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121.
Juan José Miranda-Bront Isabel Méndez-Díaz Paula Zabala 《European Journal of Operational Research》2014
The Time-Dependent Travelling Salesman Problem (TDTSP) is a generalization of the traditional TSP where the travel cost between two cities depends on the moment of the day the arc is travelled. In this paper, we focus on the case where the travel time between two cities depends not only on the distance between them, but also on the position of the arc in the tour. We consider two formulations proposed in the literature, we analyze the relationship between them and derive several families of valid inequalities and facets. In addition to their theoretical properties, they prove to be very effective in the context of a Branch and Cut algorithm. 相似文献
122.
David R. Morrison Edward C. Sewell Sheldon H. Jacobson 《European Journal of Operational Research》2014
The simple assembly line balancing problem (SALBP) is a well-studied NP-complete problem for which a new problem database of generated instances was published in 2013. This paper describes the application of a branch, bound, and remember (BB&R) algorithm using the cyclic best-first search strategy to this new database to produce provably exact solutions for 86% of the unsolved problems in this database. A new backtracking rule to save memory is employed to allow the BB&R algorithm to solve many of the largest problems in the database. 相似文献
123.
In this paper, we address a service provider’s product line pricing problem for substitutable products in services, such as concerts, sporting events, or online advertisements. For each product, a static price is selected from a pre-defined set such that the total revenue is maximised. The products are differentiated by some of their attributes, and their availability is restricted due to individual capacity constraints. Furthermore, they are simultaneously sold during a common selling period at the end of which the service is delivered. Consumers differ from one another with respect to their willingness to pay, and, hence, their reservation prices vary depending on the product. In the event of a purchase, they choose the product that maximises their consumer surplus. 相似文献
124.
Charles R. Johnson 《Linear and Multilinear Algebra》2013,61(4):357-380
Suppose that the eigenvalues of an Hermitian matrix A whose graph is a tree T are known, as well as the eigenvalues of the principal submatrix of A corresponding to a certain branch of T. A method for constructing a larger tree T?', in which the branch is ‘`duplicated’', and an Hermitian matrix A′ whose graph is T?' is described. The eigenvalues of A' are all of those of A, together with those corresponding to the branch, including multiplicities. This idea is applied (1) to give a solution to the inverse eigenvalue problem for stars, (2) to prove that the known diameter lower bound, for the minimum number of distinct eigenvalues among Hermitian matrices with a given graph, is best possible for trees of bounded diameter, and (3) to increase the list of trees for which all possible lists for the possible spectra are know. A generalization of the basic branch duplication method is presented. 相似文献
125.
As models for spread of epidemics, family trees, etc., various authors have used a random tree called the uniform recursive tree. Its branching structure and the length of simple random downward walk (SRDW) on it are investigated in this paper. On the uniform recursive tree of size n, we first give the distribution law of ζn,m, the number of m-branches, whose asymptotic distribution is the Poisson distribution with parameter . We also give the joint distribution of the numbers of various branches and their covariance matrix. On Ln, the walk length of SRDW, we first give the exact expression of P(Ln=2). Finally, the asymptotic behavior of Ln is given. 相似文献
126.
127.
128.
In this paper, we prove the Lipschitz continuity with respect to the Hausdorff metric of some parametrized families of sets
in R3. This implies that many Hausdorff approximation (Hausdorff matching) problems can be reduced to searching a global minimum
of a real Lipschitz function of real variables. Practical methods are presented for obtaining reduced search spaces for these
minimization problems. 相似文献
129.
A branch-and-bound algorithm to solve the linear ordering problem for weighted tournaments 总被引:1,自引:0,他引:1
Irène Charon 《Discrete Applied Mathematics》2006,154(15):2097-2116
The linear ordering problem consists in finding a linear order at minimum remoteness from a weighted tournament T, the remoteness being the sum of the weights of the arcs that we must reverse in T to transform it into a linear order. This problem, also known as the search of a median order, or of a maximum acyclic subdigraph, or of a maximum consistent set, or of a minimum feedback arc set, is NP-hard; when all the weights of T are equal to 1, the linear ordering problem is the same as Slater's problem. In this paper, we describe the principles and the results of an exact method designed to solve the linear ordering problem for any weighted tournament. This method, of which the corresponding software is freely available at the URL address http://www.enst.fr/~charon/tournament/median.html, is based upon a branch-and-bound search with a Lagrangean relaxation as the evaluation function and a noising method for computing the initial bound. Other components are designed to reduce the BB-search-tree. 相似文献
130.
In this article, we present and validate a simplicial branch and bound duality-bounds algorithm for globally solving the linear sum-of-ratios fractional program. The algorithm computes the lower bounds called for during the branch and bound search by solving ordinary linear programming problems. These problems are derived by using Lagrangian duality theory. The algorithm applies to a wide class of linear sum-of-ratios fractional programs. Two sample problems are solved, and the potential practical and computational advantages of the algorithm are indicated. 相似文献