASA Astrophysics Data System (ADS)
Cereceda, José Luis
2015-04-01
In this note, we deal with a generalization of the harmonic numbers proposed by Conway and Guy in their Book of Numbers, namely, the so-called hyperharmonic numbers. Our main aim is to prove, by mathematical induction, the formula defining the hyperharmonic numbers in terms of ordinary harmonic numbers. Moreover, we calculate the hyperharmonic numbers as the derivative of a certain binomial coefficient.
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...
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...
Beyond natural numbers: negative number representation in parietal cortex.
Blair, Kristen P; Rosenberg-Lee, Miriam; Tsang, Jessica M; Schwartz, Daniel L; Menon, Vinod
2012-01-01
Unlike natural numbers, negative numbers do not have natural physical referents. How does the brain represent such abstract mathematical concepts? Two competing hypotheses regarding representational systems for negative numbers are a rule-based model, in which symbolic rules are applied to negative numbers to translate them into positive numbers when assessing magnitudes, and an expanded magnitude model, in which negative numbers have a distinct magnitude representation. Using an event-related functional magnetic resonance imaging design, we examined brain responses in 22 adults while they performed magnitude comparisons of negative and positive numbers that were quantitatively near (difference <4) or far apart (difference >6). Reaction times (RTs) for negative numbers were slower than positive numbers, and both showed a distance effect whereby near pairs took longer to compare. A network of parietal, frontal, and occipital regions were differentially engaged by negative numbers. Specifically, compared to positive numbers, negative number processing resulted in greater activation bilaterally in intraparietal sulcus (IPS), middle frontal gyrus, and inferior lateral occipital cortex. Representational similarity analysis revealed that neural responses in the IPS were more differentiated among positive numbers than among negative numbers, and greater differentiation among negative numbers was associated with faster RTs. Our findings indicate that despite negative numbers engaging the IPS more strongly, the underlying neural representation are less distinct than that of positive numbers. We discuss our findings in the context of the two theoretical models of negative number processing and demonstrate how multivariate approaches can provide novel insights into abstract number representation.
Percents Are Not Natural Numbers
ERIC Educational Resources Information Center
Jacobs, Jennifer A.
2013-01-01
Adults are prone to treating percents, one representational format of rational numbers, as novel cases of natural number. This suggests that percent values are not differentiated from natural numbers; a conceptual shift from the natural numbers to the rational numbers has not yet occurred. This is most surprising, considering people are inundated…
Series of Reciprocal Triangular Numbers
ERIC Educational Resources Information Center
Bruckman, Paul; Dence, Joseph B.; Dence, Thomas P.; Young, Justin
2013-01-01
Reciprocal triangular numbers have appeared in series since the very first infinite series were summed. Here we attack a number of subseries of the reciprocal triangular numbers by methodically expressing them as integrals.
Number 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…
15. Stress Sheet, Truss number 2, span number 6, Superior ...
15. Stress Sheet, Truss number 2, span number 6, Superior Avenue viaduct. Drawing courtesy Engineering Dept., City of Cleveland. - Superior Avenue Viaduct, Cleveland East & West side, Cuyahoga Valley Vicinity, Cleveland, Cuyahoga County, OH
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…
Natural Number Bias in Operations with Missing Numbers
ERIC Educational Resources Information Center
Christou, Konstantinos P.
2015-01-01
This study investigates the hypothesis that there is a natural number bias that influences how students understand the effects of arithmetical operations involving both Arabic numerals and numbers that are represented by symbols for missing numbers. It also investigates whether this bias correlates with other aspects of students' understanding of…
Toddlers' Spontaneous Attention to Number and Verbal Number Quantification
ERIC Educational Resources Information Center
Li, Xia
2009-01-01
"S"pontaneous "a"ttention to "n"umber (SAN) is the tendency to notice the relatively abstract attribute of number despite the presence of other attributes. According to nativists, an innate concept of one to three directs young children's attention to these "intuitive numbers" in everyday situations--even before they acquire language. According to…
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…
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…
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,…
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"…
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.
Perceiving numbers influences actions in number-space synesthesia.
Arend, Isabel; Gertner, Limor; Henik, Avishai
2013-01-01
Number and space are spontaneously linked in human cognition and have been metaphorically described as a 'mental number line'. In number-space synesthetes (NSS), numbers are visualized in specific spatial arrays, in an idiosyncratic and explicit manner. Here we tested whether the numerical-spatial association that characterizes NSS has the potential to affect individual's actions when the number is not a task-relevant feature. We used a Simon task that implies stimulus-response matching. Task-irrelevant Arabic numerals (1, 4, 6, 9) appeared simultaneously at the same location as a colored target. A group of 15 age-matched controls and 4 NSS completed a 2×2 within-subjects design consisting of Simon (compatible and incompatible) and number-space (congruent and incongruent) trials. Mean reaction time (RT) and RT cumulative distribution functions across Simon and number-space conditions for both NSS and controls were analyzed. Relative to controls, synesthetes' RTs were overall affected by the number-space mapping. Moreover, synesthetes' Simon effects occurred at later response times. These results provide strong evidence that numbers are cognitively represented as action codes and that the strength of the association shapes the impact of the numerical representation on individuals' actions.
Huang, Yi Ting; Spelke, Elizabeth; Snedeker, Jesse
2014-01-01
Number words are generally used to refer to the exact cardinal value of a set, but cognitive scientists disagree about their meanings. Although most psychological analyses presuppose that numbers have exact semantics (two means EXACTLY TWO), many linguistic accounts propose that numbers have lower-bounded semantics (AT LEAST TWO), and that speakers restrict their reference through a pragmatic inference (scalar implicature). We address this debate through studies of children who are in the process of acquiring the meanings of numbers. Adults and 2- and 3-year-olds were tested in a novel paradigm that teases apart semantic and pragmatic aspects of interpretation (the covered box task). Our findings establish that when scalar implicatures are cancelled in the critical trials of this task, both adults and children consistently give exact interpretations for number words. These results, in concert with recent work on real-time processing, provide the first unambiguous evidence that number words have exact semantics. PMID:25285053
Familial Sinistrals Avoid Exact Numbers
Sauerland, Uli; Gotzner, Nicole
2013-01-01
We report data from an internet questionnaire of sixty number trivia. Participants were asked for the number of cups in their house, the number of cities they know and 58 other quantities. We compare the answers of familial sinistrals – individuals who are left-handed themselves or have a left-handed close blood-relative – with those of pure familial dextrals – right-handed individuals who reported only having right-handed close blood-relatives. We show that familial sinistrals use rounder numbers than pure familial dextrals in the survey responses. Round numbers in the decimal system are those that are multiples of powers of 10 or of half or a quarter of a power of 10. Roundness is a gradient concept, e.g. 100 is rounder than 50 or 200. We show that very round number like 100 and 1000 are used with 25% greater likelihood by familial sinistrals than by pure familial dextrals, while pure familial dextrals are more likely to use less round numbers such as 25, 60, and 200. We then use Sigurd’s (1988, Language in Society) index of the roundness of a number and report that familial sinistrals’ responses are significantly rounder on average than those of pure familial dextrals. To explain the difference, we propose that the cognitive effort of using exact numbers is greater for the familial sinistral group because their language and number systems tend to be more distributed over both hemispheres of the brain. Our data support the view that exact and approximate quantities are processed by two separate cognitive systems. Specifically, our behavioral data corroborates the view that the evolutionarily older, approximate number system is present in both hemispheres of the brain, while the exact number system tends to be localized in only one hemisphere. PMID:23544052
Familial sinistrals avoid exact numbers.
Sauerland, Uli; Gotzner, Nicole
2013-01-01
We report data from an internet questionnaire of sixty number trivia. Participants were asked for the number of cups in their house, the number of cities they know and 58 other quantities. We compare the answers of familial sinistrals--individuals who are left-handed themselves or have a left-handed close blood-relative--with those of pure familial dextrals--right-handed individuals who reported only having right-handed close blood-relatives. We show that familial sinistrals use rounder numbers than pure familial dextrals in the survey responses. Round numbers in the decimal system are those that are multiples of powers of 10 or of half or a quarter of a power of 10. Roundness is a gradient concept, e.g. 100 is rounder than 50 or 200. We show that very round number like 100 and 1000 are used with 25% greater likelihood by familial sinistrals than by pure familial dextrals, while pure familial dextrals are more likely to use less round numbers such as 25, 60, and 200. We then use Sigurd's (1988, Language in Society) index of the roundness of a number and report that familial sinistrals' responses are significantly rounder on average than those of pure familial dextrals. To explain the difference, we propose that the cognitive effort of using exact numbers is greater for the familial sinistral group because their language and number systems tend to be more distributed over both hemispheres of the brain. Our data support the view that exact and approximate quantities are processed by two separate cognitive systems. Specifically, our behavioral data corroborates the view that the evolutionarily older, approximate number system is present in both hemispheres of the brain, while the exact number system tends to be localized in only one hemisphere.
Number development and developmental dyscalculia.
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
Compendium of Experimental Cetane Numbers
Yanowitz, J.; Ratcliff, M. A.; McCormick, R. L.; Taylor, J. D.; Murphy, M. J.
2014-08-01
This report is an updated version of the 2004 Compendium of Experimental Cetane Number Data and presents a compilation of measured cetane numbers for pure chemical compounds. It includes all available single compound cetane number data found in the scientific literature up until March 2014 as well as a number of unpublished values, most measured over the past decade at the National Renewable Energy Laboratory. This Compendium contains cetane values for 389 pure compounds, including 189 hydrocarbons and 201 oxygenates. More than 250 individual measurements are new to this version of the Compendium. For many compounds, numerous measurements are included, often collected by different researchers using different methods. Cetane number is a relative ranking of a fuel's autoignition characteristics for use in compression ignition engines; it is based on the amount of time between fuel injection and ignition, also known as ignition delay. The cetane number is typically measured either in a single-cylinder engine or a constant volume combustion chamber. Values in the previous Compendium derived from octane numbers have been removed, and replaced with a brief analysis of the correlation between cetane numbers and octane numbers. The discussion on the accuracy and precision of the most commonly used methods for measuring cetane has been expanded and the data has been annotated extensively to provide additional information that will help the reader judge the relative reliability of individual results.
Counting copy number and calories.
White, Stefan
2015-08-01
Copy number variation (CNV) at several genomic loci has been associated with different human traits and diseases, but in many cases the findings could not be replicated. A new study provides insights into the degree of variation present at the amylase locus and calls into question a previous association between amylase copy number and body mass index. PMID:26220133
Toddlers' Spontaneous Attention to Number
ERIC Educational Resources Information Center
Baroody, Arthur J.; Li, Xia; Lai, Meng-lung
2008-01-01
Hannula and Lehtinen (2001, 2005) defined spontaneous focusing on numerosity (SFON) as the tendency to notice the relatively abstract attribute of number despite the presence of other attributes. According to nativists, an innate concept of one to three directs young children's attention to these "intuitive numbers" in everyday situations--even…
Spontaneous Number Representation in Mosquitofish
ERIC Educational Resources Information Center
Dadda, Marco; Piffer, Laura; Agrillo, Christian; Bisazza, Angelo
2009-01-01
While there is convincing evidence that preverbal human infants and non-human primates can spontaneously represent number, considerable debate surrounds the possibility that such capacity is also present in other animals. Fish show a remarkable ability to discriminate between different numbers of social companions. Previous work has demonstrated…
Acceptance of Others (Number Form).
ERIC Educational Resources Information Center
Masters, James R.; Laverty, Grace E.
As part of the instrumentation to assess the effectiveness of the Schools Without Failure (SWF) program in 10 elementary schools in the New Castle, Pa. School District, the Acceptance of Others (Number Form) was prepared to determine pupil's attitudes toward classmates. Given a list of all class members, pupils are asked to circle a number from 1…
Regular Numbers and Mathematical Worlds
ERIC Educational Resources Information Center
Whitacre, Ian; Bouhjar, Khalid; Bishop, Jessica Pierson; Philipp, Randolph; Schappelle, Bonnie P.
2016-01-01
Rather than describing the challenges of integer learning in terms of a transition from positive to negative numbers, we have arrived at a different perspective: We view students as inhabiting distinct mathematical worlds consisting of particular types of numbers (as construed by the students). These worlds distinguish and illuminate students'…
Pseudo-Random Number Generators
NASA Technical Reports Server (NTRS)
Howell, L. W.; Rheinfurth, M. H.
1984-01-01
Package features comprehensive selection of probabilistic distributions. Monte Carlo simulations resorted to whenever systems studied not amenable to deterministic analyses or when direct experimentation not feasible. Random numbers having certain specified distribution characteristic integral part of simulations. Package consists of collector of "pseudorandom" number generators for use in Monte Carlo simulations.
Organizing, Concerns and Control Numbers.
ERIC Educational Resources Information Center
Washington, Gene
A heuristic procedure can be used to teach organizational skills to students of technical writing. Designed to allow students on their own to explore ways that numbers can be used to give a definite shape to technical information, its central feature is a matrix composed of a series of control numbers (horizontal axis) and organizing concerns…
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…
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…
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…
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?.
Number without a language model.
Spaepen, Elizabet; Coppola, Marie; Spelke, Elizabeth S; Carey, Susan E; Goldin-Meadow, Susan
2011-02-22
Cross-cultural studies suggest that access to a conventional language containing words that can be used for counting is essential to develop representations of large exact numbers. However, cultures that lack a conventional counting system typically differ from cultures that have such systems, not only in language but also in many other ways. As a result, it is difficult to isolate the effects of language on the development of number representations. Here we examine the numerical abilities of individuals who lack conventional language for number (deaf individuals who do not have access to a usable model for language, spoken or signed) but who live in a numerate culture (Nicaragua) and thus have access to other aspects of culture that might foster the development of number. These deaf individuals develop their own gestures, called homesigns, to communicate. We show that homesigners use gestures to communicate about number. However, they do not consistently extend the correct number of fingers when communicating about sets greater than three, nor do they always correctly match the number of items in one set to a target set when that target set is greater than three. Thus, even when integrated into a numerate society, individuals who lack input from a conventional language do not spontaneously develop representations of large exact numerosities.
Reynolds number influences in aeronautics
NASA Technical Reports Server (NTRS)
Bushnell, Dennis M.; Yip, Long P.; Yao, Chung-Sheng; Lin, John C.; Lawing, Pierce L.; Batina, John T.; Hardin, Jay C.; Horvath, Thomas J.; Fenbert, James W.; Domack, Christopher S.
1993-01-01
Reynolds number, a measure of the ratio of inertia to viscous forces, is a fundamental similarity parameter for fluid flows and therefore, would be expected to have a major influence in aerodynamics and aeronautics. Reynolds number influences are generally large, but monatomic, for attached laminar (continuum) flow; however, laminar flows are easily separated, inducing even stronger, non-monatomic, Reynolds number sensitivities. Probably the strongest Reynolds number influences occur in connection with transitional flow behavior. Transition can take place over a tremendous Reynolds number range, from the order of 20 x 10(exp 3) for 2-D free shear layers up to the order of 100 x 10(exp 6) for hypersonic boundary layers. This variability in transition behavior is especially important for complex configurations where various vehicle and flow field elements can undergo transition at various Reynolds numbers, causing often surprising changes in aerodynamics characteristics over wide ranges in Reynolds number. This is further compounded by the vast parameterization associated with transition, in that any parameter which influences mean viscous flow development (e.g., pressure gradient, flow curvature, wall temperature, Mach number, sweep, roughness, flow chemistry, shock interactions, etc.), and incident disturbance fields (acoustics, vorticity, particulates, temperature spottiness, even electro static discharges) can alter transition locations to first order. The usual method of dealing with the transition problem is to trip the flow in the generally lower Reynolds number wind tunnel to simulate the flight turbulent behavior. However, this is not wholly satisfactory as it results in incorrectly scaled viscous region thicknesses and cannot be utilized at all for applications such as turbine blades and helicopter rotors, nacelles, leading edge and nose regions, and High Altitude Long Endurance and hypersonic airbreathers where the transitional flow is an innately critical
Numbered nasal discs for waterfowl
Bartonek, J.C.; Dane, C.W.
1964-01-01
Numbered nasal discs were successfully used in studies requiring large numbers of individually marked waterfowl. The procedure for constructing these discs is outlined. Blue-winged teal (Anas discors) with 5/8-inch discs, and canvasback (Aythya valisineria) and redhead (A. americana) with 3/4-inch discs can be individually identified up to 50 and 80 yards, respectively, with a gunstock-mounted, 20-power spotting scope. The particular value of these markers is their durability, the number of combinations possible, and the apparent absence of behavioral or mortality influence among such species as the blue-winged teal.
Pinning of fermionic occupation numbers.
Schilling, Christian; Gross, David; Christandl, Matthias
2013-01-25
The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states. It has been suspected since at least the 1970s, and only proved very recently, that there is a multitude of further constraints on these numbers, generalizing the Pauli principle. Here, we provide the first analytic analysis of the physical relevance of these constraints. We compute the natural occupation numbers for the ground states of a family of interacting fermions in a harmonic potential. Intriguingly, we find that the occupation numbers are almost, but not exactly, pinned to the boundary of the allowed region (quasipinned). The result suggests that the physics behind the phenomenon is richer than previously appreciated. In particular, it shows that for some models, the generalized Pauli constraints play a role for the ground state, even though they do not limit the ground-state energy. Our findings suggest a generalization of the Hartree-Fock approximation.
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.
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)
Poison control center - emergency number
For a POISON EMERGENCY call: 1-800-222-1222 ANYWHERE IN THE UNITED STATES This national hotline number will let you ... is a free and confidential service. All local poison control centers in the United States use this ...
Atomic Structure - A Numbers Game
ERIC Educational Resources Information Center
George, W. O.; Vincent, A.
1975-01-01
Emphasizes the simplicity and elegance of early discoveries related to the hydrogen spectrum and provides an elementary experimental basis of quantum theory based on a "numbers game" which can be played by students. (Author/GS)
Flagella number among Naegleria flagellates.
John, D T; Cole, T B; John, R A
1991-01-01
Scanning electron microscopy was used to determine the number of flagella on the flagellates of Naegleria australiensis, N. fowleri, N. gruberi, and N. jadini. Although the majority of flagellates had 2 flagella, there was considerable variation among individual cells. The number of flagella per flagellate varied from 1-8, with 2.4 being the average number per cell. For the different species, the average number of flagella per cell ranged from 2.0 in N. jadini to 3.1 for N. australiensis. The greatest amount of variation occurred in N. australiensis, with only 43% of the cells having 2 flagella. By contrast, 92% of N. fowleri cells had 2 flagella. Naegleria jadini and N. gruberi were intermediate with 80% and 74% biflagellates, respectively.
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.
Quantum Adder of Classical Numbers
NASA Astrophysics Data System (ADS)
Cherkas, A. V.; Chivilikhin, S. A.
2016-08-01
In this article we show the precise algorithm of functioning of quantum adder on the example of addition of two 2-bit numbers. It consists of the quantum Fourier transformer and conditional rotation gates that let us use the minimum number of qubits to get the addition realization of the sum. Despite the fact that the algorithm uses the minimum amount of operations this accelerates the process of the adder.
Graspable Objects Shape Number Processing
Ranzini, Mariagrazia; Lugli, Luisa; Anelli, Filomena; Carbone, Rossella; Nicoletti, Roberto; Borghi, Anna M.
2011-01-01
The field of numerical cognition represents an interesting case for action-based theories of cognition, since number is a special kind of abstract concept. Several studies have shown that within the parietal lobes adjacent neural regions code numerical magnitude and grasping-related information. This anatomical proximity between brain areas involved in number and sensorimotor processes may account for interactions between numerical magnitude and action. In particular, recent studies have demonstrated a causal role of action perception on numerical magnitude processing. If objects are represented in terms of actions (affordances), the causal role of action on number processing should extend to the case of objects affordances. This study investigates the relationship between numbers and objects affordances in two experiments, without (Experiment 1) or with (Experiment 2) the requirement of an action (i.e., participants were asked to hold an object in their hands during the task). The task consisted in repeating aloud the odd or even digit within a pair depending on the type of the preceding or following object. Order of presentation (object–number vs. number–object), Object type (graspable vs. ungraspable), Object size (small vs. large), and Numerical magnitude (small vs. large) were manipulated for each experiment. Experiment 1 showed a facilitation – in terms of quicker responses – for graspable over ungraspable objects preceded by numbers, and an effect of numerical magnitude after the presentation of graspable objects. Experiment 2 demonstrated that the action execution enhanced overall the sensitivity to numerical magnitude, and that at the same time it interfered with the effects of objects affordances on number processing. Overall, these findings demonstrate that numbers and graspable objects are strongly interrelated, supporting the view that abstract concepts may be grounded in the motor experience. PMID:22164141
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.
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…
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'…
Transport numbers in transdermal iontophoresis.
Mudry, Blaise; Guy, Richard H; Delgado-Charro, M Begoña
2006-04-15
Parameters determining ionic transport numbers in transdermal iontophoresis have been characterized. The transport number of an ion (its ability to carry charge) is key to its iontophoretic delivery or extraction across the skin. Using small inorganic ions, the roles of molar fraction and mobility of the co- and counterions present have been demonstrated. A direct, constant current was applied across mammalian skin in vitro. Cations were anodally delivered from either simple M(+)Cl(-) solutions (single-ion case, M(+) = sodium, lithium, ammonium, potassium), or binary and quaternary mixtures thereof. Transport numbers were deduced from ion fluxes. In the single-ion case, maximum cationic fluxes directly related to the corresponding ionic aqueous mobilities were found. Addition of co-ions decreased the transport numbers of all cations relative to the single-ion case, the degree of effect depending upon the molar fraction and mobility of the species involved. With chloride as the principal counterion competing to carry current across the skin (the in vivo situation), a maximum limit on the single or collective cation transport number was 0.6-0.8. Overall, these results demonstrate how current flowing across the skin during transdermal iontophoresis is distributed between competing ions, and establish simple rules with which to optimize transdermal iontophoretic transport.
Stochastic low Reynolds number swimmers.
Golestanian, Ramin; Ajdari, Armand
2009-05-20
As technological advances allow us to fabricate smaller autonomous self-propelled devices, it is clear that at some point directed propulsion could not come from pre-specified deterministic periodic deformation of the swimmer's body and we need to develop strategies for extracting a net directed motion from a series of random transitions in the conformation space of the swimmer. We present a theoretical formulation for describing the 'stochastic motor' that drives the motion of low Reynolds number swimmers based on this concept, and use it to study the propulsion of a simple low Reynolds number swimmer, namely, the three-sphere swimmer model. When the detailed balanced is broken and the motor is driven out of equilibrium, it can propel the swimmer in the required direction. The formulation can be used to study optimal design strategies for molecular scale low Reynolds number swimmers.
Negative Numbers and Antimatter Particles
NASA Astrophysics Data System (ADS)
Tsan, Ung Chan
Dirac's equation states that an electron implies the existence of an antielectron with the same mass (more generally same arithmetic properties) and opposite charge (more generally opposite algebraic properties). Subsequent observation of antielectron validated this concept. This statement can be extended to all matter particles; observation of antiproton, antineutron, antideuton … is in complete agreement with this view. Recently antihypertriton was observed and 38 atoms of antihydrogen were trapped. This opens the path for use in precise testing of nature's fundamental symmetries. The symmetric properties of a matter particle and its mirror antimatter particle seem to be well established. Interactions operate on matter particles and antimatter particles as well. Conservation of matter parallels addition operating on positive and negative numbers. Without antimatter particles, interactions of the Standard Model (electromagnetism, strong interaction and weak interaction) cannot have the structure of group. Antimatter particles are characterized by negative baryonic number A or/and negative leptonic number L. Materialization and annihilation obey conservation of A and L (associated to all known interactions), explaining why from pure energy (A = 0, L = 0) one can only obtain a pair of matter particle antimatter particle — electron antielectron, proton and antiproton — via materialization where the mass of a pair of particle antiparticle gives back to pure energy with annihilation. These two mechanisms cannot change the difference in the number of matter particles and antimatter particles. Thus from pure energy only a perfectly symmetric (in number) universe could be generated as proposed by Dirac but observation showed that our universe is not symmetric, it is a matter universe which is nevertheless neutral. Fall of reflection symmetries shattered the prejudice that there is no way to define in an absolute way right and left or matter and antimatter
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
Project Solo; Newsletter Number Eleven.
ERIC Educational Resources Information Center
Pittsburgh Univ., PA. Project Solo.
An experimental 9th grade computer science syllabus is proposed. The syllabus would include the technical information needed for controlling and programing the computer in a number of modes and would preview some of the areas covered in the high school curriculum. A sample module of a topic not normally taught in high school--distance and…
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…
Adjuncts Build Strength in Numbers
ERIC Educational Resources Information Center
June, Audrey Williams
2012-01-01
When professors in positions that offer no chance of earning tenure begin to stack the faculty, campus dynamics start to change. Growing numbers of adjuncts make themselves more visible. They push for roles in governance, better pay and working conditions, and recognition for work well done. And they do so at institutions where tenured faculty,…
ERIC Educational Resources Information Center
Materiales, 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…
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)
Winding number constrained contour detection.
Ming, Yansheng; Li, Hongdong; He, Xuming
2015-01-01
Salient contour detection can benefit from the integration of both contour cues and region cues. However, this task is difficult due to different nature of region representations and contour representations. To solve this problem, this paper proposes an energy minimization framework based on winding number constraints. In this framework, both region cues, such as color/texture homogeneity, and contour cues, such as local contrast and continuity, are represented in a joint objective function, which has both region and contour labels. The key problem is how to design constraints that ensure the topological consistency of the two kinds of labels. Our technique is based on the topological concept of winding number. Using a fast method for winding number computation, a small number of linear constraints are derived to ensure label consistency. Our method is instantiated by ratio-based energy functions. By successfully integrating both region and contour cues, our method shows advantages over competitive methods. Our method is extended to incorporate user interaction, which leads to further improvements.
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)
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
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…
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…
Demonstratives and Number in Korean.
ERIC Educational Resources Information Center
Ree, Joe J.
It is a generally held view that Korean lacks articles and that the category "number" in this language is unproductive. That is, the nouns in Korean can be used freely as definite and indefinite, and as singular and plural, without overt grammatical markers. Contrary to this view, the claim is made in this paper that non-unique nouns, i.e., nouns…
ERIC Educational Resources Information Center
Surrena, Michelle
2011-01-01
In order to inspire her students to work in mixed media, the author chose to highlight the art of Jasper Johns and Robert Indiana, both of whom used numbers and letters as a main focus in their art. In this article, the author describes a mixed-media printmaking project. (Contains 2 online resources.)
Number Crunching: A Sheep's Tale
ERIC Educational Resources Information Center
Sam, Chris Lam
2005-01-01
In this article, the author talks about an allegorical tale which he has written as a message for teachers of mathematics. The story is about Gordon, who led a flock of small sheep. Gordon was a mathematics genius; however, his flock criticized his teaching of numbers and his boring lectures. His furry-god-farmer advised him to share his…
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).
Determination of the Schmidt number
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.
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.
Sasanguie, Delphine; Göbel, Silke M; Moll, Kristina; Smets, Karolien; Reynvoet, Bert
2013-03-01
In this study, the performance of typically developing 6- to 8-year-old children on an approximate number discrimination task, a symbolic comparison task, and a symbolic and nonsymbolic number line estimation task was examined. For the first time, children's performances on these basic cognitive number processing tasks were explicitly contrasted to investigate which of them is the best predictor of their future mathematical abilities. Math achievement was measured with a timed arithmetic test and with a general curriculum-based math test to address the additional question of whether the predictive association between the basic numerical abilities and mathematics achievement is dependent on which math test is used. Results revealed that performance on both mathematics achievement tests was best predicted by how well childrencompared digits. In addition, an association between performance on the symbolic number line estimation task and math achievement scores for the general curriculum-based math test measuring a broader spectrum of skills was found. Together, these results emphasize the importance of learning experiences with symbols for later math abilities.
Copy number variation and schizophrenia.
St Clair, David
2009-01-01
Over the last 12 months, a series of major articles have reported associations with schizophrenia of copy number variants at 1q21, 15q11.2, 15q13.3, 16p11.2, 22q12, and Neurexin 1 loci. These are rare high-penetrant mutations that increase risk not only of schizophrenia but also of a range of other psychiatric disorders including autism and mental retardation. In some cases, the same phenotype can occur irrespective of whether the copy number variant causes a deletion or duplication. Some of these mutations occur at very high rates in human populations, but because of reduced fecundity associated with major psychiatric disorders the overall frequency in the population remains low. These new findings raise fundamental clinical and scientific questions concerning classification of major neuropsychiatric disorders, modes of inheritance, diagnostics, and genetic counseling. Although the loci identified so far account for only a small proportion of cases, many more are likely to be discovered over the next few years. A major focus of research will be to identify the key, the genetic and environmental determinants of schizophrenia risk in carriers of these copy number variants, and to discover whether their rates of mutation are unstable or fixed. PMID:18990708
Vertebral numbers and human evolution.
Williams, Scott A; Middleton, Emily R; Villamil, Catalina I; Shattuck, Milena R
2016-01-01
Ever since Tyson (1699), anatomists have noted and compared differences in the regional numbers of vertebrae among humans and other hominoids. Subsequent workers interpreted these differences in phylogenetic, functional, and behavioral frameworks and speculated on the history of vertebral numbers during human evolution. Even in a modern phylogenetic framework and with greatly expanded sample sizes of hominoid species, researchers' conclusions vary drastically, positing that hominins evolved from either a "long-backed" (numerically long lumbar column) or a "short-backed" (numerically short lumbar column) ancestor. We show that these disparate interpretations are due in part to the use of different criteria for what defines a lumbar vertebra, but argue that, regardless of which lumbar definition is used, hominins are similar to their great ape relatives in possessing a short trunk, a rare occurrence in mammals and one that defines the clade Hominoidea. Furthermore, we address the recent claim that the early hominin thoracolumbar configuration is not distinct from that of modern humans and conclude that early hominins show evidence of "cranial shifting," which might explain the anomalous morphology of several early hominin fossils. Finally, we evaluate the competing hypotheses on numbers of vertebrae and argue that the current data support a hominin ancestor with an African ape-like short trunk and lower back.
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.
A Pseudo-Random Number Generator Based on Normal Numbers
Bailey, David H.
2004-12-31
In a recent paper, Richard Crandall and the present author established that each of a certain class of explicitly given real constants, uncountably infinite in number, is b-normal, for an integer that appears in the formula defining the constant. A b-normal constant is one where every string of m digits appears in the base-b expansion of the constant with limiting frequency b{sup -m}. This paper shows how this result can be used to fashion an efficient and effective pseudo-random number generator, which generates successive strings of binary digits from one of the constants in this class. The resulting generator, which tests slightly faster than a conventional linear congruential generator, avoids difficulties with large power-of-two data access strides that may occur when using conventional generators. It is also well suited for parallel processing--each processor can quickly and independently compute its starting value, with the collective sequence generated by all processors being the same as that generated by a single processor.
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.
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.
Health manpower: numbers, distribution, quality.
Petersdorf, R G
1975-05-01
Although the "health care crisis" was thought solvable by simply increasing the number of physicians, this has turned out not to be the case. The major problems in physician manpower are geographic maldistribution with a sparsity of physicians in the rural areas and the inner city and an overproduction of specialists. Certain changes in undergraduate and postgraduate medical education have contributed to this maldistribution. There is good evidence that there is an overproduction of surgeons and of medical subspecialists such as cardiologists. Much of the excess subspecialization can be laid at the foot of graduate training programs. The role of the specialty boards in affecting career choices and with them health manpower is analyzed. Some solutions to solve the geographic and specialty maldistribution problems are suggested. It is clear that more primary care physicians including general internists, family physicians, and pediatricians are needed.
Indexing the approximate number system.
