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961.
Giorgio Ausiello Bruno Escoffier Jrme Monnot Vangelis Paschos 《Journal of Discrete Algorithms》2009,7(4):453-463
In this paper, reoptimization versions of the traveling salesman problem (TSP) are addressed. Assume that an optimum solution of an instance is given and the goal is to determine if one can maintain a good solution when the instance is subject to minor modifications. We study the case where nodes are inserted in, or deleted from, the graph. When inserting a node, we show that the reoptimization problem for MinTSP is approximable within ratio 4/3 if the distance matrix is metric. We show that, dealing with metric MaxTSP, a simple heuristic is asymptotically optimum when a constant number of nodes are inserted. In the general case, we propose a 4/5-approximation algorithm for the reoptimization version of MaxTSP. 相似文献
962.
The worst-case performances of some heuristics for the fixed linear crossing number problem (FLCNP) are analyzed. FLCNP is similar to the 2-page book crossing number problem in which the vertices of a graph are optimally
placed on a horizontal “node line” in the plane, each edge is drawn as an arc in one half-plane (page), and the objective
is to minimize the number of edge crossings. In FLCNP, the order of the vertices along the node line is predetermined and
fixed. FLCNP belongs to the class of NP-hard optimization problems Masuda et al., 1990. In this paper we show that for each
of the heuristics described, there exist classes of n-vertex, m-edge graphs which force it to obtain a number of crossings which is a function of n or m when the optimal number is a small constant. This leaves open the problem of finding a heuristic with a constant error bound
for the problem. 相似文献
963.
Dimitris A. Fotakis Sotiris E. Nikoletseas Vicky G. Papadopoulou Paul G. Spirakis 《Journal of Discrete Algorithms》2006,4(3):433
The Frequency Assignment Problem (FAP) in radio networks is the problem of assigning frequencies to transmitters exploiting frequency reuse while keeping signal interference to acceptable levels. The FAP is usually modelled by variations of the graph coloring problem. A Radiocoloring (RC) of a graph G(V,E) is an assignment function such that |Λ(u)−Λ(v)|2, when u,v are neighbors in G, and |Λ(u)−Λ(v)|1 when the distance of u,v in G is two. The discrete number of frequencies used is called order and the range of frequencies used, span. The optimization versions of the Radiocoloring Problem (RCP) are to minimize the span (min span RCP) or the order (min order RCP).In this paper, we deal with an interesting, yet not examined until now, variation of the radiocoloring problem: that of satisfying frequency assignment requests which exhibit some periodic behavior. In this case, the interference graph (modelling interference between transmitters) is some (infinite) periodic graph. Infinite periodic graphs usually model finite networks that accept periodic (in time, e.g. daily) requests for frequency assignment. Alternatively, they can model very large networks produced by the repetition of a small graph.A periodic graph G is defined by an infinite two-way sequence of repetitions of the same finite graph Gi(Vi,Ei). The edge set of G is derived by connecting the vertices of each iteration Gi to some of the vertices of the next iteration Gi+1, the same for all Gi. We focus on planar periodic graphs, because in many cases real networks are planar and also because of their independent mathematical interest.We give two basic results:
- • We prove that the min span RCP is PSPACE-complete for periodic planar graphs.
- • We provide an O(n(Δ(Gi)+σ)) time algorithm (where|Vi|=n, Δ(Gi) is the maximum degree of the graph Gi and σ is the number of edges connecting each Gi to Gi+1), which obtains a radiocoloring of a periodic planar graph G that approximates the minimum span within a ratio which tends to as Δ(Gi)+σ tends to infinity.
Keywords: Approximation algorithms; Computational complexity; Radio networks; Frequency assignment; Coloring; Periodic graphs 相似文献
964.
