Heat transfer enhancement in free convection flow of CNTs Maxwell nanofluids with four different types of molecular liquids.

PubMed

Aman, Sidra; Khan, Ilyas; Ismail, Zulkhibri; Salleh, Mohd Zuki; Al-Mdallal, Qasem M

2017-05-26

This article investigates heat transfer enhancement in free convection flow of Maxwell nanofluids with carbon nanotubes (CNTs) over a vertically static plate with constant wall temperature. Two kinds of CNTs i.e. single walls carbon nanotubes (SWCNTs) and multiple walls carbon nanotubes (MWCNTs) are suspended in four different types of base liquids (Kerosene oil, Engine oil, water and ethylene glycol). Kerosene oil-based nanofluids are given a special consideration due to their higher thermal conductivities, unique properties and applications. The problem is modelled in terms of PDE's with initial and boundary conditions. Some relevant non-dimensional variables are inserted in order to transmute the governing problem into dimensionless form. The resulting problem is solved via Laplace transform technique and exact solutions for velocity, shear stress and temperature are acquired. These solutions are significantly controlled by the variations of parameters including the relaxation time, Prandtl number, Grashof number and nanoparticles volume fraction. Velocity and temperature increases with elevation in Grashof number while Shear stress minimizes with increasing Maxwell parameter. A comparison between SWCNTs and MWCNTs in each case is made. Moreover, a graph showing the comparison amongst four different types of nanofluids for both CNTs is also plotted.

Quantification of free convection effects on 1 kg mass standards

NASA Astrophysics Data System (ADS)

Schreiber, M.; Emran, M. S.; Fröhlich, T.; Schumacher, J.; Thess, A.

2015-12-01

We determine the free-convection effects and the resulting mass differences in a high-precision mass comparator for cylindrical and spherical 1 kg mass standards at different air pressures. The temperature differences are chosen in the millikelvin range and lead to microgram updrafts. Our studies reveal a good agreement between the measurements and direct numerical simulations of the Boussinesq equations of free thermal convection. A higher sensitivity to the free convection effects is found for the spherical case compared to the cylindrical one. We also translate our results on the free convection effects into a form which is used in fluid mechanics: a dimensionless updraft coefficient as a function of the dimensionless Grashof number Gr that quantifies the thermal driving due to temperature differences. This relation displays a unique scaling behavior over nearly four decades in Gr and levels off into geometry-specific constants for the very small Grashof numbers. The obtained results provide a rational framework for estimating systematic errors in mass metrology due to the effects of free convection.

Instabilities of mixed convection flows adjacent to inclined plates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abu-Mulaweh, H.I.; Armaly, B.F.; Chen, T.S.

1987-11-01

The measurements by Sparrow and Husar and by Lloyd and Sparrow established that the onset of instability (transition from laminar to turbulent) in free convection boundary layer flow above an inclined heated plate is predominated by the wave mode of instability for inclination angles less than 14 deg, as measured from the vertical, and by the vortex mode of instability for angles greater than 17 deg. The transition Grashof number deceased as the angle of inclination increased. The predictions of Chen and Tzuoo for this flow provide trends that are similar to measured values, but the predicted critical Grashof numbersmore » deviate significantly (three orders of magnitude smaller) from measured values. The instability of mixed convection boundary layer flow adjacent to inclined heated plates have also been treated numerically by Chen and Mucoglu for wave instability and by Chen et al. for vortex instability. Comparisons with measurements of instability in mixed convection flow adjacent to inclined plates were not available in the literature. It is anticipated, however, that these predictions will underestimate the actual onset of instability, as in the free convection case. The lack of measurements in this flow domain for this geometry has motivated the present study. The onset of instability in mixed convection flow adjacent to an isothermally heated inclined plate was determined in this study through flow visualization. The buoyancy-assisting and buoyancy-opposing flow cases were examined for the flow both above and below the heated plate. The critical Grashof-Reynolds number relationships for the onset of instability in this flow domain are reported in this paper.« less

Closed Form Solutions for Unsteady Free Convection Flow of a Second Grade Fluid over an Oscillating Vertical Plate

PubMed Central

Ali, Farhad; Khan, Ilyas; Shafie, Sharidan

2014-01-01

Closed form solutions for unsteady free convection flows of a second grade fluid near an isothermal vertical plate oscillating in its plane using the Laplace transform technique are established. Expressions for velocity and temperature are obtained and displayed graphically for different values of Prandtl number Pr, thermal Grashof number Gr, viscoelastic parameter α, phase angle ωτ and time τ. Numerical values of skin friction τ 0 and Nusselt number Nu are shown in tables. Some well-known solutions in literature are reduced as the limiting cases of the present solutions. PMID:24551033

Effect of thermal radiation and chemical reaction on non-Newtonian fluid through a vertically stretching porous plate with uniform suction

NASA Astrophysics Data System (ADS)

Khan, Zeeshan; Khan, Ilyas; Ullah, Murad; Tlili, I.

2018-06-01

In this work, we discuss the unsteady flow of non-Newtonian fluid with the properties of heat source/sink in the presence of thermal radiation moving through a binary mixture embedded in a porous medium. The basic equations of motion including continuity, momentum, energy and concentration are simplified and solved analytically by using Homotopy Analysis Method (HAM). The energy and concentration fields are coupled with Dankohler and Schmidt numbers. By applying suitable transformation, the coupled nonlinear partial differential equations are converted to couple ordinary differential equations. The effect of physical parameters involved in the solutions of velocity, temperature and concentration profiles are discussed by assign numerical values and results obtained shows that the velocity, temperature and concentration profiles are influenced appreciably by the radiation parameter, Prandtl number, suction/injection parameter, reaction order index, solutal Grashof number and the thermal Grashof. It is observed that the non-Newtonian parameter H leads to an increase in the boundary layer thickness. It was established that the Prandtl number decreases thee thermal boundary layer thickness which helps in maintaining system temperature of the fluid flow. It is observed that the temperature profiles higher for heat source parameter and lower for heat sink parameter throughout the boundary layer. Fromm this simulation it is analyzed that an increase in the Schmidt number decreases the concentration boundary layer thickness. Additionally, for the sake of comparison numerical method (ND-Solve) and Adomian Decomposition Method are also applied and good agreement is found.

Finite element computation of multi-physical micropolar transport phenomena from an inclined moving plate in porous media

NASA Astrophysics Data System (ADS)

Shamshuddin, MD.; Anwar Bég, O.; Sunder Ram, M.; Kadir, A.

2018-02-01

Non-Newtonian flows arise in numerous industrial transport processes including materials fabrication systems. Micropolar theory offers an excellent mechanism for exploring the fluid dynamics of new non-Newtonian materials which possess internal microstructure. Magnetic fields may also be used for controlling electrically-conducting polymeric flows. To explore numerical simulation of transport in rheological materials processing, in the current paper, a finite element computational solution is presented for magnetohydrodynamic, incompressible, dissipative, radiative and chemically-reacting micropolar fluid flow, heat and mass transfer adjacent to an inclined porous plate embedded in a saturated homogenous porous medium. Heat generation/absorption effects are included. Rosseland's diffusion approximation is used to describe the radiative heat flux in the energy equation. A Darcy model is employed to simulate drag effects in the porous medium. The governing transport equations are rendered into non-dimensional form under the assumption of low Reynolds number and also low magnetic Reynolds number. Using a Galerkin formulation with a weighted residual scheme, finite element solutions are presented to the boundary value problem. The influence of plate inclination, Eringen coupling number, radiation-conduction number, heat absorption/generation parameter, chemical reaction parameter, plate moving velocity parameter, magnetic parameter, thermal Grashof number, species (solutal) Grashof number, permeability parameter, Eckert number on linear velocity, micro-rotation, temperature and concentration profiles. Furthermore, the influence of selected thermo-physical parameters on friction factor, surface heat transfer and mass transfer rate is also tabulated. The finite element solutions are verified with solutions from several limiting cases in the literature. Interesting features in the flow are identified and interpreted.

Steady MHD free convection heat and mass transfer flow about a vertical porous surface with thermal diffusion and induced magnetic field

NASA Astrophysics Data System (ADS)

Touhid Hossain, M. M.; Afruz-Zaman, Md.; Rahman, Fouzia; Hossain, M. Arif

2013-09-01

In this study the thermal diffusion effect on the steady laminar free convection flow and heat transfer of viscous incompressible MHD electrically conducting fluid above a vertical porous surface is considered under the influence of an induced magnetic field. The governing non-dimensional equations relevant to the problem, containing the partial differential equations, are transformed by usual similarity transformations into a system of coupled non-linear ordinary differential equations and will be solved analytically by using the perturbation technique. On introducing the non-dimensional concept and applying Boussinesq's approximation, the solutions for velocity field, temperature distribution and induced magnetic field to the second order approximations are obtained for large suction with different selected values of the established dimensionless parameters. The influences of these various establish parameters on the velocity and temperature fields and on the induced magnetic fields are exhibited under certain assumptions and are studied graphically in the present analysis. It is observed that the effects of thermal-diffusion and large suction have great importance on the velocity, temperature and induced magnetic fields and mass concentration for several fluids considered, so that their effects should be taken into account with other useful parameters associated. It is also found that the dimensionless Prandtl number, Grashof number, Modified Grashof number and magnetic parameter have an appreciable influence on the concerned independent variables.

Exact solutions for unsteady free convection flow over an oscillating plate due to non-coaxial rotation.

PubMed

Mohamad, Ahmad Qushairi; Khan, Ilyas; Ismail, Zulkhibri; Shafie, Sharidan

2016-01-01

Non-coaxial rotation has wide applications in engineering devices, e.g. in food processing such as mixer machines and stirrers with a two-axis kneader, in cooling turbine blades, jet engines, pumps and vacuum cleaners, in designing thermal syphon tubes, and in geophysical flows. Therefore, this study aims to investigate unsteady free convection flow of viscous fluid due to non-coaxial rotation and fluid at infinity over an oscillating vertical plate with constant wall temperature. The governing equations are modelled by a sudden coincidence of the axes of a disk and the fluid at infinity rotating with uniform angular velocity, together with initial and boundary conditions. Some suitable non-dimensional variables are introduced. The Laplace transform method is used to obtain the exact solutions of the corresponding non-dimensional momentum and energy equations with conditions. Solutions of the velocity for cosine and sine oscillations as well as for temperature fields are obtained and displayed graphically for different values of time ( t ), the Grashof number ( Gr ), the Prandtl number ([Formula: see text]), and the phase angle ([Formula: see text]). Skin friction and the Nusselt number are also evaluated. The exact solutions are obtained and in limiting cases, the present solutions are found to be identical to the published results. Further, the obtained exact solutions also validated by comparing with results obtained by using Gaver-Stehfest algorithm. The interested physical property such as velocity, temperature, skin friction and Nusselt number are affected by the embedded parameters time ( t ), the Grashof number ( Gr ), the Prandtl number ([Formula: see text]), and the phase angle ([Formula: see text]).

Axisymmetry breaking instabilities of natural convection in a vertical bridgman growth configuration

NASA Astrophysics Data System (ADS)

Gelfgat, A. Yu.; Bar-Yoseph, P. Z.; Solan, A.

2000-12-01

A study of the three-dimensional axisymmetry-breaking instability of an axisymmetric convective flow associated with crystal growth from bulk of melt is presented. Convection in a vertical cylinder with a parabolic temperature profile on the sidewall is considered as a representative model. The main objective is the calculation of critical parameters corresponding to a transition from the steady axisymmetric to the three-dimensional non-axisymmetric (steady or oscillatory) flow pattern. A parametric study of the dependence of the critical Grashof number Gr cr on the Prandtl number 0⩽Pr⩽0.05 (characteristic for semiconductor melts) and the aspect ratio of the cylinder 1⩽ A⩽4 ( A=height/radius) is carried out. The stability diagram Grcr(Pr, A) corresponding to the axisymmetric — three-dimensional transition is reported for the first time. The calculations are done using the spectral Galerkin method allowing an effective and accurate three-dimensional stability analysis. It is shown that the axisymmetric flow in relatively low cylinders tends to be oscillatory unstable, while in tall cylinders the instability sets in due to a steady bifurcation caused by the Rayleigh-Benard mechanism. The calculated neutral curves are non-monotonous and contain hysteresis loops. The strong dependence of the critical Grashof number and the azimuthal periodicity of the resulting three-dimensional flow indicate the importance of a comprehensive parametric stability analysis in different crystal growth configurations. In particular, it is shown that the first instability of the flow considered is always three-dimensional.

Numerical simulation of buoyancy peristaltic flow of Johnson-Segalman nanofluid in an inclined channel

NASA Astrophysics Data System (ADS)

Hayat, T.; Ayub, Sadia; Alsaedi, Ahmed; Ahmad, Bashir

2018-06-01

This study addresses mixed convection on peristaltic flow in an inclined channel. The relevant flow problem is developed for MHD Johnson-Segalman nanofluid. Hall current and thermal radiation are discussed. Channel boundaries are compliant in nature. Slip effects for velocity, temperature and concentration are examined. Long wavelength concept is employed. Variations for prominent parameters in velocity, temperature, concentration, heat transfer coefficient and streamlines are obtained via built-in numerical approach. Velocity shows significant decline for larger local temperature Grashof number. Heat transfer slows down for increasing thermophoresis and thermal slip parameters. Increase in bolus is reported for higher Weissenberg number.

Hall effects on hydromagnetic free convection flow along a porous flat plate with mass transfer

NASA Astrophysics Data System (ADS)

Hossain, M. A.; Rashid, R. I. M. A.

1987-01-01

Effect of Hall current on the unsteady free convection flow of a viscous incompressible and electrically conducting fluid, in presence of foreign gases (such as H2, CO2, H2O, NH3), along an infinite vertical porous flat plate subjected to a transpiration velocity inversely proportional to the square-root of time is investigated in the presence of a uniform transverse magnetic field. The results are discussed with the effects of the parameters Gc (the Grashof number for mass transfer), m (the Hall parameter) and Sc (the Schmidt number) for Pr = 0.71, which represents air.

Variable mass diffusion effects on free convection flow past an impulsively started infinite vertical plate

NASA Astrophysics Data System (ADS)

Rushi Kumar, B.; Jayakar, R.; Vijay Kumar, A. G.

2017-11-01

An exact analysis of the problem of free convection flow of a viscous incompressible chemically reacting fluid past an infinite vertical plate with the flow due to impulsive motion of the plate with Newtonian heating in the presence of thermal radiation and variable mass diffusion is performed. The resulting governing equations were tackled by Laplace transform technique. Finally the effects of pertinent flow parameters such as the radiation parameter, chemical reaction parameter, buoyancy ratio parameter, thermal Grashof number, Schmidt number, Prandtl number and time on the velocity, temperature, concentration and skin friction for both aiding and opposing flows were examined in detail when Pr=0.71(conducting air) and Pr=7.0(water).

Buoyancy and Pressure Driven Flow of Hot Gases in Vertical Shafts with Natural and Forced Ventilation

NASA Astrophysics Data System (ADS)

Tamm, Gunnar; Jaluria, Yogesh

2003-11-01

An experimental investigation has been carried out on the buoyancy and pressure induced flow of hot gases in vertical shafts, in order to simulate the propagation of combustion products in elevator shafts due to fire in multilevel buildings. Various geometrical configurations are studied, with regard to natural and forced ventilation imposed at the top or bottom of the vertical shaft. The aspect ratio is taken at a fixed value of 6 and the inflow conditions for the hot gases, at a vent near the bottom, are varied in terms of the Reynolds and Grashof numbers. Temperature measurements within the shaft allow a detailed study of the steady state thermal fields, from which optimal means for smoke alleviation in high-rise building fires may be developed. Flow visualization is also used to study the flow characteristics. The results obtained indicate a wall plume as the primary transport mechanism. Flow recirculation dominates at high Grashof number flows, while increased Reynolds numbers gives rise to greater mixing in the shaft. The development and stability of the flow and its effect on the spread of smoke and hot gases are assessed for the different shaft configurations and inlet conditions. It is found that the fastest smoke removal and lowest shaft temperatures occur for a configuration with natural ventilation at the top and forced ventilation up from the shaft bottom. It is also shown that forced ventilation can be used to arrest smoke spread, as well as to dilute the effects of the fire.

Bio mathematical venture for the metallic nanoparticles due to ciliary motion.

PubMed

Akbar, Noreen Sher; Butt, Adil Wahid

2016-10-01

The present investigation is associated with the contemporary study of viscous flow in a vertical tube with ciliary motion. The main flow problem has been modeled using cylindrical coordinates; flow equations are simplified to ordinary differential equations using longwave length and low Reynold's number approximation; and exact solutions have been obtained for velocity, pressure gradient and temperature. Results acquired are discussed graphically for better understanding. Streamlines for the velocity profile are plotted to discuss the trapping phenomenon. It is seen that with an increment in the Grashof number, the velocity of the governing fluids starts to decrease significantly. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Influence of Natural Convection and Thermal Radiation Multi-Component Transport in MOCVD Reactors

NASA Technical Reports Server (NTRS)

Lowry, S.; Krishnan, A.; Clark, I.

1999-01-01

The influence of Grashof and Reynolds number in Metal Organic Chemical Vapor (MOCVD) reactors is being investigated under a combined empirical/numerical study. As part of that research, the deposition of Indium Phosphide in an MOCVD reactor is modeled using the computational code CFD-ACE. The model includes the effects of convection, conduction, and radiation as well as multi-component diffusion and multi-step surface/gas phase chemistry. The results of the prediction are compared with experimental data for a commercial reactor and analyzed with respect to the model accuracy.

Two regimes of flux scaling in axially homogeneous turbulent convection in vertical tube

NASA Astrophysics Data System (ADS)

Pawar, Shashikant S.; Arakeri, Jaywant H.

2016-08-01

From experiments of axially homogeneous turbulent convection in a vertical tube using heat (Prandtl number Pr≃6 ) and brine (Pr≃600 ) we show that at sufficiently high Rayleigh numbers (Rag), the Nusselt number Nug˜(RagPr)1/2, which corresponds to the so-called ultimate regime scaling. In heat experiments below certain Rag,however,there is transition to a new regime, Nug˜(RagPr)0.3. This transition also seems to exist in earlier reported data for Pr=1 and Pr≃600 , at different Rag. However, the transition occurs at a single Grashof number, Grgc≃1.6 ×105 , and unified flux scalings for Pr≥1 , Nug/Pr˜Grg0.3, and Nug/Pr˜Grg1/2 can be given for the two regimes.

Design criterion for the heat-transfer coefficient in opposing flow, mixed convention heat transfer in a vertical tube

DOE Office of Scientific and Technical Information (OSTI.GOV)

Joye, D.D.

1996-07-01

Mixed convection heat transfer in a vertical tube with opposing flow (downflow heating) was studied experimentally for Reynolds numbers ranging from about 1,000 to 30,000 at constant Grashof numbers ranging about 1{1/2} orders of magnitude under constant wall temperature (CWT) conditions. Three correlations developed for opposing mixed convection flows in vertical conduits predicted the data reasonably well, except near and into the asymptote region for which these equations were not designed. A critical Reynolds number is developed here, above which these equations can be used for design purposes regardless of the boundary condition. Below Re{sub crit}, the correlations, the asymptotemore » equation should be used for the CWT boundary condition, which is more prevalent in process situations than the uniform heat flux (UHF) boundary condition.« less

The effect of power-law body forces on a thermally driven flow between concentric rotating spheres

NASA Technical Reports Server (NTRS)

Macaraeg, M. G.

1986-01-01

A numerical study is conducted to determine the effect of power-law body forces on a thermally-driven axisymmetric flow field confined between concentric co-rotating spheres. This study is motivated by Spacelab geophysical fluid-flow experiments, which use an electrostatic force on a dielectric fluid to simulate gravity; this force exhibits a (1/r)sup 5 distribution. Meridional velocity is found to increase when the electrostatic body force is imposed, relative to when the body force is uniform. Correlation among flow fields with uniform, inverse-square, and inverse-quintic force fields is obtained using a modified Grashof number.

The effect of power law body forces on a thermally-driven flow between concentric rotating spheres

NASA Technical Reports Server (NTRS)

Macaraeg, M. G.

1985-01-01

A numerical study is conducted to determine the effect of power-law body forces on a thermally-driven axisymmetric flow field confined between concentric co-rotating spheres. This study is motivated by Spacelab geophysical fluid-flow experiments, which use an electrostatic force on a dielectric fluid to simulate gravity; this force exhibits a (1/r)sup 5 distribution. Meridional velocity is found to increase when the electrostatic body force is imposed, relative to when the body force is uniform. Correlation among flow fields with uniform, inverse-square, and inverse-quintic force fields is obtained using a modified Grashof number.

Mixed convection heat transfer: an experimental study on Cu/heat transfer oil nanofluids inside annular tube

NASA Astrophysics Data System (ADS)

Abbasian Arani, Ali Akbar; Aberoumand, Hossein; Jafarimoghaddam, Amin; Aberoumand, Sadegh

2017-09-01

The heat transfer and flow characteristics of Cu-heat transfer oil nanofluid during mixed convection through horizontal annular tubes under uniform heat flux as boundary condition are investigated experimentally. Data were acquired at low Reynolds number ranged from about 26 to 252. The applied nanofluid prepared by Electrical Explosion of Wire technique with no nanoparticles agglomeration during nanofluid preparation process and experiments. Pure heat transfer oil and nanofluids with nanoparticles weight concentrations of 0.12, 0.36 and 0.72% were used as the working fluids. Based on these results, Effects of nanoparticles concentration, heat flux and free convection on the thermal field development are studied under buoyancy assisted flow condition for Grashof number, Richardson number between 2820 and 12,686, and 0.1-10, respectively. Results show that Nusselt number increases with an increase of nanoparticles weight concentrations from 0 to 0.72% under certain Richardson numbers.

Physiological breakdown of Jeffrey six constant nanofluid flow in an endoscope with nonuniform wall

NASA Astrophysics Data System (ADS)

Nadeem, S.; Shaheen, A.; Hussain, S.

2015-12-01

This paper analyse the endoscopic effects of peristaltic nanofluid flow of Jeffrey six-constant fluid model in the presence of magnetohydrodynamics flow. The current problem is modeled in the cylindrical coordinate system and exact solutions are managed (where possible) under low Reynolds number and long wave length approximation. The influence of emerging parameters on temperature and velocity profile are discussed graphically. The velocity equation is solved analytically by utilizing the homotopy perturbation technique strongly, while the exact solutions are computed from temperature equation. The obtained expressions for velocity , concentration and temperature is sketched during graphs and the collision of assorted parameters is evaluate for transform peristaltic waves. The solution depend on thermophoresis number Nt, local nanoparticles Grashof number Gr, and Brownian motion number Nb. The obtained expressions for the velocity, temperature, and nanoparticles concentration profiles are plotted and the impact of various physical parameters are investigated for different peristaltic waves.

Thermal and velocity slip effects on the MHD peristaltic flow with carbon nanotubes in an asymmetric channel: application of radiation therapy

NASA Astrophysics Data System (ADS)

Akbar, Noreen Sher; Nadeem, S.; Khan, Zafar Hayat

2014-10-01

Peristaltic flow is used to study the flow and heat transfer of carbon nanotubes in an asymmetric channel with thermal and velocity slip effects. Two types of carbon nanotubes, namely, single- and multi-wall carbon nanotubes are utilized to see the analysis with water as base fluids. Empirical correlations are used for the thermo-physical properties of carbon nanotubes (CNTs) in terms of solid volume fraction of CNTs. The governing equations are simplified using long wavelength and low Reynolds number approximation. Exact solutions have been evaluated for velocity, pressure gradient, the solid volume fraction of CNTs and temperature profile. The effects of various flow parameters, i.e. Hatmann number M, the solid volume fraction of the nanoparticles ϕ, Grashof number G, velocity slip parameter β, thermal slip parameter γ and Prandtl number P r are presented graphically for both single- (SWCNT) and multi-wall carbon nanotubes (MWCNT).

Mixed convection cooling of a cylinder using slot jet impingement at different circumferential angles

NASA Astrophysics Data System (ADS)

Naderipour, S.; Yousefi, T.; Ashjaee, M.; Naylor, D.

2016-08-01

An experimental study using Mach-Zehnder interferometer has been carried out to investigate the heat transfer from an isothermal horizontal circular cylinder, which is exposed to an air slot jet at different angles of jet impingement. A square edged nozzle is mounted parallel with the cylinder axis and jet flow impinges on the side of the cylinder at angles Θ = 0°, 30°, 60° and 90°. The Reynolds number varied from 240 to 1900 while the Grashof number and slot- to cylinder-spacing is kept constant at Gr = 22,300 and H/w = 7 respectively. The Richardson number varied from 0.006 to 0.4. The flow field is greatly influenced by the slot exit velocity and the buoyancy force due to density change. The local Nusselt number around the cylinder has been calculated using the infinite fringe interferograms at 10° intervals. Average Nusselt number shows that heat transfer is decreased when the angle of jet impingement is increased .

Measurement of diffusion coefficients from solution rates of bubbles

NASA Technical Reports Server (NTRS)

Krieger, I. M.

1979-01-01

The rate of solution of a stationary bubble is limited by the diffusion of dissolved gas molecules away from the bubble surface. Diffusion coefficients computed from measured rates of solution give mean values higher than accepted literature values, with standard errors as high as 10% for a single observation. Better accuracy is achieved with sparingly soluble gases, small bubbles, and highly viscous liquids. Accuracy correlates with the Grashof number, indicating that free convection is the major source of error. Accuracy should, therefore, be greatly increased in a gravity-free environment. The fact that the bubble will need no support is an additional important advantage of Spacelab for this measurement.

Couette flow of an incompressible fluid in a porous channel with mass transfer

NASA Astrophysics Data System (ADS)

Niranjana, N.; Vidhya, M.; Govindarajan, A.

2018-04-01

The present discussion deals with the study of couette flow through a porous medium of a viscous incompressible fluid between two infinite horizontal parallel porous flat plates with heat and mass transfer. The stationary plate and the plate in uniform motion are subjected to transverse sinusoidal injection and uniform suction of the fluid. Due to this type of injection velocity, the flow becomes three dimensional. The analytical solutions of the nonlinear partial differential equations of this problem are obtained by using perturbation technique. Expressions for the velocity, temperature fields and the rate of heat and mass transfers are obtained. Effects of the following parameters Schmidt number (Sc), Modified Grashof number (Gm) on the velocity, temperature and concentration fields are obtained numerically and depicted through graphs. The rate of heat and mass transfer are also analyzed.

Determination of blade-to-coolant heat-transfer coefficients on a forced-convection, water-cooled, single-stage turbine

NASA Technical Reports Server (NTRS)

Freche, John C; Schum, Eugene F

1951-01-01

Blade-to-coolant convective heat-transfer coefficients were obtained on a forced-convection water-cooled single-stage turbine over a large laminar flow range and over a portion of the transition range between laminar and turbulent flow. The convective coefficients were correlated by the general relation for forced-convection heat transfer with laminar flow. Natural-convection heat transfer was negligible for this turbine over the Grashof number range investigated. Comparison of turbine data with stationary tube data for the laminar flow of heated liquids showed good agreement. Calculated average midspan blade temperatures using theoretical gas-to-blade coefficients and blade-to-coolant coefficients from stationary-tube data resulted in close agreement with experimental data.

Counter-current convection in a volcanic conduit

NASA Astrophysics Data System (ADS)

Fowler, A. C.; Robinson, Marguerite

2018-05-01

Volcanoes of Strombolian type are able to maintain their semi-permanent eruptive states through the constant convective recycling of magma within the conduit leading from the magma chamber. In this paper we study the form of this convection using an analytic model of degassing two-phase flow in a vertical channel. We provide solutions for the flow at small Grashof and large Prandtl numbers, and we suggest that permanent steady-state counter-current convection is only possible if an initial bubbly counter-current flow undergoes a régime transition to a churn-turbulent flow. We also suggest that the magma in the chamber must be under-pressured in order for the flow to be maintained, and that this compromises the assumed form of the flow.

Onset of transition from laminar to chaos in MHD mixed convection of a lid-driven trapezoidal cavity filled with Cu-water nanofluid

DOE Office of Scientific and Technical Information (OSTI.GOV)

Azam, Mohammad, E-mail: azam09mebuet@gmail.com; Hasanuzzaman, Md., E-mail: hasanuzzaman138@gmail.com; Saha, Sumon, E-mail: sumonsaha@me.buet.ac.bd

2016-07-12

The present study investigates the thermal mixing scenarios of steady magneto-hydrodynamic (MHD) mixed convection in a two-dimensional lid-driven trapezoidal cavity filled with Cu-water nanofluid. The top wall of the cavity slides with a uniform velocity from left to right direction, while the other walls are fixed. The bottom wall is kept with a constant higher temperature than the top one. The governing mass, momentum and energy equations are expressed in non-dimensional forms and Galerkin finite element method has been employed to solve these equations. Special attention is paid on investigating the onset of transition from laminar to chaos at puremore » mixed convection case. Hence, the computations are carried out for a wide range of Reynolds numbers (Re = 0.1 − 400) and Grashof numbers (Gr = 10{sup −2} − 1.6 × 10{sup 5}) at unity Richardson number and fixed Hartmann number (Ha = 10). The variation of average Nusselt number of the bottom heated wall indicates the influence of governing parameters (Re and Gr) on heat transfer characteristics. The results are presented and explained through the visualisation of isotherms, streamlines and heatlines.« less

Mixed convection flow of sodium alginate (SA-NaAlg) based molybdenum disulphide (MoS2) nanofluids: Maxwell Garnetts and Brinkman models

NASA Astrophysics Data System (ADS)

Ahmed, Tarek Nabil; Khan, Ilyas

2018-03-01

This article aims to study the mixed convection heat transfer in non-Newtonian nanofluids over an infinite vertical plate. Mixed convection is caused due to buoyancy force and sudden plate motion. Sodium alginate (SA-NaAlg) is considered as non-Newtonian base fluid and molybdenum disulphide (MoS2) as nanoparticles are suspended in it. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell-Garnetts (MG) and Brinkman models, respectively. The flow is modeled in the form of partial differential equations with imposed physical conditions. Exact solutions for velocity and temperature fields are developed by means of the Laplace transform technique. Numerical computations are performed for different governing parameters such as non-Newtonian parameter, Grashof number and nanoparticle volume fraction and the results are plotted in various graphs. Results for skin friction and Nusselt number are presented in tabular form which show that increasing nanoparticle volume fraction leads to heat transfer enhancement and increasing skin friction.