Inglis, Matthew; Gilmore, Camilla
2014-01-01
Much recent research attention has focused on understanding individual differences in the approximate number system, a cognitive system believed to underlie human mathematical competence. To date researchers have used four main indices of ANS acuity, and have typically assumed that they measure similar properties. Here we report a study which questions this assumption. We demonstrate that the numerical ratio effect has poor test-retest reliability and that it does not relate to either Weber fractions or accuracy on nonsymbolic comparison tasks. Furthermore, we show that Weber fractions follow a strongly skewed distribution and that they have lower test-retest reliability than a simple accuracy measure. We conclude by arguing that in the future researchers interested in indexing individual differences in ANS acuity should use accuracy figures, not Weber fractions or numerical ratio effects. PMID:24361686
NASA Astrophysics Data System (ADS)
Blanco-Pillado, Jose J.; Olum, Ken D.; Shlaer, Benjamin
2014-01-01
Using recent simulation results, we provide the mass and speed spectrum of cosmic string loops. This is the quantity of primary interest for many phenomenological signatures of cosmic strings, and it can be accurately predicted using recently acquired detailed knowledge of the loop production function. We emphasize that gravitational smoothing of long strings plays a negligible role in determining the total number of existing loops. We derive a bound on the string tension imposed by recent constraints on the stochastic gravitational wave background from pulsar timing arrays, finding Gμ ≤2.8×10-9. We also provide a derivation of the Boltzmann equation for cosmic string loops in the language of differential forms.
Verification Challenges at Low Numbers
Benz, Jacob M.; Booker, Paul M.; McDonald, Benjamin S.
2013-06-01
Many papers have dealt with the political difficulties and ramifications of deep nuclear arms reductions, and the issues of “Going to Zero”. Political issues include extended deterrence, conventional weapons, ballistic missile defense, and regional and geo-political security issues. At each step on the road to low numbers, the verification required to ensure compliance of all parties will increase significantly. Looking post New START, the next step will likely include warhead limits in the neighborhood of 1000 . Further reductions will include stepping stones at1000 warheads, 100’s of warheads, and then 10’s of warheads before final elimination could be considered of the last few remaining warheads and weapons. This paper will focus on these three threshold reduction levels, 1000, 100’s, 10’s. For each, the issues and challenges will be discussed, potential solutions will be identified, and the verification technologies and chain of custody measures that address these solutions will be surveyed. It is important to note that many of the issues that need to be addressed have no current solution. In these cases, the paper will explore new or novel technologies that could be applied. These technologies will draw from the research and development that is ongoing throughout the national laboratory complex, and will look at technologies utilized in other areas of industry for their application to arms control verification.
Small number preference in guiding attention.
Cai, Yong-Chun; Li, Shuang-Xia
2015-02-01
Healthy individuals are usually biased toward small numbers when they are asked to mentally bisect number intervals or generate number sequences. Number magnitude may be represented spatially along a left-to-right mental number line. The preference for small numbers is believed to reflect the leftward spatial bias of this numerical representation. This study examined whether small numbers captured visual attention more than larger numbers. Participants were asked to detect a target pre-cued by a small or a large number. We found that the response was faster when the target was pre-cued by a small number than when pre-cued by a large number, suggesting that visual attention is preferentially allocated to small numbers. In addition, this attentional preference for small numbers was distinct for participants of different educational backgrounds. For science or engineering participants, this small number preference was enhanced by left-hand responding and was positively correlated with the small number preference in a random number generation task, suggesting that the small number preference was attributable to a leftward bias of the spatial representation. For liberal arts participants, however, left-hand responding did not enhance the small number preference and no correlations were found between the attention task and the random number generation task, suggesting that non-spatial processing mediated the small number preference. Our findings show that the small number preference occurs as early as the perceptual processing stage and distinct mechanisms underlie the preference for small numbers for participants with different educational backgrounds.
47 CFR 32.20 - Numbering convention.
Code of Federal Regulations, 2011 CFR
2011-10-01
... made by citing the account numbers to the right of the decimal point; e.g., Account 2232 rather than... FOR TELECOMMUNICATIONS COMPANIES General Instructions § 32.20 Numbering convention. (a) The number “32” (appearing to the left of the first decimal point) indicates the part number. (b) The numbers...
47 CFR 32.20 - Numbering convention.
Code of Federal Regulations, 2010 CFR
2010-10-01
... made by citing the account numbers to the right of the decimal point; e.g., Account 2232 rather than... FOR TELECOMMUNICATIONS COMPANIES General Instructions § 32.20 Numbering convention. (a) The number “32” (appearing to the left of the first decimal point) indicates the part number. (b) The numbers...
Small number preference in guiding attention.
Cai, Yong-Chun; Li, Shuang-Xia
2015-02-01
Healthy individuals are usually biased toward small numbers when they are asked to mentally bisect number intervals or generate number sequences. Number magnitude may be represented spatially along a left-to-right mental number line. The preference for small numbers is believed to reflect the leftward spatial bias of this numerical representation. This study examined whether small numbers captured visual attention more than larger numbers. Participants were asked to detect a target pre-cued by a small or a large number. We found that the response was faster when the target was pre-cued by a small number than when pre-cued by a large number, suggesting that visual attention is preferentially allocated to small numbers. In addition, this attentional preference for small numbers was distinct for participants of different educational backgrounds. For science or engineering participants, this small number preference was enhanced by left-hand responding and was positively correlated with the small number preference in a random number generation task, suggesting that the small number preference was attributable to a leftward bias of the spatial representation. For liberal arts participants, however, left-hand responding did not enhance the small number preference and no correlations were found between the attention task and the random number generation task, suggesting that non-spatial processing mediated the small number preference. Our findings show that the small number preference occurs as early as the perceptual processing stage and distinct mechanisms underlie the preference for small numbers for participants with different educational backgrounds. PMID:25354972
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…
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)
Avogadro Number and Mole: A Royal Confusion.
ERIC Educational Resources Information Center
Emiliani, Cesare
1991-01-01
There is a great deal of confusion in physics and chemistry textbooks, dictionaries, manuals, and handbooks about the definition of Avogadro's number and the term "mole." Avogadro's number is defined simply as the number of atomic mass units in one gram. Mole is defined as the mass of one Avogadro number of identical items. (Author/PR)
Contextual Effects on Number-Time Interaction
ERIC Educational Resources Information Center
Lu, Aitao; Hodges, Bert; Zhang, Jijia; Zhang, John X.
2009-01-01
Time perception has long been known to be affected by numerical representations. Recent studies further demonstrate that when participants estimate the duration of Arabic numbers, number magnitude, though task-irrelevant, biases duration judgment to produce underestimation for smaller numbers and overestimation for larger numbers. Such effects…
14 CFR 47.15 - Identification number.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 14 Aeronautics and Space 1 2010-01-01 2010-01-01 false Identification number. 47.15 Section 47.15... REGISTRATION General § 47.15 Identification number. (a) Number required. An applicant for Aircraft Registration must place a U.S. identification number (registration mark) on his Aircraft Registration...
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,...
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,...
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...
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...
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...
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....
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 8 2011-01-01 2011-01-01 false Docket number. 900.5 Section 900.5 Agriculture... Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter the proceeding may be referred to by such number....
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 8 2010-01-01 2010-01-01 false Lot number. 987.102 Section 987.102 Agriculture... RIVERSIDE COUNTY, CALIFORNIA Administrative Rules Definitions § 987.102 Lot number. Lot number is synonymous with code and means a combination of letters or numbers, or both, acceptable to the Committee,...
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...
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...
Mental number space in three dimensions.
Winter, Bodo; Matlock, Teenie; Shaki, Samuel; Fischer, Martin H
2015-10-01
A large number of experimental findings from neuroscience and experimental psychology demonstrated interactions between spatial cognition and numerical cognition. In particular, many researchers posited a horizontal mental number line, where small numbers are thought of as being to the left of larger numbers. This review synthesizes work on the mental association between space and number, indicating the existence of multiple spatial mappings: recent research has found associations between number and vertical space, as well as associations between number and near/far space. We discuss number space in three dimensions with an eye on potential origins of the different number mappings, and how these number mappings fit in with our current knowledge of brain organization and brain-culture interactions. We derive novel predictions and show how this research fits into a general view of cognition as embodied, grounded and situated.
Integrated-Circuit Pseudorandom-Number Generator
NASA Technical Reports Server (NTRS)
Steelman, James E.; Beasley, Jeff; Aragon, Michael; Ramirez, Francisco; Summers, Kenneth L.; Knoebel, Arthur
1992-01-01
Integrated circuit produces 8-bit pseudorandom numbers from specified probability distribution, at rate of 10 MHz. Use of Boolean logic, circuit implements pseudorandom-number-generating algorithm. Circuit includes eight 12-bit pseudorandom-number generators, outputs are uniformly distributed. 8-bit pseudorandom numbers satisfying specified nonuniform probability distribution are generated by processing uniformly distributed outputs of eight 12-bit pseudorandom-number generators through "pipeline" of D flip-flops, comparators, and memories implementing conditional probabilities on zeros and ones.
The Translated Dowling Polynomials and Numbers
Mangontarum, Mahid M.; Macodi-Ringia, Amila P.; Abdulcarim, Normalah S.
2014-01-01
More properties for the translated Whitney numbers of the second kind such as horizontal generating function, explicit formula, and exponential generating function are proposed. Using the translated Whitney numbers of the second kind, we will define the translated Dowling polynomials and numbers. Basic properties such as exponential generating functions and explicit formula for the translated Dowling polynomials and numbers are obtained. Convexity, integral representation, and other interesting identities are also investigated and presented. We show that the properties obtained are generalizations of some of the known results involving the classical Bell polynomials and numbers. Lastly, we established the Hankel transform of the translated Dowling numbers. PMID:27433494
40 CFR 86.1204 - Section numbering.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 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...
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...
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)
Algebraic structures of sequences of numbers
NASA Astrophysics Data System (ADS)
Huang, I.-Chiau
2012-09-01
For certain sequences of numbers, commutative rings with a module structure over a non-commutative ring are constructed. Identities of these numbers are considered as realizations of algebraic relations.
Quantity Cognition: Numbers, Numerosity, Zero and Mathematics.
Harvey, Ben M
2016-05-23
Physical quantities differ from abstract numbers and mathematics, but recent results are revealing the neural representation of both: a new study demonstrates how an absence of quantity is transformed into a representation of zero as a number.
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....
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...
7 CFR 29.32 - Identification number.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Identification number. 29.32 Section 29.32 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... INSPECTION Regulations Definitions § 29.32 Identification number. A number or a combination of letters...
46 CFR Sec. 2 - Voyage numbers.
Code of Federal Regulations, 2013 CFR
2013-10-01
... voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with... General Agent shall affix his abbreviated designation and initial voyage numbers, as NSA-13/XYZ-1....
46 CFR Sec. 2 - Voyage numbers.
Code of Federal Regulations, 2011 CFR
2011-10-01
... voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with... General Agent shall affix his abbreviated designation and initial voyage numbers, as NSA-13/XYZ-1....
46 CFR Sec. 2 - Voyage numbers.
Code of Federal Regulations, 2010 CFR
2010-10-01
... voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with... General Agent shall affix his abbreviated designation and initial voyage numbers, as NSA-13/XYZ-1....
46 CFR Sec. 2 - Voyage numbers.
Code of Federal Regulations, 2012 CFR
2012-10-01
... voyage No. 1 having the prefixed designation NSA and followed by the General Agents' abbreviated designation and voyage number, as NSA-1/ABC-1. (b) The continuity of NSA voyage numbers shall not change with... General Agent shall affix his abbreviated designation and initial voyage numbers, as NSA-13/XYZ-1....
46 CFR Sec. 2 - Voyage numbers.
Code of Federal Regulations, 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....
Evaluating Number Sense in Workforce Students
ERIC Educational Resources Information Center
Steinke, Dorothea A.
2015-01-01
Earlier institution-sponsored research revealed that about 20% of students in community college basic math and pre-algebra programs lacked a sense of part-whole relationships with whole numbers. Using the same tool with a group of 86 workforce students, about 75% placed five whole numbers on an empty number line in a way that indicated lack of…
Fascinating Fibonaccis: Mystery and Magic in Numbers.
ERIC Educational Resources Information Center
Garland, Trudi Hammel
This document presents activities and information related to Fibonacci numbers, which are based upon the Golden Ratio, in areas of the arts, sciences, and mathematics. The work is organized into eight chapters: (1) "Origins and Definitions"; (2) "Fibonacci Numbers in Nature"; (3) "Fibonacci Numbers in Art and Architecture"; (4) "Fibonacci Numbers…
Children's Use of Number Line Estimation Strategies
ERIC Educational Resources Information Center
Peeters, Dominique; Degrande, Tine; Ebersbach, Mirjam; Verschaffel, Lieven; Luwel, Koen
2016-01-01
This study tested whether second graders use benchmark-based strategies when solving a number line estimation (NLE) task. Participants were assigned to one of three conditions based on the availability of benchmarks provided on the number line. In the bounded condition, number lines were only bounded at both sides by 0 and 200, while the midpoint…
46 CFR Sec. 7 - Job order numbering.
Code of Federal Regulations, 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...
46 CFR Sec. 7 - Job order numbering.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 46 Shipping 8 2011-10-01 2011-10-01 false Job order numbering. Sec. 7 Section 7 Shipping MARITIME... REPAIRS UNDER NATIONAL SHIPPING AUTHORITY MASTER LUMP SUM REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP Contract number shall be inserted in every job order and supplemental...
46 CFR Sec. 7 - Job order numbering.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 46 Shipping 8 2013-10-01 2013-10-01 false Job order numbering. Sec. 7 Section 7 Shipping MARITIME... REPAIRS UNDER NATIONAL SHIPPING AUTHORITY MASTER LUMP SUM REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP Contract number shall be inserted in every job order and supplemental...
46 CFR Sec. 7 - Job order numbering.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 46 Shipping 8 2012-10-01 2012-10-01 false Job order numbering. Sec. 7 Section 7 Shipping MARITIME... REPAIRS UNDER NATIONAL SHIPPING AUTHORITY MASTER LUMP SUM REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP Contract number shall be inserted in every job order and supplemental...
46 CFR Sec. 7 - Job order numbering.
Code of Federal Regulations, 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...
Code of Federal Regulations, 2011 CFR
2011-07-01
... 32 National Defense 6 2011-07-01 2011-07-01 false Numbers. 1602.19 Section 1602.19 National Defense Other Regulations Relating to National Defense SELECTIVE SERVICE SYSTEM DEFINITIONS § 1602.19 Numbers. Cardinal numbers may be expressed by Arabic or Roman symbols....
Code of Federal Regulations, 2014 CFR
2014-07-01
... 32 National Defense 6 2014-07-01 2014-07-01 false Numbers. 1602.19 Section 1602.19 National Defense Other Regulations Relating to National Defense SELECTIVE SERVICE SYSTEM DEFINITIONS § 1602.19 Numbers. Cardinal numbers may be expressed by Arabic or Roman symbols....
Code of Federal Regulations, 2013 CFR
2013-07-01
... 32 National Defense 6 2013-07-01 2013-07-01 false Numbers. 1602.19 Section 1602.19 National Defense Other Regulations Relating to National Defense SELECTIVE SERVICE SYSTEM DEFINITIONS § 1602.19 Numbers. Cardinal numbers may be expressed by Arabic or Roman symbols....
Code of Federal Regulations, 2010 CFR
2010-07-01
... 32 National Defense 6 2010-07-01 2010-07-01 false Numbers. 1602.19 Section 1602.19 National Defense Other Regulations Relating to National Defense SELECTIVE SERVICE SYSTEM DEFINITIONS § 1602.19 Numbers. Cardinal numbers may be expressed by Arabic or Roman symbols....
Code of Federal Regulations, 2012 CFR
2012-07-01
... 32 National Defense 6 2012-07-01 2012-07-01 false Numbers. 1602.19 Section 1602.19 National Defense Other Regulations Relating to National Defense SELECTIVE SERVICE SYSTEM DEFINITIONS § 1602.19 Numbers. Cardinal numbers may be expressed by Arabic or Roman symbols....
47 CFR 51.203 - Number portability.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 47 Telecommunication 3 2010-10-01 2010-10-01 false Number portability. 51.203 Section 51.203 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES (CONTINUED) INTERCONNECTION Obligations of All Local Exchange Carriers § 51.203 Number portability. The rules governing number...
Technology Transfer Automated Retrieval System (TEKTRAN)
Number of functional teats is an important trait in commercial swine production. As litter size continues to increase, the number of teats must also increase to supply nutrition to all piglets. The pig displays considerable variation for number of teats; therefore, a genome-wide association (GWA) an...
The Decimal Representation of Real Numbers
ERIC Educational Resources Information Center
Kalapodi, A.
2010-01-01
The representation of natural numbers in decimal form is an unequivocal procedure while for the representation of real numbers some ambiguities concerning the existence of infinitely many digits equal to 9 still emerge. One of the most frequently confronted misunderstandings is whether 0.999...equals 1 or not, and if not what number does this…
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…
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)
49 CFR 230.47 - Boiler number.
Code of Federal Regulations, 2010 CFR
2010-10-01
..., DEPARTMENT OF TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges § 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known, shall... 49 Transportation 4 2010-10-01 2010-10-01 false Boiler number. 230.47 Section...
49 CFR 230.47 - Boiler number.
Code of Federal Regulations, 2011 CFR
2011-10-01
..., DEPARTMENT OF TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges § 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known, shall... 49 Transportation 4 2011-10-01 2011-10-01 false Boiler number. 230.47 Section...
49 CFR 230.47 - Boiler number.
Code of Federal Regulations, 2012 CFR
2012-10-01
..., DEPARTMENT OF TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges § 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known, shall... 49 Transportation 4 2012-10-01 2012-10-01 false Boiler number. 230.47 Section...
49 CFR 230.47 - Boiler number.
Code of Federal Regulations, 2013 CFR
2013-10-01
..., DEPARTMENT OF TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges § 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known, shall... 49 Transportation 4 2013-10-01 2013-10-01 false Boiler number. 230.47 Section...
49 CFR 230.47 - Boiler number.
Code of Federal Regulations, 2014 CFR
2014-10-01
..., DEPARTMENT OF TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges § 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known, shall... 49 Transportation 4 2014-10-01 2014-10-01 false Boiler number. 230.47 Section...
46 CFR 169.515 - Number required.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 46 Shipping 7 2010-10-01 2010-10-01 false Number required. 169.515 Section 169.515 Shipping COAST... and Firefighting Equipment Primary Lifesaving Equipment § 169.515 Number required. (a) Except as... additional inflatable liferafts to accommodate 25% of the persons on board or the number of...
20 CFR 404.1220 - Identification numbers.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 20 Employees' Benefits 2 2011-04-01 2011-04-01 false Identification numbers. 404.1220 Section 404... § 404.1220 Identification numbers. (a) State and local governments. When a State submits a modification... will assign a special identification number to each political subdivision included in that...
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 1 2010-01-01 2010-01-01 false Docket number. 1.414 Section 1.414 Agriculture Office... Conservation and Shortage Relief Act of 1990 (16 U.S.C. 620 et seq.) § 1.414 Docket number. Each proceeding, following its institution, shall be assigned a docket number by the Hearing Clerk, and thereafter...
46 CFR 10.207 - Identification number.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 46 Shipping 1 2011-10-01 2011-10-01 false Identification number. 10.207 Section 10.207 Shipping... CREDENTIAL General Requirements for All Merchant Mariner Credentials § 10.207 Identification number. For recordkeeping purposes only, a mariner's official MMC identification number is the individual's social...
40 CFR 265.11 - Identification number.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 40 Protection of Environment 25 2010-07-01 2010-07-01 false Identification number. 265.11 Section... FACILITIES General Facility Standards § 265.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45...
24 CFR 3280.6 - Serial number.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 24 Housing and Urban Development 5 2010-04-01 2010-04-01 false Serial number. 3280.6 Section 3280... DEVELOPMENT MANUFACTURED HOME CONSTRUCTION AND SAFETY STANDARDS General § 3280.6 Serial number. (a) A manufactured home serial number which will identify the manufacturer and the state in which the...
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 8 2011-01-01 2011-01-01 false Docket number. 900.54 Section 900.54 Agriculture... Governing Proceedings on Petitions To Modify or To Be Exempted From Marketing Orders § 900.54 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by...
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 1 2011-01-01 2011-01-01 false Docket number. 1.134 Section 1.134 Agriculture Office... Adjudicatory Proceedings Instituted by the Secretary Under Various Statutes § 1.134 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the Hearing...
47 CFR 95.671 - Serial number.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 47 Telecommunication 5 2011-10-01 2011-10-01 false Serial number. 95.671 Section 95.671 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES PERSONAL RADIO... number. The serial number of each CB transmitter must be engraved on the transmitter chassis....
7 CFR 29.133 - Identification number.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Identification number. 29.133 Section 29.133... REGULATIONS TOBACCO INSPECTION Regulations Miscellaneous § 29.133 Identification number. The Director may require the use of official identification numbers in connection with tobacco certificated or...
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 1 2011-01-01 2011-01-01 false Docket number. 1.414 Section 1.414 Agriculture Office... Conservation and Shortage Relief Act of 1990 (16 U.S.C. 620 et seq.) § 1.414 Docket number. Each proceeding, following its institution, shall be assigned a docket number by the Hearing Clerk, and thereafter...
46 CFR 10.207 - Identification number.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 46 Shipping 1 2010-10-01 2010-10-01 false Identification number. 10.207 Section 10.207 Shipping... CREDENTIAL General Requirements for All Merchant Mariner Credentials § 10.207 Identification number. For recordkeeping purposes only, a mariner's official MMC identification number is the individual's social...
47 CFR 32.6622 - Number services.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 47 Telecommunication 2 2010-10-01 2010-10-01 false Number services. 32.6622 Section 32.6622... FOR TELECOMMUNICATIONS COMPANIES Instructions for Expense Accounts § 32.6622 Number services. This account shall include costs incurred in providing customer number and classified listings. This...
40 CFR 264.11 - Identification number.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 40 Protection of Environment 26 2011-07-01 2011-07-01 false Identification number. 264.11 Section... Facility Standards § 264.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR 12746)....
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 1 2010-01-01 2010-01-01 false Docket number. 1.134 Section 1.134 Agriculture Office... Adjudicatory Proceedings Instituted by the Secretary Under Various Statutes § 1.134 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the Hearing...
7 CFR 29.133 - Identification number.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 2 2011-01-01 2011-01-01 false Identification number. 29.133 Section 29.133... REGULATIONS TOBACCO INSPECTION Regulations Miscellaneous § 29.133 Identification number. The Director may require the use of official identification numbers in connection with tobacco certificated or...
46 CFR 169.515 - Number required.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 46 Shipping 7 2011-10-01 2011-10-01 false Number required. 169.515 Section 169.515 Shipping COAST... and Firefighting Equipment Primary Lifesaving Equipment § 169.515 Number required. (a) Except as... additional inflatable liferafts to accommodate 25% of the persons on board or the number of...
27 CFR 24.115 - Registry number.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Registry number. 24.115... OF THE TREASURY LIQUORS WINE Establishment and Operations Application § 24.115 Registry number. Upon approval of the application, the appropriate TTB officer will assign a registry number to the bonded...
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 10 2011-01-01 2011-01-01 false Docket number. 1200.6 Section 1200.6 Agriculture... Governing Proceedings To Formulate and Amend an Order § 1200.6 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter...
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 10 2010-01-01 2010-01-01 false Docket number. 1200.6 Section 1200.6 Agriculture... Governing Proceedings To Formulate and Amend an Order § 1200.6 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter...
47 CFR 51.203 - Number portability.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 47 Telecommunication 3 2011-10-01 2011-10-01 false Number portability. 51.203 Section 51.203 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES (CONTINUED) INTERCONNECTION Obligations of All Local Exchange Carriers § 51.203 Number portability. The rules governing number...
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…
20 CFR 404.1220 - Identification numbers.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 20 Employees' Benefits 2 2010-04-01 2010-04-01 false Identification numbers. 404.1220 Section 404... § 404.1220 Identification numbers. (a) State and local governments. When a State submits a modification... will assign a special identification number to each political subdivision included in that...
40 CFR 265.11 - Identification number.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 40 Protection of Environment 26 2011-07-01 2011-07-01 false Identification number. 265.11 Section... FACILITIES General Facility Standards § 265.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45...
47 CFR 32.6622 - Number services.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 47 Telecommunication 2 2011-10-01 2011-10-01 false Number services. 32.6622 Section 32.6622... FOR TELECOMMUNICATIONS COMPANIES Instructions for Expense Accounts § 32.6622 Number services. This account shall include costs incurred in providing customer number and classified listings. This...
Code of Federal Regulations, 2011 CFR
2011-10-01
... 47 Telecommunication 1 2011-10-01 2011-10-01 false File numbers. 1.1405 Section 1.1405... Procedures § 1.1405 File numbers. Each complaint which appears to be essentially complete under § 1.1404 will be accepted and assigned a file number. Such assignment is for administrative purposes only and...
47 CFR 95.671 - Serial number.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 47 Telecommunication 5 2010-10-01 2010-10-01 false Serial number. 95.671 Section 95.671 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES PERSONAL RADIO... number. The serial number of each CB transmitter must be engraved on the transmitter chassis....
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 8 2010-01-01 2010-01-01 false Docket number. 900.54 Section 900.54 Agriculture... Governing Proceedings on Petitions To Modify or To Be Exempted From Marketing Orders § 900.54 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by...
27 CFR 24.115 - Registry number.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Registry number. 24.115... OF THE TREASURY LIQUORS WINE Establishment and Operations Application § 24.115 Registry number. Upon approval of the application, the appropriate TTB officer will assign a registry number to the bonded...
24 CFR 3280.6 - Serial number.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 24 Housing and Urban Development 5 2011-04-01 2011-04-01 false Serial number. 3280.6 Section 3280... DEVELOPMENT MANUFACTURED HOME CONSTRUCTION AND SAFETY STANDARDS General § 3280.6 Serial number. (a) A manufactured home serial number which will identify the manufacturer and the state in which the...
40 CFR 264.11 - Identification number.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 40 Protection of Environment 25 2010-07-01 2010-07-01 false Identification number. 264.11 Section... Facility Standards § 264.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR 12746)....
47 CFR 64.1506 - Number designation.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 47 Telecommunication 3 2011-10-01 2011-10-01 false Number designation. 64.1506 Section 64.1506... Number designation. Any interstate service described in § 64.1501(a)(1)-(2), and not subject to the exclusions contained in § 64.1501(a)(4), shall be offered only through telephone numbers beginning with a...
Number-Theoretic Functions via Convolution Rings.
ERIC Educational Resources Information Center
Berberian, S. K.
1992-01-01
Demonstrates the number theory property that the number of divisors of an integer n times the number of positive integers k, less than or equal to and relatively prime to n, equals the sum of the divisors of n using theory developed about multiplicative functions, the units of a convolution ring, and the Mobius Function. (MDH)
An Evaluation of App-Based and Paper-Based Number Lines for Teaching Number Comparison
ERIC Educational Resources Information Center
Weng, Pei-Lin; Bouck, Emily C.
2016-01-01
Number comparison is a fundamental skill required for academic and functional mathematics (e.g., time, money, purchasing) for students with disabilities. The most commonly used method to teach number comparison is number lines. Although historically paper number lines are used, app-based number lines may offer greater flexibility. This study…
27 CFR 20.179 - Package identification number or serial number.
Code of Federal Regulations, 2011 CFR
2011-04-01
... number or serial number. 20.179 Section 20.179 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO... Package identification number or serial number. (a) Requirement. A dealer who fills packages with specially denatured spirits shall mark each package with a package identification number, in accordance...
27 CFR 20.179 - Package identification number or serial number.
Code of Federal Regulations, 2010 CFR
2010-04-01
... number or serial number. 20.179 Section 20.179 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO... Package identification number or serial number. (a) Requirement. A dealer who fills packages with specially denatured spirits shall mark each package with a package identification number, in accordance...
On the binary expansions of algebraic numbers
Bailey, David H.; Borwein, Jonathan M.; Crandall, Richard E.; Pomerance, Carl
2003-07-01
Employing concepts from additive number theory, together with results on binary evaluations and partial series, we establish bounds on the density of 1's in the binary expansions of real algebraic numbers. A central result is that if a real y has algebraic degree D > 1, then the number {number_sign}(|y|, N) of 1-bits in the expansion of |y| through bit position N satisfies {number_sign}(|y|, N) > CN{sup 1/D} for a positive number C (depending on y) and sufficiently large N. This in itself establishes the transcendency of a class of reals {summation}{sub n{ge}0} 1/2{sup f(n)} where the integer-valued function f grows sufficiently fast; say, faster than any fixed power of n. By these methods we re-establish the transcendency of the Kempner--Mahler number {summation}{sub n{ge}0}1/2{sup 2{sup n}}, yet we can also handle numbers with a substantially denser occurrence of 1's. Though the number z = {summation}{sub n{ge}0}1/2{sup n{sup 2}} has too high a 1's density for application of our central result, we are able to invoke some rather intricate number-theoretical analysis and extended computations to reveal aspects of the binary structure of z{sup 2}.
Multifractal Analysis of Sunspot Number Time Series
NASA Astrophysics Data System (ADS)
Kasde, Satish Kumar; Gwal, Ashok Kumar; Sondhiya, Deepak Kumar
2016-07-01
Multifractal analysis based approaches have been recently developed as an alternative framework to study the complex dynamical fluctuations in sunspot numbers data including solar cycles 20 to 23 and ascending phase of current solar cycle 24.To reveal the multifractal nature, the time series data of monthly sunspot number are analyzed by singularity spectrum and multi resolution wavelet analysis. Generally, the multifractility in sunspot number generate turbulence with the typical characteristics of the anomalous process governing the magnetosphere and interior of Sun. our analysis shows that singularities spectrum of sunspot data shows well Gaussian shape spectrum, which clearly establishes the fact that monthly sunspot number has multifractal character. The multifractal analysis is able to provide a local and adaptive description of the cyclic components of sunspot number time series, which are non-stationary and result of nonlinear processes. Keywords: Sunspot Numbers, Magnetic field, Multifractal analysis and wavelet Transform Techniques.
Relativistic theory of tidal Love numbers
Binnington, Taylor; Poisson, Eric
2009-10-15
In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neutron star can be measured by Earth-based gravitational-wave detectors. We consider a spherical body deformed by an external tidal field, and provide precise and meaningful definitions for electric-type and magnetic-type Love numbers; and these are computed for polytropic equations of state. The theory applies to black holes as well, and we find that the relativistic Love numbers of a nonrotating black hole are all zero.
Deafness for the meanings of number words.
Caño, Agnès; Rapp, Brenda; Costa, Albert; Juncadella, Montserrat
2008-01-15
We describe the performance of an aphasic individual who showed a selective impairment affecting his comprehension of auditorily presented number words and not other word categories. His difficulty in number word comprehension was restricted to the auditory modality, given that with visual stimuli (written words, Arabic numerals and pictures) his comprehension of number and non-number words was intact. While there have been previous reports of selective difficulty or sparing of number words at the semantic and post-semantic levels, this is the first reported case of a pre-semantic deficit that is specific to the category of number words. This constitutes evidence that lexical semantic distinctions are respected by modality-specific neural mechanisms responsible for providing access to the meanings of words.
Self-correcting random number generator
Humble, Travis S.; Pooser, Raphael C.
2016-09-06
A system and method for generating random numbers. The system may include a random number generator (RNG), such as a quantum random number generator (QRNG) configured to self-correct or adapt in order to substantially achieve randomness from the output of the RNG. By adapting, the RNG may generate a random number that may be considered random regardless of whether the random number itself is tested as such. As an example, the RNG may include components to monitor one or more characteristics of the RNG during operation, and may use the monitored characteristics as a basis for adapting, or self-correcting, to provide a random number according to one or more performance criteria.
Deafness for the meanings of number words
Caño, Agnès; Rapp, Brenda; Costa, Albert; Juncadella, Montserrat
2008-01-01
We describe the performance of an aphasic individual who showed a selective impairment affecting his comprehension of auditorily presented number words and not other word categories. His difficulty in number word comprehension was restricted to the auditory modality, given that with visual stimuli (written words, Arabic numerals and pictures) his comprehension of number and non-number words was intact. While there have been previous reports of selective difficulty or sparing of number words at the semantic and post-semantic levels, this is the first reported case of a pre-semantic deficit that is specific to the category of number words. This constitutes evidence that lexical semantic distinctions are respected by modality-specific neural mechanisms responsible for providing access to the meanings of words. PMID:17915265
Factoring numbers with a single interferogram
Tamma, Vincenzo; Zhang Heyi; He Xuehua; Shih Yanhua; Garuccio, Augusto; Schleich, Wolfgang P.
