NASA Technical Reports Server (NTRS)
Eckert, E R G; Diaguila, A J
1955-01-01
Report presents the results of an investigation conducted to study free-convection heat transfer in a stationary vertical tube closed at the bottom. The walls of the tube were heated, and heated air in the tube was continuously replaced by fresh cool air at the top. The tube was designed to provide a gravitational field with Grashof numbers of a magnitude comparable with those generated by the centrifugal field in rotating-blade coolant passages (10(8) to 10(13)). Local heat-transfer coefficients in the turbulent-flow range and the temperature field within the fluid were obtained.
NASA Astrophysics Data System (ADS)
Ooi, Seng-Keat
2005-11-01
Lock-exchange gravity current flows produced by the instantaneous release of a heavy fluid are investigated using 3-D well resolved Large Eddy Simulation simulations at Grashof numbers up to 8*10^9. It is found the 3-D simulations correctly predict a constant front velocity over the initial slumping phase and a front speed decrease proportional to t-1/3 (the time t is measured from the release) over the inviscid phase, in agreement with theory. The evolution of the current in the simulations is found to be similar to that observed experimentally by Hacker et al. (1996). The effect of the dynamic LES model on the solutions is discussed. The energy budget of the current is discussed and the contribution of the turbulent dissipation to the total dissipation is analyzed. The limitations of less expensive 2D simulations are discussed; in particular their failure to correctly predict the spatio-temporal distributions of the bed shear stresses which is important in determining the amount of sediment the gravity current can entrain in the case in advances of a loose bed.
NASA Technical Reports Server (NTRS)
Eckert, E R G; Diaguila, A J
1952-01-01
Local free-convection heat-transfer coefficients and temperature fields in the turbulent flow range were obtained within a vertical, stationary tube closed at the boom, heated along its walls, and having a length-to-diameter ratio of 5. Convective heat-transfer coefficients were correlated by the general relations for free-convection heat transfer. These coefficients, converted to dimensionless Nusselt numbers were 35 percent below known relations for vertical flat plates. Air temperature measurements within the tube indicated a thin boundary layer along the heated wall surface and unstable conditions in the air flow.
NASA Astrophysics Data System (ADS)
Miroshnichenko, E.; Kit, E.; Gelfgat, A. Yu.
2016-03-01
A parametric experimental study of the cold plume instability that appears in the large-Prandtl-number Czochralski melt flows is reported. The critical temperature difference (the critical Grashof number) and the frequency of appearing oscillations were measured for varying Prandtl numbers, aspect ratios of the melt, and crystal/crucible radii ratio. The measurements were carried out by two independent and fully non-intrusive experimental techniques. The results are reported as dimensional and dimensionless parametric dependences, and then are joined into relatively simple empirical relations showing how the critical Grashof number and the frequency of emerging oscillations depend on other parameters.
ERIC Educational Resources Information Center
Swafford, Jane; McGinty, Robert
1978-01-01
A concrete approach to prime numbers is presented using rectangles and triangles to construct a building for each number so that each story represents a pair of factors and the triangular-shaped roof represents the number. (MP)
ERIC Educational Resources Information Center
Crawford, David
1997-01-01
Presents three number games for mathematics classrooms designed to improve the learning of number concepts. Game topics include determining products, arranging mathematical signs, and factoring. (ASK)
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.
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 numberâ€¦
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
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 andâ€¦
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, oneâ€¦
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 overâ€¦
NASA Technical Reports Server (NTRS)
2006-01-01
29 January 2006 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows a spotted, high latitude plain, south of the Argyre basin. When the image was received from Mars by the MOC operations team, they noticed -- with a sense of humor -- the number '8' on this martian surface. The '8' is located at the center-right and is formed by the rims of two old impact craters that have been eroded and partly-filled and partly-buried beneath the surface.
Location near: 68.6oS, 38.4oW Image width: 3 km (1.9 mi) Illumination from: upper left Season: Southern Summer
Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids.
Schumacher, JĂ¶rg; GĂ¶tzfried, Paul; Scheel, Janet D
2015-08-01
Turbulent convection is often present in liquids with a kinematic viscosity much smaller than the diffusivity of the temperature. Here we reveal why these convection flows obey a much stronger level of fluid turbulence than those in which kinematic viscosity and thermal diffusivity are the same; i.e., the Prandtl number Pr is unity. We compare turbulent convection in air at Pr=0.7 and in liquid mercury at Pr=0.021. In this comparison the Prandtl number at constant Grashof number Gr is varied, rather than at constant Rayleigh number Ra as usually done. Our simulations demonstrate that the turbulent Kolmogorov-like cascade is extended both at the large- and small-scale ends with decreasing Pr. The kinetic energy injection into the flow takes place over the whole cascade range. In contrast to convection in air, the kinetic energy injection rate is particularly enhanced for liquid mercury for all scales larger than the characteristic width of thermal plumes. As a consequence, mean values and fluctuations of the local strain rates are increased, which in turn results in significantly enhanced enstrophy production by vortex stretching. The normalized distributions of enstrophy production in the bulk and the ratio of the principal strain rates are found to agree for both Prs. Despite the different energy injection mechanisms, the principal strain rates also agree with those in homogeneous isotropic turbulence conducted at the same Reynolds numbers as for the convection flows. Our results have thus interesting implications for small-scale turbulence modeling of liquid metal convection in astrophysical and technological applications. PMID:26195793
Enhanced enstrophy generation for turbulent convection in low-Prandtl-number fluids
Schumacher, JĂ¶rg; GĂ¶tzfried, 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
Topics in Number Theory: The Number Game.
ERIC Educational Resources Information Center
Batra, Laj, Ed.; And Others
This teacher's guide contains nine topics in number theory. Suggested questions for the teacher, short investigations, and possible exercises for the student are included. Chapter 1 is an introduction to sequences and series using geoboard activities involving triangular numbers, square numbers, rectangular numbers, and pentagonal numbers. Theâ€¦
Length-scale estimates for the LANS- Î± equations in terms of the Reynolds number
NASA Astrophysics Data System (ADS)
Gibbon, J. D.; Holm, D. D.
2006-08-01
Foias, Holm and Titi [C. Foias, D.D. Holm, E.S. Titi, The three dimensional viscous Camassa-Holm equations and their relation to the Navier-Stokes equations and turbulence theory, J. Dynam. Differential Equations 14 (2002) 1-35] have settled the problem of existence and uniqueness for the 3D LANS- Î± equations on periodic box [0. There still remains the problem, first introduced by Doering and Foias [C.R. Doering, C. Foias, Energy dissipation in body-forced turbulence, J. Fluid Mech. 467 (2002) 289-306] for the Navier-Stokes equations, of obtaining estimates in terms of the Reynolds number Re, whose character depends on the fluid response, as opposed to the Grashof number, whose character depends on the forcing. Re is defined as Re=Uâ„“/Î˝ where U is a bounded spatio-temporally averaged Navier-Stokes velocity field and â„“ the characteristic scale of the forcing. It is found that the inverse Kolmogorov length is estimated by â„“Î»k-1â‰¤c (Re. Moreover, the estimate of Foias, Holm and Titi for the fractal dimension of the global attractor, in terms of Re, comes out to be dF(A)â‰¤c {VÎ±V}/{â„“1/2(} Re where VÎ±=()3 and Vâ„“=(. It is also shown that there exists a series of time-averaged inverse squared length scales whose members, <Îşn,02>, are estimated as (nâ‰Ą1) â„“2<Îşn,02>â‰¤cVÎ±{n-1}/{n}Re(+c1Re(lnRe). The upper bound on the first member of the hierarchy <Îş1,02> coincides with the inverse squared Taylor micro-scale to within log-corrections.
The Prandtl number effect on the transition in natural convection along a vertical surface
Bejan, A.; Lage, J.L. )
1990-08-01
As is often the case, the decision to embark on a new project was triggered by a set of coincidental and mutually reinforcing observations: (i) There is a definite lack of information (theoretical, numerical, experimental) on natural convection in low-Pr fluids (Lykoudis, 1989). This observation was stressed recently also by Wolff et al. (1988). (ii) Georgiadis (1989) drew attention to the line of work represented by Chao et al. (1982) and Bertin and Ozoe (1986), who showed numerically that the onset of Benard convection appears to be influence by the Prandtl number in the Pr < 1 range. (iii) The authors were struck by Bertin and Ozoe's (1986) discovery that they were unable to obtain numerically a steady flow below a certain Prandtl number (Pr = 0.001), even though the Rayleigh number based on height seemed sufficiently low (Ra = 2,800). The present study was motivated by these observations and the apparent suggestion that in low-Pr fluids the laminar flow expires at unexpectedly low Rayleigh numbers. This idea is particularly interesting if they think of the natural convection boundary layer near a vertical wall, for which the textbook teaches to associate the constant Ra {approx} 10{sup 9} with the height of transition to the turbulent flow, regardless of the Prandtl number (e.g., Incropera and DeWitt, 1985, p. 427). In order to test this idea, the authors reexamined the experimental record of observations on transition in vertical natural convection boundary layer flow. Indeed, the empirical data described next show that the Prandtl number has a strong influence on the transition Rayleigh number. In low-Pr fluids the transition occurs at Rayleigh numbers much lower than the often-mentioned Ra {approx} 10{sup 9}, while in high-Pr fluids the transition Rayleigh number is higher than 10{sup 9}. It appears that the constant Grashof number Gr {approx} 10{sup 9} (i.e., not Ra {approx} 10{sup 9}) marks the transition in the wide Pr range 0.001-1000.
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…
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 toâ€¦
ERIC Educational Resources Information Center
Gurganus, Susan
2004-01-01
"Number sense" is "an intuition about numbers that is drawn from all varied meanings of number" (NCTM, 1989, p. 39). Students with number sense understand that numbers are representative of objects, magnitudes, relationships, and other attributes; that numbers can be operated on, compared, and used for communication. It is fundamental knowledgeâ€¦
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,â€¦
ERIC Educational Resources Information Center
Lamb, John, Jr.
1989-01-01
Describes several phenomena in which interesting properties of numbers are demonstrated. Includes discussions of amicable, perfect, and sociable numbers. Presents computer programs for conducting a number chain search. (RT)
ERIC Educational Resources Information Center
Burkhart, Jerry
2009-01-01
Prime numbers are often described as the "building blocks" of natural numbers. This article shows how the author and his students took this idea literally by using prime factorizations to build numbers with blocks. In this activity, students explore many concepts of number theory, including the relationship between greatest common factors and…
ERIC Educational Resources Information Center
Wilkie, James E. B.; Bodenhausen, Galen V.
2012-01-01
We examined the possibility that nonsocial, highly generic concepts are gendered. Specifically, we investigated the gender connotations of Arabic numerals. Across several experiments, we show that the number 1 and other odd numbers are associated with masculinity, whereas the number 2 and other even numbers are associated with femininity, in waysâ€¦
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 andâ€¦
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…
PET: [number sign]1 is number one
Miller, C.
1994-09-01
Subsidized in the beginning by bottle deposits, now spurred by the ability of curbside recycling to collect more than soda bottles, polyethylene terephthalate (PET) recycling has made great strides in the last 10 years. Its growth rate and increased market demand are the envy of many other materials. Appropriate, if not deliberately, this number-one resin is listed under the Society for the Plastics Industry's resin identification code as [number sign]1. Unlike most recyclables, the market demand for recycled PET is greater than the supply. As a result, demand not supply, is fueling the increase in PET recycling.
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. Withâ€¦
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
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 numbersâ€¦
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 ofâ€¦
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 1Â million to 1Â 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 conceptionsâ€¦
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. Eratosthenesâ€¦
ERIC Educational Resources Information Center
Landy, David; Silbert, Noah; Goldin, Aleah
2013-01-01
Despite their importance in public discourse, numbers in the range of 1 million to 1 trillion are notoriously difficult to understand. We examine magnitude estimation by adult Americans when placing large numbers on a number line and when qualitatively evaluating descriptions of imaginary geopolitical scenarios. Prior theoretical conceptions…
ERIC Educational Resources Information Center
Allen, G. Donald
2014-01-01
In human history, the origin of the numbers came from definite practical needs. Indeed, there is strong evidence that numbers were created before writing. The number "1", dating back at least 20,000 years, was found as a counting symbol on a bone. The famous statement by the German mathematician Leopold Kronecker (1823-1891), "God…
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 20,000Â years, was found as a counting symbol on a bone. The famous statement by the German mathematician Leopold Kronecker (1823-1891), "Godâ€¦
Wilkie, James E B; Bodenhausen, Galen V
2012-05-01
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 that influence judgments of stimuli arbitrarily paired with numerical cues; specifically, babies' faces and foreign names were more likely to be judged as "male" when paired with odd versus even numbers. The power of logically irrelevant numerical stimuli to connote masculinity or femininity reflects the pervasiveness of gender as a social scaffolding for generating understandings of abstract concepts. PMID:21767039
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.
ERIC Educational Resources Information Center
Leadership, 2007
2007-01-01
Education, it seems, is increasingly driven by the numbers. Whether it is measuring student performance or a school district's ability to balance the books, one will find data out there about it. So much data, in fact, that it is difficult to sort through all the numbers to get the needed information. This article describes California's Ed-Dataâ€¦
Avogadro's Number Ferromagnetically
ERIC Educational Resources Information Center
Houari, Ahmed
2010-01-01
Avogadro's number, usually denoted by N[subscript A], plays a fundamental role in both physics and chemistry. It defines the extremely useful concept of the mole, which is the base unit of the amount of matter in the international system of units. The fundamental character of this number can also be illustrated by its appearance in the definitions…
Templates, Numbers & Watercolors.
ERIC Educational Resources Information Center
Clemesha, David J.
1990-01-01
Describes how a second-grade class used large templates to draw and paint five-digit numbers. The lesson integrated artistic knowledge and vocabulary with their mathematics lesson in place value. Students learned how draftspeople use templates, and they studied number paintings by Charles Demuth and Jasper Johns. (KM)
First Graders' Number Knowledge
ERIC Educational Resources Information Center
Thomas, Jonathan N.; Tabor, Pamela D.; Wright, Robert J.
2010-01-01
As young children make sense of mathematics, they begin to see with new eyes. What once was uncertain may now be determined. Objects become countable; fingers become tools; and numbers become more than just names. Educators revel in such developments--which mark significant progress toward more sophisticated understanding of number--and workâ€¦
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 definitionsâ€¦
ERIC Educational Resources Information Center
Cole, Milton W.
2009-01-01
Numbers--of publications, grant money, PhD students, and invited talks, for example--play too large a role in assessments of faculty. The author's thirty-five years of experience in higher education have convinced him that overreliance on such numbers is a big problem, especially, but not exclusively, in the sciences. Every scientist recognizes…
ERIC Educational Resources Information Center
Lustick, David
1997-01-01
Describes a simple activity that explores and reveals the principles of significant figures and scientific notation using a 500 gram bag of unpopped popcorn. Students must devise a method for determining the number of kernels in the bag. (DDR)
ERIC Educational Resources Information Center
Anthony, Glenda J.; Walshaw, Margaret A.
2004-01-01
This article discusses the challenges students face in making sense of zero as a number. A range of different student responses to a computation problem involving zero reveal students' different understandings of zero.
2014-01-01
Scientists go to great lengths to ensure that data are collected and analysed properly, so why, asks Eve Marder, do they apply different standards to data about the number of times research papers have been cited and viewed? PMID:24692454
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)
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.
[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.
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 mathâ€¦
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'â€¦
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
Doyle, William R.
2010-01-01
Some say that the educators now have a gender-stratified system of higher education, with nearly 60 percent of all undergraduates being women and fewer men attending each year. The battle for gender equity for women in higher education has been a long and contentious one. In the decades since, increasing numbers of women have gone to college, toâ€¦
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 andâ€¦
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
Lew, Gordon
This illustrated children's book teaches the numbers 1-10 by counting familiar people and animals. It is one of a series written primarily to provide Chinese-American youngsters with reading materials of their own. Teachers and parents outside the Chinese community who are interested in giving children a healthy and positive outlook toward theâ€¦
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 anâ€¦
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
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…
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.
Kerfoot, Karlene
2005-01-01
We measure to determine where we stand financially or in our quality outcomes. As people see the connection of measures and the success of the company, everything makes more sense. Izzo (2005) writes that profits/net margins are important to an organization and are like oxygen to a person. If we have oxygen, we can focus on the important things in life; if we don't we are preoccupied with gasping for air. Organizations are the same way. With the oxygen of profits, organizations can focus on those things that matter most to the staff and the customer. But when the search for profits becomes obsessive because of greed for excess profits or impending financial doom, everybody loses. Izzo (2005) reminds us that organizations shouldn't exist for only profit, just as people don't exist for only oxygen. Oxygen is merely an enabler for us to do the work of living. Measurement and numbers are the oxygen needed to achieve excellence. As people in organizations use numbers as their servants rather than being slaves to numbers, everyone will succeed. If the use of measurement is seen as punitive, and not a system of serving people to attain that zest for business and a higher mission, we will not achieve the level of excellence our people, patients, and communities deserve. PMID:16033147
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.
Rocker, Graeme M; Verma, Jennifer Y; Demmons, Jillian; Mittmann, Nicole
2015-01-01
The 'Number Needed to Treat' (NNT) is a useful measure for estimating the number of patients that would need to receive a therapeutic intervention to avoid one of the adverse events that the treatment is designed to prevent. We explored the possibility of an adaption of NNT to estimate the 'Number Needed to $ave' (NN$) as a new, conceptual systems metric to estimate potential cost-savings to the health system from implementation of a treatment, or in this case, a program. We used the outcomes of the INSPIRED COPD Outreach ProgramTM to calculate that 26 patients would need to complete the program to avoid healthcare expenditures of $100,000, based on hospital bed days avoided. The NN$ does not translate into 'cost savings' per se, but redirection of resource expenditures for other purposes. We propose that the NN$ metric, if further developed, could help to inform system-level resource allocation decisions in a manner similar to the way that the NNT metric helps to inform individual-level treatment decisions. PMID:25662619
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.; Oâ€™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
Modular redundant number systems
1998-05-31
With the increased use of public key cryptography, faster modular multiplication has become an important cryptographic issue. Almost all public key cryptography, including most elliptic curve systems, use modular multiplication. Modular multiplication, particularly for the large public key modulii, is very slow. Increasing the speed of modular multiplication is almost synonymous with increasing the speed of public key cryptography. There are two parts to modular multiplication: multiplication and modular reduction. Though there are fast methods for multiplying and fast methods for doing modular reduction, they do not mix well. Most fast techniques require integers to be in a special form. These special forms are not related and converting from one form to another is more costly than using the standard techniques. To this date it has been better to use the fast modular reduction technique coupled with standard multiplication. Standard modular reduction is much more costly than standard multiplication. Fast modular reduction (Montgomery`s method) reduces the reduction cost to approximately that of a standard multiply. Of the fast multiplication techniques, the redundant number system technique (RNS) is one of the most popular. It is simple, converting a large convolution (multiply) into many smaller independent ones. Not only do redundant number systems increase speed, but the independent parts allow for parallelization. RNS form implies working modulo another constant. Depending on the relationship between these two constants; reduction OR division may be possible, but not both. This paper describes a new technique using ideas from both Montgomery`s method and RNS. It avoids the formula problem and allows fast reduction and multiplication. Since RNS form is used throughout, it also allows the entire process to be parallelized.
7 CFR 29.9205 - Identification number (farm serial number).
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 2 2013-01-01 2013-01-01 false Identification number (farm serial number). 29.9205 Section 29.9205 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE... number (farm serial number). The serial number assigned to an individual farm by the appropriate...
7 CFR 29.9205 - Identification number (farm serial number).
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 2 2012-01-01 2012-01-01 false Identification number (farm serial number). 29.9205 Section 29.9205 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE... number (farm serial number). The serial number assigned to an individual farm by the appropriate...
7 CFR 29.9205 - Identification number (farm serial number).
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 2 2014-01-01 2014-01-01 false Identification number (farm serial number). 29.9205 Section 29.9205 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE... number (farm serial number). The serial number assigned to an individual farm by the appropriate...
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...