Numerical and Experimental Studies of the Natural Convection Flow Within a Horizontal Cylinder Subjected to a Uniformly Cold Wall Boundary Condition. Ph.D. Thesis - Va. Poly. Inst. and State Univ.

NASA Technical Reports Server (NTRS)

Stewart, R. B.

1972-01-01

Numberical solutions are obtained for the quasi-compressible Navier-Stokes equations governing the time dependent natural convection flow within a horizontal cylinder. The early time flow development and wall heat transfer is obtained after imposing a uniformly cold wall boundary condition on the cylinder. Solutions are also obtained for the case of a time varying cold wall boundary condition. Windware explicit differ-encing is used for the numerical solutions. The viscous truncation error associated with this scheme is controlled so that first order accuracy is maintained in time and space. The results encompass a range of Grashof numbers from 8.34 times 10,000 to 7 times 10 to the 7th power which is within the laminar flow regime for gravitationally driven fluid flows. Experiments within a small scale instrumented horizontal cylinder revealed the time development of the temperature distribution across the boundary layer and also the decay of wall heat transfer with time.

Effect of axial magnetic field on three-dimensional instability of natural convection in a vertical Bridgman growth configuration

NASA Astrophysics Data System (ADS)

Gelfgat, A. Yu.; Bar-Yoseph, P. Z.; Solan, A.

2001-08-01

A study of the effect of an externally imposed magnetic field on the axisymmetry-breaking instability of an axisymmetric convective flow, associated with crystal growth from bulk of melt, is presented. Convection in a vertical cylinder with a parabolic temperature profile on the sidewall is considered as a representative model. A parametric study of the dependence of the critical Grashof number Gr cr on the Hartmann number Ha for fixed values of the Prandtl number (Pr=0.015) and the aspect ratio of the cylinder ( A=height/radius=1, 2 and 3) is carried out. The stability diagram Gr cr(Ha) corresponding to the axisymmetric—three-dimensional transition for increasing values of the axial magnetic field is obtained. The calculations are done using the spectral Galerkin method allowing an effective and accurate three-dimensional stability analysis. It is shown that at relatively small values of Ha the axisymmetric flow tends to be oscillatory unstable. After the magnitude of the magnetic field (Ha) exceeds a certain value the instability switches to a steady bifurcation caused by the Rayleigh-Bénard mechanism.

Opposed-flow flame spread and extinction in mixed-convection boundary layers

NASA Technical Reports Server (NTRS)

Altenkirch, R. A.; Wedha-Nayagam, M.

1989-01-01

Experimental data for flame spread down thin fuel samples in an opposing, mixed-convection, boundary-layer flow are analyzed to determine the gas-phase velocity that characterizes how the flame reacts as it spreads toward the leading edge of the fuel sample into a thinning boundary layer. In the forced-flow limit where the cube of the Reynolds number divided by the Grashof number, Re exp 3/Gr, is large, L(q)/L(e), where L(q) is a theoretical flame standoff distance at extinction and L(e) is the measured distance from the leading edge of the sample where extinction occurs, is found to be proportional to Re exp n with n = -0.874 and Re based on L(e). The value of n is established by the character of the flow field near the leading edge of the flame. The Re dependence is used, along with a correction for the mixed-convection situation where Re exp 3/Gr is not large, to construct a Damkohler number with which the measured spread rates correlate for all values of Re exp 3/Gr.

Development of thermal stratification and destratification scaling concepts. Volume 1: Definition of thermal stratification scaling parameters and experimental investigations

NASA Technical Reports Server (NTRS)

Lovrich, T. N.; Schwartz, S. H.

1975-01-01

The dimensionless parameters associated with the thermal stratification and pressure history of a heated container of liquid and its vapor were examined. The Modified Grashof number, the Fourier number, and an Interface number were parameterized using a single test liquid, Freon 113. Cylindrical test tanks with spherical dome end caps were built. Blanket heaters covered the tanks and thermocouples monitored the temperatures of the liquid, the ullage, the tank walls, and the foam insulation encapsulating the tank. A centrifuge was used for the 6 inch tank to preserve the same scaling parameter values between it and the larger tanks. Tests were conducted over a range of Gr* values and the degree of scaling was checked by comparing the dimensionless pressures and temperatures for each scaled pair of tests. Results indicate that the bulk liquid temperature, the surface temperature of the liquid, and the tank pressure can be scaled with the three dimensionless parameters. Some deviation was, however, found in the detailed temperature profiles between the scaled pairs of tests.

Bio-mathematical analysis for the peristaltic flow of single wall carbon nanotubes under the impact of variable viscosity and wall properties.

PubMed

Shahzadi, Iqra; Sadaf, Hina; Nadeem, Sohail; Saleem, Anber

2017-02-01

The main objective of this paper is to study the Bio-mathematical analysis for the peristaltic flow of single wall carbon nanotubes under the impact of variable viscosity and wall properties. The right and the left walls of the curved channel possess sinusoidal wave that is travelling along the outer boundary. The features of the peristaltic motion are determined by using long wavelength and low Reynolds number approximation. Exact solutions are determined for the axial velocity and for the temperature profile. Graphical results have been presented for velocity profile, temperature and stream function for various physical parameters of interest. Symmetry of the curved channel is disturbed for smaller values of the curvature parameter. It is found that the altitude of the velocity profile increases for larger values of variable viscosity parameter for both the cases (pure blood as well as single wall carbon nanotubes). It is detected that velocity profile increases with increasing values of rigidity parameter. It is due to the fact that an increase in rigidity parameter decreases tension in the walls of the blood vessels which speeds up the blood flow for pure blood as well as single wall carbon nanotubes. Increase in Grashof number decreases the fluid velocity. This is due to the reason that viscous forces play a prominent role that's why increase in Grashof number decreases the velocity profile. It is also found that temperature drops for increasing values of nanoparticle volume fraction. Basically, higher thermal conductivity of the nanoparticles plays a key role for quick heat dissipation, and this justifies the use of the single wall carbon nanotubes in different situations as a coolant. Exact solutions are calculated for the temperature and the velocity profile. Symmetry of the curved channel is destroyed due to the curvedness for velocity, temperature and contour plots. Addition of single wall carbon nanotubes shows a decrease in fluid temperature. Trapping

Determining modes for the 3D Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Cheskidov, Alexey; Dai, Mimi; Kavlie, Landon

2018-07-01

We introduce a determining wavenumber for the forced 3D Navier-Stokes equations (NSE) defined for each individual solution. Even though this wavenumber blows up if the solution blows up, its time average is uniformly bounded for all solutions on the weak global attractor. The bound is compared to Kolmogorov's dissipation wavenumber and the Grashof constant.

A study of unsteady physiological magneto-fluid flow and heat transfer through a finite length channel by peristaltic pumping.

PubMed

Tripathi, Dharmendra; Bég, O Anwar

2012-08-01

Magnetohydrodynamic peristaltic flows arise in controlled magnetic drug targeting, hybrid haemodynamic pumps and biomagnetic phenomena interacting with the human digestive system. Motivated by the objective of improving an understanding of the complex fluid dynamics in such flows, we consider in the present article the transient magneto-fluid flow and heat transfer through a finite length channel by peristaltic pumping. Reynolds number is small enough and the wavelength to diameter ratio is large enough to negate inertial effects. Analytical solutions for temperature field, axial velocity, transverse velocity, pressure gradient, local wall shear stress, volume flowrate and averaged volume flowrate are obtained. The effects of the transverse magnetic field, Grashof number and thermal conductivity on the flow patterns induced by peristaltic waves (sinusoidal propagation along the length of channel) are studied using graphical plots. The present study identifies that greater pressure is required to propel the magneto-fluid by peristaltic pumping in comparison to a non-conducting Newtonian fluid, whereas, a lower pressure is required if heat transfer is effective. The analytical solutions further provide an important benchmark for future numerical simulations.

Number Sense on the Number Line

ERIC Educational Resources Information Center

Woods, Dawn Marie; Ketterlin Geller, Leanne; Basaraba, Deni

2018-01-01

A strong foundation in early number concepts is critical for students' future success in mathematics. Research suggests that visual representations, like a number line, support students' development of number sense by helping them create a mental representation of the order and magnitude of numbers. In addition, explicitly sequencing instruction…

Analysis of heat transfer for unsteady MHD free convection flow of rotating Jeffrey nanofluid saturated in a porous medium

NASA Astrophysics Data System (ADS)

Mohd Zin, Nor Athirah; Khan, Ilyas; Shafie, Sharidan; Alshomrani, Ali Saleh

In this article, the influence of thermal radiation on unsteady magnetohydrodynamics (MHD) free convection flow of rotating Jeffrey nanofluid passing through a porous medium is studied. The silver nanoparticles (AgNPs) are dispersed in the Kerosene Oil (KO) which is chosen as conventional base fluid. Appropriate dimensionless variables are used and the system of equations is transformed into dimensionless form. The resulting problem is solved using the Laplace transform technique. The impact of pertinent parameters including volume fraction φ , material parameters of Jeffrey fluid λ1 , λ , rotation parameter r , Hartmann number Ha , permeability parameter K , Grashof number Gr , Prandtl number Pr , radiation parameter Rd and dimensionless time t on velocity and temperature profiles are presented graphically with comprehensive discussions. It is observed that, the rotation parameter, due to the Coriolis force, tends to decrease the primary velocity but reverse effect is observed in the secondary velocity. It is also observed that, the Lorentz force retards the fluid flow for both primary and secondary velocities. The expressions for skin friction and Nusselt number are also evaluated for different values of emerging parameters. A comparative study with the existing published work is provided in order to verify the present results. An excellent agreement is found.

A numerical study of magnetohydrodynamic transport of nanofluids over a vertical stretching sheet with exponential temperature-dependent viscosity and buoyancy effects

NASA Astrophysics Data System (ADS)

Akbar, Noreen Sher; Tripathi, Dharmendra; Khan, Zafar Hayat; Bég, O. Anwar

2016-09-01

In this paper, a mathematical study is conducted of steady incompressible flow of a temperature-dependent viscous nanofluid from a vertical stretching sheet under applied external magnetic field and gravitational body force effects. The Reynolds exponential viscosity model is deployed. Electrically-conducting nanofluids are considered which comprise a suspension of uniform dimension nanoparticles suspended in viscous base fluid. The nanofluid sheet is extended with a linear velocity in the axial direction. The Buonjiornio model is utilized which features Brownian motion and thermophoresis effects. The partial differential equations for mass, momentum, energy and species (nano-particle concentration) are formulated with magnetic body force term. Viscous and Joule dissipation effects are neglected. The emerging nonlinear, coupled, boundary value problem is solved numerically using the Runge-Kutta fourth order method along with a shooting technique. Graphical solutions for velocity, temperature, concentration field, skin friction and Nusselt number are presented. Furthermore stream function plots are also included. Validation with Nakamura's finite difference algorithm is included. Increasing nanofluid viscosity is observed to enhance temperatures and concentrations but to reduce velocity magnitudes. Nusselt number is enhanced with both thermal and species Grashof numbers whereas it is reduced with increasing thermophoresis parameter and Schmidt number. The model is applicable in nano-material manufacturing processes involving extruding sheets.

The Mental Number Line in Dyscalculia: Impaired Number Sense or Access From Symbolic Numbers?

PubMed

Lafay, Anne; St-Pierre, Marie-Catherine; Macoir, Joël

Numbers may be manipulated and represented mentally over a compressible number line oriented from left to right. According to numerous studies, one of the primary reasons for dyscalculia is related to improper understanding of the mental number line. Children with dyscalculia usually show difficulty when they have to place Arabic numbers on a physical number line. However, it remains unclear whether they have a deficit with the mental number line per se or a deficit with accessing it from nonsymbolic and/or symbolic numbers. Quebec French-speaking 8- to 9-year-old children with (24) and without (37) dyscalculia were assessed with transcoding tasks ( number-to-position and position-to-number) designed to assess the acuity of the mental number line with Arabic and spoken numbers as well as with analogic numerosities. Results showed that children with dyscalculia produced a larger percentage absolute error than children without mathematics difficulties in every task except the number-to-position transcoding task with analogic numerosities. Hence, these results suggested that children with dyscalculia do not have a general deficit of the mental number line but rather a deficit with accessing it from symbolic numbers.

Beyond Natural Numbers: Negative Number Representation in Parietal Cortex

PubMed Central

Blair, Kristen P.; Rosenberg-Lee, Miriam; Tsang, Jessica M.; Schwartz, Daniel L.; Menon, Vinod

2012-01-01

Unlike natural numbers, negative numbers do not have natural physical referents. How does the brain represent such abstract mathematical concepts? Two competing hypotheses regarding representational systems for negative numbers are a rule-based model, in which symbolic rules are applied to negative numbers to translate them into positive numbers when assessing magnitudes, and an expanded magnitude model, in which negative numbers have a distinct magnitude representation. Using an event-related functional magnetic resonance imaging design, we examined brain responses in 22 adults while they performed magnitude comparisons of negative and positive numbers that were quantitatively near (difference <4) or far apart (difference >6). Reaction times (RTs) for negative numbers were slower than positive numbers, and both showed a distance effect whereby near pairs took longer to compare. A network of parietal, frontal, and occipital regions were differentially engaged by negative numbers. Specifically, compared to positive numbers, negative number processing resulted in greater activation bilaterally in intraparietal sulcus (IPS), middle frontal gyrus, and inferior lateral occipital cortex. Representational similarity analysis revealed that neural responses in the IPS were more differentiated among positive numbers than among negative numbers, and greater differentiation among negative numbers was associated with faster RTs. Our findings indicate that despite negative numbers engaging the IPS more strongly, the underlying neural representation are less distinct than that of positive numbers. We discuss our findings in the context of the two theoretical models of negative number processing and demonstrate how multivariate approaches can provide novel insights into abstract number representation. PMID:22363276

Beyond natural numbers: negative number representation in parietal cortex.

PubMed

Blair, Kristen P; Rosenberg-Lee, Miriam; Tsang, Jessica M; Schwartz, Daniel L; Menon, Vinod

2012-01-01

Unlike natural numbers, negative numbers do not have natural physical referents. How does the brain represent such abstract mathematical concepts? Two competing hypotheses regarding representational systems for negative numbers are a rule-based model, in which symbolic rules are applied to negative numbers to translate them into positive numbers when assessing magnitudes, and an expanded magnitude model, in which negative numbers have a distinct magnitude representation. Using an event-related functional magnetic resonance imaging design, we examined brain responses in 22 adults while they performed magnitude comparisons of negative and positive numbers that were quantitatively near (difference <4) or far apart (difference >6). Reaction times (RTs) for negative numbers were slower than positive numbers, and both showed a distance effect whereby near pairs took longer to compare. A network of parietal, frontal, and occipital regions were differentially engaged by negative numbers. Specifically, compared to positive numbers, negative number processing resulted in greater activation bilaterally in intraparietal sulcus (IPS), middle frontal gyrus, and inferior lateral occipital cortex. Representational similarity analysis revealed that neural responses in the IPS were more differentiated among positive numbers than among negative numbers, and greater differentiation among negative numbers was associated with faster RTs. Our findings indicate that despite negative numbers engaging the IPS more strongly, the underlying neural representation are less distinct than that of positive numbers. We discuss our findings in the context of the two theoretical models of negative number processing and demonstrate how multivariate approaches can provide novel insights into abstract number representation.

Natural convection heat transfer in an oscillating vertical cylinder

PubMed Central

Ali Shah, Nehad; Tassaddiq, Asifa; Mustapha, Norzieha; Kechil, Seripah Awang

2018-01-01

This paper studies the heat transfer analysis caused due to free convection in a vertically oscillating cylinder. Exact solutions are determined by applying the Laplace and finite Hankel transforms. Expressions for temperature distribution and velocity field corresponding to cosine and sine oscillations are obtained. The solutions that have been obtained for velocity are presented in the forms of transient and post-transient solutions. Moreover, these solutions satisfy both the governing differential equation and all imposed initial and boundary conditions. Numerical computations and graphical illustrations are used in order to study the effects of Prandtl and Grashof numbers on velocity and temperature for various times. The transient solutions for both cosine and sine oscillations are also computed in tables. It is found that, the transient solutions are of considerable interest up to the times t = 15 for cosine oscillations and t = 1.75 for sine oscillations. After these moments, the transient solutions can be neglected and, the fluid moves according with the post-transient solutions. PMID:29304161

Natural convection heat transfer in an oscillating vertical cylinder.

PubMed

Khan, Ilyas; Ali Shah, Nehad; Tassaddiq, Asifa; Mustapha, Norzieha; Kechil, Seripah Awang

2018-01-01

This paper studies the heat transfer analysis caused due to free convection in a vertically oscillating cylinder. Exact solutions are determined by applying the Laplace and finite Hankel transforms. Expressions for temperature distribution and velocity field corresponding to cosine and sine oscillations are obtained. The solutions that have been obtained for velocity are presented in the forms of transient and post-transient solutions. Moreover, these solutions satisfy both the governing differential equation and all imposed initial and boundary conditions. Numerical computations and graphical illustrations are used in order to study the effects of Prandtl and Grashof numbers on velocity and temperature for various times. The transient solutions for both cosine and sine oscillations are also computed in tables. It is found that, the transient solutions are of considerable interest up to the times t = 15 for cosine oscillations and t = 1.75 for sine oscillations. After these moments, the transient solutions can be neglected and, the fluid moves according with the post-transient solutions.

The Mental Number Line in Dyscalculia: Impaired Number Sense or Access from Symbolic Numbers?

ERIC Educational Resources Information Center

Lafay, Anne; St-Pierre, Marie-Catherine; Macoir, Joël

2017-01-01

Numbers may be manipulated and represented mentally over a compressible number line oriented from left to right. According to numerous studies, one of the primary reasons for dyscalculia is related to improper understanding of the mental number line. Children with dyscalculia usually show difficulty when they have to place Arabic numbers on a…

Parameterizing by the Number of Numbers

NASA Astrophysics Data System (ADS)

Fellows, Michael R.; Gaspers, Serge; Rosamond, Frances A.

The usefulness of parameterized algorithmics has often depended on what Niedermeier has called "the art of problem parameterization". In this paper we introduce and explore a novel but general form of parameterization: the number of numbers. Several classic numerical problems, such as Subset Sum, Partition, 3-Partition, Numerical 3-Dimensional Matching, and Numerical Matching with Target Sums, have multisets of integers as input. We initiate the study of parameterizing these problems by the number of distinct integers in the input. We rely on an FPT result for Integer Linear Programming Feasibility to show that all the above-mentioned problems are fixed-parameter tractable when parameterized in this way. In various applied settings, problem inputs often consist in part of multisets of integers or multisets of weighted objects (such as edges in a graph, or jobs to be scheduled). Such number-of-numbers parameterized problems often reduce to subproblems about transition systems of various kinds, parameterized by the size of the system description. We consider several core problems of this kind relevant to number-of-numbers parameterization. Our main hardness result considers the problem: given a non-deterministic Mealy machine M (a finite state automaton outputting a letter on each transition), an input word x, and a census requirement c for the output word specifying how many times each letter of the output alphabet should be written, decide whether there exists a computation of M reading x that outputs a word y that meets the requirement c. We show that this problem is hard for W[1]. If the question is whether there exists an input word x such that a computation of M on x outputs a word that meets c, the problem becomes fixed-parameter tractable.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Riggs, J.B.

An experimental test model, which is dynamically similar to an actual UCC (Underground Coal Conversion) system, has been used to determine fluid flow patterns and local heat transfer that occur in the UCC burn cavity. This study was designed to provide insight into the little understood mechanisms (i.e., heat transfer and oxygen transport to the cavity walls) which control maximum cavity width, and therefore resource recovery during UCC. The dynamically similar flow model has been designed by equating the Grashof and Reynolds number of the UCC system and the flow model, which employs water as its fluid. Equating the Grashofmore » number results in a scale factor of 0.13 while equating the Reynolds number yields a volumetric flow rate of water for the model of 30 gallons per minute. Qualitative studies were conducted with the flow model for both a void cavity and a cavity partially filled with simulated rubble. These studies provided insight into the combined effects of forced and free convection in a UCC cavity. In addition, dimensionless correlations were developed for the heat transfer to side walls for the case of a void cavity and these results can be used to predict oxygen transport to the side wall in a UCC cavity.« less

Lagrangian transport in a class of three-dimensional buoyancy-driven flows

NASA Astrophysics Data System (ADS)

Contreras, Sebastian; Speetjens, Michel; Clercx, Herman

2017-11-01

The study concerns the Lagrangian dynamics of three-dimensional (3D) buoyancy-driven cavity flows under steady and laminar conditions due to a global temperature gradient imposed via an opposite hot and cold sidewall. This serves as archetypal configuration for natural-convection flows in which gravity is perpendicular to the global temperature gradient. Limited insight into the Lagrangian properties of this class of flows motivates this study. The 3D Lagrangian dynamics are investigated in terms of the generic structure of the Lagrangian flow topology that is described in terms of the Grashof number (Gr) and the Prandtl number (Pr). Gr is the principal control parameter for the flow topology: vanishing Gr yields a state of closed streamlines (integrable state); increasing Gr causes the formation of toroidal coherent structures embedded in chaotic streamlines governed by Hamiltonian mechanisms. Fluid inertia prevails for ``smaller'' Gr. A buoyancy-induced bifurcation of the flow topology occurs for ``larger'' Gr and underlies the emergence of ``secondary rolls'' and secondary tori for ``larger'' Pr. Stagnation points and corresponding manifold interactions are key to the dynamics. S.C. acknowledges financial support from Consejo Nacional de Ciencia y Tecnología (CONACYT).

Nanostructures study of CNT nanofluids transport with temperature-dependent variable viscosity in a muscular tube

NASA Astrophysics Data System (ADS)

Akbar, Noreen Sher; Abid, Syed Ali; Tripathi, Dharmendra; Mir, Nazir Ahmed

2017-03-01

The transport of single-wall carbon nanotube (CNT) nanofluids with temperature-dependent variable viscosity is analyzed by peristaltically driven flow. The main flow problem has been modeled using cylindrical coordinates and flow equations are simplified to ordinary differential equations using long wavelength and low Reynolds' number approximation. Analytical solutions have been obtained for axial velocity, pressure gradient and temperature. Results acquired are discussed graphically for better understanding. It is observed that with an increment in the Grashof number the velocity of the governing fluids starts to decrease significantly and the pressure gradient is higher for pure water as compared to single-walled carbon nanotubes due to low density. As the specific heat is very high for pure water as compared to the multi-wall carbon nanotubes, it raises temperature of the muscles, in the case of pure water, as compared to the multi-walled carbon nanotubes. Furthermore, it is noticed that the trapped bolus starts decreasing in size as the buoyancy forces are dominant as compared to viscous forces. This model may be applicable in biomedical engineering and nanotechnology to design the biomedical devices.

A scientific report on heat transfer analysis in mixed convection flow of Maxwell fluid over an oscillating vertical plate.

PubMed

Khan, Ilyas; Shah, Nehad Ali; Dennis, L C C

2017-03-15

This scientific report investigates the heat transfer analysis in mixed convection flow of Maxwell fluid over an oscillating vertical plate with constant wall temperature. The problem is modelled in terms of coupled partial differential equations with initial and boundary conditions. Some suitable non-dimensional variables are introduced in order to transform the governing problem into dimensionless form. The resulting problem is solved via Laplace transform method and exact solutions for velocity, shear stress and temperature are obtained. These solutions are greatly influenced with the variation of embedded parameters which include the Prandtl number and Grashof number for various times. In the absence of free convection, the corresponding solutions representing the mechanical part of velocity reduced to the well known solutions in the literature. The total velocity is presented as a sum of both cosine and sine velocities. The unsteady velocity in each case is arranged in the form of transient and post transient parts. It is found that the post transient parts are independent of time. The solutions corresponding to Newtonian fluids are recovered as a special case and comparison between Newtonian fluid and Maxwell fluid is shown graphically.

A scientific report on heat transfer analysis in mixed convection flow of Maxwell fluid over an oscillating vertical plate

NASA Astrophysics Data System (ADS)

Khan, Ilyas; Shah, Nehad Ali; Dennis, L. C. C.

2017-03-01

This scientific report investigates the heat transfer analysis in mixed convection flow of Maxwell fluid over an oscillating vertical plate with constant wall temperature. The problem is modelled in terms of coupled partial differential equations with initial and boundary conditions. Some suitable non-dimensional variables are introduced in order to transform the governing problem into dimensionless form. The resulting problem is solved via Laplace transform method and exact solutions for velocity, shear stress and temperature are obtained. These solutions are greatly influenced with the variation of embedded parameters which include the Prandtl number and Grashof number for various times. In the absence of free convection, the corresponding solutions representing the mechanical part of velocity reduced to the well known solutions in the literature. The total velocity is presented as a sum of both cosine and sine velocities. The unsteady velocity in each case is arranged in the form of transient and post transient parts. It is found that the post transient parts are independent of time. The solutions corresponding to Newtonian fluids are recovered as a special case and comparison between Newtonian fluid and Maxwell fluid is shown graphically.

The Effect of MHD on Free Convection with Periodic Temperature and Concentration in the Presence of Thermal Radiation and Chemical Reaction

NASA Astrophysics Data System (ADS)

Zigta, B.; Koya, P. R.

2017-12-01

This paper studies the effect of magneto hydrodynamics on unsteady free convection between a pair of infinite vertical Couette plates. The temperature of the plates and concentration between the plates vary with time. Convection between the plates is considered in the presence of thermal radiation and chemical reaction. The solution is obtained using perturbation techniques. These techniques are used to transform nonlinear coupled partial differential equations to a system of ordinary differential equations. The resulting equations are solved analytically. The solution is expressed in terms of power series with some small parameter. The effect of various parameters, viz., velocity, temperature and concentration, has been discussed. Mat lab code simulation study is carried out to support the theoretical results. The result shows that as the thermal radiation parameter R increases, the temperature decreases near the moving porous plate while it approaches to a zero in the region close to the boundary layer of the stationary plate. Moreover, as the modified Grashof number, i.e., based on concentration difference, increases, the velocity of the fluid flow increases hence the concentration decreases. An increase in both the chemical reaction parameter and Schmidt number results in decreased concentration.

A scientific report on heat transfer analysis in mixed convection flow of Maxwell fluid over an oscillating vertical plate

PubMed Central

Khan, Ilyas; Shah, Nehad Ali; Dennis, L. C. C.

2017-01-01

This scientific report investigates the heat transfer analysis in mixed convection flow of Maxwell fluid over an oscillating vertical plate with constant wall temperature. The problem is modelled in terms of coupled partial differential equations with initial and boundary conditions. Some suitable non-dimensional variables are introduced in order to transform the governing problem into dimensionless form. The resulting problem is solved via Laplace transform method and exact solutions for velocity, shear stress and temperature are obtained. These solutions are greatly influenced with the variation of embedded parameters which include the Prandtl number and Grashof number for various times. In the absence of free convection, the corresponding solutions representing the mechanical part of velocity reduced to the well known solutions in the literature. The total velocity is presented as a sum of both cosine and sine velocities. The unsteady velocity in each case is arranged in the form of transient and post transient parts. It is found that the post transient parts are independent of time. The solutions corresponding to Newtonian fluids are recovered as a special case and comparison between Newtonian fluid and Maxwell fluid is shown graphically. PMID:28294186

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 office...

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 office...

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 office...

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 office...

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 office...

A non-linear study of fluctuating fluid flow on MHD mixed convection through a vertical permeable plate

NASA Astrophysics Data System (ADS)

Babu, R. Suresh; Rushi Kumar, B.

2017-11-01

In this paper, an analytical solution for an unsteady (independent of time), MHD mixed convection, two-dimensional (x and y), laminar, viscous flow of an incompressible fluid through a vertical permeable plate in a porous medium was developed with these assumptions:(i) the suction velocity (which is normal to the plate)and the free stream velocity both fluctuate with respect to time with a fixed mean; (ii) the wall temperature is constant;(iii) difference between the temperature of the plate and the free stream is moderately large due to the free convection currents. Based on the physical configuration of the model, the governing equations are derived and are non-dimensionalize using dimensionless parameters. The resultant nonlinear partial differential equations are solved using double regular perturbation technique analytically. The results are computed numerically to understand the behaviour of the fluid (i.e., effects of MHD, viscosity, body force etc.) for various non-dimensional parameters involving like Grashof number Gr, Prandtl number Pr, Hartmann number M, Eckert number E, the Viscous ratio λ and so on for velocity and temperature. These results are found to be in good agreement with known results available in the literature in the absence of few physical parameters. The numerical values of the above said flow is discussed through graphs on velocity and temperature.

MHD biconvective flow of Powell Eyring nanofluid over stretched surface

NASA Astrophysics Data System (ADS)

Naseem, Faiza; Shafiq, Anum; Zhao, Lifeng; Naseem, Anum

2017-06-01

The present work is focused on behavioral characteristics of gyrotactic microorganisms to describe their role in heat and mass transfer in the presence of magnetohydrodynamic (MHD) forces in Powell-Eyring nanofluids. Implications concerning stretching sheet with respect to velocity, temperature, nanoparticle concentration and motile microorganism density were explored to highlight influential parameters. Aim of utilizing microorganisms was primarily to stabilize the nanoparticle suspension due to bioconvection generated by the combined effects of buoyancy forces and magnetic field. Influence of Newtonian heating was also analyzed by taking into account thermophoretic mechanism and Brownian motion effects to insinuate series solutions mediated by homotopy analysis method (HAM). Mathematical model captured the boundary layer regime that explicitly involved contemporary non linear partial differential equations converted into the ordinary differential equations. To depict nanofluid flow characteristics, pertinent parameters namely bioconvection Lewis number Lb, traditional Lewis number Le, bioconvection Péclet number Pe, buoyancy ratio parameter Nr, bioconvection Rayleigh number Rb, thermophoresis parameter Nt, Hartmann number M, Grashof number Gr, and Eckert number Ec were computed and analyzed. Results revealed evidence of hydromagnetic bioconvection for microorganism which was represented by graphs and tables. Our findings further show a significant effect of Newtonian heating over a stretching plate by examining the coefficient values of skin friction, local Nusselt number and the local density number. Comparison was made between Newtonian fluid and Powell-Eyring fluid on velocity field and temperature field. Results are compared of with contemporary studies and our findings are found in excellent agreement with these studies.

Number sense in the transition from natural to rational numbers.