2011-02-15
We construct an analog computer based on light interference to encode the hyperbolic function f({zeta}){identical_to}1/{zeta} into a sequence of skewed curlicue functions. The resulting interferogram when scaled appropriately allows us to find the prime number decompositions of integers. We implement this idea exploiting polychromatic optical interference in a multipath interferometer and factor seven-digit numbers. We give an estimate for the largest number that can be factored by this scheme.
Demonstrations of the Enormity of Avogadro's Number.
ERIC Educational Resources Information Center
Diemente, Damon
1998-01-01
Describes three calculations used to make students aware of the size of Avogadro's number: (1) the new size of a 6-inch diameter ball with volume increased by a factor of Avogadro's number; (2) the number of moles of sand grains in the Sahara Desert; and (3) the dimensions and length of a mole of hydrogen atoms shaped into a cube, a square, and a…
Graceful label numbering in optical MPLS networks
NASA Astrophysics Data System (ADS)
Arkut, Ibrahim C.; Arkut, Refik C.; Ghani, Nasir
2000-09-01
This paper explores the positive effects of the new multi protocol label switching (MPLS) routing platform in IP networks. In particular, novel node numbering algorithms based upon graceful numbering of trees are presented. The first part presents the application of the well-known graceful numbering of spanning caterpillars to the MPLS multicast routing problem. In the second part of the paper, the numbering algorithm is adjusted for the case of unicast routing in the framework of IP-over-WDM optical networks using MPLS, e.g., particularly lambda-labeling and multi protocol lambda switching.
Generalized Ramsey numbers through adiabatic quantum optimization
NASA Astrophysics Data System (ADS)
Ranjbar, Mani; Macready, William G.; Clark, Lane; Gaitan, Frank
2016-09-01
Ramsey theory is an active research area in combinatorics whose central theme is the emergence of order in large disordered structures, with Ramsey numbers marking the threshold at which this order first appears. For generalized Ramsey numbers r( G, H), the emergent order is characterized by graphs G and H. In this paper we: (i) present a quantum algorithm for computing generalized Ramsey numbers by reformulating the computation as a combinatorial optimization problem which is solved using adiabatic quantum optimization; and (ii) determine the Ramsey numbers r({{T}}m,{{T}}n) for trees of order m,n = 6,7,8, most of which were previously unknown.
CRC octane number requirement survey 1992
Not Available
1993-08-01
An annual statistical survey of octane number requirements of current model vehicles is conducted by the Coordinating Research Council, Inc. Test data have been obtained by ten companies on 184 1992 vehicles including passenger cars and light-duty trucks and vans, of which 88 were equipped with knock sensors. Octane number requirements were determined by testing at maximum-throttle conditions, as well as at part-throttle, with four unleaded fuel series of varying sensitivities, one containing 15 percent methyl tertiary butyl ether. Requirements are expressed as the (R+M)/2 octane number, Research octane number, and Motor octane number of the reference fuel producing knock which was recurrent and repeatable at the lowest audible level. Estimated octane number requirements for the total vehicles are weighted in proportion to the 1992 vehicle model production and/or sales figures. The octane number requirements of 1992 models with average sensitivity unleaded fuels were 85.1 (R+M)/2 octane numbers at the 50 percent satisfaction level, and 92.0 (R+M)/2 octane numbers at the 90 percent satisfaction level. In order to make a more powerful test of statistical significance of the FBRUM fuel series, the 1991 ONRS was pooled with the 1992 ONRS and compared with the pooled data for the FBRU fuel series. There was no significant difference between the two fuel series up to about 90 percent satisfaction. Beyond 90 percent satisfaction, the variability in the data is high.
CRC octane-number-requirement survey, 1990
Not Available
1991-07-01
An annual statistical survey of octane number requirements of current model vehicles is conducted by the Coordinating Research Council, Inc. Test data have been obtained by seventeen companies on 356 1990 vehicles including passenger cars and light-duty trucks and vans, of which 169 were equipped with knock sensors. Octane number requirements were determined by testing at maximum-throttle conditions, as well as at part-throttle, with three unleaded fuel series of varying sensitivities. Requirements are expressed as the (R+M)/2 octane number, Research octane number, and Motor octane number of the reference fuel producing knock which was recurrent and repeatable at the lowest audible level. Estimated octane number requirements for the total vehicles are weighted in proportion to the 1990 vehicle model production and/or sales figures. The octane number requirements of 1990 models with average sensitivity unleaded fuels were 85.4 (R+M)/2 octane numbers at the 50 percent satisfaction level, and 89.2 (R+M)/2 octane numbers at the 90 percent satisfaction level.
CRC octane number requirement survey for 1989
Not Available
1990-08-01
An annual statistical survey of octane number requirements of current model vehicles is conducted by the Coordinating Research Council, Inc. Test data have been obtained by eighteen companies on 391 1989 vehicles including passenger cars and light-duty trucks and vans, of which 179 were equipped with knock sensors. Maximum octane number requirements were determined by testing at maximum-throttle conditions, as well as at part-throttle, with three unleaded fuel series of varying sensitivities. Requirements are expressed as the (R+M)/2 octane number, Research octane number, and Motor octane number of the reference fuel producing knock which was recurrent and repeatable at the lowest audible level. Estimated octane number requirements for the total vehicles are weighted in proportion to the 1989 vehicle model production and/or sales figures. The maximum octane number requirements of 1989 models with average sensitivity unleaded fuels were 85.1 (R+M)/2 octane numbers at the 50 percent satisfaction level, and 89.2 (R+M)/2 octane numbers at the 90 percent satisfaction level. Comparison with previous Surveys are made in this report.
Calculating Atomic Number Densities for Uranium
1993-01-01
Provides method to calculate atomic number densities of selected uranium compounds and hydrogenous moderators for use in nuclear criticality safety analyses at gaseous diffusion uranium enrichment facilities.
Continental anthropogenic primary particle number emissions
NASA Astrophysics Data System (ADS)
Paasonen, Pauli; Kupiainen, Kaarle; Klimont, Zbigniew; Visschedijk, Antoon; Denier van der Gon, Hugo A. C.; Amann, Markus
2016-06-01
Atmospheric aerosol particle number concentrations impact our climate and health in ways different from those of aerosol mass concentrations. However, the global, current and future anthropogenic particle number emissions and their size distributions are so far poorly known. In this article, we present the implementation of particle number emission factors and the related size distributions in the GAINS (Greenhouse Gas-Air Pollution Interactions and Synergies) model. This implementation allows for global estimates of particle number emissions under different future scenarios, consistent with emissions of other pollutants and greenhouse gases. In addition to determining the general particulate number emissions, we also describe a method to estimate the number size distributions of the emitted black carbon particles. The first results show that the sources dominating the particle number emissions are different to those dominating the mass emissions. The major global number source is road traffic, followed by residential combustion of biofuels and coal (especially in China, India and Africa), coke production (Russia and China), and industrial combustion and processes. The size distributions of emitted particles differ across the world, depending on the main sources: in regions dominated by traffic and industry, the number size distribution of emissions peaks in diameters range from 20 to 50 nm, whereas in regions with intensive biofuel combustion and/or agricultural waste burning, the emissions of particles with diameters around 100 nm are dominant. In the baseline (current legislation) scenario, the particle number emissions in Europe, Northern and Southern Americas, Australia, and China decrease until 2030, whereas especially for India, a strong increase is estimated. The results of this study provide input for modelling of the future changes in aerosol-cloud interactions as well as particle number related adverse health effects, e.g. in response to tightening
Kong, Feng; Zhao, Jingjing; You, Xuqun
2012-01-01
Past research suggested that negative numbers could be represented in terms of their components in the visual modality. The present study examined the processing of negative numbers in the auditory modality and whether it is affected by context. Experiment 1 employed a stimuli detection task where only negative numbers were presented binaurally. Experiment 2 employed the same task, but both positive and negative numbers were mixed as cues. A reverse attentional spatial-numerical association of response codes (SNARC) effect for negative numbers was obtained in these two experiments. Experiment 3 employed a number classification task where only negative numbers were presented binaurally. Experiment 4 employed the same task, but both positive and negative numbers were mixed. A reverse SNARC effect for negative numbers was obtained in these two experiments. These findings suggest that negative numbers in the auditory modality are generated from the set of positive numbers, thus supporting a components representation.
Historical Objections against the Number Line
ERIC Educational Resources Information Center
Heeffer, Albrecht
2011-01-01
Historical studies on the development of mathematical concepts will help mathematics teachers to relate their students' difficulties in understanding to conceptual problems in the history of mathematics. We argue that one popular tool for teaching about numbers, the number line, may not be fit for early teaching of operations involving negative…
Code of Federal Regulations, 2010 CFR
2010-07-01
... 41 Public Contracts and Property Management 3 2010-07-01 2010-07-01 false Numbering. 105-1.109 Section 105-1.109 Public Contracts and Property Management Federal Property Management Regulations System (Continued) GENERAL SERVICES ADMINISTRATION 1-INTRODUCTION 1.1-Regulations System § 105-1.109 Numbering....
Keypad Geometry and Divisibility of Numbers
ERIC Educational Resources Information Center
Van Dyke, Frances; Keynes, Michael
2010-01-01
In this article, the authors show how students can form familiar geometric figures on the calculator keypad and generate numbers that are all divisible by a common number. Students are intrigued by the results and want to know "why it works". The activities can be presented and students given an extended amount of time to think about them. As…
Neural correlates of merging number words.
Hung, Yi-Hui; Pallier, Christophe; Dehaene, Stanislas; Lin, Yi-Chen; Chang, Acer; Tzeng, Ovid J-L; Wu, Denise H
2015-11-15
Complex number words (e.g., "twenty two") are formed by merging together several simple number words (e.g., "twenty" and "two"). In the present study, we explored the neural correlates of this operation and investigated to what extent it engages brain areas involved processing numerical quantity and linguistic syntactic structure. Participants speaking two typologically distinct languages, French and Chinese, were required to read aloud sequences of simple number words while their cerebral activity was recorded by functional magnetic resonance imaging. Each number word could either be merged with the previous ones (e.g., 'twenty three') or not (e.g., 'three twenty'), thus forming four levels ranging from lists of number words to complex numerals. When a number word could be merged with the preceding ones, it was named faster than when it could not. Neuroimaging results showed that the number of merges correlated with activation in the left inferior frontal gyrus and in the left inferior parietal lobule. Consistent findings across Chinese and French participants suggest that these regions serve as the neural bases for forming complex number words in different languages.
Estimating Avogadro's number from skylight and airlight
NASA Astrophysics Data System (ADS)
Pesic, Peter
2005-01-01
Naked-eye determinations of the visual range yield order-of-magnitude estimates of Avogadro's number, using an argument of Rayleigh. Alternatively, by looking through a cardboard tube, we can compare airlight and skylight and give another estimate of this number using the law of atmospheres.
Language Influence on Children's Cognitive Number Representation
ERIC Educational Resources Information Center
Alsawaie, Othman N.
2004-01-01
This study examined the effect of language on children's cognitive representation of number. The sample for the study consisted of 90 Arabic speaking children with a mean age of 80 months. Children were interviewed individually and asked to represent written two-digit numbers using base-10 blocks. A new approach for testing the linguistic…
Good Morning, Numbers Day: Motivating for Mathematics
ERIC Educational Resources Information Center
Ramentol, Salvador Vidal
2011-01-01
The aversion that many girls and boys experience towards mathematics has been one of the author's major concerns since he started teaching. In this article, he describes a project called "Numbers Day" that was designed to improve students' attitudes toward mathematics. There are many features of Numbers Day that teachers might incorporate into…
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 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL PRACTICE AND PROCEDURE Pole Attachment Complaint Procedures § 1.1405 File numbers. Each complaint which appears to be essentially complete under § 1.1404...
Number of Oxidations Relative to Methylene.
ERIC Educational Resources Information Center
Kjonaas, Richard A.
1986-01-01
Describes a new way of quantifying organic oxidation-reduction reactions that extends the traditional method of assigning oxidation numbers by replacing them with NORM's (Number of Oxidations Relative to Methylene). This modification allows the system to be applied to more complex examples without the cumbersomeness inherent in the original…
Inhibition, Conflict Detection, and Number Conservation
ERIC Educational Resources Information Center
Lubin, Amélie; Simon, Grégory; Houdé, Olivier; De Neys, Wim
2015-01-01
The acquisition of number conservation is a critical step in children's numerical and mathematical development. Classic developmental studies have established that children's number conservation is often biased by misleading intuitions. However, the precise nature of these conservation errors is not clear. A key question is whether conservation…
On the Concept Image of Complex Numbers
ERIC Educational Resources Information Center
Nordlander, Maria Cortas; Nordlander, Edvard
2012-01-01
A study of how Swedish students understand the concept of complex numbers was performed. A questionnaire was issued reflecting the student view of own perception. Obtained answers show a variety of concept images describing how students adopt the concept of complex numbers. These concept images are classified into four categories in order to…
When Symbolic Spatial Cues Go before Numbers
ERIC Educational Resources Information Center
Herrera, Amparo; Macizo, Pedro
2011-01-01
This work explores the effect of spatial cueing on number processing. Participants performed a parity judgment task. However, shortly before the target number, a cue (arrow pointing to left, arrow pointing to right or a cross) was centrally presented. In Experiment 1, in which responses were lateralized, the cue direction modulated the interaction…
National Resources [and] National Toll Free Numbers.
ERIC Educational Resources Information Center
National Information Center for Children and Youth with Disabilities, Washington, DC.
This resource list provides names, addresses, and telephone numbers of 13 information clearinghouses and 42 organizations providing information on children and youth with disabilities. Telephone numbers are designated as either voice or text telephone. Spanish-language resources are also indicated. A list of organizations that have national…
Infinite Sums of M-Bonacci Numbers
ERIC Educational Resources Information Center
A-iru, Muniru A.
2009-01-01
In this note, we construct infinite series using M-bonacci numbers in a manner similar to that used in previous studies and investigate the convergence of the series to an integer. Our results generalize the ones obtained for Fibonacci numbers.
Families of Linear Recurrences for Catalan Numbers
ERIC Educational Resources Information Center
Gauthier, N.
2011-01-01
Four different families of linear recurrences are derived for Catalan numbers. The derivations rest on John Riordan's 1973 generalization of Catalan numbers to a set of polynomials. Elementary differential and integral calculus techniques are used and the results should be of interest to teachers and students of introductory courses in calculus…
The Second Strong Law of Small Numbers.
ERIC Educational Resources Information Center
Guy, Richard K.
1990-01-01
Presented are 44 examples in which students are invited to guess what pattern of numbers is emerging and to decide whether the pattern will persist. Topics of examples include Pascal's triangle, integers, vertices, Fibonacci numbers, power series, partition functions, and Euler's theorem. The answers to all problems are included. (KR)
Fostering Number Sense through Digits and Dice
ERIC Educational Resources Information Center
Wiest, Lynda R.
2006-01-01
Games are among the many types of activities that can be used to help promote number sense. Chosen and used wisely, games encourage learning and motivate many students to grasp concepts more quickly and fully. This article describes a popular and easy-to-implement number sense game--called Digits and Dice--most commonly used in conjunction with…
Teaching Number in the Early Elementary Years
ERIC Educational Resources Information Center
Cain, Chris R.; Faulkner, Valerie N.
2011-01-01
The widely adopted Common Core State Standards for Mathematics (CCSSM) are designed to deepen instruction of number sense and will demand that elementary school teachers have a strong understanding of number. These changes arrive at a time when it is still understood that teachers and the curriculum in the United States have not been fundamentally…
21 CFR 1210.21 - Permit number.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 21 Food and Drugs 8 2013-04-01 2013-04-01 false Permit number. 1210.21 Section 1210.21 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) REGULATIONS... IMPORT MILK ACT Permit Control § 1210.21 Permit number. Each permit issued under the Federal Import...
21 CFR 1210.21 - Permit number.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 21 Food and Drugs 8 2011-04-01 2011-04-01 false Permit number. 1210.21 Section 1210.21 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) REGULATIONS... IMPORT MILK ACT Permit Control § 1210.21 Permit number. Each permit issued under the Federal Import...
21 CFR 1210.21 - Permit number.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Permit number. 1210.21 Section 1210.21 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) REGULATIONS... IMPORT MILK ACT Permit Control § 1210.21 Permit number. Each permit issued under the Federal Import...
21 CFR 1210.21 - Permit number.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 21 Food and Drugs 8 2012-04-01 2012-04-01 false Permit number. 1210.21 Section 1210.21 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) REGULATIONS... IMPORT MILK ACT Permit Control § 1210.21 Permit number. Each permit issued under the Federal Import...
21 CFR 1210.21 - Permit number.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 21 Food and Drugs 8 2014-04-01 2014-04-01 false Permit number. 1210.21 Section 1210.21 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) REGULATIONS... IMPORT MILK ACT Permit Control § 1210.21 Permit number. Each permit issued under the Federal Import...
Learning Disabled: Number Concepts, Primary Grades.
ERIC Educational Resources Information Center
National Center on Educational Media and Materials for the Handicapped, Columbus, OH.
Selected from the National Instructional Materials Information System (NIMIS)--a computer based on-line interactive retrieval system on special education materials--the bibliography covers 62 materials for teaching number concepts to learning disabled students at the primary grades. Entries are presented in order of NIMIS accession number and…
46 CFR 169.541 - Number required.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 46 Shipping 7 2010-10-01 2010-10-01 false Number required. 169.541 Section 169.541 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) NAUTICAL SCHOOLS SAILING SCHOOL VESSELS Lifesaving and Firefighting Equipment Personal Flotation Devices § 169.541 Number required. Each vessel must...
46 CFR 169.541 - Number required.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 46 Shipping 7 2011-10-01 2011-10-01 false Number required. 169.541 Section 169.541 Shipping COAST GUARD, DEPARTMENT OF HOMELAND SECURITY (CONTINUED) NAUTICAL SCHOOLS SAILING SCHOOL VESSELS Lifesaving and Firefighting Equipment Personal Flotation Devices § 169.541 Number required. Each vessel must...
Math Sense: Whole Numbers and Money.
ERIC Educational Resources Information Center
Phillips, Jan
This book is designed to help students gain the range of math skills they need to succeed in life, work, and on standardized tests; overcome math anxiety; discover math as interesting and purposeful; and develop good number sense. Topics covered in this book include whole numbers and addition, subtraction, multiplication, and division. Lessons are…
From Whole Numbers to Invert and Multiply
ERIC Educational Resources Information Center
Cavey, Laurie O.; Kinzel, Margaret T.
2014-01-01
Teachers report that engaging students in solving contextual problems is an important part of supporting student understanding of algorithms for fraction division. Meaning for whole-number operations is a crucial part of making sense of contextual problems involving rational numbers. The authors present a developed instructional sequence to…
ERIC Educational Resources Information Center
Goldenhersh, Barbara, Ed.
This document consists of three issues of the journal "Seedbed," an outcome of the Teachers' Center Project at Southern Illinois University at Edwardsville (SIUE). Issue Number 29 contains 67 articles on teachers' ideas that they thought worth sharing with other teachers. Issue Number 30 consists of a single paper, "Children and Mathematics in the…
Nonclassicality in phase-number uncertainty relations
Matia-Hernando, Paloma; Luis, Alfredo
2011-12-15
We show that there are nonclassical states with lesser joint fluctuations of phase and number than any classical state. This is rather paradoxical since one would expect classical coherent states to be always of minimum uncertainty. The same result is obtained when we replace phase by a phase-dependent field quadrature. Number and phase uncertainties are assessed using variance and Holevo relation.
Clinicopathological assessment of the nephron number
Tsuboi, Nobuo; Kanzaki, Go; Koike, Kentaro; Kawamura, Tetsuya; Ogura, Makoto; Yokoo, Takashi
2014-01-01
Recent studies have demonstrated much larger variability in the total number of nephrons in normal populations than previously suspected. In addition, it has been suggested that individuals with a low nephron number may have an increased lifetime risk of hypertension or renal insufficiency, emphasizing the importance of evaluating the nephron number in each individual. In view of the fact that all previous reports of the nephron number were based on analyses of autopsy kidneys, the identification of surrogate markers detectable in living subjects is needed in order to enhance understanding of the clinical significance of this parameter. In this review, we summarize the clinicopathological factors and findings indicating a reduction in the nephron number, focusing particularly on those found at the time of a preserved renal function. PMID:25852857
Low Reynolds number airfoil survey, volume 1
NASA Technical Reports Server (NTRS)
Carmichael, B. H.
1981-01-01
The differences in flow behavior two dimensional airfoils in the critical chordlength Reynolds number compared with lower and higher Reynolds number are discussed. The large laminar separation bubble is discussed in view of its important influence on critical Reynolds number airfoil behavior. The shortcomings of application of theoretical boundary layer computations which are successful at higher Reynolds numbers to the critical regime are discussed. The large variation in experimental aerodynamic characteristic measurement due to small changes in ambient turbulence, vibration, and sound level is illustrated. The difficulties in obtaining accurate detailed measurements in free flight and dramatic performance improvements at critical Reynolds number, achieved with various types of boundary layer tripping devices are discussed.
Ramsey numbers and adiabatic quantum computing.
Gaitan, Frank; Clark, Lane
2012-01-01
The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers R(m,n) with m, n≥3, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers R(m,n). We show how the computation of R(m,n) can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for 5≤s≤7. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class quantum Merlin Arthur.
Compendium of Experimental Cetane Number Data
Murphy, M. J.; Taylor, J. D.; McCormick, R. L.
2004-09-01
In this report, we present a compilation of reported cetane numbers for pure chemical compounds. The compiled database contains cetane values for 299 pure compounds, including 156 hydrocarbons and 143 oxygenates. Cetane number is a relative ranking of fuels based on the amount of time between fuel injection and ignition. The cetane number is typically measured either in a combustion bomb or in a single-cylinder research engine. This report includes cetane values from several different measurement techniques - each of which has associated uncertainties. Additionally, many of the reported values are determined by measuring blending cetane numbers, which introduces significant error. In many cases, the measurement technique is not reported nor is there any discussion about the purity of the compounds. Nonetheless, the data in this report represent the best pure compound cetane number values available from the literature as of August 2004.
Zooming in and out from the Mental Number Line: Evidence for a Number Range Effect
ERIC Educational Resources Information Center
Pinhas, Michal; Pothos, Emmanuel M.; Tzelgov, Joseph
2013-01-01
The representation of numbers is commonly viewed as an ordered continuum of magnitudes, referred to as the "mental number line." Previous work has repeatedly shown that number representations evoked by a given task can be easily altered, yielding an ongoing discussion about the basic properties of the mental number line and how malleable…
ERIC Educational Resources Information Center
Schneider, Michael; Grabner, Roland H.; Paetsch, Jennifer
2009-01-01
As indicated by the distance effect and the spatial-numerical association of response codes (SNARC) effect, natural numbers are mentally represented on a number line. Purportedly, this number line underlies children's number sense, which supports the acquisition of more advanced mathematical competencies. In 3 studies with a total of 429 fifth and…
Number Worlds: Visual and Experimental Access to Elementary Number Theory Concepts
ERIC Educational Resources Information Center
Sinclair, Nathalie; Zazkis, Rina; Liljedahl, Peter
2004-01-01
Recent research demonstrates that many issues related to the structure of natural numbers and the relationship among numbers are not well grasped by students. In this article, we describe a computer-based learning environment called "Number Worlds" that was designed to support the exploration of elementary number theory concepts by making the…
Exploring number space by random digit generation.
Loetscher, Tobias; Brugger, Peter
2007-07-01
There is some evidence that human subjects preferentially select small numbers when asked to sample numbers from large intervals "at random". A retrospective analysis of single digit frequencies in 16 independent experiments with the Mental Dice Task (generation of digits 1-6 during 1 min) confirmed the occurrence of small-number biases (SNBs) in 488 healthy subjects. A subset of these experiments suggested a spatial nature of this bias in the sense of a "leftward" shift along the number line. First, individual SNBs were correlated with leftward deviations in a number line bisection task (but unrelated to the bisection of physical lines). Second, in 20 men, the magnitude of SNBs significantly correlated with leftward attentional biases in the judgment of chimeric faces. Finally, cognitive activation of the right hemisphere enhanced SNBs in 20 different men, while left hemisphere activation reduced them. Together, these findings provide support for a spatial component in random number generation. Specifically, they allow an interpretation of SNBs in terms of "pseudoneglect in number space." We recommend the use of random digit generation for future explorations of spatial-attentional asymmetries in numerical processing and discuss methodological issues relevant to prospective designs.
Language and number: a bilingual training study.
Spelke, E S; Tsivkin, S
2001-01-01
Three experiments investigated the role of a specific language in human representations of number. Russian-English bilingual college students were taught new numerical operations (Experiment 1), new arithmetic equations (Experiments 1 and 2), or new geographical or historical facts involving numerical or non-numerical information (Experiment 3). After learning a set of items in each of their two languages, subjects were tested for knowledge of those items, and new items, in both languages. In all the studies, subjects retrieved information about exact numbers more effectively in the language of training, and they solved trained problems more effectively than untrained problems. In contrast, subjects retrieved information about approximate numbers and non-numerical facts with equal efficiency in their two languages, and their training on approximate number facts generalized to new facts of the same type. These findings suggest that a specific, natural language contributes to the representation of large, exact numbers but not to the approximate number representations that humans share with other mammals. Language appears to play a role in learning about exact numbers in a variety of contexts, a finding with implications for practice in bilingual education. The findings prompt more general speculations about the role of language in the development of specifically human cognitive abilities.
The 2015 Revision of the Sunspot Number
NASA Astrophysics Data System (ADS)
Svalgaard, L.
2014-12-01
Our knowledge of the long-term evolution of solar activity and of its primary modulation, the 11-year cycle, largely depends on a single direct observational record: the visual sunspot counts that retrace the last 4 centuries, since the invention of the astronomical telescope. Currently, this activity index is available in two main forms: the International Sunspot Number initiated by R. Wolf in 1849 and the Group Number constructed more recently by Hoyt and Schatten (1998a,b). Unfortunately, those two series do not match by various aspects, inducing confusions and contradictions when used in crucial contemporary studies of the solar dynamo or of the solar forcing on the Earth climate. Recently, new efforts have been undertaken to diagnose and correct flaws and biases affecting both sunspot series, in the framework of a series of dedicated Sunspot Number Workshops. Here, we present a global overview of our current understanding of the sunspot number calibration. While the early part of the sunspot record before 1800 is still characterized by large uncertainties due to poorly observed periods, the more recent sunspot numbers are mainly affected by three main inhomogeneities: in 1880-1915 for the Group Number and in 1947 and 1980-2014 for the Sunspot Number. The newly corrected series clearly indicates a progressive decline of solar activity before the onset of the Maunder Minimum, while the slowly rising trend of the activity after the Maunder Minimum is strongly reduced, suggesting that by the mid 18th century, solar activity had already returned to the level of those observed in recent solar cycles in the 20th century. We finally conclude with future prospects opened by this epochal revision of the Sunspot Number, the first one since Wolf himself, and its reconciliation with the Group Number, a long-awaited modernization that will feed solar cycle research into the 21st century.
Hyperimmunity and A-computable universal numberings
NASA Astrophysics Data System (ADS)
Issakhov, Assylbek
2016-08-01
Whether there exists a computable universal numbering for a computable family is the key question in theory of numberings. In a very general setting, this problem was explored in [Yu. L. Ershov, Theory of Numberings, Handbook of Computability Theory, North-Holland; Amsterdam: Stud. Log. Found. Math., Vol. 140, pp. 473-503, 1999]. For sets A that are Turing jumps of the empty set, the problem was treated in [S. A. Badaev, S. S. Goncharov, and A. Sorbi, Computability and Models, 11-44 (2003)] and other papers. In this work, we investigate families of total functions computable relative to hyperimmune and hyperimmune-free oracles.
Critical points and number of master integrals
NASA Astrophysics Data System (ADS)
Lee, Roman N.; Pomeransky, Andrei A.
2013-11-01
We consider the question about the number of master integrals for a multiloop Feynman diagram. We show that, for a given set of denominators, this number is totally determined by the critical points of the polynomials entering either of the two representations: the parametric representation and the Baikov representation. In particular, for the parametric representation the corresponding polynomial is just the sum of Symanzik polynomials. The relevant topological invariant is the sum of the Milnor numbers of the proper critical points. We present a Mathematica package Mint to automatize the counting of the master integrals for the typical case, when all critical points are isolated.
A study of the drawing number system
Navarro, S.
1987-05-01
This document defines the procedures used for the drawing number system at Sandia National Laboratories. A detailed description of the methods used for identifying drawings includes the value ranges, meanings, and historical use of such items are drawing prefix, suffix, part numbers, and nomenclature. Rules used for making changes to drawings are defined since certain types of changes may result in generating new drawing numbers. Exceptions to established procedures are also identified. The information in this document is being used to develop the logical data model for the ADDS-II engineering information management application.
Generation of pseudo-random numbers
NASA Technical Reports Server (NTRS)
Howell, L. W.; Rheinfurth, M. H.
1982-01-01
Practical methods for generating acceptable random numbers from a variety of probability distributions which are frequently encountered in engineering applications are described. The speed, accuracy, and guarantee of statistical randomness of the various methods are discussed.
Short-term memory for numbers.
Chapanis, A; Moulden, J V
1990-04-01
Each of 52 (25 female and 27 male) high school students reproduced from memory 1000 eight-digit numbers after viewing each number for 5 s. Subjects were given unlimited time to reproduce the numbers and were allowed to change their reproductions. The range of errors was very large: from 71 to 2231 out of 8000 digits reproduced by each subject. Every subject showed a serial position effect and almost the same effect--about 70% of subjects made the greatest number of errors at the seventh digit. Female subjects made significantly more errors than did the males. Every subject improved his or her score by making changes. Data are given on the relative difficulty of recalling each of the 10 digits, the 100 doublets (pairs of digits), and the 1000 triplets (sets of three digits).
Infiltration formulas by curve number procedure.
Chen, C.-L.
1982-01-01
The Soil Conservation Service (SCS) curve number procedure for estimating runoff volume is examined in terms of the validity and applicability of the derived infiltration equations. -from ASCE Publications Abstracts
An Application of Number Theory to Cryptology.
ERIC Educational Resources Information Center
Snow, Joanne R.
1989-01-01
Discussed is an application of number theory to cryptology that can be used with secondary school students. Background on the topics is given first, followed by an explanation for use of the topic. (MNS)
Rhizobial gibberellin negatively regulates host nodule number
Tatsukami, Yohei; Ueda, Mitsuyoshi
2016-01-01
In legume–rhizobia symbiosis, the nodule number is controlled to ensure optimal growth of the host. In Lotus japonicus, the nodule number has been considered to be tightly regulated by host-derived phytohormones and glycopeptides. However, we have discovered a symbiont-derived phytohormonal regulation of nodule number in Mesorhizobium loti. In this study, we found that M. loti synthesized gibberellic acid (GA) under symbiosis. Hosts inoculated with a GA-synthesis-deficient M. loti mutant formed more nodules than those inoculated with the wild-type form at four weeks post inoculation, indicating that GA from already-incorporated rhizobia prevents new nodule formation. Interestingly, the genes for GA synthesis are only found in rhizobial species that inhabit determinate nodules. Our findings suggest that the already-incorporated rhizobia perform GA-associated negative regulation of nodule number to prevent delayed infection by other rhizobia. PMID:27307029
A Fast Coulometric Estimation of Avogadro's Number
NASA Astrophysics Data System (ADS)
Thomas, Nicholas C.
2007-10-01
Using simple materials found in any high school or college laboratory, an electrochemical method of determining Avogadro's number is presented. Once set up, the measurement can be completed in about 5 minutes.
Decay of Turbulence at High Reynolds Numbers
NASA Astrophysics Data System (ADS)
Sinhuber, Michael; Bodenschatz, Eberhard; Bewley, Gregory P.
2015-01-01
Turbulent motions in a fluid decay at a certain rate once stirring has stopped. The role of the most basic parameter in fluid mechanics, the Reynolds number, in setting the decay rate is not generally known. This Letter concerns the high-Reynolds-number limit of the process. In a classical grid-turbulence wind-tunnel experiment that both reaches higher Reynolds numbers than ever before and covers a wide range of them (1 04
Ideal photon number amplifier and duplicator
NASA Technical Reports Server (NTRS)
Dariano, G. M.