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...
van Gijn, J
2000-01-01
The round figure for the current year has stirred people's minds in anticipation. Numbers have acquired great significance also in today's medical science. The Paris physician Pierre Charles Alexandre Louis (1787-1872) is considered the founding father of the numerical method in medicine. At first the principle of aggregating data from different individuals aroused much resistance and even disgust: Claude Bernard was a leading figure among those who warned that one will never find a mean in nature, and that grouping findings together obscures the true relationship between biological phenomena. True enough, statistical significance is not a characteristic of nature itself. Significant differences or risk reductions do not necessarily imply clinical relevance, and results obtained in a group of patients are rarely applicable to an individual patient in the consultation room. Likewise, the health of a human being cannot be captured in biochemical, radiological or other technical measures, nor in disease-specific scales that reduce well-being to one or two digits. The editors of this journal will remain keen on publishing numerical studies that contribute to evidence-based medicine, but at the same time they will continue to foster the art of reporting illness from the point of view of the sick person. PMID:10665294
Quasar number density evolution
NASA Technical Reports Server (NTRS)
Stocke, J. T.; Perrenod, S. C.
1981-01-01
A simple model of quasar number density evolution is presented based on the occurrence of quasar-like radio galaxies (i.e., strong optical emission lines and type 2 radio morphology) exclusively in regions of low galaxy and intergalactic medium (IGM) density. This suggests a limit for the IGM density of 10 to the -4th (+ or - 1) per cu cm below which quasars are allowed to form and above which they are not allowed. In the recent past (z not greater than 1), the inferred quasar environments are the outskirts of clusters and near the centers of groups of galaxies. However, models of rich cluster evolution consistent with current X-ray observations predict gas densities of less than 10 to the -4th per cu cm in cluster cores in the more distant past (z between 1 and 5). This suggests that quasars were allowed to form in the cores of rich clusters at those epochs, which explains both the rich absorption spectra of high-redshift quasars and the absence of clusters surrounding quasars at lower redshift.
Percents Are Not Natural Numbers
ERIC Educational Resources Information Center
Jacobs, Jennifer A.
2013-01-01
Adults are prone to treating percents, one representational format of rational numbers, as novel cases of natural number. This suggests that percent values are not differentiated from natural numbers; a conceptual shift from the natural numbers to the rational numbers has not yet occurred. This is most surprising, considering people are inundated…
Percents Are Not Natural Numbers
ERIC Educational Resources Information Center
Jacobs, Jennifer A.
2013-01-01
Adults are prone to treating percents, one representational format of rational numbers, as novel cases of natural number. This suggests that percent values are not differentiated from natural numbers; a conceptual shift from the natural numbers to the rational numbers has not yet occurred. This is most surprising, considering people are inundatedâ€¦
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 wasâ€¦
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…
Representing Numbers: Prime and Irrational
ERIC Educational Resources Information Center
Zazkis, Rina
2005-01-01
This article draws an analogy between prime and irrational numbers with respect to how these numbers are defined and how they are perceived by learners. Excerpts are presented from two research studies: a study on understanding prime numbers by pre-service elementary school teachers and a study on understanding irrational numbers by pre-service…
Representing Numbers: Prime and Irrational
ERIC Educational Resources Information Center
Zazkis, Rina
2005-01-01
This article draws an analogy between prime and irrational numbers with respect to how these numbers are defined and how they are perceived by learners. Excerpts are presented from two research studies: a study on understanding prime numbers by pre-service elementary school teachers and a study on understanding irrational numbers by pre-serviceâ€¦
A Study of Hyperperfect Numbers
NASA Astrophysics Data System (ADS)
McCranie, Judson S.
2000-01-01
A number n is k-hyperperfect for some integer k if n = 1 + k s(n), where s(n) is the sum of the proper divisors of n. The 1-hyperperfect numbers are the familiar perfect numbers. This paper presents some theorems, conjectures and tables concerning hyperperfect numbers. All hyperperfect numbers less than 1011 have been computed. Evidence is presented suggesting that a published conjecture is false.
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
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 toâ€¦
Irrational Numbers on the Number Line--Where Are They?
ERIC Educational Resources Information Center
Sirotic, N.; Zazkis, R.
2007-01-01
This paper reports part of an ongoing investigation into the understanding of irrational numbers by prospective secondary school teachers. It focuses on the representation of irrational numbers as points on a number line. In a written questionnaire, followed by a clinical interview, participants were asked to indicate the exact location of theâ€¦
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 ofâ€¦
Relating Mason number to Bingham number in magnetorheological fluids
NASA Astrophysics Data System (ADS)
Sherman, Stephen G.; Becnel, Andrew C.; Wereley, Norman M.
2015-04-01
Magnetorheological (MR) fluids are described using two nondimensional numbers, the Bingham and Mason numbers. The Mason number is the ratio of particle magnetic forces to viscous forces and describes the behavior of MR fluids at the microscopic, particle level scale. At the macroscopic, continuum scale, Bingham number is the ratio of yield stress to viscous stress, and describes the bulk motion of the fluid. If these two nondimensional numbers can be related, then microscopic models can be directly compared to macroscopic results. We show that if microscopic and macroscopic forces are linearly related, then Bingham and Mason number are inversely related, or, alternatively, that the product of the Bingham number and the Mason number is a constant. This relationship is experimentally validated based on measurements of apparent viscosity on a high shear rate, Îł Ë™ â‰ 10 000s-1, Searle cell rheometer. This relationship between Mason number and Bingham number is then used to analyze a Mason number based result, and is also used to inform the MR fluid device design process.
Number games, magnitude representation, and basic number skills in preschoolers.
Whyte, Jemma Catherine; Bull, Rebecca
2008-03-01
The effect of 3 intervention board games (linear number, linear color, and nonlinear number) on young children's (mean age = 3.8 years) counting abilities, number naming, magnitude comprehension, accuracy in number-to-position estimation tasks, and best-fit numerical magnitude representations was examined. Pre- and posttest performance was compared following four 25-min intervention sessions. The linear number board game significantly improved children's performance in all posttest measures and facilitated a shift from a logarithmic to a linear representation of numerical magnitude, emphasizing the importance of spatial cues in estimation. Exposure to the number card games involving nonsymbolic magnitude judgments and association of symbolic and nonsymbolic quantities, but without any linear spatial cues, improved some aspects of children's basic number skills but not numerical estimation precision. PMID:18331146
ERIC Educational Resources Information Center
Jue, Brian
2010-01-01
Separate a three-digit number into its component digits. After raising each digit to the third power and computing the sum of the cubes, determine how often the original number reappears. Modular arithmetic is used to reduce the number of potential solutions to a more manageable quantity. (Contains 4 tables.)
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,â€¦
ERIC Educational Resources Information Center
Huang, Yi Ting; Spelke, Elizabeth; Snedeker, Jesse
2013-01-01
Number words are generally used to refer to the exact cardinal value of a set, but cognitive scientists disagree about their meanings. Although most psychological analyses presuppose that numbers have exact semantics ("two" means exactly two), many linguistic accounts propose that numbers have lower-bounded semantics (at least two), andâ€¦
Random Numbers and Quantum Computers
ERIC Educational Resources Information Center
McCartney, Mark; Glass, David
2002-01-01
The topic of random numbers is investigated in such a way as to illustrate links between mathematics, physics and computer science. First, the generation of random numbers by a classical computer using the linear congruential generator and logistic map is considered. It is noted that these procedures yield only pseudo-random numbers since…
ERIC Educational Resources Information Center
Huang, Yi Ting; Spelke, Elizabeth; Snedeker, Jesse
2013-01-01
Number words are generally used to refer to the exact cardinal value of a set, but cognitive scientists disagree about their meanings. Although most psychological analyses presuppose that numbers have exact semantics ("two" means exactly two), many linguistic accounts propose that numbers have lower-bounded semantics (at least two), and…
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 sinceâ€¦
Extending the Number Line to Make Connections with Number Theory.
ERIC Educational Resources Information Center
Graviss, Tom; Greaver, Joanne
1992-01-01
Shares a coded version of the number line to provide concrete experiences for learning abstract concepts. Using the fundamental theorem of arithmetic, appropriate coded symbols are determined for the prime factorization of each natural number and used to study the concepts of greatest common divisor, least common multiple, square roots, andâ€¦
Reprint Series: Prime Numbers and Perfect Numbers. RS-2.
ERIC Educational Resources Information Center
Schaaf, William L., Ed.
This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series makes available expository articles which appeared in a variety of mathematical periodicals. Topics covered include: (1) the prime numbers; (2) mathematical sieves; (3) the factorgram; and (4) perfect numbers. (MP)
Nieder, Andreas
2016-06-01
Humans and non-human primates share an elemental quantification system that resides in a dedicated neural network in the parietal and frontal lobes. In this cortical network, 'number neurons' encode the number of elements in a set, its cardinality or numerosity, irrespective of stimulus appearance across sensory motor systems, and from both spatial and temporal presentation arrays. After numbers have been extracted from sensory input, they need to be processed to support goal-directed behaviour. Studying number neurons provides insights into how information is maintained in working memory and transformed in tasks that require rule-based decisions. Beyond an understanding of how cardinal numbers are encoded, number processing provides a window into the neuronal mechanisms of high-level brain functions. PMID:27150407
Chaotic Nonlinear Prime Number Function
NASA Astrophysics Data System (ADS)
Mateos, Luis A.
2011-06-01
Dynamical systems in nature, such as heartbeat patterns, DNA sequence pattern, prime number distribution, etc., exhibit nonlinear (chaotic) space-time fluctuations and exact quantification of the fluctuation pattern for predictability purposes has not yet been achieved [1]. In this paper a chaotic-nonlinear prime number function P(s) is developed, from which prime numbers are generated and decoded while composite numbers are encoded over time following the Euler product methodology, which works on sequences progressively culled from multiples of the preceding primes. By relating this P(s) to a virtually closed 2D number line manifold, it is possible to represent the evolving in time of nonlinear (chaotic) systems to a final value where the system becomes stable, becomes linear. This nonlinear prime number function is proposed as a chaotic model system able to describe chaotic systems.
Huang, Yi Ting; Spelke, Elizabeth; Snedeker, Jesse
2014-01-01
Number words are generally used to refer to the exact cardinal value of a set, but cognitive scientists disagree about their meanings. Although most psychological analyses presuppose that numbers have exact semantics (two means EXACTLY TWO), many linguistic accounts propose that numbers have lower-bounded semantics (AT LEAST TWO), and that speakers restrict their reference through a pragmatic inference (scalar implicature). We address this debate through studies of children who are in the process of acquiring the meanings of numbers. Adults and 2- and 3-year-olds were tested in a novel paradigm that teases apart semantic and pragmatic aspects of interpretation (the covered box task). Our findings establish that when scalar implicatures are cancelled in the critical trials of this task, both adults and children consistently give exact interpretations for number words. These results, in concert with recent work on real-time processing, provide the first unambiguous evidence that number words have exact semantics. PMID:25285053
Huang, Yi Ting; Spelke, Elizabeth; Snedeker, Jesse
2013-01-01
Number words are generally used to refer to the exact cardinal value of a set, but cognitive scientists disagree about their meanings. Although most psychological analyses presuppose that numbers have exact semantics (two means EXACTLY TWO), many linguistic accounts propose that numbers have lower-bounded semantics (AT LEAST TWO), and that speakers restrict their reference through a pragmatic inference (scalar implicature). We address this debate through studies of children who are in the process of acquiring the meanings of numbers. Adults and 2- and 3-year-olds were tested in a novel paradigm that teases apart semantic and pragmatic aspects of interpretation (the covered box task). Our findings establish that when scalar implicatures are cancelled in the critical trials of this task, both adults and children consistently give exact interpretations for number words. These results, in concert with recent work on real-time processing, provide the first unambiguous evidence that number words have exact semantics. PMID:25285053
Dynamic Virtual Credit Card Numbers
NASA Astrophysics Data System (ADS)
Molloy, Ian; Li, Jiangtao; Li, Ninghui
Theft of stored credit card information is an increasing threat to e-commerce. We propose a dynamic virtual credit card number scheme that reduces the damage caused by stolen credit card numbers. A user can use an existing credit card account to generate multiple virtual credit card numbers that are either usable for a single transaction or are tied with a particular merchant. We call the scheme dynamic because the virtual credit card numbers can be generated without online contact with the credit card issuers. These numbers can be processed without changing any of the infrastructure currently in place; the only changes will be at the end points, namely, the card users and the card issuers. We analyze the security requirements for dynamic virtual credit card numbers, discuss the design space, propose a scheme using HMAC, and prove its security under the assumption the underlying function is a PRF.
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
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.
Measuring Distance of Fuzzy Numbers by Trapezoidal Fuzzy Numbers
NASA Astrophysics Data System (ADS)
Hajjari, Tayebeh
2010-11-01
Fuzzy numbers and more generally linguistic values are approximate assessments, given by experts and accepted by decision-makers when obtaining value that is more accurate is impossible or unnecessary. Distance between two fuzzy numbers plays an important role in linguistic decision-making. It is reasonable to define a fuzzy distance between fuzzy objects. To achieve this aim, the researcher presents a new distance measure for fuzzy numbers by means of improved centroid distance method. The metric properties are also studied. The advantage is the calculation of the proposed method is far simple than previous approaches.
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…
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 generatingâ€¦
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
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 glanceâ€¦
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, theâ€¦
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 demonstratedâ€¦
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 1â€¦
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…
Know Your Blood Sugar Numbers If you have diabetes, keeping your blood sugar (glucose) numbers in your target range can help you feel ... Prevention There are two ways to measure blood sugar. 1 The A1C is a lab test that ...
The Multiplication of Signed Numbers.
ERIC Educational Resources Information Center
Zlot, William; Roberts, Ralph E.
1982-01-01
Certain properties of lenses provide a physical model of the mathematical concepts of multiplication of integral numbers and of similarity transformations in geometry. Further, they can provide a realistic concrete representation for rules governing multiplication of signed numbers. Suggestions for problems and classroom demonstrations involvingâ€¦
Number Talks Build Numerical Reasoning
ERIC Educational Resources Information Center
Parrish, Sherry D.
2011-01-01
"Classroom number talks," five- to fifteen-minute conversations around purposefully crafted computation problems, are a productive tool that can be incorporated into classroom instruction to combine the essential processes and habits of mind of doing math. During number talks, students are asked to communicate their thinking when presenting andâ€¦
ERIC Educational Resources Information Center
Avital, Shmuel; Grinblat, Uri
1983-01-01
The material focuses on the power and usefulness of the number three and is presented as though the number was being interviewed. Among the issues covered in the presentation is the impossibility of dividing an angle into three equal parts using just a straight edge and a compass. (Author/MP)
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--evenâ€¦
Some Ideas About Number Theory.
ERIC Educational Resources Information Center
Barnett, I. A.
The material in this booklet is designed for non-professional mathematicians who have an interest in the theory of numbers. The author presents some elementary results of number theory without involving detailed proofs. Much of the material has direct application for secondary school mathematics teachers. A brief account of the nature of numberâ€¦
Quantum Computing and Number Theory
NASA Astrophysics Data System (ADS)
Sasaki, Yoshitaka
2013-09-01
The prime factorization can be efficiently solved on a quantum computer. This result was given by Shor in 1994. In the first half of this article, a review of Shor's algorithm with mathematical setups is given. In the second half of this article, the prime number theorem which is an essential tool to understand the distribution of prime numbers is given.
ERIC Educational Resources Information Center
Pomerance, Carl
1982-01-01
Until recently the testing of a 100-digit number to determine whether it is prime or composite could have taken a century. However, in the past two years a method has been developed enabling a computer to determine the primality of an arbitrary number in about 40 seconds of running time. (Author/JN)
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?.
NASA Astrophysics Data System (ADS)
Talmi, Igal
2008-11-01
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
2011-01-01
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. PMID:21300893
Reynolds number influences in aeronautics
NASA Technical Reports Server (NTRS)
Bushnell, Dennis M.; Yip, Long P.; Yao, Chung-Sheng; Lin, John C.; Lawing, Pierce L.; Batina, John T.; Hardin, Jay C.; Horvath, Thomas J.; Fenbert, James W.; Domack, Christopher S.
1993-01-01
Reynolds number, a measure of the ratio of inertia to viscous forces, is a fundamental similarity parameter for fluid flows and therefore, would be expected to have a major influence in aerodynamics and aeronautics. Reynolds number influences are generally large, but monatomic, for attached laminar (continuum) flow; however, laminar flows are easily separated, inducing even stronger, non-monatomic, Reynolds number sensitivities. Probably the strongest Reynolds number influences occur in connection with transitional flow behavior. Transition can take place over a tremendous Reynolds number range, from the order of 20 x 10(exp 3) for 2-D free shear layers up to the order of 100 x 10(exp 6) for hypersonic boundary layers. This variability in transition behavior is especially important for complex configurations where various vehicle and flow field elements can undergo transition at various Reynolds numbers, causing often surprising changes in aerodynamics characteristics over wide ranges in Reynolds number. This is further compounded by the vast parameterization associated with transition, in that any parameter which influences mean viscous flow development (e.g., pressure gradient, flow curvature, wall temperature, Mach number, sweep, roughness, flow chemistry, shock interactions, etc.), and incident disturbance fields (acoustics, vorticity, particulates, temperature spottiness, even electro static discharges) can alter transition locations to first order. The usual method of dealing with the transition problem is to trip the flow in the generally lower Reynolds number wind tunnel to simulate the flight turbulent behavior. However, this is not wholly satisfactory as it results in incorrectly scaled viscous region thicknesses and cannot be utilized at all for applications such as turbine blades and helicopter rotors, nacelles, leading edge and nose regions, and High Altitude Long Endurance and hypersonic airbreathers where the transitional flow is an innately critical portion of the problem.
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.
Fibonacci Numbers and the Spreadsheet.
ERIC Educational Resources Information Center
Verderber, Nadine L.
1991-01-01
Described is a classroom activity incorporating a computer spreadsheet to study number patterns generated by the Fibonacci sequence. Included are examples and suggestions for the use of the spreadsheet in other recursive relationships. (JJK)
Integral Presentations of Catalan Numbers
ERIC Educational Resources Information Center
Dana-Picard, Thierry
2010-01-01
We compute in three different ways the same definite parametric integral. By-products are the derivation of a combinatorial identity and two integral presentations of Catalan numbers. One of them leads to a presentation using the [gamma] function.
Semantic processing of neglected numbers.
Sackur, JĂ©rĂ´me; Naccache, Lionel; Pradat-Diehl, Pascale; Azouvi, Philippe; Mazevet, Dominique; Katz, Rose; Cohen, Laurent; Dehaene, Stanislas
2008-06-01
While neglected stimuli can still be processed, few studies have directly addressed the issue of the unconscious access to semantics. In order to clarify this issue, we engaged four patients with unilateral left spatial neglect in a number comparison task. Each target number was preceded by a lateralized number prime, either in the intact or neglected hemifield (HF). Both group analyses and the intensive study of a single patient show that left (neglected) as well as right (consciously perceived) number primes affect performance: primes representing quantities that fall on the same side of the reference as the target lead to faster categorization. This congruency effect is highly suggestive of numerical semantic processing of neglected stimuli. Absence of conscious perception of neglected primes was evaluated using a combination of subjective and objective measures of performance in forced-choice tasks. PMID:18472037
Possible number of different neutrinos
Manko, V.I.; Markov, M.A.
1986-05-01
It is hypothesized that the number of different types of neutrinos may be related to the dimensionality of the space. This relationship is illustrated by a model of a four-dimensional relativistic oscillator which is an element of a relativistic string. It is shown that the total number of different neutrinos may vary from three to five (depending on the model), in agreement with astrophysical data. 5 references.
Digital random-number generator
NASA Technical Reports Server (NTRS)
Brocker, D. H.
1973-01-01
For binary digit array of N bits, use N noise sources to feed N nonlinear operators; each flip-flop in digit array is set by nonlinear operator to reflect whether amplitude of generator which feeds it is above or below mean value of generated noise. Fixed-point uniform distribution random number generation method can also be used to generate random numbers with other than uniform distribution.
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 typologicalâ€¦
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…
Experimental Determination of Ramsey Numbers
NASA Astrophysics Data System (ADS)
Bian, Zhengbing; Chudak, Fabian; Macready, William G.; Clark, Lane; Gaitan, Frank
2013-09-01
Ramsey theory is a highly active research area in mathematics that studies the emergence of order in large disordered structures. Ramsey numbers mark the threshold at which order first appears and are extremely difficult to calculate due to their explosive rate of growth. Recently, an algorithm that can be implemented using adiabatic quantum evolution has been proposed that calculates the two-color Ramsey numbers R(m,n). Here we present results of an experimental implementation of this algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(m,2) for 4â‰¤mâ‰¤8. The R(8,2) computation used 84 qubits of which 28 were computational qubits. This computation is the largest experimental implementation of a scientifically meaningful adiabatic evolution algorithm that has been done to date.