PubMed

Van Hoof, Jo; Verschaffel, Lieven; Van Dooren, Wim

2017-03-01

Rational numbers are of critical importance both in mathematics and in other fields of science. However, they form a stumbling block for learners. One widely known source of the difficulty learners have with rational numbers is the natural number bias, that is the tendency to (inappropriately) apply natural number properties in rational number tasks. Still, it has been shown that a good understanding of natural numbers is highly predictive for mathematics achievement in general, and for performance on rational number tasks in particular. In this study, we further investigated the relation between learners' natural and rational number knowledge, specifically in cases where a natural number bias may lead to errors. Participants were 140 sixth graders from six different primary schools. Participants completed a symbolic and a non-symbolic natural number comparison task, a number line estimation task, and a rational number sense test. Learners' natural number knowledge was found to be a good predictor of their rational number knowledge. However, after first controlling for learners' general mathematics achievement, their natural number knowledge only predicted the subaspect of operations with rational numbers. The results of this study suggest that the relation between learners' natural and rational number knowledge can largely be explained by their relation with learners' general mathematics achievement. © 2016 The British Psychological Society.

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

ERIC Educational Resources Information Center

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

2013-01-01

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

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…

Promote Number Sense

ERIC Educational Resources Information Center

Gurganus, Susan

2004-01-01

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

Rational-number comparison across notation: Fractions, decimals, and whole numbers.

PubMed

Hurst, Michelle; Cordes, Sara

2016-02-01

Although fractions, decimals, and whole numbers can be used to represent the same rational-number values, it is unclear whether adults conceive of these rational-number magnitudes as lying along the same ordered mental continuum. In the current study, we investigated whether adults' processing of rational-number magnitudes in fraction, decimal, and whole-number notation show systematic ratio-dependent responding characteristic of an integrated mental continuum. Both reaction time (RT) and eye-tracking data from a number-magnitude comparison task revealed ratio-dependent performance when adults compared the relative magnitudes of rational numbers, both within the same notation (e.g., fractions vs. fractions) and across different notations (e.g., fractions vs. decimals), pointing to an integrated mental continuum for rational numbers across notation types. In addition, eye-tracking analyses provided evidence of an implicit whole-number bias when we compared values in fraction notation, and individual differences in this whole-number bias were related to the individual's performance on a fraction arithmetic task. Implications of our results for both cognitive development research and math education are discussed. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

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

PubMed

Whyte, Jemma Catherine; Bull, Rebecca

2008-03-01

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

Numbers Defy the Law of Large Numbers

ERIC Educational Resources Information Center

Falk, Ruma; Lann, Avital Lavie

2015-01-01

As the number of independent tosses of a fair coin grows, the rates of heads and tails tend to equality. This is misinterpreted by many students as being true also for the absolute numbers of the two outcomes, which, conversely, depart unboundedly from each other in the process. Eradicating that misconception, as by coin-tossing experiments,…

Number 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…

Flow of magnetic particles in blood with isothermal heating: A fractional model for two-phase flow

NASA Astrophysics Data System (ADS)

Ali, Farhad; Imtiaz, Anees; Khan, Ilyas; Sheikh, Nadeem Ahmad

2018-06-01

In the sixteenth century, medical specialists were of the conclusion that magnet can be utilized for the treatment or wipe out the illnesses from the body. On this basis, the research on magnet advances day by day for the treatment of different types of diseases in mankind. This study aims to investigate the effect of magnetic field and their applications in human body specifically in blood. Blood is a non-Newtonian fluid because its viscosity depends strongly on the fraction of volume occupied by red cells also called the hematocrit. Therefore, in this paper blood is considered as an example of non-Newtonian Casson fluid. The blood flow is considered in a vertical cylinder together with heat transfer due to mixed conviction caused by buoyancy force and the external pressure gradient. Effect of magnetic field on the velocities of blood and magnetic particles is also considered. The problem is modelled using the Caputo-Fabrizio derivative approach. The governing fractional partial differential equations are solved using Laplace and Hankel transformation techniques and exact solutions are obtained. Effects of different parameters such as Grashof number, Prandtl number, Casson fluid parameter and fractional parameters, and magnetic field are shown graphically. Both velocity profiles increase with the increase of Grashoff number and Casson fluid parameter and reduce with the increase of magnetic field.

Hupa Numbers.

ERIC Educational Resources Information Center

Bennett, Ruth, Ed.; And Others

An introduction to the Hupa number system is provided in this workbook, one in a series of numerous materials developed to promote the use of the Hupa language. The book is written in English with Hupa terms used only for the names of numbers. The opening pages present the numbers from 1-10, giving the numeral, the Hupa word, the English word, and…

Number Sense in the Transition from Natural to Rational Numbers

ERIC Educational Resources Information Center

Van Hoof, Jo; Verschaffel, Lieven; Van Dooren, Wim

2017-01-01

Background: Rational numbers are of critical importance both in mathematics and in other fields of science. However, they form a stumbling block for learners. One widely known source of the difficulty learners have with rational numbers is the natural number bias, that is the tendency to (inappropriately) apply natural number properties in…

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.

Effect of finite particle number sampling on baryon number fluctuations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Steinheimer, Jan; Koch, Volker

The effects of finite particle number sampling on the net baryon number cumulants, extracted from fluid dynamical simulations, are studied. The commonly used finite particle number sampling procedure introduces an additional Poissonian (or multinomial if global baryon number conservation is enforced) contribution which increases the extracted moments of the baryon number distribution. If this procedure is applied to a fluctuating fluid dynamics framework, one severely overestimates the actual cumulants. We show that the sampling of so-called test particles suppresses the additional contribution to the moments by at least one power of the number of test particles. We demonstrate this methodmore » in a numerical fluid dynamics simulation that includes the effects of spinodal decomposition due to a first-order phase transition. Furthermore, in the limit where antibaryons can be ignored, we derive analytic formulas which capture exactly the effect of particle sampling on the baryon number cumulants. These formulas may be used to test the various numerical particle sampling algorithms.« less

Effect of finite particle number sampling on baryon number fluctuations

DOE PAGES

Steinheimer, Jan; Koch, Volker

2017-09-28

The effects of finite particle number sampling on the net baryon number cumulants, extracted from fluid dynamical simulations, are studied. The commonly used finite particle number sampling procedure introduces an additional Poissonian (or multinomial if global baryon number conservation is enforced) contribution which increases the extracted moments of the baryon number distribution. If this procedure is applied to a fluctuating fluid dynamics framework, one severely overestimates the actual cumulants. We show that the sampling of so-called test particles suppresses the additional contribution to the moments by at least one power of the number of test particles. We demonstrate this methodmore » in a numerical fluid dynamics simulation that includes the effects of spinodal decomposition due to a first-order phase transition. Furthermore, in the limit where antibaryons can be ignored, we derive analytic formulas which capture exactly the effect of particle sampling on the baryon number cumulants. These formulas may be used to test the various numerical particle sampling algorithms.« less

Estimating large numbers.

PubMed

Landy, David; Silbert, Noah; Goldin, Aleah

2013-07-01

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 predict a log-to-linear shift: People will either place numbers linearly or will place numbers according to a compressive logarithmic or power-shaped function (Barth & Paladino, ; Siegler & Opfer, ). While about half of people did estimate numbers linearly over this range, nearly all the remaining participants placed 1 million approximately halfway between 1 thousand and 1 billion, but placed numbers linearly across each half, as though they believed that the number words "thousand, million, billion, trillion" constitute a uniformly spaced count list. Participants in this group also tended to be optimistic in evaluations of largely ineffective political strategies, relative to linear number-line placers. The results indicate that the surface structure of number words can heavily influence processes for dealing with numbers in this range, and it can amplify the possibility that analogous surface regularities are partially responsible for parallel phenomena in children. In addition, these results have direct implications for lawmakers and scientists hoping to communicate effectively with the public. Copyright © 2013 Cognitive Science Society, Inc.

Approximate number sense, symbolic number processing, or number-space mappings: what underlies mathematics achievement?

PubMed

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

2013-03-01

In this study, the performance of typically developing 6- to 8-year-old children on an approximate number discrimination task, a symbolic comparison task, and a symbolic and nonsymbolic number line estimation task was examined. For the first time, children's performances on these basic cognitive number processing tasks were explicitly contrasted to investigate which of them is the best predictor of their future mathematical abilities. Math achievement was measured with a timed arithmetic test and with a general curriculum-based math test to address the additional question of whether the predictive association between the basic numerical abilities and mathematics achievement is dependent on which math test is used. Results revealed that performance on both mathematics achievement tests was best predicted by how well childrencompared digits. In addition, an association between performance on the symbolic number line estimation task and math achievement scores for the general curriculum-based math test measuring a broader spectrum of skills was found. Together, these results emphasize the importance of learning experiences with symbols for later math abilities. Copyright © 2012 Elsevier Inc. All rights reserved.

Numerical study of magnetic field on mixed convection and entropy generation of nanofluid in a trapezoidal enclosure

NASA Astrophysics Data System (ADS)

Aghaei, Alireza; Khorasanizadeh, Hossein; Sheikhzadeh, Ghanbarali; Abbaszadeh, Mahmoud

2016-04-01

The flow under influence of magnetic field is experienced in cooling electronic devices and voltage transformers, nuclear reactors, biochemistry and in physical phenomenon like geology. In this study, the effects of magnetic field on the flow field, heat transfer and entropy generation of Cu-water nanofluid mixed convection in a trapezoidal enclosure have been investigated. The top lid is cold and moving toward right or left, the bottom wall is hot and the side walls are insulated and their angle from the horizon are 15°, 30°, 45° and 60°. Simulations have been carried out for constant Grashof number of 104, Reynolds numbers of 30, 100, 300 and 1000, Hartmann numbers of 25, 50, 75 and 100 and nanoparticles volume fractions of zero up to 0.04. The finite volume method and SIMPLER algorithm have been utilized to solve the governing equations numerically. The results showed that with imposing the magnetic field and enhancing it, the nanofluid convection and the strength of flow decrease and the flow tends toward natural convection and finally toward pure conduction. For this reason, for all of the considered Reynolds numbers and volume fractions, by increasing the Hartmann number the average Nusselt number decreases. Furthermore, for any case with constant Reynolds and Hartmann numbers by increasing the volume fraction of nanoparticles the maximum stream function decreases. For all of the studied cases, entropy generation due to friction is negligible and the total entropy generation is mainly due to irreversibility associated with heat transfer and variation of the total entropy generation with Hartmann number is similar to that of the average Nusselt number. With change in lid movement direction at Reynolds number of 30 the average Nusselt number and total entropy generation are changed, but at Reynolds number of 1000 it has a negligible effect.

Are Numbers Gendered?

ERIC Educational Resources Information Center

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

2012-01-01

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

On the relation between grammatical number and cardinal numbers in development.

PubMed

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.

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.

Are numbers gendered?

PubMed

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.

27 CFR 20.179 - Package identification number or serial number.

Code of Federal Regulations, 2011 CFR

2011-04-01

... the time of a change, the numbering series in use at the time of the change may be continued. (Sec... at the same time on which all of the marks required by § 20.178 (a)(1) and (a)(3) through (a)(8) are... number “1” and continuing in regular sequence. The dealer shall use a separate but similar number series...

27 CFR 20.179 - Package identification number or serial number.

Code of Federal Regulations, 2013 CFR

2013-04-01

... the time of a change, the numbering series in use at the time of the change may be continued. (Sec... at the same time on which all of the marks required by § 20.178 (a)(1) and (a)(3) through (a)(8) are... number “1” and continuing in regular sequence. The dealer shall use a separate but similar number series...

27 CFR 20.179 - Package identification number or serial number.

Code of Federal Regulations, 2012 CFR

2012-04-01

... the time of a change, the numbering series in use at the time of the change may be continued. (Sec... at the same time on which all of the marks required by § 20.178 (a)(1) and (a)(3) through (a)(8) are... number “1” and continuing in regular sequence. The dealer shall use a separate but similar number series...

27 CFR 20.179 - Package identification number or serial number.

Code of Federal Regulations, 2014 CFR

2014-04-01

... the time of a change, the numbering series in use at the time of the change may be continued. (Sec... at the same time on which all of the marks required by § 20.178 (a)(1) and (a)(3) through (a)(8) are... number “1” and continuing in regular sequence. The dealer shall use a separate but similar number series...

27 CFR 20.179 - Package identification number or serial number.

Code of Federal Regulations, 2010 CFR

2010-04-01

... the time of a change, the numbering series in use at the time of the change may be continued. (Sec... at the same time on which all of the marks required by § 20.178 (a)(1) and (a)(3) through (a)(8) are... number “1” and continuing in regular sequence. The dealer shall use a separate but similar number series...

Ordering of Z-numbers

NASA Astrophysics Data System (ADS)

Mohamad, Daud; Shaharani, Saidatull Akma; Kamis, Nor Hanimah

2017-08-01

The concept of Z-number which was introduced by Zadeh in 2010 has captured attention by many due to its enormous applications in the area of Computing with Words (CWW). A Z-number is an ordered pair of fuzzy numbers, (A, R), where A essentially plays the role of fuzzy restriction which is a real-valued uncertain variable and R is a measure of reliability of the first component. Besides its theoretical development, Z-numbers have been successfully applied to decision making problems under uncertain environment. In any decision making evaluation using Z-number, ideally the final outcome of the calculation should also be in Z-number. A question will arise: how do we order the Z-numbers so that the preference of the alternatives can be ranked appropriately? In this paper, we propose a method of ordering the Z-number via the transformation of the Z-numbers to fuzzy numbers. The Z-number will then be ranked using a ranking fuzzy number method. The proposed method will be tested in several combinations of Z-numbers to investigate its effectiveness. The effect of different values of A and R towards the ordering of Z-numbers is analyzed and discussed.

Combustion of Interacting Droplet Arrays in a Microgravity Environment

NASA Technical Reports Server (NTRS)

Dietrich, Daniel L.; Struk, Peter M.; Kitano, Kunihiro; Ikeda, Koji; Honma, Senji

1997-01-01

This research program involves the study of single droplets and linear arrays of droplets in weakly-buoyant and non-bouyant environments. The primary purpose of the single droplet work was to (1) provide a data base from which to compare droplet array results and (2) to correlate the effects of buoyancy on flame shape. Traditionally convective effects in droplet combustion are represented in terms of the Reynolds number, Re, for forced convection and the Grashof number, Gr, for natural convection. Typically, corrections to the burning rate constant for convective effects are written in terms of Re or Gr(exp 1). The Stefan velocity is not included in these correlations, even though from purely physical reasons, one would expect it to be important, especially at higher burning rates. The flame distortion due to convective effects is less documented quantitatively. Kumagai and Isoda do predict flame shape in natural and forced convective flow fields. Their focus, however, was to predict the actual flame dimensions. Law and co-workers used reduced pressure, high oxidizer ambients to obtain spherical flames. This implies that buoyant flows were reduced at the low pressures, as indicated by a very small Grashof number. Ross et al, however, using scaling arguments showed that reducing the pressure does not have a large effect on the magnitude of the buoyant velocity. Struk et al showed elongated flame shapes during simulated (porous sphere) droplet combustion. The elongation of the flames was due to residual gravity levels aboard the reduced gravity aircraft on which the experiments were conducted. These flame shapes, as well as some data from the literature were interpreted based on a dimensionless grouping called the sphericity parameter, Sp. Sp is the ratio of a characteristic computed buoyant velocity to the Stefan velocity at the flame front. One purpose of the droplet arrays work is to extend the database and theories that exist for single droplets into the regime

Numbers in Action.

PubMed

Rugani, Rosa; Sartori, Luisa

2016-01-01

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

All Square Chiliagonal Numbers

ERIC Educational Resources Information Center

A?iru, Muniru A.

2016-01-01

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

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)

Universal Number Library

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lloyd, G. Scott

This floating-point arithmetic library contains a software implementation of Universal Numbers (unums) as described by John Gustafson [1]. The unum format is a superset of IEEE 754 floating point with several advantages. Computing with unums provides more accurate answers without rounding errors, underflow or overflow. In contrast to fixed-sized IEEE numbers, a variable number of bits can be used to encode unums. This all allows number with only a few significant digits or with a small dynamic range to be represented more compactly.

Estimating Large Numbers

ERIC Educational Resources Information Center

Landy, David; Silbert, Noah; Goldin, Aleah

2013-01-01

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

Efficient and robust quantum random number generation by photon number detection

DOE Office of Scientific and Technical Information (OSTI.GOV)

Applegate, M. J.; Cavendish Laboratory, University of Cambridge, 19 JJ Thomson Avenue, Cambridge CB3 0HE; Thomas, O.

2015-08-17

We present an efficient and robust quantum random number generator based upon high-rate room temperature photon number detection. We employ an electric field-modulated silicon avalanche photodiode, a type of device particularly suited to high-rate photon number detection with excellent photon number resolution to detect, without an applied dead-time, up to 4 photons from the optical pulses emitted by a laser. By both measuring and modeling the response of the detector to the incident photons, we are able to determine the illumination conditions that achieve an optimal bit rate that we show is robust against variation in the photon flux. Wemore » extract random bits from the detected photon numbers with an efficiency of 99% corresponding to 1.97 bits per detected photon number yielding a bit rate of 143 Mbit/s, and verify that the extracted bits pass stringent statistical tests for randomness. Our scheme is highly scalable and has the potential of multi-Gbit/s bit rates.« less

The Numbered Forest.

ERIC Educational Resources Information Center

Kissner, Emily

2000-01-01

Describes the activity of numbering trees in which students number trees or find the numbered trees and observe other features according to class time. This activity aims to increase student tracking, mapping, and writing skills and integrate them with math skills. Suggests follow up activities that focus on reading, writing, and language skills.…

Discovery: Prime Numbers

ERIC Educational Resources Information Center

de Mestre, Neville

2008-01-01

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

Sum-Difference Numbers

ERIC Educational Resources Information Center

Shi, Yixun

2010-01-01

Starting with an interesting number game sometimes used by school teachers to demonstrate the factorization of integers, "sum-difference numbers" are defined. A positive integer n is a "sum-difference number" if there exist positive integers "x, y, w, z" such that n = xy = wz and x ? y = w + z. This paper characterizes all sum-difference numbers…

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

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

15. Stress Sheet, Truss number 2, span number 6, Superior Avenue viaduct. Drawing courtesy Engineering Dept., City of Cleveland. - Superior Avenue Viaduct, Cleveland East & West side, Cuyahoga Valley Vicinity, Cleveland, Cuyahoga County, OH

When Numbers Get Heavy: Is the Mental Number Line Exclusively Numerical?

PubMed Central

Holmes, Kevin J.; Lourenco, Stella F.

2013-01-01

The mental number line, with its left-to-right orientation of increasing numerical values, is often regarded as evidence for a unique connection between space and number. Yet left-to-right orientation has been shown to extend to other dimensions, consistent with a general magnitude system wherein different magnitudes share neural and conceptual resources. Such observations raise a fundamental, yet relatively unexplored, question about spatial-numerical associations: What is the nature of the information represented along the mental number line? Here we show that this information is not exclusive to number, simultaneously accommodating numerical and non-numerical magnitudes. Participants completed the classic SNARC (Spatial-Numerical Association of Response Codes) task while sometimes wearing wrist weights. Weighting the left wrist–thereby linking less and more weight to right and left, respectively–worked against left-to-right orientation of number, leaving no behavioral trace of the mental number line. Our findings point to the dynamic integration of magnitude dimensions, with spatial organization instantiating representational currency (i.e., more/less relations) shared across magnitudes. PMID:23484023

Spatial displacement of numbers on a vertical number line in spatial neglect.

PubMed

Mihulowicz, Urszula; Klein, Elise; Nuerk, Hans-Christoph; Willmes, Klaus; Karnath, Hans-Otto

2015-01-01

Previous studies that investigated the association of numbers and space in humans came to contradictory conclusions about the spatial character of the mental number magnitude representation and about how it may be influenced by unilateral spatial neglect. The present study aimed to disentangle the debated influence of perceptual vs. representational aspects via explicit mapping of numbers onto space by applying the number line estimation paradigm with vertical orientation of stimulus lines. Thirty-five acute right-brain damaged stroke patients (6 with neglect) were asked to place two-digit numbers on vertically oriented lines with 0 marked at the bottom and 100 at the top. In contrast to the expected, nearly linear mapping in the control patient group, patients with spatial neglect overestimated the position of numbers in the lower middle range. The results corroborate spatial characteristics of the number magnitude representation. In neglect patients, this representation seems to be biased towards the ipsilesional side, independent of the physical orientation of the task stimuli.

Baryon number, lepton number, and operator dimension in the Standard Model

DOE PAGES

Kobach, Andrew

2016-05-19

In this study, we prove that for a given operator in the Standard Model (SM) with baryon number ΔB and lepton number ΔL, that the operator's dimension is even (odd) if (ΔB - ΔL)/2 is even (odd). Consequently, this establishes the veracity of statements that were long observed or expected to be true, but not proven, e.g., operators with ΔB - ΔL = 0 are of even dimension, ΔB - ΔL must be an even number, etc. These results remain true even if the SM is augmented by any number of right-handed neutrinos with ΔL = 1.

A Z-number-based decision making procedure with ranking fuzzy numbers method

NASA Astrophysics Data System (ADS)

Mohamad, Daud; Shaharani, Saidatull Akma; Kamis, Nor Hanimah

2014-12-01

The theory of fuzzy set has been in the limelight of various applications in decision making problems due to its usefulness in portraying human perception and subjectivity. Generally, the evaluation in the decision making process is represented in the form of linguistic terms and the calculation is performed using fuzzy numbers. In 2011, Zadeh has extended this concept by presenting the idea of Z-number, a 2-tuple fuzzy numbers that describes the restriction and the reliability of the evaluation. The element of reliability in the evaluation is essential as it will affect the final result. Since this concept can still be considered as new, available methods that incorporate reliability for solving decision making problems is still scarce. In this paper, a decision making procedure based on Z-numbers is proposed. Due to the limitation of its basic properties, Z-numbers will be first transformed to fuzzy numbers for simpler calculations. A method of ranking fuzzy number is later used to prioritize the alternatives. A risk analysis problem is presented to illustrate the effectiveness of this proposed procedure.

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) Number. 25.315 Section 25.315 Grants and Agreements Office of Management and Budget Guidance for Grants... paragraph C.2 of the award term in Appendix A to this part. ...

Building Numbers from Primes

ERIC Educational Resources Information Center

Burkhart, Jerry

2009-01-01

Prime numbers are often described as the "building blocks" of natural numbers. This article shows how the author and his students took this idea literally by using prime factorizations to build numbers with blocks. In this activity, students explore many concepts of number theory, including the relationship between greatest common factors and…

Modeling of multiphase flow with solidification and chemical reaction in materials processing

NASA Astrophysics Data System (ADS)

Wei, Jiuan

Understanding of multiphase flow and related heat transfer and chemical reactions are the keys to increase the productivity and efficiency in industrial processes. The objective of this thesis is to utilize the computational approaches to investigate the multiphase flow and its application in the materials processes, especially in the following two areas: directional solidification, and pyrolysis and synthesis. In this thesis, numerical simulations will be performed for crystal growth of several III-V and II-VI compounds. The effects of Prandtl and Grashof numbers on the axial temperature profile, the solidification interface shape, and melt flow are investigated. For the material with high Prandtl and Grashof numbers, temperature field and growth interface will be significantly influenced by melt flow, resulting in the complicated temperature distribution and curved interface shape, so it will encounter tremendous difficulty using a traditional Bridgman growth system. A new design is proposed to reduce the melt convection. The geometric configuration of top cold and bottom hot in the melt will dramatically reduce the melt convection. The new design has been employed to simulate the melt flow and heat transfer in crystal growth with large Prandtl and Grashof numbers and the design parameters have been adjusted. Over 90% of commercial solar cells are made from silicon and directional solidification system is the one of the most important method to produce multi-crystalline silicon ingots due to its tolerance to feedstock impurities and lower manufacturing cost. A numerical model is developed to simulate the silicon ingot directional solidification process. Temperature distribution and solidification interface location are presented. Heat transfer and solidification analysis are performed to determine the energy efficiency of the silicon production furnace. Possible improvements are identified. The silicon growth process is controlled by adjusting heating power and

Numerical simulation of convection and heat transfer in Czochralski crystal growth by multiple-relaxation-time LBM

NASA Astrophysics Data System (ADS)

Liu, Ding; Huang, Weichao; Zhang, Ni

2017-07-01

A two-dimensional axisymmetric swirling model based on the lattice Boltzmann method (LBM) in a pseudo Cartesian coordinate system is posited to simulate Czochralski (Cz) crystal growth in this paper. Specifically, the multiple-relaxation-time LBM (MRT-LBM) combined with the finite difference method (FDM) is used to analyze the melt convection and heat transfer in the process of Cz crystal growth. An incompressible axisymmetric swirling MRT-LB D2Q9 model is applied to solve for the axial and radial velocities by inserting thermal buoyancy and rotational inertial force into the two-dimensional lattice Boltzmann equation. In addition, the melt temperature and the azimuthal velocity are solved by MRT-LB D2Q5 models, and the crystal temperature is solved by FDM. The comparison results of stream functions values of different methods demonstrate that our hybrid model can be used to simulate the fluid-thermal coupling in the axisymmetric swirling model correctly and effectively. Furthermore, numerical simulations of melt convection and heat transfer are conducted under the conditions of high Grashof (Gr) numbers, within the range of 105 ˜ 107, and different high Reynolds (Re) numbers. The experimental results show our hybrid model can obtain the exact solution of complex crystal-growth models and analyze the fluid-thermal coupling effectively under the combined action of natural convection and forced convection.

The flow patterning capability of localized natural convection.

PubMed

Huang, Ling-Ting; Chao, Ling

2016-09-14

Controlling flow patterns to align materials can have various applications in optics, electronics, and biosciences. In this study, we developed a natural-convection-based method to create desirable spatial flow patterns by controlling the locations of heat sources. Fluid motion in natural convection is induced by the spatial fluid density gradient that is caused by the established spatial temperature gradient. To analyze the patterning resolution capability of this method, we used a mathematical model combined with nondimensionalization to correlate the flow patterning resolution with experimental operating conditions. The nondimensionalized model suggests that the flow pattern and resolution is only influenced by two dimensionless parameters, and , where Gr is the Grashof number, representing the ratio of buoyancy to the viscous force acting on a fluid, and Pr is the Prandtl number, representing the ratio of momentum diffusivity to thermal diffusivity. We used the model to examine all of the flow behaviors in a wide range of the two dimensionless parameter group and proposed a flow pattern state diagram which suggests a suitable range of operating conditions for flow patterning. In addition, we developed a heating wire with an angular configuration, which enabled us to efficiently examine the pattern resolution capability numerically and experimentally. Consistent resolutions were obtained between the experimental results and model predictions, suggesting that the state diagram and the identified operating range can be used for further application.

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) Number. 25.315 Section 25.315 Grants and Agreements Office of Management and Budget Guidance for Grants... meaning given in paragraph C.2 of the award term in Appendix A to this part. ...

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) Number. 25.315 Section 25.315 Grants and Agreements Office of Management and Budget Guidance for Grants... meaning given in paragraph C.2 of the award term in Appendix A to this part. ...

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) Number. 25.315 Section 25.315 Grants and Agreements Office of Management and Budget Guidance for Grants... meaning given in paragraph C.2 of the award term in appendix A to this part. ...

Of colored numbers and numbered colors: interactive processes in grapheme-color synesthesia.

PubMed

Gebuis, Titia; Nijboer, Tanja C W; van der Smagt, Maarten J

2009-01-01

Grapheme-color synesthetes experience a specific color when they see a grapheme but they do not report to perceive a grapheme when a color is presented. In this study, we investigate whether color can still evoke number-processes even when a vivid number experience is absent. We used color-number and number-color priming, both revealing faster responses in congruent compared to incongruent conditions. Interestingly, the congruency effect was of similar magnitude for both conditions, and a numerical distance effect was present only in the color-number priming task. In addition, a priming task in which synesthetes had to judge the parity of a colored number revealed faster responses in parity congruent than in parity incongruent trials. These combined results demonstrate that synesthesia is indeed bi-directional and of similar strength in both directions. Furthermore, they illustrate the precise nature of these interactions and show that the direction of these interactions is determined by task demands, not by the more vividly experienced aspect of the stimulus.

Inappropriately Applying Natural Number Properties in Rational Number Tasks: Characterizing the Development of the Natural Number Bias through Primary and Secondary Education

ERIC Educational Resources Information Center

van Hoof, Jo; Verschaffel, Lieven; van Dooren, Wim

2015-01-01

The natural number bias is known to explain many difficulties learners have with understanding rational numbers. The research field distinguishes three aspects where natural number properties are sometimes inappropriately applied in rational number tasks: density, size, and operations. The overall goal of this study was to characterize the…

Numbers and brains.

PubMed

Gallistel, C R

2017-12-01

The representation of discrete and continuous quantities appears to be ancient and pervasive in animal brains. Because numbers are the natural carriers of these representations, we may discover that in brains, it's numbers all the way down.

Small numbers are sensed directly, high numbers constructed from size and density.

PubMed

Zimmermann, Eckart

2018-04-01

Two theories compete to explain how we estimate the numerosity of visual object sets. The first suggests that the apparent numerosity is derived from an analysis of more low-level features like size and density of the set. The second theory suggests that numbers are sensed directly. Consistent with the latter claim is the existence of neurons in parietal cortex which are specialized for processing the numerosity of elements in the visual scene. However, recent evidence suggests that only low numbers can be sensed directly whereas the perception of high numbers is supported by the analysis of low-level features. Processing of low and high numbers, being located at different levels of the neural hierarchy should involve different receptive field sizes. Here, I tested this idea with visual adaptation. I measured the spatial spread of number adaptation for low and high numerosities. A focused adaptation spread of high numerosities suggested the involvement of early neural levels where receptive fields are comparably small and the broad spread for low numerosities was consistent with processing of number neurons which have larger receptive fields. These results provide evidence for the claim that different mechanism exist generating the perception of visual numerosity. Whereas low numbers are sensed directly as a primary visual attribute, the estimation of high numbers however likely depends on the area size over which the objects are spread. Copyright © 2017 Elsevier B.V. All rights reserved.

Animal cognition. Number-space mapping in the newborn chick resembles humans' mental number line.

PubMed

Rugani, Rosa; Vallortigara, Giorgio; Priftis, Konstantinos; Regolin, Lucia

2015-01-30

Humans represent numbers along a mental number line (MNL), where smaller values are located on the left and larger on the right. The origin of the MNL and its connections with cultural experience are unclear: Pre-verbal infants and nonhuman species master a variety of numerical abilities, supporting the existence of evolutionary ancient precursor systems. In our experiments, 3-day-old domestic chicks, once familiarized with a target number (5), spontaneously associated a smaller number (2) with the left space and a larger number (8) with the right space. The same number (8), though, was associated with the left space when the target number was 20. Similarly to humans, chicks associate smaller numbers with the left space and larger numbers with the right space. Copyright © 2015, American Association for the Advancement of Science.