1992-01-01
The photon number-amplification and number-duplication mechanism are analyzed in the ideal case. The search for unitary evolutions leads to consider also a number-deamplification mechanism, the symmetry between amplification and deamplification being broken by the integer-value nature of the number operator. Both transformations, amplification and duplication, need an auxiliary field which, in the case of amplification, turns out to be amplified in the inverse way. Input-output energy conservation is accounted for using a classical pump or through frequency-conversion of the fields. Ignoring one of the fields is equivalent to considering the amplifier as an open system involving entropy production. The Hamiltonians of the ideal devices are given and compared with those of realistic systems.
Chaotic behaviour of high Mach number flows
NASA Technical Reports Server (NTRS)
Varvoglis, H.; Ghosh, S.
1985-01-01
The stability of the super-Alfvenic flow of a two-fluid plasma model with respect to the Mach number and the angle between the flow direction and the magnetic field is investigated. It is found that, in general, a large scale chaotic region develops around the initial equilibrium of the laminar flow when the Mach number exceeds a certain threshold value. After reaching a maximum the size of this region begins shrinking and goes to zero as the Mach number tends to infinity. As a result high Mach number flows in time independent astrophysical plasmas may lead to the formation of 'quasi-shocks' in the presence of little or no dissipation.
Large Numbers and Calculators: A Classroom Activity.
ERIC Educational Resources Information Center
Arcavi, Abraham; Hadas, Nurit
1989-01-01
Described is an activity demonstrating how a scientific calculator can be used in a mathematics classroom to introduce new content while studying a conventional topic. Examples of reading and writing large numbers, and reading hidden results are provided. (YP)
Links to Literature: Popping Up Number Sense.
ERIC Educational Resources Information Center
Hopkins, Lindy
1995-01-01
Describes a school-wide project using popcorn to gain number sense by learning more about a million. Used the books "How Much Is a Million?" and "If You Made a Million" to introduce the project. (MKR)
Predicting unknown species numbers using discovery curves
Bebber, Daniel P; Marriott, Francis H.C; Gaston, Kevin J; Harris, Stephen A; Scotland, Robert W
2007-01-01
A common approach to estimating the total number of extant species in a taxonomic group is to extrapolate from the temporal pattern of known species descriptions. A formal statistical approach to this problem is provided. The approach is applied to a number of global datasets for birds, ants, mosses, lycophytes, monilophytes (ferns and horsetails), gymnosperms and also to New World grasses and UK flowering plants. Overall, our results suggest that unless the inventory of a group is nearly complete, estimating the total number of species is associated with very large margins of error. The strong influence of unpredictable variations in the discovery process on species accumulation curves makes these data unreliable in estimating total species numbers. PMID:17456460
Animal cognition. Number-space mapping in the newborn chick resembles humans' mental number line.
Rugani, Rosa; Vallortigara, Giorgio; Priftis, Konstantinos; Regolin, Lucia
2015-01-30
Humans represent numbers along a mental number line (MNL), where smaller values are located on the left and larger on the right. The origin of the MNL and its connections with cultural experience are unclear: Pre-verbal infants and nonhuman species master a variety of numerical abilities, supporting the existence of evolutionary ancient precursor systems. In our experiments, 3-day-old domestic chicks, once familiarized with a target number (5), spontaneously associated a smaller number (2) with the left space and a larger number (8) with the right space. The same number (8), though, was associated with the left space when the target number was 20. Similarly to humans, chicks associate smaller numbers with the left space and larger numbers with the right space.
Detecting prime numbers via roots of polynomials
NASA Astrophysics Data System (ADS)
Dobbs, David E.
2012-04-01
It is proved that an integer n ≥ 2 is a prime (resp., composite) number if and only if there exists exactly one (resp., more than one) nth-degree monic polynomial f with coefficients in Z n , the ring of integers modulo n, such that each element of Z n is a root of f. This classroom note could find use in any introductory course on abstract algebra or elementary number theory.
All-optical fast random number generator.
Li, Pu; Wang, Yun-Cai; Zhang, Jian-Zhong
2010-09-13
We propose a scheme of all-optical random number generator (RNG), which consists of an ultra-wide bandwidth (UWB) chaotic laser, an all-optical sampler and an all-optical comparator. Free from the electric-device bandwidth, it can generate 10Gbit/s random numbers in our simulation. The high-speed bit sequences can pass standard statistical tests for randomness after all-optical exclusive-or (XOR) operation.
Characteristic Numbers of Matrix Lie Algebras
NASA Astrophysics Data System (ADS)
Zhang, Yu-Feng; Fan, En-Gui
2008-04-01
A notion of characteristic number of matrix Lie algebras is defined, which is devoted to distinguishing various Lie algebras that are used to generate integrable couplings of soliton equations. That is, the exact classification of the matrix Lie algebras by using computational formulas is given. Here the characteristic numbers also describe the relations between soliton solutions of the stationary zero curvature equations expressed by various Lie algebras.
Algebraic independence of p-adic numbers
NASA Astrophysics Data System (ADS)
Nesterenko, Yu V.
2008-06-01
We prove lower bounds for the transcendence degree of fields generated by values of the p-adic exponential function. In particular, we estimate the transcendence degree of the field \\mathbb Q(e^{\\alpha_1},\\dots,e^{\\alpha_d}), where \\alpha_1,\\dots,\\alpha_d are algebraic (over the field of rational numbers) p-adic numbers that form a basis of a finite extension of \\mathbb Q.
Computing the isoperimetric number of a graph
Golovach, P.A.
1995-01-01
Let G be a finite graph. Denote by {partial_derivative}X, where X {contained_in} VG, the set of edges of the graph G with one end in X and the other end in the set VG{backslash}X. The ratio i(G) = min {vert_bar}{vert_bar}X{vert_bar}/{vert_bar}X{vert_bar}, where the minimum is over all nonempty subsets X of the set VG such that {vert_bar}X{vert_bar} {le} {vert_bar} VG {vert_bar}/2, is called the isoperimetric number of the graph G. It is easy to see that the isoperimetric number may be used as a {open_quotes}measure of connectivity{close_quotes} of the graph. The problem of determining the isoperimetric number is clearly linked with graph partition problems, which often arise in various applications. The isoperimetric number is also important for studying Riemann surfaces. These and other applications of the isoperimetric number justify the analysis of graphs of this kind. The properties of the isoperimetric number are presented in more detail elsewhere. It is shown elsewhere that the computation of the isoperimetric number is an NP-hard problem for graphs with multiple edges. We will show that the decision problem {open_quotes}given the graph G and two integers s and t decide if i(G) {le} s/t{close_quotes} is NP-complete even for simple graphs with vertex degrees not exceeding 3. Note that the isoperimetric number of a tree can be computed by a known polynomial-time algorithm.
Binet's formula for generalized tribonacci numbers
NASA Astrophysics Data System (ADS)
Cereceda, José Luis
2015-11-01
In this note, we derive Binet's formula for the general term ? of the generalized tribonacci sequence. This formula gives ? explicitly as a function of the index n, the roots of the associated characteristic equation, and the initial terms ?, ?, and ?. By way of illustration, we obtain Binet's formula for the Cordonnier, Perrin, and Van der Laan numbers. In addition, we establish a double identity that can be regarded as a parent of Binet's formula for generalized tribonacci numbers.
SESAME equation of state number 7740: Polycarbonate
Boettger, J.C.
1991-06-01
An equation of state (EOS) for polycarbonate (a widely used polymer) has been generated with the computer code GRIZZLY and will be added to the SESAME library as material number 7740. Although a number of the input parameter used in the calculations are based on rough estimates. 7740 provides a good match to experimental Hugoniot data and should be reliable on or near the principal Hugoniot. 6 refs., 1 fig.
A feeling for the numbers in biology
Phillips, Rob; Milo, Ron
2009-01-01
Although the quantitative description of biological systems has been going on for centuries, recent advances in the measurement of phenomena ranging from metabolism to gene expression to signal transduction have resulted in a new emphasis on biological numeracy. This article describes the confluence of two different approaches to biological numbers. First, an impressive array of quantitative measurements make it possible to develop intuition about biological numbers ranging from how many gigatons of atmospheric carbon are fixed every year in the process of photosynthesis to the number of membrane transporters needed to provide sugars to rapidly dividing Escherichia coli cells. As a result of the vast array of such quantitative data, the BioNumbers web site has recently been developed as a repository for biology by the numbers. Second, a complementary and powerful tradition of numerical estimates familiar from the physical sciences and canonized in the so-called “Fermi problems” calls for efforts to estimate key biological quantities on the basis of a few foundational facts and simple ideas from physics and chemistry. In this article, we describe these two approaches and illustrate their synergism in several particularly appealing case studies. These case studies reveal the impact that an emphasis on numbers can have on important biological questions. PMID:20018695
Chromosome number evolution in skippers (Lepidoptera, Hesperiidae)
Lukhtanov, Vladimir A.
2014-01-01
Abstract Lepidoptera (butterflies and moths), as many other groups of animals and plants, simultaneously represent preservation of ancestral karyotype in the majority of families with a high degree of chromosome number instability in numerous independently evolved phylogenetic lineages. However, the pattern and trends of karyotype evolution in some Lepidoptera families are poorly studied. Here I provide a survey of chromosome numbers in skippers (family Hesperiidae) based on intensive search and analysis of published data. I demonstrate that the majority of skippers preserve the haploid chromosome number n=31 that seems to be an ancestral number for the Hesperiidae and the order Lepidoptera at whole. However, in the tribe Baorini the derived number n=16 is the most typical state which can be used as a (syn)apomorphic character in further phylogenetic investigations. Several groups of skippers display extreme chromosome number variations on within-species (e.g. the representatives of the genus Carcharodus Hübner, [1819]) and between-species (e.g. the genus Agathymus Freeman, 1959) levels. Thus, these groups can be used as model systems for future analysis of the phenomenon of chromosome instability. Interspecific chromosomal differences are also shown to be useful for discovering and describing new cryptic species of Hesperiidae representing in such a way a powerful tool in biodiversity research. Generally, the skipper butterflies promise to be an exciting group that will significantly contribute to the growing knowledge of patterns and processes of chromosome evolution. PMID:25610542
Time dependence of adiabatic particle number
NASA Astrophysics Data System (ADS)
Dabrowski, Robert; Dunne, Gerald V.
2016-09-01
We consider quantum field theoretic systems subject to a time-dependent perturbation, and discuss the question of defining a time-dependent particle number not just at asymptotic early and late times, but also during the perturbation. Naïvely, this is not a well-defined notion for such a nonequilibrium process, as the particle number at intermediate times depends on a basis choice of reference states with respect to which particles and antiparticles are defined, even though the final late-time particle number is independent of this basis choice. The basis choice is associated with a particular truncation of the adiabatic expansion. The adiabatic expansion is divergent, and we show that if this divergent expansion is truncated at its optimal order, a universal time dependence is obtained, confirming a general result of Dingle and Berry. This optimally truncated particle number provides a clear picture of quantum interference effects for perturbations with nontrivial temporal substructure. We illustrate these results using several equivalent definitions of adiabatic particle number: the Bogoliubov, Riccati, spectral function and Schrödinger picture approaches. In each approach, the particle number may be expressed in terms of the tiny deviations between the exact and adiabatic solutions of the Ermakov-Milne equation for the associated time-dependent oscillators.
Complex architecture of primes and natural numbers.
García-Pérez, Guillermo; Serrano, M Ángeles; Boguñá, Marián
2014-08-01
Natural numbers can be divided in two nonoverlapping infinite sets, primes and composites, with composites factorizing into primes. Despite their apparent simplicity, the elucidation of the architecture of natural numbers with primes as building blocks remains elusive. Here, we propose a new approach to decoding the architecture of natural numbers based on complex networks and stochastic processes theory. We introduce a parameter-free non-Markovian dynamical model that naturally generates random primes and their relation with composite numbers with remarkable accuracy. Our model satisfies the prime number theorem as an emerging property and a refined version of Cramér's conjecture about the statistics of gaps between consecutive primes that seems closer to reality than the original Cramér's version. Regarding composites, the model helps us to derive the prime factors counting function, giving the probability of distinct prime factors for any integer. Probabilistic models like ours can help to get deeper insights about primes and the complex architecture of natural numbers.
Persistent consequences of atypical early number concepts
Mazzocco, Michèle M. M.; Murphy, Melissa M.; Brown, Ethan C.; Rinne, Luke; Herold, Katherine H.
2013-01-01
How does symbolic number knowledge performance help identify young children at risk for poor mathematics achievement outcomes? In research and practice, classification of mathematics learning disability (MLD, or dyscalculia) is typically based on composite scores from broad measures of mathematics achievement. These scores do predict later math achievement levels, but do not specify the nature of math difficulties likely to emerge among students at greatest risk for long-term mathematics failure. Here we report that gaps in 2nd and 3rd graders' number knowledge predict specific types of errors made on math assessments at Grade 8. Specifically, we show that early whole number misconceptions predict slower and less accurate performance, and atypical computational errors, on Grade 8 arithmetic tests. We demonstrate that basic number misconceptions can be detected by idiosyncratic responses to number knowledge items, and that when such misconceptions are evident during primary school they persist throughout the school age years, with variable manifestation throughout development. We conclude that including specific qualitative assessments of symbolic number knowledge in primary school may provide greater specificity of the types of difficulties likely to emerge among students at risk for poor mathematics outcomes. PMID:24027540
Courant number and unsteady flow computation
Lai, Chintu; ,
1993-01-01
The Courant number C, the key to unsteady flow computation, is a ratio of physical wave velocity, ??, to computational signal-transmission velocity, ??, i.e., C = ??/??. In this way, it uniquely relates a physical quantity to a mathematical quantity. Because most unsteady open-channel flows are describable by a set of n characteristic equations along n characteristic paths, each represented by velocity ??i, i = 1,2,....,n, there exist as many as n components for the numerator of C. To develop a numerical model, a numerical integration must be made on each characteristic curve from an earlier point to a later point on the curve. Different numerical methods are available in unsteady flow computation due to the different paths along which the numerical integration is actually performed. For the denominator of C, the ?? defined as ?? = ?? 0 = ??x/??t has been customarily used; thus, the Courant number has the familiar form of C?? = ??/??0. This form will be referred to as ???common Courant number??? in this paper. The commonly used numerical criteria C?? for stability, neutral stability and instability, are imprecise or not universal in the sense that r0 does not always reflect the true maximum computational data-transmission speed of the scheme at hand, i.e., Ctau is no indication for the Courant constraint. In view of this , a new Courant number, called the ???natural Courant number???, Cn, that truly reflects the Courant constraint, has been defined. However, considering the numerous advantages inherent in the traditional C??, a useful and meaningful composite Courant number, denoted by C??* has been formulated from C??. It is hoped that the new aspects of the Courant number discussed herein afford the hydraulician a broader perspective, consistent criteria, and unified guidelines, with which to model various unsteady flows.
Which numbers do you have in mind? Number generation is influenced by reading direction.
Göbel, Silke M; Maier, Carolin A; Shaki, Samuel
2015-09-01
In Western participants, small numbers are associated with left and larger numbers with right space. A biological account proposes that brain asymmetries lead to these attentional asymmetries in number space. In contrast, a cultural account proposes that the direction of this association is shaped by reading direction. We explored whether number generation is influenced by reading direction in participants from a left-to-right (UK) and a right-to-left (Arab) reading culture. Participants generated numbers randomly while lying on their left and right side. The mean number generated by participants from a left-to-right reading culture was smaller when they lay on their left than on their right side, and the opposite was found for participants from a right-to-left reading culture. Asymmetries in number space observed in number generation are more compatible with a cultural than biological account.
Unpredictability and the transmission of numbers
NASA Astrophysics Data System (ADS)
Myers, John M.; Madjid, F. Hadi
2016-03-01
Curiously overlooked in physics is its dependence on the transmission of numbers. For example, the transmission of numerical clock readings is implicit in the concept of a coordinate system. The transmission of numbers and other logical distinctions is often achieved over a computer-mediated communications network in the face of an unpredictable environment. By unpredictable we mean something stronger than the spread of probabilities over given possible outcomes, namely an opening to unforeseeable possibilities. Unpredictability, until now overlooked in theoretical physics, makes the transmission of numbers interesting. Based on recent proofs within quantum theory that provide a theoretical foundation to unpredictability, here we show how regularities in physics rest on a background of channels over which numbers are transmitted. As is known to engineers of digital communications, numerical transmissions depend on coordination reminiscent of the cycle of throwing and catching by players tossing a ball back and forth. In digital communications, the players are computers, and the required coordination involves unpredictably adjusting "live clocks" that step these computers through phases of a cycle. We show how this phasing, which we call logical synchronization, constrains number-carrying networks, and, if a spacetime manifold in invoked, put "stripes" on spacetime. Via its logically synchronized channels, a network of live clocks serves as a reference against which to locate events. Such a network in any case underpins a coordinate frame, and in some cases the direct use of a network can be tailored to investigate an unpredictable environment. Examples include explorations of gravitational variations near Earth.
On Generalizations of the Stirling Number Triangles
NASA Astrophysics Data System (ADS)
Lang, Wolfdieter
2000-09-01
Sequences of generalized Stirling numbers of both kinds are introduced. These sequences of triangles (i.e. infinite-dimensional lower triangular matrices) of numbers will be denoted by S2(k;n,m) and S1(k;n,m) with k in Z. The original Stirling number triangles of the second and first kind arise when k = 1. S2(2;n,m) is identical with the unsigned S1(2;n,m) triangle, called S1p(2;n,m), which also represents the triangle of signless Lah numbers. Certain associated number triangles, denoted by s2(k;n,m) and s1(k;n,m), are also defined. Both s2(2;n,m) and s1(2;n + 1, m + 1) form Pascal's triangle, and s2(-1,n,m) turns out to be Catalan's triangle. Generating functions are given for the columns of these triangles. Each S2(k) and S1(k) matrix is an example of a Jabotinsky matrix. Therefore the generating functions for the rows of these triangular arrays constitute exponential convolution polynomials. The sequences of the row sums of these triangles are also considered. These triangles are related to the problem of obtaining finite transformations from infinitesimal ones generated by x^k d/dx, for k in Z.
Small and large number discrimination in guppies.
Piffer, Laura; Agrillo, Christian; Hyde, Daniel C
2012-03-01
Non-verbal numerical behavior in human infants, human adults, and non-human primates appears to be rooted in two distinct mechanisms: a precise system for tracking and comparing small numbers of items simultaneously (up to 3 or 4 items) and an approximate system for estimating numerical magnitude of a group of objects. The most striking evidence that these two mechanisms are distinct comes from the apparent inability of young human infants and non-human primates to compare quantites across the small (<3 or 4)/large (>4) number boundary. We ask whether this distinction is present in lower animal species more distantly related to humans, guppies (Poecilia reticulata). We found that, like human infants and non-human primates, fish succeed at comparisons between large numbers only (5 vs. 10), succeed at comparisons between small numbers only (3 vs. 4), but systematically fail at comparisons that closely span the small/large boundary (3 vs. 5). Furthermore, increasing the distance between the small and large number resulted in successful discriminations (3 vs. 6, 3 vs. 7, and 3 vs. 9). This pattern of successes and failures is similar to those observed in human infants and non-human primates to suggest that the two systems are present and functionally distinct across a wide variety of animal species. PMID:21909934
Magnetic Reynolds Number Effects in Compressible Turbulence
NASA Astrophysics Data System (ADS)
Ladeinde, Foluso; Gaitonde, Datta V.
2002-11-01
This research pertains to compressible MHD turbulence which, unlike the traditional emphasis on astrophysical problems, is motivated by the application to aerospace engineering. In this case, the magnetic Reynolds number, operatorname Re_σ, is small compared to unity, and the magnetic pressure Reynolds number, operatornameRe_b, is large. Other parameters of the problem include the standard kinetic energy Reynolds number, operatornameRe, and the acoustic Mach number, M_1. The Alfvénic Mach number, M_2 ˜ operatornameRe_b-1/2 and so it does not represent a new parameter. The problem under investigation involves decaying turbulence and the initial state is characterized in terms of the pseudosound density correction, δρ(x), the pressure fluctuation, δ p(x), the average kinetic energy, E_kin=<ρ uot u>/2, and the magnetic energy, E_mag=< b% otb>/(2M_2^2), where u is the fluctuating velocity field and b is the fluctuating magnetic induction field. We also have the internal energy, E_int, the cross helicity, H_c, and the location of the initial flow within the E/A-E/2Hc diagram,(S. Ghosh and W. H. Matthaeus, Phys. Fluids B 2) (7), 1520 (1990). where E is the total energy, A=
Photon number resolving in picosecond laser pulses
NASA Astrophysics Data System (ADS)
Blazej, Josef; Hamal, Karel
2005-04-01
We are reporting on research and development in the field of thin-layer planar silicon avalanche photodiodes operated as photon counters in a Geiger mode. We have developed and tested a technique, which permits an estimation of the photon number initiated a detection process. It can be applied in a time correlated photon counting experiment simultaneously with originally required time interval estimation. The principal limitation is a using of laser pulse with width below 30 ps to achieve detection concurrent in compare with carrier multiplication speed. The number of photons which triggered the avalanche is estimated on the basis of the effective rise-time difference of the avalanche current. The active quenching and gating circuit provides two uniform electrical pulses, and the time interval between them is related to the number of photons detected. The strong temporal correlation between avalanche start and one of pulses is preserved. Employing the picosecond event timing device, the photon number can be estimated within the dynamical range from 1 up to 1000 photons with the resolution better than a factor of three. The avalanche structure is operated on temperature achievable by thermo-electrical cooling. The applications of presented technique are in any time correlated photon counting (TCPC) measurement where the additional information about signal strength, i.e. statistical number of photons in laser pulse, is interesting. Other applications in the testing of quantum-well-based single photon light sources or squeezed light sources are expected.
ERIC Educational Resources Information Center
Cohen, Dale J.; Sarnecka, Barbara W.
2014-01-01
Children's understanding of numbers is often assessed using a number-line task, where the child is shown a line labeled with 0 at one end and a higher number (e.g., 100) at the other end. The child is then asked where on the line some intermediate number (e.g., 70) should go. Performance on this task changes predictably during childhood, and…
An Exploratory Study of a Number Sense Program to Develop Kindergarten Students' Number Proficiency
ERIC Educational Resources Information Center
Sood, Sheetal; Jitendra, Asha K.
2013-01-01
This study examined the effectiveness of a number sense program on kindergarten students' number proficiency and responsiveness to treatment as a function of students' risk for mathematics difficulties. The program targeted development of relationships among numbers (e.g., spatial, more and less). A total of 101 kindergarten students (not at risk:…
Federal Register 2010, 2011, 2012, 2013, 2014
2013-06-19
... multiple devices. See Nathan Ingram, iOS 6 unifies your Apple ID and phone number for improved iMessage and...-unified-apple-id-phone-number (``Now, if someone calls your phone number for Facetime, you'll be able to... and not your Apple ID email.''). 25. In light of these changes, in this Notice we seek comment on...
The Numbers Game: Phasing in Generated ID Numbers at the University of Oregon
ERIC Educational Resources Information Center
Eveland, Sue
2005-01-01
With all the recent headlines about security breaches and information loss at financial and educational institutions, the higher education community needs to address the issue of using social security numbers as ID numbers. The University of Oregon undertook a change process to assign generated ID numbers to all records in their information…
PHD filtering with localised target number variance
NASA Astrophysics Data System (ADS)
Delande, Emmanuel; Houssineau, Jérémie; Clark, Daniel
2013-05-01
Mahler's Probability Hypothesis Density (PHD filter), proposed in 2000, addresses the challenges of the multipletarget detection and tracking problem by propagating a mean density of the targets in any region of the state space. However, when retrieving some local evidence on the target presence becomes a critical component of a larger process - e.g. for sensor management purposes - the local target number is insufficient unless some confidence on the estimation of the number of targets can be provided as well. In this paper, we propose a first implementation of a PHD filter that also includes an estimation of localised variance in the target number following each update step; we then illustrate the advantage of the PHD filter + variance on simulated data from a multiple-target scenario.
Random Numbers from a Delay Equation
NASA Astrophysics Data System (ADS)
Self, Julian; Mackey, Michael C.
2016-10-01
Delay differential equations can have "chaotic" solutions that can be used to mimic Brownian motion. Since a Brownian motion is random in its velocity, it is reasonable to think that a random number generator might be constructed from such a model. In this preliminary study, we consider one specific example of this and show that it satisfies criteria commonly employed in the testing of random number generators (from TestU01's very stringent "Big Crush" battery of tests). A technique termed digit discarding, commonly used in both this generator and physical RNGs using laser feedback systems, is discussed with regard to the maximal Lyapunov exponent. Also, we benchmark the generator to a contemporary common method: the multiple recursive generator, MRG32k3a. Although our method is about 7 times slower than MRG32k3a, there is in principle no apparent limit on the number of possible values that can be generated from the scheme we present here.
Droplet Number Concentration Value-Added Product
Riihimaki, L.; McFarlane, S.; Sivaraman, C.
2014-06-01
The ndrop_mfrsr value-added product (VAP) provides an estimate of the cloud droplet number concentration of overcast water clouds retrieved from cloud optical depth from the multi-filter rotating shadowband radiometer (MFRSR) instrument and liquid water path (LWP) retrieved from the microwave radiometer (MWR). When cloud layer information is available from vertically pointing lidar and radars in the Active Remote Sensing of Clouds (ARSCL) product, the VAP also provides estimates of the adiabatic LWP and an adiabatic parameter (beta) that indicates how divergent the LWP is from the adiabatic case. quality control (QC) flags (qc_drop_number_conc), an uncertainty estimate (drop_number_conc_toterr), and a cloud layer type flag (cloud_base_type) are useful indicators of the quality and accuracy of any given value of the retrieval. Examples of these major input and output variables are given in sample plots in section 6.0.
Seniority Number in Valence Bond Theory.
Chen, Zhenhua; Zhou, Chen; Wu, Wei
2015-09-01
In this work, a hierarchy of valence bond (VB) methods based on the concept of seniority number, defined as the number of singly occupied orbitals in a determinant or an orbital configuration, is proposed and applied to the studies of the potential energy curves (PECs) of H8, N2, and C2 molecules. It is found that the seniority-based VB expansion converges more rapidly toward the full configuration interaction (FCI) or complete active space self-consistent field (CASSCF) limit and produces more accurate PECs with smaller nonparallelity errors than its molecular orbital (MO) theory-based analogue. Test results reveal that the nonorthogonal orbital-based VB theory provides a reverse but more efficient way to truncate the complete active Hilbert space by seniority numbers.
Large numbers hypothesis. II - Electromagnetic radiation
NASA Technical Reports Server (NTRS)
Adams, P. J.
1983-01-01
This paper develops the theory of electromagnetic radiation in the units covariant formalism incorporating Dirac's large numbers hypothesis (LNH). A direct field-to-particle technique is used to obtain the photon propagation equation which explicitly involves the photon replication rate. This replication rate is fixed uniquely by requiring that the form of a free-photon distribution function be preserved, as required by the 2.7 K cosmic radiation. One finds that with this particular photon replication rate the units covariant formalism developed in Paper I actually predicts that the ratio of photon number to proton number in the universe varies as t to the 1/4, precisely in accord with LNH. The cosmological red-shift law is also derived and it is shown to differ considerably from the standard form of (nu)(R) - const.
Approximate resolution of hard numbering problems
Bailleux, O.; Chabrier, J.J.
1996-12-31
We present a new method for estimating the number of solutions of constraint satisfaction problems. We use a stochastic forward checking algorithm for drawing a sample of paths from a search tree. With this sample, we compute two values related to the number of solutions of a CSP instance. First, an unbiased estimate, second, a lower bound with an arbitrary low error probability. We will describe applications to the Boolean Satisfiability problem and the Queens problem. We shall give some experimental results for these problems.
Parametric number covariance in quantum chaotic spectra.
Vinayak; Kumar, Sandeep; Pandey, Akhilesh
2016-03-01
We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation method and obtain compact expressions for the covariance. We illustrate the universality of this measure by presenting the spectral analysis of the quantum kicked rotors for the time-reversal invariant and time-reversal noninvariant cases. A local version of the parametric number variance introduced earlier is also investigated.
Probing lepton number violation on three frontiers
Deppisch, Frank F.
2013-12-30
Neutrinoless double beta decay constitutes the main probe for lepton number violation at low energies, motivated by the expected Majorana nature of the light but massive neutrinos. On the other hand, the theoretical interpretation of the (non-)observation of this process is not straightforward as the Majorana neutrinos can destructively interfere in their contribution and many other New Physics mechanisms can additionally mediate the process. We here highlight the potential of combining neutrinoless double beta decay with searches for Tritium decay, cosmological observations and LHC physics to improve the quantitative insight into the neutrino properties and to unravel potential sources of lepton number violation.
Simulations of motor unit number estimation techniques
NASA Astrophysics Data System (ADS)
Major, Lora A.; Jones, Kelvin E.
2005-06-01
Motor unit number estimation (MUNE) is an electrodiagnostic procedure used to evaluate the number of motor axons connected to a muscle. All MUNE techniques rely on assumptions that must be fulfilled to produce a valid estimate. As there is no gold standard to compare the MUNE techniques against, we have developed a model of the relevant neuromuscular physiology and have used this model to simulate various MUNE techniques. The model allows for a quantitative analysis of candidate MUNE techniques that will hopefully contribute to consensus regarding a standard procedure for performing MUNE.
NASA Astrophysics Data System (ADS)
Lockwood, M.; Owens, M. J.; Barnard, L.
2016-09-01
We use five test data series to search for, and quantify, putative discontinuities around 1946 in five different annual-mean sunspot-number or sunspot-group-number data sequences. The data series tested are the original and new versions of the Wolf/Zürich/International sunspot number composite [ R_{ISNv1} and R_{ISNv2}] (respectively Clette et al. in Adv. Space Res. 40, 919, 2007 and Clette et al. in The Solar Activity Cycle 35, Springer, New York, 2015); the corrected version of R ISNv1 proposed by Lockwood, Owens, and Barnard (J. Geophys. Res. 119, 5193, 2014a) [ R C]; the new "backbone" group-number composite proposed by Svalgaard and Schatten (Solar Phys. 291, 2016) [ R_{BB}]; and the new group-number composite derived by Usoskin et al. (Solar Phys. 291, 2016) [ R_{UEA}]. The test data series used are the group-number [ NG] and total sunspot area [ A G] from the Royal Observatory, Greenwich/Royal Greenwich Observatory (RGO) photoheliographic data; the Ca K index from the recent re-analysis of Mount Wilson Observatory (MWO) spectroheliograms in the Calcium uc(ii) K ion line; the sunspot-group-number from the MWO sunspot drawings [ N_{MWO}]; and the dayside ionospheric F2-region critical frequencies measured by the Slough ionosonde [foF2]. These test data all vary in close association with sunspot numbers, in some cases non-linearly. The tests are carried out using both the before-and-after fit-residual comparison method and the correlation method of Lockwood, Owens, and Barnard, applied to annual mean data for intervals iterated to minimise errors and to eliminate uncertainties associated with the precise date of the putative discontinuity. It is not assumed that the correction required is by a constant factor, nor even linear in sunspot number. It is shown that a non-linear correction is required by RC, R_{BB}, and R_{ISNv1, but not by R_{ISNv2} or R_{UEA}. The five test datasets give very similar results in all cases. By multiplying the probability
The 17 GHz active region number
Selhorst, C. L.; Pacini, A. A.; Costa, J. E. R.; Giménez de Castro, C. G.; Valio, A.; Shibasaki, K.
2014-08-01
We report the statistics of the number of active regions (NAR) observed at 17 GHz with the Nobeyama Radioheliograph between 1992, near the maximum of cycle 22, and 2013, which also includes the maximum of cycle 24, and we compare with other activity indexes. We find that NAR minima are shorter than those of the sunspot number (SSN) and radio flux at 10.7 cm (F10.7). This shorter NAR minima could reflect the presence of active regions generated by faint magnetic fields or spotless regions, which were a considerable fraction of the counted active regions. The ratio between the solar radio indexes F10.7/NAR shows a similar reduction during the two minima analyzed, which contrasts with the increase of the ratio of both radio indexes in relation to the SSN during the minimum of cycle 23-24. These results indicate that the radio indexes are more sensitive to weaker magnetic fields than those necessary to form sunspots, of the order of 1500 G. The analysis of the monthly averages of the active region brightness temperatures shows that its long-term variation mimics the solar cycle; however, due to the gyro-resonance emission, a great number of intense spikes are observed in the maximum temperature study. The decrease in the number of these spikes is also evident during the current cycle 24, a consequence of the sunspot magnetic field weakening in the last few years.
