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Simple Expression (simple + expression)
Selected AbstractsEdge-transitive lattice netsACTA CRYSTALLOGRAPHICA SECTION A, Issue 5 2009Olaf Delgado-Friedrichs Lattice nets have one vertex in the topological unit cell. Some two- and three-periodic lattice nets with one kind of edge (edge-transitive) are described. Simple expressions for the topological density of the two-periodic nets are found empirically. Thirteen infinite families of three-periodic cubic lattice nets and hexagonal, trigonal and tetragonal families are identified. [source] A Phenomenological Probe Model of Fast Ion Measurement Using a Hybrid Directional ProbeCONTRIBUTIONS TO PLASMA PHYSICS, Issue 5-7 2008K. Nagaoka Abstract A phenomenological probe model was developed for quantitative fast-ion-measurement using a hybrid directional probe (HDP), which is a directional probe to measure ion current and heat flux at the same position. The secondary electrons due to fast-ion-injection onto the probe surface enhances the ion-saturation-current, thus a thermal probe method was required for quantitative measurement of fast ions. The model gives a simple expression of the secondary electron yield as a function of ion currents and heat fluxes measured by the HDP, and can determine the net fast-ion-current without the calibrations of the thermal probe method. The model was applied to the experimental results of fast-ion-measurements using a HDP in CHS, and the secondary electron yield obtained by the model agrees with the calibration results of the HDP. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A new broadband uniform accuracy doa estimator,EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONS, Issue 6 2002Mohammad Ghavami Conventional estimators of the bearing angle suffer from different accuracies for different angles. In the method discussed in this letter, a set of two-dimensional digital filters are employed for beamforming. Each filter is called a fan filter and performs broadband characteristics. It will be shown analytically that the accuracy of the bearing estimation is strongly dependent to the angle of arrival in such a way that it is maximum in the broadside and minimum in the endfire of the antenna. We will derive a simple expression for calculating the number of coefficients necessary for beamforming with uniform accuracy. A set of filters is then designed according to this criteria. It will be demonstrated by computer simulations that in the presence of noisy broadband incoming signals, the estimation of different arriving angles is accomplished with almost the same accuracy and hence using this method a complex and separately sectored antenna wilt not be required. [source] Free fermions violate the area law for entanglement entropyFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7-9 2010R.C. Helling Abstract We show that the entanglement entropy associated to a region grows faster than the area of its boundary surface. This is done by proving a special case of a conjecture due to Widom that yields a surprisingly simple expression for the leading behaviour of the entanglement entropy. [source] Theoretical performance analysis of the multi-stage gas,solid fluidized bed air preheaterINTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 10 2001Sang Il Park Abstract The multi-stage fluidized bed can be used to preheat the combustion air by recovering the waste heat from the exhaust gas from industrial furnaces. The dilute-phase fluidized bed may be formed to exclude the excessive pressure drop across the multi-stage fluidized bed. But, in this case, the solid particles do not reach to the thermal equilibrium due to relatively short residence time in each layer of fluidized bed. In this study, a theoretical analysis on the dilute phase multistage fluidized bed heat exchanger was performed. A parameter related to the degree of thermal equilibrium between gas and solid particles at the dilute-phase fluidized beds was derived. Using this parameter, a relatively simple expression was obtained for the thermal efficiencies of the multi-stage fluidized bed heat exchanger and air preheater. Copyright © 2001 John Wiley & Sons, Ltd. [source] Time-of-flight neutron powder diffraction with a thick-walled sample cellJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 3 2007M. P. Pitt The time-of-flight diffraction techniques that are normally practiced at pulsed neutron sources afford opportunities that are not readily available at continuous fixed-wavelength sources. The present work concerns the increasing trend in materials science to study samples in complex non-ambient environments, such as high gas pressure. Taking the example of a sample cell in which a material is studied under fluid pressure, the optimization of the cell design for best data collection rate is considered. The design of