Report number codes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nelson, R.N.

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 thismore » 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.« less

An Evaluation of App-Based and Paper-Based Number Lines for Teaching Number Comparison

ERIC Educational Resources Information Center

Weng, Pei-Lin; Bouck, Emily C.

2016-01-01

Number comparison is a fundamental skill required for academic and functional mathematics (e.g., time, money, purchasing) for students with disabilities. The most commonly used method to teach number comparison is number lines. Although historically paper number lines are used, app-based number lines may offer greater flexibility. This study…

On the effect of thermodiffusion on solute segregation during the growth of semiconductor materials by the vertical Bridgman method

NASA Astrophysics Data System (ADS)

Ben Sassi, Mokhtar; Kaddeche, Slim; Lappa, Marcello; Millet, Séverine; Henry, Daniel; Ben Hadid, Hamda

2017-01-01

The effect of thermodiffusion on dopant distribution in the melt and in the grown crystal is investigated numerically for a vertical Bridgman configuration for situations of pure thermal convection corresponding to dilute alloys. The dopant distribution is shown to be significantly affected by the Soret parameter value. The sensitivity of the system to a variety of parameters, including the Grashof number and the so-called furnace residence time, i.e. the time during which the crucible is maintained in the furnace before initiating the solidification process, is assessed by means of parametric simulations. Moreover, the results indicate that variations in the sign of the Soret parameter can lead to diametrically opposite behaviors, while an increase in the intensity of the thermal convection generally leads to a mitigation of the effects induced by thermodiffusion. On the basis of the numerical results some useful criteria are drawn which could help crystal growers to discern the complex interrelations among the various parameters under one's control (that are not independent of one another) and to elaborate rational guidelines relating to strategies to be used to improve the quality of the resulting crystals.

Transient thermal analysis of a titanium multiwall thermal protection system

NASA Technical Reports Server (NTRS)

Blosser, M. L.

1982-01-01

The application of the SPAR thermal analyzer to the thermal analysis of a thermal protection system concept is discussed. The titanium multiwall thermal protection system concept consists of alternate flat and dimpled sheets which are joined together at the crests of the dimples and formed into 30 cm by 30 cm (12 in. by 12 in.) tiles. The tiles are mechanically attached to the structure. The complex tile geometry complicates thermal analysis. Three modes of heat transfer were considered: conduction through the gas inside the tile, conduction through the metal, and radiation between the various layers. The voids between the dimpled and flat sheets were designed to be small enough so that natural convection is insignificant (e.g., Grashof number 1000). A two step approach was used in the thermal analysis of the multiwall thermal protection system. First, an effective normal (through-the-thickness) thermal conductivity was obtained from a steady state analysis using a detailed SPAR finite element model of a small symmetric section of the multiwall tile. This effective conductivity was then used in simple one dimensional finite element models for preliminary analysis of several transient heat transfer problems.

The Fibonacci Numbers.

ERIC Educational Resources Information Center

Onstad, Torgeir

1991-01-01

After a brief historical account of Leonardo Pisano Fibonacci, some basic results concerning the Fibonacci numbers are developed and proved, and entertaining examples are described. Connections are made between the Fibonacci numbers and the Golden Ratio, biological nature, and other combinatorics examples. (MDH)

Number-unconstrained quantum sensing

NASA Astrophysics Data System (ADS)

Mitchell, Morgan W.

2017-12-01

Quantum sensing is commonly described as a constrained optimization problem: maximize the information gained about an unknown quantity using a limited number of particles. Important sensors including gravitational wave interferometers and some atomic sensors do not appear to fit this description, because there is no external constraint on particle number. Here, we develop the theory of particle-number-unconstrained quantum sensing, and describe how optimal particle numbers emerge from the competition of particle-environment and particle-particle interactions. We apply the theory to optical probing of an atomic medium modeled as a resonant, saturable absorber, and observe the emergence of well-defined finite optima without external constraints. The results contradict some expectations from number-constrained quantum sensing and show that probing with squeezed beams can give a large sensitivity advantage over classical strategies when each is optimized for particle number.

The r-Stirling Numbers.

DTIC Science & Technology

1982-12-01

partitions, the restriction being that the first r elements must be in distinct cycles and respectively distinct subsets. The combinatorial and algebraic ...symmetric functions The Stirling numbers of the first kind, ("], for ixed n, are the elementary symmetric functions or the numbers 1,...,n (see, e.g., [4 or...5J). The r-Stirling numbers of the Iirst kind are the elementary symmetric runctions or the numbers r,... ,n. --- -4i: ? - , , .i

Tests of Sunspot Number Sequences: 4. Discontinuities Around 1946 in Various Sunspot Number and Sunspot-Group-Number Reconstructions

NASA Astrophysics Data System (ADS)

Lockwood, M.; Owens, M. J.; Barnard, L.

2016-11-01

We use five test data series to search for, and quantify, putative discontinuities around 1946 in five different annual-mean sunspot-number or sunspot-group-number data sequences. The data series tested are the original and new versions of the Wolf/Zürich/International sunspot number composite [R_{{ISNv1}} and R_{{ISNv2}}] (respectively Clette et al. in Adv. Space Res. 40, 919, 2007 and Clette et al. in The Solar Activity Cycle 35, Springer, New York, 2015); the corrected version of R ISNv1 proposed by Lockwood, Owens, and Barnard ( J. Geophys. Res. 119, 5193, 2014a) [R C]; the new "backbone" group-number composite proposed by Svalgaard and Schatten ( Solar Phys. 291, 2016) [R_{{BB}}]; and the new group-number composite derived by Usoskin et al. ( Solar Phys. 291, 2016) [R_{{UEA}}]. The test data series used are the group-number [NG] and total sunspot area [A G] from the Royal Observatory, Greenwich/Royal Greenwich Observatory (RGO) photoheliographic data; the Ca K index from the recent re-analysis of Mount Wilson Observatory (MWO) spectroheliograms in the Calcium ii K ion line; the sunspot-group-number from the MWO sunspot drawings [N_{{MWO}}]; and the dayside ionospheric F2-region critical frequencies measured by the Slough ionosonde [foF2]. These test data all vary in close association with sunspot numbers, in some cases non-linearly. The tests are carried out using both the before-and-after fit-residual comparison method and the correlation method of Lockwood, Owens, and Barnard, applied to annual mean data for intervals iterated to minimise errors and to eliminate uncertainties associated with the precise date of the putative discontinuity. It is not assumed that the correction required is by a constant factor, nor even linear in sunspot number. It is shown that a non-linear correction is required by RC, R_{BB}, and R_{{ISNv1}}, but not by R_{{ISNv2}} or R_{{UEA}}. The five test datasets give very similar results in all cases. By multiplying the probability

Multiple numeric competencies: When a number is not just a number.

PubMed

Peters, Ellen; Bjalkebring, Par

2015-05-01

A growing body of evidence demonstrates the practical and theoretical importance of numeracy in evaluations and choices involving numeric information, an importance that goes beyond simple accuracy in performing mathematical computations. Numeric competency, however, may be multiply determined, but little research has examined potentially separable influences in evaluations and choice. In the present article, we describe 3 numeric competencies and begin to disentangle their effects. Participants (N = 111) completed a series of tasks in 4 1-hr sessions. We first examined relations between objective numeracy, subjective numeracy, and symbolic-number mapping abilities (thought to tap into internal representations of numeric magnitude and the mapping of symbolic numbers onto those representations) using a structural equation model. We then explored their dissociations in numeric and nonnumeric tasks. Higher vs. lower scores in objective numeracy were associated with explicit number operations, including number comparisons and calculations. Those with more vs. less exact mapping had better numeric memory (but not nonnumeric) and produced valuations that were closer to (but did not equal) a risky gamble's expected value, indicating a link with superior number intuitions. Finally, individuals lower vs. higher in subjective numeracy had more negative emotional reactions to numbers and were less motivated and/or confident in numeric tasks. It was less clear whether subjective numeracy might also relate to more general motivations and metacognitions involving nonnumeric information. We conclude that numeric competencies should be used in a more targeted fashion to understand their multiple mechanisms in people's evaluations, choices, and life outcomes. (c) 2015 APA, all rights reserved).

Number Sense Made Simple Using Number Patterns

ERIC Educational Resources Information Center

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

2011-01-01

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

Reform by the Numbers.

ERIC Educational Resources Information Center

Hanford, Terry; White, Kathleen

1991-01-01

Although numbers such as average test scores or dropout rates can capture part of a school system's success or failure, school statistics seldom tell the whole story. School board members should realize that numbers might measure compliance or process, rather than improvement. Also, improvements in numbers might reflect changes in assessment…

Cosmological baryon and lepton number in the presence of electroweak fermion-number violation

NASA Technical Reports Server (NTRS)

Harvey, Jeffrey A.; Turner, Michael S.

1990-01-01

In the presence of rapid fermion-number violation due to nonperturbative electroweak effects certain relations between the baryon number of the Universe and the lepton numbers of the Universe are predicted. In some cases the electron-neutrino asymmetry is exactly specified in terms of the baryon asymmetry. Without introducing new particles, beyond the usual quarks and leptons, it is necessary that the Universe possess a nonzero value of B - L prior to the epoch of fermion-number violation if baryon and lepton asymmetries are to survive. Contrary to intuition, even though electroweak processes violate B + L, a nonzero value of B + L persists after the epoch of rapid fermion-number violation. If the standard model is extended to include lepton-number violation, for example through Majorana neutrino masses, then electroweak processes will reduce the baryon number to zero even in the presence of an initial B - L unless 20 M(sub L) approximately greater than the square root of (T(sub B - L) m(sub P1)) where M(sub L) sets the scale of lepton number violation and T(sub B - L) is the temperature at which a B - L asymmetry is produced. In many models this implies that neutrinos must be so light that they cannot contribute appreciably to the mass density of the Universe.

Engaging Whole-Number Knowledge for Rational-Number Leaning Using a Computer-Based Tool.

ERIC Educational Resources Information Center

Hunting, Robert P.; And Others

1996-01-01

This constructivist teaching experiment investigated the role of whole-number knowledge in fraction learning. Two nine-year-old students worked for one year with a computer program (Copycat) and demonstrated that the development of whole-number knowledge and rational-number knowledge is interdependent. Contains 59 references. (KMC)

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…

Number Sense and Number Nonsense: Understanding the Challenges of Learning Math

ERIC Educational Resources Information Center

Krasa, Nancy; Shunkwiler, Sara

2009-01-01

How do children learn math--and why do some children struggle with it? The answers are in "Number Sense and Number Nonsense," a straightforward, reader-friendly book for education professionals and an invaluable multidisciplinary resource for researchers. More than a first-ever research synthesis, this highly accessible book brings math…

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…

The Remarkable Number "1"

ERIC Educational Resources Information Center

Allen, G. Donald

2014-01-01

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

The Numbers Game: Phasing in Generated ID Numbers at the University of Oregon

ERIC Educational Resources Information Center

Eveland, Sue

2005-01-01

With all the recent headlines about security breaches and information loss at financial and educational institutions, the higher education community needs to address the issue of using social security numbers as ID numbers. The University of Oregon undertook a change process to assign generated ID numbers to all records in their information…

Unbounding the mental number line—new evidence on children's spatial representation of numbers

PubMed Central

Link, Tanja; Huber, Stefan; Nuerk, Hans-Christoph; Moeller, Korbinian

2014-01-01

Number line estimation (i.e., indicating the position of a given number on a physical line) is a standard assessment of children's spatial representation of number magnitude. Importantly, there is an ongoing debate on the question in how far the bounded task version with start and endpoint given (e.g., 0 and 100) might induce specific estimation strategies and thus may not allow for unbiased inferences on the underlying representation. Recently, a new unbounded version of the task was suggested with only the start point and a unit fixed (e.g., the distance from 0 to 1). In adults this task provided a less biased index of the spatial representation of number magnitude. Yet, so far there are no children data available for the unbounded number line estimation task. Therefore, we conducted a cross-sectional study on primary school children performing both, the bounded and the unbounded version of the task. We observed clear evidence for systematic strategic influences (i.e., the consideration of reference points) in the bounded number line estimation task for children older than grade two whereas there were no such indications for the unbounded version for any one of the age groups. In summary, the current data corroborate the unbounded number line estimation task to be a valuable tool for assessing children's spatial representation of number magnitude in a systematic and unbiased manner. Yet, similar results for the bounded and the unbounded version of the task for first- and second-graders may indicate that both versions of the task might assess the same underlying representation for relatively younger children—at least in number ranges familiar to the children assessed. This is of particular importance for inferences about the nature and development of children's magnitude representation. PMID:24478734

Beyond the Mental Number Line: A Neural Network Model of Number-Space Interactions

ERIC Educational Resources Information Center

Chen, Qi; Verguts, Tom

2010-01-01

It is commonly assumed that there is an interaction between the representations of number and space (e.g., [Dehaene et al., 1993] and [Walsh, 2003]), typically ascribed to a mental number line. The exact nature of this interaction has remained elusive, however. Here we propose that spatial aspects are not inherent to number representations, but…

Innate or Acquired? - Disentangling Number Sense and Early Number Competencies.

PubMed

Siemann, Julia; Petermann, Franz

2018-01-01

The clinical profile termed developmental dyscalculia (DD) is a fundamental disability affecting children already prior to arithmetic schooling, but the formal diagnosis is often only made during school years. The manifold associated deficits depend on age, education, developmental stage, and task requirements. Despite a large body of studies, the underlying mechanisms remain dubious. Conflicting findings have stimulated opposing theories, each presenting enough empirical support to remain a possible alternative. A so far unresolved question concerns the debate whether a putative innate number sense is required for successful arithmetic achievement as opposed to a pure reliance on domain-general cognitive factors. Here, we outline that the controversy arises due to ambiguous conceptualizations of the number sense. It is common practice to use early number competence as a proxy for innate magnitude processing, even though it requires knowledge of the number system. Therefore, such findings reflect the degree to which quantity is successfully transferred into symbols rather than informing about quantity representation per se . To solve this issue, we propose a three-factor account and incorporate it into the partly overlapping suggestions in the literature regarding the etiology of different DD profiles. The proposed view on DD is especially beneficial because it is applicable to more complex theories identifying a conglomerate of deficits as underlying cause of DD.

Compendium of Experimental Cetane Numbers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yanowitz, Janet; Ratcliff, Matthew A.; McCormick, Robert L.

This report is an updated version of the 2014 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 December 2016 as well as a number of previously unpublished values, most measured over the past decade at the National Renewable Energy Laboratory. This version of the compendium contains cetane values for 496 pure compounds, including 204 hydrocarbons and 292 oxygenates. 176 individual measurements are new to this version of the compendium, all of them collected using ASTMmore » Method D6890, which utilizes an Ignition Quality Tester (IQT) a type of constant-volume combustion chamber. For many compounds, numerous measurements are included, often collected by different researchers using different methods. The text of this document is unchanged from the 2014 version, except for the numbers of compounds in Section 3.1, the Appendices, Table 1. Primary Cetane Number Data Sources and Table 2. Number of Measurements Included in Compendium. 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 number has been expanded, and the data have been annotated extensively to provide additional information that will help the reader judge the relative reliability of individual results.« less

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.

76 FR 79607 - Local Number Portability Porting Interval and Validation Requirements; Telephone Number Portability

Federal Register 2010, 2011, 2012, 2013, 2014

2011-12-22

... 11-1954] Local Number Portability Porting Interval and Validation Requirements; Telephone Number... information when the new service provider requests a CSR: any working telephone number associated with the...://www.fcc.gov/cgb/ecfs . For detailed instructions for submitting comments and additional information on...

Familial Sinistrals Avoid Exact Numbers

PubMed Central

Sauerland, Uli; Gotzner, Nicole

2013-01-01

We report data from an internet questionnaire of sixty number trivia. Participants were asked for the number of cups in their house, the number of cities they know and 58 other quantities. We compare the answers of familial sinistrals – individuals who are left-handed themselves or have a left-handed close blood-relative – with those of pure familial dextrals – right-handed individuals who reported only having right-handed close blood-relatives. We show that familial sinistrals use rounder numbers than pure familial dextrals in the survey responses. Round numbers in the decimal system are those that are multiples of powers of 10 or of half or a quarter of a power of 10. Roundness is a gradient concept, e.g. 100 is rounder than 50 or 200. We show that very round number like 100 and 1000 are used with 25% greater likelihood by familial sinistrals than by pure familial dextrals, while pure familial dextrals are more likely to use less round numbers such as 25, 60, and 200. We then use Sigurd’s (1988, Language in Society) index of the roundness of a number and report that familial sinistrals’ responses are significantly rounder on average than those of pure familial dextrals. To explain the difference, we propose that the cognitive effort of using exact numbers is greater for the familial sinistral group because their language and number systems tend to be more distributed over both hemispheres of the brain. Our data support the view that exact and approximate quantities are processed by two separate cognitive systems. Specifically, our behavioral data corroborates the view that the evolutionarily older, approximate number system is present in both hemispheres of the brain, while the exact number system tends to be localized in only one hemisphere. PMID:23544052

Familial sinistrals avoid exact numbers.

PubMed

Sauerland, Uli; Gotzner, Nicole

2013-01-01

We report data from an internet questionnaire of sixty number trivia. Participants were asked for the number of cups in their house, the number of cities they know and 58 other quantities. We compare the answers of familial sinistrals--individuals who are left-handed themselves or have a left-handed close blood-relative--with those of pure familial dextrals--right-handed individuals who reported only having right-handed close blood-relatives. We show that familial sinistrals use rounder numbers than pure familial dextrals in the survey responses. Round numbers in the decimal system are those that are multiples of powers of 10 or of half or a quarter of a power of 10. Roundness is a gradient concept, e.g. 100 is rounder than 50 or 200. We show that very round number like 100 and 1000 are used with 25% greater likelihood by familial sinistrals than by pure familial dextrals, while pure familial dextrals are more likely to use less round numbers such as 25, 60, and 200. We then use Sigurd's (1988, Language in Society) index of the roundness of a number and report that familial sinistrals' responses are significantly rounder on average than those of pure familial dextrals. To explain the difference, we propose that the cognitive effort of using exact numbers is greater for the familial sinistral group because their language and number systems tend to be more distributed over both hemispheres of the brain. Our data support the view that exact and approximate quantities are processed by two separate cognitive systems. Specifically, our behavioral data corroborates the view that the evolutionarily older, approximate number system is present in both hemispheres of the brain, while the exact number system tends to be localized in only one hemisphere.

Transitional boundary layer in low-Prandtl-number convection at high Rayleigh number

NASA Astrophysics Data System (ADS)

Schumacher, Joerg; Bandaru, Vinodh; Pandey, Ambrish; Scheel, Janet

2016-11-01

The boundary layer structure of the velocity and temperature fields in turbulent Rayleigh-Bénard flows in closed cylindrical cells of unit aspect ratio is revisited from a transitional and turbulent viscous boundary layer perspective. When the Rayleigh number is large enough the boundary layer dynamics at the bottom and top plates can be separated into an impact region of downwelling plumes, an ejection region of upwelling plumes and an interior region (away from side walls) that is dominated by a shear flow of varying orientation. This interior plate region is compared here to classical wall-bounded shear flows. The working fluid is liquid mercury or liquid gallium at a Prandtl number of Pr = 0 . 021 for a range of Rayleigh numbers of 3 ×105 <= Ra <= 4 ×108 . The momentum transfer response to these system parameters generates a fluid flow in the closed cell with a macroscopic flow Reynolds number that takes values in the range of 1 . 8 ×103 <= Re <= 4 . 6 ×104 . It is shown that particularly the viscous boundary layers for the largest Ra are highly transitional and obey some properties that are directly comparable to transitional channel flows at friction Reynolds numbers below 100. This work is supported by the Deutsche Forschungsgemeinschaft.

Self-correcting random number generator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Humble, Travis S.; Pooser, Raphael C.

2016-09-06

A system and method for generating random numbers. The system may include a random number generator (RNG), such as a quantum random number generator (QRNG) configured to self-correct or adapt in order to substantially achieve randomness from the output of the RNG. By adapting, the RNG may generate a random number that may be considered random regardless of whether the random number itself is tested as such. As an example, the RNG may include components to monitor one or more characteristics of the RNG during operation, and may use the monitored characteristics as a basis for adapting, or self-correcting, tomore » provide a random number according to one or more performance criteria.« less

Cognitive access to numbers: the philosophical significance of empirical findings about basic number abilities.

PubMed

Giaquinto, Marcus

2017-02-19

How can we acquire a grasp of cardinal numbers, even the first very small positive cardinal numbers, given that they are abstract mathematical entities? That problem of cognitive access is the main focus of this paper. All the major rival views about the nature and existence of cardinal numbers face difficulties; and the view most consonant with our normal thought and talk about numbers, the view that cardinal numbers are sizes of sets, runs into the cognitive access problem. The source of the problem is the plausible assumption that cognitive access to something requires causal contact with it. It is argued that this assumption is in fact wrong, and that in this and similar cases, we should accept that a certain recognize-and-distinguish capacity is sufficient for cognitive access. We can then go on to solve the cognitive access problem, and thereby support the set-size view of cardinal numbers, by paying attention to empirical findings about basic number abilities. To this end, some selected studies of infants, pre-school children and a trained chimpanzee are briefly discussed.This article is part of a discussion meeting issue 'The origins of numerical abilities'. © 2017 The Author(s).

Zooming in and out from the Mental Number Line: Evidence for a Number Range Effect

ERIC Educational Resources Information Center

Pinhas, Michal; Pothos, Emmanuel M.; Tzelgov, Joseph

2013-01-01

The representation of numbers is commonly viewed as an ordered continuum of magnitudes, referred to as the "mental number line." Previous work has repeatedly shown that number representations evoked by a given task can be easily altered, yielding an ongoing discussion about the basic properties of the mental number line and how malleable…

Number development and developmental dyscalculia.

PubMed

von Aster, Michael G; Shalev, Ruth S

2007-11-01

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

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.

Positive approach: Implications for the relation between number theory and geometry, including connection to Santilli mathematics, from Fibonacci reconstitution of natural numbers and of prime numbers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johansen, Stein E., E-mail: stein.johansen@svt.ntnu.no

2014-12-10

The paper recapitulates some key elements in previously published results concerning exact and complete reconstitution of the field of natural numbers, both as ordinal and as cardinal numbers, from systematic unfoldment of the Fibonacci algorithm. By this natural numbers emerge as Fibonacci 'atoms' and 'molecules' consistent with the notion of Zeckendorf sums. Here, the sub-set of prime numbers appears not as the primary numbers, but as an epistructure from a deeper Fibonacci constitution, and is thus targeted from a 'positive approach'. In the Fibonacci reconstitution of number theory natural numbers show a double geometrical aspect: partly as extension in spacemore » and partly as position in a successive structuring of space. More specifically, the natural numbers are shown to be distributed by a concise 5:3 code structured from the Fibonacci algorithm via Pascal's triangle. The paper discusses possible implications for the more general relation between number theory and geometry, as well as more specifically in relation to hadronic mathematics, initiated by R.M. Santilli, and also briefly to some other recent science linking number theory more directly to geometry and natural systems.« less

Quantum random number generator

DOEpatents

Pooser, Raphael C.

2016-05-10

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

Compendium of Experimental Cetane Numbers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yanowitz, J.; Ratcliff, M. A.; McCormick, R. L.

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,more » 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.« less

Different brains process numbers differently: structural bases of individual differences in spatial and nonspatial number representations.

PubMed

Krause, Florian; Lindemann, Oliver; Toni, Ivan; Bekkering, Harold

2014-04-01

A dominant hypothesis on how the brain processes numerical size proposes a spatial representation of numbers as positions on a "mental number line." An alternative hypothesis considers numbers as elements of a generalized representation of sensorimotor-related magnitude, which is not obligatorily spatial. Here we show that individuals' relative use of spatial and nonspatial representations has a cerebral counterpart in the structural organization of the posterior parietal cortex. Interindividual variability in the linkage between numbers and spatial responses (faster left responses to small numbers and right responses to large numbers; spatial-numerical association of response codes effect) correlated with variations in gray matter volume around the right precuneus. Conversely, differences in the disposition to link numbers to force production (faster soft responses to small numbers and hard responses to large numbers) were related to gray matter volume in the left angular gyrus. This finding suggests that numerical cognition relies on multiple mental representations of analogue magnitude using different neural implementations that are linked to individual traits.

Innate or Acquired? – Disentangling Number Sense and Early Number Competencies

PubMed Central

Siemann, Julia; Petermann, Franz

2018-01-01

The clinical profile termed developmental dyscalculia (DD) is a fundamental disability affecting children already prior to arithmetic schooling, but the formal diagnosis is often only made during school years. The manifold associated deficits depend on age, education, developmental stage, and task requirements. Despite a large body of studies, the underlying mechanisms remain dubious. Conflicting findings have stimulated opposing theories, each presenting enough empirical support to remain a possible alternative. A so far unresolved question concerns the debate whether a putative innate number sense is required for successful arithmetic achievement as opposed to a pure reliance on domain-general cognitive factors. Here, we outline that the controversy arises due to ambiguous conceptualizations of the number sense. It is common practice to use early number competence as a proxy for innate magnitude processing, even though it requires knowledge of the number system. Therefore, such findings reflect the degree to which quantity is successfully transferred into symbols rather than informing about quantity representation per se. To solve this issue, we propose a three-factor account and incorporate it into the partly overlapping suggestions in the literature regarding the etiology of different DD profiles. The proposed view on DD is especially beneficial because it is applicable to more complex theories identifying a conglomerate of deficits as underlying cause of DD. PMID:29725316

Genetics by the Numbers

MedlinePlus

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

32 CFR 1602.19 - Numbers.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 32 National Defense 6 2011-07-01 2011-07-01 false Numbers. 1602.19 Section 1602.19 National Defense Other Regulations Relating to National Defense SELECTIVE SERVICE SYSTEM DEFINITIONS § 1602.19 Numbers. Cardinal numbers may be expressed by Arabic or Roman symbols. ...

32 CFR 1602.19 - Numbers.

Code of Federal Regulations, 2010 CFR

2010-07-01

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

32 CFR 1602.19 - Numbers.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 32 National Defense 6 2012-07-01 2012-07-01 false Numbers. 1602.19 Section 1602.19 National Defense Other Regulations Relating to National Defense SELECTIVE SERVICE SYSTEM DEFINITIONS § 1602.19 Numbers. Cardinal numbers may be expressed by Arabic or Roman symbols. ...

32 CFR 1602.19 - Numbers.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 32 National Defense 6 2013-07-01 2013-07-01 false Numbers. 1602.19 Section 1602.19 National Defense Other Regulations Relating to National Defense SELECTIVE SERVICE SYSTEM DEFINITIONS § 1602.19 Numbers. Cardinal numbers may be expressed by Arabic or Roman symbols. ...

32 CFR 1602.19 - Numbers.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 32 National Defense 6 2014-07-01 2014-07-01 false Numbers. 1602.19 Section 1602.19 National Defense Other Regulations Relating to National Defense SELECTIVE SERVICE SYSTEM DEFINITIONS § 1602.19 Numbers. Cardinal numbers may be expressed by Arabic or Roman symbols. ...

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.

A Generalization of the Formula for the Triangular Number of the Sum and Product of Natural Numbers

ERIC Educational Resources Information Center

Asiru, M. A.

2008-01-01

This note generalizes the formula for the triangular number of the sum and product of two natural numbers to similar results for the triangular number of the sum and product of "r" natural numbers. The formula is applied to derive formula for the sum of an odd and an even number of consecutive triangular numbers.

Verification of Numerical Programs: From Real Numbers to Floating Point Numbers

NASA Technical Reports Server (NTRS)

Goodloe, Alwyn E.; Munoz, Cesar; Kirchner, Florent; Correnson, Loiec

2013-01-01

Numerical algorithms lie at the heart of many safety-critical aerospace systems. The complexity and hybrid nature of these systems often requires the use of interactive theorem provers to verify that these algorithms are logically correct. Usually, proofs involving numerical computations are conducted in the infinitely precise realm of the field of real numbers. However, numerical computations in these algorithms are often implemented using floating point numbers. The use of a finite representation of real numbers introduces uncertainties as to whether the properties veri ed in the theoretical setting hold in practice. This short paper describes work in progress aimed at addressing these concerns. Given a formally proven algorithm, written in the Program Verification System (PVS), the Frama-C suite of tools is used to identify sufficient conditions and verify that under such conditions the rounding errors arising in a C implementation of the algorithm do not affect its correctness. The technique is illustrated using an algorithm for detecting loss of separation among aircraft.

[Projection of prisoner numbers].

PubMed

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.

Number-phase minimum-uncertainty state with reduced number uncertainty in a Kerr nonlinear interferometer

NASA Astrophysics Data System (ADS)

Kitagawa, M.; Yamamoto, Y.

1987-11-01

An alternative scheme for generating amplitude-squeezed states of photons based on unitary evolution which can properly be described by quantum mechanics is presented. This scheme is a nonlinear Mach-Zehnder interferometer containing an optical Kerr medium. The quasi-probability density (QPD) and photon-number distribution of the output field are calculated, and it is demonstrated that the reduced photon-number uncertainty and enhanced phase uncertainty maintain the minimum-uncertainty product. A self-phase-modulation of the single-mode quantized field in the Kerr medium is described based on localized operators. The spatial evolution of the state is demonstrated by QPD in the Schroedinger picture. It is shown that photon-number variance can be reduced to a level far below the limit for an ordinary squeezed state, and that the state prepared using this scheme remains a number-phase minimum-uncertainty state until the maximum reduction of number fluctuations is surpassed.

What exactly do numbers mean?

PubMed Central

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

2014-01-01

Number words are generally used to refer to the exact cardinal value of a set, but cognitive scientists disagree about their meanings. Although most psychological analyses presuppose that numbers have exact semantics (two means EXACTLY TWO), many linguistic accounts propose that numbers have lower-bounded semantics (AT LEAST TWO), and that speakers restrict their reference through a pragmatic inference (scalar implicature). We address this debate through studies of children who are in the process of acquiring the meanings of numbers. Adults and 2- and 3-year-olds were tested in a novel paradigm that teases apart semantic and pragmatic aspects of interpretation (the covered box task). Our findings establish that when scalar implicatures are cancelled in the critical trials of this task, both adults and children consistently give exact interpretations for number words. These results, in concert with recent work on real-time processing, provide the first unambiguous evidence that number words have exact semantics. PMID:25285053

46 CFR 10.207 - Identification number.

Code of Federal Regulations, 2010 CFR

2010-10-01

... recordkeeping purposes only, a mariner's official MMC identification number is the individual's social security number. However, a unique serial number, and not the social security number, will appear on the... 46 Shipping 1 2010-10-01 2010-10-01 false Identification number. 10.207 Section 10.207 Shipping...