Arithmetic for First Graders Lacking Number Concepts
ERIC Educational Resources Information Center
Kamii, Constance; Rummelsburg, Judith
2008-01-01
To build cognitive foundation for number, twenty-six low-performing, low-SES first graders did mathematical physical-knowledge activities, such as "bowling," during the first half of the year. As their arithmetic readiness developed, they tried more word problems and games. At the end of the year, these children did better in mental arithmetic and…
NSDC Policy Points. Volume 1, Number 4
ERIC Educational Resources Information Center
National Staff Development Council, 2009
2009-01-01
"NSDC Policy Points" is a newsletter published by the National Staff Development Council (NSDC). This issue of "NSDC Policy Points" discusses why collaborative learning is critical to professional development. Included in this newsletter is an article about team learning in Cedar Rapids, Iowa. [For Volume 1, Number 3 of "NSDC Policy Points," see…
Satellite situation report, volume 31, number 1
NASA Technical Reports Server (NTRS)
1991-01-01
Data computed at GSFC, NORAD, or provided by satellite owners is reported. A space objects box score is presented of objects in orbit and decayed objects. Data of objects in orbit is presented in tabular form and the table headings include name of the object, catalog number, source, launch date, period minutes, inclination, apogee KM., perigee KM., and transmitting frequency.
University Admissions. Policy Note. Number 3
ERIC Educational Resources Information Center
Group of Eight (NJ1), 2012
2012-01-01
University admissions, like many other aspects of the higher education sector, are going through a time of significant change. From 2012, universities will receive full funding under the Commonwealth Grants Scheme (CGS) for as many places as they offer. Previously, the Government limited the number of funded places, with a tolerance band for…
Demonstrations of the Enormity of Avogadro's Number
NASA Astrophysics Data System (ADS)
Diemente, Damon
1998-12-01
Most high-school students learn of Avogadro's number for the first time when they begin study of the mole concept. It is important to impress students with the enormity of Avogadro's number and the concomitant minuscularity of the atom, and papers addressing this need have regularly appeared in this Journal. The present article describes three new problems used annually at Trinity School to make the impression. The first two problems are suitable to be assigned as homework. The first of these uses Avogadro's number simply as a scaling factor; the second, requiring more attention to units, is a calculation of the number of moles of sand grains in the Sahara Desert. The third problem is a series of related calculations that requires some closer in-class mathematical analysis and culminates in an astonishing result. All calculations are done in familiar English units, because with them I have found the results to be more immediately impressive to American students. Conversion factors to metric units can be applied if teachers find that desirable.
The Quantitative Basis of Children's Number Concepts.
ERIC Educational Resources Information Center
Riley, Christine A.; And Others
The purpose of this study was to examine how children represent and compare number symbols. Pre-school, kindergarten, first, third, and fifth grade children and college students judged which of two visually presented digits was numerically larger. Twelve individuals were tested at each grade level. Response latencies were collected. Children at…
Sustaining Student Numbers in the Competitive Marketplace
ERIC Educational Resources Information Center
Szekeres, Judy
2010-01-01
The climate of competition for students in the higher education sector makes it imperative that institutions increase their marketing efforts, both domestically and internationally, to help sustain student numbers. In Australia, the Bradley Report and the government response, which will do away with quotas, allows for a much freer market than…
Mirror Numbers and Wigner's ``Unreasonable Effectiveness''
NASA Astrophysics Data System (ADS)
Berezin, Alexander
2006-04-01
Wigner's ``unreasonable effectiveness of mathematics in physics'' can be augmented by concept of mirror number (MN). It is defined as digital string infinite in both directions. Example is ()5141327182() where first 5 digits is Pi ``spelled'' backward (``mirrored'') and last 5 digits is the beginning of decimal exp1 string. Let MN be constructed from two different transcendental (or algebraically irrational) numbers, set of such MNs is Cantor-uncountable. Most MNs have contain any finite digital sequence repeated infinitely many times. In spirit of ``Contact'' (C.Sagan) each normal MN contains ``Library of Babel'' of all possible texts and patterns (J.L.Borges). Infinite at both ends, MN do not have any numerical values and, contrary to numbers written in positional systems, all digits in MNs have equal weight -- sort of ``numerological democracy''. In Pythagorean-Platonic models (space-time and physical world originating from pure numbers) idea of MN resolves paradox of ``beginning'' (or ``end'') of time. Because in MNs all digits have equal status, (quantum) randomness leads to more uniform and fully ergodic phase trajectories (cf. F.Dyson, Infinite in All Directions) .
Random numbers certified by Bell's theorem.
Pironio, S; Acín, A; Massar, S; de la Giroday, A Boyer; Matsukevich, D N; Maunz, P; Olmschenk, S; Hayes, D; Luo, L; Manning, T A; Monroe, C
2010-04-15
Randomness is a fundamental feature of nature and a valuable resource for applications ranging from cryptography and gambling to numerical simulation of physical and biological systems. Random numbers, however, are difficult to characterize mathematically, and their generation must rely on an unpredictable physical process. Inaccuracies in the theoretical modelling of such processes or failures of the devices, possibly due to adversarial attacks, limit the reliability of random number generators in ways that are difficult to control and detect. Here, inspired by earlier work on non-locality-based and device-independent quantum information processing, we show that the non-local correlations of entangled quantum particles can be used to certify the presence of genuine randomness. It is thereby possible to design a cryptographically secure random number generator that does not require any assumption about the internal working of the device. Such a strong form of randomness generation is impossible classically and possible in quantum systems only if certified by a Bell inequality violation. We carry out a proof-of-concept demonstration of this proposal in a system of two entangled atoms separated by approximately one metre. The observed Bell inequality violation, featuring near perfect detection efficiency, guarantees that 42 new random numbers are generated with 99 per cent confidence. Our results lay the groundwork for future device-independent quantum information experiments and for addressing fundamental issues raised by the intrinsic randomness of quantum theory. PMID:20393558
Golden Proportions for the Generalized Tribonacci Numbers
ERIC Educational Resources Information Center
Shah, Devbhadra V.; Mehta, Darshana A.
2009-01-01
It is known that the ratios of consecutive terms of Fibonacci and Tribonacci sequences converge to the fixed ratio. In this article, we consider the generalized form of Tribonacci numbers and derive the "golden proportion" for the whole family of this generalized sequence. (Contains 2 tables.)
Number Bingo. Technical Note No. 7.
ERIC Educational Resources Information Center
Gunter, Jock
Designed for use in rural Ecuador, addition and multiplication bingo games which promote number recognition and fluency in arithmetic operations are described. These skills are necessary for successful transaction at the market place where rural Ecuadorians must be able to buy goods and make change. The leader calls out a mathematical problem and…
Particle Test Fluence: What's the Right Number?
NASA Technical Reports Server (NTRS)
LaBel, Kenneth A.
2016-01-01
While we have been utilizing standard fluence levels such as those listed in the JESD57 document, we have begun revisiting what an appropriate test fluence is when it comes to qualifying a device for single events. Instead of a fixed fluence level or until a specific number of events occurs, a different thought process is required.
Oxidation Numbers in the Study of Metabolism
ERIC Educational Resources Information Center
Bentley, Ronald; Franzen, James; Chasteen, Thomas G.
2002-01-01
The calculation and use of oxidation numbers in the study of metabolic reactions are discussed for normal oxidations (alcohol dehydrogenase and the NAD+/NADH couple, propanediol dehydratase) and for enzymatic reactions with a "hidden" redox component (transamination, the coupled conversion of ethylamine to ethanol, and the biomethylation of…
Computation of Semantic Number from Morphological Information
ERIC Educational Resources Information Center
Berent, Iris; Pinker, Steven; Tzelgov, Joseph; Bibi, Uri; Goldfarb, Liat
2005-01-01
The distinction between singular and plural enters into linguistic phenomena such as morphology, lexical semantics, and agreement and also must interface with perceptual and conceptual systems that assess numerosity in the world. Three experiments examine the computation of semantic number for singulars and plurals from the morphological…
Mass-induced transition in fermion number
Aragao de Carvalho, C.; Pureza, J. M.
1989-05-15
We show that if we increase the mass of fermions in interaction with a topological (kink) scalar background in 1+1 dimensions, the fractional fermion number of the system will eventually vanish. The transition is sharp and corresponds to the disappearance of localized states from the spectrum of a Dirac operator which is exactly solvable. Possible applications to different physical systems are discussed.
9 CFR 351.6 - Official number.
Code of Federal Regulations, 2012 CFR
2012-01-01
... CERTIFICATION CERTIFICATION OF TECHNICAL ANIMAL FATS FOR EXPORT Procedure for Obtaining Service: Administration of Program § 351.6 Official number. The Administrator will assign a certified technical animal fat... to identify all certified technical animal fat prepared or stored by the plant....
9 CFR 351.6 - Official number.
Code of Federal Regulations, 2011 CFR
2011-01-01
... CERTIFICATION CERTIFICATION OF TECHNICAL ANIMAL FATS FOR EXPORT Procedure for Obtaining Service: Administration of Program § 351.6 Official number. The Administrator will assign a certified technical animal fat... to identify all certified technical animal fat prepared or stored by the plant....
9 CFR 351.6 - Official number.
Code of Federal Regulations, 2013 CFR
2013-01-01
... CERTIFICATION CERTIFICATION OF TECHNICAL ANIMAL FATS FOR EXPORT Procedure for Obtaining Service: Administration of Program § 351.6 Official number. The Administrator will assign a certified technical animal fat... to identify all certified technical animal fat prepared or stored by the plant....
9 CFR 351.6 - Official number.
Code of Federal Regulations, 2014 CFR
2014-01-01
... CERTIFICATION CERTIFICATION OF TECHNICAL ANIMAL FATS FOR EXPORT Procedure for Obtaining Service: Administration of Program § 351.6 Official number. The Administrator will assign a certified technical animal fat... to identify all certified technical animal fat prepared or stored by the plant....
47 CFR 64.1506 - Number designation.
Code of Federal Regulations, 2010 CFR
2010-10-01
... Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES (CONTINUED) MISCELLANEOUS RULES RELATING TO COMMON CARRIERS Interstate Pay-Per-Call and Other Information Services § 64.1506 Number designation. Any interstate service described in § 64.1501(a)(1)-(2), and not subject to...
The LSS Review. Volume 3, Number 1
ERIC Educational Resources Information Center
Hoag, Lydia, Ed.
2004-01-01
A growing number of American students are nonnative English speakers. These students are vulnerable to early school exit and schools are facing more and more such students each year. Presently, about 56% of all public school teachers in the United States have at least one English language learner (ELL) student in their class, but less than 20% of…
Question Number Two: How Many Factors?
ERIC Educational Resources Information Center
Goodwyn, Fara
2012-01-01
Exploratory factor analysis involves five key decisions. The second decision, how many factors to retain, is the focus of the current paper. Extracting too many or too few factors often leads to devastating effects on study results. The advantages and disadvantages of the most effective and/or most utilized strategies to determine the number of…
EXPERIMENTAL RETRIEVAL SYSTEMS STUDIES, REPORT NUMBER 3.
ERIC Educational Resources Information Center
ANDERSON, RONALD R.; AND OTHERS
CONTENTS--(1) AN ASSOCIATIVITY TECHNIQUE FOR AUTOMATICALLY OPTIMIZING RETRIEVAL RESULTS BY RONALD R. ANDERSON. AN ASSOCIATIVE TECHNIQUE BY WHICH IT IS POSSIBLE TO AUTOMATICALLY EXPAND AND NARROW THE NUMBER OF DOCUMENTS RETRIEVED AND TO RETRIEVE DOCUMENTS RELATED TO A REQUEST EVEN THOUGH THEY MAY NOT BE INDEXED BY THE EXACT TERMS OF THE REQUEST IS…
Chinese Number Words, Culture, and Mathematics Learning
ERIC Educational Resources Information Center
Ng, Sharon Sui Ngan; Rao, Nirmala
2010-01-01
This review evaluates the role of language--specifically, the Chinese-based system of number words and the simplicity of Chinese mathematical terms--in explaining the relatively superior performance of Chinese and other East Asian students in cross-national studies of mathematics achievement. Relevant research is critically reviewed focusing on…
Counting on Using a Number Game
ERIC Educational Resources Information Center
Betts, Paul
2015-01-01
Counting all and counting on are distinct counting strategies that can be used to compute such quantities as the total number of objects in two sets (Wright, Martland, and Stafford 2010). Given five objects and three more objects, for example, children who use counting all to determine quantity will count both collections; that is, they count…
Authenticating "Number the Stars" Using Nonfiction Resources
ERIC Educational Resources Information Center
Groce, Robin D.
2009-01-01
"Number the Stars" by Lois Lowry is a popular historical novel for adolescent readers about the Nazi occupation of Copenhagen, Denmark during World War II and the efforts of Danish resisters who successfully rescued 98% of that nation's Jewish population. While this 1998 book is considered to be a fictional account, most of the events in the story…
24 CFR 3280.6 - Serial number.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 24 Housing and Urban Development 5 2014-04-01 2014-04-01 false Serial number. 3280.6 Section 3280.6 Housing and Urban Development Regulations Relating to Housing and Urban Development (Continued) OFFICE OF ASSISTANT SECRETARY FOR HOUSING-FEDERAL HOUSING COMMISSIONER, DEPARTMENT OF HOUSING AND......
A Knack for Numbers: Paquita Friday
ERIC Educational Resources Information Center
Yates, Eleanor Lee
2005-01-01
Back in middle school Dr. Paquita Friday began helping keep books at her grandmother's pharmacy during inventory. It was no chore, she recalls. It was fun. By then, of course, she already knew she had a knack for numbers. Today Friday is gaining recognition for her research in accounting stock market disclosures and winning awards for her teaching…
Skin test reactivity and number of siblings.
von Mutius, E.; Martinez, F. D.; Fritzsch, C.; Nicolai, T.; Reitmeir, P.; Thiemann, H. H.
1994-01-01
OBJECTIVE--To investigate the relation between skin test reactivity in children and number of siblings. DESIGN--Cross sectional survey among schoolchildren aged 9-11 years. Skin prick tests in the children and self completion of written questionnaire by their parents. SUBJECTS--5030 children in Munich and 2623 children in Leipzig and Halle, Germany. MAIN OUTCOME MEASURES--Atopic status assessed by skin prick tests. RESULTS--After possible confounders were controlled for, the prevalence of atopic sensitisation decreased linearly with increasing number of siblings (odds ratio = 0.96 for one sibling, 0.67 for five or more siblings; P = 0.005). In atopic children the severity of the skin test reaction as assessed by the weal size was not associated with the number of siblings. CONCLUSIONS--Factors directly or indirectly related to the number of siblings may decrease the susceptibility of children to become atopic. Thus, declining family size may in part contribute to the increased prevalence of atopic diseases reported in Western countries over the past few decades. PMID:8142793
Vantage Theory, VT2, and Number.
ERIC Educational Resources Information Center
Allan, Keith
2002-01-01
Reviews vantage theory and makes a claim that it does not replace, but coexists with a semantics for color terms. Identifies basic facts about countability in English, and presents further evidence of the fact that the grammar of number and quantification in English is exploited to reveal different conceptualizations of what is spoken of. Claims…
Radical Software. Number Two. The Electromagnetic Spectrum.
ERIC Educational Resources Information Center
Korot, Beryl, Ed.; Gershuny, Phyllis, Ed.
1970-01-01
In an effort to foster the innovative uses of television technology, this tabloid format periodical details social, educational, and artistic experiments with television and lists a large number of experimental videotapes available from various television-centered groups and individuals. The principal areas explored in this issue include cable…
The Emperor's Perfect Map: Leadership by Numbers
ERIC Educational Resources Information Center
Heffernan, Amanda
2016-01-01
This paper establishes that system-generated data profiles are influencing the work of principals in three Queensland state schools. Drawing upon Foucault's notions of governance, as well as research emphasising performative cultures and the importance placed upon numbers and data in education, this paper uses the tale of the Emperor's map as a…
The Development of Semantic Components of Number.
ERIC Educational Resources Information Center
Walker, Alice A.
In this paper the author reviews and synthesizes the research literature concerning the developmental relationships between conservation of number and linguistic capability in handling of quantitative and relational terms. Several models for the development of these competencies are discussed. On the basis of this review the author concludes that…
Early Concepts of Number and Counting
ERIC Educational Resources Information Center
Box, Katherine; Scott, Paul
2004-01-01
Before primitive man had grasped the concept of number, the written word or even speech, he was able to count. This was important for keeping track of food supplies, sending messages, trading between villages and even keeping track of how many animals were in their herd. Counting was done in various ways, but in all cases, the underlying principle…
Estimate octane numbers using an enhanced method
Twu, C.H.; Coon, J.E.
1997-03-01
An improved model, based on the Twu-Coon method, is not only internally consistent, but also retains the same level of accuracy as the previous model in predicting octanes of gasoline blends. The enhanced model applies the same binary interaction parameters to components in each gasoline cut and their blends. Thus, the enhanced model can blend gasoline cuts in any order, in any combination or from any splitting of gasoline cuts and still yield the identical value of octane number for blending the same number of gasoline cuts. Setting binary interaction parameters to zero for identical gasoline cuts during the blending process is not required. The new model changes the old model`s methodology so that the same binary interaction parameters can be applied between components inside a gasoline cut as are applied to the same components between gasoline cuts. The enhanced model is more consistent in methodology than the original model, but it has equal accuracy for predicting octane numbers of gasoline blends, and it has the same number of binary interaction parameters. The paper discusses background, enhancement of the Twu-Coon interaction model, and three examples: blend of 2 identical gasoline cuts, blend of 3 gasoline cuts, and blend of the same 3 gasoline cuts in a different order.
Irrational Numbers Can "In-Spiral" You
ERIC Educational Resources Information Center
Lewis, Leslie D.
2007-01-01
This article describes the instructional process of helping students visualize irrational numbers. Students learn to create a spiral, called "the wheel of Theodorus," which demonstrates irrational and rational lengths. Examples of student work help the reader appreciate the delightful possibilities of this project. (Contains 4 figures.)
Sequence Factorial of "g"-Gonal Numbers
ERIC Educational Resources Information Center
Asiru, Muniru A.
2013-01-01
The gamma function, which has the property to interpolate the factorial whenever the argument is an integer, is a special case (the case "g"?=?2) of the general term of the sequence factorial of "g"-gonal numbers. In relation to this special case, a formula for calculating the general term of the sequence factorial of any…
Visualizing the Arithmetic of Complex Numbers
ERIC Educational Resources Information Center
Soto-Johnson, Hortensia
2014-01-01
The Common Core State Standards Initiative stresses the importance of developing a geometric and algebraic understanding of complex numbers in their different forms (i.e., Cartesian, polar and exponential). Unfortunately, most high school textbooks do not offer such explanations much less exercises that encourage students to bridge geometric and…
A Geometrical Application of Number Theory
ERIC Educational Resources Information Center
Srinivasan, V. K.
2013-01-01
Any quadruple of natural numbers {a, b, c, d} is called a "Pythagorean quadruple" if it satisfies the relationship "a[superscript 2] + b[superscript 2] + c[superscript 2]". This "Pythagorean quadruple" can always be identified with a rectangular box of dimensions "a greater than 0," "b greater than…
9 CFR 355.8 - Official number.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 9 Animals and Animal Products 2 2014-01-01 2014-01-01 false Official number. 355.8 Section 355.8 Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY... CERTIFICATION CERTIFIED PRODUCTS FOR DOGS, CATS, AND OTHER CARNIVORA; INSPECTION, CERTIFICATION,...
9 CFR 355.8 - Official number.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 9 Animals and Animal Products 2 2011-01-01 2011-01-01 false Official number. 355.8 Section 355.8 Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY... CERTIFICATION CERTIFIED PRODUCTS FOR DOGS, CATS, AND OTHER CARNIVORA; INSPECTION, CERTIFICATION,...
9 CFR 355.8 - Official number.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 9 Animals and Animal Products 2 2013-01-01 2013-01-01 false Official number. 355.8 Section 355.8 Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY... CERTIFICATION CERTIFIED PRODUCTS FOR DOGS, CATS, AND OTHER CARNIVORA; INSPECTION, CERTIFICATION,...
9 CFR 355.8 - Official number.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 9 Animals and Animal Products 2 2010-01-01 2010-01-01 false Official number. 355.8 Section 355.8 Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY... CERTIFICATION CERTIFIED PRODUCTS FOR DOGS, CATS, AND OTHER CARNIVORA; INSPECTION, CERTIFICATION,...
Synesthesia and Number Cognition in Children
ERIC Educational Resources Information Center
Green, Jennifer A. K.; Goswami, Usha
2008-01-01
Grapheme-color synesthesia, when achromatic digits evoke an experience of a specific color (photisms), has been shown to be consistent, involuntary, and linked with number concept in adults, yet there have been no comparable investigations with children. We present a systematic study of grapheme-color synesthesia in children aged between 7 and 15…
The aerodynamics of small Reynolds numbers
NASA Technical Reports Server (NTRS)
Schmitz, F. W.
1980-01-01
Aerodynamic characteristics of wing model gliders and bird wings in particular are discussed. Wind tunnel measurements and aerodynamics of small Reynolds numbers are enumerated. Airfoil behavior in the critical transition from laminar to turbulent boundary layer, which is more important to bird wing models than to large airplanes, was observed. Experimental results are provided, and an artificial bird wing is described.
A Framework for Remediating Number Combination Deficits
ERIC Educational Resources Information Center
Fuchs, Lynn S.; Powell, Sarah R.; Seethaler, Pamela M.; Fuchs, Douglas; Hamlett, Carol L.; Cirino, Paul T.; Fletcher, Jack M.
2010-01-01
This article introduces a framework for the remediation of number combination (NC) deficits. Research on the remediation of NC deficits is summarized, and research program studies are used to illustrate the 3 approaches to remediation. The Framework comprises a 2-stage system of remediation. The less intensive stage implementing 1 of 3…
9 CFR 351.6 - Official number.
Code of Federal Regulations, 2010 CFR
2010-01-01
... Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY... CERTIFICATION CERTIFICATION OF TECHNICAL ANIMAL FATS FOR EXPORT Procedure for Obtaining Service: Administration of Program § 351.6 Official number. The Administrator will assign a certified technical animal...
English Teachers' Journal (Israel), Number 25.
ERIC Educational Resources Information Center
English Teachers' Journal (Israel), 1981
1981-01-01
This number of a journal devoted to ideas for teachers of English as a second language (ESL) contains the following articles: (1) "Teaching Grammar as Part of Meaningful Communication" by Raphael Gefen, (2) "Does the School Have a Role to Play in Teaching Environmental Awareness?" by Ora Herzog, (3) "Identifying with Jewish Traditions in the…
Ordered chromatic number of planar maps
Simmons, G.J.
1982-01-01
In this paper it is shown that there exist planar maps and orderings of the regions of those maps foe which no finite number of colors will suffice for a parsimonious proper coloring. In particular, planar maps with 0(2/sup n/2/) regions are exhibited that require n colors for their proper ordered coloring.
Proofs in Number Theory: History and Heresy.
ERIC Educational Resources Information Center
Rowland, Tim
The domain of number theory lends itself particularly well to generic argument, presented with the intention of conveying the force and structure of a conventional generalized argument through the medium of a particular case. The potential of generic examples as a didactic tool is virtually unrecognized. Although the use of such examples has good…
Understanding Quantum Numbers in General Chemistry Textbooks
ERIC Educational Resources Information Center
Niaz, Mansoor; Fernandez, Ramon
2008-01-01
Quantum numbers and electron configurations form an important part of the general chemistry curriculum and textbooks. The objectives of this study are: (1) Elaboration of a framework based on the following aspects: (a) Origin of the quantum hypothesis, (b) Alternative interpretations of quantum mechanics, (c) Differentiation between an orbital and…
Poison control center - Emergency number (image)
For a poison emergency call 1-800-222-1222 anywhere in the United States. This national hotline number will let you ... is a free and confidential service. All local poison control centers in the U.S. use this national ...
Autotelic Behavior in Socialization. Report Number 29.
ERIC Educational Resources Information Center
Inbar, Michael; Stoll, Clarice S.
A selective review of the literature on the socialization effect of games uncovers a varied and increasing number of hypotheses, but only little and scattered evidence. Direct studies of play and game functions are primarily in uncontrolled clinical reports. Therefore, a pilot study was conducted as a preliminary attempt to establish correlational…
Preferential solvation: dividing surface vs excess numbers.
Shimizu, Seishi; Matubayasi, Nobuyuki
2014-04-10
How do osmolytes affect the conformation and configuration of supramolecular assembly, such as ion channel opening and actin polymerization? The key to the answer lies in the excess solvation numbers of water and osmolyte molecules; these numbers are determinable solely from experimental data, as guaranteed by the phase rule, as we show through the exact solution theory of Kirkwood and Buff (KB). The osmotic stress technique (OST), in contrast, purposes to yield alternative hydration numbers through the use of the dividing surface borrowed from the adsorption theory. However, we show (i) OST is equivalent, when it becomes exact, to the crowding effect in which the osmolyte exclusion dominates over hydration; (ii) crowding is not the universal driving force of the osmolyte effect (e.g., actin polymerization); (iii) the dividing surface for solvation is useful only for crowding, unlike in the adsorption theory which necessitates its use due to the phase rule. KB thus clarifies the true meaning and limitations of the older perspectives on preferential solvation (such as solvent binding models, crowding, and OST), and enables excess number determination without any further assumptions. PMID:24689966
Number variance for arithmetic hyperbolic surfaces
NASA Astrophysics Data System (ADS)
Luo, W.; Sarnak, P.
1994-03-01
We prove that the number variance for the spectrum of an arithmetic surface is highly nonrigid in part of the universal range. In fact it is close to having a Poisson behavior. This fact was discovered numerically by Schmit, Bogomolny, Georgeot and Giannoni. It has its origin in the high degeneracy of the length spectrum, first observed by Selberg.
Preferential solvation: dividing surface vs excess numbers.
Shimizu, Seishi; Matubayasi, Nobuyuki
2014-04-10
How do osmolytes affect the conformation and configuration of supramolecular assembly, such as ion channel opening and actin polymerization? The key to the answer lies in the excess solvation numbers of water and osmolyte molecules; these numbers are determinable solely from experimental data, as guaranteed by the phase rule, as we show through the exact solution theory of Kirkwood and Buff (KB). The osmotic stress technique (OST), in contrast, purposes to yield alternative hydration numbers through the use of the dividing surface borrowed from the adsorption theory. However, we show (i) OST is equivalent, when it becomes exact, to the crowding effect in which the osmolyte exclusion dominates over hydration; (ii) crowding is not the universal driving force of the osmolyte effect (e.g., actin polymerization); (iii) the dividing surface for solvation is useful only for crowding, unlike in the adsorption theory which necessitates its use due to the phase rule. KB thus clarifies the true meaning and limitations of the older perspectives on preferential solvation (such as solvent binding models, crowding, and OST), and enables excess number determination without any further assumptions.
Long-term Trend of Sunspot Numbers
NASA Astrophysics Data System (ADS)
Gao, P. X.
2016-10-01
Using the Hilbert–Huang Transform method, we investigate the long-term trend of yearly mean total sunspot numbers in the time interval of 1700–2015, which come from the World Data Center—the sunspot Index and long-term solar observations. The main findings of this study are summarized below. (1) From the adaptive trend, which is extracted from the yearly mean total sunspot numbers, we can find that the value gradually increases during the time period 1700–1975, then decreases gradually from 1975 to 2015. (2) The Centennial Gleissberg Cycle is extracted from the yearly mean total sunspot numbers and confirms that a new grand minimum is in progress; the Dalton Minimum, the Gleissberg Minimum, and low level of solar activity during solar cycle 24 (the part of the new grand minimum) all can be understood as minima of the Centennial Gleissberg Cycle. (3) Based on the adaptive (overall) trend, and the 100-year and longer timescale trend of yearly mean total sunspot numbers, we can infer that the level of solar activity during the new grand minimum may be close to that during the Gleissberg Minimum, slightly higher than that during the Dalton Minimum, and significantly higher than that during the Maunder Minimum. Our results do not support the suggestion that a new grand minimum, somewhat resembling the Maunder Minimum, is in progress.
How Do Students Misunderstand Number Representations?
ERIC Educational Resources Information Center
Herman, Geoffrey L.; Zilles, Craig; Loui, Michael C.
2011-01-01
We used both student interviews and diagnostic testing to reveal students' misconceptions about number representations in computing systems. This article reveals that students who have passed an undergraduate level computer organization course still possess surprising misconceptions about positional notations, two's complement representation, and…
Maple Explorations, Perfect Numbers, and Mersenne Primes
ERIC Educational Resources Information Center
Ghusayni, B.
2005-01-01
Some examples from different areas of mathematics are explored to give a working knowledge of the computer algebra system Maple. Perfect numbers and Mersenne primes, which have fascinated people for a very long time and continue to do so, are studied using Maple and some questions are posed that still await answers.
Toward a Coherent Treatment of Negative Numbers
ERIC Educational Resources Information Center
Kreith, Kurt; Mendle, Al
2013-01-01
The transition from whole numbers to integers involves challenges for both students and teachers. Leadership in mathematics education calls for an ability to translate depth of understanding into effective teaching methods, and this landscape includes alternative treatments of familiar topics. Noting the multiple meanings associated with the…
Assessments: Numbers, Context, Graphics, and Assumptions
ERIC Educational Resources Information Center
Zorin, Barbara; Hunsader, Patricia D.; Thompson, Denisse R.
2013-01-01
This article shows how to modify classroom evaluation items to avoid four potential difficulties that limit a teacher's insight into students' mathematical understanding by addressing these issues: (1) poor choice of numbers; (2) implausible or inappropriate contexts; (3) inclusion of graphics that do not help make learning visible; and…
Magnetic Particle Recovery of Serial Numbers
D. Utrata; M.J. Johnson
2003-10-01
One method used by crime labs to recover obliterated serial numbers in steel firearms (ferrous samples) is the magnetic particle technique. The use of this method is predicated on the detection of metal deformation present under stamped serial numbers after the visible stamp has been removed. Equipment specialized for this detection is not used in these attempts; a portable magnetic yoke used typically for flaw detection on large weldments or structures, along with dry visible magnetic powders, have been the tools of criminologists working in this area. Crime labs have reported low success rates using these tools [1, 2]. This is not surprising when one considers that little formal development has apparently evolved for use in such investigations since the publication of seminal work in this area some time ago [3]. The aim of this project is to investigate specific aspects of magnetic particle inspection for serial number recovery. This includes attempts to understand the magnetic characteristics of different steels that affect their performance in the test, such as varying results for carbon steels and alloy steels after different thermal and forming treatments. Also investigated are the effects of the nature of the sample magnetization (AC, rectified DC, and true DC) and the use of various detection media, such as visible powders and fluorescent sprays, on test outcome. Additionally, some aspects of surface preparation of firearm samples prior to number recovery were included in this work. The scope of this report includes a brief overview of the magnetic particle inspection method in general and its applications to forensic serial number recovery. This is followed by a description of how such investigations were simulated on lab samples, including a look at how the microstructure of a given steel will affect its performance in the test. Investigations into the serial number recovery in a series of ferromagnetic firearms (both steel and certain stainless steels
Quantum abacus for counting and factorizing numbers
Suslov, M. V.; Lesovik, G. B.; Blatter, G.
2011-05-15
We generalize the binary quantum counting algorithm of Lesovik, Suslov, and Blatter [Phys. Rev. A 82, 012316 (2010)] to higher counting bases. The algorithm makes use of qubits, qutrits, and qudits to count numbers in a base-2, base-3, or base-d representation. In operating the algorithm, the number n
Quantum abacus for counting and factorizing numbers
NASA Astrophysics Data System (ADS)
Suslov, M. V.; Lesovik, G. B.; Blatter, G.
