共查询到20条相似文献,搜索用时 31 毫秒
1.
A. Fujii, and later J. Steuding, considered an asymptotic formula for the sum of values of the Dirichlet L-function taken at the nontrivial zeros of another Dirichlet L-function. Here we improve the error term of this asymptotic formula. 相似文献
2.
Yuji Sakamoto Nakahiro Yoshida 《Annals of the Institute of Statistical Mathematics》2009,61(3):629-661
For an unknown parameter in the drift function of a diffusion process, we consider an M-estimator based on continuously observed data, and obtain its distributional asymptotic expansion up to the third order.
Our setting covers the misspecified cases. To represent the coefficients in the asymptotic expansion, we derive some formulas
for asymptotic cumulants of stochastic integrals, which are widely applicable to many other problems. Furthermore, asymptotic
properties of cumulants of mixing processes will be also studied in a general setting. 相似文献
3.
Antonio Campo 《Numerical Methods for Partial Differential Equations》2004,20(6):820-830
The principal goal of this article is to present two asymptotic solutions for the classical Graetz‐Nusselt problem. The method of lines (MOL) has been adopted for solving the governing partial differential energy equation in two independent variables in an asymptotic manner. Two temperature subfields are determined semianalytically: one for small x (x → 0) and the other for large x (x → ∞). Later, the two asymptotic mean Nusselt number subdistributions, Nu X→0(x) and Nu X→∞(x), blend themselves into a generalized correlation equation for the mean Nusselt number distribution Nu (x) covering the entire x‐domain. The simplicity of the MOL procedure, combined with the high quality asymptotic mean Nusselt number subdistributions, provides an alternative methodology for solving the Graetz‐Nusselt problem without using higher level mathematics. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004. 相似文献
4.
Properties of the set T
s
of “particularly nonnormal numbers” of the unit interval are studied in detail (T
s
consists of real numbers x some of whose s-adic digits have the asymptotic frequencies in the nonterminating s-adic expansion of x, and some do not). It is proved that the set T
s
is residual in the topological sense (i.e., it is of the first Baire category) and is generic in the sense of fractal geometry
(T
s
is a superfractal set, i.e., its Hausdorff-Besicovitch dimension is equal to 1). A topological and fractal classification
of sets of real numbers via analysis of asymptotic frequencies of digits in their s-adic expansions is presented.
Dedicated to V. S. Korolyuk on occasion of his 80th birthday
__________
Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 9, pp. 1163–1170, September, 2005. 相似文献
5.
6.
This paper discusses the asymptotic behavior of the loss probability for general queues with finite GI/M/1 type structure such as GI/M/c/K, SM/M/1/K and GI/MSP/1/K queues. We find an explicit expression for the asymptotic behavior of the loss probability as K tends to infinity. With the result, it is shown that the loss probability tends to 0 at a geometric rate.
This research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology
Research Center) support program supervised by the IITA (Institute of Information Technology Assessment). 相似文献
7.
In this paper we investigate the approximation behaviour of the so‐called Hermite–Fejér interpolation operator based on the zeros of Jacobi polynomials. As a result we obtain the asymptotic formula of approximation rate for these operators. Moreover, such a formula is valid for any individual continuous function. We will also study the K ‐functional deduced by this operator. Consequently the asymptotic term of this K ‐functional is established. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
8.
Solomon W. Harrar Arjun K. Gupta 《Annals of the Institute of Statistical Mathematics》2007,59(3):531-556
In this paper we derive the asymptotic expansion of the null distribution of the F-statistic in one-way ANOVA under non-normality. The asymptotic framework is when the number of treatments is moderate but
sample size per treatment (replication size) is small. This kind of asymptotics will be relevant, for example, to agricultural
screening trials where large number of cultivars are compared with few replications per cultivar. There is also a huge potential
for the application of this kind of asymptotics in microarray experiments. Based on the asymptotic expansion we will devise
a transformation that speeds up the convergence to the limiting distribution. The results indicate that the approximation
based on limiting distribution are unsatisfactory unless number of treatments is very large. Our numerical investigations
reveal that our asymptotic expansion performs better than other methods in the literature when there is skewness in the data
or even when the data comes from a symmetric distribution with heavy tails. 相似文献
9.