Stochastic low Reynolds number swimmers
NASA Astrophysics Data System (ADS)
Golestanian, Ramin; Ajdari, Armand
2009-05-01
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.
Experimental determination of Ramsey numbers.
Bian, Zhengbing; Chudak, Fabian; Macready, William G; Clark, Lane; Gaitan, Frank
2013-09-27
Ramsey theory is a highly active research area in mathematics that studies the emergence of order in large disordered structures. Ramsey numbers mark the threshold at which order first appears and are extremely difficult to calculate due to their explosive rate of growth. Recently, an algorithm that can be implemented using adiabatic quantum evolution has been proposed that calculates the two-color Ramsey numbers R(m,n). Here we present results of an experimental implementation of this algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(m,2) for 4â‰¤mâ‰¤8. The R(8,2) computation used 84 qubits of which 28 were computational qubits. This computation is the largest experimental implementation of a scientifically meaningful adiabatic evolution algorithm that has been done to date. PMID:24116761
Nanoplasmonics of prime number arrays.
Forestiere, Carlo; Walsh, Gary F; Miano, Giovanni; Dal Negro, Luca
2009-12-21
In this paper, we investigate the plasmonic near-field localization and the far-field scattering properties of non-periodic arrays of Ag nanoparticles generated by prime number sequences in two spatial dimensions. In particular, we demonstrate that the engineering of plasmonic arrays with large spectral flatness and particle density is necessary to achieve a high density of electromagnetic hot spots over a broader frequency range and a larger area compared to strongly coupled periodic and quasi-periodic structures. Finally, we study the far-field scattering properties of prime number arrays illuminated by plane waves and we discuss their angular scattering properties. The study of prime number arrays of metal nanoparticles provides a novel strategy to achieve broadband enhancement and localization of plasmonic fields for the engineering of nanoscale nano-antenna arrays and active plasmonic structures. PMID:20052140
Newborn infants perceive abstract numbers.
Izard, VĂ©ronique; Sann, Coralie; Spelke, Elizabeth S; Streri, Arlette
2009-06-23
Although infants and animals respond to the approximate number of elements in visual, auditory, and tactile arrays, only human children and adults have been shown to possess abstract numerical representations that apply to entities of all kinds (e.g., 7 samurai, seas, or sins). Do abstract numerical concepts depend on language or culture, or do they form a part of humans' innate, core knowledge? Here we show that newborn infants spontaneously associate stationary, visual-spatial arrays of 4-18 objects with auditory sequences of events on the basis of number. Their performance provides evidence for abstract numerical representations at the start of postnatal experience. PMID:19520833
Biotechnology at low Reynolds numbers.
Brody, J P; Yager, P; Goldstein, R E; Austin, R H
1996-01-01
The shrinking of liquid handling systems to the micron and submicron size range entails moving into the area of small Reynolds numbers. The fluid dynamics in this regime are very different from the macroscale. We present an intuitive explanation of how the different physics of small Reynolds numbers flow, along with microscopic sizes, can influence device design, and give examples from our own work using fluid flow in microfabricated devices designed for biological processing. Images FIGURE 1 FIGURE 9 FIGURE 10 FIGURE 11 FIGURE 12 FIGURE 13 PMID:8968612
Arrighi, Roberto; Togoli, Irene; Burr, David C.
2014-01-01
Much evidence has accumulated to suggest that many animals, including young human infants, possess an abstract sense of approximate quantity, a number sense. Most research has concentrated on apparent numerosity of spatial arrays of dots or other objects, but a truly abstract sense of number should be capable of encoding the numerosity of any set of discrete elements, however displayed and in whatever sensory modality. Here, we use the psychophysical technique of adaptation to study the sense of number for serially presented items. We show that numerosity of both auditory and visual sequences is greatly affected by prior adaptation to slow or rapid sequences of events. The adaptation to visual stimuli was spatially selective (in external, not retinal coordinates), pointing to a sensory rather than cognitive process. However, adaptation generalized across modalities, from auditory to visual and vice versa. Adaptation also generalized across formats: adapting to sequential streams of flashes affected the perceived numerosity of spatial arrays. All these results point to a perceptual system that transcends vision and audition to encode an abstract sense of number in space and in time. PMID:25377454
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.)
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) "Urbanâ€¦
Distance Effects in Number Agreement
ERIC Educational Resources Information Center
Schweppe, Judith
2013-01-01
One pronoun production experiment and one pronoun comprehension experiment were performed to investigate the role of grammatical number information in long-distance anaphora, with referent and pronoun either in adjacent sentences or separated by an intervening sentence. The experiments tested the assumption that the influence of grammatical numberâ€¦
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
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 ofâ€¦
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 andâ€¦
Strouhal number for free swimming
NASA Astrophysics Data System (ADS)
Saadat, Mehdi; van Buren, Tyler; Floryan, Daniel; Smits, Alexander; Haj-Hariri, Hossein
2015-11-01
In this work, we present experimental results to explore the implications of free swimming for Strouhal number (as an outcome) in the context of a simple model for a fish that consists of a 2D virtual body (source of drag) and a 2D pitching foil (source of thrust) representing cruising with thunniform locomotion. The results validate the findings of Saadat and Haj-Hariri (2012): for pitching foils thrust coefficient is a function of Strouhal number for all gaits having amplitude less than a certain critical value. Equivalently, given the balance of thrust and drag forces at cruise, Strouhal number is only a function of the shape, i.e. drag coefficient and area, and essentially a constant for high enough swimming speeds for which the mild dependence of drag coefficient on the speed vanishes. Furthermore, a dimensional analysis generalizes the findings. A scaling analysis shows that the variation of Strouhal number with cruising speed is functionally related to the variation of body drag coefficient with speed. Supported by ONR MURI Grant N00014-14-1-0533.
Oxidation Numbers and Their Limitations.
ERIC Educational Resources Information Center
Woolf, A. A.
1988-01-01
Reviews a method for determining oxidation numbers in covalent compounds and balancing mixed organic-inorganic or purely organic systems. Points out ambiguities presented when adjacent atoms have small or zero electronegativity differences. Presents other limitations that arise when using electronegativity values. (CW)
Residual number processing in dyscalculia.
Cappelletti, Marinella; Price, Cathy J
2014-01-01
Developmental dyscalculia - a congenital learning disability in understanding numerical concepts - is typically associated with parietal lobe abnormality. However, people with dyscalculia often retain some residual numerical abilities, reported in studies that otherwise focused on abnormalities in the dyscalculic brain. Here we took a different perspective by focusing on brain regions that support residual number processing in dyscalculia. All participants accurately performed semantic and categorical colour-decision tasks with numerical and non-numerical stimuli, with adults with dyscalculia performing slower than controls in the number semantic tasks only. Structural imaging showed less grey-matter volume in the right parietal cortex in people with dyscalculia relative to controls. Functional MRI showed that accurate number semantic judgements were maintained by parietal and inferior frontal activations that were common to adults with dyscalculia and controls, with higher activation for participants with dyscalculia than controls in the right superior frontal cortex and the left inferior frontal sulcus. Enhanced activation in these frontal areas was driven by people with dyscalculia who made faster rather than slower numerical decisions; however, activation could not be accounted for by response times per se, because it was greater for fast relative to slow dyscalculics but not greater for fast controls relative to slow dyscalculics. In conclusion, our results reveal two frontal brain regions that support efficient number processing in dyscalculia. PMID:24266008
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 hisâ€¦
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, surfaceâ€¦
Questioning Zero and Negative Numbers
ERIC Educational Resources Information Center
Wilcox, Virginia B.
2008-01-01
After experiencing a Developing Mathematical Ideas (DMI) class on the construction of algebraic concepts surrounding zero and negative numbers, the author conducted an interview with a first grader to determine the youngster's existing level of understanding about these topics. Uncovering young students' existing understanding can provide focusâ€¦
Residual number processing in dyscalculiaâ†
Cappelletti, Marinella; Price, Cathy J.
2013-01-01
Developmental dyscalculia â€“ a congenital learning disability in understanding numerical concepts â€“ is typically associated with parietal lobe abnormality. However, people with dyscalculia often retain some residual numerical abilities, reported in studies that otherwise focused on abnormalities in the dyscalculic brain. Here we took a different perspective by focusing on brain regions that support residual number processing in dyscalculia. All participants accurately performed semantic and categorical colour-decision tasks with numerical and non-numerical stimuli, with adults with dyscalculia performing slower than controls in the number semantic tasks only. Structural imaging showed less grey-matter volume in the right parietal cortex in people with dyscalculia relative to controls. Functional MRI showed that accurate number semantic judgements were maintained by parietal and inferior frontal activations that were common to adults with dyscalculia and controls, with higher activation for participants with dyscalculia than controls in the right superior frontal cortex and the left inferior frontal sulcus. Enhanced activation in these frontal areas was driven by people with dyscalculia who made faster rather than slower numerical decisions; however, activation could not be accounted for by response times per se, because it was greater for fast relative to slow dyscalculics but not greater for fast controls relative to slow dyscalculics. In conclusion, our results reveal two frontal brain regions that support efficient number processing in dyscalculia. PMID:24266008
Herculano-Houzel, Suzana; Avelino-de-Souza, Kamilla; Neves, Kleber; PorfĂrio, Jairo; Messeder, DĂ©bora; Mattos FeijĂł, Larissa; Maldonado, JosĂ©; 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
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 talk to ... ncbi.nlm.nih.gov/pubmed/12630734 . Shannon MW. Emergency management of poisoning. In: Shannon MW, Borron SW, ...
Arithmetic priming from neglected numbers.
Rusconi, Elena; Priftis, Konstantinos; Rusconi, Maria Luisa; Umilta, Carlo
2006-01-01
Patient AM, with left visuospatial neglect, and 31 healthy participants performed a parity judgment task on numbers presented to their right parafovea. Target numbers were preceded by a pair of digits (prime) appearing peripherally for 100Â ms either in their left (LVF) or in their right visual field (RVF), which participants had to ignore. In healthy participants, when primes were arithmetically related to the following target, performance was significantly slower than when primes and targets were not related. In contrast, AM's performance was slower in the related than in the control condition when prime digits appeared in his RVF, whereas it was faster in the related than in the control condition when prime digits appeared in his LVF. This suggests that neglected numbers were nevertheless processed at least until the level of stored arithmetic knowledge. Thus, visuospatial neglect does not prevent neglected numbers from accessing their representations in arithmetic networks, which seems to be a highly automatised skill. Moreover, AM's pattern of data (i.e., interference from RVF primes vs. facilitation from LVF primes) supports the hypothesis of a link between conscious attention and inhibitory processes, as proposed by Fuentes and Humphreys (1996). PMID:21049329
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 inâ€¦
Are cirrus ice number concentrations sensitive to aerosol number concentrations?
NASA Astrophysics Data System (ADS)
Kay, J. E.; Wood, R.; Baker, M.
2006-12-01
The first indirect aerosol effect on climate, the Twomey effect, states that an increase in the number concentrations of aerosols (Naerosol) will increase the number concentration of cloud droplets and for a fixed water content, produce brighter clouds (Twomey, 1974). Previous studies have shown that the Twomey effect is not important for cirrus (e.g., DeMott et al., 1997, Jensen and Toon, 1994). In most cirrus models, Naerosol does not affect the number concentration of ice crystals (Nice) because the growth of the first few ice crystals quickly draws down the relative humidity, reduces homogeneous nucleation rates, and inhibits further freezing. Using a parcel model with binned ice microphysics, we find that the sensitivity of Nice to Naerosol depends on the deposition coefficient (Î±ice), i.e., the fraction of impinging water vapor molecules that are able to attach to an ice crystal surface. With low Î±ice (Î±ice < 0.01), such those measured by Magee (2006), Nice is very sensitive to Naerosol. The sensitivity of Nice to Naerosol increases with a low Î±ice because the first few ice crystals grow inefficiently and take longer to reduce homogeneous nucleation rates. As a result, a larger fraction of the available Naerosol can freeze stochastically. In contrast, with large Î±ice (Î±ice > 0.1), Nice depends primarily on the updraft velocity and is largely independent of Naerosol. Using timescales and Nice calculated from our numerical experiments, we describe how the sensitivity of Nice to Naerosol depends on the assumed Î±ice, the updraft velocity, and the temperature.
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).
Large Number Discrimination by Mosquitofish
Agrillo, Christian; Piffer, Laura; Bisazza, Angelo
2010-01-01
Background Recent studies have demonstrated that fish display rudimentary numerical abilities similar to those observed in mammals and birds. The mechanisms underlying the discrimination of small quantities (<4) were recently investigated while, to date, no study has examined the discrimination of large numerosities in fish. Methodology/Principal Findings Subjects were trained to discriminate between two sets of small geometric figures using social reinforcement. In the first experiment mosquitofish were required to discriminate 4 from 8 objects with or without experimental control of the continuous variables that co-vary with number (area, space, density, total luminance). Results showed that fish can use the sole numerical information to compare quantities but that they preferentially use cumulative surface area as a proxy of the number when this information is available. A second experiment investigated the influence of the total number of elements to discriminate large quantities. Fish proved to be able to discriminate up to 100 vs. 200 objects, without showing any significant decrease in accuracy compared with the 4 vs. 8 discrimination. The third experiment investigated the influence of the ratio between the numerosities. Performance was found to decrease when decreasing the numerical distance. Fish were able to discriminate numbers when ratios were 1â¶2 or 2â¶3 but not when the ratio was 3â¶4. The performance of a sample of undergraduate students, tested non-verbally using the same sets of stimuli, largely overlapped that of fish. Conclusions/Significance Fish are able to use pure numerical information when discriminating between quantities larger than 4 units. As observed in human and non-human primates, the numerical system of fish appears to have virtually no upper limit while the numerical ratio has a clear effect on performance. These similarities further reinforce the view of a common origin of non-verbal numerical systems in all vertebrates. PMID:21203508
NASA Astrophysics Data System (ADS)
Richman, Robert M.
1998-05-01
A recent paper has argued that the derivation of the periodic table using quantum numbers is a topic that should be eliminated from introductory chemistry courses because it is too abstract, mysterious, and esoteric. A rebuttal is offered based on the claim that it would be wrong to omit discussions of the inductive approach of Mendeleev and the deductive approach initiated by Schroedinger, because they compose the consummate example of that interaction of empirical and rational epistemologies that defines how chemists think.
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.
Semantic alignment and number comparison.
Campbell, Jamie I D; Sacher, Sean G
2012-01-01
Are the quantity representations activated by Arabic digits influenced by semantic context? We developed a novel paradigm to examine semantic alignment effects (e.g., Bassok et al. in J Exp Psychol Learn Mem Cogn 34:343-352, 2008) in number comparison. A horizontal word pair (either less more or few many) appeared for 480Â ms to prime either relative magnitude (less more) or quantity (few many). Then a horizontal pair of single digits that were either successors (near) or differed by at least four (far) appeared above the word pair. Participants indicated verbally whether or not the word and digit pairs were congruent with respect to left-to-right ascending or descending relative magnitude. The RT advantage for far number pairs compared to near pairs (the distance effect) was greater with magnitude primes (81Â ms) than quantity primes (17Â ms), demonstrating a semantic alignment effect. This effect disappeared in Experiment 2 in which participants received identical stimuli but named the larger of the two digits and were free to ignore the primes. Nonetheless, mean RT in Experiment 2 was faster with prime and target pairs both ascending or both descending, but only with quantity primes. This prime-dependent order-congruity effect suggests that semantic alignment with respect to numerical order affected number comparison in Experiment 2. The results thereby demonstrate that number comparison exhibits task-dependent semantic alignment effects and recruits distinct numerical representations as a function of semantic context (e.g., Cohen Kadosh and Walsh in Behav Brain Sci 32:313-373, 2009). PMID:21461771
Sasanguie, Delphine; GĂ¶bel, 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. PMID:23270796
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 AlfvĂ©n 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 Ëś0.3 Ď„c , where Ď„c 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.
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. Am J Phys Anthropol 159:S19-S36, 2016. Â© 2016 Wiley Periodicals, Inc. PMID:26808105
Automatic Assignment of EC Numbers
Egelhofer, Volker; Schomburg, Ida; Schomburg, Dietmar
2010-01-01
A wide range of research areas in molecular biology and medical biochemistry require a reliable enzyme classification system, e.g., drug design, metabolic network reconstruction and system biology. When research scientists in the above mentioned areas wish to unambiguously refer to an enzyme and its function, the EC number introduced by the Nomenclature Committee of the International Union of Biochemistry and Molecular Biology (IUBMB) is used. However, each and every one of these applications is critically dependent upon the consistency and reliability of the underlying data for success. We have developed tools for the validation of the EC number classification scheme. In this paper, we present validated data of 3788 enzymatic reactions including 229 sub-subclasses of the EC classification system. Over 80% agreement was found between our assignment and the EC classification. For 61 (i.e., only 2.5%) reactions we found that their assignment was inconsistent with the rules of the nomenclature committee; they have to be transferred to other sub-subclasses. We demonstrate that our validation results can be used to initiate corrections and improvements to the EC number classification scheme. PMID:20126531
Quasiperpendicular High Mach Number Shocks.
Sulaiman, A H; Masters, A; Dougherty, M K; Burgess, D; Fujimoto, M; Hospodarsky, G B
2015-09-18
Shock waves exist throughout the Universe and are fundamental to understanding the nature of collisionless plasmas. Reformation is a process, driven by microphysics, which typically occurs at high Mach number supercritical shocks. While ongoing studies have investigated this process extensively both theoretically and via simulations, their observations remain few and far between. In this Letter we present a study of very high Mach number shocks in a parameter space that has been poorly explored and we identify reformation using in situ magnetic field observations from the Cassini spacecraft at 10 AU. This has given us an insight into quasiperpendicular shocks across 2 orders of magnitude in AlfvĂ©n Mach number (M_{A}) which could potentially bridge the gap between modest terrestrial shocks and more exotic astrophysical shocks. For the first time, we show evidence for cyclic reformation controlled by specular ion reflection occurring at the predicted time scale of ~0.3Ď„_{c}, where Ď„_{c} is the ion gyroperiod. In addition, we experimentally reveal the relationship between reformation and M_{A} and focus on the magnetic structure of such shocks to further show that for the same M_{A}, a reforming shock exhibits stronger magnetic field amplification than a shock that is not reforming. PMID:26430997
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.
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 GÎĽ â‰¤2.8Ă—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.
2013-07-16
This paper will explore the difficulties of deep reductions by examining the technical verification challenges. At each step on the road to low numbers, the verification required to ensure compliance of all parties will increase significantly. Looking post New START, the next step will likely include warhead limits in the neighborhood of 1000 (Pifer 2010). Further reductions will include stepping stones at 100â€™s of warheads, and then 10â€™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, 100â€™s, 10â€™s. For each, the issues and challenges will be discussed, potential solutions will be identified, and the verification technologies and chain of custody measures that address these solutions will be surveyed. It is important to note that many of the issues that need to be addressed have no current solution. In these cases, the paper will explore new or novel technologies that could be applied. These technologies will draw from the research and development that is ongoing throughout the national lab complex, and will look at technologies utilized in other areas of industry for their application to arms control verification.
Verification Challenges at Low Numbers
Benz, Jacob M.; Booker, Paul M.; McDonald, Benjamin S.
2013-06-01
Many papers have dealt with the political difficulties and ramifications of deep nuclear arms reductions, and the issues of â€śGoing to Zeroâ€ť. 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, 100â€™s of warheads, and then 10â€™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, 100â€™s, 10â€™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.
Numbers, Counting, and Infinity in Middle Schools.
ERIC Educational Resources Information Center
Meconi, L. J.
1992-01-01
Discusses the use of middle-school students' natural understanding of large numbers to introduce the concept of infinity. Presents activities that investigate infinite sets by demonstrating a one-to-one correspondence between the counting numbers and the given set. Examples include prime numbers, Fibonacci numbers, fractions, even and odd numbers,â€¦
Department of Defense Worldwide Numbers for TBI
... Us FAQs About Traumatic Brain Injury TBI & the Military DoD Worldwide Numbers for TBI Education Resources Training & ... Members & Veterans Family & Caregivers Medical Providers TBI & the Military DoD Worldwide Numbers for TBI DoD Worldwide Numbers ...