2011-05-01
We generalize the binary quantum counting algorithm of Lesovik, Suslov, and Blatter [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.82.012316 82, 012316 (2010)] to higher counting bases. The algorithm makes use of qubits, qutrits, and qudits to count numbers in a base-2, base-3, or base-d representation. In operating the algorithm, the number n
MHD Turbulence at Moderate Magnetic Reynolds Number
NASA Technical Reports Server (NTRS)
Knaepen, B.; Kassinos, S.; Carati, D.
2003-01-01
In the present article we will consider the decay of MHD turbulence under the influence of a strong external magnetic field at moderate magnetic Reynolds numbers. Typical values of R(sub m) that are considered here range from R(sub m) approx. 0.1 to R(sub m) approx. 20. As a comparison, the initial kinetic Reynolds number common to all our simulations is Re(sub L) = 199. This means that the range of Prandtl numbers explored is 5 x 10(exp -4) to 10(exp -1). Our motivation is mainly to exhibit how the transition from the QS approximation to FMHD occurs. At the lowest values of R(sub m) studied here, the QS approximation is shown to model the flow faithfully. However, for the higher values of R(sub m) considered, it is clearly inadequate but can be replaced by another approximation which will be referred to as the Quasi-Linear (QL) approximation. Another objective of the present study is to describe how variations in the magnetic Reynolds number (while maintaining all other parameters constant) affect the dynamics of the flow. This complements past studies where variations in either the strength of the external magnetic field or the kinetic Reynolds number were considered. This article is organized as follows. In section 2 we recall the definition of the quasi-static approximation. Section 3 is devoted to the description of the numerical experiments performed using the quasi-static approximation and full MHD. In section 4 we describe the quasi-linear approximation and test it numerically against full MHD. A concluding summary is given in section 5.
Low Ekman Number Dynamos in Cartesian Geometry
NASA Astrophysics Data System (ADS)
Stellmach, S.; Hansen, U.
2002-12-01
Fully self consistent 3d dynamo simulations in spherical geometry have become an important part of geomagnetic research during the last years. The parameter range accesible for these models is quite limited and far away from the values estimated for the Earth's core. Especially viscous effects are overestimated by many orders of magnitude in all models published today. In view of these difficulties, we use a plane layer dynamo model which is computationally less demanding to study dynamo processes in the regime of low viscosity. The calculations we present employ Ekman numbers in the range E=10-4-5 x 10-6 without using parameterizations such as hyperdiffusion. Full inertia with Pr=1 is included where Pr denotes the Prandtl number. We find subcritical dynamos which remain stable for two magnetic decay times and an example of an initially stable subcritical dynamo which starts to decay after more than one magnetic diffusion time. For both supercritical and subcritical cases, the force balances are analyzed in detail. We show that at low Ekman number the leading order force balance in our calculations is between Coriolis, buoyancy, pressure and Lorentz forces while both inertial and viscous forces are small in the bulk of the layer. The resulting flow is strongly influenced by the Taylor-Proudman effect and dominated by small scale structures. In the range of investigated Ekman numbers, the dominating length scales decrease with decreasing E. Although Taylor's constraint is not satisfied in the entire domain we find that the spatial mean value of the normalized Taylor integrals decreases with decreasing Ekman number.
The effect of Prandtl number on mixing in low Reynolds number Kelvin-Helmholtz billows
NASA Astrophysics Data System (ADS)
Rahmani, M.; Seymour, B. R.; Lawrence, G. A.
2016-05-01
The effect of Prandtl number on mixing in temporally evolving Kelvin-Helmholtz (KH) instabilities at low to moderate Reynolds numbers is studied through direct numerical simulation. We distinguish between the mixing induced by the primary billow and the mixing generated by three-dimensional motions by performing each simulation in two and three dimensions. The results indicate that the time evolution of the rate of two- and three-dimensional mixing through different stages of the life cycle of KH flow is significantly influenced by the Prandtl number. As the Prandtl number increases, the final amount of mixing increases for Reynolds that are too low to support active three-dimensional motions. This trend is the opposite in sufficiently high Reynolds number KH flows that can overcome viscous effects and develop significant three-dimensional instabilities. While the mixing generated in the two-dimensional flows, uniform in the span-wise direction, is not significantly dependent on the Prandtl number, the turbulent mixing induced by three-dimensional motions is a function of the Prandtl number. We observe a steady increase in the total amount of mixing for buoyancy Reynolds numbers above 7, consistent with the results of Shih et al. ["Parameterization of turbulent fluxes and scales using homogeneous sheared stably stratified turbulence simulations," J. Fluid Mech. 525, 193-214 (2005)]. Both maximum instantaneous and cumulative mixing efficiencies exhibit a decreasing trend with increasing Prandtl number. We compare the dependence of the mixing efficiency on Prandtl number to previous studies.
Courant Number and Mach Number Insensitive CE/SE Euler Solvers
NASA Technical Reports Server (NTRS)
Chang, Sin-Chung
2005-01-01
It has been known that the space-time CE/SE method can be used to obtain ID, 2D, and 3D steady and unsteady flow solutions with Mach numbers ranging from 0.0028 to 10. However, it is also known that a CE/SE solution may become overly dissipative when the Mach number is very small. As an initial attempt to remedy this weakness, new 1D Courant number and Mach number insensitive CE/SE Euler solvers are developed using several key concepts underlying the recent successful development of Courant number insensitive CE/SE schemes. Numerical results indicate that the new solvers are capable of resolving crisply a contact discontinuity embedded in a flow with the maximum Mach number = 0.01.
A Revised Collection of Sunspot Group Numbers
NASA Astrophysics Data System (ADS)
Vaquero, J. M.; Svalgaard, L.; Carrasco, V. M. S.; Clette, F.; Lefèvre, L.; Gallego, M. C.; Arlt, R.; Aparicio, A. J. P.; Richard, J.-G.; Howe, R.
2016-09-01
We describe a revised collection of the number of sunspot groups from 1610 to the present. This new collection is based on the work of Hoyt and Schatten (Solar Phys. 179, 189, 1998). The main changes are the elimination of a considerable number of observations during the Maunder Minimum (hereafter, MM) and the inclusion of several long series of observations. Numerous minor changes are also described. Moreover, we have calculated the active-day percentage during the MM from this new collection as a reliable index of the solar activity. Thus, the level of solar activity obtained in this work is greater than the level obtained using the original Hoyt and Schatten data, although it remains compatible with a grand minimum of solar activity. The new collection is available in digital format.
Finite-particle-number approach to physics
Noyes, H.P.
1982-10-01
Starting from a discrete, self-generating and self-organizing, recursive model and self-consistent interpretive rules we construct: the scale constants of physics (3,10,137,1.7x10/sup 38/); 3+1 Minkowski space with a discrete metric and the algebraic bound ..delta.. is an element of ..delta.. tau is greater than or equal to 1; the Einstein-deBroglie relation; algebraic double slit interference; a single-time momentum-space scattering theory connected to laboratory experience; an approximation to wave functions; local phase severance and hence both distant correlations and separability; baryon number, lepton number, charge and helicity; m/sub p//m/sub e/; a cosmology not in disagreement with current observations.
The MCNP5 Random number generator
Brown, F. B.; Nagaya, Y.
2002-01-01
MCNP and other Monte Carlo particle transport codes use random number generators to produce random variates from a uniform distribution on the interval. These random variates are then used in subsequent sampling from probability distributions to simulate the physical behavior of particles during the transport process. This paper describes the new random number generator developed for MCNP Version 5. The new generator will optionally preserve the exact random sequence of previous versions and is entirely conformant to the Fortran-90 standard, hence completely portable. In addition, skip-ahead algorithms have been implemented to efficiently initialize the generator for new histories, a capability that greatly simplifies parallel algorithms. Further, the precision of the generator has been increased, extending the period by a factor of 10{sup 5}. Finally, the new generator has been subjected to 3 different sets of rigorous and extensive statistical tests to verify that it produces a sufficiently random sequence.
Operational conditions for random-number generation
NASA Astrophysics Data System (ADS)
Compagner, A.
1995-11-01
Ensemble theory is used to describe arbitrary sequences of integers, whether formed by the decimals of π or produced by a roulette or by any other means. Correlation coefficients of any range and order are defined as Fourier transforms of the ensemble weights. Competing definitions of random sequences are considered. Special attention is given to sequences of random numbers needed for Monte Carlo calculations. Different recipes for those sequences lead to correlations that vary in range and order, but the total amount of correlation is the same for all sequences of a given length (without internal periodicities). For maximum-length sequences produced by linear algorithms, most correlation coefficients are zero, but the remaining ones are of absolute value 1. In well-tempered sequences, these complete correlations are of high order or of very long range. General conditions to be obeyed by random-number generators are discussed and a qualitative method for comparing different recipes is given.
AMR for low Mach number reacting flow
Bell, John B.
2004-01-16
We present a summary of recent progress on the development and application of adaptive mesh refinement algorithms for low Mach number reacting flows. Our approach uses a form of the low Mach number equations based on a general equation of state that discretely conserves both mass and energy. The discretization methodology is based on a robust projection formulation that accommodates large density contrasts. The algorithm supports modeling of multicomponent systems and incorporates an operator-split treatment of stiff reaction terms. The basic computational approach is embedded in an adaptive projection framework that uses structured hierarchical grids with subcycling in time that preserves the discrete conservation properties of the underlying single-grid algorithm. We present numerical examples illustrating the application of the methodology to turbulent premixed combustion and nuclear flames in type Ia supernovae.
Quark number fluctuations at high temperatures
Petreczky, P.; Hegde, P.; Velytsky, A.
2009-11-01
We calculate the second, fourth and sixth order quark number fluctuations in the deconfined phase of 2+1 flavor QCD using lattices with temporal extent N{sub t} = 4,6,8 and 12. We consider light, strange and charm quarks. We use p4 action for valence quarks and gauge configurations generated with p4 action with physical value of the strange quark mass and light quark mass m{sub q} = 0.1 m{sub s} generated by the RBC-Bielefeld collaboration. We observe that for all quark masses the quark number fluctuations rapidly get close to the corresponding ideal gas limits. We compare our results to predictions of a quasi-particle model and resummed high temperature perturbative calculations. We also investigate correlations among different flavor channels.
Secure Computation with Fixed-Point Numbers
NASA Astrophysics Data System (ADS)
Catrina, Octavian; Saxena, Amitabh
Secure computation is a promising approach to business problems in which several parties want to run a joint application and cannot reveal their inputs. Secure computation preserves the privacy of input data using cryptographic protocols, allowing the parties to obtain the benefits of data sharing and at the same time avoid the associated risks. These business applications need protocols that support all the primitive data types and allow secure protocol composition and efficient application development. Secure computation with rational numbers has been a challenging problem. We present in this paper a family of protocols for multiparty computation with rational numbers using fixed-point representation. This approach offers more efficient solutions for secure computation than other usual representations.
Predict octane number for gasoline blends
Zahed, A.H.; Mullah, S.A.; Bashir, M.D. )
1993-05-01
A model with five independent variables is used to predict the octane number of gasoline blends with more accuracy than any previous model. Often, it is useful to know the resulting octane number before the gasoline is blended. Clearly, such a model is useful because good predictive models have been few and far between. With high-powered and faster personal computers, regressional analyses are quite easy to perform with many more independent variables. The objective here was to develop an empirical equation using the regressional analyses are quite easy to perform with many more independent variables. The objective here was to develop an empirical equation using the regression analysis technique to predict the octane rating of 16 blends of motor gasoline. Predicted results for the 16 blends of gasolines were compared with experimental results obtained on CFR engines. Predicted results from the proposed empirical model were in agreement with the experimental data with an average deviational error of 0.54%.
Saccades compress space, time and number.
Burr, David C; Ross, John; Binda, Paola; Morrone, M Concetta
2010-12-01
It has been suggested that space, time and number are represented on a common subjective scale. Saccadic eye movements provide a fascinating test. Saccades compress the perceived magnitude of spatial separations and temporal intervals to approximately half of their true value. The question arises as to whether saccades also compress number. They do, and compression follows a very similar time course for all three attributes: it is maximal at saccadic onset and decreases to veridicality within a window of approximately 50ms. These results reinforce the suggestion of a common perceptual metric, which is probably mediated by the intraparietal cortex; they further suggest that before each saccade the common metric for all three is reset, possibly to pave the way for a fresh analysis of the post-saccadic situation.
Hot wire in low Reynolds number flow
NASA Technical Reports Server (NTRS)
Kolb, M. A.; Covert, E. E.
1984-01-01
Progress reports were issued on the following experiments: (1) low Reynolds number flow phenomenon of periodic vortex shedding in the wake behind a cylinder as studied by applying the hot wire anemometer technique of flow measurement. The downstream diffusion of these shed vortices was of prime concern. An evaluation of the performance of the hot wire at low Reynolds number is also considered. (2) A brief examination of the back sections of the Wright Brothers wind tunnel circuits were conducted to establish whether or not gross flow deviations were present at corners, or turning vane regions. A calibration of the test sections was done. (3) The attractiveness of using rembedded grids for airfoil calculations modeled by the Euler equations was explored. These calculations were extended to C-type grids and then to Navier-Stokes calculations,
Bridge condition assessment using D numbers.
Deng, Xinyang; Hu, Yong; Deng, Yong
2014-01-01
Bridge condition assessment is a complex problem influenced by many factors. The uncertain environment increases more its complexity. Due to the uncertainty in the process of assessment, one of the key problems is the representation of assessment results. Though there exists many methods that can deal with uncertain information, however, they have more or less deficiencies. In this paper, a new representation of uncertain information, called D numbers, is presented. It extends the Dempster-Shafer theory. By using D numbers, a new method is developed for the bridge condition assessment. Compared to these existing methods, the proposed method is simpler and more effective. An illustrative case is given to show the effectiveness of the new method.
Sensitivity in risk analyses with uncertain numbers.
Tucker, W. Troy; Ferson, Scott
2006-06-01
Sensitivity analysis is a study of how changes in the inputs to a model influence the results of the model. Many techniques have recently been proposed for use when the model is probabilistic. This report considers the related problem of sensitivity analysis when the model includes uncertain numbers that can involve both aleatory and epistemic uncertainty and the method of calculation is Dempster-Shafer evidence theory or probability bounds analysis. Some traditional methods for sensitivity analysis generalize directly for use with uncertain numbers, but, in some respects, sensitivity analysis for these analyses differs from traditional deterministic or probabilistic sensitivity analyses. A case study of a dike reliability assessment illustrates several methods of sensitivity analysis, including traditional probabilistic assessment, local derivatives, and a ''pinching'' strategy that hypothetically reduces the epistemic uncertainty or aleatory uncertainty, or both, in an input variable to estimate the reduction of uncertainty in the outputs. The prospects for applying the methods to black box models are also considered.
Low Reynolds number, long endurance aircraft design
Foch, R.J.; Ailinger, K.G. )
1992-02-01
Airplanes are typically designed to maximize range at the highest practical cruising speed. However, several missions require extended duration rather than range, and favor the slowest possible cruise speed. Such missions include surveillance, radio relay, and ship's electronic decoy. These missions are ideally suited for advanced technology unmanned aircraft, either remotely piloted or autonomous. Feasibility studies have been conducted and flight demonstrator prototypes of such unique aircraft have been under steady research and development at the Naval Research Laboratory since 1978. This paper discusses the design aspects and tradeoffs unique to small, slow speed long endurance unmanned aircraft operating at wing chord Reynolds numbers between 150,000 and 500,000. Additionally, many of these low Reynolds number-driven design features have applicability to high altitude, long endurance aircraft. 6 refs.
NASA Technical Reports Server (NTRS)
Wilson, Robert M.
2014-01-01
Examined are the yearly variations and ratios of sunspot number, the number of sunspot groups, and the total corrected sunspot area for the interval 1875-2013. While yearly sunspot number independently correlates strongly (r = 0.98) with the yearly number of sunspot groups (y = -2 + 11.99x) and the total corrected sunspot area (y = 5 + 0.059x), the strongest correlation (Ry12 = 0.99) is the one based on the bivariate fit of sunspot number against the combined variations of the number of sunspot groups and sunspot area (y = 1 + 5.88x1 + 0.031x2, where y refers to sunspot number, x1 refers to the number of sunspot groups, and x2 refers to the sunspot area). While all cycle minima based on the bivariate fit are concurrent with the observed minimum in sunspot number, cycle maxima are sometimes found to differ. For sunspot cycles 12, 19, 20, and 23, cycle maximum is inferred to have occurred in 1884, 1958, 1970, and 2002, respectively, rather than in 1883, 1957, 1968, and 2000, based on the observed sunspot number. Also, cycle 19's maximum amplitude based on observed sunspot number seems too high in comparison to that found using the bivariate fit. During the 139-year interval 1875-2013, the difference between the observed and predicted sunspot number based on the bivariate fit is <1 standard error of estimate (se) (<6.4) for 111 years, between 1 and <2 se (6.4 to <12.8) for 28 years, and =2 se (=12.8) for only 4 years, these years being 1957 (16.6), 1978 (-15.8), 1980 (23), and 1982 (-16.3). For sunspot cycle 24, the difference between observed and predicted values has been only -0.7 and 3.2 (=0.5 se).
Teleportation-based number-state manipulation with number-sum measurement
Kitagawa, Akira; Yamamoto, Katsuji
2003-10-01
We examine various manipulations of photon number states which can be implemented by teleportation technique with number-sum measurement. The preparations of the Einstein-Podolsky-Rosen resources as well as the number-sum measurement resulting in projection to certain Bell state may be done conditionally with linear optical elements, i.e., beam splitters, phase shifters, and zero-one-photon detectors. Squeezed vacuum states are used as primary entanglement resource, while single-photon sources are not required.
48 CFR 304.7001 - Numbering acquisitions.
Code of Federal Regulations, 2013 CFR
2013-10-01
.... AHRQ: A ASPR/OAMCG: O CDC: D CMS: M FDA: F HRSA: H IHS: I NIH: N PSC: P SAMHSA: S (3) The three-digit... Institute, NIH, may number its first contract for fiscal year 2009 as HHSN261200900001C. (Note: When more... identification code of the servicing agency: AHRQ: A ASPR/OAMCG: O CDC: D CMS: M FDA: F HRSA: H IHS: I NIH: N...
48 CFR 304.7001 - Numbering acquisitions.
Code of Federal Regulations, 2014 CFR
2014-10-01
.... AHRQ: A ASPR/OAMCG: O CDC: D CMS: M FDA: F HRSA: H IHS: I NIH: N PSC: P SAMHSA: S (3) The three-digit... Institute, NIH, may number its first contract for fiscal year 2009 as HHSN261200900001C. (Note: When more... identification code of the servicing agency: AHRQ: A ASPR/OAMCG: O CDC: D CMS: M FDA: F HRSA: H IHS: I NIH: N...
48 CFR 304.7001 - Numbering acquisitions.
Code of Federal Regulations, 2012 CFR
2012-10-01
.... AHRQ: A ASPR/OAMCG: O CDC: D CMS: M FDA: F HRSA: H IHS: I NIH: N PSC: P SAMHSA: S (3) The three-digit... Institute, NIH, may number its first contract for fiscal year 2009 as HHSN261200900001C. (Note: When more... identification code of the servicing agency: AHRQ: A ASPR/OAMCG: O CDC: D CMS: M FDA: F HRSA: H IHS: I NIH: N...
On the Decimal Numbers Base "n"
ERIC Educational Resources Information Center
Poon, K.-K.; Yeung, K.-W.; Shiu, W.-C.
2005-01-01
This paper focuses on the representation of a proper fraction "a"/"b" by a decimal number base "n" where "n" is any integer greater than 1. The scope is narrowed to look at only fractions where "a","b" are positive integers with "a" less than "b" and "b" not equal to 0 nor equal to 1. Some relationships were found between "b" and "n", which…
Particle number fluctuations in a canonical ensemble
Begun, V.V.; Gazdzicki, M.; Gorenstein, M.I.; Zozulya, O.S.
2004-09-01
Fluctuations of charged particle number are studied in the canonical ensemble. In the infinite volume limit the fluctuations in the canonical ensemble are different from the fluctuations in the grand canonical one. Thus, the well-known equivalence of both ensembles for the average quantities does not extend for the fluctuations. In view of the possible relevance of the results for the analysis of fluctuations in nuclear collisions at high energies, a role of the limited kinematical acceptance is studied.
Linking numbers, spin, and statistics of solitons
NASA Technical Reports Server (NTRS)
Wilczek, F.; Zee, A.
1983-01-01
The spin and statistics of solitons in the (2 + 1)- and (3 + 1)-dimensional nonlinear sigma models is considered. For the (2 + 1)-dimensional case, there is the possibility of fractional spin and exotic statistics; for 3 + 1 dimensions, the usual spin-statistics relation is demonstrated. The linking-number interpretation of the Hopf invariant and the use of suspension considerably simplify the analysis.
Measurement of nonvolatile particle number size distribution
NASA Astrophysics Data System (ADS)
Gkatzelis, G. I.; Papanastasiou, D. K.; Florou, K.; Kaltsonoudis, C.; Louvaris, E.; Pandis, S. N.
2016-01-01
An experimental methodology was developed to measure the nonvolatile particle number concentration using a thermodenuder (TD). The TD was coupled with a high-resolution time-of-flight aerosol mass spectrometer, measuring the chemical composition and mass size distribution of the submicrometer aerosol and a scanning mobility particle sizer (SMPS) that provided the number size distribution of the aerosol in the range from 10 to 500 nm. The method was evaluated with a set of smog chamber experiments and achieved almost complete evaporation (> 98 %) of secondary organic as well as freshly nucleated particles, using a TD temperature of 400 °C and a centerline residence time of 15 s. This experimental approach was applied in a winter field campaign in Athens and provided a direct measurement of number concentration and size distribution for particles emitted from major pollution sources. During periods in which the contribution of biomass burning sources was dominant, more than 80 % of particle number concentration remained after passing through the thermodenuder, suggesting that nearly all biomass burning particles had a nonvolatile core. These remaining particles consisted mostly of black carbon (60 % mass contribution) and organic aerosol (OA; 40 %). Organics that had not evaporated through the TD were mostly biomass burning OA (BBOA) and oxygenated OA (OOA) as determined from AMS source apportionment analysis. For periods during which traffic contribution was dominant 50-60 % of the particles had a nonvolatile core while the rest evaporated at 400 °C. The remaining particle mass consisted mostly of black carbon with an 80 % contribution, while OA was responsible for another 15-20 %. Organics were mostly hydrocarbon-like OA (HOA) and OOA. These results suggest that even at 400 °C some fraction of the OA does not evaporate from particles emitted from common combustion processes, such as biomass burning and car engines, indicating that a fraction of this type of OA
Laser interrogation of latent vehicle registration number
Russo, R.E. |; Pelkey, G.E.; Grant, P.; Whipple, R.E.; Andresen, B.D.
1994-09-01
A recent investigation involved automobile registration numbers as important evidentiary specimens. In California, as in most states, small, thin metallic decals are issued to owners of vehicles each year as the registration is renewed. The decals are applied directly to the license plate of the vehicle and typically on top of the previous year`s expired decal. To afford some degree of security, the individual registration decals have been designed to tear easily; they cannot be separated from each other, but can be carefully removed intact from the metal license plate by using a razor blade. In September 1993, the City of Livermore Police Department obtained a blue 1993 California decal that had been placed over an orange 1992 decal. The two decals were being investigated as possible evidence in a case involving vehicle registration fraud. To confirm the suspicion and implicate a suspect, the department needed to known the registration number on the bottom (completely covered) 1992 decal. The authors attempted to use intense and directed light to interrogate the colored stickers. Optical illumination using a filtered white-light source partially identified the latent number. However, the most successful technique used a tunable dye laser pumped by a pulsed Nd:YAG laser. By selectively tuning the wavelength and intensity of the dye laser, backlit illumination of the decals permitted visualization of the underlying registration number through the surface of the top sticker. With optimally-tuned wavelength and intensity, 100% accuracy was obtained in identifying the sequence of latent characters. The advantage of optical techniques is their completely nondestructive nature, thus preserving the evidence for further interrogation or courtroom presentation.
Detecting Prime Numbers via Roots of Polynomials
ERIC Educational Resources Information Center
Dobbs, David E.
2012-01-01
It is proved that an integer n [greater than or equal] 2 is a prime (resp., composite) number if and only if there exists exactly one (resp., more than one) nth-degree monic polynomial f with coefficients in Z[subscript n], the ring of integers modulo n, such that each element of Z[subscript n] is a root of f. This classroom note could find use in…
Condition number estimation of preconditioned matrices.
Kushida, Noriyuki
2015-01-01
The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results. The Lanczos connection based method provides the condition numbers of coefficient matrices of systems of linear equations with information obtained through the preconditioned conjugate gradient method. Estimating the condition number of preconditioned matrices is sometimes important when describing the effectiveness of new preconditionerers or selecting adequate preconditioners. Operating a preconditioner on a coefficient matrix is the simplest method of estimation. However, this is not possible for large-scale computing, especially if computation is performed on distributed memory parallel computers. This is because, the preconditioned matrices become dense, even if the original matrices are sparse. Although the Lanczos connection method can be used to calculate the condition number of preconditioned matrices, it is not considered to be applicable to large-scale problems because of its weakness with respect to numerical errors. Therefore, we have developed a robust and parallelizable method based on Hager's method. The feasibility studies are curried out for the diagonal scaling preconditioner and the SSOR preconditioner with a diagonal matrix, a tri-daigonal matrix and Pei's matrix. As a result, the Lanczos connection method contains around 10% error in the results even with a simple problem. On the other hand, the new method contains negligible errors. In addition, the newly developed method returns reasonable solutions when the Lanczos connection method fails with Pei's matrix, and matrices generated with the finite element method.
Semantics and the Number of English Sentences.
ERIC Educational Resources Information Center
Bjurlof, Thomas; Jamieson, Dale
It has long been said that there are an infinite number of English sentences. "This is the cat that caught the rat" is an Enqlish sentence. So is "This is the cat that caught the rat that stole the cheese.""This is the cat with white paws that caught the rat that stole the cheese" is unobjectionable as well. Since a clear cutoff point cannot be…
Nowcasting sunshine number using logistic modeling
NASA Astrophysics Data System (ADS)
Brabec, Marek; Badescu, Viorel; Paulescu, Marius
2013-04-01
In this paper, we present a formalized approach to statistical modeling of the sunshine number, binary indicator of whether the Sun is covered by clouds introduced previously by Badescu (Theor Appl Climatol 72:127-136, 2002). Our statistical approach is based on Markov chain and logistic regression and yields fully specified probability models that are relatively easily identified (and their unknown parameters estimated) from a set of empirical data (observed sunshine number and sunshine stability number series). We discuss general structure of the model and its advantages, demonstrate its performance on real data and compare its results to classical ARIMA approach as to a competitor. Since the model parameters have clear interpretation, we also illustrate how, e.g., their inter-seasonal stability can be tested. We conclude with an outlook to future developments oriented to construction of models allowing for practically desirable smooth transition between data observed with different frequencies and with a short discussion of technical problems that such a goal brings.
Droplet Number Concentration Value Added Product
2015-08-06
Cloud droplet number concentration is an important factor in understanding aerosol-cloud interactions. As aerosol concentration increases, it is expected that droplet number concentration (Nd) will increase and droplet size will decrease, for a given liquid water path. This will greatly affect cloud albedo as smaller droplets reflect more shortwave radiation; however, the magnitude and variability of these processes under different environmental conditions is still uncertain.McComiskey et al. (2009) have implemented a method, based onBoers andmore » Mitchell (1994), for calculating Nd from ground-based remote sensing measurements of optical depth and liquid water path. They show that the magnitude of the aerosol-cloud interactions (ACI) varies with a range of factors, including the relative value of the cloud liquid water path (LWP), the aerosol size distribution, and the cloud updraft velocity. Estimates of Nd under a range of cloud types and conditions and at a variety of sites are needed to further quantify the impacts of aerosol cloud interactions. In order to provide data sets for studying aerosol-cloud interactions, the McComiskey et al. (2009) method was implemented as the Droplet Number Concentration (NDROP) value-added product (VAP).« less
Droplet Number Concentration Value Added Product
Chitra Sivaraman, PNNL
2015-08-06
Cloud droplet number concentration is an important factor in understanding aerosol-cloud interactions. As aerosol concentration increases, it is expected that droplet number concentration (Nd) will increase and droplet size will decrease, for a given liquid water path. This will greatly affect cloud albedo as smaller droplets reflect more shortwave radiation; however, the magnitude and variability of these processes under different environmental conditions is still uncertain.McComiskey et al. (2009) have implemented a method, based onBoers and Mitchell (1994), for calculating Nd from ground-based remote sensing measurements of optical depth and liquid water path. They show that the magnitude of the aerosol-cloud interactions (ACI) varies with a range of factors, including the relative value of the cloud liquid water path (LWP), the aerosol size distribution, and the cloud updraft velocity. Estimates of Nd under a range of cloud types and conditions and at a variety of sites are needed to further quantify the impacts of aerosol cloud interactions. In order to provide data sets for studying aerosol-cloud interactions, the McComiskey et al. (2009) method was implemented as the Droplet Number Concentration (NDROP) value-added product (VAP).
Vacuum Fluctuations, Cosmogenesis and Prime Number Gaps
NASA Astrophysics Data System (ADS)
Berezin, Alexander A.
2002-10-01
Starting from E.Tryon (1973), idea of cosmogenesis through quantum tunnelling "from nothing" became popular. Both complimentary streams of it, inflationary models (Guth, Linde) and quantum parallelism (Everett, Deutsch), require some starting point as, e.g., concretisation of Leibnitz Principle (Omnibus ex nihil decendis sufficit unum). This leads to propositional conjecture (axiom?) that (meta)physical "Platonic Pressure" of infinitude of numbers and Cantor "alephs" becomes an engine for self-generation of physical universe directly out of mathematics: inexhaustibility of Number Theory (NT) drives cosmogenesis. While physics in other quantum branches of inflating universe (Megaverse) can be (arbitrary) different from ours, NT is not (it is unique, absolute, immutable and infinitely resourceful). Energy-time uncertainty principle (UP) allows indefinite lifetime provided we start from total zero energy. Analogue of UP in NT is theorem by H.Maier (1981) stating the existence of arbitrary long trails of isolated primes such that each next gap is arbitrary greater than average gap (logN). On physical level these arbitrary large deviations from Prime Number Theorem translate into permissiveness of (arbitrary) large quantum fluctuations.
Sometimes area counts more than number
Hurewitz, Felicia; Gelman, Rochel; Schnitzer, Brian
2006-01-01
Using an interference paradigm, we show across three experiments that adults' order judgments of numbers, sizes, or combined area of dots in pairs of arrays occur spontaneously and automatically, but at different speeds and levels of accuracy. Experiment 1 used circles whose sizes varied between but not within arrays. Variation in circle size interfered with judgments of which array had more circles. Experiment 2 used displays in which circle size varied within and between arrays. Between-array differences in the amount of “circle stuff” (area occupied by circles) interfered with judgments of number. Experiment 3 examined whether variation in number also interferes with judgments of area. Interference between discrete and continuous stimulus dimensions occurred in both directions, although it was stronger from the continuous to the discrete than vice versa. These results bear on interpretations of studies with infants and preschoolers wherein subjects respond on the basis of continuous quantity rather than discrete quantity. In light of our results with adults, these findings do not license the conclusion that young children cannot represent discrete quantity. Absent data on attentional hierarchies and speed of processing, it is premature to conclude that infant and child quantity processes are fundamentally different from that of adults. PMID:17159143
Low-Reynolds-number swimming at pycnoclines.
Doostmohammadi, Amin; Stocker, Roman; Ardekani, Arezoo M
2012-03-01
Microorganisms play pivotal functions in the trophic dynamics and biogeochemistry of aquatic ecosystems. Their concentrations and activities often peak at localized hotspots, an important example of which are pycnoclines, where water density increases sharply with depth due to gradients in temperature or salinity. At pycnoclines organisms are exposed to different environmental conditions compared to the bulk water column, including reduced turbulence, slow mass transfer, and high particle and predator concentrations. Here we show that, at an even more fundamental level, the density stratification itself can affect microbial ecology at pycnoclines, by quenching the flow signature, increasing the energetic expenditure, and stifling the nutrient uptake of motile organisms. We demonstrate this through numerical simulations of an archetypal low-Reynolds-number swimmer, the "squirmer." We identify the Richardson number--the ratio of buoyancy forces to viscous forces--as the fundamental parameter that quantifies the effects of stratification. These results demonstrate an unexpected effect of buoyancy on low-Reynolds-number swimming, potentially affecting a broad range of abundant organisms living at pycnoclines in oceans and lakes.