primary- and scattered-beam masks for eliminating background scattering from the sample cell and the correction of the data for cell and sample attenuation are addressed. The outputs of this work include a simple expression for the optimum wall thickness of a thick-walled sample cell, a procedure for accurately determining the required mask aperture width for any scattering angle, more compact expressions for some of the results of the work of Paalman & Pings [J. Appl. Phys. (1962), 33, 2635,2639] on absorption corrections, and guidance as to the correction of diffraction profiles for cell and background effects. Examples are given, drawn from studies of materials under hydrogen gas pressures up to 1800,bar in cells constructed from Ti2.1Zr and Inconel. [source] The asymptotic variance of the estimated roots in a cointegrated vector autoregressive modelJOURNAL OF TIME SERIES ANALYSIS, Issue 6 2003Søren Johansen Abstract., We show that the asymptotic distribution of the estimated stationary roots in a vector autoregressive model is Gaussian. A simple expression for the asymptotic variance in terms of the roots and the eigenvectors of the companion matrix is derived. The results are extended to the cointegrated vector autoregressive model and we discuss the implementation of the results for complex roots. [source] Measurement of Spin Diffusion Coefficients in Glassy Polymers: Failure of a Simple Scaling LawMACROMOLECULAR CHEMISTRY AND PHYSICS, Issue 2 2008Bernard Meurer Abstract For a series of polymers, the spin diffusion coefficients D do not scale as predicted from a simple expression based on regularly spaced nuclei. We compare D for PVA and polystyrene with their side group either protonated or deuterated. For polystyrene, D is considerably reduced from 600,800 to 65 nm2,·,s,1. For PVA, D is already small for the fully protonated chain and is only slightly reduced from 170 to 130 nm2,·,s,1. This indicates that the rapidly rotating methyl group does not contribute appreciably to spin diffusion between neighboring chains and confirms that the mean proton density is not the pertinent parameter to control D. [source] Evaluation of radial voidage profiles in packed beds of low-aspect ratiosTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 6 2000Nestor J. Mariani Abstract The relationship between the radial voidage profile, ,(r), and the radial distribution of centres of mono-sized spherical particles, f(r), is revised. A close expression is given for the section S(r1, rc), the area of the segment of a cylindrical surface of radius r intersected by a particle centred at rC. From this expression, ,(r) can be evaluated straightforwardly from the knowledge of f(r). The range 1, a , 2 of aspect ratios (a = dT/dp is then analysed specifically. For this range, the distribution of spherical particles has been characterized theoretically (Govindarao et al., 1992) and a simple expression allows the evaluation of ,(r). The use of this expression for actual catalyst particles, imperfect spheres showing a distribution of sizes, in finally analyzed. La relation entre le profil de vide radial,,(r), et la distribution radiale des centres de particules sphériques de taille unique, f(r), est examinée. Une expression analytique est donnée pour la section S(r,rc), la région du segment d'une surface cylindrique de rayon r intersectée par une particule centrée en rc. À partir de cette expression, il est possible d'évaluer ,(r) directement à partir de f(r). La gamme des élance-ments 1 , a , 2 (a =d, / dp est ensuite évaluée spéci-fiquement. Pour cette gamme, la distribution des particules sphériques a été caractérisée de manière thérique (Govindarao et al., 1992) et une expression simple permet l'évaluation de ,(r). Enfin, on analyse l'emploi de cette expression pour des particules de catalyseurs réelles, des sphères imparfaites présentant une distribution des tailles. [source] Large deviations of multiclass M/G/1 queues,THE CANADIAN JOURNAL OF STATISTICS, Issue 3 2009André Dabrowski Abstract Consider a multiclass M/G/1 queue where queued customers are served in their order of arrival at a rate which depends on the customer class. We model this system using a chain with states represented by a tree. Since the service time distribution depends on the customer class, the stationary distribution is not of product form so there is no simple expression for the stationary distribution. Nevertheless, we can find a harmonic function on this chain which provides information about the asymptotics of this stationary distribution. The associated h -transformation produces a change of measure that increases the arrival rate of customers and decreases the departure rate thus making large deviations common. The Canadian Journal of Statistics 37: 327,346; 2009 © 2009 Statistical Society of Canada Considérons une file d'attente M/G/1 multicatégorie où les