The main difficulties in the Laplace’s method of asymptotic expansions of integrals are originated by a change of variables. We propose a variant of the method which avoids that change of variables and simplifies the computations. On the one hand, the calculation of the coefficients of the asymptotic expansion is remarkably simpler. On the other hand, the asymptotic sequence is as simple as in the standard Laplace’s method: inverse powers of the asymptotic variable. New asymptotic expansions of the Gamma function Γ(z) for large z and the Gauss hypergeometric function 2F1(a,b,c;z) for large b and c are given as illustrations. An explicit formula for the coefficients of the classical Stirling expansion of Γ(z) is also given. 相似文献
10.
In this paper, we investigate the exact distribution of the waiting time for ther-th ℓ-overlapping occurrence of success-runs of a specified length in a sequence of two state Markov dependent trials. The
probability generating functions are derived explicitly, and as asymptotic results, relationships of a negative binomial distribution
of orderk and an extended Poisson distribution of orderk are discussed. We provide further insights into the run-related problems from the viewpoint of the ℓ-overlapping enumeration
scheme. We also study the exact distribution of the number of ℓ-overlapping occurrences of success-runs in a fixed number
of trials and derive the probability generating functions. The present work extends several properties of distributions of
orderk and leads us a new type of geneses of the discrete distributions. 相似文献
11.
Consider a graph G on n vertices satisfying the following Ore‐type condition: for any two nonadjacent vertices x and y of G, we have . We conjecture that if we color the edges of G with two colors then the vertex set of G can be partitioned to two vertex disjoint monochromatic cycles of distinct colors. In this article, we prove an asymptotic version of this conjecture. 相似文献
12.
In the present paper, we consider the Bezier variant Mn,α(f,x) of the generalized Durrmeyer type operators, and obtain an estimate on the rate of convergence of Mn,α(f,x) for the decomposition technique of functions of bounded variation. In the end we propose an open problem for the readers and give an asymptotic formula for these generalized Durrmeyer type operators. 相似文献
13.
We investigate the asymptotic behavior of the eigenvalues and the eigenfunctions of q‐Sturm‐Liouville eigenvalue problems. For this aim we study the asymptotic behavior of q‐trigonometric functions as well as fundamental sets of solutions of the associated second order q‐difference equation. As in classical Sturm‐Liouville theory, the eigenvalues behave like zeros of q‐trigonometric functions and the eigenfunctions behave like q‐trigonometric functions. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
14.
We study the large time behavior of viscosity solutions of Hamilton–Jacobi equations with periodic boundary data on bounded domains. We establish a result on convergence of viscosity solutions to state constraint asymptotic solutions or periodic asymptotic solutions depending on the sign of critical value as time goes to infinity. 相似文献
15.
Luc Pronzato 《Mathematica Slovaca》2009,59(5):611-626
We consider the design of c-optimal experiments for the estimation of a scalar function h(θ) of the parameters θ in a nonlinear regression model. A c-optimal design ξ* may be singular, and we derive conditions ensuring the asymptotic normality of the Least-Squares estimator of h(θ) for a singular design over a finite space. As illustrated by an example, the singular designs for which asymptotic normality
holds typically depend on the unknown true value of θ, which makes singular c-optimal designs of no practical use in nonlinear situations. Some simple alternatives are then suggested for constructing
nonsingular designs that approach a c-optimal design under some conditions. 相似文献
16.