CRC octane number requirement rating workshop 1992
Not Available
1992-10-01
An octane number requirement rating workshop was conducted. The objective of the workshop was to improve the application of the CRC E-15 Technique for Determination of Octane Number Requirement of Light-Duty Vehicles. The workshop was to improve the skills of those with minimal experience and provide experienced raters a forum for interacting with other raters of similar experience. Investigative procedures and techniques were encouraged to provide data regarding the latest electronic engine controls such as knock sensors and adaptive learning strategies. Eleven 1991 and 1992 model year vehicles were used for track practice and testing. Five of the vehicles were equipped with auxiliary fuel systems to allow operation on the octane number reference fuels. The other six vehicles were equipped with tachometers and vacuum gauges for determination of transmission shift characteristics. Several scan tools were available and were used on most of the GM vehicles to monitor knock sensor activity and spark timing. The test fuels used were full-boiling range unleaded fuels.
Low-Reynolds-number swimming at pycnoclines.
Doostmohammadi, Amin; Stocker, Roman; Ardekani, Arezoo M
2012-03-01
Microorganisms play pivotal functions in the trophic dynamics and biogeochemistry of aquatic ecosystems. Their concentrations and activities often peak at localized hotspots, an important example of which are pycnoclines, where water density increases sharply with depth due to gradients in temperature or salinity. At pycnoclines organisms are exposed to different environmental conditions compared to the bulk water column, including reduced turbulence, slow mass transfer, and high particle and predator concentrations. Here we show that, at an even more fundamental level, the density stratification itself can affect microbial ecology at pycnoclines, by quenching the flow signature, increasing the energetic expenditure, and stifling the nutrient uptake of motile organisms. We demonstrate this through numerical simulations of an archetypal low-Reynolds-number swimmer, the "squirmer." We identify the Richardson number--the ratio of buoyancy forces to viscous forces--as the fundamental parameter that quantifies the effects of stratification. These results demonstrate an unexpected effect of buoyancy on low-Reynolds-number swimming, potentially affecting a broad range of abundant organisms living at pycnoclines in oceans and lakes. PMID:22355147
Tidal Love Numbers of Neutron Stars
Hinderer, Tanja
2008-04-20
For a variety of fully relativistic polytropic neutron star models we calculate the star's tidal Love number k{sub 2}. Most realistic equations of state for neutron stars can be approximated as a polytrope with an effective index n {approx} 0.5-1.0. The equilibrium stellar model is obtained by numerical integration of the Tolman-Oppenheimer-Volkhov equations. We calculate the linear l = 2 static perturbations to the Schwarzschild spacetime following the method of Thorne and Campolattaro. Combining the perturbed Einstein equations into a single second-order differential equation for the perturbation to the metric coefficient g{sub tt} and matching the exterior solution to the asymptotic expansion of the metric in the star's local asymptotic rest frame gives the Love number. Our results agree well with the Newtonian results in the weak field limit. The fully relativistic values differ from the Newtonian values by up to {approx}24%. The Love number is potentially measurable in gravitational wave signals from inspiralling binary neutron stars.
Observer variability in estimating numbers: An experiment
Erwin, R.M.
1982-01-01
Census estimates of bird populations provide an essential framework for a host of research and management questions. However, with some exceptions, the reliability of numerical estimates and the factors influencing them have received insufficient attention. Independent of the problems associated with habitat type, weather conditions, cryptic coloration, ete., estimates may vary widely due only to intrinsic differences in observers? abilities to estimate numbers. Lessons learned in the field of perceptual psychology may be usefully applied to 'real world' problems in field ornithology. Based largely on dot discrimination tests in the laboratory, it was found that numerical abundance, density of objects, spatial configuration, color, background, and other variables influence individual accuracy in estimating numbers. The primary purpose of the present experiment was to assess the effects of observer, prior experience, and numerical range on accuracy in estimating numbers of waterfowl from black-and-white photographs. By using photographs of animals rather than black dots, I felt the results could be applied more meaningfully to field situations. Further, reinforcement was provided throughout some experiments to examine the influence of training on accuracy.
Canonical number systems, counting automata and fractals
NASA Astrophysics Data System (ADS)
Scheicher, Klaus; Thuswaldner, Jörg M.
2002-07-01
In this paper we study properties of the fundamental domain [script F][beta] of number systems, which are defined in rings of integers of number fields. First we construct addition automata for these number systems. Since [script F][beta] defines a tiling of the n-dimensional vector space, we ask, which tiles of this tiling ‘touch’ [script F][beta]. It turns out that the set of these tiles can be described with help of an automaton, which can be constructed via an easy algorithm which starts with the above-mentioned addition automaton. The addition automaton is also useful in order to determine the box counting dimension of the boundary of [script F][beta]. Since this boundary is a so-called graph-directed self-affine set, it is not possible to apply the general theory for the calculation of the box counting dimension of self similar sets. Thus we have to use direct methods.
Reynolds number effects in combustion noise
NASA Technical Reports Server (NTRS)
Seshan, P. K.
1981-01-01
Acoustic emission spectra have been obtained for non-premixed turbulent combustion from two small diameter laboratory gas burners, two commercial gas burners and a large gas burner in the firebox of a Babcock-Wilcox Boiler (50,000 lb steam/hr). The changes in burner size and firing rate represent changes in Reynolds number and changes in air/fuel ratio represent departure from stoichiometric proportions. The combustion efficiency was measured independently through gas analysis. The acoustic spectra obtained from the various burners exhibit a persistent shape over the Reynolds number range of 8200-82,000. The spectra were analyzed for identification of a predictable frequency domain that is most responsive to, and readily correlated with, combustion efficiency. A simple parameter (consisting of the ratio of the average acoustic power output in the most responsive frequency bandwidth to the acoustic power level of the loudest frequency) is proposed whose value increases significantly and unmistakably as combustion efficiency approaches 100%. The dependence of the most responsive frequency domain on the various Reynolds numbers associated with turbulent jets is discussed.
Source-Independent Quantum Random Number Generation
NASA Astrophysics Data System (ADS)
Cao, Zhu; Zhou, Hongyi; Yuan, Xiao; Ma, Xiongfeng
2016-01-01
Quantum random number generators can provide genuine randomness by appealing to the fundamental principles of quantum mechanics. In general, a physical generator contains two parts—a randomness source and its readout. The source is essential to the quality of the resulting random numbers; hence, it needs to be carefully calibrated and modeled to achieve information-theoretical provable randomness. However, in practice, the source is a complicated physical system, such as a light source or an atomic ensemble, and any deviations in the real-life implementation from the theoretical model may affect the randomness of the output. To close this gap, we propose a source-independent scheme for quantum random number generation in which output randomness can be certified, even when the source is uncharacterized and untrusted. In our randomness analysis, we make no assumptions about the dimension of the source. For instance, multiphoton emissions are allowed in optical implementations. Our analysis takes into account the finite-key effect with the composable security definition. In the limit of large data size, the length of the input random seed is exponentially small compared to that of the output random bit. In addition, by modifying a quantum key distribution system, we experimentally demonstrate our scheme and achieve a randomness generation rate of over 5 ×103 bit /s .
On the relation between grammatical number and cardinal numbers in development.
Sarnecka, Barbara W
2014-01-01
This mini-review focuses on the question of how the grammatical number system of a child's language may help the child learn the meanings of cardinal number words (e.g., "one" and "two"). Evidence from young children learning English, Russian, Japanese, Mandarin, Slovenian, or Saudi Arabic suggests that trajectories of number-word learning differ for children learning different languages. Children learning English, which distinguishes between singular and plural, seem to learn the meaning of the cardinal number "one" earlier than children learning Japanese or Mandarin, which have very little singular/plural marking. Similarly, children whose languages have a singular/dual/plural system (Slovenian and Saudi Arabic) learn the meaning of "two" earlier than English-speaking children. This relation between grammatical and cardinal number may shed light on how humans acquire cardinal-number concepts. There is an ongoing debate about whether mental symbols for small cardinalities (concepts for "oneness," "twoness," etc.) are innate or learned. Although an effect of grammatical number on number-word learning does not rule out nativist accounts, it seems more consistent with constructivist accounts, which portray the number-learning process as one that requires significant conceptual change.
Urizar-Lanz, Inigo; Toth, Geza
2010-05-15
We consider a number-operator-annihilation-operator uncertainty as a well-behaved alternative to the number-phase uncertainty relation, and examine its properties. We find a formulation in which the bound on the product of uncertainties depends on the expectation value of the particle number. Thus, while the bound is not a constant, it is a quantity that can easily be controlled in many systems. The uncertainty relation is approximately saturated by number-phase intelligent states. This allows us to define amplitude squeezing, connecting coherent states to Fock states, without a reference to a phase operator. We propose several setups for an experimental verification.
On the relation between grammatical number and cardinal numbers in development
Sarnecka, Barbara W.
2014-01-01
This mini-review focuses on the question of how the grammatical number system of a child’s language may help the child learn the meanings of cardinal number words (e.g., “one” and “two”). Evidence from young children learning English, Russian, Japanese, Mandarin, Slovenian, or Saudi Arabic suggests that trajectories of number-word learning differ for children learning different languages. Children learning English, which distinguishes between singular and plural, seem to learn the meaning of the cardinal number “one” earlier than children learning Japanese or Mandarin, which have very little singular/plural marking. Similarly, children whose languages have a singular/dual/plural system (Slovenian and Saudi Arabic) learn the meaning of “two” earlier than English-speaking children. This relation between grammatical and cardinal number may shed light on how humans acquire cardinal-number concepts. There is an ongoing debate about whether mental symbols for small cardinalities (concepts for “oneness,” “twoness,” etc.) are innate or learned. Although an effect of grammatical number on number-word learning does not rule out nativist accounts, it seems more consistent with constructivist accounts, which portray the number-learning process as one that requires significant conceptual change. PMID:25346709
Preston Probe Calibrations at High Reynolds Number
NASA Technical Reports Server (NTRS)
Smits, Alexander J.
1998-01-01
The overall goal of the research effort is to study the performance of two Preston probes designed by NASA Langley Research Center across an unprecedented range of Reynolds number (based on friction velocity and probe diameter), and perform an accurate calibration over the same Reynolds number range. Using the Superpipe facility in Princeton, two rounds of experiments were performed. In each round of experiments for each Reynolds number, the pressure gradient, static pressure from the Preston probes and the total pressure from the Preston probes were measured. In the first round, 3 Preston probes having outer diameters of 0.058 inches, 0.083 inches and 0.203 inches were tested over a large range of pipe Reynolds numbers. Two data reduction methods were employed: first, the static pressure measured on the Preston probe was used to calculate P (modified Preston probe configuration), and secondly, the static pressure measured at the reference pressure tap was used to calculate P (un-modified Preston probe configuration). For both methods, the static pressure was adjusted to correspond with the static pressure at the Preston probe tip using the pressure gradient. The measurements for Preston probes with diameters of 0.058 inches, and 0.083 inches respectively were performed in the test pipe before it was polished a second time. Therefore, the measurements at high pipe Reynolds numbers may have been affected by roughness. In the second round of experiments the 0.058 inches and 0.083 inches diameter, un-modified probes were tested after the pipe was polished and prepared to ensure that the surface was smooth. The average velocity was estimated by assuming that the connection between the centerline velocity and the average velocity was known, and by using a Pitot tube to measure the centerline velocity. A preliminary error estimate suggests that it is possible to introduce a 1% to 2% error in estimating the average velocity using this approach. The evidence on the errors
Variation of curve number with storm depth
NASA Astrophysics Data System (ADS)
Banasik, K.; Hejduk, L.
2012-04-01
The NRCS Curve Number (known also as SCS-CN) method is well known as a tool in predicting flood runoff depth from small ungauged catchment. The traditional way of determination the CNs, based on soil characteristics, land use and hydrological conditions, seemed to have tendency to overpredict the floods in some cases. Over 30 year rainfall-runoff data, collected in two small (A=23.4 & 82.4 km2), lowland, agricultural catchments in Center of Poland (Banasik & Woodward 2010), were used to determine runoff Curve Number and to check a tendency of changing. The observed CN declines with increasing storm size, which according recent views of Hawkins (1993) could be classified as a standard response of watershed. The analysis concluded, that using CN value according to the procedure described in USDA-SCS Handbook one receives representative value for estimating storm runoff from high rainfall depths in the analyzes catchments. This has been confirmed by applying "asymptotic approach" for estimating the watershed curve number from the rainfall-runoff data. Furthermore, the analysis indicated that CN, estimated from mean retention parameter S of recorded events with rainfall depth higher than initial abstraction, is also approaching the theoretical CN. The observed CN, ranging from 59.8 to 97.1 and from 52.3 to 95.5, in the smaller and the larger catchment respectively, declines with increasing storm size, which has been classified as a standard response of watershed. The investigation demonstrated also changeability of the CN during a year, with much lower values during the vegetation season. Banasik K. & D.E. Woodward (2010). "Empirical determination of curve number for a small agricultural watrshed in Poland". 2nd Joint Federal Interagency Conference, Las Vegas, NV, June 27 - July 1, 2010 (http://acwi.gov/sos/pubs/2ndJFIC/Contents/10E_Banasik_ 28_02_10. pdf). Hawkins R. H. (1993). "Asymptotic determination of curve numbers from data". Journal of Irrigation and Drainage
Cosmological baryon and lepton number in the presence of electroweak fermion-number violation
NASA Technical Reports Server (NTRS)
Harvey, Jeffrey A.; Turner, Michael S.
1990-01-01
In the presence of rapid fermion-number violation due to nonperturbative electroweak effects certain relations between the baryon number of the Universe and the lepton numbers of the Universe are predicted. In some cases the electron-neutrino asymmetry is exactly specified in terms of the baryon asymmetry. Without introducing new particles, beyond the usual quarks and leptons, it is necessary that the Universe possess a nonzero value of B - L prior to the epoch of fermion-number violation if baryon and lepton asymmetries are to survive. Contrary to intuition, even though electroweak processes violate B + L, a nonzero value of B + L persists after the epoch of rapid fermion-number violation. If the standard model is extended to include lepton-number violation, for example through Majorana neutrino masses, then electroweak processes will reduce the baryon number to zero even in the presence of an initial B - L unless 20 M(sub L) approximately greater than the square root of (T(sub B - L) m(sub P1)) where M(sub L) sets the scale of lepton number violation and T(sub B - L) is the temperature at which a B - L asymmetry is produced. In many models this implies that neutrinos must be so light that they cannot contribute appreciably to the mass density of the Universe.
Number Sense and Number Nonsense: Understanding the Challenges of Learning Math
ERIC Educational Resources Information Center
Krasa, Nancy; Shunkwiler, Sara
2009-01-01
How do children learn math--and why do some children struggle with it? The answers are in "Number Sense and Number Nonsense," a straightforward, reader-friendly book for education professionals and an invaluable multidisciplinary resource for researchers. More than a first-ever research synthesis, this highly accessible book brings math…
48 CFR 52.204-6 - Data Universal Numbering System (DUNS) Number.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 48 Federal Acquisition Regulations System 2 2010-10-01 2010-10-01 false Data Universal Numbering System (DUNS) Number. 52.204-6 Section 52.204-6 Federal Acquisition Regulations System FEDERAL ACQUISITION REGULATION (CONTINUED) CLAUSES AND FORMS SOLICITATION PROVISIONS AND CONTRACT CLAUSES Text of Provisions and Clauses 52.204-6 Data...
Making Numbers Your Friends: A Set of "Make This Number" Activities
ERIC Educational Resources Information Center
Chick, Helen
2009-01-01
Fluency with basic number facts is vital for students' progress in mathematics. Not only does it contribute to students' facility with mental computation and algorithms, but an understanding of numbers and their properties builds a foundation for future mathematical work including algebra. There are many activities that can help students "make…
48 CFR 52.204-6 - Data Universal Numbering System Number.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 48 Federal Acquisition Regulations System 2 2014-10-01 2014-10-01 false Data Universal Numbering System Number. 52.204-6 Section 52.204-6 Federal Acquisition Regulations System FEDERAL ACQUISITION.... (viii) Chief executive officer/key manager. (ix) Line of business (industry). (x) Company...
Effect of Reynolds Number and Mach Number on flow angularity probe sensitivity
NASA Technical Reports Server (NTRS)
Smith, L. A.; Adcock, J. B.
1986-01-01
Preliminary calibrations were performed on nine flow angularity probes in the Langley 7- by 10-Foot High-Speed Tunnel (7 x 10 HST) and the Langley 0.3-Meter Transonic Cryogenic Tunnel (0.3-m TCT). These probes will be used in surveying the test section flows of the National Transonic Facility (NTF). The probes used in this study have a pyramid head with five pressure orifices. The calibrations consisted of both isolated probe measurements and rake-mounted multiprobe measurements that covered a range of subsonic Mach numbers up to 0.90 and Reynolds numbers per foot up to 40 X 10 to the 6th power. The preliminary calibration in the 7 x 10 HST included testing the probes both individually and in a rake. The 0.3-m TCT calibration tested two probes singly at varying Reynolds numbers. The results from these tests include Mach number, Reynolds number, and rake-mounting effects. The results of these tests showed probe sensitivity to be slightly affected by Mach number. At Reynolds numbers per foot above 10 x 10 to the 6th power, the probe did not exhibit a Reynolds number sensitivity.
How to Learn the Natural Numbers: Inductive Inference and the Acquisition of Number Concepts
ERIC Educational Resources Information Center
Margolis, Eric; Laurence, Stephen
2008-01-01
Theories of number concepts often suppose that the natural numbers are acquired as children learn to count and as they draw an induction based on their interpretation of the first few count words. In a bold critique of this general approach, Rips, Asmuth, Bloomfield [Rips, L., Asmuth, J. & Bloomfield, A. (2006). Giving the boot to the bootstrap:…
Health Code Number (HCN) Development Procedure
Petrocchi, Rocky; Craig, Douglas K.; Bond, Jayne-Anne; Trott, Donna M.; Yu, Xiao-Ying
2013-09-01
This report provides the detailed description of health code numbers (HCNs) and the procedure of how each HCN is assigned. It contains many guidelines and rationales of HCNs. HCNs are used in the chemical mixture methodology (CMM), a method recommended by the department of energy (DOE) for assessing health effects as a result of exposures to airborne aerosols in an emergency. The procedure is a useful tool for proficient HCN code developers. Intense training and quality assurance with qualified HCN developers are required before an individual comprehends the procedure to develop HCNs for DOE.
Mff-Analysis of Zurich Sunspot Numbers
NASA Astrophysics Data System (ADS)
Nefedyev, Yuri; Panischev, Oleg; Demin, Sergey
2016-07-01
In this paper we consider the dynamic and stochastic properties of the solar activity by using the Memory Function Formalism (MFF) to analyze the Zurich sunspot numbers. This approach allows to study the statistical memory effects and dynamic alteration in the considered dynamics. The phase portraits are the simple graphical method to analyze the dynamic properties of solar activity. Power spectra of the memory functions allow to reveal the frequency characteristics of the solar activity in different relaxation levels. The non-Markovian parameter describes the memory effects in considered dynamics. Work was supported by grants RFBR 15-02-01638-a and 16-02-00496-a.
Risk communication: Uncertainties and the numbers game
Ortigara, M.
1995-08-30
The science of risk assessment seeks to characterize the potential risk in situations that may pose hazards to human health or the environment. However, the conclusions reached by the scientists and engineers are not an end in themselves - they are passed on to the involved companies, government agencies, legislators, and the public. All interested parties must then decide what to do with the information. Risk communication is a type of technical communication that involves some unique challenges. This paper first defines the relationships between risk assessment, risk management, and risk communication and then explores two issues in risk communication: addressing uncertainty and putting risk number into perspective.
Minimal polar swimmer at low Reynolds number.
Pandey, Ankita; Simha, R Aditi
2012-06-01
We propose a minimal model for a polar swimmer, consisting of two spheres connected by a rigid slender arm, at low Reynolds number. The propulsive velocity for the proposed model is the maximum for any swimming cycle with the same variations in its two degrees of freedom and its displacement in a cycle is achieved entirely in one step. The stroke averaged flow field generated by the contractile swimmer at large distances is found to be dipolar. In addition, the changing radius of one of the spheres generates the field of a potential doublet centered at its initial position.
Distribution for the number of coauthors
NASA Astrophysics Data System (ADS)
Hsu, Jiann-Wien; Huang, Ding-Wei
2009-11-01
We study the coauthorship distribution by analyzing the number of coauthors on each paper published in Physical Review Letters and Physical Review for the last decade. We propose that the structure of the distribution can be understood as the result of a two-parameter Poisson process. We develop a dynamic model of dual mechanisms to simulate the personal and group collaborations. In this model, the single-author papers are portrayed as a leftover from the collaboration process. We also comment on the huge collaborations involving hundreds of coauthors.
Getting DNA copy numbers without control samples
2012-01-01
Background The selection of the reference to scale the data in a copy number analysis has paramount importance to achieve accurate estimates. Usually this reference is generated using control samples included in the study. However, these control samples are not always available and in these cases, an artificial reference must be created. A proper generation of this signal is crucial in terms of both noise and bias. We propose NSA (Normality Search Algorithm), a scaling method that works with and without control samples. It is based on the assumption that genomic regions enriched in SNPs with identical copy numbers in both alleles are likely to be normal. These normal regions are predicted for each sample individually and used to calculate the final reference signal. NSA can be applied to any CN data regardless the microarray technology and preprocessing method. It also finds an optimal weighting of the samples minimizing possible batch effects. Results Five human datasets (a subset of HapMap samples, Glioblastoma Multiforme (GBM), Ovarian, Prostate and Lung Cancer experiments) have been analyzed. It is shown that using only tumoral samples, NSA is able to remove the bias in the copy number estimation, to reduce the noise and therefore, to increase the ability to detect copy number aberrations (CNAs). These improvements allow NSA to also detect recurrent aberrations more accurately than other state of the art methods. Conclusions NSA provides a robust and accurate reference for scaling probe signals data to CN values without the need of control samples. It minimizes the problems of bias, noise and batch effects in the estimation of CNs. Therefore, NSA scaling approach helps to better detect recurrent CNAs than current methods. The automatic selection of references makes it useful to perform bulk analysis of many GEO or ArrayExpress experiments without the need of developing a parser to find the normal samples or possible batches within the data. The method is
Wave-number spectrum of electroencephalographic signals.
O'Connor, S C; Robinson, P A; Chiang, A K I
2002-12-01
A recently developed, physiologically based continuum model of corticothalamic electrodynamics is used to derive the theoretical form of the electroencephalographic wave-number spectrum and its projection onto a one-dimensional recording array. The projected spectrum is found to consist of a plateau followed by regions of power-law decrease with various exponents, which are dependent on both model parameters and temporal frequency. The theoretical spectrum is compared with experimental results obtained in other studies, showing good agreement. The model provides a framework for understanding the nature of the spatial power spectrum by linking the underlying physiology with the large-scale dynamics of the brain. PMID:12513316
47 CFR 52.20 - Thousands-block number pooling.
Code of Federal Regulations, 2011 CFR
2011-10-01
... number pooling as a mandatory nationwide numbering resource optimization strategy, all carriers, except... resources are assigned. (2) All service providers required to participate in thousands-block number...
Binary droplet collision at high Weber number.
Pan, Kuo-Long; Chou, Ping-Chung; Tseng, Yu-Jen
2009-09-01
By using the techniques developed for generating high-speed droplets, we have systematically investigated binary droplet collision when the Weber number (We) was increased from the range usually tested in previous studies on the order of 10 to a much larger value of about 5100 for water (a droplet at 23 m/s with a diameter of 0.7 mm). Various liquids were also used to explore the effects of viscosity and surface tension. Specifically, beyond the well-known regimes at moderate We's, which exhibited coalescence, separation, and separation followed by satellite droplets, we found different behaviors showing a fingering lamella, separation after fingering, breakup of outer fingers, and prompt splattering into multiple secondary droplets as We was increased. The critical Weber numbers that mark the boundaries between these impact regimes are identified. The specific impact behaviors, such as fingering and prompt splattering or splashing, share essential similarity with those also observed in droplet-surface impacts, whereas substantial variations in the transition boundaries may result from the disparity of the boundary conditions at impacts. To compare the outcomes of both types of collisions, a simple model based on energy conservation was carried out to predict the maximum diameter of an expanding liquid disk for a binary droplet collision. The results oppose the dominance of viscous drag, as proposed by previous studies, as the main deceleration force to effect a Rayleigh-Taylor instability and ensuing periphery fingers, which may further lead to the formations of satellite droplets. PMID:19905206
Low-Reynolds-number swimming at pycnoclines
Doostmohammadi, Amin; Stocker, Roman; Ardekani, Arezoo M.
2012-01-01
Microorganisms play pivotal functions in the trophic dynamics and biogeochemistry of aquatic ecosystems. Their concentrations and activities often peak at localized hotspots, an important example of which are pycnoclines, where water density increases sharply with depth due to gradients in temperature or salinity. At pycnoclines organisms are exposed to different environmental conditions compared to the bulk water column, including reduced turbulence, slow mass transfer, and high particle and predator concentrations. Here we show that, at an even more fundamental level, the density stratification itself can affect microbial ecology at pycnoclines, by quenching the flow signature, increasing the energetic expenditure, and stifling the nutrient uptake of motile organisms. We demonstrate this through numerical simulations of an archetypal low-Reynolds-number swimmer, the “squirmer.” We identify the Richardson number—the ratio of buoyancy forces to viscous forces—as the fundamental parameter that quantifies the effects of stratification. These results demonstrate an unexpected effect of buoyancy on low-Reynolds-number swimming, potentially affecting a broad range of abundant organisms living at pycnoclines in oceans and lakes. PMID:22355147
Backwater number scaling of alluvial bed forms
NASA Astrophysics Data System (ADS)
Shaw, John B.; McElroy, Brandon
2016-08-01
The backwater number, Bw, compares the backwater length scale to the length scale of alluvial bed forms. We derive theory to show that Bw plays an important role in determining the behavior and scaling of morphodynamic systems. When Bw ≫ 1, spatial patterns in deposition and erosion derive from flow accelerations associated with changes in flow depth, and bed evolution is akin to a kinematic wave. When Bw ≪ 1, the spatial pattern of shear stress is determined by variations in energy slope, and alluvial beds experience topographic dispersion. This theory is confirmed using a numerical model and data compiled from the literature. We present a data set of Bw for bed forms ranging from dunes to river deltas, including field and experimental measurements. For field-scale measurements, we find that dunes have Bw > 49, braid bars exist in the range Bw = [7.1,17], meanders have a range Bw = [7.1,18], and river mouth deposition ranges over Bw = [7.4,29]. Further, alluvial morphologies that are easily recreated in the laboratory (dunes and avulsions) have overlapping field and laboratory Bw ranges. In contrast, alluvial forms that have traditionally been difficult to recreate (meanders and river mouth processes) have field Bw that are difficult to match in laboratory settings. Large experimental Froude numbers are shown to reduce experimental Bw and incite diffusional behavior. Finally, we demonstrate the utility of Bw scaling for estimating fundamental scales in sedimentary systems.
Copy Number Studies in Noisy Samples
Ginsbach, Philip; Chen, Bowang; Jiang, Yanxiang; Engelter, Stefan T.; Grond-Ginsbach, Caspar
2013-01-01
System noise was analyzed in 77 Affymetrix 6.0 samples from a previous clinical study of copy number variation (CNV). Twenty-three samples were classified as eligible for CNV detection, 29 samples as ineligible and 25 were classified as being of intermediate quality. New software (“noise-free-cnv”) was developed to visualize the data and reduce system noise. Fresh DNA preparations were more likely to yield eligible samples (p < 0.001). Eligible samples had higher rates of successfully genotyped SNPs (p < 0.001) and lower variance of signal intensities (p < 0.001), yielded fewer CNV findings after Birdview analysis (p < 0.001), and showed a tendency to yield fewer PennCNV calls (p = 0.053). The noise-free-cnv software visualized trend patterns of noise in the signal intensities across the ordered SNPs, including a wave pattern of noise, being co-linear with the banding pattern of metaphase chromosomes, as well as system deviations of individual probe sets (per-SNP noise). Wave noise and per-SNP noise occurred independently and could be separately removed from the samples. We recommend a two-step procedure of CNV validation, including noise reduction and visual inspection of all CNV calls, prior to molecular validation of a selected number of putative CNVs.
Binary droplet collision at high Weber number
NASA Astrophysics Data System (ADS)
Pan, Kuo-Long; Chou, Ping-Chung; Tseng, Yu-Jen
2009-09-01
By using the techniques developed for generating high-speed droplets, we have systematically investigated binary droplet collision when the Weber number (We) was increased from the range usually tested in previous studies on the order of 10 to a much larger value of about 5100 for water (a droplet at 23 m/s with a diameter of 0.7 mm). Various liquids were also used to explore the effects of viscosity and surface tension. Specifically, beyond the well-known regimes at moderate We’s, which exhibited coalescence, separation, and separation followed by satellite droplets, we found different behaviors showing a fingering lamella, separation after fingering, breakup of outer fingers, and prompt splattering into multiple secondary droplets as We was increased. The critical Weber numbers that mark the boundaries between these impact regimes are identified. The specific impact behaviors, such as fingering and prompt splattering or splashing, share essential similarity with those also observed in droplet-surface impacts, whereas substantial variations in the transition boundaries may result from the disparity of the boundary conditions at impacts. To compare the outcomes of both types of collisions, a simple model based on energy conservation was carried out to predict the maximum diameter of an expanding liquid disk for a binary droplet collision. The results oppose the dominance of viscous drag, as proposed by previous studies, as the main deceleration force to effect a Rayleigh-Taylor instability and ensuing periphery fingers, which may further lead to the formations of satellite droplets.
Why to compare absolute numbers of mitochondria.
Schmitt, Sabine; Schulz, Sabine; Schropp, Eva-Maria; Eberhagen, Carola; Simmons, Alisha; Beisker, Wolfgang; Aichler, Michaela; Zischka, Hans
2014-11-01
Prompted by pronounced structural differences between rat liver and rat hepatocellular carcinoma mitochondria, we suspected these mitochondrial populations to differ massively in their molecular composition. Aiming to reveal these mitochondrial differences, we came across the issue on how to normalize such comparisons and decided to focus on the absolute number of mitochondria. To this end, fluorescently stained mitochondria were quantified by flow cytometry. For rat liver mitochondria, this approach resulted in mitochondrial protein contents comparable to earlier reports using alternative methods. We determined similar protein contents for rat liver, heart and kidney mitochondria. In contrast, however, lower protein contents were determined for rat brain mitochondria and for mitochondria from the rat hepatocellular carcinoma cell line McA 7777. This result challenges mitochondrial comparisons that rely on equal protein amounts as a typical normalization method. Exemplarily, we therefore compared the activity and susceptibility toward inhibition of complex II of rat liver and hepatocellular carcinoma mitochondria and obtained significant discrepancies by either normalizing to protein amount or to absolute mitochondrial number. Importantly, the latter normalization, in contrast to the former, demonstrated a lower complex II activity and higher susceptibility toward inhibition in hepatocellular carcinoma mitochondria compared to liver mitochondria. These findings demonstrate that solely normalizing to protein amount may obscure essential molecular differences between mitochondrial populations.