consommateurs dans la file d'attente sont servis selon leur ordre d'arrivée à un taux dépendant de leur catégorie de consommateurs. Nous modélisons ce système en utilisant une chaîne où les états sont représentés à l'aide d'un arbre. Puisque la distribution du temps de service dépend du type de consommateurs, la distribution stationnaire ne peut pas s'écrire sous la forme d'un produit. Par conséquent, il n'existe pas d'expression simple pour représenter la distribution stationnaire. Cependant, nous pouvons obte-nir une transformation harmonique de cette chaîne contenant de l'information sur les propriétés asymptotiques de cette distribution stationnaire. La transformation- h associée conduit à un chan-gement de mesure qui augmente le taux d'arrivée et décroît le taux de service ce qui augmente la probabilité de grandes déviations. La revue canadienne de statistique 37: 327,346; 2009 © 2009 Société statistique du Canada [source] Prediction-based estimating functionsTHE ECONOMETRICS JOURNAL, Issue 2 2000Michael Sørensen A generalization of martingale estimating functions is presented which is useful when there are no natural or easily calculated martingales that can be used to construct a class of martingale estimating functions. An estimating function of the new type, which is based on linear predictors, is called a prediction-based estimating functions. Special attention is given to classes of prediction-based estimating functions given by a finite-dimensional space of predictors. It is demonstrated that such a class of estimating functions has most of the attractive properties of martingale estimating functions. In particular, a simple expression is found for the optimal estimating function. This type of prediction-based estimating functions only involve unconditional moments, in contrast to the martingale estimating functions where conditional moments are required. Thus, for applications to discretely observed continuous time models, a considerably smaller amount of simulation is, in general, needed for these than for martingale estimating functions. This is also true of the optimal prediction-based estimating functions. Conditions are given that ensure the existence, consistency and asymptotic normality of the corresponding estimators. The new method is applied to inference for sums of Ornstein,Uhlenbeck-type processes and stochastic volatility models. Stochastic volatility models are studied in considerable detail. It is demonstrated that for inference about models by Hull and White and Chesney and Scott, an explicit optimal prediction-based estimating function can be found so that no simulations are needed. [source] Linear waves in a symmetric equatorial channelTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 624 2007C. Erlick Abstract Using a scaling that allows us to separate the effects of the gravity wave speed from those of boundary location, we reduce the equations for linear waves in a zonal channel on the equatorial beta-plane to a single-parameter eigenvalue problem of the Schrödinger type with parabolic potential. The single parameter can be written , = (,,)2/,1/2, where , = gH(2,R),2, ,, is half the channel width, g is the acceleration due to gravity, H is the typical height of the troposphere or ocean, , is the Earth's rotational frequency, and R is the Earth's radius. The Schrödinger-type equation has exact analytical solutions in the limits , , 0 and , , ,, and one can use these to write an approximate expression for the solution that is accurate everywhere to within 4%. In addition to the simple expression for the eigenvalues, the concise and unified theory also yields explicit expressions for the associated eigenfunctions, which are pure sinusoidal in the , , 0 limit and Gaussian in the , , , limit. Using the same scaling, we derive an eigenvalue formulation for linear waves in an equatorial channel on the sphere with a simple explicit formula for the dispersion relation accurate to O{(,,)2}. From this, we find that the phase velocity of the anti-Kelvin mode on the sphere differs by as much as 10% from , ,1/2. Integrating the linearized shallow-water equations on the sphere, we find that for for larger , and ,,, the phase speeds of all of the negative modes differ substantially from their phase speeds on the beta-plane. Furthermore, the dispersion relations of all of the waves in the equatorial channel on the sphere approach those on the unbounded sphere in a smooth asymptotic fashion, which is not true for the equatorial channel on the beta-plane. Copyright © 2007 Royal Meteorological Society [source] EFFECTS OF GENETIC DRIFT ON VARIANCE COMPONENTS UNDER A GENERAL MODEL OF EPISTASISEVOLUTION, Issue 10 2004N.H. Barton Abstract We analyze the changes in the mean and variance components of a quantitative trait caused by changes in allele frequencies, concentrating on the effects of genetic drift. We use a