FAA Registry - Aircraft - N-Number Inquiry

Science.gov Websites

Skip to page content Federal Aviation Administration Aircraft Inquiries N-number Serial Number -Number Online In Writing Reserved N-Number Renewal Online Request for Aircraft Records Online Help Main Menu Aircraft Registration Aircraft Downloadable Database Definitions N-Number Format Registrations at

NRL Plasma Formulary

DTIC Science & Technology

2006-01-01

1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law , no...Description SI Gaussian Faraday’s law ∇ × E = −∂B ∂t ∇ × E = − 1 c ∂B ∂t Ampere’s law ∇ × H = ∂D ∂t + J ∇ × H = 1 c ∂D ∂t + 4π c J Poisson equation ∇ · D = ρ...gravitational or V/NL buoyancy force)1/2 Gay– Lussac Ga 1/β∆T Inverse of relative change in volume during heating Grashof Gr gL3β∆T/ν2 Buoyancy force/viscous

NRL (Naval Research Laboratory) Plasma Formulary. Revised.

DTIC Science & Technology

1987-01-01

ac)- 1 Resistance 4 7r o /Ar (Co//1o ) 1/2 Time 1 c Velocity Ck c- 18 MAXWELL’S EQUATIONS Name or Description SI f Gaussian OB 1lOB Faraday’s law V...x E -- V x E =- D t c Ot OD 1OD 4 -r Ampere’s law V x H = 6 +J x H = -+-J t c Ot c Poisson equation V • D = p V • D = 41rp [Absence of magnetic V...force/gravitational or V/NL buoyancy force) 1/ 2 Gay- Lussac Ga 1/1AT Inverse of relative change in volume during heating Grashof Gr gL S AT/ v

FAA Registry - Aircraft - N-Number Inquiry

Science.gov Websites

Skip to page content Federal Aviation Administration Aircraft Inquiries N-number Serial Number / Expired / Canceled Registration Reports Recent Registration N-number Availability Request A Reserved N -Number Online In Writing Reserved N-Number Renewal Online Request for Aircraft Records Online Help Main

An exploratory study of a number sense program to develop kindergarten students' number proficiency.

PubMed

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: 22 control and 36 experimental; at risk: 18 and 25) from five classrooms in a high-poverty elementary school participated in the study. Using a quasi-experimental design, classrooms were randomly assigned to either the intervention (number sense instruction, NSI) or control condition. Results indicated significant differences favoring the treatment students on all measures of number sense (e.g., spatial relationships, more and less relationships, benchmarks of five and ten, nonverbal calculations) at posttest and on a 3-week retention test. Furthermore, the effects were not mediated by at-risk status, suggesting that NSI may benefit a wide range of students. Implications in terms of preventing early mathematical learning difficulties are discussed.

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…

Earthquake number forecasts testing

NASA Astrophysics Data System (ADS)

Kagan, Yan Y.

2017-10-01

We study the distributions of earthquake numbers in two global earthquake catalogues: Global Centroid-Moment Tensor and Preliminary Determinations of Epicenters. The properties of these distributions are especially required to develop the number test for our forecasts of future seismic activity rate, tested by the Collaboratory for Study of Earthquake Predictability (CSEP). A common assumption, as used in the CSEP tests, is that the numbers are described by the Poisson distribution. It is clear, however, that the Poisson assumption for the earthquake number distribution is incorrect, especially for the catalogues with a lower magnitude threshold. In contrast to the one-parameter Poisson distribution so widely used to describe earthquake occurrences, the negative-binomial distribution (NBD) has two parameters. The second parameter can be used to characterize the clustering or overdispersion of a process. We also introduce and study a more complex three-parameter beta negative-binomial distribution. We investigate the dependence of parameters for both Poisson and NBD distributions on the catalogue magnitude threshold and on temporal subdivision of catalogue duration. First, we study whether the Poisson law can be statistically rejected for various catalogue subdivisions. We find that for most cases of interest, the Poisson distribution can be shown to be rejected statistically at a high significance level in favour of the NBD. Thereafter, we investigate whether these distributions fit the observed distributions of seismicity. For this purpose, we study upper statistical moments of earthquake numbers (skewness and kurtosis) and compare them to the theoretical values for both distributions. Empirical values for the skewness and the kurtosis increase for the smaller magnitude threshold and increase with even greater intensity for small temporal subdivision of catalogues. The Poisson distribution for large rate values approaches the Gaussian law, therefore its skewness

Sensible and Crazy Numbers

ERIC Educational Resources Information Center

Russo, James

2017-01-01

Using a game-based context and concentrating explicitly on language, students in the early years are able to make sense about place value amid the vagaries of the English language in naming numbers. This conceptual approach to understanding place value allows students to further develop number strategies beyond counting by ones.

The Child's Conception of Number.

ERIC Educational Resources Information Center

Piaget, Jean

Based on the hypothesis that the construction of number is closely related to the development of logic, this book records a series of experiments investigating classes, relations, and numbers as cognitive domains. The author finds that number is organized, stage after stage, in close connection with the gradual elaboration of systems of inclusions…

Mental Number Line, Number Line Estimation, and Mathematical Achievement: Their Interrelations in Grades 5 and 6

ERIC Educational Resources Information Center

Schneider, Michael; Grabner, Roland H.; Paetsch, Jennifer

2009-01-01

As indicated by the distance effect and the spatial-numerical association of response codes (SNARC) effect, natural numbers are mentally represented on a number line. Purportedly, this number line underlies children's number sense, which supports the acquisition of more advanced mathematical competencies. In 3 studies with a total of 429 fifth and…

Comparison of the Variations of Sunspot Number, Number of Sunspot Groups, and Sunspot Area, 1875 -2013

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).

Coordinating Numeric and Linear Units: Elementary Students' Strategies for Locating Whole Numbers on the Number Line

ERIC Educational Resources Information Center

Saxe, Geoffrey B.; Shaughnessy, Meghan M.; Gearhart, Maryl; Haldar, Lina Chopra

2013-01-01

Two investigations of fifth graders' strategies for locating whole numbers on number lines revealed patterns in students' coordination of numeric and linear units. In Study 1, we investigated the effects of context on students' placements of three numbers on an open number line. For one group ("n"?=?24), the line was presented in a…

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

A Lesson in Number Pattern

ERIC Educational Resources Information Center

Fletcher, Rodney

2008-01-01

This article presents a guided investigation into the spacial relationships between the centres of the squares in a Fibonacci tiling. It is essentially a lesson in number pattern, but includes work with surds, coordinate geometry, and some elementary use of complex numbers. The investigation could be presented to students in a number of ways…

Recent Research on Number Learning.

ERIC Educational Resources Information Center

Kieren, Thomas E., Ed.

Presented are materials related to the work of the Number and Measure and Rational Numbers working group of the Georgia Center for the Study of the Learning and Teaching of Mathematics. Much of the content reports on attempts to bring constructs from developmental psychology and mathematics to bear in understanding children's ideas of number and…

First Graders' Number Knowledge

ERIC Educational Resources Information Center

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

2010-01-01

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

Numbers Sense

ERIC Educational Resources Information Center

Kathotia, Vinay

2009-01-01

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

Old and New Magic Numbers

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 situationmore » 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?.« less

Role of Turbulent Prandtl Number on Heat Flux at Hypersonic Mach Numbers

NASA Technical Reports Server (NTRS)

Xiao, X.; Edwards, J. R.; Hassan, H. A.; Gaffney, R. L., Jr.

2007-01-01

A new turbulence model suited for calculating the turbulent Prandtl number as part of the solution is presented. The model is based on a set of two equations: one governing the variance of the enthalpy and the other governing its dissipation rate. These equations were derived from the exact energy equation and thus take into consideration compressibility and dissipation terms. The model is used to study two cases involving shock wave/boundary layer interaction at Mach 9.22 and Mach 5.0. In general, heat transfer prediction showed great improvement over traditional turbulence models where the turbulent Prandtl number is assumed constant. It is concluded that using a model that calculates the turbulent Prandtl number as part of the solution is the key to bridging the gap between theory and experiment for flows dominated by shock wave/boundary layer interactions.

Role of Turbulent Prandtl Number on Heat Flux at Hypersonic Mach Numbers

NASA Technical Reports Server (NTRS)

Gaffney, R. L., Jr.; Xiao, X.; Edwards, J. R.; Hassan, H. A.

2005-01-01

A new turbulence model suited for calculating the turbulent Prandtl number as part of the solution is presented. The model is based on a set of two equations: one governing the variance of the enthalpy and the other governing its dissipation rate. These equations were derived from the exact energy equation and thus take into consideration compressibility and dissipation terms. The model is used to study two cases involving shock wave/boundary layer interaction at Mach 9.22 and Mach 5.0. In general, heat transfer prediction showed great improvement over traditional turbulence models where the turbulent Prandtl number is assumed constant. It is concluded that using a model that calculates the turbulent Prandtl number as part of the solution is the key to bridging the gap between theory and experiment for flows dominated by shock wave/boundary layer interactions.

Hyperquarks and generation number

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buchmann, Alfons J.; Schmid, Michael L.

2005-03-01

In a model in which quarks and leptons are built up from two spin-(1/2) preons as fundamental entities, a new class of fermionic bound states (hyperquarks) arises. It turns out that these hyperquarks are necessary to fulfill the 't Hooft anomaly constraint, which then links the number of fermionic generations to the number of colors and hypercolors.

Number word use in toddlerhood is associated with number recall performance at seven years of age.

PubMed

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.

14 CFR 47.15 - Identification number.

Code of Federal Regulations, 2010 CFR

2010-01-01

... REGISTRATION General § 47.15 Identification number. (a) Number required. An applicant for Aircraft Registration must place a U.S. identification number (registration mark) on his Aircraft Registration Application... holder of a Dealer's Aircraft Registration Certificate who applies for a temporary registration number...

Number Guessing

ERIC Educational Resources Information Center

Sezin, Fatin

2009-01-01

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

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…

Object-based neglect in number processing

PubMed Central

2013-01-01

Recent evidence suggests that neglect patients seem to have particular problems representing relatively smaller numbers corresponding to the left part of the mental number line. However, while this indicates space-based neglect for representational number space little is known about whether and - if so - how object-based neglect influences number processing. To evaluate influences of object-based neglect in numerical cognition, a group of neglect patients and two control groups had to compare two-digit numbers to an internally represented standard. Conceptualizing two-digit numbers as objects of which the left part (i.e., the tens digit should be specifically neglected) we were able to evaluate object-based neglect for number magnitude processing. Object-based neglect was indicated by a larger unit-decade compatibility effect actually reflecting impaired processing of the leftward tens digits. Additionally, faster processing of within- as compared to between-decade items provided further evidence suggesting particular difficulties in integrating tens and units into the place-value structure of the Arabic number system. In summary, the present study indicates that, in addition to the spatial representation of number magnitude, also the processing of place-value information of multi-digit numbers seems specifically impaired in neglect patients. PMID:23343126

Contextual Effects on Number-Time Interaction

ERIC Educational Resources Information Center

Lu, Aitao; Hodges, Bert; Zhang, Jijia; Zhang, John X.

2009-01-01

Time perception has long been known to be affected by numerical representations. Recent studies further demonstrate that when participants estimate the duration of Arabic numbers, number magnitude, though task-irrelevant, biases duration judgment to produce underestimation for smaller numbers and overestimation for larger numbers. Such effects…

7 CFR 900.5 - Docket number.

Code of Federal Regulations, 2012 CFR

2012-01-01

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

7 CFR 900.5 - Docket number.

Code of Federal Regulations, 2013 CFR

2013-01-01

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

7 CFR 900.5 - Docket number.

Code of Federal Regulations, 2011 CFR

2011-01-01

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

7 CFR 900.5 - Docket number.

Code of Federal Regulations, 2014 CFR

2014-01-01

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

7 CFR 900.5 - Docket number.

Code of Federal Regulations, 2010 CFR

2010-01-01

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

THE DISCOUNTED REPRODUCTIVE NUMBER FOR EPIDEMIOLOGY

PubMed Central

Reluga, Timothy C.; Medlock, Jan; Galvani, Alison

2013-01-01

The basic reproductive number, , and the effective reproductive number, , are commonly used in mathematical epidemiology as summary statistics for the size and controllability of epidemics. However, these commonly used reproductive numbers can be misleading when applied to predict pathogen evolution because they do not incorporate the impact of the timing of events in the life-history cycle of the pathogen. To study evolution problems where the host population size is changing, measures like the ultimate proliferation rate must be used. A third measure of reproductive success, which combines properties of both the basic reproductive number and the ultimate proliferation rate, is the discounted reproductive number . The discounted reproductive number is a measure of reproductive success that is an individual’s expected lifetime offspring production discounted by the background population growth rate. Here, we draw attention to the discounted reproductive number by providing an explicit definition and a systematic application framework. We describe how the discounted reproductive number overcomes the limitations of both the standard reproductive numbers and proliferation rates, and show that is closely connected to Fisher’s reproductive values for different life-history stages PMID:19364158

Unsteady laminar flow with convective heat transfer through a rotating curved square duct with small curvature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mondal, Rabindra Nath, E-mail: rnmondal71@yahoo.com; Shaha, Poly Rani; Roy, Titob

Unsteady laminar flow with convective heat transfer through a curved square duct rotating at a constant angular velocity about the center of curvature is investigated numerically by using a spectral method, and covering a wide range of the Taylor number −300≤Tr≤1000 for the Dean number Dn = 1000. A temperature difference is applied across the vertical sidewalls for the Grashof number Gr = 100, where the outer wall is heated and the inner wall cooled, the top and bottom walls being adiabatic. Flow characteristics are investigated with the effects of rotational parameter, Tr, and the pressure-driven parameter, Dn, for themore » constant curvature 0.001. Time evolution calculations as well as their phase spaces show that the unsteady flow undergoes through various flow instabilities in the scenario ‘multi-periodic → chaotic → steady-state → periodic → multi-periodic → chaotic’, if Tr is increased in the positive direction. For negative rotation, however, time evolution calculations show that the flow undergoes in the scenario ‘multi-periodic → periodic → steady-state’, if Tr is increased in the negative direction. Typical contours of secondary flow patterns and temperature profiles are obtained at several values of Tr, and it is found that the unsteady flow consists of two- to six-vortex solutions if the duct rotation is involved. External heating is shown to generate a significant temperature gradient at the outer wall of the duct. This study also shows that there is a strong interaction between the heating-induced buoyancy force and the centrifugal-Coriolis instability in the curved channel that stimulates fluid mixing and consequently enhances heat transfer in the fluid.« less

The Translated Dowling Polynomials and Numbers.

PubMed

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

2014-01-01

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

7 CFR 75.48 - Identification number.

Code of Federal Regulations, 2014 CFR

2014-01-01

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

7 CFR 75.48 - Identification number.

Code of Federal Regulations, 2013 CFR

2013-01-01

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

7 CFR 987.102 - Lot number.

Code of Federal Regulations, 2010 CFR

2010-01-01

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

7 CFR 987.102 - Lot number.

Code of Federal Regulations, 2011 CFR

2011-01-01

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

7 CFR 987.102 - Lot number.

Code of Federal Regulations, 2013 CFR

2013-01-01

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

7 CFR 75.48 - Identification number.

Code of Federal Regulations, 2010 CFR

2010-01-01

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

7 CFR 987.102 - Lot number.

Code of Federal Regulations, 2014 CFR

2014-01-01

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

7 CFR 75.48 - Identification number.

Code of Federal Regulations, 2012 CFR

2012-01-01

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

7 CFR 987.102 - Lot number.

Code of Federal Regulations, 2012 CFR

2012-01-01

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

7 CFR 75.48 - Identification number.

Code of Federal Regulations, 2011 CFR

2011-01-01

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

9 CFR 355.8 - Official number.

Code of Federal Regulations, 2013 CFR

2013-01-01

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

9 CFR 355.8 - Official number.

Code of Federal Regulations, 2012 CFR

2012-01-01

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

7 CFR 29.32 - Identification number.

Code of Federal Regulations, 2010 CFR

2010-01-01

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

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... Steam Gauges § 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known, shall be stamped on the steam dome or manhole flange. If the builder's number cannot be obtained, an...

9 CFR 355.8 - Official number.

Code of Federal Regulations, 2014 CFR

2014-01-01

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

7 CFR 29.32 - Identification number.

Code of Federal Regulations, 2013 CFR

2013-01-01

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

7 CFR 29.32 - Identification number.

Code of Federal Regulations, 2014 CFR

2014-01-01

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

7 CFR 29.32 - Identification number.

Code of Federal Regulations, 2011 CFR

2011-01-01

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

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... Steam Gauges § 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known, shall be stamped on the steam dome or manhole flange. If the builder's number cannot be obtained, an...

7 CFR 29.32 - Identification number.

Code of Federal Regulations, 2012 CFR

2012-01-01

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

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... Steam Gauges § 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known, shall be stamped on the steam dome or manhole flange. If the builder's number cannot be obtained, an...

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... Steam Gauges § 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known, shall be stamped on the steam dome or manhole flange. If the builder's number cannot be obtained, an...

Low Reynolds Number Vehicles

DTIC Science & Technology

1985-02-01

numbers. At high altitudes aircraft gas turbine engine fan, compressor, and turbine blades with their small chords encounter Reynolds numhers...light man-carrying/man-powered aircraft , minl-RPVs at low altitude, and wind turbines . Since the airfoil section forms the basic element in the...Wind turbine blades also require high aerodynamic efficiency and all-weather capabilities. The need for efficient low Reynolds number airfoils which

Dimensionless numbers in additive manufacturing

NASA Astrophysics Data System (ADS)

Mukherjee, T.; Manvatkar, V.; De, A.; DebRoy, T.

2017-02-01

The effects of many process variables and alloy properties on the structure and properties of additively manufactured parts are examined using four dimensionless numbers. The structure and properties of components made from 316 Stainless steel, Ti-6Al-4V, and Inconel 718 powders for various dimensionless heat inputs, Peclet numbers, Marangoni numbers, and Fourier numbers are studied. Temperature fields, cooling rates, solidification parameters, lack of fusion defects, and thermal strains are examined using a well-tested three-dimensional transient heat transfer and fluid flow model. The results show that lack of fusion defects in the fabricated parts can be minimized by strengthening interlayer bonding using high values of dimensionless heat input. The formation of harmful intermetallics such as laves phases in Inconel 718 can be suppressed using low heat input that results in a small molten pool, a steep temperature gradient, and a fast cooling rate. Improved interlayer bonding can be achieved at high Marangoni numbers, which results in vigorous circulation of liquid metal, larger pool dimensions, and greater depth of penetration. A high Fourier number ensures rapid cooling, low thermal distortion, and a high ratio of temperature gradient to the solidification growth rate with a greater tendency of plane front solidification.

7 CFR 46.20 - Lot numbers.

Code of Federal Regulations, 2011 CFR

2011-01-01

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

7 CFR 46.20 - Lot numbers.

Code of Federal Regulations, 2013 CFR

2013-01-01

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

7 CFR 46.20 - Lot numbers.

Code of Federal Regulations, 2014 CFR

2014-01-01

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

7 CFR 46.20 - Lot numbers.

Code of Federal Regulations, 2012 CFR

2012-01-01

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

7 CFR 46.20 - Lot numbers.

Code of Federal Regulations, 2010 CFR

2010-01-01

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

Degenerate Cauchy numbers of the third kind.

PubMed

Pyo, Sung-Soo; Kim, Taekyun; Rim, Seog-Hoon

2018-01-01

Since Cauchy numbers were introduced, various types of Cauchy numbers have been presented. In this paper, we define degenerate Cauchy numbers of the third kind and give some identities for the degenerate Cauchy numbers of the third kind. In addition, we give some relations between four kinds of the degenerate Cauchy numbers, the Daehee numbers and the degenerate Bernoulli numbers.

Mach number dependence of electron heating at high Mach number interplanetary shocks in the inner heliospere

NASA Astrophysics Data System (ADS)

Matsukiyo, Shuichi

In the inner heliosphere a variety of interplanetary shocks with different Mach numbers are expected to be present. A possible maximum Mach number at 0.3AU from the sun is esti-mated to be about 40. Efficiency of electron heating in such high Mach number shocks is one of the outstanding issues of space plasma physics as well as astrophysics. Here, from this aspect, electron heating rate through microinstabilities generated in the transition region of a quasi-perpendicular shock for wide range of Mach numbers is investigated. Saturation levels of effective electron temperature as a result of modified two-stream instability (MTSI) are es-timated by using a semianalytic approach which we call an extended quasilinear analysis here. The results are compared with one-dimensional full particle-in-cell simulations. It is revealed that Mach number dependence of the effective electron temperature is weak when a Mach num-ber is below a certain critical value. Above the critical value, electron temperature increases being proportional to an upstream flow energy because of that a dominant microinstability in the foot changes from the MTSI to Buneman instability. The critical Mach number is roughly estimated to be a few tens.

Numbers and space: associations and dissociations.

PubMed

Nathan, Merav Ben; Shaki, Samuel; Salti, Moti; Algom, Daniel

2009-06-01

A cornerstone of contemporary research in numerical cognition is the surprising link found between numbers and space. In particular, people react faster and more accurately to small numbers with a left-hand key and to large numbers with a right-hand key. Because this contingency is found in a variety of tasks, it has been taken to support the automatic activation of magnitude as well as the notion of a mental number line arranged from left to right. The present study challenges the presence of a link between left-right location, on the one hand, and small-large number, on the other hand. We show that a link exists between space and relative magnitude, a relationship that might or might not be unique to numbers.

The Relationship between Children's Familiarity with Numbers and Their Performance in Bounded and Unbounded Number Line Estimations

ERIC Educational Resources Information Center

Ebersbach, Mirjam; Luwel, Koen; Verschaffel, Lieven

2015-01-01

Children's estimation skills on a bounded and unbounded number line task were assessed in the light of their familiarity with numbers. Kindergartners, first graders, and second graders (N = 120) estimated the position of numbers on a 1--100 number line, marked with either two reference points (i.e., 1 and 10: unbounded condition) or three…

Number theoretical foundations in cryptography

NASA Astrophysics Data System (ADS)

Atan, Kamel Ariffin Mohd

2017-08-01

In recent times the hazards in relationships among entities in different establishments worldwide have generated exciting developments in cryptography. Central to this is the theory of numbers. This area of mathematics provides very rich source of fundamental materials for constructing secret codes. Some number theoretical concepts that have been very actively used in designing crypto systems will be highlighted in this presentation. This paper will begin with introduction to basic number theoretical concepts which for many years have been thought to have no practical applications. This will include several theoretical assertions that were discovered much earlier in the historical development of number theory. This will be followed by discussion on the "hidden" properties of these assertions that were later exploited by designers of cryptosystems in their quest for developing secret codes. This paper also highlights some earlier and existing cryptosystems and the role played by number theoretical concepts in their constructions. The role played by cryptanalysts in detecting weaknesses in the systems developed by cryptographers concludes this presentation.

33 CFR 173.15 - Vessel number required.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 33 Navigation and Navigable Waters 2 2011-07-01 2011-07-01 false Vessel number required. 173.15...) BOATING SAFETY VESSEL NUMBERING AND CASUALTY AND ACCIDENT REPORTING Numbering § 173.15 Vessel number...: (1) It has a number issued on a certificate of number by the issuing authority in the State in which...

33 CFR 173.15 - Vessel number required.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 33 Navigation and Navigable Waters 2 2014-07-01 2014-07-01 false Vessel number required. 173.15...) BOATING SAFETY VESSEL NUMBERING AND CASUALTY AND ACCIDENT REPORTING Numbering § 173.15 Vessel number...: (1) It has a number issued on a certificate of number by the issuing authority in the State of...

33 CFR 173.15 - Vessel number required.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 33 Navigation and Navigable Waters 2 2012-07-01 2012-07-01 false Vessel number required. 173.15...) BOATING SAFETY VESSEL NUMBERING AND CASUALTY AND ACCIDENT REPORTING Numbering § 173.15 Vessel number...: (1) It has a number issued on a certificate of number by the issuing authority in the State of...

Can a safety-in-numbers effect and a hazard-in-numbers effect co-exist in the same data?

PubMed

Elvik, Rune

2013-11-01

Safety-in-numbers denotes a non-linear relationship between exposure (traffic volume) and the number of accidents, characterised by declining risk as traffic volume increases. There is safety-in-numbers when the number of accidents increases less than proportional to traffic volume, e.g. a doubling of traffic volume is associated with less than a doubling of the number of accidents. Hazard-in-numbers, a less-used concept, refers to the opposite effect: the number of accidents increases more than in proportion to traffic volume, e.g. is more than doubled when traffic volume is doubled. This paper discusses whether a safety-in-numbers effect and a hazard-in-numbers effect can co-exist in the same data. It is concluded that both effects can exist in a given data set. The paper proposes to make a distinction between partial safety-in-numbers and complete safety-in-numbers. Another issue that has been raised in discussions about the safety-in-numbers effect is whether the effect found in some studies is an artefact created by the way exposure was measured. The paper discusses whether measuring exposure as a rate or a share, e.g. kilometres travelled per inhabitant per year, will generate a safety-in-numbers effect as a statistical artefact. It is concluded that this is the case. The preferred measure of exposure is a count of the number of road users. The count should not be converted to a rate or to the share any group of road user contribute to total traffic volume. Copyright © 2013 Elsevier Ltd. All rights reserved.

iMAST Quarterly, Number 4, 1999

DTIC Science & Technology

1999-01-01

ELEMENT NUMBER 6 . AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Penn State... 6 Calendar of Events .............................................. 8 Good-bye We are rapidly approaching the end of 1999 and...U.Ed. ARL 00- 6 DIRECTOR’S CORNER iMAST Quarterly 1999 No. 4 3 FEATURE ARTICLE Focus on Environmentally Friendly Technologies Automated Paint

Who can escape the natural number bias in rational number tasks? A study involving students and experts.

PubMed

Obersteiner, Andreas; Hoof, Jo Van; Verschaffel, Lieven; Dooren, Wim Van

2016-08-01

Many learners have difficulties with rational number tasks because they persistently rely on their natural number knowledge, which is not always applicable. Studies show that such a natural number bias can mislead not only children but also educated adults. It is still unclear whether and under what conditions mathematical expertise enables people to be completely unaffected by such a bias on tasks in which people with less expertise are clearly biased. We compared the performance of eighth-grade students and expert mathematicians on the same set of algebraic expression problems that addressed the effect of arithmetic operations (multiplication and division). Using accuracy and response time measures, we found clear evidence for a natural number bias in students but no traces of a bias in experts. The data suggested that whereas students based their answers on their intuitions about natural numbers, expert mathematicians relied on their skilled intuitions about algebraic expressions. We conclude that it is possible for experts to be unaffected by the natural number bias on rational number tasks when they use strategies that do not involve natural numbers. © 2015 The British Psychological Society.

Asymptotics of quantum weighted Hurwitz numbers

NASA Astrophysics Data System (ADS)

Harnad, J.; Ortmann, Janosch

2018-06-01

This work concerns both the semiclassical and zero temperature asymptotics of quantum weighted double Hurwitz numbers. The partition function for quantum weighted double Hurwitz numbers can be interpreted in terms of the energy distribution of a quantum Bose gas with vanishing fugacity. We compute the leading semiclassical term of the partition function for three versions of the quantum weighted Hurwitz numbers, as well as lower order semiclassical corrections. The classical limit is shown to reproduce the simple single and double Hurwitz numbers studied by Okounkov and Pandharipande (2000 Math. Res. Lett. 7 447–53, 2000 Lett. Math. Phys. 53 59–74). The KP-Toda τ-function that serves as generating function for the quantum Hurwitz numbers is shown to have the τ-function of Okounkov and Pandharipande (2000 Math. Res. Lett. 7 447–53, 2000 Lett. Math. Phys. 53 59–74) as its leading term in the classical limit, and, with suitable scaling, the same holds for the partition function, the weights and expectations of Hurwitz numbers. We also compute the zero temperature limit of the partition function and quantum weighted Hurwitz numbers. The KP or Toda τ-function serving as generating function for the quantum Hurwitz numbers are shown to give the one for Belyi curves in the zero temperature limit and, with suitable scaling, the same holds true for the partition function, the weights and the expectations of Hurwitz numbers.

The precision of mapping between number words and the approximate number system predicts children's formal math abilities.

PubMed

Libertus, Melissa E; Odic, Darko; Feigenson, Lisa; Halberda, Justin

2016-10-01

Children can represent number in at least two ways: by using their non-verbal, intuitive approximate number system (ANS) and by using words and symbols to count and represent numbers exactly. Furthermore, by the time they are 5years old, children can map between the ANS and number words, as evidenced by their ability to verbally estimate numbers of items without counting. How does the quality of the mapping between approximate and exact numbers relate to children's math abilities? The role of the ANS-number word mapping in math competence remains controversial for at least two reasons. First, previous work has not examined the relation between verbal estimation and distinct subtypes of math abilities. Second, previous work has not addressed how distinct components of verbal estimation-mapping accuracy and variability-might each relate to math performance. Here, we addressed these gaps by measuring individual differences in ANS precision, verbal number estimation, and formal and informal math abilities in 5- to 7-year-old children. We found that verbal estimation variability, but not estimation accuracy, predicted formal math abilities, even when controlling for age, expressive vocabulary, and ANS precision, and that it mediated the link between ANS precision and overall math ability. These findings suggest that variability in the ANS-number word mapping may be especially important for formal math abilities. Copyright © 2016 Elsevier Inc. All rights reserved.

The natural number bias and its role in rational number understanding in children with dyscalculia. Delay or deficit?