The Decimal Number System and Young Children
ERIC Educational Resources Information Center
Harrison, John
2006-01-01
In this article, the author believes that a visual image of the number system is helpful to everyone, especially children, in understanding what is, after all, an abstract idea. The simplest model is the number line, a row of equally spaced numbers, starting at zero. This illustrates the continuous progression of the natural numbers, moving to theâ€¦
Visuospatial Priming of the Mental Number Line
ERIC Educational Resources Information Center
Stoianov, Ivilin; Kramer, Peter; Umilta, Carlo; Zorzi, Marco
2008-01-01
It has been argued that numbers are spatially organized along a "mental number line" that facilitates left-hand responses to small numbers, and right-hand responses to large numbers. We hypothesized that whenever the representations of visual and numerical space are concurrently activated, interactions can occur between them, before response…
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 effectsâ€¦
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)
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 Â§ 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,...
Visuospatial Priming of the Mental Number Line
ERIC Educational Resources Information Center
Stoianov, Ivilin; Kramer, Peter; Umilta, Carlo; Zorzi, Marco
2008-01-01
It has been argued that numbers are spatially organized along a "mental number line" that facilitates left-hand responses to small numbers, and right-hand responses to large numbers. We hypothesized that whenever the representations of visual and numerical space are concurrently activated, interactions can occur between them, before responseâ€¦
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.
Federal Register 2010, 2011, 2012, 2013, 2014
2010-02-01
... COMMISSION 47 CFR Part 52 Local Number Portability Porting Interval and Validation Requirements; Telephone Number Portability AGENCY: Federal Communications Commission. ACTION: Proposed rule. SUMMARY: The... November 2, 2009, the North American Numbering Council (NANC) Local Number Portability...
Federal Register 2010, 2011, 2012, 2013, 2014
2013-06-19
... Requirements for IP-Enabled Services Providers; Telephone Number Portability et al. AGENCY: Federal... termination, intercarrier compensation, IP interconnection, local number portability, number cost allocation... ensure that numbers are made available on an ``equitable'' basis, to advance the...
46 CFR Sec. 7 - Job order numbering.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 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
... 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
... 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
... REPAIRS UNDER NATIONAL SHIPPING AUTHORITY MASTER LUMP SUM REPAIR CONTRACT-NSA-LUMPSUMREP Sec. 7 Job order numbering. (a) The NSA-LUMPSUMREP Contract number shall be inserted in every job order and supplemental...
46 CFR Sec. 7 - Job order numbering.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 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...
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)
The Many Pearls of Number Theory
ERIC Educational Resources Information Center
Prielipp, Robert W.
1970-01-01
Presents information about prime numbers which the elementary or junior high school teacher might introduce to students. Gives five definition statements followed by at least one theorem and its proof. Introduces some historical aspects to prime numbers. (RR)
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. PMID:27218850
Youth Gangs: A Look At the Numbers.
ERIC Educational Resources Information Center
Miller, Walter
1982-01-01
Reports findings of a study of law-violating youth groups and group members in the United States. Number of groups, membership, geographical distribution, and relationships between variables such as number of gangs and city size are reported. (RH)
NASA Astrophysics Data System (ADS)
M"Uller, Tom
2007-09-01
An odd prime number p is called anti-elite if only finitely many Fermat numbers are quadratic non-residues to p. This concept is the exact opposite to that of elite prime numbers. We study some fundamental properties of anti-elites and show that there are infinitely many of them. A computational search among all the numbers up to 100 billion yielded 84 anti-elite primes.
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 midpointâ€¦
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 Â§ 1602.19 Numbers. Cardinal numbers may be expressed by Arabic or Roman symbols....
Code of Federal Regulations, 2011 CFR
2011-07-01
... 32 National Defense 6 2011-07-01 2011-07-01 false Numbers. 1602.19 Section 1602.19 National Defense Other Regulations Relating to National Defense SELECTIVE SERVICE SYSTEM DEFINITIONS Â§ 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 Â§ 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 Â§ 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 Â§ 1602.19 Numbers. Cardinal numbers may be expressed by Arabic or Roman symbols....
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, 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....
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, 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....
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)
18 CFR 367.4 - Numbering system.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 18 Conservation of Power and Water Resources 1 2013-04-01 2013-04-01 false Numbering system. 367.4... NATURAL GAS ACT UNIFORM SYSTEM OF ACCOUNTS FOR CENTRALIZED SERVICE COMPANIES SUBJECT TO THE PROVISIONS OF... Instructions Â§ 367.4 Numbering system. (a) The account numbering plan used in this part consists of a system...
18 CFR 367.4 - Numbering system.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 18 Conservation of Power and Water Resources 1 2011-04-01 2011-04-01 false Numbering system. 367.4... NATURAL GAS ACT UNIFORM SYSTEM OF ACCOUNTS FOR CENTRALIZED SERVICE COMPANIES SUBJECT TO THE PROVISIONS OF... Instructions Â§ 367.4 Numbering system. (a) The account numbering plan used in this part consists of a system...
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 ofâ€¦
Code of Federal Regulations, 2010 CFR
2010-10-01
... 47 Telecommunication 1 2010-10-01 2010-10-01 false File numbers. 1.1405 Section 1.1405... Procedures Â§ 1.1405 File numbers. Each complaint which appears to be essentially complete under Â§ 1.1404 will be accepted and assigned a file number. Such assignment is for administrative purposes only and...
47 CFR 32.20 - Numbering convention.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 47 Telecommunication 2 2013-10-01 2013-10-01 false Numbering convention. 32.20 Section 32.20 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES UNIFORM SYSTEM OF ACCOUNTS FOR TELECOMMUNICATIONS COMPANIES General Instructions Â§ 32.20 Numbering convention. (a) The number...
47 CFR 32.20 - Numbering convention.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 47 Telecommunication 2 2011-10-01 2011-10-01 false Numbering convention. 32.20 Section 32.20 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES UNIFORM SYSTEM OF ACCOUNTS FOR TELECOMMUNICATIONS COMPANIES General Instructions Â§ 32.20 Numbering convention. (a) The number...
47 CFR 32.20 - Numbering convention.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 47 Telecommunication 2 2012-10-01 2012-10-01 false Numbering convention. 32.20 Section 32.20 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES UNIFORM SYSTEM OF ACCOUNTS FOR TELECOMMUNICATIONS COMPANIES General Instructions Â§ 32.20 Numbering convention. (a) The number...
47 CFR 32.20 - Numbering convention.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 47 Telecommunication 2 2014-10-01 2014-10-01 false Numbering convention. 32.20 Section 32.20 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES UNIFORM SYSTEM OF ACCOUNTS FOR TELECOMMUNICATIONS COMPANIES General Instructions Â§ 32.20 Numbering convention. (a) The number...
18 CFR 367.4 - Numbering system.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 18 Conservation of Power and Water Resources 1 2010-04-01 2010-04-01 false Numbering system. 367.4... NATURAL GAS ACT UNIFORM SYSTEM OF ACCOUNTS FOR CENTRALIZED SERVICE COMPANIES SUBJECT TO THE PROVISIONS OF... Instructions Â§ 367.4 Numbering system. (a) The account numbering plan used in this part consists of a system...
47 CFR 32.20 - Numbering convention.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 47 Telecommunication 2 2010-10-01 2010-10-01 false Numbering convention. 32.20 Section 32.20 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES UNIFORM SYSTEM OF ACCOUNTS FOR TELECOMMUNICATIONS COMPANIES General Instructions Â§ 32.20 Numbering convention. (a) The number â€ś32â€ť (appearing to the left of the...
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 Â§ 47.15 Registration number. (a) Number required. An applicant for aircraft...
47 CFR 95.671 - Serial number.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 47 Telecommunication 5 2013-10-01 2013-10-01 false Serial number. 95.671 Section 95.671... SERVICES Technical Regulations Additional Certification Requirements for Cb Transmitters § 95.671 Serial number. The serial number of each CB transmitter must be engraved on the transmitter chassis....
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... SERVICES Technical Regulations Additional Certification Requirements for Cb Transmitters § 95.671 Serial number. The serial number of each CB transmitter must be engraved on the transmitter chassis....
47 CFR 95.671 - Serial number.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 47 Telecommunication 5 2012-10-01 2012-10-01 false Serial number. 95.671 Section 95.671... SERVICES Technical Regulations Additional Certification Requirements for Cb Transmitters § 95.671 Serial number. The serial number of each CB transmitter must be engraved on the transmitter chassis....
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... SERVICES Technical Regulations Additional Certification Requirements for Cb Transmitters § 95.671 Serial number. The serial number of each CB transmitter must be engraved on the transmitter chassis....
47 CFR 95.671 - Serial number.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 47 Telecommunication 5 2014-10-01 2014-10-01 false Serial number. 95.671 Section 95.671 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES PERSONAL RADIO SERVICES Technical Regulations Additional Certification Requirements for Cb Transmitters § 95.671 Serial number. The serial number of each...
Insights into Our Understandings of Large Numbers
ERIC Educational Resources Information Center
Kastberg, Signe E.; Walker, Vicki
2008-01-01
This article explores prospective teachers' understandings of one million to gain insights into the development of adult understanding of large numbers. Themes in the prospective teachers' work included number associated with a quantity of objects, number as an abstraction, and additive and multiplicative approaches. The authors suggest that theâ€¦
49 CFR 230.47 - Boiler number.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 49 Transportation 4 2013-10-01 2013-10-01 false Boiler number. 230.47 Section 230.47..., DEPARTMENT OF TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges Â§ 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known,...
49 CFR 230.47 - Boiler number.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 49 Transportation 4 2012-10-01 2012-10-01 false Boiler number. 230.47 Section 230.47..., DEPARTMENT OF TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges Â§ 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known,...
49 CFR 230.47 - Boiler number.
Code of Federal Regulations, 2014 CFR
2014-10-01
... 49 Transportation 4 2014-10-01 2014-10-01 false Boiler number. 230.47 Section 230.47..., DEPARTMENT OF TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges Â§ 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known,...
49 CFR 230.47 - Boiler number.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 49 Transportation 4 2011-10-01 2011-10-01 false Boiler number. 230.47 Section 230.47..., DEPARTMENT OF TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges Â§ 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known,...
49 CFR 230.47 - Boiler number.
Code of Federal Regulations, 2010 CFR
2010-10-01
..., DEPARTMENT OF TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges Â§ 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...
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)
Teach Kids about Numbers All around Us
ERIC Educational Resources Information Center
Hudson, Hannah Trierweiler
2011-01-01
Recognizing the role numbers play in people's everyday lives is crucial to students' math understanding now and down the road. That's why Bob Krech, a curriculum specialist in New Jersey's West Windsor-Plainsboro district, likes to teach a lesson he calls "Numbers All Around Us." This lesson uses real-world examples to show that numbers helpâ€¦
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 Â§ 51.203 Number portability. The rules governing number...
Reading the World through Very Large Numbers
ERIC Educational Resources Information Center
Greer, Brian; Mukhopadhyay, Swapna
2010-01-01
One original, and continuing, source of interest in large numbers is observation of the natural world, such as trying to count the stars on a clear night or contemplation of the number of grains of sand on the seashore. Indeed, a search of the internet quickly reveals many discussions of the relative numbers of stars and grains of sand. Bigâ€¦
18 CFR 367.4 - Numbering system.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 18 Conservation of Power and Water Resources 1 2014-04-01 2014-04-01 false Numbering system. 367.4... NATURAL GAS ACT UNIFORM SYSTEM OF ACCOUNTS FOR CENTRALIZED SERVICE COMPANIES SUBJECT TO THE PROVISIONS OF... Instructions Â§ 367.4 Numbering system. (a) The account numbering plan used in this part consists of a system...
Ocular drift along the mental number line.
Myachykov, Andriy; Ellis, Rob; Cangelosi, Angelo; Fischer, Martin H
2016-05-01
We examined the spontaneous association between numbers and space by documenting attention deployment and the time course of associated spatial-numerical mapping with and without overt oculomotor responses. In Experiment 1, participants maintained central fixation while listening to number names. In Experiment 2, they made horizontal target-direct saccades following auditory number presentation. In both experiments, we continuously measured spontaneous ocular drift in horizontal space during and after number presentation. Experiment 2 also measured visual-probe-directed saccades following number presentation. Reliable ocular drift congruent with a horizontal mental number line emerged during and after number presentation in both experiments. Our results provide new evidence for the implicit and automatic nature of the oculomotor resonance effect associated with the horizontal spatial-numerical mapping mechanism. PMID:26724955
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 studyâ€¦
2 CFR 25.315 - Data Universal Numbering System (DUNS) Number.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 2 Grants and Agreements 1 2012-01-01 2012-01-01 false Data Universal Numbering System (DUNS...-AWARD RESPONSIBILITIES UNIVERSAL IDENTIFIER AND CENTRAL CONTRACTOR REGISTRATION Definitions Â§ 25.315 Data Universal Numbering System (DUNS) Number. Data Universal Numbering System (DUNS) Number has...
2 CFR 25.315 - Data Universal Numbering System (DUNS) Number.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 2 Grants and Agreements 1 2013-01-01 2013-01-01 false Data Universal Numbering System (DUNS...-AWARD RESPONSIBILITIES UNIVERSAL IDENTIFIER AND CENTRAL CONTRACTOR REGISTRATION Definitions Â§ 25.315 Data Universal Numbering System (DUNS) Number. Data Universal Numbering System (DUNS) Number has...
2 CFR 25.315 - Data Universal Numbering System (DUNS) Number.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 2 Grants and Agreements 1 2011-01-01 2011-01-01 false Data Universal Numbering System (DUNS...-award responsibilities UNIVERSAL IDENTIFIER AND CENTRAL CONTRACTOR REGISTRATION Definitions Â§â€‰25.315 Data Universal Numbering System (DUNS) Number. Data Universal Numbering System (DUNS) Number has...
2 CFR 25.315 - Data Universal Numbering System (DUNS) Number.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 2 Grants and Agreements 1 2014-01-01 2014-01-01 false Data Universal Numbering System (DUNS... Reserved UNIVERSAL IDENTIFIER AND CENTRAL CONTRACTOR REGISTRATION Definitions Â§ 25.315 Data Universal Numbering System (DUNS) Number. Data Universal Numbering System (DUNS) Number has the meaning given...
Interaction of Number Magnitude and Auditory Localization.
Golob, Edward J; Lewald, JĂ¶rg; Jungilligens, Johannes; Getzmann, Stephan
2016-01-01
The interplay of perception and memory is very evident when we perceive and then recognize familiar stimuli. Conversely, information in long-term memory may also influence how a stimulus is perceived. Prior work on number cognition in the visual modality has shown that in Western number systems long-term memory for the magnitude of smaller numbers can influence performance involving the left side of space, while larger numbers have an influence toward the right. Here, we investigated in the auditory modality whether a related effect may bias the perception of sound location. Subjects (nâ€‰=â€‰28) used a swivel pointer to localize noise bursts presented from various azimuth positions. The noise bursts were preceded by a spoken number (1-9) or, as a nonsemantic control condition, numbers that were played in reverse. The relative constant error in noise localization (forward minus reversed speech) indicated a systematic shift in localization toward more central locations when the number was smaller and toward more peripheral positions when the preceding number magnitude was larger. These findings do not support the traditional left-right number mapping. Instead, the results may reflect an overlap between codes for number magnitude and codes for sound location as implemented by two channel models of sound localization, or possibly a categorical mapping stage of small versus large magnitudes. PMID:26562857
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}.
Deafness for the meanings of number words
CaĂ±o, AgnĂ¨s; 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
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.
Riemann equation for prime number diffusion
NASA Astrophysics Data System (ADS)
Chen, Wen; Liang, Yingjie
2015-05-01
This study makes the first attempt to propose the Riemann diffusion equation to describe in a manner of partial differential equation and interpret in physics of diffusion the classical Riemann method for prime number distribution. The analytical solution of this equation is the well-known Riemann representation. The diffusion coefficient is dependent on natural number, a kind of position-dependent diffusivity diffusion. We find that the diffusion coefficient of the Riemann diffusion equation is nearly a straight line having a slope 0.99734 in the double-logarithmic axis. Consequently, an approximate solution of the Riemann diffusion equation is obtained, which agrees well with the Riemann representation in predicting the prime number distribution. Moreover, we interpret the scale-free property of prime number distribution via a power law function with 1.0169 the scale-free exponent in respect to logarithmic transform of the natural number, and then the fractal characteristic of prime number distribution is disclosed.
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 aâ€¦
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.
Factoring numbers with a single interferogram
NASA Astrophysics Data System (ADS)
Tamma, Vincenzo; Zhang, Heyi; He, Xuehua; Garuccio, Augusto; Schleich, Wolfgang P.; Shih, Yanhua
2011-02-01
We construct an analog computer based on light interference to encode the hyperbolic function f(Î¶)â‰ˇ1/Î¶ 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.
Generation of large prime numbers from a sequence of previous prime numbers
NASA Astrophysics Data System (ADS)
Samir, Brahim Belhaouari; Rezk, Youssef A. Y.
2012-09-01
A prime number is co-prime with all the primes as well. This paper utilizes this fact by generating larger prime numbers based on a set of smaller prime numbers. The prime numbers are ordered and each two consecutive primes are coupled to generate their co-prime number formula extending this process larger prime sequence is established. Will the process help us produce larger prime numbers faster and more efficiently? This paper investigates the described process.
CRC octane number requirement survey 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 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.
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.
Calculating Atomic Number Densities for Uranium
Energy Science and Technology Software Center (ESTSC)
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.
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.
Predicting the required number of training samples
NASA Technical Reports Server (NTRS)
Kalayeh, H. M.; Landgrebe, D. A.
1982-01-01
A criterion which measures the quality of the estimate of the covariance matrix of a multivariate normal distribution is developed. Based on this criterion, the necessary number of training samples is predicted. Experimental results which are used as a guide for determining the number of training samples are included.
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…
A Generalization of the Prime Number Theorem
ERIC Educational Resources Information Center
Bruckman, Paul S.
2008-01-01
In this article, the author begins with the prime number theorem (PNT), and then develops this into a more general theorem, of which many well-known number theoretic results are special cases, including PNT. He arrives at an asymptotic relation that allows the replacement of certain discrete sums involving primes into corresponding differentiable…
Deafness for the Meanings of Number Words
ERIC Educational Resources Information Center
Cano, Agnes; 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) hisâ€¦
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 toâ€¦
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 withâ€¦
Number Conservation in Two West African Societies.
ERIC Educational Resources Information Center
Posner, Jill K.; Baroody, Arthur J.
1979-01-01
Examines the effects of cultural and educational variables on the development of number conservation among Baoule (agricultural group) children and Dioula (merchant group) children. Results suggest that both school and a merchant culture provide for acquisition of a mature number concept, supporting the "functional learning systems" approach toâ€¦
New Numbers in Mathematics in South Africa
ERIC Educational Resources Information Center
Engelbrecht, Johann; Harding, Ansie
2009-01-01
This article is a follow-up of a study conducted in 2000 by the same authors on trends in numbers of mathematics majors at South African universities. Data from 12 universities for the 2000-2007 period is investigated. The previously observed trend of general and dramatic decrease in numbers of mathematics majors appears to have been reversed andâ€¦
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 fundamentallyâ€¦
MRI Turbulence at High Reynolds Numbers
NASA Astrophysics Data System (ADS)
Walker, Justin; Boldyrev, Stanislav; Lesur, Geoffroy
2014-10-01
The properties of magnetic turbulence driven by the magnetorotational instability (MRI) are studied at large Reynolds numbers by simulation. The results are compared with previous published results at lower Reynolds number and with forced magnetohydrodynamic (MHD) turbulence. Preliminary results suggest that spectra exhibit a power law within a short inertial range, and similarities and differences with the inertial range in MHD turbulence are established.
Atomic Fisher information versus atomic number
NASA Astrophysics Data System (ADS)
Nagy, Ă.; Sen, K. D.
