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41.
Jørgen Bang‐Jensen Tilde My Christiansen Alessandro Maddaloni 《Journal of Graph Theory》2017,85(2):545-567
The k‐linkage problem is as follows: given a digraph and a collection of k terminal pairs such that all these vertices are distinct; decide whether D has a collection of vertex disjoint paths such that is from to for . A digraph is k‐linked if it has a k‐linkage for every choice of 2k distinct vertices and every choice of k pairs as above. The k‐linkage problem is NP‐complete already for [11] and there exists no function such that every ‐strong digraph has a k‐linkage for every choice of 2k distinct vertices of D [17]. Recently, Chudnovsky et al. [9] gave a polynomial algorithm for the k‐linkage problem for any fixed k in (a generalization of) semicomplete multipartite digraphs. In this article, we use their result as well as the classical polynomial algorithm for the case of acyclic digraphs by Fortune et al. [11] to develop polynomial algorithms for the k‐linkage problem in locally semicomplete digraphs and several classes of decomposable digraphs, including quasi‐transitive digraphs and directed cographs. We also prove that the necessary condition of being ‐strong is also sufficient for round‐decomposable digraphs to be k‐linked, obtaining thus a best possible bound that improves a previous one of . Finally we settle a conjecture from [3] by proving that every 5‐strong locally semicomplete digraph is 2‐linked. This bound is also best possible (already for tournaments) [1]. 相似文献
42.
On Vaporizing Water Flow in Hot Sub-Vertical Rock Fractures 总被引:1,自引:0,他引:1
Water injection into unsaturated fractured rock at above-boiling temperatures gives rise to complex fluid flow and heat transfer processes. Examples include water injection into depleted vapor-dominated geothermal reservoirs, and emplacement of heat-generating nuclear wastes in unsaturated fractured rock. We conceptualize fractures as two-dimensional heterogeneous porous media, and use geostatistical techniques to generate synthetic permeability distributions in the fracture plane. Water flow in hot high-angle fractures is simulated numerically, taking into account the combined action of gravity, capillary, and pressure forces, and conductive heat transfer from the wall rocks which gives rise to strong vaporization. In heterogeneous fractures boiling plumes are found to have dendritic shapes, and to be subject to strong lateral flow effects. Fractures with spatially-averaged homogeneous permeabilities tend to give poor approximations for vaporization behavior and liquid migration patterns. Depending on water flow rates, rock temperature, and fracture permeability, liquid water can migrate considerable distances through fractured rock that is at above-boiling temperatures and be only partially vaporized. 相似文献
43.
Bueckner‘s work conjugate integral customarily adopted for linear elastic materials is established for an interface crack in dissimilar anisotropic materials. The difficulties in separating Stroh‘s six complex arguments involved in the integral for the dissimilar materials are overcome and then the explicit function representations of the integral are given and studied in detail. It is found that the pseudo-orthogonal properties of the eigenfunction expansion form (EEF) for a crack presented previously in isotropic elastic cases, in isotopic bimaterial cases, and in orthotropic cases are also valid in the present dissimilar arbitrary anisotropic cases. The relation between Bueckner‘s work conjugate integral and the J-integral in these cases is obtained by introducing a complementary stressdisplacement state. Finally, some useful path-independent integrals and weight functions are proposed for calculating the crack tip parameters such as the stress intensity factors. 相似文献
44.
In an edge-colored graph, let dc(v) be the number of colors on the edges incident to v and let δc(G) be the minimum dc(v) over all vertices v∈G. In this work, we consider sharp conditions on δc(G) which imply the existence of properly edge-colored paths and cycles, meaning no two consecutive edges have the same color. 相似文献
45.
46.
We call the digraph D an k-colored digraph if the arcs of D are colored with k colors. A subdigraph H of D is called monochromatic if all of its arcs are colored alike. A set N⊆V(D) is said to be a kernel by monochromatic paths if it satisfies the following two conditions: (i) for every pair of different vertices u,v∈N, there is no monochromatic directed path between them, and (ii) for every vertex x∈(V(D)?N), there is a vertex y∈N such that there is an xy-monochromatic directed path. In this paper, we prove that if D is an k-colored digraph that can be partitioned into two vertex-disjoint transitive tournaments such that every directed cycle of length 3,4 or 5 is monochromatic, then D has a kernel by monochromatic paths. This result gives a positive answer (for this family of digraphs) of the following question, which has motivated many results in monochromatic kernel theory: Is there a natural numberlsuch that if a digraphDisk-colored so that every directed cycle of length at mostlis monochromatic, thenDhas a kernel by monochromatic paths? 相似文献
47.
Aurélien Deya Massimiliano Gubinelli Martina Hofmanová Samy Tindel 《Journal of Functional Analysis》2019,276(12):3577-3645
We introduce a general weak formulation for PDEs driven by rough paths, as well as a new strategy to prove well-posedness. Our procedure is based on a combination of fundamental a priori estimates with (rough) Gronwall-type arguments. In particular this approach does not rely on any sort of transformation formula (flow transformation, Feynman–Kac representation formula etc.) and is therefore rather flexible. As an application, we study conservation laws driven by rough paths establishing well–posedness for the corresponding kinetic formulation. 相似文献
48.
Computing shortest paths with two or more conflicting optimization criteria is a fundamental problem in transportation and
logistics. We study the problem of finding all Pareto-optimal solutions for the multi-criteria single-source shortest-path
problem with nonnegative edge lengths. The standard approaches are generalizations of label-setting (Dijkstra) and label-correcting
algorithms, in which the distance labels are multi-dimensional and more than one distance label is maintained for each node.
The crucial parameter for the run time and space consumption is the total number of Pareto optima. In general, this value
can be exponentially large in the input size. However, in various practical applications one can observe that the input data
has certain characteristics, which may lead to a much smaller number—small enough to make the problem efficiently tractable
from a practical viewpoint. For typical characteristics which occur in various applications we study in this paper whether
we can bound the size of the Pareto set to a polynomial size or not. These characteristics are also evaluated (1) on a concrete
application scenario (computing the set of best train connections in view of travel time, fare, and number of train changes)
and (2) on a simplified randomized model. It will turn out that the number of Pareto optima on each visited node is restricted
by a small constant in our concrete application, and that the size of the Pareto set is much smaller than our worst case bounds
in the randomized model.
A preliminary short version of this paper appeared in the Proceedings of the 5th Workshop on Algorithm Engineering (WAE 2001),
LNCS 2141, Springer Verlag, pp. 185–197 (2001) under the title “Pareto shortest paths is often feasible in practice.” 相似文献
49.
LIQIAO XUJUNMING ZHANGZHONGLIANG 《高校应用数学学报(英文版)》1995,10(2):215-222
We show that the maximum number of intersections between two plane rectangular paths with lengths m and n: 2 ≤ m ≤ n, is 4n 2, if m=4 and n≡1(mod 3); and it is mn 1 otherwise. 相似文献
50.
T. Rapcsák 《Journal of Optimization Theory and Applications》2005,127(1):165-176
Some properties of the spaces of paths are studied in order to define and characterize the local convexity of sets belonging
to smooth manifolds and the local convexity of functions defined on local convex sets of smooth manifolds.
This paper is dedicated to the memory of Guido Stampacchia. This research was supported in part by the Hungarian Scientific
Research Fund, Grants OTKA-T043276 and OTKA-T043241, and by CNR, Rome, Italy. 相似文献