PubMed

Van Hoof, Jo; Verschaffel, Lieven; Ghesquière, Pol; Van Dooren, Wim

2017-12-01

Previous research indicated that in several cases learners' errors on rational number tasks can be attributed to learners' tendency to (wrongly) apply natural number properties. There exists a large body of literature both on learners' struggle with understanding the rational number system and on the role of the natural number bias in this struggle. However, little is known about this phenomenon in learners with dyscalculia. We investigated the rational number understanding of learners with dyscalculia and compared it with the rational number understanding of learners without dyscalculia. Three groups of learners were included: sixth graders with dyscalculia, a chronological age match group, and an ability match group. The results showed that the rational number understanding of learners with dyscalculia is significantly lower than that of typically developing peers, but not significantly different from younger learners, even after statistically controlling for mathematics achievement. Next to a delay in their mathematics achievement, learners with dyscalculia seem to have an extra delay in their rational number understanding, compared with peers. This is especially the case in those rational number tasks where one has to inhibit natural number knowledge to come to the right answer. Copyright © 2017 Elsevier Ltd. All rights reserved.

48 CFR 304.7001 - Numbering acquisitions.

Code of Federal Regulations, 2011 CFR

2011-10-01

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

Calibrating the mental number line.

PubMed

Izard, Véronique; Dehaene, Stanislas

2008-03-01

Human adults are thought to possess two dissociable systems to represent numbers: an approximate quantity system akin to a mental number line, and a verbal system capable of representing numbers exactly. Here, we study the interface between these two systems using an estimation task. Observers were asked to estimate the approximate numerosity of dot arrays. We show that, in the absence of calibration, estimates are largely inaccurate: responses increase monotonically with numerosity, but underestimate the actual numerosity. However, insertion of a few inducer trials, in which participants are explicitly (and sometimes misleadingly) told that a given display contains 30 dots, is sufficient to calibrate their estimates on the whole range of stimuli. Based on these empirical results, we develop a model of the mapping between the numerical symbols and the representations of numerosity on the number line.

Predicting first-grade mathematics achievement: the contributions of domain-general cognitive abilities, nonverbal number sense, and early number competence.

PubMed

Hornung, Caroline; Schiltz, Christine; Brunner, Martin; Martin, Romain

2014-01-01

Early number competence, grounded in number-specific and domain-general cognitive abilities, is theorized to lay the foundation for later math achievement. Few longitudinal studies have tested a comprehensive model for early math development. Using structural equation modeling and mediation analyses, the present work examined the influence of kindergarteners' nonverbal number sense and domain-general abilities (i.e., working memory, fluid intelligence, and receptive vocabulary) and their early number competence (i.e., symbolic number skills) on first grade math achievement (i.e., arithmetic, shape and space skills, and number line estimation) assessed 1 year later. Latent regression models revealed that nonverbal number sense and working memory are central building blocks for developing early number competence in kindergarten and that early number competence is key for first grade math achievement. After controlling for early number competence, fluid intelligence significantly predicted arithmetic and number line estimation while receptive vocabulary significantly predicted shape and space skills. In sum we suggest that early math achievement draws on different constellations of number-specific and domain-general mechanisms.

Predicting first-grade mathematics achievement: the contributions of domain-general cognitive abilities, nonverbal number sense, and early number competence

PubMed Central

Hornung, Caroline; Schiltz, Christine; Brunner, Martin; Martin, Romain

2014-01-01

Early number competence, grounded in number-specific and domain-general cognitive abilities, is theorized to lay the foundation for later math achievement. Few longitudinal studies have tested a comprehensive model for early math development. Using structural equation modeling and mediation analyses, the present work examined the influence of kindergarteners' nonverbal number sense and domain-general abilities (i.e., working memory, fluid intelligence, and receptive vocabulary) and their early number competence (i.e., symbolic number skills) on first grade math achievement (i.e., arithmetic, shape and space skills, and number line estimation) assessed 1 year later. Latent regression models revealed that nonverbal number sense and working memory are central building blocks for developing early number competence in kindergarten and that early number competence is key for first grade math achievement. After controlling for early number competence, fluid intelligence significantly predicted arithmetic and number line estimation while receptive vocabulary significantly predicted shape and space skills. In sum we suggest that early math achievement draws on different constellations of number-specific and domain-general mechanisms. PMID:24772098

Ordinality and the nature of symbolic numbers.

PubMed

Lyons, Ian M; Beilock, Sian L

2013-10-23

The view that representations of symbolic and nonsymbolic numbers are closely tied to one another is widespread. However, the link between symbolic and nonsymbolic numbers is almost always inferred from cardinal processing tasks. In the current work, we show that considering ordinality instead points to striking differences between symbolic and nonsymbolic numbers. Human behavioral and neural data show that ordinal processing of symbolic numbers (Are three Indo-Arabic numerals in numerical order?) is distinct from symbolic cardinal processing (Which of two numerals represents the greater quantity?) and nonsymbolic number processing (ordinal and cardinal judgments of dot-arrays). Behaviorally, distance-effects were reversed when assessing ordinality in symbolic numbers, but canonical distance-effects were observed for cardinal judgments of symbolic numbers and all nonsymbolic judgments. At the neural level, symbolic number-ordering was the only numerical task that did not show number-specific activity (greater than control) in the intraparietal sulcus. Only activity in left premotor cortex was specifically associated with symbolic number-ordering. For nonsymbolic numbers, activation in cognitive-control areas during ordinal processing and a high degree of overlap between ordinal and cardinal processing networks indicate that nonsymbolic ordinality is assessed via iterative cardinality judgments. This contrasts with a striking lack of neural overlap between ordinal and cardinal judgments anywhere in the brain for symbolic numbers, suggesting that symbolic number processing varies substantially with computational context. Ordinal processing sheds light on key differences between symbolic and nonsymbolic number processing both behaviorally and in the brain. Ordinality may prove important for understanding the power of representing numbers symbolically.

Compilation of Reprints Number 64.

DTIC Science & Technology

1987-11-01

EFFECT 01 llt’ItRO(;lNEN II 1 S IN "D)" ON Till: DUlCA reprint R..VIT OF 6) D tI, PERFORMING ORG. REPORT NUMBER 7 AUTHoR(.) S CONTRACT OR GRANT NUMBER...I MENKt;, WILLI:\\M NO0() 14- 84 - C- 0218 9 PERFORMING ORGANIZATION NAME AND ADORESS 10 PROGRAM ELEMENT, PROJECT TASK AREA & WORK UNIT NUMBERS...mainly increase it. We did not identify any major effect of scatterer aspect ratio on the decay rate in the one relevant test that we performed (dikes

Thermo-fluid-dynamics of natural convection around a heated vertical plate with a critical assessment of the standard similarity theory

NASA Astrophysics Data System (ADS)

Guha, Abhijit; Nayek, Subhajit

2017-10-01

A compulsory element of all textbooks on natural convection has been a detailed similarity analysis for laminar natural convection on a heated semi-infinite vertical plate and a routinely used boundary condition for such analysis is u = 0 at x = 0. The same boundary condition continues to be assumed in related theoretical analyses, even in recent publications. The present work examines the consequence of this long-held assumption, which appears to have never been questioned in the literature, on the fluid dynamics and heat transfer characteristics. The assessment has been made here by solving the Navier-Stokes equations numerically with two boundary conditions—one with constrained velocity at x = 0 to mimic the similarity analysis and the other with no such constraints simulating the case of a heated vertical plate in an infinite expanse of the quiescent fluid medium. It is found that the fluid flow field given by the similarity theory is drastically different from that given by the computational fluid dynamics (CFD) simulations with unconstrained velocity. This also reflects on the Nusselt number, the prediction of the CFD simulations with unconstrained velocity being quite close to the experimentally measured values at all Grashof and Prandtl numbers (this is the first time theoretically computed values of the average Nusselt number N u ¯ are found to be so close to the experimental values). The difference of the Nusselt number (Δ N u ¯ ) predicted by the similarity theory and that by the CFD simulations (as well as the measured values), both computed with a high degree of precision, can be very significant, particularly at low Grashof numbers and at Prandtl numbers far removed from unity. Computations show that within the range of investigations (104 ≤ GrL ≤ 108, 0.01 ≤ Pr ≤ 100), the maximum value of Δ N u ¯ may be of the order 50%. Thus, for quantitative predictions, the available theory (i.e., similarity analysis) can be rather inadequate. With

47 CFR 51.203 - Number portability.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 47 Telecommunication 3 2010-10-01 2010-10-01 false Number portability. 51.203 Section 51.203 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES (CONTINUED) INTERCONNECTION Obligations of All Local Exchange Carriers § 51.203 Number portability. The rules governing number portability...

47 CFR 51.203 - Number portability.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 47 Telecommunication 3 2012-10-01 2012-10-01 false Number portability. 51.203 Section 51.203 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES (CONTINUED) INTERCONNECTION Obligations of All Local Exchange Carriers § 51.203 Number portability. The rules governing number portability...

47 CFR 51.203 - Number portability.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 47 Telecommunication 3 2014-10-01 2014-10-01 false Number portability. 51.203 Section 51.203 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES (CONTINUED) INTERCONNECTION Obligations of All Local Exchange Carriers § 51.203 Number portability. The rules governing number portability...

47 CFR 51.203 - Number portability.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 47 Telecommunication 3 2011-10-01 2011-10-01 false Number portability. 51.203 Section 51.203 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES (CONTINUED) INTERCONNECTION Obligations of All Local Exchange Carriers § 51.203 Number portability. The rules governing number portability...

47 CFR 51.203 - Number portability.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 47 Telecommunication 3 2013-10-01 2013-10-01 false Number portability. 51.203 Section 51.203 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES (CONTINUED) INTERCONNECTION Obligations of All Local Exchange Carriers § 51.203 Number portability. The rules governing number portability...

Schmidt-number witnesses and bound entanglement

NASA Astrophysics Data System (ADS)

Sanpera, Anna; Bruß, Dagmar; Lewenstein, Maciej

2001-05-01

The Schmidt number of a mixed state characterizes the minimum Schmidt rank of the pure states needed to construct it. We investigate the Schmidt number of an arbitrary mixed state by studying Schmidt-number witnesses that detect it. We present a canonical form of such witnesses and provide constructive methods for their optimization. Finally, we present strong evidence that all bound entangled states with positive partial transpose in C3⊗C3 have Schmidt number 2.

48 CFR 204.7003 - Basic PII number.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 48 Federal Acquisition Regulations System 3 2014-10-01 2014-10-01 false Basic PII number. 204.7003... OF DEFENSE GENERAL ADMINISTRATIVE MATTERS Uniform Procurement Instrument Identification Numbers 204.7003 Basic PII number. (a) Elements of a number. The number consists of 13 alpha-numeric characters...

48 CFR 204.7003 - Basic PII number.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 48 Federal Acquisition Regulations System 3 2013-10-01 2013-10-01 false Basic PII number. 204.7003... OF DEFENSE GENERAL ADMINISTRATIVE MATTERS Uniform Procurement Instrument Identification Numbers 204.7003 Basic PII number. (a) Elements of a number. The number consists of 13 alpha-numeric characters...

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 § 32.20 Numbering convention. (a) The number “32...

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 § 32.20 Numbering convention. (a) The number “32...

7 CFR 29.133 - Identification number.

Code of Federal Regulations, 2013 CFR

2013-01-01

... 7 Agriculture 2 2013-01-01 2013-01-01 false Identification number. 29.133 Section 29.133... REGULATIONS TOBACCO INSPECTION Regulations Miscellaneous § 29.133 Identification number. The Director may require the use of official identification numbers in connection with tobacco certificated or sampled...

47 CFR 32.6622 - Number services.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 47 Telecommunication 2 2010-10-01 2010-10-01 false Number services. 32.6622 Section 32.6622... FOR TELECOMMUNICATIONS COMPANIES Instructions for Expense Accounts § 32.6622 Number services. This account shall include costs incurred in providing customer number and classified listings. This includes...

47 CFR 32.6622 - Number services.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 47 Telecommunication 2 2012-10-01 2012-10-01 false Number services. 32.6622 Section 32.6622... FOR TELECOMMUNICATIONS COMPANIES Instructions for Expense Accounts § 32.6622 Number services. This account shall include costs incurred in providing customer number and classified listings. This includes...

47 CFR 32.6622 - Number services.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 47 Telecommunication 2 2013-10-01 2013-10-01 false Number services. 32.6622 Section 32.6622... FOR TELECOMMUNICATIONS COMPANIES Instructions for Expense Accounts § 32.6622 Number services. This account shall include costs incurred in providing customer number and classified listings. This includes...

7 CFR 29.133 - Identification number.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 2 2010-01-01 2010-01-01 false Identification number. 29.133 Section 29.133... REGULATIONS TOBACCO INSPECTION Regulations Miscellaneous § 29.133 Identification number. The Director may require the use of official identification numbers in connection with tobacco certificated or sampled...

7 CFR 29.133 - Identification number.

Code of Federal Regulations, 2012 CFR

2012-01-01

... 7 Agriculture 2 2012-01-01 2012-01-01 false Identification number. 29.133 Section 29.133... REGULATIONS TOBACCO INSPECTION Regulations Miscellaneous § 29.133 Identification number. The Director may require the use of official identification numbers in connection with tobacco certificated or sampled...

47 CFR 32.6622 - Number services.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 47 Telecommunication 2 2014-10-01 2014-10-01 false Number services. 32.6622 Section 32.6622... FOR TELECOMMUNICATIONS COMPANIES Instructions for Expense Accounts § 32.6622 Number services. This account shall include costs incurred in providing customer number and classified listings. This includes...

7 CFR 29.133 - Identification number.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 2 2014-01-01 2014-01-01 false Identification number. 29.133 Section 29.133... REGULATIONS TOBACCO INSPECTION Regulations Miscellaneous § 29.133 Identification number. The Director may require the use of official identification numbers in connection with tobacco certificated or sampled...

47 CFR 32.6622 - Number services.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 47 Telecommunication 2 2011-10-01 2011-10-01 false Number services. 32.6622 Section 32.6622... FOR TELECOMMUNICATIONS COMPANIES Instructions for Expense Accounts § 32.6622 Number services. This account shall include costs incurred in providing customer number and classified listings. This includes...

7 CFR 29.133 - Identification number.

Code of Federal Regulations, 2011 CFR

2011-01-01

... 7 Agriculture 2 2011-01-01 2011-01-01 false Identification number. 29.133 Section 29.133... REGULATIONS TOBACCO INSPECTION Regulations Miscellaneous § 29.133 Identification number. The Director may require the use of official identification numbers in connection with tobacco certificated or sampled...

75 FR 18572 - Facility Control Numbers

Federal Register 2010, 2011, 2012, 2013, 2014

2010-04-12

... DEPARTMENT OF THE TREASURY Internal Revenue Service Facility Control Numbers AGENCY: Internal Revenue Service (IRS), Treasury. ACTION: Notice of planned use of Facility Control Numbers. SUMMARY: The IRS has developed and is publishing in this issue of the Federal Register, Facility Control Numbers to...

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 § 32.20 Numbering convention. (a) The number “32...

14 CFR 47.15 - Registration number.

Code of Federal Regulations, 2011 CFR

2011-01-01

... REGISTRATION General § 47.15 Registration number. (a) Number required. An applicant for aircraft registration must place a U.S. registration number (registration mark) on the Aircraft Registration Application, AC... Dealer's Aircraft Registration Certificate, AC Form 8050-6, who applies for a temporary registration...

14 CFR 47.15 - Registration number.

Code of Federal Regulations, 2013 CFR

2013-01-01

... REGISTRATION General § 47.15 Registration number. (a) Number required. An applicant for aircraft registration must place a U.S. registration number (registration mark) on the Aircraft Registration Application, AC... Dealer's Aircraft Registration Certificate, AC Form 8050-6, who applies for a temporary registration...

14 CFR 47.15 - Registration number.

Code of Federal Regulations, 2014 CFR

2014-01-01

... REGISTRATION General § 47.15 Registration number. (a) Number required. An applicant for aircraft registration must place a U.S. registration number (registration mark) on the Aircraft Registration Application, AC... Dealer's Aircraft Registration Certificate, AC Form 8050-6, who applies for a temporary registration...

14 CFR 47.15 - Registration number.

Code of Federal Regulations, 2012 CFR

2012-01-01

... REGISTRATION General § 47.15 Registration number. (a) Number required. An applicant for aircraft registration must place a U.S. registration number (registration mark) on the Aircraft Registration Application, AC... Dealer's Aircraft Registration Certificate, AC Form 8050-6, who applies for a temporary registration...

Quantum random number generation

DOE PAGES

Ma, Xiongfeng; Yuan, Xiao; Cao, Zhu; ...

2016-06-28

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

14821AT LANCE, Missile Number 2419, Round Number 349APT, 12 May 1980.

DTIC Science & Technology

1980-05-01

WSTRUCTIONUREPOT DCUMNTAIONPAG EPORE COMPLEMON PORN REPORT NUMBER 2GOTACCESSION NO S. RECIPIENT’S CATALOG NUMBER TDR 1148 __7 0_____T___ ~. *.~----...,S. TYPE OF...Data at 0815 MDT ---------- 4 4. White Sands Desert Site (WSD) Significant Level Data at 0815 MDT ------------------------------------ 5 5. WSD Upper...humidity, dew point (0 C), density (gm/n,3), Wind direction and speed, and cloud cover were made at the LC-39 Met Site at T-0 minutes. (2) Monitor of

1 CFR 21.35 - OMB control numbers.

Code of Federal Regulations, 2012 CFR

2012-01-01

... 1 General Provisions 1 2012-01-01 2012-01-01 false OMB control numbers. 21.35 Section 21.35... PROCESSING OF DOCUMENTS PREPARATION OF DOCUMENTS SUBJECT TO CODIFICATION General Omb Control Numbers § 21.35 OMB control numbers. To display OMB control numbers in agency regulations, those numbers shall be...

1 CFR 21.35 - OMB control numbers.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 1 General Provisions 1 2014-01-01 2012-01-01 true OMB control numbers. 21.35 Section 21.35 General... DOCUMENTS PREPARATION OF DOCUMENTS SUBJECT TO CODIFICATION General Omb Control Numbers § 21.35 OMB control numbers. To display OMB control numbers in agency regulations, those numbers shall be placed...

1 CFR 21.35 - OMB control numbers.

Code of Federal Regulations, 2013 CFR

2013-01-01

... 1 General Provisions 1 2013-01-01 2012-01-01 true OMB control numbers. 21.35 Section 21.35 General... DOCUMENTS PREPARATION OF DOCUMENTS SUBJECT TO CODIFICATION General Omb Control Numbers § 21.35 OMB control numbers. To display OMB control numbers in agency regulations, those numbers shall be placed...

1 CFR 21.35 - OMB control numbers.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 1 General Provisions 1 2010-01-01 2010-01-01 false OMB control numbers. 21.35 Section 21.35... PROCESSING OF DOCUMENTS PREPARATION OF DOCUMENTS SUBJECT TO CODIFICATION General Omb Control Numbers § 21.35 OMB control numbers. To display OMB control numbers in agency regulations, those numbers shall be...

Lepton number violation in theories with a large number of standard model copies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kovalenko, Sergey; Schmidt, Ivan; Paes, Heinrich

2011-03-01

We examine lepton number violation (LNV) in theories with a saturated black hole bound on a large number of species. Such theories have been advocated recently as a possible solution to the hierarchy problem and an explanation of the smallness of neutrino masses. On the other hand, the violation of the lepton number can be a potential phenomenological problem of this N-copy extension of the standard model as due to the low quantum gravity scale black holes may induce TeV scale LNV operators generating unacceptably large rates of LNV processes. We show, however, that this issue can be avoided bymore » introducing a spontaneously broken U{sub 1(B-L)}. Then, due to the existence of a specific compensation mechanism between contributions of different Majorana neutrino states, LNV processes in the standard model copy become extremely suppressed with rates far beyond experimental reach.« less

How to Learn the Natural Numbers: Inductive Inference and the Acquisition of Number Concepts

ERIC Educational Resources Information Center

Margolis, Eric; Laurence, Stephen

2008-01-01

Theories of number concepts often suppose that the natural numbers are acquired as children learn to count and as they draw an induction based on their interpretation of the first few count words. In a bold critique of this general approach, Rips, Asmuth, Bloomfield [Rips, L., Asmuth, J. & Bloomfield, A. (2006). Giving the boot to the bootstrap:…

Lattice stick number of knots

NASA Astrophysics Data System (ADS)

Huang, Yuanfei; Yang, Weiling

2017-12-01

The minimal number of straight line segments required to construct a polygonal presentation of the knot K in the cubic lattice is called the lattice stick number of the knot K, denoted by S_L(K) . It is known that S_L(K)≥slant15 if the crossing number of K, C_r(K) , satisfies C_r(K)≥slant5 , and the main result of this paper is to improve this to S_L(K)≥slant16 if C_r(K)≥slant5 . Furthermore, we will show that S_L(K)=16 for K=51 and K=52 which implies that this lower bound cannot be improved except for knots with higher crossing numbers. Project supported by the NSFC grants 11531006, 11371367 and 11271290, and the Fundamental Research Funds for the Central Universities 20720160038 and Fujian Province young and middle-aged teacher education research project JA15016.

Resolving Number Ambiguities during Language Comprehension

ERIC Educational Resources Information Center

Bader, Markus; Haussler, Jana

2009-01-01

This paper investigates how readers process number ambiguous noun phrases in subject position. A speeded-grammaticality judgment experiment and two self-paced reading experiments were conducted involving number ambiguous subjects in German verb-end clauses. Number preferences for individual nouns were estimated by means of two questionnaire…

47 CFR 95.671 - Serial number.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 47 Telecommunication 5 2010-10-01 2010-10-01 false Serial number. 95.671 Section 95.671 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES PERSONAL RADIO... number. The serial number of each CB transmitter must be engraved on the transmitter chassis. [53 FR...

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... number. The serial number of each CB transmitter must be engraved on the transmitter chassis. [53 FR...

20 CFR 404.1220 - Identification numbers.

Code of Federal Regulations, 2012 CFR

2012-04-01

... 20 Employees' Benefits 2 2012-04-01 2012-04-01 false Identification numbers. 404.1220 Section 404... § 404.1220 Identification numbers. (a) State and local governments. When a State submits a modification... will assign a special identification number to each political subdivision included in that modification...

47 CFR 95.671 - Serial number.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 47 Telecommunication 5 2011-10-01 2011-10-01 false Serial number. 95.671 Section 95.671 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES PERSONAL RADIO... number. The serial number of each CB transmitter must be engraved on the transmitter chassis. [53 FR...

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 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES PERSONAL RADIO... number. The serial number of each CB transmitter must be engraved on the transmitter chassis. [53 FR...

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 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) SAFETY AND SPECIAL RADIO SERVICES PERSONAL RADIO... number. The serial number of each CB transmitter must be engraved on the transmitter chassis. [53 FR...

20 CFR 404.1220 - Identification numbers.

Code of Federal Regulations, 2014 CFR

2014-04-01

... 20 Employees' Benefits 2 2014-04-01 2014-04-01 false Identification numbers. 404.1220 Section 404... § 404.1220 Identification numbers. (a) State and local governments. When a State submits a modification... will assign a special identification number to each political subdivision included in that modification...

46 CFR 10.207 - Identification number.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 46 Shipping 1 2011-10-01 2011-10-01 false Identification number. 10.207 Section 10.207 Shipping... CREDENTIAL General Requirements for All Merchant Mariner Credentials § 10.207 Identification number. For recordkeeping purposes only, a mariner's official MMC identification number is the individual's social security...

46 CFR 10.207 - Identification number.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 46 Shipping 1 2013-10-01 2013-10-01 false Identification number. 10.207 Section 10.207 Shipping... CREDENTIAL General Requirements for All Merchant Mariner Credentials § 10.207 Identification number. For recordkeeping purposes only, a mariner's official MMC identification number is the individual's social security...

20 CFR 404.1220 - Identification numbers.

Code of Federal Regulations, 2013 CFR

2013-04-01

... 20 Employees' Benefits 2 2013-04-01 2013-04-01 false Identification numbers. 404.1220 Section 404... § 404.1220 Identification numbers. (a) State and local governments. When a State submits a modification... will assign a special identification number to each political subdivision included in that modification...

20 CFR 404.1220 - Identification numbers.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 20 Employees' Benefits 2 2011-04-01 2011-04-01 false Identification numbers. 404.1220 Section 404... § 404.1220 Identification numbers. (a) State and local governments. When a State submits a modification... will assign a special identification number to each political subdivision included in that modification...

46 CFR 10.207 - Identification number.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 46 Shipping 1 2012-10-01 2012-10-01 false Identification number. 10.207 Section 10.207 Shipping... CREDENTIAL General Requirements for All Merchant Mariner Credentials § 10.207 Identification number. For recordkeeping purposes only, a mariner's official MMC identification number is the individual's social security...

46 CFR 10.207 - Identification number.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 46 Shipping 1 2014-10-01 2014-10-01 false Identification number. 10.207 Section 10.207 Shipping... CREDENTIAL General Requirements for All Merchant Mariner Credentials § 10.207 Identification number. For recordkeeping purposes only, a mariner's official MMC identification number is the individual's social security...

49 CFR 230.47 - Boiler number.

Code of Federal Regulations, 2010 CFR

2010-10-01

..., DEPARTMENT OF TRANSPORTATION STEAM LOCOMOTIVE INSPECTION AND MAINTENANCE STANDARDS Boilers and Appurtenances Steam Gauges § 230.47 Boiler number. (a) Generally. The builder's number of the boiler, if known, shall be stamped on the steam dome or manhole flange. If the builder's number cannot be obtained, an...

Relativistic theory of tidal Love numbers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Binnington, Taylor; Poisson, Eric

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 providemore » 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.« less

33 CFR 173.19 - Other numbers prohibited.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 33 Navigation and Navigable Waters 2 2012-07-01 2012-07-01 false Other numbers prohibited. 173.19...) BOATING SAFETY VESSEL NUMBERING AND CASUALTY AND ACCIDENT REPORTING Numbering § 173.19 Other numbers prohibited. No person may operate a vessel to which this part applies that has any number that is not issued...

33 CFR 173.19 - Other numbers prohibited.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 33 Navigation and Navigable Waters 2 2014-07-01 2014-07-01 false Other numbers prohibited. 173.19...) BOATING SAFETY VESSEL NUMBERING AND CASUALTY AND ACCIDENT REPORTING Numbering § 173.19 Other numbers prohibited. No person may operate a vessel to which this part applies that has any number that is not issued...

On counting the rational numbers

NASA Astrophysics Data System (ADS)

Almada, Carlos

2010-12-01

In this study, we show how to construct a function from the set ? of natural numbers that explicitly counts the set ? 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 without any prior knowledge of the Unique Prime Factorization Theorem or other nonelementary results. Unlike Cantor's function, the one we propose makes it very easy to determine what rational number, in unreduced form, is in a given position on the list and vice versa.

7 CFR 1.134 - Docket number.

Code of Federal Regulations, 2013 CFR

2013-01-01

... 7 Agriculture 1 2013-01-01 2013-01-01 false Docket number. 1.134 Section 1.134 Agriculture Office... Adjudicatory Proceedings Instituted by the Secretary Under Various Statutes § 1.134 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the Hearing Clerk...

40 CFR 265.11 - Identification number.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 40 Protection of Environment 27 2013-07-01 2013-07-01 false Identification number. 265.11 Section... FACILITIES General Facility Standards § 265.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR...

46 CFR 169.515 - Number required.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 46 Shipping 7 2014-10-01 2014-10-01 false Number required. 169.515 Section 169.515 Shipping COAST... and Firefighting Equipment Primary Lifesaving Equipment § 169.515 Number required. (a) Except as... additional inflatable liferafts to accommodate 25% of the persons on board or the number of persons...

7 CFR 1.134 - Docket number.

Code of Federal Regulations, 2011 CFR

2011-01-01

... 7 Agriculture 1 2011-01-01 2011-01-01 false Docket number. 1.134 Section 1.134 Agriculture Office... Adjudicatory Proceedings Instituted by the Secretary Under Various Statutes § 1.134 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the Hearing Clerk...

7 CFR 1.134 - Docket number.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 1 2014-01-01 2014-01-01 false Docket number. 1.134 Section 1.134 Agriculture Office... Adjudicatory Proceedings Instituted by the Secretary Under Various Statutes § 1.134 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the Hearing Clerk...

46 CFR 169.515 - Number required.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 46 Shipping 7 2012-10-01 2012-10-01 false Number required. 169.515 Section 169.515 Shipping COAST... and Firefighting Equipment Primary Lifesaving Equipment § 169.515 Number required. (a) Except as... additional inflatable liferafts to accommodate 25% of the persons on board or the number of persons...

40 CFR 265.11 - Identification number.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 40 Protection of Environment 26 2011-07-01 2011-07-01 false Identification number. 265.11 Section... FACILITIES General Facility Standards § 265.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR...

7 CFR 1.134 - Docket number.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 1 2010-01-01 2010-01-01 false Docket number. 1.134 Section 1.134 Agriculture Office... Adjudicatory Proceedings Instituted by the Secretary Under Various Statutes § 1.134 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the Hearing Clerk...

7 CFR 1.134 - Docket number.

Code of Federal Regulations, 2012 CFR

2012-01-01

... 7 Agriculture 1 2012-01-01 2012-01-01 false Docket number. 1.134 Section 1.134 Agriculture Office... Adjudicatory Proceedings Instituted by the Secretary Under Various Statutes § 1.134 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the Hearing Clerk...

46 CFR 169.515 - Number required.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 46 Shipping 7 2011-10-01 2011-10-01 false Number required. 169.515 Section 169.515 Shipping COAST... and Firefighting Equipment Primary Lifesaving Equipment § 169.515 Number required. (a) Except as... additional inflatable liferafts to accommodate 25% of the persons on board or the number of persons...

46 CFR 169.515 - Number required.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 46 Shipping 7 2010-10-01 2010-10-01 false Number required. 169.515 Section 169.515 Shipping COAST... and Firefighting Equipment Primary Lifesaving Equipment § 169.515 Number required. (a) Except as... additional inflatable liferafts to accommodate 25% of the persons on board or the number of persons...

40 CFR 265.11 - Identification number.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 40 Protection of Environment 26 2014-07-01 2014-07-01 false Identification number. 265.11 Section... FACILITIES General Facility Standards § 265.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR...

40 CFR 265.11 - Identification number.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 40 Protection of Environment 27 2012-07-01 2012-07-01 false Identification number. 265.11 Section... FACILITIES General Facility Standards § 265.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR...

40 CFR 265.11 - Identification number.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 40 Protection of Environment 25 2010-07-01 2010-07-01 false Identification number. 265.11 Section... FACILITIES General Facility Standards § 265.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR...

46 CFR 169.515 - Number required.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 46 Shipping 7 2013-10-01 2013-10-01 false Number required. 169.515 Section 169.515 Shipping COAST... and Firefighting Equipment Primary Lifesaving Equipment § 169.515 Number required. (a) Except as... additional inflatable liferafts to accommodate 25% of the persons on board or the number of persons...

