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41.
This paper deals with the maximum triangle packing problem. For this problem, Hassin and Rubinstein gave a randomized polynomial-time approximation algorithm that achieves an expected ratio of for any constant ?>0. By modifying their algorithm, we obtain a new randomized polynomial-time approximation algorithm for the problem which achieves an expected ratio of 0.5257(1−?) for any constant ?>0. 相似文献
42.
关于随机真度的若干注记 总被引:1,自引:1,他引:0
以随机真度为基础,在三值R_0命题逻辑系统中给出了三种不同的近似推理模式并讨论了它们之间的关系,其次利用根的性质得出误差定义的若干推理结果. 相似文献
43.
Judit Nagy-Gyrgy 《Journal of Discrete Algorithms》2009,7(4):411-419
We study the randomized k-server problem on metric spaces consisting of widely separated subspaces. We give a method which extends existing algorithms to larger spaces with the growth rate of the competitive quotients being at most O(logk). This method yields o(k)-competitive algorithms solving the randomized k-server problem for some special underlying metric spaces, e.g. HSTs of “small” height (but unbounded degree). HSTs are important tools for probabilistic approximation of metric spaces. 相似文献
44.
Jakob Creutzig Steffen Dereich Thomas Müller-Gronbach Klaus Ritter 《Foundations of Computational Mathematics》2009,9(4):391-429
We study numerical integration of Lipschitz functionals on a Banach space by means of deterministic and randomized (Monte
Carlo) algorithms. This quadrature problem is shown to be closely related to the problem of quantization and to the average
Kolmogorov widths of the underlying probability measure. In addition to the general setting, we analyze, in particular, integration
with respect to Gaussian measures and distributions of diffusion processes. We derive lower bounds for the worst case error
of every algorithm in terms of its cost, and we present matching upper bounds, up to logarithms, and corresponding almost
optimal algorithms. As auxiliary results, we determine the asymptotic behavior of quantization numbers and Kolmogorov widths
for diffusion processes.
相似文献
45.
Benjamin Doerr 《Discrete Applied Mathematics》2006,154(4):650-659
We propose an advanced randomized coloring algorithm for the problem of balanced colorings of hypergraphs (discrepancy problem). Instead of independently coloring the vertices with a random color, we try to use structural information about the hypergraph in the design of the random experiment by imposing suitable dependencies. This yields colorings having smaller discrepancy. We also obtain more information about the coloring, or, conversely, we may enforce the random coloring to have special properties. There are some algorithmic advantages as well.We apply our approach to hypergraphs of d-dimensional boxes and to finite geometries. Among others results, we gain a factor 2d/2 decrease in the discrepancy of the boxes, and reduce the number of random bits needed to generate good colorings for the geometries down to (from n). The latter also speeds up the corresponding derandomization by a factor of . 相似文献
46.
Our randomized preprocessing enables pivoting-free and orthogonalization-free solution of homogeneous linear systems of equations. In the case of Toeplitz inputs, we decrease the estimated solution time from quadratic to nearly linear, and our tests show dramatic decrease of the CPU time as well. We prove numerical stability of our approach and extend it to solving nonsingular linear systems, inversion and generalized (Moore-Penrose) inversion of general and structured matrices by means of Newton’s iteration, approximation of a matrix by a nearby matrix that has a smaller rank or a smaller displacement rank, matrix eigen-solving, and root-finding for polynomial and secular equations and for polynomial systems of equations. Some by-products and extensions of our study can be of independent technical intersest, e.g., our extensions of the Sherman-Morrison-Woodbury formula for matrix inversion, our estimates for the condition number of randomized matrix products, and preprocessing via augmentation. 相似文献
47.
Sanjeeb Dash 《Operations Research Letters》2010,38(2):109-114
We prove a monotone interpolation property for split cuts which, together with results from Pudlák (1997) [20], implies that cutting-plane proofs which use split cuts (or, equivalently, mixed-integer rounding cuts or Gomory mixed-integer cuts) have exponential length in the worst case. 相似文献
48.
The Spanning Tree Protocol routes traffic on shortest path trees. If some edges fail, the traffic has to be rerouted consequently, setting up alternative trees. In this paper we design efficient algorithms to compute polynomial-size integer weights so as to enforce the following stability property: if q=O(1) edges fail, traffic demands that are not affected by the failures are not redirected. Stability is a goal pursued by network operators in order to minimize transmission delays due to the restoration process. 相似文献
49.
This paper examines an M[x]/G/1 queueing system with a randomized vacation policy and at most J vacations. Whenever the system is empty, the server immediately takes a vacation. If there is at least one customer found waiting in the queue upon returning from a vacation, the server will be immediately activated for service. Otherwise, if no customers are waiting for service at the end of a vacation, the server either remains idle with probability p or leaves for another vacation with probability 1-p. This pattern continues until the number of vacations taken reaches J. If the system is empty by the end of the J th vacation, the server is dormant idly in the system. If there is one or more customers arrive at server idle state, the server immediately starts his services for the arrivals. For such a system, we derive the distributions of important characteristics, such as system size distribution at a random epoch and at a departure epoch, system size distribution at busy period initiation epoch, idle period and busy period, etc. Finally, a cost model is developed to determine the joint suitable parameters (p∗,J∗) at a minimum cost, and some numerical examples are presented for illustrative purpose. 相似文献
50.