We consider the Survivable Network Design Problem (SNDP) and the Symmetric Traveling Salesman Problem (STSP). We give simpler proofs of the existence of a -edge and 1-edge in any extreme point of the natural LP relaxations for the SNDP and STSP, respectively. We formulate a common generalization of both problems and show our results by a new counting argument. We also obtain a simpler proof of the existence of a -edge in any extreme point of the set-pair LP relaxation for the element connectivitySurvivable Network Design Problem (). 相似文献
965.
Said S. Adi Cristina G. Fernandes Fábio Viduani Martinez Marco A. Stefanes Yoshiko Wakabayashi 《Discrete Applied Mathematics》2010,158(12):1315-1086
We study the following problem. Given two sequences x and y over a finite alphabet, find a repetition-free longest common subsequence of x and y. We show several algorithmic results, a computational complexity result, and we describe a preliminary experimental study based on the proposed algorithms. We also show that this problem is APX-hard. 相似文献
966.
Yael Maduel 《Discrete Applied Mathematics》2010,158(13):1424-1432
The Tree Augmentation Problem (TAP) is: given a tree T=(V,E) and a set E of edges (called links) on V disjoint to E, find a minimum-size edge-subset F⊆E such that T+F is 2-edge-connected. TAP is equivalent to the problem of finding a minimum-size edge-cover F⊆E of a laminar set-family. We consider the restriction, denoted LL-TAP, of TAP to instances when every link in E connects two leaves of T. The best approximation ratio for TAP is 3/2, obtained by Even et al. (2001, 2009, 2008) [3], [4] and [5], and no better ratio was known for LL-TAP. All the previous approximation algorithms that achieve a ratio better than 2 for TAP, or even for LL-TAP, have been quite involved.For LL-TAP we obtain the following approximation ratios: 17/12 for general trees, 11/8 for trees of height 3, and 4/3 for trees of height 2. We also give a very simple3/2-approximation algorithm (for general trees) and prove that it computes a solution of size at most , where t is the minimum size of an edge-cover of the leaves, and t∗ is the optimal value of the natural LP-relaxation for the problem of covering the leaf edges only. This provides the first evidence that the integrality gap of a natural LP-relaxation for LL-TAP is less than 2. 相似文献
967.
We prove that two dual operator spaces X and Y are stably isomorphic if and only if there exist completely isometric normal representations ? and ψ of X and Y, respectively, and ternary rings of operators M1, M2 such that and . We prove that this is equivalent to certain canonical dual operator algebras associated with the operator spaces being stably isomorphic. We apply these operator space results to prove that certain dual operator algebras are stably isomorphic if and only if they are isomorphic. Consequently, we obtain that certain complex domains are biholomorphically equivalent if and only if their algebras of bounded analytic functions are Morita equivalent in our sense. Finally, we provide examples motivated by the theory of CSL algebras. 相似文献
968.
We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite-dimensional operator algebras and algebras that can be represented as the scalar multipliers of a vector-valued reproducing kernel Hilbert space. We use these to further develop a quantized function theory for various domains that extends and unifies Agler's theory of commuting contractions and the Arveson-Drury-Popescu theory of commuting row contractions. We obtain analogous factorization theorems, prove that the algebras that we obtain are dual operator algebras and show that for many domains, supremums over all commuting tuples of operators satisfying certain inequalities are obtained over all commuting tuples of matrices. 相似文献
969.
970.
We consider the problem of scheduling a set of n independent jobs on m parallel machines, where each job can only be scheduled on a subset of machines called its processing set. The machines are linearly ordered, and the processing set of job j is given by two machine indexes aj and bj; i.e., job j can only be scheduled on machines aj,aj+1,…,bj. Two distinct processing sets are either nested or disjoint. Preemption is not allowed. Our goal is to minimize the makespan. It is known that the problem is strongly NP-hard and that there is a list-type algorithm with a worst-case bound of 2-1/m. In this paper we give an improved algorithm with a worst-case bound of 7/4. For two and three machines, the algorithm gives a better worst-case bound of 5/4 and 3/2, respectively. 相似文献