2006-12-01
It is shown that the Thomas Fermi Fisher information is negative. A slightly more sophisticated model proposed by GĂˇspĂˇr provides a qualitatively correct expression for the Fisher information: GĂˇspĂˇr's Fisher information is proportional to the two-third power of the atomic number. Accurate numerical calculations show an almost linear dependence on the atomic number.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 47 Telecommunication 1 2012-10-01 2012-10-01 false File numbers. 1.1405 Section 1.1405 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL PRACTICE AND PROCEDURE Grants by Random Selection Pole Attachment Complaint Procedures Â§ 1.1405 File numbers. Each complaint which appears to be...
Code of Federal Regulations, 2013 CFR
2013-10-01
... 47 Telecommunication 1 2013-10-01 2013-10-01 false File numbers. 1.1405 Section 1.1405 Telecommunication FEDERAL COMMUNICATIONS COMMISSION GENERAL PRACTICE AND PROCEDURE Grants by Random Selection Pole Attachment Complaint Procedures Â§ 1.1405 File numbers. Each complaint which appears to be...
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 originalâ€¦
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 Â§ 105-1.109 Numbering....
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.
27 CFR 24.115 - Registry number.
Code of Federal Regulations, 2010 CFR
2010-04-01
..., bonded wine cellar, or taxpaid wine bottling house. The registry number will be used in all... OF THE TREASURY LIQUORS WINE Establishment and Operations Application Â§ 24.115 Registry number. Upon... be shown where required on labels and markings of containers or cases filled at the wine...
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…
7 CFR 75.48 - Identification number.
Code of Federal Regulations, 2012 CFR
2012-01-01
... AND CERTIFICATION OF QUALITY OF AGRICULTURAL AND VEGETABLE SEEDS Miscellaneous Â§ 75.48 Identification number. The Director may require the use of official identification numbers in connection with seed... Director and shall be attached to, or stamped, printed, or stenciled on the lot of seed certificated...
7 CFR 75.48 - Identification number.
Code of Federal Regulations, 2011 CFR
2011-01-01
... AND CERTIFICATION OF QUALITY OF AGRICULTURAL AND VEGETABLE SEEDS Miscellaneous Â§ 75.48 Identification number. The Director may require the use of official identification numbers in connection with seed... Director and shall be attached to, or stamped, printed, or stenciled on the lot of seed certificated...
7 CFR 75.48 - Identification number.
Code of Federal Regulations, 2014 CFR
2014-01-01
... AND CERTIFICATION OF QUALITY OF AGRICULTURAL AND VEGETABLE SEEDS Miscellaneous Â§ 75.48 Identification number. The Director may require the use of official identification numbers in connection with seed... Director and shall be attached to, or stamped, printed, or stenciled on the lot of seed certificated...
7 CFR 75.48 - Identification number.
Code of Federal Regulations, 2010 CFR
2010-01-01
... AND CERTIFICATION OF QUALITY OF AGRICULTURAL AND VEGETABLE SEEDS Miscellaneous Â§ 75.48 Identification number. The Director may require the use of official identification numbers in connection with seed... Director and shall be attached to, or stamped, printed, or stenciled on the lot of seed certificated...
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 calculusâ€¦
Locating Fractions on a Number Line
ERIC Educational Resources Information Center
Wong, Monica
2013-01-01
Understanding fractions remains problematic for many students. The use of the number line aids in this understanding, but requires students to recognise that a fraction represents the distance from zero to a dot or arrow marked on a number line which is a linear scale. This article continues the discussion from "Identifying Fractions on aâ€¦
Inhibition, Conflict Detection, and Number Conservation
ERIC Educational Resources Information Center
Lubin, AmĂ©lie; Simon, GrĂ©gory; HoudĂ©, 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 conservationâ€¦
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)
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…
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...
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, 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, 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, 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...
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 nationalâ€¦
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 toâ€¦
Number Theory in the Elementary School.
ERIC Educational Resources Information Center
Beougher, Elton E.
The paper presents reasons for teaching topics from number theory to elementary school students: (1) it can help reveal why numbers "act" in a certain way when added, multiplied, etc., (2) it offers drill material in new areas of mathematics, (3) it can develop interest - as mathematical enrichment, (4) it offers opportunities for students toâ€¦
Laboratory Mathematics. Curriculum Booklet 6 - Number Theory.
ERIC Educational Resources Information Center
Rogers, Sandra
This booklet is one of a set of five booklets which comprise the basic curriculum for "Mathematics Laboratories for Disadvantaged Students," a nationally validated Title III ESEA project. This publication provides evaluation materials and student materials related to number theory. Topics included in this booklet are prime and composite numbers,â€¦
A Generalization of the Prime Number Theorem
ERIC Educational Resources Information Center
Bruckman, Paul S.
2008-01-01
In this article, the author begins with the prime number theorem (PNT), and then develops this into a more general theorem, of which many well-known number theoretic results are special cases, including PNT. He arrives at an asymptotic relation that allows the replacement of certain discrete sums involving primes into corresponding differentiableâ€¦
A prime number approach to biological sequencing.
Greer, W; Barrett, A N; Sowden, J M
1985-03-01
Computational sequencing of nucleic acid and amino acid sequences is placing increasing demands on computer resources. The use of prime numbers is explored as a convenient means of improving program speed and reducing storage requirements. It is concluded that the application of the prime number approach leads to significant increases in speed and some reduction in storage requirements. PMID:3840126
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 theâ€¦
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 intoâ€¦
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.
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.
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.
LEAN: laser-etched aqua number
NASA Astrophysics Data System (ADS)
Schell, Karel J.
1998-04-01
A security device on a banknote has to be recognized immediately by the general public and has to enable the general public to establish the genuineness of the banknote. This is the so-called first line of defense. Recently the development of the ability to establish the genuiness has gained momentum and is called 'self authenticating.' Comparing the banknote number with a 'watermark number' can do authenticating. The watermark number is engraved by a laser beam in the paper and is -- as the printed number -- different for each note. Recent progress in the material processing by laser enables the engraving of the individual watermark number for each banknote in line with the production process.
Ramsey Numbers and Adiabatic Quantum Computing
NASA Astrophysics Data System (ADS)
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, nâ‰Ą3, 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 5â‰¤sâ‰¤7. We then discuss the algorithmâ€™s experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class quantum Merlin Arthur.
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
Random numbers spring from alpha decay
Frigerio, N.A.; Sanathanan, L.P.; Morley, M.; Clark, N.A.; Tyler, S.A.
1980-05-01
Congruential random number generators, which are widely used in Monte Carlo simulations, are deficient in that the number they generate are concentrated in a relatively small number of hyperplanes. While this deficiency may not be a limitation in small Monte Carlo studies involving a few variables, it introduces a significant bias in large simulations requiring high resolution. This bias was recognized and assessed during preparations for an accident analysis study of nuclear power plants. This report describes a random number device based on the radioactive decay of alpha particles from a /sup 235/U source in a high-resolution gas proportional counter. The signals were fed to a 4096-channel analyzer and for each channel the frequency of signals registered in a 20,000-microsecond interval was recorded. The parity bits of these frequency counts (0 for an even count and 1 for an odd count) were then assembled in sequence to form 31-bit binary random numbers and transcribed to a magnetic tape. This cycle was repeated as many times as were necessary to create 3 million random numbers. The frequency distribution of counts from the present device conforms to the Brockwell-Moyal distribution, which takes into account the dead time of the counter (both the dead time and decay constant of the underlying Poisson process were estimated). Analysis of the count data and tests of randomness on a sample set of the 31-bit binary numbers indicate that this random number device is a highly reliable source of truly random numbers. Its use is, therefore, recommended in Monte Carlo simulations for which the congruential pseudorandom number generators are found to be inadequate. 6 figures, 5 tables.
Code of Federal Regulations, 2012 CFR
2012-04-01
... registration number and drug listing number. 207.35 Section 207.35 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) DRUGS: GENERAL REGISTRATION OF PRODUCERS OF DRUGS AND... Notification of registrant; drug establishment registration number and drug listing number. (a) FDA...
Code of Federal Regulations, 2011 CFR
2011-04-01
... registration number and drug listing number. 207.35 Section 207.35 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) DRUGS: GENERAL REGISTRATION OF PRODUCERS OF DRUGS AND... Notification of registrant; drug establishment registration number and drug listing number. (a) FDA...
Code of Federal Regulations, 2014 CFR
2014-04-01
... registration number and drug listing number. 207.35 Section 207.35 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) DRUGS: GENERAL REGISTRATION OF PRODUCERS OF DRUGS AND... Notification of registrant; drug establishment registration number and drug listing number. (a) FDA...
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 andâ€¦
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 theâ€¦
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 malleableâ€¦
Estimating shorebird numbers at migration stopover sites
Farmer, A.; Durbian, F.
2006-01-01
We describe a method for estimating the total number of shorebirds that use a migration stopover site during spring and fall migration. We combined weekly shorebird counts with parameter estimates for detection probability, sampled proportion, and length of stay on the Squaw Creek National Wildlife Refuge. Double sampling was used to determine detection probability and estimated values varied among wetland units from a low of 0.07 to a high of 0.82. The sampled proportion of most wetland units was 100% but was lower in some of the larger units. Length of stay (measured for Pectoral [Calidris melanotos] and Least Sandpipers [C. minutilla] combined) averaged 10.0 days in spring and 3.7 days in fall. Spring shorebird numbers were approximately five times greater than fall numbers on the Refuge. Annual shorebird numbers varied among years from an estimated low in 2003 of 15 734 to a high in 2002 of 69 570. Peak daily counts during study years averaged only 12% of estimated spring totals and 4% of fall totals. An estimate of shorebird numbers based on summing weekly counts, not corrected for detection probability or sampled proportion, would have been only 21% (spring) to 31% (fall) of the total number of birds. These results reveal that peak counts and nonadjusted counts can significantly underestimate the number of shorebirds that use migration stopover sites in the midcontinent of North America. ?? The Cooper Ornithological Society 2006.
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.
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.
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.
New technique for number-plate recognition
NASA Astrophysics Data System (ADS)
Guo, Jie; Shi, Peng-Fei
2001-09-01
This paper presents an alternative algorithm for number plate recognition. The algorithm consists of three modules. Respectively, they are number plate location module, character segmentation module and character recognition module. Number plate location module extracts the number plate from the detected car image by analyzing the color and the texture properties. Different from most license plate location methods, the algorithm has fewer limits to the car size, the car position in the image and the image background. Character segmentation module applies connected region algorithm both to eliminate noise points and to segment characters. Touching characters and broken characters can be processed correctly. Character recognition module recognizes characters with HHIC (Hierarchical Hybrid Integrated Classifier). The system has been tested with 100 images obtained from crossroad and parking lot, etc, where the cars have different size, position, background and illumination. Successful recognition rate is about 92%. The average processing time is 1.2 second.
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
Networking of large numbers of satellites
NASA Astrophysics Data System (ADS)
Brayer, Kenneth; Collins, William E.; Crane, Peter C.
Networking a large number of satellites for the passage of command and traffic control is examined. The characteristics of the 16-node double loop model utilized in this study are discussed. Equations for calculating the delay for a specific pair of nodes and the throughput of the ring are presented. In order to calculate the hop length, it is necessary to know the number of satellites within the line-of-sight of a given satellite. The performance of a number of satellites is evaluated. It is noted that, using the double ring routing of short forward hops and long backward hops, it is possible to traverse a ring by sending a message on a small fraction of the links in that ring. Networking large numbers of satellites to deliver traffic is applicable to SDI.
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.
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)
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
Decay of turbulence at high reynolds numbers.
Sinhuber, Michael; Bodenschatz, Eberhard; Bewley, Gregory P
2015-01-23
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 (10^{4}
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)
Copy Number Variation across European Populations
Chen, Wanting; Hayward, Caroline; Wright, Alan F.; Hicks, Andrew A.; Vitart, Veronique; Knott, Sara; Wild, Sarah H.; Pramstaller, Peter P.; Wilson, James F.; Rudan, Igor; Porteous, David J.
2011-01-01
Genome analysis provides a powerful approach to test for evidence of genetic variation within and between geographical regions and local populations. Copy number variants which comprise insertions, deletions and duplications of genomic sequence provide one such convenient and informative source. Here, we investigate copy number variants from genome wide scans of single nucleotide polymorphisms in three European population isolates, the island of Vis in Croatia, the islands of Orkney in Scotland and the South Tyrol in Italy. We show that whereas the overall copy number variant frequencies are similar between populations, their distribution is highly specific to the population of origin, a finding which is supported by evidence for increased kinship correlation for specific copy number variants within populations. PMID:21829696
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.
The high Reynolds number cryogenic wind tunnel.
NASA Technical Reports Server (NTRS)
Goodyer, M. J.; Kilgore, R. A.
1972-01-01
Theoretical considerations indicate that cooling the wind-tunnel test gas to cryogenic temperatures will provide a large increase in test Reynolds number with no increase in dynamic pressure while reducing the tunnel drive-power requirements. Studies have been made to determine the expected variations of Reynolds number and other parameters over wide ranges of Mach number, pressure, and temperature with due regard to avoiding liquefaction and adverse real-gas effects. Practical operational procedures have been developed in a low-speed prototype cryogenic wind tunnel. Aerodynamic experiments in the facility have demonstrated the theoretically predicted variations in Reynolds number and drive power. Force and moment measurements on a wing model mounted on a water-jacketed strain-gage sting balance have demonstrated the feasibility of operation of such balances in a cryogenic environment.
Bethe's quantum numbers and rigged configurations
NASA Astrophysics Data System (ADS)
Kirillov, Anatol N.; Sakamoto, Reiho
2016-04-01
We propose a method to determine the quantum numbers, which we call the rigged configurations, for the solutions to the Bethe ansatz equations for the spin-1/2 isotropic Heisenberg model under the periodic boundary condition. Our method is based on the observation that the sums of Bethe's quantum numbers within each string behave particularly nicely. We confirm our procedure for all solutions for length 12 chain (totally 923 solutions).
Predicting apparent Sherwood numbers for fluidized beds
Groenewold, H.; Tsotsas, E.
1999-09-01
Mass transfer data of bubbling fluidized beds have been reevaluated with a new model which is completely predictive. The model is based on a two-phase approach with active bypass, formally plug flow for the suspension gas and a consideration of backmixing in the main kinetic coefficient, i.e. in the apparent particle-to-fluid Sherwood number. A good agreement with experimental results of various authors with a broad range of Reynolds numbers and particle diameters is demonstrated.
Large Number Discrimination in Newborn Fish
Piffer, Laura; Miletto Petrazzini, Maria Elena; Agrillo, Christian
2013-01-01
Quantitative abilities have been reported in a wide range of species, including fish. Recent studies have shown that adult guppies (Poecilia reticulata) can spontaneously select the larger number of conspecifics. In particular the evidence collected in literature suggest the existence of two distinct systems of number representation: a precise system up to 4 units, and an approximate system for larger numbers. Spontaneous numerical abilities, however, seem to be limited to 4 units at birth and it is currently unclear whether or not the large number system is absent during the first days of life. In the present study, we investigated whether newborn guppies can be trained to discriminate between large quantities. Subjects were required to discriminate between groups of dots with a 0.50 ratio (e.g., 7 vs. 14) in order to obtain a food reward. To dissociate the roles of number and continuous quantities that co-vary with numerical information (such as cumulative surface area, space and density), three different experiments were set up: in Exp. 1 number and continuous quantities were simultaneously available. In Exp. 2 we controlled for continuous quantities and only numerical information was available; in Exp. 3 numerical information was made irrelevant and only continuous quantities were available. Subjects successfully solved the tasks in Exp. 1 and 2, providing the first evidence of large number discrimination in newborn fish. No discrimination was found in experiment 3, meaning that number acuity is better than spatial acuity. A comparison with the onset of numerical abilities observed in shoal-choice tests suggests that training procedures can promote the development of numerical abilities in guppies. PMID:23626824
Determining Ramsey numbers on a quantum computer
NASA Astrophysics Data System (ADS)
Wang, Hefeng
2016-03-01
We present a quantum algorithm for computing the Ramsey numbers whose computational complexity grows superexponentially with the number of vertices of a graph on a classical computer. The problem is mapped to a decision problem on a quantum computer, and a probe qubit is coupled to a register that represents the problem and detects the energy levels of the problem Hamiltonian. The decision problem is solved by detecting the decay dynamics of the probe qubit.
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.
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 HĂĽbner, [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
Chromosome number evolution in skippers (Lepidoptera, Hesperiidae).
Lukhtanov, Vladimir A
2014-01-01
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 HĂĽbner, [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
Mechanisms of Chromosome Number Evolution in Yeast
Gordon, Jonathan L.; Byrne, Kevin P.; Wolfe, Kenneth H.
2011-01-01
The whole-genome duplication (WGD) that occurred during yeast evolution changed the basal number of chromosomes from 8 to 16. However, the number of chromosomes in post-WGD species now ranges between 10 and 16, and the number in non-WGD species (Zygosaccharomyces, Kluyveromyces, Lachancea, and Ashbya) ranges between 6 and 8. To study the mechanism by which chromosome number changes, we traced the ancestry of centromeres and telomeres in each species. We observe only two mechanisms by which the number of chromosomes has decreased, as indicated by the loss of a centromere. The most frequent mechanism, seen 8 times, is telomere-to-telomere fusion between two chromosomes with the concomitant death of one centromere. The other mechanism, seen once, involves the breakage of a chromosome at its centromere, followed by the fusion of the two arms to the telomeres of two other chromosomes. The only mechanism by which chromosome number has increased in these species is WGD. Translocations and inversions have cycled telomere locations, internalizing some previously telomeric genes and creating novel telomeric locations. Comparison of centromere structures shows that the length of the CDEII region is variable between species but uniform within species. We trace the complete rearrangement history of the Lachancea kluyveri genome since its common ancestor with Saccharomyces and propose that its exceptionally low level of rearrangement is a consequence of the loss of the non-homologous end joining (NHEJ) DNA repair pathway in this species. PMID:21811419
Complex architecture of primes and natural numbers.
GarcĂa-PĂ©rez, Guillermo; Serrano, M Ăngeles; BoguĂ±Ăˇ, MariĂˇn
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 CramĂ©r's conjecture about the statistics of gaps between consecutive primes that seems closer to reality than the original CramĂ©r'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. PMID:25215780
Complex architecture of primes and natural numbers
NASA Astrophysics Data System (ADS)
GarcĂa-PĂ©rez, Guillermo; Serrano, M. Ăngeles; BoguĂ±Ăˇ, MariĂˇn
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 CramĂ©r's conjecture about the statistics of gaps between consecutive primes that seems closer to reality than the original CramĂ©r'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.
Riemann equation for prime number diffusion.
Chen, Wen; Liang, Yingjie
2015-05-01
This study makes the first attempt to propose the Riemann diffusion equation to describe in a manner of partial differential equation and interpret in physics of diffusion the classical Riemann method for prime number distribution. The analytical solution of this equation is the well-known Riemann representation. The diffusion coefficient is dependent on natural number, a kind of position-dependent diffusivity diffusion. We find that the diffusion coefficient of the Riemann diffusion equation is nearly a straight line having a slope 0.99734 in the double-logarithmic axis. Consequently, an approximate solution of the Riemann diffusion equation is obtained, which agrees well with the Riemann representation in predicting the prime number distribution. Moreover, we interpret the scale-free property of prime number distribution via a power law function with 1.0169 the scale-free exponent in respect to logarithmic transform of the natural number, and then the fractal characteristic of prime number distribution is disclosed. PMID:26026319
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 â€śFermi problemsâ€ť 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
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.
Mining for Numbers. A Heuristic Approach to Some Prime Number Work
ERIC Educational Resources Information Center
Tapson, Frank
1973-01-01
Whole numbers written in spiral or triangular patterns with spaces occupied by prime numbers blocked in produces interesting visual patterns. Described is a game based on these patterns that may be played at many different levels. (JP)
Federal Register 2010, 2011, 2012, 2013, 2014
2011-12-22
... COMMISSION 47 CFR Part 52 Local Number Portability Porting Interval and Validation Requirements; Telephone Number Portability AGENCY: Federal Communications Commission. ACTION: Proposed rule; comments requested... Documents in Rulemaking Proceedings, 63 FR 24121 (1998). Electronic Filers: Comments may be...
Unpredictability and the transmission of numbers
NASA Astrophysics Data System (ADS)
Myers, John M.; Madjid, F. Hadi
2015-08-01
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.
Variable copy number DNA sequences in rice.