33 CFR 173.33 - Removal of number.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 33 Navigation and Navigable Waters 2 2012-07-01 2012-07-01 false Removal of number. 173.33 Section...) BOATING SAFETY VESSEL NUMBERING AND CASUALTY AND ACCIDENT REPORTING Numbering § 173.33 Removal of number. The person whose name appears on a certificate of number as the owner of a vessel shall remove the...

33 CFR 173.19 - Other numbers prohibited.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 33 Navigation and Navigable Waters 2 2011-07-01 2011-07-01 false Other numbers prohibited. 173.19...) BOATING SAFETY VESSEL NUMBERING AND CASUALTY AND ACCIDENT REPORTING Numbering § 173.19 Other numbers prohibited. No person may use a vessel to which this part applies that has any number that is not issued by...

33 CFR 173.33 - Removal of number.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 33 Navigation and Navigable Waters 2 2014-07-01 2014-07-01 false Removal of number. 173.33 Section...) BOATING SAFETY VESSEL NUMBERING AND CASUALTY AND ACCIDENT REPORTING Numbering § 173.33 Removal of number. The person whose name appears on a certificate of number as the owner of a vessel shall remove the...

Ramsey numbers and adiabatic quantum computing.

PubMed

Gaitan, Frank; Clark, Lane

2012-01-06

The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers R(m,n) with m, n≥3, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers R(m,n). We show how the computation of R(m,n) can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for 5≤s≤7. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class quantum Merlin Arthur.

The Numbers Game.

ERIC Educational Resources Information Center

Lustick, David

1997-01-01

Describes a simple activity that explores and reveals the principles of significant figures and scientific notation using a 500 gram bag of unpopped popcorn. Students must devise a method for determining the number of kernels in the bag. (DDR)

20 CFR 404.1220 - Identification numbers.

Code of Federal Regulations, 2010 CFR

2010-04-01

... numbers for payroll record units. SSA assigns, at a State's request, unit numbers to payroll record units within a State or political subdivision. When a State requests separate payroll record unit numbers, it must furnish the following: (1) The name of each payroll record unit for the coverage group; and (2...

46 CFR Sec. 2 - Voyage numbers.

Code of Federal Regulations, 2012 CFR

2012-10-01

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

46 CFR Sec. 2 - Voyage numbers.

Code of Federal Regulations, 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, 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. ...

Identifying Fractions on a Number Line

ERIC Educational Resources Information Center

Wong, Monica

2013-01-01

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

40 CFR 264.11 - Identification number.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 40 Protection of Environment 25 2010-07-01 2010-07-01 false Identification number. 264.11 Section... Facility Standards § 264.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR 12746). [45 FR...

7 CFR 900.54 - Docket number.

Code of Federal Regulations, 2011 CFR

2011-01-01

... 7 Agriculture 8 2011-01-01 2011-01-01 false Docket number. 900.54 Section 900.54 Agriculture... Governing Proceedings on Petitions To Modify or To Be Exempted From Marketing Orders § 900.54 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the...

7 CFR 1200.6 - Docket number.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 10 2014-01-01 2014-01-01 false Docket number. 1200.6 Section 1200.6 Agriculture... Governing Proceedings To Formulate and Amend an Order § 1200.6 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter the...

24 CFR 3280.6 - Serial number.

Code of Federal Regulations, 2013 CFR

2013-04-01

... 24 Housing and Urban Development 5 2013-04-01 2013-04-01 false Serial number. 3280.6 Section 3280... DEVELOPMENT MANUFACTURED HOME CONSTRUCTION AND SAFETY STANDARDS General § 3280.6 Serial number. (a) A manufactured home serial number which will identify the manufacturer and the state in which the manufactured...

7 CFR 1200.6 - Docket number.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 10 2010-01-01 2010-01-01 false Docket number. 1200.6 Section 1200.6 Agriculture... Governing Proceedings To Formulate and Amend an Order § 1200.6 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter the...

24 CFR 3280.6 - Serial number.

Code of Federal Regulations, 2012 CFR

2012-04-01

... 24 Housing and Urban Development 5 2012-04-01 2012-04-01 false Serial number. 3280.6 Section 3280... DEVELOPMENT MANUFACTURED HOME CONSTRUCTION AND SAFETY STANDARDS General § 3280.6 Serial number. (a) A manufactured home serial number which will identify the manufacturer and the state in which the manufactured...

7 CFR 900.54 - Docket number.

Code of Federal Regulations, 2012 CFR

2012-01-01

... 7 Agriculture 8 2012-01-01 2012-01-01 false Docket number. 900.54 Section 900.54 Agriculture... Governing Proceedings on Petitions To Modify or To Be Exempted From Marketing Orders § 900.54 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the...

47 CFR 1.1405 - File numbers.

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... Attachment Complaint Procedures § 1.1405 File numbers. Each complaint which appears to be essentially complete under § 1.1404 will be accepted and assigned a file number. Such assignment is for administrative...

40 CFR 264.11 - Identification number.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 40 Protection of Environment 27 2012-07-01 2012-07-01 false Identification number. 264.11 Section... Facility Standards § 264.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR 12746). [45 FR...

27 CFR 24.115 - Registry number.

Code of Federal Regulations, 2013 CFR

2013-04-01

... 27 Alcohol, Tobacco Products and Firearms 1 2013-04-01 2013-04-01 false Registry number. 24.115... OF THE TREASURY ALCOHOL WINE Establishment and Operations Application § 24.115 Registry number. Upon approval of the application, the appropriate TTB officer will assign a registry number to the bonded winery...

7 CFR 900.54 - Docket number.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Docket number. 900.54 Section 900.54 Agriculture... Governing Proceedings on Petitions To Modify or To Be Exempted From Marketing Orders § 900.54 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the...

27 CFR 24.115 - Registry number.

Code of Federal Regulations, 2014 CFR

2014-04-01

... 27 Alcohol, Tobacco Products and Firearms 1 2014-04-01 2014-04-01 false Registry number. 24.115... OF THE TREASURY ALCOHOL WINE Establishment and Operations Application § 24.115 Registry number. Upon approval of the application, the appropriate TTB officer will assign a registry number to the bonded winery...

40 CFR 264.11 - Identification number.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 40 Protection of Environment 26 2014-07-01 2014-07-01 false Identification number. 264.11 Section... Facility Standards § 264.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR 12746). [45 FR...

27 CFR 24.115 - Registry number.

Code of Federal Regulations, 2012 CFR

2012-04-01

... 27 Alcohol, Tobacco Products and Firearms 1 2012-04-01 2012-04-01 false Registry number. 24.115... OF THE TREASURY LIQUORS WINE Establishment and Operations Application § 24.115 Registry number. Upon approval of the application, the appropriate TTB officer will assign a registry number to the bonded winery...

40 CFR 264.11 - Identification number.

Code of Federal Regulations, 2013 CFR

2013-07-01

... 40 Protection of Environment 27 2013-07-01 2013-07-01 false Identification number. 264.11 Section... Facility Standards § 264.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR 12746). [45 FR...

24 CFR 3280.6 - Serial number.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 24 Housing and Urban Development 5 2011-04-01 2011-04-01 false Serial number. 3280.6 Section 3280... DEVELOPMENT MANUFACTURED HOME CONSTRUCTION AND SAFETY STANDARDS General § 3280.6 Serial number. (a) A manufactured home serial number which will identify the manufacturer and the state in which the manufactured...

47 CFR 1.1405 - File numbers.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 47 Telecommunication 1 2014-10-01 2014-10-01 false File numbers. 1.1405 Section 1.1405... Attachment Complaint Procedures § 1.1405 File numbers. Each complaint which appears to be essentially complete under § 1.1404 will be accepted and assigned a file number. Such assignment is for administrative...

47 CFR 1.1405 - File numbers.

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... Attachment Complaint Procedures § 1.1405 File numbers. Each complaint which appears to be essentially complete under § 1.1404 will be accepted and assigned a file number. Such assignment is for administrative...

7 CFR 1200.6 - Docket number.

Code of Federal Regulations, 2012 CFR

2012-01-01

... 7 Agriculture 10 2012-01-01 2012-01-01 false Docket number. 1200.6 Section 1200.6 Agriculture... Governing Proceedings To Formulate and Amend an Order § 1200.6 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter the...

7 CFR 1200.6 - Docket number.

Code of Federal Regulations, 2013 CFR

2013-01-01

... 7 Agriculture 10 2013-01-01 2013-01-01 false Docket number. 1200.6 Section 1200.6 Agriculture... Governing Proceedings To Formulate and Amend an Order § 1200.6 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the hearing clerk and thereafter the...

7 CFR 900.54 - Docket number.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 8 2014-01-01 2014-01-01 false Docket number. 900.54 Section 900.54 Agriculture... Governing Proceedings on Petitions To Modify or To Be Exempted From Marketing Orders § 900.54 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the...

7 CFR 900.54 - Docket number.

Code of Federal Regulations, 2013 CFR

2013-01-01

... 7 Agriculture 8 2013-01-01 2013-01-01 false Docket number. 900.54 Section 900.54 Agriculture... Governing Proceedings on Petitions To Modify or To Be Exempted From Marketing Orders § 900.54 Docket number. Each proceeding, immediately following its institution, shall be assigned a docket number by the...

24 CFR 3280.6 - Serial number.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 24 Housing and Urban Development 5 2010-04-01 2010-04-01 false Serial number. 3280.6 Section 3280... DEVELOPMENT MANUFACTURED HOME CONSTRUCTION AND SAFETY STANDARDS General § 3280.6 Serial number. (a) A manufactured home serial number which will identify the manufacturer and the state in which the manufactured...

40 CFR 264.11 - Identification number.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 40 Protection of Environment 26 2011-07-01 2011-07-01 false Identification number. 264.11 Section... Facility Standards § 264.11 Identification number. Every facility owner or operator must apply to EPA for an EPA identification number in accordance with the EPA notification procedures (45 FR 12746). [45 FR...

24 CFR 3280.6 - Serial number.

Code of Federal Regulations, 2014 CFR

2014-04-01

... 24 Housing and Urban Development 5 2014-04-01 2014-04-01 false Serial number. 3280.6 Section 3280... DEVELOPMENT MANUFACTURED HOME CONSTRUCTION AND SAFETY STANDARDS General § 3280.6 Serial number. (a) A manufactured home serial number which will identify the manufacturer and the state in which the manufactured...

Pleiotropic Stabilizing Selection Limits the Number of Polymorphic Loci to at Most the Number of Characters

PubMed Central

Hastings, A.; Hom, C. L.

1989-01-01

We demonstrate that, in a model incorporating weak Gaussian stabilizing selection on n additively determined characters, at most n loci are polymorphic at a stable equilibrium. The number of characters is defined to be the number of independent components in the Gaussian selection scheme. We also assume linkage equilibrium, and that either the number of loci is large enough that the phenotypic distribution in the population can be approximated as multivariate Gaussian or that selection is weak enough that the mean fitness of the population can be approximated using only the mean and the variance of the characters in the population. Our results appear to rule out antagonistic pleiotropy without epistasis as a major force in maintaining additive genetic variation in a uniform environment. However, they are consistent with the maintenance of variability by genotype-environment interaction if a trait in different environments corresponds to different characters and the number of different environments exceeds the number of polymorphic loci that affect the trait. PMID:2767424

Pinning of fermionic occupation numbers.

PubMed

Schilling, Christian; Gross, David; Christandl, Matthias

2013-01-25

The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states. It has been suspected since at least the 1970s, and only proved very recently, that there is a multitude of further constraints on these numbers, generalizing the Pauli principle. Here, we provide the first analytic analysis of the physical relevance of these constraints. We compute the natural occupation numbers for the ground states of a family of interacting fermions in a harmonic potential. Intriguingly, we find that the occupation numbers are almost, but not exactly, pinned to the boundary of the allowed region (quasipinned). The result suggests that the physics behind the phenomenon is richer than previously appreciated. In particular, it shows that for some models, the generalized Pauli constraints play a role for the ground state, even though they do not limit the ground-state energy. Our findings suggest a generalization of the Hartree-Fock approximation.

Generating functions for weighted Hurwitz numbers

NASA Astrophysics Data System (ADS)

Guay-Paquet, Mathieu; Harnad, J.

2017-08-01

Double Hurwitz numbers enumerating weighted n-sheeted branched coverings of the Riemann sphere or, equivalently, weighted paths in the Cayley graph of Sn generated by transpositions are determined by an associated weight generating function. A uniquely determined 1-parameter family of 2D Toda τ -functions of hypergeometric type is shown to consist of generating functions for such weighted Hurwitz numbers. Four classical cases are detailed, in which the weighting is uniform: Okounkov's double Hurwitz numbers for which the ramification is simple at all but two specified branch points; the case of Belyi curves, with three branch points, two with specified profiles; the general case, with a specified number of branch points, two with fixed profiles, the rest constrained only by the genus; and the signed enumeration case, with sign determined by the parity of the number of branch points. Using the exponentiated quantum dilogarithm function as a weight generator, three new types of weighted enumerations are introduced. These determine quantum Hurwitz numbers depending on a deformation parameter q. By suitable interpretation of q, the statistical mechanics of quantum weighted branched covers may be related to that of Bosonic gases. The standard double Hurwitz numbers are recovered in the classical limit.

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)

47 CFR 1.1405 - File numbers.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 47 Telecommunication 1 2011-10-01 2011-10-01 false File numbers. 1.1405 Section 1.1405... Procedures § 1.1405 File numbers. Each complaint which appears to be essentially complete under § 1.1404 will be accepted and assigned a file number. Such assignment is for administrative purposes only and does...

47 CFR 1.1405 - File numbers.

Code of Federal Regulations, 2010 CFR

2010-10-01

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

Some types of parent number talk count more than others: relations between parents' input and children's cardinal-number knowledge.

PubMed

Gunderson, Elizabeth A; Levine, Susan C

2011-09-01

Before they enter preschool, children vary greatly in their numerical and mathematical knowledge, and this knowledge predicts their achievement throughout elementary school (e.g. Duncan et al., 2007; Ginsburg & Russell, 1981). Therefore, it is critical that we look to the home environment for parental inputs that may lead to these early variations. Recent work has shown that the amount of number talk that parents engage in with their children is robustly related to a critical aspect of mathematical development - cardinal-number knowledge (e.g. knowing that the word 'three' refers to sets of three entities; Levine, Suriyakham, Rowe, Huttenlocher & Gunderson, 2010). The present study characterizes the different types of number talk that parents produce and investigates which types are most predictive of children's later cardinal-number knowledge. We find that parents' number talk involving counting or labeling sets of present, visible objects is related to children's later cardinal-number knowledge, whereas other types of parent number talk are not. In addition, number talk that refers to large sets of present objects (i.e. sets of size 4 to 10 that fall outside children's ability to track individual objects) is more robustly predictive of children's later cardinal-number knowledge than talk about smaller sets. The relation between parents' number talk about large sets of present objects and children's cardinal-number knowledge remains significant even when controlling for factors such as parents' socioeconomic status and other measures of parents' number and non-number talk. © 2011 Blackwell Publishing Ltd.

Four-Digit Numbers Which Are Squared Sums

ERIC Educational Resources Information Center

Coughlin, Heather; Jue, Brian

2009-01-01

There is a very natural way to divide a four-digit number into 2 two-digit numbers. Applying an algorithm to this pair of numbers, determine how often the original four-digit number reappears. (Contains 3 tables.)

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…

Figurate Numbers in the Classroom.

ERIC Educational Resources Information Center

Norman, F. Alexander

1991-01-01

A series of activities involving figurate numbers that allow students at various levels to integrate numerical, geometric, arithmetic, patterning, measuring, and problem-solving skills are presented. A discussion of the geometric and numerical aspects of figurate numbers is included. Appended are IBM Logo procedures that will create pentagonal…

Number Talks Build Numerical Reasoning

ERIC Educational Resources Information Center

Parrish, Sherry D.

2011-01-01

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

Reynolds Number Effects in Transonic Flow

DTIC Science & Technology

1988-12-01

the asme one as used for the results shown in figure 3.5-10 and -11). Also the corrals - tion between shock Mach number and Reynolds number at the flow...hypercritical, was derived from the conditions on the cylinder in normal flow utilizing the relation for the effective Reynolds number K= Reef /Re0 (see

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 § 367.4 Numbering system. (a) The account numbering plan used in this part consists of a system of...

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 § 367.4 Numbering system. (a) The account numbering plan used in this part consists of a system of...

47 CFR 64.1506 - Number designation.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 47 Telecommunication 3 2014-10-01 2014-10-01 false Number designation. 64.1506 Section 64.1506... Number designation. Any interstate service described in § 64.1501(a)(1)-(2), and not subject to the exclusions contained in § 64.1501(a)(4), shall be offered only through telephone numbers beginning with a 900...

47 CFR 64.1506 - Number designation.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 47 Telecommunication 3 2011-10-01 2011-10-01 false Number designation. 64.1506 Section 64.1506... Number designation. Any interstate service described in § 64.1501(a)(1)-(2), and not subject to the exclusions contained in § 64.1501(a)(4), shall be offered only through telephone numbers beginning with a 900...

47 CFR 64.1506 - Number designation.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 47 Telecommunication 3 2013-10-01 2013-10-01 false Number designation. 64.1506 Section 64.1506... Number designation. Any interstate service described in § 64.1501(a)(1)-(2), and not subject to the exclusions contained in § 64.1501(a)(4), shall be offered only through telephone numbers beginning with a 900...

47 CFR 64.1506 - Number designation.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 47 Telecommunication 3 2012-10-01 2012-10-01 false Number designation. 64.1506 Section 64.1506... Number designation. Any interstate service described in § 64.1501(a)(1)-(2), and not subject to the exclusions contained in § 64.1501(a)(4), shall be offered only through telephone numbers beginning with a 900...

Finding numbers in the brain.

PubMed

Gallistel, C R

2017-02-19

After listing functional constraints on what numbers in the brain must do, I sketch the two's complement fixed-point representation of numbers because it has stood the test of time and because it illustrates the non-obvious ways in which an effective coding scheme may operate. I briefly consider its neurobiological implementation. It is easier to imagine its implementation at the cell-intrinsic molecular level, with thermodynamically stable, volumetrically minimal polynucleotides encoding the remembered numbers, than at the circuit level, with plastic synapses encoding them.This article is part of a discussion meeting issue 'The origins of numerical abilities'. © 2017 The Author(s).

Toddlers' Spontaneous Attention to Number

ERIC Educational Resources Information Center

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

2008-01-01

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

Savaaksrat Kisitchisit (Numbers 1-10).

ERIC Educational Resources Information Center

Pulu, Tupou L.; And Others

This first grade workbook is designed for children in bilingual Inupiat-English programs in the Alaskan villages of Ambler, Kiana, Kobuk, Noorvik, Selawik, and Shungnak. Each page has a particular number, a corresponding picture with an appropriate caption, and lines for the child to use in writing the number. (CFM)

Seedbed, Numbers 29-31, 1988.

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…

Investigating the Randomness of Numbers

ERIC Educational Resources Information Center

Pendleton, Kenn L.

2009-01-01

The use of random numbers is pervasive in today's world. Random numbers have practical applications in such far-flung arenas as computer simulations, cryptography, gambling, the legal system, statistical sampling, and even the war on terrorism. Evaluating the randomness of extremely large samples is a complex, intricate process. However, the…

Regular Numbers and Mathematical Worlds

ERIC Educational Resources Information Center

Whitacre, Ian; Bouhjar, Khalid; Bishop, Jessica Pierson; Philipp, Randolph; Schappelle, Bonnie P.

2016-01-01

Rather than describing the challenges of integer learning in terms of a transition from positive to negative numbers, we have arrived at a different perspective: We view students as inhabiting distinct mathematical worlds consisting of particular types of numbers (as construed by the students). These worlds distinguish and illuminate students'…

7 CFR 1.414 - Docket number.

Code of Federal Regulations, 2011 CFR

2011-01-01

... 7 Agriculture 1 2011-01-01 2011-01-01 false Docket number. 1.414 Section 1.414 Agriculture Office... Conservation and Shortage Relief Act of 1990 (16 U.S.C. 620 et seq.) § 1.414 Docket number. Each proceeding, following its institution, shall be assigned a docket number by the Hearing Clerk, and thereafter the...

7 CFR 1.414 - Docket number.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 7 Agriculture 1 2014-01-01 2014-01-01 false Docket number. 1.414 Section 1.414 Agriculture Office... Conservation and Shortage Relief Act of 1990 (16 U.S.C. 620 et seq.) § 1.414 Docket number. Each proceeding, following its institution, shall be assigned a docket number by the Hearing Clerk, and thereafter the...

7 CFR 1.414 - Docket number.

Code of Federal Regulations, 2013 CFR

2013-01-01

... 7 Agriculture 1 2013-01-01 2013-01-01 false Docket number. 1.414 Section 1.414 Agriculture Office... Conservation and Shortage Relief Act of 1990 (16 U.S.C. 620 et seq.) § 1.414 Docket number. Each proceeding, following its institution, shall be assigned a docket number by the Hearing Clerk, and thereafter the...

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... IMPORT MILK ACT Permit Control § 1210.21 Permit number. Each permit issued under the Federal Import Milk Act, including each temporary permit, shall bear an individual number. The right to the use of such...

7 CFR 1.414 - Docket number.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 1 2010-01-01 2010-01-01 false Docket number. 1.414 Section 1.414 Agriculture Office... Conservation and Shortage Relief Act of 1990 (16 U.S.C. 620 et seq.) § 1.414 Docket number. Each proceeding, following its institution, shall be assigned a docket number by the Hearing Clerk, and thereafter the...

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... IMPORT MILK ACT Permit Control § 1210.21 Permit number. Each permit issued under the Federal Import Milk Act, including each temporary permit, shall bear an individual number. The right to the use of such...

7 CFR 1.414 - Docket number.

Code of Federal Regulations, 2012 CFR

2012-01-01

... 7 Agriculture 1 2012-01-01 2012-01-01 false Docket number. 1.414 Section 1.414 Agriculture Office... Conservation and Shortage Relief Act of 1990 (16 U.S.C. 620 et seq.) § 1.414 Docket number. Each proceeding, following its institution, shall be assigned a docket number by the Hearing Clerk, and thereafter the...

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... IMPORT MILK ACT Permit Control § 1210.21 Permit number. Each permit issued under the Federal Import Milk Act, including each temporary permit, shall bear an individual number. The right to the use of such...

Breaking down number syntax: spared comprehension of multi-digit numbers in a patient with impaired digit-to-word conversion.

PubMed

Dotan, Dror; Friedmann, Naama; Dehaene, Stanislas

2014-10-01

Can the meaning of two-digit Arabic numbers be accessed independently of their verbal-phonological representations? To answer this question we explored the number processing of ZN, an aphasic patient with a syntactic deficit in digit-to-verbal transcoding, who could hardly read aloud two-digit numbers, but could read them as single digits ("four, two"). Neuropsychological examination showed that ZN's deficit was neither in the digit input nor in the phonological output processes, as he could copy and repeat two-digit numbers. His deficit thus lied in a central process that converts digits to abstract number words and sends this information to phonological retrieval processes. Crucially, in spite of this deficit in number transcoding, ZN's two-digit comprehension was spared in several ways: (1) he could calculate two-digit additions; (2) he showed good performance in a two-digit comparison task, and a continuous distance effect; and (3) his performance in a task of mapping numbers to positions on an unmarked number line showed a logarithmic (nonlinear) factor, indicating that he represented two-digit Arabic numbers as holistic two-digit quantities. Thus, at least these aspects of number comprehension can be performed without converting the two-digit number from digits to verbal representation.

48 CFR 52.204-6 - Data Universal Numbering System (DUNS) Number.

Code of Federal Regulations, 2011 CFR

2011-10-01

...) Via the Internet at http://fedgov.dnb.com/webform or if the offeror does not have internet access, it...) accounts (see Subpart 32.11) for the same concern. (b) If the offeror does not have a DUNS number, it...

The Remarkable Number "1"

NASA Astrophysics Data System (ADS)

Allen, G. Donald

2014-09-01

In human history, the origin of the numbers came from definite practical needs. Indeed, there is strong evidence that numbers were created before writing. The number "1", dating back at least 20,000 years, was found as a counting symbol on a bone. The famous statement by the German mathematician Leopold Kronecker (1823-1891), "God made the integers; all else is the work of man," has spawned a lively modern philosophical discussion, and this discussion begins by trying to get a philosophical handle on "1." This approach remains under heavy discussion, and is more-or-less unresolved (Frege in Die Grundlagen der Arithmetik (English: The foundations of arithmetic). Polhman, 1884). In this note, we consider the many facets of "one" in it many guises and applications. Nonetheless, "one" has multiple meanings, from the very practical to the abstract, from mathematics to science to basically everything. We examine here a mere slice of mathematical history with a focus on the most basic and applicable concept therein. It troubles many, particularly students, even today.

Role of Turbulent Prandtl Number on Heat Flux at Hypersonic Mach Number

NASA Technical Reports Server (NTRS)

Xiao, X.; Edwards, J. R.; Hassan, H. A.

2004-01-01

Present simulation of turbulent flows involving shock wave/boundary layer interaction invariably overestimates heat flux by almost a factor of two. One possible reason for such a performance is a result of the fact that the turbulence models employed make use of Morkovin's hypothesis. This hypothesis is valid for non-hypersonic Mach numbers and moderate rates of heat transfer. At hypersonic Mach numbers, high rates of heat transfer exist in regions where shock wave/boundary layer interactions are important. As a result, one should not expect traditional turbulence models to yield accurate results. The goal of this investigation is to explore the role of a variable Prandtl number formulation in predicting heat flux in flows dominated by strong shock wave/boundary layer interactions. The intended applications involve external flows in the absence of combustion such as those encountered in supersonic inlets. This can be achieved by adding equations for the temperature variance and its dissipation rate. Such equations can be derived from the exact Navier-Stokes equations. Traditionally, modeled equations are based on the low speed energy equation where the pressure gradient term and the term responsible for energy dissipation are ignored. It is clear that such assumptions are not valid for hypersonic flows. The approach used here is based on the procedure used in deriving the k-zeta model, in which the exact equations that governed k, the variance of velocity, and zeta, the variance of vorticity, were derived and modeled. For the variable turbulent Prandtl number, the exact equations that govern the temperature variance and its dissipation rate are derived and modeled term by term. The resulting set of equations are free of damping and wall functions and are coordinate-system independent. Moreover, modeled correlations are tensorially consistent and invariant under Galilean transformation. The final set of equations will be given in the paper.

BIHE@20: By the Numbers

ERIC Educational Resources Information Center

Black Issues in Higher Education, 2004

2004-01-01

Over the past 20 years, higher education has seen significant growth in the numbers of both associate's and bachelor's degrees conferred on students in the United States, particularly women and minorities. For example, the number of associate's degrees conferred on African American women between 1980 and 2000 nearly doubled, tripling for American…

Fractions, Number Lines, Third Graders

ERIC Educational Resources Information Center

Cramer, Kathleen; Ahrendt, Sue; Monson, Debra; Wyberg, Terry; Colum, Karen

2017-01-01

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) outlines ambitious goals for fraction learning, starting in third grade, that include the use of the number line model. Understanding and constructing fractions on a number line are particularly complex tasks. The current work of the authors centers on ways to successfully…

9 CFR 381.25 - Official establishment numbers.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 9 Animals and Animal Products 2 2010-01-01 2010-01-01 false Official establishment numbers. 381.25... Establishment Numbers; Separation of Establishments and Other Requirements; Withdrawal of Inspection § 381.25 Official establishment numbers. An official establishment number shall be assigned to each establishment...

9 CFR 381.25 - Official establishment numbers.

Code of Federal Regulations, 2012 CFR

2012-01-01

... 9 Animals and Animal Products 2 2012-01-01 2012-01-01 false Official establishment numbers. 381.25... Establishment Numbers; Separation of Establishments and Other Requirements; Withdrawal of Inspection § 381.25 Official establishment numbers. An official establishment number shall be assigned to each establishment...

49 CFR 229.105 - Steam generator number.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 49 Transportation 4 2013-10-01 2013-10-01 false Steam generator number. 229.105 Section 229.105....105 Steam generator number. An identification number shall be marked on the steam generator's separator and that number entered on FRA Form F 6180-49A. ...

9 CFR 381.25 - Official establishment numbers.

Code of Federal Regulations, 2011 CFR

2011-01-01

... 9 Animals and Animal Products 2 2011-01-01 2011-01-01 false Official establishment numbers. 381.25... Establishment Numbers; Separation of Establishments and Other Requirements; Withdrawal of Inspection § 381.25 Official establishment numbers. An official establishment number shall be assigned to each establishment...

49 CFR 229.105 - Steam generator number.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 49 Transportation 4 2014-10-01 2014-10-01 false Steam generator number. 229.105 Section 229.105....105 Steam generator number. An identification number shall be marked on the steam generator's separator and that number entered on FRA Form F 6180-49A. ...

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

PubMed

Lenormand, Maxime; Huet, Sylvie; Deffuant, Guillaume

2012-01-01

We use a minimum requirement approach to derive the number of jobs in proximity services per inhabitant in French rural municipalities. We first classify the municipalities according to their time distance in minutes by car to the municipality where the inhabitants go the most frequently to get services (called MFM). For each set corresponding to a range of time distance to MFM, we perform a quantile regression estimating the minimum number of service jobs per inhabitant that we interpret as an estimation of the number of proximity jobs per inhabitant. We observe that the minimum number of service jobs per inhabitant is smaller in small municipalities. Moreover, for municipalities of similar sizes, when the distance to the MFM increases, the number of jobs of proximity services per inhabitant increases.

Causal evidence of the involvement of the number form area in the visual detection of numbers and letters.

PubMed

Grotheer, Mareike; Ambrus, Géza Gergely; Kovács, Gyula

2016-05-15

Recent research suggests the existence of a visual area selectively processing numbers in the human inferior temporal cortex (number form area (NFA); Abboud et al., 2015; Grotheer et al., 2016; Shum et al., 2013). The NFA is thought to be involved in the preferential encoding of numbers over false characters, letters and non-number words (Grotheer et al., 2016; Shum et al., 2013), independently of the sensory modality (Abboud et al., 2015). However, it is not yet clear if this area is mandatory for normal number processing. The present study exploited the fact that high-resolution fMRI can be applied to identify the NFA individually (Grotheer et al., 2016) and tested if transcranial magnetic stimulation (TMS) of this area interferes with stimulus processing in a selective manner. Double-pulse TMS targeted at the right NFA significantly impaired the detection of briefly presented and masked Arabic numbers in comparison to vertex stimulation. This suggests the NFA to be necessary for fluent number processing. Surprisingly, TMS of the NFA also impaired the detection of Roman letters. On the other hand, stimulation of the lateral occipital complex (LO) had neither an effect on the detection of numbers nor on letters. Our results show, for the first time, that the NFA is causally involved in the early visual processing of numbers as well as of letters. Copyright © 2016 Elsevier Inc. All rights reserved.

