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21.
Dominique Picard Karine Tribouley 《Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques》2002,38(6):1023
We consider here i.i.d. variables which are distributed according to a Pareto
up to some point x1 and a Pareto
(with a different parameter) after this point. This model constitutes an approximation for estimating extreme tail probabilities, especially for financial or insurance data. We estimate the parameters by maximizing the likelihood of the sample, and investigate the rates of convergence and the asymptotic laws. We find here a problem which is very close to the change point question from the point of view of limits of experiments. Especially, the rates of convergence and the limiting law obtained here are the same as in a change point framework. Simulations are giving an illustration of the quality of the procedure. 相似文献
22.
W. Schmitendorf 《Journal of Optimization Theory and Applications》1979,27(1):135-146
Optimal control problems with a vector performance index and uncertainty in the state equations are investigated. Nature chooses the uncertainty, subject to magnitude bounds. For these problems, a definition of optimality is presented. This definition reduces to that of a minimax control in the case of a scalar cost and to Pareto optimality when there is no uncertainty or disturbance present. Sufficient conditions for a control to satisfy this definition of optimality are derived. These conditions are in terms of a related two-player zero-sum differential game and suggest a technique for determining the optimal control. The results are illustrated with an example.This research was supported by AFOSR under Grant No. 76-2923. 相似文献
23.
W. Stadler 《Journal of Optimization Theory and Applications》1979,29(1):1-52
In this survey, the history of the subject from 1776 until 1960 is presented. A brief biographical sketch of Vilfredo Pareto is given first. Then, the more or less simultaneous development of the concepts of utility, preference, and welfare theory follows, with results which go back to Hausdorff and Cantor. A brief discussion of the work of Borel and von Neumann as initiators of game theory is included. Each of these areas has developed enough to warrant its own survey; hence, they are reviewed here only insofar as they provide necessary foundations. Thereafter, the concepts of efficiency, vector maximum problem, and Pareto optimality are reviewed in connection with production theory, programming, and economics. The survey is presented within a unified mathematical framework, and the emphasis is on mathematical results, rather than psychological or socio-economic discussion. To enable the reader to draw conclusions without having to obtain each article himself, the results have been presented in somewhat more detail than usual. 相似文献
24.
The paper is concerned with a non-cooperative differential game for two players. We first consider Nash equilibrium solutions in feedback form. In this case, we show that the Cauchy problem for the value functions is generically ill-posed. Looking at vanishing viscosity approximations, one can construct special solutions in the form of chattering controls, but these also appear to be unstable. In the second part of the paper we propose an alternative semi-cooperative pair of strategies for the two players, seeking a Pareto optimum instead of a Nash equilibrium. In this case, we prove that the corresponding Hamiltonian system for the value functions is always weakly hyperbolic.Revised: May 2004 相似文献
25.
LiWei Hai-liangYang 《应用数学学报(英文版)》2004,20(3):495-506
In this paper we first consider a risk process in which claim inter-arrival times and the time untilthe first claim have an Erlang (2) distribution.An explicit solution is derived for the probability of ultimateruin,given an initial reserve of u when the claim size follows a Pareto distribution.Follow Ramsay,Laplacetransforms and exponential integrals are used to derive the solution,which involves a single integral of realvalued functions along the positive real line,and the integrand is not of an oscillating kind.Then we showthat the ultimate ruin probability can be expressed as the sum of expected values of functions of two differentGamma random variables.Finally,the results are extended to the Erlang(n) case.Numerical examples aregiven to illustrate the main results. 相似文献
26.
Heavy tailed durations of regional rainfall 总被引:1,自引:0,他引:1
Durations of rain events and drought events over a given region provide important information about the water resources of
the region. Of particular interest is the shape of upper tails of the probability distributions of such durations. Recent
research suggests that the underlying probability distributions of such durations have heavy tails of hyperbolic type, across
a wide range of spatial scales from 2 km to 120 km. These findings are based on radar measurements of spatially averaged rain
rate (SARR) over a tropical oceanic region. The present work performs a nonparametric inference on the Pareto tail-index of
wet and dry durations at each of those spatial scales, based on the same data, and compares it with conclusions based on the
classical Hill estimator. The results are compared and discussed.
The authors express sincere thanks to the Mathematisches Forschungsinstitut Oberwolfach (MFO) for facilitating their collaboration
under a “Research in Pairs” project hosted at MFO during March 5–25, 2006. The research of the second and third authors was supported by the project
LC06024. 相似文献
27.
A fast Pareto genetic algorithm approach for solving expensive multiobjective optimization problems 总被引:1,自引:0,他引:1
We present a new multiobjective evolutionary algorithm (MOEA), called fast Pareto genetic algorithm (FastPGA), for the simultaneous
optimization of multiple objectives where each solution evaluation is computationally- and/or financially-expensive. This
is often the case when there are time or resource constraints involved in finding a solution. FastPGA utilizes a new ranking
strategy that utilizes more information about Pareto dominance among solutions and niching relations. New genetic operators
are employed to enhance the proposed algorithm’s performance in terms of convergence behavior and computational effort as
rapid convergence is of utmost concern and highly desired when solving expensive multiobjective optimization problems (MOPs).
Computational results for a number of test problems indicate that FastPGA is a promising approach. FastPGA yields similar
performance to that of the improved nondominated sorting genetic algorithm (NSGA-II), a widely-accepted benchmark in the MOEA
research community. However, FastPGA outperforms NSGA-II when only a small number of solution evaluations are permitted, as
would be the case when solving expensive MOPs. 相似文献
28.
V. P. Maslov 《Mathematical Notes》2005,78(5-6):807-813
The notion of density of a finite set is introduced. We prove a general theorem of set theory which refines the Gibbs, Bose-Einstein, and Pareto distributions as well as the Zipf law. 相似文献
29.
Satya Prakash Pranav Kumar B.V.N.S. Prasad Anuj Gupta 《European Journal of Operational Research》2008
A cost–time trade-off bulk transportation problem with the objectives to minimize the total cost and duration of bulk transportation without according priorities to them is considered. The entire requirement of each destination is to be met from one source only; however a source can supply to any number of destinations subject to the availability of the commodity at it. Two new algorithms are provided to obtain the set of Pareto optimal solutions of this problem. This work extends and generalizes the work related to single-objective and prioritized two-objective bulk transportation problems done in the past while providing flexibility in decision making. 相似文献
30.
In the literature, methods for the construction of piecewise linear upper and lower bounds for the approximation of univariate convex functions have been proposed. We study the effect of the use of transformations on the approximation of univariate (convex) functions. In this paper, we show that these transformations can be used to construct upper and lower bounds for nonconvex functions. Moreover, we show that by using such transformations of the input variable or the output variable, we obtain tighter upper and lower bounds for the approximation of convex functions than without these approximations. We show that these transformations can be applied to the approximation of a (convex) Pareto curve that is associated with a (convex) bi-objective optimization problem. 相似文献