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521.
Let XH = {XH(s),s ∈RN1} and X K = {XK(t),t ∈R N2} be two independent anisotropic Gaussian random fields with values in R d with indices H =(H1,...,HN1) ∈(0,1)N1,K =(K1,...,KN2) ∈(0,1) N2,respectively.Existence of intersections of the sample paths of X H and X K is studied.More generally,let E1■RN1,E2■RN2 and FRd be Borel sets.A necessary condition and a sufficient condition for P{(XH(E1)∩XK(E2))∩F≠Ф}>0 in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1×E2×F in the metric space(RN1+N2+d,) are proved,where is a metric defined in terms of H and K.These results are applicable to solutions of stochastic heat equations driven by space-time Gaussian noise and fractional Brownian sheets. 相似文献
522.
《Molecular physics》2012,110(19-20):2493-2501
The extended S1/S0 conical intersection seam for the photochemical 2s?+?2s, 2s?+?2a and 2a?+?2a cycloadditions of two ethylene molecules has been documented using the methodology described by Sicilia et al. (J. Chem. Theory Comput. 4, 257 (2008)). Two additional critical points on this prototype crossing seam were found as a result, although both lie more than 100?kcal?mol?1 above the rhomboidal crossing located previously, and are not minima in the intersection space. Using VB theory, the branching space conditions for the conical intersection can be derived analytically, in fair agreement with calculated CASSCF results. Woodward–Hoffmann symmetry forbidden and allowed reactions are associated with the same extended conical intersection seam in this case. 相似文献
523.
We show that the infinite matroid intersection conjecture of Nash-Williams implies the infinite Menger theorem proved by Aharoni and Berger in 2009.We prove that this conjecture is true whenever one matroid is nearly finitary and the second is the dual of a nearly finitary matroid, where the nearly finitary matroids form a superclass of the finitary matroids.In particular, this proves the infinite matroid intersection conjecture for finite-cycle matroids of 2-connected, locally finite graphs with only a finite number of vertex-disjoint rays. 相似文献
524.
Selçuk Kayacan 《代数通讯》2018,46(4):1492-1505
The intersection graph of a group G is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper non-trivial subgroups of G, and there is an edge between two distinct vertices H and K if and only if H∩K≠1 where 1 denotes the trivial subgroup of G. In this paper, we classify finite solvable groups whose intersection graphs are not 2-connected and finite nilpotent groups whose intersection graphs are not 3-connected. Our methods are elementary. 相似文献
525.
Mindaugas Bloznelis 《Discrete Mathematics》2010,310(19):2560-2566
Let S(1),…,S(n),T(1),…,T(n) be random subsets of the set [m]={1,…,m}. We consider the random digraph D on the vertex set [n] defined as follows: the arc i→j is present in D whenever S(i)∩T(j)≠0?. Assuming that the pairs of sets (S(i),T(i)), 1≤i≤n, are independent and identically distributed, we study the in- and outdegree distributions of a typical vertex of D as n,m→∞. 相似文献
526.
《Random Structures and Algorithms》2018,52(4):662-679
When each vertex is assigned a set, the intersection graph generated by the sets is the graph in which two distinct vertices are joined by an edge if and only if their assigned sets have a nonempty intersection. An interval graph is an intersection graph generated by intervals in the real line. A chordal graph can be considered as an intersection graph generated by subtrees of a tree. In 1999, Karoński, Scheinerman, and Singer‐Cohen introduced a random intersection graph by taking randomly assigned sets. The random intersection graph has n vertices and sets assigned to the vertices are chosen to be i.i.d. random subsets of a fixed set M of size m where each element of M belongs to each random subset with probability p, independently of all other elements in M. In 2000, Fill, Scheinerman, and Singer‐Cohen showed that the total variation distance between the random graph and the Erdös‐Rényi graph tends to 0 for any if , where is chosen so that the expected numbers of edges in the two graphs are the same. In this paper, it is proved that the total variation distance still tends to 0 for any whenever . 相似文献
527.
《组合设计杂志》2018,26(4):154-173
Given a combinatorial design with block set , the block‐intersection graph (BIG) of is the graph that has as its vertex set, where two vertices and are adjacent if and only if . The i‐block‐intersection graph (i‐BIG) of is the graph that has as its vertex set, where two vertices and are adjacent if and only if . In this paper, several constructions are obtained that start with twofold triple systems (TTSs) with Hamiltonian 2‐BIGs and result in larger TTSs that also have Hamiltonian 2‐BIGs. These constructions collectively enable us to determine the complete spectrum of TTSs with Hamiltonian 2‐BIGs (equivalently TTSs with cyclic 2‐intersecting Gray codes) as well as the complete spectrum for TTSs with 2‐BIGs that have Hamilton paths (i.e. for TTSs with 2‐intersecting Gray codes). In order to prove these spectrum results, we sometimes require ingredient TTSs that have large partial parallel classes; we prove lower bounds on the sizes of partial parallel classes in arbitrary TTSs, and then construct larger TTSs with both cyclic 2‐intersecting Gray codes and parallel classes. 相似文献
528.
信号交叉口延误是评价城市道路运行效率和服务水平的重要度量.通过推导首次提出城市平面信号交叉路口另一类随机控制延误模型.与文献相比,从形式来看该模型计算起来更简便,且计算出的延误时间与文献延误模型计算时间比较相差甚微,实例与仿真证明该模型操作性强可用度高. 相似文献
529.
530.