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111.
We prove a structure theorem for evolution equations in the state space of a discrete classical system fulfilling a class ofH theorems. TheseH theorems are proved to give strong implications on the time behavior of the solutions. All the results are demonstrated by examples (Boltzmann-like equations, for example). 相似文献
112.
A.Larry Wright 《Journal of multivariate analysis》1982,12(2):178-185
Two related almost sure limit theorems are obtained in connection with a stochastic process {ξ(t), ?∞ < t < ∞} with independent increments. The first result deals with the existence of a simultaneous stabilizing function H(t) such that for almost all sample functions of the process. The second result deals with a wide-sense stationary process whose random spectral distributions is ξ. It addresses the question: Under what conditions does converge as T → ∞ for all τ for almost all sample functions? 相似文献
113.
R. F. Baum 《Journal of Optimization Theory and Applications》1976,19(1):89-116
Existence theorems are proved for usual Lagrange control systems, in which the time domain is unbounded. As usual in Lagrange problems, the cost functional is an improper integral, the state equation is a system of ordinary differential equations, with assigned boundary conditions, and constraints may be imposed on the values of the state and control variables. It is shown that the boundary conditions at infinity require a particular analysis. Problems of this form can be found in econometrics (e.g., infinite-horizon economic models) and operations research (e.g., search problems).The author wishes to thank Professor L. Cesari for his many helpful comments and assistance in the preparation of this paper. This work was sponsored by the United States Air Force under Grants Nos. AF-AFOSR-69-1767-A and AFOSR-69-1662. 相似文献
114.
Multivalued convexity and optimization: A unified approach to inequality and equality constraints 总被引:5,自引:0,他引:5
J. Borwein 《Mathematical Programming》1977,13(1):183-199
Multivalued functions satisfying a general convexity condition are examined in the first section. The second section establishes a general transposition theorem for such functions and develops an abstract multiplier principle for them. In particular both convex inequality and linear equality constraints are seen to satisfy the same generalized constraint qualification. The final section examines quasi-convex programmes. 相似文献
115.
M. L. Puterman 《Journal of Optimization Theory and Applications》1977,22(1):103-116
In this paper, we consider the problem of optimally controlling a diffusion process on a closed bounded region ofR
n with reflection at the boundary. Employing methods similar to Fleming (Ref. 1), we present a constructive proof that there exists an optimal Markov control that is measurable or lower semicontinuous. We prove further that the expected cost function corresponding to the optimal control is the unique solution of the quasilinear parabolic differential equation of dynamic programming with Neumann boundary conditions and that there exists a diffusion process (in the sense of Stroock and Varadhan) corresponding to the optimal control.This work was partially supported by the National Science Foundation, Grant No. GK-18339, by the Office of Naval Research, Grant No. NR-042-264, and by the National Research Council of Canada, Grant No. A3609.The author would like to thank S. R. Pliska, J. Pisa, and N. Trudinger for helpful suggestions. He is especially grateful to Professor A. F. Veinott, Jr., for help and advice in the preparation of the doctoral dissertation, on which part of this paper is based. Finally, he wishes to thank one of the referees for the careful reading and constructive comments on an earlier version of this paper. 相似文献
116.
117.
118.
Donald L. Iglehart 《Stochastic Processes and their Applications》1974,2(3):211-241
Weak convergence of probability measures on function spaces has been active area of research in recent years. While the theory has a somewhat abstract base, it is extremely useful in a wide variety of problems and we believe has much to offer to applied probability. Our aim in this survey paper is to discuss those aspects of the theory which are relevant to work in applied probability. After an introduction to the foundations of weak convergence, we shall discuss partial sum, point, Markov and extremal processes. These processes form the building blocks for many of the important models of applied probability. 相似文献
119.
Z. A. Enikeeva 《Lithuanian Mathematical Journal》2005,45(1):24-33
We obtain a limit theorem of convergence in distribution for random polygonal lines defined by sums of independent random variables with replacements. In a particular case, the limit is the Gaussian Ornstein-Uhlenbeck process.__________Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 1, pp. 33–44, January–March, 2005.Translated by V. Mackeviius 相似文献
120.
Nils?Lid?Hjort Andrea?OngaroEmail author 《Statistical Inference for Stochastic Processes》2005,8(3):227-254
Two characterisations of a random mean from a Dirichlet process, as a limit of finite sums of a simple symmetric form and
as a solution of a certain stochastic equation, are developed and investigated. These are used to reach results on and new
insights into the distributions of such random means. In particular, identities involving functional transforms and recursive
moment formulae are established. Furthermore, characterisations for several choices of the Dirichlet process parameter (leading
to symmetric, unimodal, stable, and finite mixture distributions) are provided. Our methods lead to exact simulation recipes
for prior and posterior random means, an approximation algorithm for the exact densities of these means, and limiting normality
theorems for posterior distributions. The theory also extends to mixtures of Dirichlet processes and to the case of several
random means simultaneously. 相似文献