general representation of epistasis and dominance that allows an arbitrary relation between genotype and phenotype for any number of diallelic loci. We assume initial and final Hardy-Weinberg and linkage equilibrium in our analyses of drift-induced changes. Random drift generates transient linkage disequilibria that cause correlations between allele frequency fluctuations at different loci. However, we show that these have negligible effects, at least for interactions among small numbers of loci. Our analyses are based on diffusion approximations that summarize the effects of drift in terms of F, the inbreeding coefficient, interpreted as the expected proportional decrease in heterozygosity at each locus. For haploids, the variance of the trait mean after a population bottleneck is var(,z,) =where n is the number of loci contributing to the trait variance, VA(1)=VA is the additive genetic variance, and VA(k) is the kth-order additive epistatic variance. The expected additive genetic variance after the bottleneck, denoted (V*A), is closely related to var(,z,); (V*A) (1 ,F)Thus, epistasis inflates the expected additive variance above VA(1 ,F), the expectation under additivity. For haploids (and diploids without dominance), the expected value of every variance component is inflated by the existence of higher order interactions (e.g., third-order epistasis inflates (V*AA)). This is not true in general with diploidy, because dominance alone can reduce (V*A) below VA(1 ,F) (e.g., when dominant alleles are rare). Without dominance, diploidy produces simple expressions: var(,z,)==1 (2F) kVA(k) and (V*A) = (1 ,F)k(2F)k-1VA(k) With dominance (and even without epistasis), var(,z,)and (V*A) no longer depend solely on the variance components in the base population. For small F, the expected additive variance simplifies to (V*A)(1 ,F) VA+ 4FVAA+2FVD+2FCAD, where CAD is a sum of two terms describing covariances between additive effects and dominance and additive × dominance interactions. Whether population bottlenecks lead to expected increases in additive variance depends primarily on the ratio of nonadditive to additive genetic variance in the base population, but dominance precludes simple predictions based solely on variance components. We illustrate these results using a model in which genotypic values are drawn at random, allowing extreme and erratic epistatic interactions. Although our analyses clarify the conditions under which drift is expected to increase VA, we question the evolutionary importance of such increases. [source] A simple model of hillslope response for overland flow generationHYDROLOGICAL PROCESSES, Issue 17 2001Professor Carmelo Agnese Abstract This paper deals with the derivation of the hydrological response of a hillslope on the assumption of quick runoff by surface runoff generation. By using the simple non-linear storage based model, first proposed by Horton, an analytical solution of the overland flow equations over a plane hillslope was derived. This solution establishes a generalization for different flow regimes of Horton's original solution, which is valid for the transitional flow regime only. The solution proposed was compared successfully with that of Horton and, for the turbulent flow regime, to the one derived from kinematic wave theory. This solution can be applied easily to both stationary and non-stationary rainfall excess events. An analytical solution for the instantaneous response function (IRF) was also derived. Finally, simple expressions to compute peak and time to peak of IRF are proposed. Copyright © 2001 John Wiley & Sons, Ltd. [source] Shape, shear and flexion: an analytic flexion formalism for realistic mass profiles,MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2009P. D. Lasky ABSTRACT Flexion is a non-linear gravitational lensing effect that arises from gradients in the convergence and shear across an image. We derive a formalism that describes non-linear gravitational lensing by a circularly symmetric lens in the thin-lens approximation. This provides us with relatively simple expressions for first- and second-flexion in terms of only the surface density and projected mass distribution of the lens. We give details of exact lens models, in particular providing flexion calculations for a Sérsic-law profile, which has become increasingly popular over recent years. We further provide a single resource for the analytic forms of convergence, shear, first- and second-flexion for the following mass distributions: a point mass, singular isothermal sphere (SIS); Navarro,Frenk,White (NFW) profile; Sérsic-law profile. We quantitatively compare these mass distributions and show that the convergence and first-flexion are better indicators of the Sérsic shape parameter, while for the concentration of NFW profiles the shear and second-flexion terms are preferred. [source] | |||||||||||||||||||