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191.
We consider a continuous-time branching random walk on the integer lattice d (d 1 ) with a finite number of branching sources, or catalysts. The random walk is assumed to be spatially homogeneous and irreducible. The branching mechanism at each catalyst, being independent of the random walk, is governed by a Markov branching process. The quantities of interest are the local numbers of particles (at each site) and the total population size. In the present paper, we derive and analyze the Kolmogorov type backward equations for the corresponding Laplace generating functions and also for the successive integer moments and the process extinction probability. In particular, existence and uniqueness theorems are proved and the problem of explosion is studied in some detail. We then rewrite these equations in the form of integral equations of renewal type, which may serve as a convenient tool for the study of the process long-time behavior. The paper also provides a technical foundation to some results published before without detailed proofs. 相似文献
192.
C. G. Dufour 《Journal of statistical physics》1977,17(2):61-70
The entropy is written as a density series expansion involving a new kind of cumulant. These are defined as usual from the so-called reduced distribution functions. The first four terms of the series expansion of the entropy are shown to be identical to the known result. When density corrections are retained up to theuth order, the entropy is proved to obey approximately a conservation theorem. Finally, a discussion of nonequilibrium and equilibrium properties of the grand canonical ensemble is presented. 相似文献
193.
Tyan and Thomas (J. Multivariate Anal.5 (1975), 227–235), have given a characterization of a class of bivariate distributions which yields, as a special case, a characterization of a class of bivariate Poisson distributions. In this paper we develop an analogous characterization of a class of bivariate Poisson processes and give some properties and examples of such processes. 相似文献
194.
Nicholas J. Daras 《BIT Numerical Mathematics》2004,44(2):245-257
The first aim of this paper is the study and determination of the best choices (pointwise, L
2 and uniform) for the generating polynomial of a Padé-type approximation to the Taylor series of a function analytic in an open planar disk. The second aim is to characterize the corresponding Hermite polynomial and to give some estimates for the uniform norm of a Padé-type approximation error. 相似文献
195.
A model of a self-interacting directed animal, which also interacts with a solid wall, is studied as a model of a directed branched polymer which can undergo both a collapse and an adsorption transition. The directed animal is confined to a 45° wedge, and it interacts with one of the walls of this wedge. The existence of a thermodynamic limit in this model shown, and the presence of an adsorption transition is demonstrated by using constructive techniques. By comparing this model to a process of directed percolation, we show that there is also a collapse or -transition in this model. We examine directed percolation in a wedge to show that there is a collapse phase present for arbitrary large values of the adsorption activity. The generating function of adsorbing directed animals in a half-space is found next from which we find the tricritical exponents associated with the adsorption transition. A full solution for a collapsing directed animal seems intractible, so instead we examine the collapse transition of a model of column convex directed animals with a contact activity next. 相似文献
196.
Jos M. Rocha‐Martínez 《商业与工业应用随机模型》2001,17(4):345-360
Three imperfect repair strategies, derived from a discrete‐time model of failure and repair, are implemented on items brand A (car, computer, washer, etc.), which are low quality with respect to equivalent items brand B (the leading brand in the market) in the sense that items brand A usually fail faster than items brand B do, in order to increase their lifetimes so that they have a chance to compete in durability against items brand B. The implementation of those strategies is performed by probabilistic simulations of the model. The effectiveness of these strategies is measured by comparing the expected ‘output’ lifetimes of items brand A under each strategy with respect to the expected lifetime of items brand B and the mean value of the total number of repair actions required on items brand A under one strategy with respect to the other two. The algorithm for designing a computer program for simulating those strategies is included. Some results concerning a relationship between a generalized memoryless property of geometric (exponential) distributions and the convolution property of probability (moment) generating functions are detected and also included. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
197.
On the isometric isomorphism of probabilistic metric spaces 总被引:1,自引:0,他引:1
刘明学 《应用数学和力学(英文版)》2002,23(5):614-617
IntroductionTherearetwokindsofisometricisomorphisminprobabilisticmetricspacetheory (see[1 -9] ) .ThefirstisthataPMspace (E ,F)isisometricallyisomorphictoanotherPMspace(E′,F′) ,andthesecondisthataPMspaces(E ,F)isisometricallyisomorphictoageneratingspaceofquasi_met… 相似文献
198.
A universal symplectic structure for a Newtonian system including
nonconservative cases can be constructed in the framework of Birkhoffian
generalization of Hamiltonian mechanics. In this paper the symplectic
geometry structure of Birkhoffian system is discussed, then the
symplecticity of Birkhoffian phase flow is presented. Based on these
properties we give a way to construct symplectic schemes for Birkhoffian
systems by using the generating function method. 相似文献
199.
Gui Yu Yang 《数学学报(英文版)》2011,27(8):1645-1654
In this paper we describe explicitly the generating relations for the Grothendieck groups of trivial extension algebras of
tame hereditary algebras. 相似文献
200.
《Journal of computational and graphical statistics》2013,22(2):339-351
This article considers small sample asymptotics for the distribution of the total loss Sn of a credit risk portfolio. For portfolios with a few exceptionally high potential loss values, the distribution of Sn turns out to be bimodal. Direct approximation by Esscher tilting does not capture this feature. An improved recursive algorithm is proposed. The new approach leads to a more accurate small sample approximation that models bimodality in the presence of outliers. The results are illustrated by a simulated example as well as an example of an observed credit risk portfolio. 相似文献