In recent works [ 1 ] and [ 2 ], we have proposed more systematic versions of the Laplace’s and saddle point methods for asymptotic expansions of integrals. Those variants of the standard methods avoid the classical change of variables and give closed algebraic formulas for the coefficients of the expansions. In this work we apply the ideas introduced in [ 1 ] and [ 2 ] to the uniform method “saddle point near a pole.” We obtain a computationally more systematic version of that uniform asymptotic method for integrals having a saddle point near a pole that, in many interesting examples, gives a closed algebraic formula for the coefficients. The asymptotic sequence is given, in general, in terms of exponential integrals of fractional order (or incomplete gamma functions). In particular, when the order of the saddle point is two, the basic approximant is given in terms of the error function (as in the standard method). As an application, we obtain new asymptotic expansions of the Gauss Hypergeometric function 2F1(a, b, c; z) for large b and c with c > b + 1 . 相似文献
17.
Sergueï A. Nazarov Adlia Sequeira Juha H. Videman 《Journal de Mathématiques Pures et Appliquées》2001,80(10):445
In this paper our objective is to provide physically reasonable solutions for the stationary Navier–Stokes equations in a two-dimensional domain with two outlets to infinity, a semi-strip Π− and a half-plane K. The same problem in an aperture domain, i.e. in a domain with two half-plane outlets to infinity, has been studied but only under symmetry restrictions on the data. Here, we assume that the main asymptotic term of the solution takes an antisymmetric form in K and apply the technique of weighted spaces with detached asymptotics, i.e. we use spaces where the functions have prescribed asymptotic forms in the outlets.After first showing that the corresponding Stokes problem admits a unique solution if and only if certain compatibility conditions are satisfied, we write the Navier–Stokes equations as a perturbation of the Stokes problem and the crucial compatibility condition as an algebraic equation by which the flux becomes determined. Assuming that the coefficient of the main (antisymmetric) asymptotic term of the solution in K does not vanish and that the data are sufficiently small, we use a contraction principle to solve the Navier–Stokes system coupled with the algebraic equation.Finally, we discuss the ill-posedness of the Navier–Stokes problem with prescribed flux. 相似文献
18.
Spatial‐skin effect for eigenvibrations of a thick cascade junction with ‘heavy’ concentrated masses
A spectral problem for the Laplace operator in a thick cascade junction with concentrated masses is considered. This cascade junction consists of the junction's body and a great number of ?‐alternating thin rods belonging to two classes. One class consists of rods of finite length, and the second one consists of rods of small length of order . The density of the junction is of order on the rods from the second class and outside of them. The asymptotic behavior of eigenvalues and eigenfunctions of this problem is studied as ? → 0. There exist five qualitatively different cases in the asymptotic behavior of eigenmagnitudes as ? → 0, namely the case of ‘light’ concentrated (α ∈ (0,1)), ‘middle’ concentrated (α = 1), and ‘heavy’ concentrated masses (α ∈ (1, + ∞ )) that we divide into ‘slightly heavy’ concentrated (α ∈ (1,2)), ‘intermediate heavy’ concentrated (α = 2), and ‘very heavy’ concentrated masses (α > 2). In the paper, we study in detail the influence of the concentrated masses on the asymptotic behavior if α ∈ (1,2). We construct the leading terms of asymptotic expansions both for the eigenvalues and eigenfunctions and prove the corresponding asymptotic estimates. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
19.
We study the asymptotic behaviour in time of incompressible non‐Newtonian fluids in the whole space assuming that initial data also belong to L1. Firstly, we consider the weak solution to the power‐law model with non‐zero external forces and we find the asymptotic behaviour in time of this solution in the same class of existence and uniqueness with p?. Secondly, we are interested in the asymptotic behaviour of weak solutions to the second grade model, and finally, we deal with the asymptotic behaviour in time of weak solutions to a simplified model of viscoelastic fluids of the Oldroyd type. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
20.
In this paper we analyze the M/M/c retrial queue using the censoring technique. This technique allows us to carry out an asymptotic analysis, which leads to
interesting and useful asymptotic results. Based on the asymptotic analysis, we develop two methods for obtaining approximations
to the stationary probabilities, from which other performance metrics can be obtained. We demonstrate that the two proposed
approximations are good alternatives to existing approximation methods. We expect that the technique used here can be applied
to other retrial queueing models. 相似文献