The Precision of Mapping Between Number Words and the Approximate Number System Predicts Children’s Formal Math Abilities

PubMed Central

Libertus, Melissa E.; Odic, Darko; Feigenson, Lisa; Halberda, Justin

2016-01-01

Children can represent number in at least two ways: by using their non-verbal, intuitive Approximate Number System (ANS), and by using words and symbols to count and represent numbers exactly. Further, by the time they are five years old, children can map between the ANS and number words, as evidenced by their ability to verbally estimate numbers of items without counting. How does the quality of the mapping between approximate and exact numbers relate to children’s math abilities? The role of the ANS-number word mapping in math competence remains controversial for at least two reasons. First, previous work has not examined the relation between verbal estimation and distinct subtypes of math abilities. Second, previous work has not addressed how distinct components of verbal estimation – mapping accuracy and variability – might each relate to math performance. Here, we address these gaps by measuring individual differences in ANS precision, verbal number estimation, and formal and informal math abilities in 5- to 7-year-old children. We found that verbal estimation variability, but not estimation accuracy, predicted formal math abilities even when controlling for age, expressive vocabulary, and ANS precision, and that it mediated the link between ANS precision and overall math ability. These findings suggest that variability in the ANS-number word mapping may be especially important for formal math abilities. PMID:27348475

27 CFR 19.242 - Employer identification number.

Code of Federal Regulations, 2011 CFR

2011-04-01

... number. 19.242 Section 19.242 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE... for Employer Identification Numbers § 19.242 Employer identification number. The proprietor must enter the employer identification number (EIN) assigned to it by the Internal Revenue Service on each form...

26 CFR 301.6109-1 - Identifying numbers.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 26 Internal Revenue 18 2011-04-01 2011-04-01 false Identifying numbers. 301.6109-1 Section 301... numbers. (a) In general—(1) Taxpayer identifying numbers—(i) Principal types. There are several types of taxpayer identifying numbers that include the following: social security numbers, Internal Revenue Service...

26 CFR 301.6109-1 - Identifying numbers.

Code of Federal Regulations, 2013 CFR

2013-04-01

... 26 Internal Revenue 18 2013-04-01 2013-04-01 false Identifying numbers. 301.6109-1 Section 301... numbers. (a) In general—(1) Taxpayer identifying numbers—(i) Principal types. There are several types of taxpayer identifying numbers that include the following: social security numbers, Internal Revenue Service...

26 CFR 301.6109-1 - Identifying numbers.

Code of Federal Regulations, 2012 CFR

2012-04-01

... 26 Internal Revenue 18 2012-04-01 2012-04-01 false Identifying numbers. 301.6109-1 Section 301... numbers. (a) In general—(1) Taxpayer identifying numbers—(i) Principal types. There are several types of taxpayer identifying numbers that include the following: social security numbers, Internal Revenue Service...

32 CFR 1615.6 - Selective service number.

Code of Federal Regulations, 2011 CFR

2011-07-01

... 32 National Defense 6 2011-07-01 2011-07-01 false Selective service number. 1615.6 Section 1615.6... REGISTRATION § 1615.6 Selective service number. Every registrant shall be given a selective service number. The Social Security Account Number will not be used for this purpose. ...

26 CFR 301.6109-1 - Identifying numbers.

Code of Federal Regulations, 2014 CFR

2014-04-01

... 26 Internal Revenue 18 2014-04-01 2014-04-01 false Identifying numbers. 301.6109-1 Section 301... numbers. (a) In general—(1) Taxpayer identifying numbers—(i) Principal types. There are several types of taxpayer identifying numbers that include the following: social security numbers, Internal Revenue Service...

The Algebra of Complex Numbers.

ERIC Educational Resources Information Center

LePage, Wilbur R.

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

Competing features influence children's attention to number.

PubMed

Chan, Jenny Yun-Chen; Mazzocco, Michèle M M

2017-04-01

Spontaneous focus on numerosity (SFON), an attentional process that some consider distinct from number knowledge, predicts later mathematical skills. Here we assessed the "spontaneity" and malleability of SFON using a picture-matching task. We asked children to view a target picture and to choose which of four other pictures matched the target. We tested whether attention to number (defined as number-based matches) was affected by (a) age, (b) the presence of very noticeable (or salient) features among alternative match choices, and (c) the examiner's use of motor actions to emphasize numerosity. Although adults attended to number more frequently than did preschoolers, the salience of competing features affected responses to number in both age groups. Specifically, number-based matches were more likely when alternative choices matched the target on features of low versus high salience (e.g., the relative location within a picture frame vs. color). In addition, adults' attention to number was more frequent if their first exposure to number-based matches occurred with alternative choices that matched the target on low salience features. This order by salience interaction was not observed among children. Simply observing motor actions that emphasized number (i.e., tapping stimuli) did not enhance children's attention to number. The results extend previous findings on SFON and provide evidence for the contextual influences on, and malleability of, attention to number. Copyright © 2016 Elsevier Inc. All rights reserved.

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.

46 CFR 114.900 - OMB control numbers.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 46 Shipping 4 2012-10-01 2012-10-01 false OMB control numbers. 114.900 Section 114.900 Shipping... control numbers. (a) Purpose. This section lists the control numbers assigned to information collection... current control number assigned by the Director of OMB for each approved agency information collection...

46 CFR 114.900 - OMB control numbers.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 46 Shipping 4 2014-10-01 2014-10-01 false OMB control numbers. 114.900 Section 114.900 Shipping... control numbers. (a) Purpose. This section lists the control numbers assigned to information collection... current control number assigned by the Director of OMB for each approved agency information collection...

Colour by Numbers

ERIC Educational Resources Information Center

Wetherell, Chris

2017-01-01

This is an edited extract from the keynote address given by Dr. Chris Wetherell at the 26th Biennial Conference of the Australian Association of Mathematics Teachers Inc. The author investigates the surprisingly rich structure that exists within a simple arrangement of numbers: the times tables.

Number-space mapping in human infants.

PubMed

de Hevia, Maria Dolores; Spelke, Elizabeth S

2010-05-01

Mature representations of number are built on a core system of numerical representation that connects to spatial representations in the form of a mental number line. The core number system is functional in early infancy, but little is known about the origins of the mapping of numbers onto space. In this article, we show that preverbal infants transfer the discrimination of an ordered series of numerosities to the discrimination of an ordered series of line lengths. Moreover, infants construct relationships between numbers and line lengths when they are habituated to unordered pairings that vary positively, but not when they are habituated to unordered pairings that vary inversely. These findings provide evidence that a predisposition to relate representations of numerical magnitude to spatial length develops early in life. A central foundation of mathematics, science, and technology therefore emerges prior to experience with language, symbol systems, or measurement devices.

Organizing, Concerns and Control Numbers.

ERIC Educational Resources Information Center

Washington, Gene

A heuristic procedure can be used to teach organizational skills to students of technical writing. Designed to allow students on their own to explore ways that numbers can be used to give a definite shape to technical information, its central feature is a matrix composed of a series of control numbers (horizontal axis) and organizing concerns…

9 CFR 590.150 - Official plant numbers.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 9 Animals and Animal Products 2 2010-01-01 2010-01-01 false Official plant numbers. 590.150... of Service § 590.150 Official plant numbers. An official plant number shall be assigned to each plant granted inspection service. Such plant number shall be used to identify all containers of inspected...

9 CFR 590.150 - Official plant numbers.

Code of Federal Regulations, 2012 CFR

2012-01-01

... 9 Animals and Animal Products 2 2012-01-01 2012-01-01 false Official plant numbers. 590.150... of Service § 590.150 Official plant numbers. An official plant number shall be assigned to each plant granted inspection service. Such plant number shall be used to identify all containers of inspected...

9 CFR 590.150 - Official plant numbers.

Code of Federal Regulations, 2013 CFR

2013-01-01

... 9 Animals and Animal Products 2 2013-01-01 2013-01-01 false Official plant numbers. 590.150... of Service § 590.150 Official plant numbers. An official plant number shall be assigned to each plant granted inspection service. Such plant number shall be used to identify all containers of inspected...

9 CFR 590.150 - Official plant numbers.

Code of Federal Regulations, 2014 CFR

2014-01-01

... 9 Animals and Animal Products 2 2014-01-01 2014-01-01 false Official plant numbers. 590.150... of Service § 590.150 Official plant numbers. An official plant number shall be assigned to each plant granted inspection service. Such plant number shall be used to identify all containers of inspected...

16 CFR 301.26 - Registered identification numbers.

Code of Federal Regulations, 2011 CFR

2011-01-01

... 16 Commercial Practices 1 2011-01-01 2011-01-01 false Registered identification numbers. 301.26... numbers. (a) Registered numbers for use as the required identification in lieu of the name on fur product... (d) of this section. (b)(1) Registered identification numbers shall be used only by the person or...

27 CFR 53.187 - OMB control numbers.

Code of Federal Regulations, 2012 CFR

2012-04-01

... 27 Alcohol, Tobacco Products and Firearms 2 2012-04-01 2011-04-01 true OMB control numbers. 53.187... numbers. (a) Purpose. This section collects and displays the control numbers assigned to collections of... control numbers assigned by OMB to collections of information in the regulations in this part. (b) Display...

19 CFR 24.5 - Filing identification number.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 19 Customs Duties 1 2010-04-01 2010-04-01 false Filing identification number. 24.5 Section 24.5... TREASURY CUSTOMS FINANCIAL AND ACCOUNTING PROCEDURE § 24.5 Filing identification number. (a) Generally..., Notification of Importer's Number or Application for Importer's Number, or Notice of Change of Name or Address...

19 CFR 24.5 - Filing identification number.

Code of Federal Regulations, 2013 CFR

2013-04-01

... 19 Customs Duties 1 2013-04-01 2013-04-01 false Filing identification number. 24.5 Section 24.5... TREASURY CUSTOMS FINANCIAL AND ACCOUNTING PROCEDURE § 24.5 Filing identification number. (a) Generally..., Notification of Importer's Number or Application for Importer's Number, or Notice of Change of Name or Address...

27 CFR 46.102 - Employer identification number.

Code of Federal Regulations, 2012 CFR

2012-04-01

... number. 46.102 Section 46.102 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE....102 Employer identification number. (a) Requirement. The employer identification number (as defined in 26 CFR 301.7701-12) of the taxpayer who has been assigned such a number must be shown on each special...

27 CFR 31.115 - Employer identification number.

Code of Federal Regulations, 2011 CFR

2011-04-01

... number. 31.115 Section 31.115 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE....115 Employer identification number. (a) Requirement. The employer identification number (as defined in 26 CFR 301.7701-12) of a dealer who has been assigned such a number must be shown on each...

16 CFR 303.20 - Registered identification numbers.

Code of Federal Regulations, 2011 CFR

2011-01-01

... 16 Commercial Practices 1 2011-01-01 2011-01-01 false Registered identification numbers. 303.20... identification numbers. (a) Registered numbers for use as the required identification in lieu of the name on... the form set out in paragraph (d) of this section. (b)(1) Registered identification numbers shall be...

19 CFR 24.5 - Filing identification number.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 19 Customs Duties 1 2011-04-01 2011-04-01 false Filing identification number. 24.5 Section 24.5... TREASURY CUSTOMS FINANCIAL AND ACCOUNTING PROCEDURE § 24.5 Filing identification number. (a) Generally..., Notification of Importer's Number or Application for Importer's Number, or Notice of Change of Name or Address...

46 CFR 169.117 - OMB control numbers.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 46 Shipping 7 2014-10-01 2014-10-01 false OMB control numbers. 169.117 Section 169.117 Shipping... Provisions § 169.117 OMB control numbers. (a) Purpose. This section collects and displays the control numbers... that agencies display a current control number assigned by the Director of OMB for each approved agency...

46 CFR 175.900 - OMB control numbers.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 46 Shipping 7 2014-10-01 2014-10-01 false OMB control numbers. 175.900 Section 175.900 Shipping...) GENERAL PROVISIONS § 175.900 OMB control numbers. (a) Purpose. This section lists the control numbers... that agencies display a current control number assigned by the Director of OMB for each approved agency...

27 CFR 40.359 - Employer identification number.

Code of Federal Regulations, 2012 CFR

2012-04-01

... number. 40.359 Section 40.359 Alcohol, Tobacco Products and Firearms ALCOHOL AND TOBACCO TAX AND TRADE... identification number. The employer identification number (EIN) (defined at 26 CFR 301.7701-12) of a manufacturer of cigarette papers and/or tubes who has been assigned such a number shall be shown on each...

46 CFR 169.117 - OMB control numbers.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 46 Shipping 7 2012-10-01 2012-10-01 false OMB control numbers. 169.117 Section 169.117 Shipping... Provisions § 169.117 OMB control numbers. (a) Purpose. This section collects and displays the control numbers... that agencies display a current control number assigned by the Director of OMB for each approved agency...

46 CFR 175.900 - OMB control numbers.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 46 Shipping 7 2012-10-01 2012-10-01 false OMB control numbers. 175.900 Section 175.900 Shipping...) GENERAL PROVISIONS § 175.900 OMB control numbers. (a) Purpose. This section lists the control numbers... that agencies display a current control number assigned by the Director of OMB for each approved agency...

Preschoolers' Number Sense

ERIC Educational Resources Information Center

Moomaw, Sally; Carr, Victoria; Boat, Mary; Barnett, David

2010-01-01

A child's demonstration of his conceptual understanding of number bodes well for his future success in school mathematics. As youngsters' thinking becomes more logical, they apply one-to-one correspondence relationships to quantification. Yet, reliable assessment of young children's mathematical ability is difficult because of social and emotional…

33 CFR 174.23 - Form of number.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 33 Navigation and Navigable Waters 2 2012-07-01 2012-07-01 false Form of number. 174.23 Section... of number. (a) Each number must consist of two capital letters denoting the State of the issuing... numerals followed by not more than three capital letters (example: WN 567 EFG). (b) A number suffix must...

33 CFR 174.23 - Form of number.

Code of Federal Regulations, 2014 CFR

2014-07-01

... 33 Navigation and Navigable Waters 2 2014-07-01 2014-07-01 false Form of number. 174.23 Section... of number. (a) Each number must consist of two capital letters denoting the State of the issuing... numerals followed by not more than three capital letters (example: WN 567 EFG). (b) A number suffix must...

7 CFR 63.505 - OMB control number.

Code of Federal Regulations, 2013 CFR

2013-01-01

... 7 Agriculture 3 2013-01-01 2013-01-01 false OMB control number. 63.505 Section 63.505 Agriculture... IMPROVEMENT CENTER General Provisions Miscellaneous § 63.505 OMB control number. The control number assigned... pursuant to the Paperwork Reduction Act of 1995, 44 U.S.C. Chapter 35, is OMB control number 0505-new. ...

Relativistic theory of surficial Love numbers

NASA Astrophysics Data System (ADS)

Landry, Philippe; Poisson, Eric

2014-06-01

A relativistic theory of surficial Love numbers, which characterize the surface deformation of a body subjected to tidal forces, was initiated by Damour and Nagar. We revisit this effort in order to extend it, clarify some of its aspects, and simplify its computational implementation. First, we refine the definition of surficial Love numbers proposed by Damour and Nagar and formulate it directly in terms of the deformed curvature of the body's surface, a meaningful geometrical quantity. Second, we develop a unified theory of surficial Love numbers that applies equally well to material bodies and black holes. Third, we derive a compactness-dependent relation between the surficial and (electric-type) gravitational Love numbers of a perfect-fluid body and show that it reduces to the familiar Newtonian relation when the compactness is small. And fourth, we simplify the tasks associated with the practical computation of the surficial and gravitational Love numbers for a material body.

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…

Core Knowledge, Language, and Number

ERIC Educational Resources Information Center

Spelke, Elizabeth S.

2017-01-01

The natural numbers may be our simplest, most useful, and best-studied abstract concepts, but their origins are debated. I consider this debate in the context of the proposal, by Gallistel and Gelman, that natural number system is a product of cognitive evolution and the proposal, by Carey, that it is a product of human cultural history. I offer a…

The Decimal Number System and Young Children

ERIC Educational Resources Information Center

Harrison, John

2006-01-01

In this article, the author believes that a visual image of the number system is helpful to everyone, especially children, in understanding what is, after all, an abstract idea. The simplest model is the number line, a row of equally spaced numbers, starting at zero. This illustrates the continuous progression of the natural numbers, moving to the…

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.

Measurement uncertainty of ester number, acid number and patchouli alcohol of patchouli oil produced in Yogyakarta

NASA Astrophysics Data System (ADS)

Istiningrum, Reni Banowati; Saepuloh, Azis; Jannah, Wirdatul; Aji, Didit Waskito

2017-03-01

Yogyakarta is one of patchouli oil distillation center in Indonesia. The quality of patchouli oil greatly affect its market price. Therefore, testing quality of patchouli oil parameters is an important concern, one through determination of the measurement uncertainty. This study will determine the measurement uncertainty of ester number, acid number and content of patchouli alcohol through a bottom up approach. Source contributor to measurement uncertainty of ester number is a mass of the sample, a blank and sample titration volume, the molar mass of KOH, HCl normality, and replication. While the source contributor of the measurement uncertainty of acid number is the mass of the sample, the sample titration volume, the relative mass and normality of KOH, and repetition. Determination of patchouli alcohol by Gas Chromatography considers the sources of measurement uncertainty only from repeatability because reference materials are not available.

Cortical areas involved in Arabic number reading.

PubMed

Roux, F-E; Lubrano, V; Lauwers-Cances, V; Giussani, C; Démonet, J-F

2008-01-15

Distinct functional pathways for processing words and numbers have been hypothesized from the observation of dissociated impairments of these categories in brain-damaged patients. We aimed to identify the cortical areas involved in Arabic number reading process in patients operated on for various brain lesions. Direct cortical electrostimulation was prospectively used in 60 brain mappings. We used object naming and two reading tasks: alphabetic script (sentences and number words) and Arabic number reading. Cortical areas involved in Arabic number reading were identified according to location, type of interference, and distinctness from areas associated with other language tasks. Arabic number reading was sustained by small cortical areas, often extremely well localized (<1 cm(2)). Over 259 language sites detected, 43 (17%) were exclusively involved in Arabic number reading (no sentence or word number reading interference detected in these sites). Specific Arabic number reading interferences were mainly found in three regions: the Broca area (Brodmann area 45), the anterior part of the dominant supramarginal gyrus (Brodmann area 40; p < 0.0001), and the temporal-basal area (Brodmann area 37; p < 0.05). Diverse types of interferences were observed (reading arrest, phonemic or semantic paraphasia). Error patterns were fairly similar across temporal, parietal, and frontal stimulation sites, except for phonemic paraphasias, which were found only in supramarginal gyrus. Our findings strongly support the fact that the acquisition through education of specific symbolic entities, such as Arabic numbers, could result in the segregation and the specialization of anatomically distinct brain areas.

Symbolic Number Skills Predict Growth in Nonsymbolic Number Skills in Kindergarteners

ERIC Educational Resources Information Center

Lyons, Ian M.; Bugden, Stephanie; Zheng, Samuel; De Jesus, Stefanie; Ansari, Daniel

2018-01-01

There is currently considerable discussion about the relative influences of evolutionary and cultural factors in the development of early numerical skills. In particular, there has been substantial debate and study of the relationship between approximate, nonverbal (approximate magnitude system [AMS]) and exact, symbolic (symbolic number system…

A Comprehensive High Performance Predictive Tool for Fusion Liquid Metal Hydromagnetics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, Peter; Chhabra, Rupanshi; Munipalli, Ramakanth

In Phase I SBIR project, HyPerComp and Texcel initiated the development of two induction-based MHD codes as a predictive tool for fusion hydro-magnetics. The newly-developed codes overcome the deficiency of other MHD codes based on the quasi static approximation by defining a more general mathematical model that utilizes the induced magnetic field rather than the electric potential as the main electromagnetic variable. The UCLA code is a finite-difference staggered-mesh code that serves as a supplementary tool to the massively-parallel finite-volume code developed by HyPerComp. As there is no suitable experimental data under blanket-relevant conditions for code validation, code-to-code comparisons andmore » comparisons against analytical solutions were successfully performed for three selected test cases: (1) lid-driven MHD flow, (2) flow in a rectangular duct in a transverse magnetic field, and (3) unsteady finite magnetic Reynolds number flow in a rectangular enclosure. The performed tests suggest that the developed codes are accurate and robust. Further work will focus on enhancing the code capabilities towards higher flow parameters and faster computations. At the conclusion of the current Phase-II Project we have completed the preliminary validation efforts in performing unsteady mixed-convection MHD flows (against limited data that is currently available in literature), and demonstrated flow behavior in large 3D channels including important geometrical features. Code enhancements such as periodic boundary conditions, unmatched mesh structures are also ready. As proposed, we have built upon these strengths and explored a much increased range of Grashof numbers and Hartmann numbers under various flow conditions, ranging from flows in a rectangular duct to prototypic blanket modules and liquid metal PFC. Parametric studies, numerical and physical model improvements to expand the scope of simulations, code demonstration, and continued validation activities have

The elephant brain in numbers

PubMed Central

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

2014-01-01

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

46 CFR 193.60-5 - Number required.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 46 Shipping 7 2014-10-01 2014-10-01 false Number required. 193.60-5 Section 193.60-5 Shipping... EQUIPMENT Fire Axes § 193.60-5 Number required. (a) All vessels shall carry at least the minimum number of... necessary for the proper protection of the vessel. Table 193.60-5(a) Gross tons Over Not over Number of axes...

46 CFR 76.60-5 - Number required.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 46 Shipping 3 2012-10-01 2012-10-01 false Number required. 76.60-5 Section 76.60-5 Shipping COAST... § 76.60-5 Number required. (a) All vessels except barges shall carry at least the minimum number of... necessary for the proper protection of the vessel. Table 76.60-5(a) Gross tons Over Not over Number of axes...

46 CFR 76.60-5 - Number required.

Code of Federal Regulations, 2014 CFR

2014-10-01

... 46 Shipping 3 2014-10-01 2014-10-01 false Number required. 76.60-5 Section 76.60-5 Shipping COAST... § 76.60-5 Number required. (a) All vessels except barges shall carry at least the minimum number of... necessary for the proper protection of the vessel. Table 76.60-5(a) Gross tons Over Not over Number of axes...

46 CFR 193.60-5 - Number required.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 46 Shipping 7 2013-10-01 2013-10-01 false Number required. 193.60-5 Section 193.60-5 Shipping... EQUIPMENT Fire Axes § 193.60-5 Number required. (a) All vessels shall carry at least the minimum number of... necessary for the proper protection of the vessel. Table 193.60-5(a) Gross tons Over Not over Number of axes...

46 CFR 193.60-5 - Number required.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 46 Shipping 7 2011-10-01 2011-10-01 false Number required. 193.60-5 Section 193.60-5 Shipping... EQUIPMENT Fire Axes § 193.60-5 Number required. (a) All vessels shall carry at least the minimum number of... necessary for the proper protection of the vessel. Table 193.60-5(a) Gross tons Over Not over Number of axes...

46 CFR 76.60-5 - Number required.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 46 Shipping 3 2013-10-01 2013-10-01 false Number required. 76.60-5 Section 76.60-5 Shipping COAST... § 76.60-5 Number required. (a) All vessels except barges shall carry at least the minimum number of... necessary for the proper protection of the vessel. Table 76.60-5(a) Gross tons Over Not over Number of axes...

46 CFR 193.60-5 - Number required.

Code of Federal Regulations, 2010 CFR

2010-10-01

... 46 Shipping 7 2010-10-01 2010-10-01 false Number required. 193.60-5 Section 193.60-5 Shipping... EQUIPMENT Fire Axes § 193.60-5 Number required. (a) All vessels shall carry at least the minimum number of... necessary for the proper protection of the vessel. Table 193.60-5(a) Gross tons Over Not over Number of axes...

46 CFR 76.60-5 - Number required.

Code of Federal Regulations, 2011 CFR

2011-10-01

... 46 Shipping 3 2011-10-01 2011-10-01 false Number required. 76.60-5 Section 76.60-5 Shipping COAST... § 76.60-5 Number required. (a) All vessels except barges shall carry at least the minimum number of... necessary for the proper protection of the vessel. Table 76.60-5(a) Gross tons Over Not over Number of axes...

46 CFR 193.60-5 - Number required.

Code of Federal Regulations, 2012 CFR

2012-10-01

... 46 Shipping 7 2012-10-01 2012-10-01 false Number required. 193.60-5 Section 193.60-5 Shipping... EQUIPMENT Fire Axes § 193.60-5 Number required. (a) All vessels shall carry at least the minimum number of... necessary for the proper protection of the vessel. Table 193.60-5(a) Gross tons Over Not over Number of axes...

Australian DefenceScience. Volume 12, Number 3, Spring

DTIC Science & Technology

2004-01-01

Australian DEFENCESCIENCE Spring Issue Volume 12 Number 3 2004 Autonomous UAV flight a world first Missile countermeasures – from flares to lasers...4. TITLE AND SUBTITLE Australian DefenceScience. Volume 12 , Number 3 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S...ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S) 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 12 . DISTRIBUTION/AVAILABILITY STATEMENT Approved for public

47 CFR 52.20 - Thousands-block number pooling.

Code of Federal Regulations, 2013 CFR

2013-10-01

... 47 Telecommunication 3 2013-10-01 2013-10-01 false Thousands-block number pooling. 52.20 Section... (CONTINUED) NUMBERING Number Portability § 52.20 Thousands-block number pooling. (a) Definition. Thousands-block number pooling is a process by which the 10,000 numbers in a central office code (NXX) are...

Deafness for the meanings of number words

PubMed Central

Caño, Agnès; Rapp, Brenda; Costa, Albert; Juncadella, Montserrat

2008-01-01

We describe the performance of an aphasic individual who showed a selective impairment affecting his comprehension of auditorily presented number words and not other word categories. His difficulty in number word comprehension was restricted to the auditory modality, given that with visual stimuli (written words, Arabic numerals and pictures) his comprehension of number and non-number words was intact. While there have been previous reports of selective difficulty or sparing of number words at the semantic and post-semantic levels, this is the first reported case of a pre-semantic deficit that is specific to the category of number words. This constitutes evidence that lexical semantic distinctions are respected by modality-specific neural mechanisms responsible for providing access to the meanings of words. PMID:17915265

Introducing Complex Numbers

ERIC Educational Resources Information Center

Trudgian, Timothy

2009-01-01

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

Random numbers from vacuum fluctuations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shi, Yicheng; Kurtsiefer, Christian, E-mail: christian.kurtsiefer@gmail.com; Center for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543

2016-07-25

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

Analysis of the Relationship between the "n"th Root Which Is a Whole Number and the "n" Consecutive Odd Numbers

ERIC Educational Resources Information Center

Kwenge, Erasmus; Mwewa, Peter; Mulenga, H. M.

2015-01-01

The study was undertaken to establish the relationship between the roots of the perfect numbers and the "n" consecutive odd numbers. Odd numbers were arranged in such a way that their sums were either equal to the perfect square number or equal to a cube. The findings on the patterns and relationships of the numbers showed that there was…

Copy Number Variation across European Populations

PubMed Central

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

Heat transfer about a vertical permeable membrane

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kaviany, M.

1988-05-01

The natural convection heat transfer about both sides of vertical walls without any seepage has been studied and the effects of the wall thickness and thermal conductivity on the local and average heat transfer rates have been determined. Viskanta and Lankford have concluded that in predicting the heat transfer rate through the wall, for low-thermal-conductivity walls the a priori unknown wall surface temperatures can be walls the a priori unknown wall surface temperatures can be estimated as the arithmetic average of the reservoir temperatures without loss of accuracy (for most practical situations). Sparrow and Prakash treated the surface temperature asmore » variable but used the local temperature along with the available isothermal boundary-layer analysis for determination of the local heat transfer rate and found this to be reasonable at relatively low Grashof numbers. In this study the heat trasnfer rate between two reservoirs of different temperature connected in part through a permeable membrane is analyzed. Rather than solving the complete problem numerically for the three domains (fluid-wall-fluid), the available results on the effects of suction and blowing on the natural convection boundary layer are used in an analysis of the membranes with low thermal conductivity and small seepage velocities, which are characteristic of membranes considered. This will lead to rather simple expressions for the determination of the heat transfer rate.« less

Experimental determination of Ramsey numbers.

PubMed

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 4≤m≤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.

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 4≤m≤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.

Microglial numbers attain adult levels after undergoing a rapid decrease in cell number in the third postnatal week.

PubMed

Nikodemova, Maria; Kimyon, Rebecca S; De, Ishani; Small, Alissa L; Collier, Lara S; Watters, Jyoti J

2015-01-15

During postnatal development, microglia, CNS resident innate immune cells, are essential for synaptic pruning, neuronal apoptosis and remodeling. During this period microglia undergo morphological and phenotypic transformations; however, little is known about how microglial number and density is regulated during postnatal CNS development. We found that after an initial increase during the first 14 postnatal days, microglial numbers in mouse brain began declining in the third postnatal week and were reduced by 50% by 6weeks of age; these "adult" levels were maintained until at least 9months of age. Microglial CD11b levels increased, whereas CD45 and ER-MP58 declined between P10 and adulthood, consistent with a maturing microglial phenotype. Our data indicate that both increased microglial apoptosis and a decreased proliferative capacity contribute to the developmental reduction in microglial numbers. We found no correlation between developmental reductions in microglial numbers and brain mRNA levels of Cd200, Cx3Cl1, M-Csf or Il-34. We tested the ability of M-Csf-overexpression, a key growth factor promoting microglial proliferation and survival, to prevent microglial loss in the third postnatal week. Mice overexpressing M-Csf in astrocytes had higher numbers of microglia at all ages tested. However, the developmental decline in microglial numbers still occurred, suggesting that chronically elevated M-CSF is unable to overcome the developmental decrease in microglial numbers. Whereas the identity of the factor(s) regulating microglial number and density during development remains to be determined, it is likely that microglia respond to a "maturation" signal since the reduction in microglial numbers coincides with CNS maturation. Copyright © 2014 Elsevier B.V. All rights reserved.