Kikuchi, S; Takaiwa, F; Oono, K
1987-12-01
We have cloned two types of variable copy number DNA sequences from the rice embryo genome. One of these sequences, which was cloned in pRB301, was amplified about 50-fold during callus formation and diminished in copy number to the embryonic level during regeneration. The other clone, named pRB401, showed the reciprocal pattern. The copy numbers of both sequences were changed even in the early developmental stage and eliminated from nuclear DNA along with growth of the plant. Sequencing analysis of the pRB301 insert revealed some open reading frames and direct repeat structures, but corresponding sequences were not identified in the EMBL and LASL DNA databases. Sequencing of the nuclear genomic fragment cloned in pRB401 revealed the presence of the 3'rps12-rps7 region of rice chloroplast DNA. Our observations suggest that during callus formation (dedifferentiation), regeneration and the growth process the copy numbers of some DNA sequences are variable and that nuclear integrated chloroplast DNA acts as a variable copy number sequence in the rice genome. Based on data showing a common sequence in mitochondria and chloroplast DNA of maize (Stern and Lonsdale 1982) and that the rps12 gene of tobacco chloroplast DNA is a divided gene (Torazawa et al. 1986), it is suggested that the sequence on the inverted repeat structure of chloroplast DNA may have the character of a movable genetic element. PMID:3481021
True random numbers from amplified quantum vacuum.
Jofre, M; Curty, M; Steinlechner, F; Anzolin, G; Torres, J P; Mitchell, M W; Pruneri, V
2011-10-10
Random numbers are essential for applications ranging from secure communications to numerical simulation and quantitative finance. Algorithms can rapidly produce pseudo-random outcomes, series of numbers that mimic most properties of true random numbers while quantum random number generators (QRNGs) exploit intrinsic quantum randomness to produce true random numbers. Single-photon QRNGs are conceptually simple but produce few random bits per detection. In contrast, vacuum fluctuations are a vast resource for QRNGs: they are broad-band and thus can encode many random bits per second. Direct recording of vacuum fluctuations is possible, but requires shot-noise-limited detectors, at the cost of bandwidth. We demonstrate efficient conversion of vacuum fluctuations to true random bits using optical amplification of vacuum and interferometry. Using commercially-available optical components we demonstrate a QRNG at a bit rate of 1.11 Gbps. The proposed scheme has the potential to be extended to 10 Gbps and even up to 100 Gbps by taking advantage of high speed modulation sources and detectors for optical fiber telecommunication devices. PMID:21997077
Nonlinear dynamos at infinite magnetic Prandtl number.
Alexakis, Alexandros
2011-03-01
The dynamo instability is investigated in the limit of infinite magnetic Prandtl number. In this limit the fluid is assumed to be very viscous so that the inertial terms can be neglected and the flow is enslaved to the forcing. The forcing consist of an external forcing function that drives the dynamo flow and the resulting Lorentz force caused by the back reaction of the magnetic field. The flows under investigation are the Archontis flow and the ABC flow forced at two different scales. The investigation covers roughly 3 orders of magnitude of the magnetic Reynolds number above onset. All flows show a weak increase of the averaged magnetic energy as the magnetic Reynolds number is increased. Most of the magnetic energy is concentrated in flat elongated structures that produce a Lorentz force with small solenoidal projection so that the resulting magnetic field configuration is almost force free. Although the examined system has zero kinetic Reynolds number at sufficiently large magnetic Reynolds number the structures are unstable to small scale fluctuations that result in a chaotic temporal behavior. PMID:21517581
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.
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, andâ€¦
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:…
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:â€¦
Numbers, Thoughts, and Things: The Ontology of Numbers for Children and Adults.
ERIC Educational Resources Information Center
Sophian, Catherine; Wood, Amy
1996-01-01
Adapted Keil's predictability method to examine adults' and preschoolers' conceptions of numbers, focusing on the ontological distinction between numbers and sets of objects. Found that children, like adults, attribute spatial-arrangement properties to collections much more than to numbers, although both are considered to have quantitativeâ€¦
Federal Register 2010, 2011, 2012, 2013, 2014
2011-09-30
... COMMISSION 47 CFR Part 52 Local Number Portability Porting Interval and Validation Requirements; Telephone Number Portability AGENCY: Federal Communications Commission. ACTION: Proposed rule; comments requested... submitted a report on local number portability (LNP) Best Practice 67. The Report notes that since...
Energy Dependence of the Hounsfield Number
Brooks, Rodney A.
1977-01-01
A standard definition is proposed for the Hounsfield number. Any CT number can be converted to the Hounsfield scale after performing a simple calibration using air and water. The energy dependence of the Hounsfield number H is given by the expression H = (Hc + Hp Q)/(1 + Q), where Hc and Hp are the Compton and photoelectric coefficients of the material being measured, expressed in Hounsfield units, and Q is the â€śquality factorâ€ť of the scanner. Q can be measured by performing a scan of a single calibrating material, such as a KI solution. By applying this analysis to dual-energy scans, the Compton and photoelectric coefficients of an unknown substance may easily be obtained. This can lead to a limited degree of chemical identification.
High Reynolds Number Thermal Stability Experiments
NASA Technical Reports Server (NTRS)
Emens, Jessica M.; Brown, Sarah P.; Frederick Robert A., Jr.; Wood, A. John
2004-01-01
This work represents preliminary thermal stability results for liquid hydrocarbon fuels. High Reynolds Number Thermal Stability experiments with Jet A and RP-1 resulted in a quantitative measurement of the thermal stability. Each fuel flowed through a heated capillary tube that held the outlet temperature at 290 C. An optical pyrometer measured the surface temperature of the tube at 12 locations as a function of time. The High Reynolds Number Thermal Stability number was then determined using standards published by the American Society for Testing and Materials. The results for Jet A showed lower thermal stability than similar tests conducted at another facility. The RP-1 results are the first reported using this technique. Because the temperature rise on the capillary tube during testing for the RP-1 fuels was not significant, a new standard for the testing conditions should be developed for these types of fuels.
Electron heating in superhigh Mach number shocks
NASA Technical Reports Server (NTRS)
Papadopoulos, K.
1988-01-01
Fluid and MHD models, as well as direct extrapolation of the earth's bow shock measurements in the high Mach number (HMN) range to the superhigh Mach number (SHMN) range predict that the downstream electron pressure is only a negligible fraction of the Rankine-Hugoniot downstream pressure. Following Alfven, plasma physics experimental-theoretical data combined with magnetospheric observations were used to probe the physics of the SHMN shocks. It is shown that inclusion of proper plasma physics considerations in the interaction of the reflected and transmitted ions and the electrons at the 'foot' of the shock leads to the surprising result that electron heating can dominate in the SHNM range. A stationary model of the shock structure is derived and shown to be the result of extrapolation of the high Mach number shock physics wiht incorporation of collective interactions at the foot.
Congruent numbers with many prime factors
Tian, Ye
2012-01-01
Mohammed Ben Alhocain, in an Arab manuscript of the 10th century, stated that the principal object of the theory of rational right triangles is to find a square that when increased or diminished by a certain number, m becomes a square [Dickson LE (1971) History of the Theory of Numbers (Chelsea, New York), Vol 2, Chap 16]. In modern language, this object is to find a rational point of infinite order on the elliptic curve . Heegner constructed such rational points in the case that m are primes congruent to 5,7 modulo 8 or twice primes congruent to 3 modulo 8 [Monsky P (1990) Math Z 204:45â€“68]. We extend Heegner's result to integers m with many prime divisors and give a sketch in this report. The full details of all the proofs will be given in ref. 1 [Tian Y (2012) Congruent Numbers and Heegner Points, arXiv:1210.8231]. PMID:23213259
National transonic facility Mach number system
NASA Technical Reports Server (NTRS)
Kern, F. A.; Knight, C. W.; Zasimowich, R. F.
1985-01-01
The Mach number system for the Langley Research Center's National Transonic Facility was designed to measure pressures to determine Mach number to within + or - 0.002. Nine calibration laboratory type fused quartz gages, four different range gages for the total pressure measurement, and five different range gages for the static pressure measurement were used to satisfy the accuracy requirement over the 103,000-890,000 Pa total pressure range of the tunnel. The system which has been in operation for over 1 year is controlled by a programmable data process controller to select, through the operation of solenoid valves, the proper range fused quartz gage to maximize the measurement accuracy. The pressure gage's analog outputs are digitized by the process controller and transmitted to the main computer for Mach number computation. An automatic two-point on-line calibration of the nine quartz gages is provided using a high accuracy mercury manometer.
A new methodology for detecting source number
NASA Astrophysics Data System (ADS)
Lei, Tianhu; Roberts, Timothy P. L.
2011-03-01
Current methods for detecting source number in magnetic source image (MSI) have some shortcomings: i) they are somewhat subjective, ii) various MSIs employ different indexes, and iii) the number of the potential sources in MSI via Beamforming may be underestimated. The new approach extracts a principal component from each trial which serves as a (one) representative virtual channel for that trial. Principal components from all trials are combined to form a (one) synthesized trial. The information criterion is applied to this synthesized trial to select an optimal estimate of the source number. PCA reduces noise and captures the greatest variability in each trial, the synthesized trial reduces data fluctuations among trials and also reduces the dimensions of the covariance matrix. The approach is entirely data-driven and is suitable for detecting seizures and interictal spikes in epilepsy patients.
Nusselt number scaling in tokamak plasma turbulence
Takeda, K.; Benkadda, S.; Hamaguchi, S.; Wakatani, M.
2005-05-15
Anomalous heat transport caused by ion temperature gradient (ITG) driven turbulence in tokamak plasmas is evaluated from numerical simulations of the two-dimensional (2D) partial-differential equations of the ITG model and of a reduced 1D version derived from a quasilinear approximation. In the strongly turbulent state, intermittent bursts of thermal transport are observed in both cases. In the strongly turbulent regime, the reduced model as well as the direct numerical simulation show that the Nusselt number Nu (normalized heat flux) scales with the normalized ion pressure gradient K{sub i} as Nu{proportional_to}K{sub i}{sup 1/3}. Since the Rayleigh number for ITG turbulence is proportional to K{sub i}, the Nusselt number scaling for ITG turbulence is thus similar to the classical thermal transport scaling for Rayleigh-Benard convections in neutral fluids.
Segmental copy number variation shapes tissue transcriptomes.
Henrichsen, Charlotte N; Vinckenbosch, Nicolas; Zöllner, Sebastian; Chaignat, Evelyne; Pradervand, Sylvain; Schütz, Frédéric; Ruedi, Manuel; Kaessmann, Henrik; Reymond, Alexandre
2009-04-01
Copy number variation (CNV) is a key source of genetic diversity, but a comprehensive understanding of its phenotypic effect is only beginning to emerge. We have generated a CNV map in wild mice and classical inbred strains. Genome-wide expression data from six major organs show not only that expression of genes within CNVs tend to correlate with copy number changes, but also that CNVs influence the expression of genes in their vicinity, an effect that extends up to half a megabase. Genes within CNVs show lower expression and more specific spatial expression patterns than genes mapping elsewhere. Our analyses reveal differential constraint on copy number changes of genes expressed in different tissues. Dosage alterations of brain-expressed genes are less frequent than those of other genes and are buffered by tighter transcriptional regulation. Our study provides initial evidence that CNVs shape tissue transcriptomes on a global scale. PMID:19270705
Boundary induced nonlinearities at small Reynolds numbers
NASA Astrophysics Data System (ADS)
Sbragaglia, M.; Sugiyama, K.
2007-04-01
We investigate the importance of boundary slip at finite Reynolds numbers for mixed boundary conditions. Nonlinear effects are induced by the non-homogeneity of the boundary condition and change the symmetry properties of the flow with an overall mean flow reduction. To explain the observed drag modification, exact reciprocal relations in the presence of heterogeneous boundary conditions are derived. The small-Reynolds-number limit predicts a reduction of the mean flow rate from the creeping flow to be proportional to the second power of the Reynolds number. To further support our theoretical analysis, numerical simulations with the lattice Boltzmann method (LBM) and finite difference method (FDM) are performed and reveal a pronounced numerical efficiency of LBM with respect to FDM.
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.
PHD filtering with localised target number variance
NASA Astrophysics Data System (ADS)
Delande, Emmanuel; Houssineau, JĂ©rĂ©mie; 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.
Number counts and dynamical vacuum cosmologies
NASA Astrophysics Data System (ADS)
Devi, N. Chandrachani; Borges, H. A.; Carneiro, S.; Alcaniz, J. S.
2015-03-01
We study non-linear structure formation in an interacting model of the dark sector of the Universe in which the dark energy density decays linearly with the Hubble parameter, ĎÎ› âť H, leading to a constant-rate creation of cold dark matter. We derive all relevant expressions to calculate the mass function and the cluster number density using the Sheth-Torman formalism and show that the effect of the interaction process is to increase the number of bound structures of large masses (M â‰ł 1014 MâŠ™ h-1) when compared to the standard Î› cold dark matter model. Since these models are not reducible to each other, this number counts signature can in principle be tested in future surveys.
Prime number variant of concealed trigeminy.
Medeiros, C M; Medeiros, N P; de Nonohay, N C; Rodrigues, R
1985-10-01
A 53-year-old man with myocardial infarction was found to have frequent premature ventricular beats. The predominant pattern was classical concealed trigeminy; i.e., the number of conducted sinus beats, S, between extrasystoles satisfied the equation S = 3n + 2, where "n" is zero or any positive integer. Two other transient patterns also occurred. The first one was characterized by exceptional values of S, which satisfied the equation S = 3n + 3. In the second transient pattern, all values of S fitted the classical equation, but there were singularly absent values; i.e., the "n" in the equation was exclusively an odd number, giving rise to only prime numbers of interectopic conducted sinus beats. It is proposed in this last form that there are two sites of fixed block proximal to a variable distal block in a re-entry loop responsible for the ventricular extrasystoles. PMID:2415650
Autocorrelation peaks in congruential pseudorandom number generators
NASA Technical Reports Server (NTRS)
Neuman, F.; Merrick, R. B.
1976-01-01
The complete correlation structure of several congruential pseudorandom number generators (PRNG) of the same type and small cycle length was studied to deal with the problem of congruential PRNG almost repeating themselves at intervals smaller than their cycle lengths, during simulation of bandpass filtered normal random noise. Maximum period multiplicative and mixed congruential generators were studied, with inferences drawn from examination of several tractable members of a class of random number generators, and moduli from 2 to the 5th power to 2 to the 9th power. High correlation is shown to exist in mixed and multiplicative congruential random number generators and prime moduli Lehmer generators for shifts a fraction of their cycle length. The random noise sequences in question are required when simulating electrical noise, air turbulence, or time variation of wind parameters.
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.
Reynolds number effects on turbulent pipe flow
NASA Astrophysics Data System (ADS)
Hultmark, Marcus
The scaling of the mean velocities in turbulent wall-bounded flows is fairly well understood, but the scaling of the turbulence is not. This lack of understanding, particularly at high Reynolds number, limits our ability to predict important quantities such as drag on a vehicle, heat transfer from a hot surface or the melting of the ice caps. What makes the study of turbulence very complicated (numerically and experimentally) is that it is characterized by a large range of scales and this range increases with Reynolds number. At high Reynolds number, numerical investigations become extraordinarily difficult, and all previous experiments have been compromised by inadequate instrumentation and a lack of high quality facilities. In this thesis I report a set of measurements that give new insight into the behavior of pipe flow turbulence at high Reynolds number. To obtain reliable and accurate data, the limitations in current measurement techniques were investigated and quantified. To reduce the effects of these limitations, we developed a novel nano-scale velocity sensor that can resolve scales an order of magnitude smaller than conventional sensors. This, combined with facilities that can produce extreme Reynolds numbers, allows us to study flows never before possible. The results show that the scaling of the turbulence, in a pipe, is much more similar to the scaling of the mean velocities than previously believed. This behavior only becomes evident at high Reynolds numbers, much higher than previous experiments could attain. The results also reveal fundamental differences between the scaling of the turbulence in pipes and boundary layers, two canonical flows previously believed to behave similarly.
Searches for violation of muon number conservation
Redwine, R.P.
1981-01-01
The question of violation of muon number conservation is one which has occupied considerable attention and resources in recent years. The first generation of experiments at the medium energy accelerators has now been completed and the next generation of experiments is ready to begin. The history of muon number conservation is reviewed, including the reasons for the present belief that the conservation law may not be exact. The experiments that have been completed in the last few years are discussed. The new experiments that are being mounted and planned at several laboratories are discussed, and the relationship of these types of experiments to other studies, such as searches for neutrino oscillations, are considered.
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.
Type number and rigidity of fibred surfaces
Markov, P E
2001-02-28
Infinitesimal l-th order bendings, 1{<=}l{<=}{infinity}, of higher-dimensional surfaces are considered in higher-dimensional flat spaces (for l={infinity} an infinitesimal bending is assumed to be an analytic bending). In terms of the Allendoerfer type number, criteria are established for the (r,l)-rigidity (in the terminology of Sabitov) of such surfaces. In particular, an (r,l)-infinitesimal analogue is proved of the classical theorem of Allendoerfer on the unbendability of surfaces with type number {>=}3 and the class of (r,l)-rigid fibred surfaces is distinguished.
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.
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.
Thermocapillary bubble migration for large Marangoni Numbers
NASA Technical Reports Server (NTRS)
Balasubramaniam, R.
1987-01-01
The thermocapillary motion of spherical bubbles present in an unbounded liquid with a linear temperature distribution, when the Reynolds number and the Marangoni number are large is analyzed. Previous calculations of the terminal velocity performed for this parametric range did not take into complete consideration the thermal boundary layer present near the surface of the bubble. A scaling analysis is presented for this problem. The thermal boundary layer is analyzed by an integral method. The resulting terminal velocity is lower than the one previously calculated, though it is of the same order of magnitude.
Parametric number covariance in quantum chaotic spectra
NASA Astrophysics Data System (ADS)
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.
Nielsen, Rasmus; Tarpy, David R; Reeve, H Kern
2003-11-01
Estimating paternity and genetic relatedness is central to many empirical and theoretical studies of social insects. The two important measures of a queen's mating number are her actual number of mates and her effective number of mates. Estimating the effective number of mates is mathematically identical to the problem of estimating the effective number of alleles in population genetics, a common measure of genetic variability introduced by Kimura & Crow (1964). We derive a new bias-corrected estimator of effective number of types (mates or alleles) and compare this new method to previous methods for estimating true and effective numbers of types using Monte Carlo simulations. Our simulation results suggest that the examined estimators of the true number of types have very similar statistical properties, whereas the estimators of effective number of types have quite different statistical properties. Moreover, our new proposed estimator of effective number of types is approximately unbiased, and has considerably lower variance than the original estimator. Our new method will help researchers more accurately estimate intracolony genetic relatedness of social insects, which is an important measure in understanding their ecology and social behaviour. It should also be of use in population genetic studies in which the effective number of alleles is of interest. PMID:14629394
Hyde, Daniel C; Spelke, Elizabeth S
2009-06-01
Behavioral and brain imaging research indicates that human infants, humans adults, and many nonhuman animals represent large nonsymbolic numbers approximately, discriminating between sets with a ratio limit on accuracy. Some behavioral evidence, especially with human infants, suggests that these representations differ from representations of small numbers of objects. To investigate neural signatures of this distinction, event-related potentials were recorded as adult humans passively viewed the sequential presentation of dot arrays in an adaptation paradigm. In two studies, subjects viewed successive arrays of a single number of dots interspersed with test arrays presenting the same or a different number; numerical range (small numerical quantities 1-3 vs. large numerical quantities 8-24) and ratio difference varied across blocks as continuous variables were controlled. An early-evoked component (N1), observed over widespread posterior scalp locations, was modulated by absolute number with small, but not large, number arrays. In contrast, a later component (P2p), observed over the same scalp locations, was modulated by the ratio difference between arrays for large, but not small, numbers. Despite many years of experience with symbolic systems that apply equally to all numbers, adults spontaneously process small and large numbers differently. They appear to treat small-number arrays as individual objects to be tracked through space and time, and large-number arrays as cardinal values to be compared and manipulated. PMID:18752403
Number word use in toddlerhood is associated with number recall performance at seven years of age.