Measuring glomerular number from kidney MRI images
NASA Astrophysics Data System (ADS)
Thiagarajan, Jayaraman J.; Natesan Ramamurthy, Karthikeyan; Kanberoglu, Berkay; Frakes, David; Bennett, Kevin; Spanias, Andreas
2016-03-01
Measuring the glomerular number in the entire, intact kidney using non-destructive techniques is of immense importance in studying several renal and systemic diseases. Commonly used approaches either require destruction of the entire kidney or perform extrapolation from measurements obtained from a few isolated sections. A recent magnetic resonance imaging (MRI) method, based on the injection of a contrast agent (cationic ferritin), has been used to effectively identify glomerular regions in the kidney. In this work, we propose a robust, accurate, and low-complexity method for estimating the number of glomeruli from such kidney MRI images. The proposed technique has a training phase and a low-complexity testing phase. In the training phase, organ segmentation is performed on a few expert-marked training images, and glomerular and non-glomerular image patches are extracted. Using non-local sparse coding to compute similarity and dissimilarity graphs between the patches, the subspace in which the glomerular regions can be discriminated from the rest are estimated. For novel test images, the image patches extracted after pre-processing are embedded using the discriminative subspace projections. The testing phase is of low computational complexity since it involves only matrix multiplications, clustering, and simple morphological operations. Preliminary results with MRI data obtained from five kidneys of rats show that the proposed non-invasive, low-complexity approach performs comparably to conventional approaches such as acid maceration and stereology.
Multiplex congruence network of natural numbers
Yan, Xiao-Yong; Wang, Wen-Xu; Chen, Guan-Rong; Shi, Ding-Hua
2016-01-01
Congruence theory has many applications in physical, social, biological and technological systems. Congruence arithmetic has been a fundamental tool for data security and computer algebra. However, much less attention was devoted to the topological features of congruence relations among natural numbers. Here, we explore the congruence relations in the setting of a multiplex network and unveil some unique and outstanding properties of the multiplex congruence network. Analytical results show that every layer therein is a sparse and heterogeneous subnetwork with a scale-free topology. Counterintuitively, every layer has an extremely strong controllability in spite of its scale-free structure that is usually difficult to control. Another amazing feature is that the controllability is robust against targeted attacks to critical nodes but vulnerable to random failures, which also differs from ordinary scale-free networks. The multi-chain structure with a small number of chain roots arising from each layer accounts for the strong controllability and the abnormal feature. The multiplex congruence network offers a graphical solution to the simultaneous congruences problem, which may have implication in cryptography based on simultaneous congruences. Our work also gains insight into the design of networks integrating advantages of both heterogeneous and homogeneous networks without inheriting their limitations. PMID:27029650
Copy number variation in bipolar disorder
Green, EK; Rees, E; Walters, JTR; Smith, K-G; Forty, L; Grozeva, D; Moran, JL; Sklar, P; Ripke, S; Chambert, KD; Genovese, G; McCarroll, SA; Jones, I; Jones, L; Owen, MJ; O’Donovan, MC; Craddock, N; Kirov, G
2016-01-01
Large (>100 kb), rare (<1% in the population) copy number variants (CNVs) have been shown to confer risk for schizophrenia (SZ), but the findings for bipolar disorder (BD) are less clear. In a new BD sample from the United Kingdom (n = 2591), we have examined the occurrence of CNVs and compared this with previously reported samples of 6882 SZ and 8842 control subjects. When combined with previous data, we find evidence for a contribution to BD for three SZ-associated CNV loci: duplications at 1q21.1 (P = 0.022), deletions at 3q29 (P = 0.03) and duplications at 16p11.2 (P = 2.3 × 10−4). The latter survives multiple-testing correction for the number of recurrent large CNV loci in the genome. Genes in 20 regions (total of 55 genes) were enriched for rare exonic CNVs among BD cases, but none of these survives correction for multiple testing. Finally, our data provide strong support for the hypothesis of a lesser contribution of very large (>500 kb) CNVs in BD compared with SZ, most notably for deletions >1 Mb (P = 9 × 10−4). PMID:25560756
Apollo by the Numbers: A Statistical Reference
NASA Technical Reports Server (NTRS)
Orloff, Richard; Garber, Stephen (Technical Monitor)
2000-01-01
The purpose of this work is to provide researchers, students, and space enthusiasts with a comprehensive reference for facts about Project Apollo, America's effort to put humans in the Moon. Research for this work started in 1988, when the author discovered that, despite the number of excellent books that focused on the drama of events that highlighted Apollo, there were none that focused on the drama of the numbers. This book is separated into two parts. The first part contains narratives for the Apollo 1 fire and the 11 flown Apollo missions. Included after each narrative is a series of data tables, followed by a comprehensive timeline of events from just before liftoff to just after crew and spacecraft recovery. The second part contains more than 50 tables. These tables organize much of the data from the narratives in one place so they can be compared among all missions. The tables offer additional data as well. The reader can select a specific mission narrative or specific data table by consulting the Table of Contents.
Multiplex congruence network of natural numbers.
Yan, Xiao-Yong; Wang, Wen-Xu; Chen, Guan-Rong; Shi, Ding-Hua
2016-01-01
Congruence theory has many applications in physical, social, biological and technological systems. Congruence arithmetic has been a fundamental tool for data security and computer algebra. However, much less attention was devoted to the topological features of congruence relations among natural numbers. Here, we explore the congruence relations in the setting of a multiplex network and unveil some unique and outstanding properties of the multiplex congruence network. Analytical results show that every layer therein is a sparse and heterogeneous subnetwork with a scale-free topology. Counterintuitively, every layer has an extremely strong controllability in spite of its scale-free structure that is usually difficult to control. Another amazing feature is that the controllability is robust against targeted attacks to critical nodes but vulnerable to random failures, which also differs from ordinary scale-free networks. The multi-chain structure with a small number of chain roots arising from each layer accounts for the strong controllability and the abnormal feature. The multiplex congruence network offers a graphical solution to the simultaneous congruences problem, which may have implication in cryptography based on simultaneous congruences. Our work also gains insight into the design of networks integrating advantages of both heterogeneous and homogeneous networks without inheriting their limitations. PMID:27029650
Natural occupation numbers: when do they vanish?
Giesbertz, K J H; van Leeuwen, R
2013-09-14
The non-vanishing of the natural orbital (NO) occupation numbers of the one-particle density matrix of many-body systems has important consequences for the existence of a density matrix-potential mapping for nonlocal potentials in reduced density matrix functional theory and for the validity of the extended Koopmans' theorem. On the basis of Weyl's theorem we give a connection between the differentiability properties of the ground state wavefunction and the rate at which the natural occupations approach zero when ordered as a descending series. We show, in particular, that the presence of a Coulomb cusp in the wavefunction leads, in general, to a power law decay of the natural occupations, whereas infinitely differentiable wavefunctions typically have natural occupations that decay exponentially. We analyze for a number of explicit examples of two-particle systems that in case the wavefunction is non-analytic at its spatial diagonal (for instance, due to the presence of a Coulomb cusp) the natural orbital occupations are non-vanishing. We further derive a more general criterium for the non-vanishing of NO occupations for two-particle wavefunctions with a certain separability structure. On the basis of this criterium we show that for a two-particle system of harmonically confined electrons with a Coulombic interaction (the so-called Hookium) the natural orbital occupations never vanish.
Multiplex congruence network of natural numbers.
Yan, Xiao-Yong; Wang, Wen-Xu; Chen, Guan-Rong; Shi, Ding-Hua
2016-03-31
Congruence theory has many applications in physical, social, biological and technological systems. Congruence arithmetic has been a fundamental tool for data security and computer algebra. However, much less attention was devoted to the topological features of congruence relations among natural numbers. Here, we explore the congruence relations in the setting of a multiplex network and unveil some unique and outstanding properties of the multiplex congruence network. Analytical results show that every layer therein is a sparse and heterogeneous subnetwork with a scale-free topology. Counterintuitively, every layer has an extremely strong controllability in spite of its scale-free structure that is usually difficult to control. Another amazing feature is that the controllability is robust against targeted attacks to critical nodes but vulnerable to random failures, which also differs from ordinary scale-free networks. The multi-chain structure with a small number of chain roots arising from each layer accounts for the strong controllability and the abnormal feature. The multiplex congruence network offers a graphical solution to the simultaneous congruences problem, which may have implication in cryptography based on simultaneous congruences. Our work also gains insight into the design of networks integrating advantages of both heterogeneous and homogeneous networks without inheriting their limitations.
A Numbering System for MFS Transporter Proteins
Lee, Joanna; Sands, Zara A.; Biggin, Philip C.
2016-01-01
The Major Facilitator Superfamily (MFS) is one of the largest classes of secondary active transporters and is widely expressed in many domains of life. It is characterized by a common 12-transmembrane helix motif that allows the selective transport of a vast range of diverse substrates across the membrane. MFS transporters play a central role in many physiological processes and are increasingly recognized as potential drug targets. Despite intensive efforts, there are still only a handful of crystal structures and therefore homology modeling is likely to be a necessary process for providing models to interpret experiments for many years to come. However, the diversity of sequences and the multiple conformational states these proteins can exist in makes the process significantly more complicated, especially for sequences for which there is very little sequence identity to known templates. Inspired by the approach adopted many years ago for GPCRs, we have analyzed the large number of MFS sequences now available alongside the current structural information to propose a series of conserved contact points that can provide additional guidance for the homology modeling process. To enable cross-comparison across MFS models we also present a numbering scheme that can be used to provide a point of reference within each of the 12 transmembrane regions. PMID:27314000
Multiplex congruence network of natural numbers
NASA Astrophysics Data System (ADS)
Yan, Xiao-Yong; Wang, Wen-Xu; Chen, Guan-Rong; Shi, Ding-Hua
2016-03-01
Congruence theory has many applications in physical, social, biological and technological systems. Congruence arithmetic has been a fundamental tool for data security and computer algebra. However, much less attention was devoted to the topological features of congruence relations among natural numbers. Here, we explore the congruence relations in the setting of a multiplex network and unveil some unique and outstanding properties of the multiplex congruence network. Analytical results show that every layer therein is a sparse and heterogeneous subnetwork with a scale-free topology. Counterintuitively, every layer has an extremely strong controllability in spite of its scale-free structure that is usually difficult to control. Another amazing feature is that the controllability is robust against targeted attacks to critical nodes but vulnerable to random failures, which also differs from ordinary scale-free networks. The multi-chain structure with a small number of chain roots arising from each layer accounts for the strong controllability and the abnormal feature. The multiplex congruence network offers a graphical solution to the simultaneous congruences problem, which may have implication in cryptography based on simultaneous congruences. Our work also gains insight into the design of networks integrating advantages of both heterogeneous and homogeneous networks without inheriting their limitations.
The universal numbers. From Biology to Physics.
Marchal, Bruno
2015-12-01
I will explain how the mathematicians have discovered the universal numbers, or abstract computer, and I will explain some abstract biology, mainly self-reproduction and embryogenesis. Then I will explain how and why, and in which sense, some of those numbers can dream and why their dreams can glue together and must, when we assume computationalism in cognitive science, generate a phenomenological physics, as part of a larger phenomenological theology (in the sense of the greek theologians). The title should have been "From Biology to Physics, through the Phenomenological Theology of the Universal Numbers", if that was not too long for a title. The theology will consist mainly, like in some (neo)platonist greek-indian-chinese tradition, in the truth about numbers' relative relations, with each others, and with themselves. The main difference between Aristotle and Plato is that Aristotle (especially in its common and modern christian interpretation) makes reality WYSIWYG (What you see is what you get: reality is what we observe, measure, i.e. the natural material physical science) where for Plato and the (rational) mystics, what we see might be only the shadow or the border of something else, which might be non physical (mathematical, arithmetical, theological, …). Since Gödel, we know that Truth, even just the Arithmetical Truth, is vastly bigger than what the machine can rationally justify. Yet, with Church's thesis, and the mechanizability of the diagonalizations involved, machines can apprehend this and can justify their limitations, and get some sense of what might be true beyond what they can prove or justify rationally. Indeed, the incompleteness phenomenon introduces a gap between what is provable by some machine and what is true about that machine, and, as Gödel saw already in 1931, the existence of that gap is accessible to the machine itself, once it is has enough provability abilities. Incompleteness separates truth and provable, and machines can
The universal numbers. From Biology to Physics.
Marchal, Bruno
2015-12-01
I will explain how the mathematicians have discovered the universal numbers, or abstract computer, and I will explain some abstract biology, mainly self-reproduction and embryogenesis. Then I will explain how and why, and in which sense, some of those numbers can dream and why their dreams can glue together and must, when we assume computationalism in cognitive science, generate a phenomenological physics, as part of a larger phenomenological theology (in the sense of the greek theologians). The title should have been "From Biology to Physics, through the Phenomenological Theology of the Universal Numbers", if that was not too long for a title. The theology will consist mainly, like in some (neo)platonist greek-indian-chinese tradition, in the truth about numbers' relative relations, with each others, and with themselves. The main difference between Aristotle and Plato is that Aristotle (especially in its common and modern christian interpretation) makes reality WYSIWYG (What you see is what you get: reality is what we observe, measure, i.e. the natural material physical science) where for Plato and the (rational) mystics, what we see might be only the shadow or the border of something else, which might be non physical (mathematical, arithmetical, theological, …). Since Gödel, we know that Truth, even just the Arithmetical Truth, is vastly bigger than what the machine can rationally justify. Yet, with Church's thesis, and the mechanizability of the diagonalizations involved, machines can apprehend this and can justify their limitations, and get some sense of what might be true beyond what they can prove or justify rationally. Indeed, the incompleteness phenomenon introduces a gap between what is provable by some machine and what is true about that machine, and, as Gödel saw already in 1931, the existence of that gap is accessible to the machine itself, once it is has enough provability abilities. Incompleteness separates truth and provable, and machines can
Cohen, Dale J.; Sarnecka, Barbara W.
2016-01-01
Children’s understanding of numbers is often assessed using a number-line task, where the child is shown a line labeled with 0 at one end and a higher number (e.g., 100) at the other end. The child is then asked where on the line some intermediate number (e.g., 70) should go. Performance on this task changes predictably during childhood, and this has often been interpreted as evidence of a change in the child’s psychological representation of integer quantities. The present article presents theoretical and empirical evidence that the change in number-line performance actually reflects the development of measurement skills used in the task. We compare 2 versions of the number-line task: the bounded version used in the literature and a new, unbounded version. Results indicate that it is only children’s performance on the bounded task (which requires subtraction or division) that changes markedly with age. In contrast, children’s performance on the unbounded task (which requires only addition) remains fairly constant as they get older. Thus, developmental changes in performance on the traditional bounded number-line task likely reflect the growth of task-specific measurement skills rather than changes in the child’s understanding of numerical quantities. PMID:24512172
A Z-number-based decision making procedure with ranking fuzzy numbers method
NASA Astrophysics Data System (ADS)
Mohamad, Daud; Shaharani, Saidatull Akma; Kamis, Nor Hanimah
2014-12-01
The theory of fuzzy set has been in the limelight of various applications in decision making problems due to its usefulness in portraying human perception and subjectivity. Generally, the evaluation in the decision making process is represented in the form of linguistic terms and the calculation is performed using fuzzy numbers. In 2011, Zadeh has extended this concept by presenting the idea of Z-number, a 2-tuple fuzzy numbers that describes the restriction and the reliability of the evaluation. The element of reliability in the evaluation is essential as it will affect the final result. Since this concept can still be considered as new, available methods that incorporate reliability for solving decision making problems is still scarce. In this paper, a decision making procedure based on Z-numbers is proposed. Due to the limitation of its basic properties, Z-numbers will be first transformed to fuzzy numbers for simpler calculations. A method of ranking fuzzy number is later used to prioritize the alternatives. A risk analysis problem is presented to illustrate the effectiveness of this proposed procedure.
Quantity without numbers and numbers without quantity in the parietal cortex
Cappelletti, Marinella; Muggleton, Neil; Walsh, Vincent
2009-01-01
A dominant view in numerical cognition is that processing the quantity indicated by numbers (e.g. deciding the larger between two numbers such as ‘12.07’ or ‘15.02’) relies on the intraparietal regions (IPS) of the cerebral cortex. However, it remains unclear whether the IPS could play a more general role in numerical cognition, for example in (1) quantity processing even with non-numerical stimuli (e.g. choosing the larger of ‘bikini’ and ‘coat’); and/or (2) conceptual tasks involving numbers beyond those requiring quantity processing (e.g. attributing a summer date to either ‘12.07’ or ‘15.02’). In this study we applied fMRI-guided TMS to the left and right IPS, while independently manipulating stimulus and task. Our results showed that IPS involvement in numerical cognition is neither stimulus-specific nor specific for conceptual tasks. Thus, quantity judgments with numerical and non-numerical stimuli were equally affected by IPS-TMS, as well as a number conceptual task not requiring quantity comparisons. However, IPS-TMS showed no impairment for perceptual decisions on numbers without any conceptual processing (i.e. colour judgment), nor for conceptual decisions that did not involve quantity or number stimuli (e.g. summer object: ‘bikini’ or ‘coat’?). These results are consistent with proposals that the parietal areas are engaged in the conceptual representation of numbers but they challenge the most common view that number processing is so automatic that the simple presentation of numbers activates the IPS and a sense of magnitude. Rather, our results show that the IPS is only necessary when conceptual operations need to be explicitly oriented to numerical concepts. PMID:19236924
Compressible turbulent mixing: Effects of Schmidt number.
Ni, Qionglin
2015-05-01
We investigated by numerical simulations the effects of Schmidt number on passive scalar transport in forced compressible turbulence. The range of Schmidt number (Sc) was 1/25∼25. In the inertial-convective range the scalar spectrum seemed to obey the k(-5/3) power law. For Sc≫1, there appeared a k(-1) power law in the viscous-convective range, while for Sc≪1, a k(-17/3) power law was identified in the inertial-diffusive range. The scaling constant computed by the mixed third-order structure function of the velocity-scalar increment showed that it grew over Sc, and the effect of compressibility made it smaller than the 4/3 value from incompressible turbulence. At small amplitudes, the probability distribution function (PDF) of scalar fluctuations collapsed to the Gaussian distribution whereas, at large amplitudes, it decayed more quickly than Gaussian. At large scales, the PDF of scalar increment behaved similarly to that of scalar fluctuation. In contrast, at small scales it resembled the PDF of scalar gradient. Furthermore, the scalar dissipation occurring at large magnitudes was found to grow with Sc. Due to low molecular diffusivity, in the Sc≫1 flow the scalar field rolled up and got mixed sufficiently. However, in the Sc≪1 flow the scalar field lost the small-scale structures by high molecular diffusivity and retained only the large-scale, cloudlike structures. The spectral analysis found that the spectral densities of scalar advection and dissipation in both Sc≫1 and Sc≪1 flows probably followed the k(-5/3) scaling. This indicated that in compressible turbulence the processes of advection and dissipation except that of scalar-dilatation coupling might deferring to the Kolmogorov picture. It then showed that at high wave numbers, the magnitudes of spectral coherency in both Sc≫1 and Sc≪1 flows decayed faster than the theoretical prediction of k(-2/3) for incompressible flows. Finally, the comparison with incompressible results showed that
Polarimetric Retrievals of Cloud Droplet Number Concentrations
NASA Astrophysics Data System (ADS)
Sinclair, K.; Cairns, B.; Hair, J. W.; Hu, Y.; Hostetler, C. A.
2014-12-01
Cloud droplet number concentration (CDNC) is one of the most significant microphysical properties of liquid clouds and is essential for the understanding of aerosol-cloud interaction. It impacts radiative forcing, cloud evolution, precipitation, global climate and, through observation, can be used to monitor the cloud albedo effect, or the first indirect effect. The IPCC's Fifth Assessment Report continues to consider aerosol-cloud interactions as one of the largest uncertainties in radiative forcing of climate. The SABOR experiment, which was a NASA-led ship and air campaign off the east coast of the United States during July and August of 2014, provided an opportunity for the Research Scanning Polarimeter (RSP) to develop and cross-validate a new approach of sensing CDNC with the High Spectral Resolution Lidar (HSRL). The RSP is an airborne prototype of the Aerosol Polarimetry Sensor (APS) that was on-board the Glory satellite. It is a scanning sensor that provides high-precision measurements of polarized and full-intensity radiances at multiple angles over a wide spectral range. The distinctive feature of the polarimetric technique is that it does not make any assumption of the liquid water profile within the cloud. The approach involves (1) estimating the droplet size distribution from polarized reflectance observations in the rainbow, (2) using polarized reflectance to estimate above cloud water vapor and total reflectance to find how much near infra-red light is being absorbed in clouds, (3) finding cloud physical thickness from the absorption and cloud top pressure retrievals assuming a saturated mixing ratio for water vapor and (4) determining the cloud droplet number concentration from the physical thickness and droplet size distribution retrievals. An overview of the polarimetric technique will be presented along with the results of applying the new approach to SABOR campaign data. An analysis of the algorithm's performance when compared with the HSRL
M-Bonacci Numbers and Their Finite Sums
ERIC Educational Resources Information Center
Chamberlain, Joel; Higgings, Nathan; Yurekli, Osman
2003-01-01
The note considers M-bonacci numbers, which are a generalization of Fibonacci numbers. Two new summation formulas for M-bonacci numbers are given. The formulas are generalizations of the two summation formulas for Fibonacci numbers. (Contains 2 tables.)
Four-Digit Numbers Which Are Squared Sums
ERIC Educational Resources Information Center
Coughlin, Heather; Jue, Brian
2009-01-01
There is a very natural way to divide a four-digit number into 2 two-digit numbers. Applying an algorithm to this pair of numbers, determine how often the original four-digit number reappears. (Contains 3 tables.)
The story of the social security number.
Puckett, Carolyn
2009-01-01
The use of the Social Security number (SSN) has expanded significantly since its inception in 1936. Created merely to keep track of the earnings history of U.S. workers for Social Security entitlement and benefit computation purposes, it has come to be used as a nearly universal identifier. Assigned at birth, the SSN enables government agencies to identify individuals in their records and businesses to track an individual's financial information. This article explores the history and meaning of the SSN and the Social Security card, as well as the Social Security Administration's (SSA's) SSN master file, generally known as the Numident. The article also traces the historical expansion of SSN use and the steps SSA has taken to enhance SSN integrity.
Copy Number Variants in pharmacogenetic genes
He, Yijing; Hoskins, Janelle M.; McLeod, Howard L.
2011-01-01
Variation in drug efficacy and toxicity remains an important clinical concern. Presently, single nucleotide polymorphisms (SNP) only explain a portion of this problem, even in situations where the pharmacological trait is clearly heritable. The Human CNV Project identified copy number variations (CNVs) across approximately 12% of the human genome, and these CNVs were considered causes of diseases. Although the contribution of CNVs to the pathogenesis of many common diseases is questionable, CNVs play a clear role in drug related genes by altering drug metabolizing and drug response. Here we provide a comprehensive review of the clinical relevance of CNVs to drug efficacy, toxicity, disease prevalence in world populations and discuss the implication of using CNVs as diagnosis in clinical intervention. PMID:21388883
From entanglement witness to generalized Catalan numbers
NASA Astrophysics Data System (ADS)
Cohen, E.; Hansen, T.; Itzhaki, N.
2016-07-01
Being extremely important resources in quantum information and computation, it is vital to efficiently detect and properly characterize entangled states. We analyze in this work the problem of entanglement detection for arbitrary spin systems. It is demonstrated how a single measurement of the squared total spin can probabilistically discern separable from entangled many-particle states. For achieving this goal, we construct a tripartite analogy between the degeneracy of entanglement witness eigenstates, tensor products of SO(3) representations and classical lattice walks with special constraints. Within this framework, degeneracies are naturally given by generalized Catalan numbers and determine the fraction of states that are decidedly entangled and also known to be somewhat protected against decoherence. In addition, we introduce the concept of a “sterile entanglement witness”, which for large enough systems detects entanglement without affecting much the system’s state. We discuss when our proposed entanglement witness can be regarded as a sterile one.
From entanglement witness to generalized Catalan numbers.
Cohen, E; Hansen, T; Itzhaki, N
2016-07-27
Being extremely important resources in quantum information and computation, it is vital to efficiently detect and properly characterize entangled states. We analyze in this work the problem of entanglement detection for arbitrary spin systems. It is demonstrated how a single measurement of the squared total spin can probabilistically discern separable from entangled many-particle states. For achieving this goal, we construct a tripartite analogy between the degeneracy of entanglement witness eigenstates, tensor products of SO(3) representations and classical lattice walks with special constraints. Within this framework, degeneracies are naturally given by generalized Catalan numbers and determine the fraction of states that are decidedly entangled and also known to be somewhat protected against decoherence. In addition, we introduce the concept of a "sterile entanglement witness", which for large enough systems detects entanglement without affecting much the system's state. We discuss when our proposed entanglement witness can be regarded as a sterile one.
Determination of Avogadro's Number by Improved Electroplating
NASA Astrophysics Data System (ADS)
Seiglie, Carlos A.
2003-06-01
A quick and accurate measurement of Avogadro‘s number from the amount of plated material can be made using a modification of an established electrolytic experiment. The experiment was modified to prevent loss of the copper plated at the cathode (copper plate) as a result of poor plating. The copper plating thus obtained was a firmly bonded and smooth layer, and the percent error of the results was reduced from approximately 20% to about 1% (the small error remaining is caused by the ammeter limits, not loss of plated mass). Control of the current during the experiment was also easier. If copper is not available it can be replaced by commonly available, inexpensive metals such as iron, zinc, or nickel.
Representing exact number visually using mental abacus.
Frank, Michael C; Barner, David
2012-02-01
Mental abacus (MA) is a system for performing rapid and precise arithmetic by manipulating a mental representation of an abacus, a physical calculation device. Previous work has speculated that MA is based on visual imagery, suggesting that it might be a method of representing exact number nonlinguistically, but given the limitations on visual working memory, it is unknown how MA structures could be stored. We investigated the structure of the representations underlying MA in a group of children in India. Our results suggest that MA is represented in visual working memory by splitting the abacus into a series of columns, each of which is independently stored as a unit with its own detailed substructure. In addition, we show that the computations of practiced MA users (but not those of control participants) are relatively insensitive to verbal interference, consistent with the hypothesis that MA is a nonlinguistic format for exact numerical computation. PMID:21767040
Calculations of low Reynolds number rocket nozzles
NASA Technical Reports Server (NTRS)
Kim, Suk C.
1993-01-01
The performance of low-thrust rocket nozzles was studied with a full Navier-Stokes code. The effect of the reduction of the nozzle length on the viscous loss and on the two-dimensional loss due to the increase in the nozzle exit angle was examined by calculating the flowfield and performance values of hydrogen resistojet nozzle with various lengths and shapes (such as 20-deg or 30-deg conical nozzles and a nozzle whose wall contour is given by the Rao nozzle optimization code). It was found that the vacuum specific impulse value of the 30-deg conical nozzle was the highest and that of the contoured nozzle was the lowest among the three nozzles, whose throat Reynolds number and area ratio were 1150 and 82, respectively.
A circle swimmer at low Reynolds number.
Ledesma-Aguilar, R; Löwen, H; Yeomans, J M
2012-08-01
Swimming in circles occurs in a variety of situations at low Reynolds number. Here we propose a simple model for a swimmer that undergoes circular motion, generalising the model of a linear swimmer proposed by Najafi and Golestanian (Phys. Rev. E 69, 062901 (2004)). Our model consists of three solid spheres arranged in a triangular configuration, joined by two links of time-dependent length. For small strokes, we discuss the motion of the swimmer as a function of the separation angle between its links. We find that swimmers describe either clockwise or anticlockwise circular motion depending on the tilting angle in a non-trivial manner. The symmetry of the swimmer leads to a quadrupolar decay of the far flow field. We discuss the potential extensions and experimental realisation of our model.
Counting Children with Tuberculosis: Why Numbers Matter
Seddon, James A; Jenkins, Helen E; Liu, Li; Cohen, Ted; Black, Robert E; Becerra, Mercedes C.; Graham, Stephen M; Sismanidis, Charalambos; Dodd, Peter J
2016-01-01
Summary In the last five years, childhood tuberculosis (TB) has received increasing attention from international organisations, national tuberculosis programmes, and academics. For the first time, a number of different groups are developing techniques to estimate the burden of childhood TB. We review the challenges in diagnosing TB in children and the reasons cases in children can go unreported. We discuss the importance of an accurate understanding of burden for identifying problems in programme delivery, targeting interventions, monitoring trends, setting targets, allocating resources appropriately and providing strong advocacy. We briefly review the estimates produced by new analytical methods, outline the reasons for recent improvements in our understanding, and potential future directions. We conclude that while innovation, collaboration and better data have improved our understanding of childhood TB burden, it remains substantially incomplete. PMID:26564535
Representing exact number visually using mental abacus.
Frank, Michael C; Barner, David
2012-02-01
Mental abacus (MA) is a system for performing rapid and precise arithmetic by manipulating a mental representation of an abacus, a physical calculation device. Previous work has speculated that MA is based on visual imagery, suggesting that it might be a method of representing exact number nonlinguistically, but given the limitations on visual working memory, it is unknown how MA structures could be stored. We investigated the structure of the representations underlying MA in a group of children in India. Our results suggest that MA is represented in visual working memory by splitting the abacus into a series of columns, each of which is independently stored as a unit with its own detailed substructure. In addition, we show that the computations of practiced MA users (but not those of control participants) are relatively insensitive to verbal interference, consistent with the hypothesis that MA is a nonlinguistic format for exact numerical computation.
Love number can be hard to measure
NASA Astrophysics Data System (ADS)
Yagi, Kent; Yunes, Nicolás
2014-01-01
The waveform phase for a neutron star binary can be split into point-particle terms and finite-size terms (characterized by the Love number) that account for equation-of-state effects. The latter first enter at fifth post-Newtonian (5PN) order (i.e., proportional to the tenth power of the orbital velocity), but the former are only known completely to 3.5PN order, with higher-order terms only known to leading order in the mass ratio. We here find that not including point-particle terms at 4PN order to leading and first order in the mass ratio in the template model can severely deteriorate our ability to measure the equation of state. This problem can be solved if one uses numerical waveforms once their own systematic errors are under control.
Health equipment information, number 115, October 1983
Not Available
1984-01-01
Contents: Squibb Surgicare Ltd: System 2-Stoma Bridge for loop ostomy; Electronic and medical equipment: guidance on documentation required for maintenance; Assessment of the radio-opacity of catheters; IEC Publication number 731: dosimeters with ionization chambers as used in radiotherapy; Seminar on digital radiology; Economic appraisal of a Mobile CT Scanning Service; Equipment for the disabled; Evaluation of the Greiner G300 Analyser; Launch of Occupational Therapists' Reference Book 1983/4; Summary of health notices (hazard): 1 April 1983-31 August 1983; Safety Information Bulletin No 9-May 1983: Summary of items; Safety Information Bulletin No 10-July 1983: Summary of items; Safety Information Bulletin No 11-September 1983: Summary of items; Amendment to HEI 112 July 1983: evaluation of ECG Recorders.
Boole: From Calculating Numbers to Calculating Thoughts
NASA Astrophysics Data System (ADS)
Friend, Michèle
We are often taught in a first course in the history of logic or in the philosophy of mathematics that Frege singlehandedly invented second-order logic, and that there was no one close to his achievements before him. In a slightly more sophisticated version of the same course, a qualifying nod is made in the direction of Boole, who did "bring quantifiers to logic". But the student is given the impression that Boole, like Frege, rose ex nihilo from the weedy wasteland of Aristotelian syllogistic reasoning. While this is not a wholly mistaken impression, it is misleading, and should be corrected. Boole was working in the context of a revival of logic - where "logic", especially as it was being taught in England, was gradually being prised away from the doxa of Aristotelian syllogistic reasoning. It is in this context that Boole made innovative contributions by bringing together a number of ideas. The combination brought us closer to our modern conception of logic.
From entanglement witness to generalized Catalan numbers
Cohen, E.; Hansen, T.; Itzhaki, N.
2016-01-01
Being extremely important resources in quantum information and computation, it is vital to efficiently detect and properly characterize entangled states. We analyze in this work the problem of entanglement detection for arbitrary spin systems. It is demonstrated how a single measurement of the squared total spin can probabilistically discern separable from entangled many-particle states. For achieving this goal, we construct a tripartite analogy between the degeneracy of entanglement witness eigenstates, tensor products of SO(3) representations and classical lattice walks with special constraints. Within this framework, degeneracies are naturally given by generalized Catalan numbers and determine the fraction of states that are decidedly entangled and also known to be somewhat protected against decoherence. In addition, we introduce the concept of a “sterile entanglement witness”, which for large enough systems detects entanglement without affecting much the system’s state. We discuss when our proposed entanglement witness can be regarded as a sterile one. PMID:27461089