Libertus, Melissa E; Marschik, Peter B; Einspieler, Christa
2014-01-01
Previous studies have shown that verbal working memory and vocabulary acquisition are linked in early childhood. However, it is unclear whether acquisition of a narrow range of words during toddlerhood may be particularly related to recall of the same words later in life. Here we asked whether vocabulary acquisition of number words, location and quantifier terms over the first three years of life are associated with verbal and visuospatial working memory at seven years. Our results demonstrate that children who produced more number words between 20-26 months and started to produce the number words 1-10 earlier showed greater number recall at 7 years of age. This link was specific to numbers and neither extended to quantifier and location terms nor verbal and visuospatial working memory performance with other stimuli. These findings suggest a category-specific link between the mental lexicon of number words and working memory for numbers at an early age. PMID:24892835
Effective number of subjects and number of raters for inter-rater reliability studies.
Saito, Yuki; Sozu, Takashi; Hamada, Chikuma; Yoshimura, Isao
2006-05-15
A reliability study in which multiple raters evaluate multiple subjects was assumed in order to confirm the inter-rater reliability of rating scales. The two-way ANOVA model defining subjects and raters as random effects was applied, and the combination of the number of subjects and the number of raters that minimizes variance of the intraclass correlation coefficient (ICC) with a fixed total number of ratings (number of subjects x number of raters) was studied. The results revealed that the optimal combination depends on the relative ratio (between-rater variance/error variance), and that large number of raters brings the high precision of estimation of the ICC when the relative ratio was greater. It was concluded that when information concerning the relative ratio is unreliable, the use of identical numbers of raters and subjects minimizes variance when the relative ratio is substantially large and variance is maximized, providing a good study design from the viewpoint of 'maximin'. PMID:16143966
Number Concepts without Number Lines in an Indigenous Group of Papua New Guinea
NĂşĂ±ez, Rafael; Cooperrider, Kensy; Wassmann, JĂĽrg
2012-01-01
Background The generic concept of number line, which maps numbers to unidimensional space, is a fundamental concept in mathematics, but its cognitive origins are uncertain. Two defining criteria of the number line are that (i) there is a mapping of each individual number (or numerosity) under consideration onto a specific location on the line, and (ii) that the mapping defines a unidimensional space representing numbers with a metric â€” a distance function. It has been proposed that the number line is based on a spontaneous universal human intuition, rooted directly in brain evolution, that maps number magnitude to linear space with a metric. To date, no culture lacking this intuition has been documented. Methodology/Principal Findings By means of a number line task, we investigated the universality proposal with the Yupno of Papua New Guinea. Unschooled adults did exhibit a number-to-space mapping (criterion i) but, strikingly, despite having precise cardinal number concepts, they located numbers only on the endpoints, thus failing to use the extent of the line. The produced mapping was bi-categorical and metric-free, in violation of criterion ii. In contrast, Yupnos with scholastic experience used the extent of the segment according to known standards, but they did so not as evenly as western controls, exhibiting a bias towards the endpoints. Conclusions/Significance Results suggest that cardinal number concepts can exist independently from number line representations. They also suggest that the number line mapping, although ubiquitous in the modern world, is not universally spontaneous, but rather seems to be learned through â€” and continually reinforced by â€” specific cultural practices. PMID:22558193
Shell corrections, magic numbers, and mean field
Denisov, V. Yu.
2007-02-15
It is shown that the positions of deep local minima of shell corrections associated with magic numbers in the region of superheavy nuclei depend on the parameters of the central and spin-orbit mean-field potentials. The accuracy of nuclear-mass predictions made within various models for superheavy nuclei is analyzed.
Partial Coordination Numbers in Binary Metallic Glasses
NASA Astrophysics Data System (ADS)
Miracle, Daniel B.; Laws, Kevin; Senkov, Oleg N.; Wilks, Garth B.
2012-08-01
A critical analysis of measured partial coordination numbers for binary metallic glasses as a function of composition shows a large scatter of ±1.5 but clear trends. The current work uses two topological models to predict the influence of relative atomic size and concentration on partial coordination numbers. The equations for partial coordination numbers derived from these two models can reproduce measured data within experimental scatter, suggesting that chemical effects on local structure, although present, may be relatively small. Insights gained from these models show that structural site-filling rules are different for glasses with solute atoms that are smaller than solvent atoms and for glasses where solute atoms are larger than solvent atoms. Specifically, solutes may occupy both ? and ? intercluster sites when the solute-to-solvent radius ratio R is less than 1.26, but only ? sites can be occupied by solutes when R > 1.26. This distinction gives a simple topological explanation for the observed preference for binary metallic glasses with solutes smaller than solvent atoms. In addition to structure-specific equations, simplified phenomenological equations for partial coordination numbers are given as a convenience.
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.
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.
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 cableâ€¦
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 ofâ€¦
Phylogenetic diversity measures based on Hill numbers
Chao, Anne; Chiu, Chun-Huo; Jost, Lou
2010-01-01
We propose a parametric class of phylogenetic diversity (PD) measures that are sensitive to both species abundance and species taxonomic or phylogenetic distances. This work extends the conventional parametric species-neutral approach (based on â€effective number of speciesâ€™ or Hill numbers) to take into account species relatedness, and also generalizes the traditional phylogenetic approach (based on â€total phylogenetic lengthâ€™) to incorporate species abundances. The proposed measure quantifies â€the mean effective number of speciesâ€™ over any time interval of interest, or the â€effective number of maximally distinct lineagesâ€™ over that time interval. The product of the measure and the interval length quantifies the â€branch diversityâ€™ of the phylogenetic tree during that interval. The new measures generalize and unify many existing measures and lead to a natural definition of taxonomic diversity as a special case. The replication principle (or doubling property), an important requirement for species-neutral diversity, is generalized to PD. The widely used Rao's quadratic entropy and the phylogenetic entropy do not satisfy this essential property, but a simple transformation converts each to our measures, which do satisfy the property. The proposed approach is applied to forest data for interpreting the effects of thinning. PMID:20980309
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 15â€¦
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 ORGANIZATION AND TERMINOLOGY; MANDATORY MEAT AND POULTRY PRODUCTS INSPECTION AND VOLUNTARY INSPECTION AND CERTIFICATION CERTIFIED PRODUCTS FOR DOGS,...
9 CFR 355.8 - Official number.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 9 Animals and Animal Products 2 2012-01-01 2012-01-01 false Official number. 355.8 Section 355.8 Animals and Animal Products FOOD SAFETY AND INSPECTION SERVICE, DEPARTMENT OF AGRICULTURE AGENCY ORGANIZATION AND TERMINOLOGY; MANDATORY MEAT AND POULTRY PRODUCTS INSPECTION AND VOLUNTARY INSPECTION AND CERTIFICATION CERTIFIED PRODUCTS FOR DOGS,...
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 ORGANIZATION AND TERMINOLOGY; MANDATORY MEAT AND POULTRY PRODUCTS INSPECTION AND VOLUNTARY INSPECTION AND CERTIFICATION CERTIFIED PRODUCTS FOR DOGS,...
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 ORGANIZATION AND TERMINOLOGY; MANDATORY MEAT AND POULTRY PRODUCTS INSPECTION AND VOLUNTARY INSPECTION AND CERTIFICATION CERTIFIED PRODUCTS FOR DOGS,...
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 ORGANIZATION AND TERMINOLOGY; MANDATORY MEAT AND POULTRY PRODUCTS INSPECTION AND VOLUNTARY INSPECTION AND CERTIFICATION CERTIFIED PRODUCTS FOR DOGS,...
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," seeâ€¦
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 countâ€¦
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 andâ€¦
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…
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 thanâ€¦
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. Claimsâ€¦
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 goodâ€¦
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 teachingâ€¦
Gene copy number variation in schizophrenia.
Sutrala, Smitha R; Goossens, Dirk; Williams, Nigel M; Heyrman, Lien; Adolfsson, Rolf; Norton, Nadine; Buckland, Paul R; Del-Favero, Jurgen
2007-11-01
The possibility that gene copy number variations play a role in the development of complex disorders is a topic of considerable interest. Recent reports have highlighted the large number of such variations that exist and that their occurrence varies considerably between populations. A recent report has suggested that copy number variations in four genes (GRIK3, EFNA5, AKAP5 and CACNG2) may be associated with schizophrenia. One problem with this area of study is the validation of high throughput methods such as comparative genomic hybridisation, as the latter inevitably generates false positives. We have used two contrasting methodologies to determine the validity of the findings reported above which if true would have major implications for the pathogenesis of schizophrenia. Samples from a UK population were tested using a method of allele quantification by DNA pooling and samples from Belgium and northern Sweden were tested using Multiplex Amplicon Quantification (MAQ). Both methods were used to test DNA samples used in the original investigation. No copy number variations were found for any of the genes in any samples. Our data suggests that more reliable methods need to be used to validate the existence of CNVs before full scale association studies are carried out. PMID:17826036
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 ofâ€¦
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…
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 3â€¦
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) .
Curve Numbers for Golf Course Watersheds
Technology Transfer Automated Retrieval System (TEKTRAN)
Storm event runoff is a critical component to the environmental and structural design related to hydrology. The curve number (CN) method is a robust and accepted method for determining excess rainfall. Measured CNs for golf course watersheds and for that matter hydrologic data from golf course wate...
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 thanâ€¦
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.)
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 principleâ€¦
O'Carroll, Dave; MacMahon, Ann
2016-04-01
How many nurses and midwives in the UK are professors? Who knows and does it matter? Well, we know because we've monitored them for the past 13 years - and it does matter, because the number of nursing professors is indicative of the development of academic leadership in nursing. PMID:27049996
Coxeter transformations and the number '-1'
Kolmykov, V A
2000-10-31
Coxeter transformations associated with trees are considered. The number '-1' plays an exceptional role with respect to the spectra of trees. The sets of all trees containing and not containing '-1' in the spectrum are studied. Their densities are determined, systems of generating elements and operations are found, and the properties of the edges of trees from these sets are studied.
MHD dynamos at low magnetic Prandtl number
NASA Astrophysics Data System (ADS)
Ponty, Y.; Mininni, P.; Montgomery, D. C.; Pinton, J.-F.; Politano, H.; Pouquet, A.
2004-11-01
The generation of magnetic fields in celestial bodies occurs in media with very different kinematic viscosity and magnetic diffusivity. At the same time, the Reynolds numbers may be very large, with complex turbulent flows being responsible for the magnetic field amplification. We present a three-pronged numerical approach to the dynamo problem of generation of magnetic fields at small magnetic Prandtl numbers. The numerical difficulty of needing to resolve a large range of relevant scales is circumvented by combining direct numerical simulations (DNS), a Lagrangian-averaged model (the ``alpha model'' of D. Holm and collaborators), and large-eddy simulations (LES) of the MHD equations. The flow under investigation is forced by a Taylor-Green vortex term, similarly to several laboratory experiments on liquid metals. When possible, we performed overlapping simulations with the different numerical methods to ensure consistency of the results. The existence of a critical value of the magnetic Reynolds number for the exponential growth of magnetic energy was explored. Magnetic Prandtl numbers down to 0.1 and smaller were reached, and at all values explored, a dynamo threshold was found.
Genomic characteristics of cattle copy number variations
Technology Transfer Automated Retrieval System (TEKTRAN)
We performed a systematic analysis of cattle copy number variations (CNVs) using the Bovine HapMap SNP genotyping data, including 539 animals of 21 modern cattle breeds and 6 outgroups. After correcting genomic waves and considering the trio information, we identified 682 candidate CNV regions (CNVR...
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... 40 Protection of Environment 19 2010-07-01 2010-07-01 false Section numbering. 86.1204 Section 86.1204 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) AIR PROGRAMS...
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... 40 Protection of Environment 19 2011-07-01 2011-07-01 false Section numbering. 86.1204 Section 86.1204 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) AIR PROGRAMS...
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 storyâ€¦
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 forâ€¦
ANARCI: antigen receptor numbering and receptor classification
Dunbar, James; Deane, Charlotte M.
2016-01-01
Motivation: Antibody amino-acid sequences can be numbered to identify equivalent positions. Such annotations are valuable for antibody sequence comparison, protein structure modelling and engineering. Multiple different numbering schemes exist, they vary in the nomenclature they use to annotate residue positions, their definitions of position equivalence and their popularity within different scientific disciplines. However, currently no publicly available software exists that can apply all the most widely used schemes or for which an executable can be obtained under an open license. Results: ANARCI is a tool to classify and number antibody and T-cell receptor amino-acid variable domain sequences. It can annotate sequences with the five most popular numbering schemes: Kabat, Chothia, Enhanced Chothia, IMGT and AHo. Availability and implementation: ANARCI is available for download under GPLv3 license at opig.stats.ox.ac.uk/webapps/anarci. A web-interface to the program is available at the same address. Contact: deane@stats.ox.ac.uk PMID:26424857
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 anyâ€¦
NASA Astrophysics Data System (ADS)
Brekke, Lee; Freund, Peter G. O.
1993-10-01
The boundary of the ordinary open string world sheet is the real line. Along with the usual open string, one can consider p-adic open strings whose world sheet has as boundary the p-adic line instead (the points on this boundary are labelled by p-adic numbers rather than real numbers). The world sheet itself is then no longer a continous manifold but becomes a discrete homogeneous Bethe lattice, or Bruhat-Tits tree of incidence number p + 1. The p-adic strings thus correspond to specific discretizations of the world sheet. Studying all these discretizations (one for each prime p) together, as suggested by number theory, sheds new light on the ordinary string, via adelic product formulae. One is also led this way to a new type of string, the adelic string. These issues and their generalization to closed strings are discussed after a self-contained mathematical introduction. Other physical systems with natural p-adic counterparts are considered and in their context the connection between p-adic theories and quantum groups is explored.
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…
Science Books & Films, Volume XIII, Number 3.
ERIC Educational Resources Information Center
Finch, Shari, Ed.
This document provides annotated bibliographies of 205 books, 61 children's books, and 87 films all of which are science related. Each annotation includes author, publisher, title, number of pages, cost, an appraisal from highly recommended to not recommended, and level of difficulty from preschool to professional. Entries are grouped by topics…
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, andâ€¦
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.
20 CFR 404.1220 - Identification numbers.
Code of Federal Regulations, 2011 CFR
2011-04-01
.... SSA will send the State a Form SSA-214-CD, â€śNotice of Identifying Number,â€ť to inform the State of the... obtained and SSA will send a Form SSA-214-CD to the interstate instrumentality to notify it of the...
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…
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.
Determining the Number of Factors To Retain.
ERIC Educational Resources Information Center
Tanguma, Jesus
This paper presents four methods for determining the number of factors to retain: (1) determining an eigenvalue greater than unity (K1); (2) the scree test; (3) the minimum average parallel approach; and (4) parallel analysis. Three of the four methods are illustrated through an example. Although the eigenvalue greater than unity and the screeâ€¦
7 CFR 75.48 - Identification number.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 3 2013-01-01 2013-01-01 false Identification number. 75.48 Section 75.48 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing Practices), DEPARTMENT OF AGRICULTURE (CONTINUED) REGULATIONS AND STANDARDS UNDER THE AGRICULTURAL MARKETING ACT OF 1946...
Sesame equation of state number 2293, Li
Boettger, J.C.
1988-08-01
A new equation of state (EOS) for Li has been constructed and placed on the SESAME library as material number 2293. This new equation of state uses a cold curve obtained via electronic band structure calculations using the linear-muffin-tin-orbitals (LMTO) techique. 15 refs., 5 figs.
A Number Trick--Explained with Algebra.
ERIC Educational Resources Information Center
Escultura, Eddie
1983-01-01
The trick focuses on a theorem that the sum of the digits of the difference between any natural number and the sum of its digits is divisible by nine. Two conditions of using the trick are noted. The reason that the theorem works is established through a proof. (MP)
20 CFR 404.1220 - Identification numbers.
Code of Federal Regulations, 2013 CFR
2013-04-01
.... SSA will send the State a Form SSA-214-CD, â€śNotice of Identifying Number,â€ť to inform the State of the... obtained and SSA will send a Form SSA-214-CD to the interstate instrumentality to notify it of the...
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 andâ€¦
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…
Copy Number Variation in the Cattle Genome
Technology Transfer Automated Retrieval System (TEKTRAN)
Copy number variations (CNVs) are gains and losses of genomic sequence greater than 50 bp between two individuals of a species. While single nucleotide polymorphisms (SNPs) are more frequent, CNVs impact a higher percentage of genomic sequence and have potentially greater effects, including the chan...
Zero Tolerance Policies. ERIC Digest Number 146.
ERIC Educational Resources Information Center
McAndrews, Tobin
State legislatures and school boards are adopting a growing number of zero-tolerance polices toward weapons, guns, and violence. Zero-tolerance polices are rules intended to address specific school-safety issues. They have arisen in part as a response to the threat of the withdrawal of federal funds under the 1994 Gun-Free Schools Act, andâ€¦
Laboratory Mathematics. Curriculum Booklet II - Whole Numbers.
ERIC Educational Resources Information Center
Rogers, Sandra
This booklet is one of a set of five booklets which comprise the basic curriculum for "Mathematics Laboratories for Disadvantaged Students," a nationally validated Title III ESEA project. This publication provides evaluation materials and student materials related to whole numbers. Topics included are place value, addition, subtraction,â€¦
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 Â§ 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, 2010 CFR
2010-01-01
... CERTIFICATION CERTIFICATION OF TECHNICAL ANIMAL FATS FOR EXPORT Procedure for Obtaining Service: Administration of Program Â§ 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....
How Can Syntax Support Number Word Acquisition?
ERIC Educational Resources Information Center
Syrett, Kristen; Musolino, Julien; Gelman, Rochel
2012-01-01
We expand upon a previous proposal by Bloom and Wynn (1997) that young children learn about the meaning of number words by tracking their occurrence in particular syntactic environments, in combination with the discourse context in which they are used. An analysis of the Childes database (MacWhinney, 2000) reveals that the environments studied byâ€¦
Principal Evaluation. Research Action Brief Number 12.
ERIC Educational Resources Information Center
ERIC Clearinghouse on Educational Management, Eugene, OR.
The research considered here provides the basis for a number of general observations. Evaluation itself appears to be worthwhile, both as a way of measuring principal performance and of improving it by focusing attention on how principals are doing. The best evaluators appear to be teachers. District personnel and outside observers can also makeâ€¦
Cetane numbers of biodiesel and its components
Technology Transfer Automated Retrieval System (TEKTRAN)
The cetane number is one of the prime fuel quality indicators of a petrodiesel or biodiesel fuel as it relates to the tendency of the fuel to ignite in the combustion chamber. It has been established that compound structure, including chain length, branching, and the presence of double bonds, is a m...
Gauge transformations with fractional winding numbers
Abouelsaood, A.
1996-08-01
The role which gauge transformations of noninteger winding numbers might play in non-Abelian gauge theories is studied. The phase factor acquired by the semiclassical physical states in an arbitrary background gauge field when they undergo a gauge transformation of an arbitrary real winding number is calculated in the path integral formalism assuming that a {theta}{ital F{tilde F}} term added to the Lagrangian plays the same role as in the case of integer winding numbers. Requiring that these states provide a representation of the group of {open_quote}{open_quote}large{close_quote}{close_quote} gauge transformations, a condition on the allowed backgrounds is obtained. It is shown that this representability condition is only satisfied in the monopole sector of a spontaneously broken gauge theory, but not in the vacuum sector of an unbroken or a spontaneously broken non-Abelian gauge theory. It is further shown that the recent proof of the vanishing of the {theta} parameter when gauge transformations of arbitrary fractional winding numbers are allowed breaks down in precisely those cases where the representability condition is obeyed because certain gauge transformations needed for the proof, and whose existence is assumed, are either spontaneously broken or cannot be globally defined as a result of a topological obstruction. {copyright} {ital 1996 The American Physical Society.}
The 17 GHz active region number
Selhorst, C. L.; Pacini, A. A.; Costa, J. E. R.; GimĂ©nez 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.
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 andâ€¦
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…
Odd numbers of photons and teleportation
Enk, S.J. van
2003-02-01
Several teleportation protocols, namely those using entangled coherent states, entangled squeezed states, and the single-photon Einstein-Podolsky-Rosen state, are all shown to be particular instances of a more general scheme that relies on the detection of an odd number of photons.
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…
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% ofâ€¦
Random numbers certified by Bell's theorem.
Pironio, S; AcĂn, 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
Number Processing in Chinese-English Bilinguals.
ERIC Educational Resources Information Center
Campbell, Jamie I. D.; Kanz, Cindy L.; Xue, Qilin
1999-01-01
Examines number naming, magnitude selection, and simple arithmetic performed by adult Chinese-English bilinguals born and educated in China to investigate the effects of surface notation on basic numerical skills. Indicates that retrieval processes in the arithmetic and selection tasks were more efficient with Arabic than Mandarin stimuli.â€¦
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.
A Fresh Approach to Prime Numbers.
ERIC Educational Resources Information Center
Hampton, Homer F.
1979-01-01
The introduction of prime numbers in the intermediate grades should be handled with care or the concept will appear arbitrary, artificial, and unreal to the pupils. The approach suggested here is in the form of a game-like activity. A knowledge of multiplication and factors is a prerequisite. (BB)
Dynamic mental number line in simple arithmetic.
Yu, Xiaodan; Liu, Jie; Li, Dawei; Liu, Hang; Cui, Jiaxin; Zhou, Xinlin
2016-05-01
Studies have found that spatial-numerical associations could extend to arithmetic. Addition leads to rightward shift in spatial attention while subtraction leads to leftward shift (e.g., Knops et al. 2009; McCrink et al. 2007; Pinhas & Fischer 2008), which is consistent with the hypothesis of static mental number line (MNL) for arithmetic. The current investigation tested the hypothesis of dynamic mental number line which was shaped by the relative magnitudes of two operands in simple arithmetic. Horizontal and vertical electrooculograms (HEOG and VEOG) during simple arithmetic were recorded. Results showed that the direction of eye movements was dependent on the relative magnitudes of two operands. Subtraction was associated with larger rightward eye movements than addition (Experiment 1), and smaller-operand-first addition (e.g., 2+9) was associated with larger rightward eye movement than larger-operand-first addition (e.g., 9+2) only when the difference of two operands was large (Experiment 2). The results suggest that the direction of the mental number line could be dynamic during simple arithmetic, and that the eyes move along the dynamic mental number line to search for solutions. PMID:26645825
Science Books & Films, Volume XIII, Number 3.
ERIC Educational Resources Information Center
Finch, Shari, Ed.
This document provides annotated bibliographies of 205 books, 61 children's books, and 87 films all of which are science related. Each annotation includes author, publisher, title, number of pages, cost, an appraisal from highly recommended to not recommended, and level of difficulty from preschool to professional. Entries are grouped by topicsâ€¦
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.
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 morphologicalâ€¦
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 talk to ... prevention. It does NOT need to be an emergency. You can call for any reason, 24 hours ...
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.
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) will then be presented. Recommendations for modifications to current approaches used in crime labs for serial number recovery, as well as suggestions for future work, conclude this document.
MOIRCS Deep Survey. I: DRG Number Counts
NASA Astrophysics Data System (ADS)
Kajisawa, Masaru; Konishi, Masahiro; Suzuki, Ryuji; Tokoku, Chihiro; Uchimoto, Yuka; Katsuno; Yoshikawa, Tomohiro; Akiyama, Masayuki; Ichikawa, Takashi; Ouchi, Masami; Omata, Koji; Tanaka, Ichi; Nishimura, Tetsuo; Yamada, Toru
2006-12-01
We used very deep near-infrared imaging data taken with the Multi-Object InfraRed Camera and Spectrograph (MOIRCS) on the Subaru Telescope to investigate the number counts of Distant Red Galaxies (DRGs). We observed a 4' Ă— 7' field in the Great Observatories Origins Deep Survey-North (GOODS-N), and our data reached J=24.6 and K=23.2 (5Ď, Vega magnitude). The surface density of DRGs selected by J - K > 2.3 is 2.35 Â± 0.31 arcmin-2 at K < 22 and 3.54 Â± 0.38 arcmin-2 at K < 23, respectively. These values are consistent with those in the GOODS-South and FIRES. Our deep and wide data suggest that the number counts of DRGs turn over at K Ëś 22, and the surface density of the faint DRGs with K > 22 is smaller than that expected from the number counts at the brighter magnitude. The result indicates that while there are many bright galaxies at 2 < z < 4 with the relatively old stellar population and/or heavy dust extinction, the number of faint galaxies with a similar red color is relatively small. Different behavior patterns of the number counts of the DRGs and bluer galaxies with 2 < zphot < 4 at K > 22 suggest that the mass-dependent color distribution, where most of the low-mass galaxies are blue, while more massive galaxies tend to have redder colors, had already been established at that epoch.
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.
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
Baryon-number violation at accelerator energies
NASA Astrophysics Data System (ADS)
Langacker, Paul; Sahdev, Deshdeep
1983-11-01
We study an SU5 grand unified model with a stable proton. Proton stability is ensured by requiring that all interactions conserve a global quantum number Ď‡ called "chromality" and that the proton be the lightest particle to have Ď‡â‰ 0. Minimally implemented, these ideas require a doubling of fermions (conveniently labeled "standard" and "exotic") in each family and the introduction of a 5 and 45 of Higgs fields. The model may then have a relatively light color-triplet Higgs field hÎ±, which can mediate the baryon-number-nonconserving decays of exotic fermions to the standard ones. We examine the phenomenology of the model and put bounds on the masses of the particles it postulates. In particular, we find that a color triplet hÎ± of mass mh>~102mW is consistent with all the low-energy data currently available. This gives rise to the logical possibility of observing baryon-number-nonconserving events at accelerators, provided that the exotic fermions are light enough to be produced there. We study the production and decay of exotic fermions in planned e+e- and pÂŻp facilities. We find that if they exist in the relevant mass range they could be produced in sufficient numbers (typically 103-104 exotic pairs per day at CERN LEP, the Stanford Linear Collider and Fermilab Tevatron I, and ~= 10/day at the CERN SPS) for the phenomenon of baryon-number violation to be observed. Other signatures include the decay of the exotic fermions a macroscopic distance from the production vertex and the presence of two high-energy charged leptons of the same sign among the decay products.
Baryon-number violation at accelerator energies
Langacker, P.; Sahdev, D.
1983-11-01
We study an SU/sub 5/ grand unified model with a stable proton. Proton stability is ensured by requiring that all interactions conserve a global quantum number chi called ''chromality'' and that the proton be the lightest particle to have chinot =0. Minimally implemented, these ideas require a doubling of fermions (conveniently labeled ''standard'' and ''exotic'') in each family and the introduction of a 5 and 45 of Higgs fields. The model may then have a relatively light color-triplet Higgs field h/sup ..cap alpha../, which can mediate the baryon-number-nonconserving decays of exotic fermions to the standard ones. We examine the phenomenology of the model and put bounds on the masses of the particles it postulates. In particular, we find that a color triplet h/sup ..cap alpha../ of mass m/sub h/> or approx. =10/sup 2/m/sub W/ is consistent with all the low-energy data currently available. This gives rise to the logical possibility of observing baryon-number-nonconserving events at accelerators, provided that the exotic fermions are light enough to be produced there. We study the production and decay of exotic fermions in planned e/sup +/e/sup -/ and p-barp facilities. We find that if they exist in the relevant mass range they could be produced in sufficient numbers (typically 10/sup 3/--10/sup 4/ exotic pairs per day at CERN LEP, the Stanford Linear Collider and Fermilab Tevatron I, and approx. =10/day at the CERN SPS) for the phenomenon of baryon-number violation to be observed. Other signatures include the decay of the exotic fermions a macroscopic distance from the production vertex and the presence of two high-energy charged leptons of the same sign among the decay products.
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
Random Access to a Random Number Sequence
NASA Astrophysics Data System (ADS)
Canfield, E. H., Jr.; Viecelli, J. A.
1992-03-01
We have expanded the method in a recent note by Koniges and Leith [ 1 ] for a direct jump to any desired k th element Îşk of the standard linear congruential random number generator specified by Eqs. (1) and (2). The digits of k (base b) in Eq. (6) are indices for selecting elements from two precalculated arrays, P and S, Eqs. (6) and (7). These elements are combined in Eqs. (10) and (11) to give the addends of Îş k = Îş k + Î© k. The choice of the base b determines the number of digits in k (base b). For each nonzero digit, the evaluation of Eqs. (10) and (11) require two multiplications (mod m), and one add. The larger the choice for b, the fewer the digits in k (base b), and the less the arithmetic needed to evaluate Eqs. (10) and (11). For modulus m = 2 48, values of b = 2, 8, and 256 require at most 48, 16, and 6 multiplications, respectively, to evaluate Eq. (10). The expected number of multiplications is somewhat less. As noted above, only the nonzero digits of k lead to modular arithmetic calculations (zero digits imply the addition of zero and/or multiplication by unity). For a random k, base b, the probability that a random bit is nonzero is {(b - 1)}/{b}. Thus we find that the expected number of multiplications to evaluate Eq. (10) for b = 2, 8, or 256 drops to 24, 14, or 5.98, respectively. The drawback for very large base b is the storage needed for the precalculated P and S arrays, Eqs. (8) and (9). Each has b( J+ 1) elements, where J+ 1 is the maximum number of digits in k (base b). For m = 2 48, and b = 2, 8, 256, there are respectively 2 Ă— 48 = 96, 8 Ă— 15 = 120, and 256 Ă— 6 = 1536 elements in P and in S. If b is further increased, then each array size b( J+ 1) grows rapidly. On the other hand, the J+ 1 number of multiplications (mod m) needed to evaluate Eq. (10) decreases slowly. We suggest that for a 48-bit machine word length b = 256 is a good compromise between table size and achievable speedup. For a standard generator with zero additive term using base 256 reduces the overall operations count from 48 if tests, 48 register shifts, 24 multiplies, and 72 logical ands to 6 register shifts, 5.98 multiplies, and 11.98 logical ands, yielding more than a fourfold increase in speed over the base 2 case.
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.
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%.
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.
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. PMID:24696639
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.
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.
Nonequilibrium hadronization and constituent quark number scaling
Zschocke, Sven; Horvat, Szabolcs; Mishustin, Igor N.; Csernai, Laszlo P.
2011-04-15
The constituent quark number scaling of elliptic flow is studied in a nonequilibrium hadronization and freeze-out model with rapid dynamical transition from ideal, deconfined, and chirally symmetric quark-gluon plasma, to final noninteracting hadrons. In this transition a bag model of constituent quarks is considered, where the quarks gain constituent quark mass while the background bag field breaks up and vanishes. The constituent quarks then recombine into simplified hadron states, while chemical, thermal, and flow equilibrium break down one after the other. In this scenario the resulting temperatures and flow velocities of baryons and mesons are different. Using a simplified few source model of the elliptic flow, we are able to reproduce the constituent quark number scaling, with assumptions on the details of the nonequilibrium processes.
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 Ď€ 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.
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.
Bridge Condition Assessment Using D Numbers
Hu, 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. PMID:24696639
Improved predictive equations for cetane number
Ingham, M.C.; Bert, J.A.; Painter, L.J.
1986-01-01
Three new predictive equations for cetane number have been developed. Each of these equations is shown to be superior to the current cetane index equation (ASTM D976-80) for a large fuel data base. One of the equations has the further advantage of requiring only one property measurement (aniline point). The equations were developed from a detailed analysis of functional relationships between measured cetane number (ASTM D613-84) and commonly measured physical properties of diesel fuels; aniline point, density, and distillation temperatures. The data base for this study totaled 1229 fuels, including commercial fuels from the U.S. Canada, Europe, and Japan; synthetic fuels derived from tar sands, shale, and coal; and a diversity of research fuels blended from straight-run and cracked stocks. The equations were optimized using data-fitting techniques which account for bias amongst the various data sources and for measurement errors in both the dependent and independent variables.
Self-Testing Quantum Random Number Generator
NASA Astrophysics Data System (ADS)
Lunghi, Tommaso; Brask, Jonatan Bohr; Lim, Charles Ci Wen; Lavigne, Quentin; Bowles, Joseph; Martin, Anthony; Zbinden, Hugo; Brunner, Nicolas
2015-04-01
The generation of random numbers is a task of paramount importance in modern science. A central problem for both classical and quantum randomness generation is to estimate the entropy of the data generated by a given device. Here we present a protocol for self-testing quantum random number generation, in which the user can monitor the entropy in real time. Based on a few general assumptions, our protocol guarantees continuous generation of high quality randomness, without the need for a detailed characterization of the devices. Using a fully optical setup, we implement our protocol and illustrate its self-testing capacity. Our work thus provides a practical approach to quantum randomness generation in a scenario of trusted but error-prone devices.
Entanglement distillation protocols and number theory
Bombin, H.; Martin-Delgado, M.A.
2005-09-15
We show that the analysis of entanglement distillation protocols for qudits of arbitrary dimension D benefits from applying basic concepts from number theory, since the set Z{sub D}{sup n} associated with Bell diagonal states is a module rather than a vector space. We find that a partition of Z{sub D}{sup n} into divisor classes characterizes the invariant properties of mixed Bell diagonal states under local permutations. We construct a very general class of recursion protocols by means of unitary operations implementing these local permutations. We study these distillation protocols depending on whether we use twirling operations in the intermediate steps or not, and we study them both analytically and numerically with Monte Carlo methods. In the absence of twirling operations, we construct extensions of the quantum privacy algorithms valid for secure communications with qudits of any dimension D. When D is a prime number, we show that distillation protocols are optimal both qualitatively and quantitatively.
Mosaic Copy Number Variation in Human Neurons
McConnell, Michael J.; Lindberg, Michael R.; Brennand, Kristen J.; Piper, Julia C.; Voet, Thierry; Cowing-Zitron, Chris; Shumilina, Svetlana; Lasken, Roger S.; Vermeesch, Joris; Hall, Ira M.; Gage, Fred H.
2014-01-01
We used single cell genomic approaches to map DNA copy number variation (CNV) in neurons obtained from human induced pluripotent stem cell (hiPSC) lines and post-mortem human brains. We identified aneuploid neurons as well as numerous subchromosomal CNVs in euploid neurons. Neurotypic hiPSC-derived neurons had larger CNVs than fibroblasts, and several large deletions were found in hiPSC-derived neurons but not in matched neural progenitor cells. Single cell sequencing of endogenous human frontal cortex neurons revealed that 13%-41% of neurons have at least one megabase-scale de novo CNV, that deletions are twice as common as duplications, and that a subset of neurons have highly aberrant genomes marked by multiple alterations. Our results show that mosaic copy number variation is abundant in human neurons. PMID:24179226
Riemann zeros, prime numbers, and fractal potentials.
van Zyl, Brandon P; Hutchinson, David A W
2003-06-01
Using two distinct inversion techniques, the local one-dimensional potentials for the Riemann zeros and prime number sequence are reconstructed. We establish that both inversion techniques, when applied to the same set of levels, lead to the same fractal potential. This provides numerical evidence that the potential obtained by inversion of a set of energy levels is unique in one dimension. We also investigate the fractal properties of the reconstructed potentials and estimate the fractal dimensions to be D=1.5 for the Riemann zeros and D=1.8 for the prime numbers. This result is somewhat surprising since the nearest-neighbor spacings of the Riemann zeros are known to be chaotically distributed, whereas the primes obey almost Poissonlike statistics. Our findings show that the fractal dimension is dependent on both level statistics and spectral rigidity, Delta(3), of the energy levels. PMID:16241330
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,
Propagation number in periodic structures considering losses
NASA Astrophysics Data System (ADS)
MĂ©resse, P.; Renou, Y.; Vasseur, J.; Audoly, C.; Hladky, A. C.
2015-01-01
The development of absorbing or reflecting panels is of interest for underwater acoustic stealth. Most of the time, losses are not considered in the structures studied, specifically in the propagation number determination, despite the fact that most materials used, such as polymer matrices, have non negligible viscous losses. So, for a better understanding of the acoustic properties of these structures and to allow their optimization, simulations should consider the material properties, including losses. In order to obtain more realistic results from simulation, two numerical tools based on the finite element method (FEM) are proposed, with the help of the ATILA software. One is based on a differential method, the other on the transfer matrix. The two methods are first validated in the lossless case, then when losses are taken into account. Both methods give results in good agreement and give the propagation number where losses are taken into account.
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.
Entangled bases with fixed Schmidt number
NASA Astrophysics Data System (ADS)
Guo, Yu; Du, Shuanping; Li, Xiulan; Wu, Shengjun
2015-06-01
An entangled basis with a fixed Schmidt number k (EBk) is a set of orthonormal basis states with the same Schmidt number k in a product Hilbert space {{{C}}d}\\otimes {{{C}}{{d\\prime }}}. It is a generalization of both the product basis and the maximally entangled basis. We show here that for any kâ‰¤slant min \\{d,d\\prime \\}, EBk exists in {{{C}}d}\\otimes {{{C}}{{d\\prime }}} for any d and dâ€§. Consequently, general methods of constructing SEBk (EBk with the same Schmidt coefficients) and EBk (but not SEBk) are proposed. Moreover, we extend the concept of EBk to multipartite cases and find out that the multipartite EBk can be constructed similarly.
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).
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.
Surgical audit: do numbers provide good training?
Crate, I D; Griffiths, C L
1996-06-01
There has been a growing realisation that good resource planning requires effective measurement of surgical workload by good surgical audit. This paper examines the general surgical workload at the Army's tertiary referral centre, utilising the ratio of operative workload expressed as Intermediate Equivalents to total Service Equivalent Value of a Surgical team. A suggested format to enable inclusion of specialist non-surgical therapies is proposed. The limitations of "number crunching" when assessing the value of higher surgical training are discussed. PMID:8819034
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…
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 beâ€¦
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.
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 Â°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 Â°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 Â°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 is of extremely low volatility.
A high magnetic Reynolds number dynamo
NASA Technical Reports Server (NTRS)
Perkins, F. W.; Zweibel, E. G.
1987-01-01
A boundary-layer solution to a high magnetic Reynolds number R periodic dynamo model shows that: (1) flux expulsion forces the magnetic field into flux sheets; (2) the principal contribution to the alpha effect arises from regions of flow stagnation along a flux sheet; and (3) the alpha effect scales as R exp-1/2. Arguments for these effects persisting in turbulent dynamos are given.
Chromosome number variation in two antipodean floras
Peruzzi, Lorenzo; Dawson, Murray I.; Bedini, Gianni
2011-01-01
Background and aims We compared chromosome number (CN) variation in the nearly antipodean Italian and New Zealand floras to verify (i) whether patterns of variation reflect their similar latitudinal ranges or their different biogeographic/taxonomic contexts, (ii) if any differences are equally distributed across major taxa/lineages and (iii) if the frequency, number and taxonomic distribution of B-chromosomes differ between the two countries. Methodology We compared two datasets comprising 3426 (Italy) and 2525 (New Zealand) distinct cytotypes. We also compared a subset based on taxonomic orders and superimposed them onto a phylogeny of vascular plants. We used standard statistics, histograms, and either analysis of variance or Kruskalâ€“Wallis tests to analyse the data. Principal results Mean CN of the vascular New Zealand flora is about twice that of Italy. For most orders, mean CN values for New Zealand are higher than those of the Italian flora and the differences are statistically significant. Further differences in CN variation among the orders and main clades that we studied, irrespective of geographical distinctions, are revealed. No correlation was found between chromosome and B-chromosome number. Conclusions Mean CN of the whole New Zealand dataset is about twice that of the Italian flora. This suggests that extensive polyploidization played a major role in the evolution of the New Zealand vascular flora that is characterized by a rate of high endemism. Our results show that the hypothesis of a polyploid increase proportional to distance from the Equator cannot be applied to territories with the same latitudinal ranges but placed in different hemispheres. We suggest that bioclimatic gradients, rather than or in addition to latitudinal gradients, might account for a polyploidy increase. Our data also suggest that any adaptive role of B-chromosomes at geographic scale may be sought in their frequency rather than in their number. PMID:22476490
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 inâ€¦
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", whichâ€¦
Sequences of Rational Numbers Converging to Surds
ERIC Educational Resources Information Center
Fletcher, Rodney
2010-01-01
In this sequence 1/1, 7/5, 41/29, 239/169 and so on, Thomas notes that the sequence converges to square root of 2. By observation, the sequence of numbers in the numerator of the above sequence, have a pattern of generation which is the same as that in the denominator. That is, the next term is found by multiplying the previous term by six andâ€¦
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 Hagerâ€™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 Peiâ€™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 Peiâ€™s matrix, and matrices generated with the finite element method. PMID:25816331
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