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81.
Liuyong Shi Xiangtao Zhong Tao Wu Qin Bian Xiaomei Liu Huaqing Miao Yongbo Deng Binfeng Yin Teng Zhou 《Electrophoresis》2022,43(21-22):2175-2183
Due to its characteristics of noncontact, non-damage, high flux, and easy-to-achieve flexible manipulation, optically induced dielectrophoresis (ODEP) technology has been employed to manipulate microspherical biological particles, including separation, enrichment, capture, arrangement, and fusion. However, in nature, biomolecules are morphologically diverse, and some of them are rodlike. In order to illustrate the electrodynamics of rodlike particles under the action of ODEP, a transient multi-physical field coupling model of ODEP chip under the hypothesis of electrical double layer thin layer was established in this paper. The arbitrary Lagrangian–Eulerian method is used to track single-rod particle in the strong coupled flow field and electric field simultaneously. The influence of several key factors, including the applied alternating current (AC) electric voltage, the width of optical bright area, and the initial position of particle, on the trajectory of particle center was analyzed in positive dielectrophoresis (DEP) action and negative DEP action, respectively. Especially, the planar motion process of rodlike particles was discussed together. The research results reveal the electrodynamics behavior of rodlike particles based on the action of ODEP, which may provide theoretical support for the further design of rodlike biological cells manipulation chip based on AC ODEP technology in the future. 相似文献
82.
Nicholas A. Loehr 《Journal of Combinatorial Theory, Series A》2009,116(2):379-403
This article investigates a remarkable generalization of the generating function that enumerates partitions by area and number of parts. This generating function is given by the infinite product ∏i?11/(1−tqi). We give uncountably many new combinatorial interpretations of this infinite product involving partition statistics that arose originally in the context of Hilbert schemes. We construct explicit bijections proving that all of these statistics are equidistributed with the length statistic on partitions of n. Our bijections employ various combinatorial constructions involving cylindrical lattice paths, Eulerian tours on directed multigraphs, and oriented trees. 相似文献
83.
The Stochastic Eulerian Tour Problem (SETP) seeks the Eulerian tour of minimum expected length on an undirected Eulerian graph, when demand on the arcs that have to be serviced is probabilistic. The SETP is NP-hard and in this paper, we develop three constructive heuristics for this problem. The first two are greedy tour construction heuristics while the third is a sub-tour concatenation heuristic. Our experimental results show that for grid networks, the sub-tour concatenation heuristic performs well when the probability of service of each edge is greater than 0.1. For Euclidean networks, as the number of edges increases, the second heuristic performs the best among the three. Also, the expected length of our overall best solution is lower than the expected length of a random tour by up to 10% on average for grid networks and up to 2% for Euclidean networks. 相似文献
84.
The basic results are overviewed concerning the formulation of nonlinear elasticity equations in the form of symmetric hyperbolic systems in long-time studies performed under the direction of the first author. The underlying principles developed in those studies are stated, and some inaccuracies and errors are corrected. Procedures are described for computing the coefficient matrices of the equations from a given equation of state. 相似文献
85.
Ewa Marciniak Jacek Wesolowski 《Proceedings of the American Mathematical Society》1999,127(11):3329-3338
Asymptotic expansions of any order for expectations of inverses of random variables with positive binomial and negative binomial distributions are obtained in terms of the Eulerian polynomials. The paper extends and improves upon an expansion due to David and Johnson (1956-7).
86.
The asymptotic properties of the numbers of spanning trees and Eulerian trails in circulant digraphs and graphs are studied.
Let
be a directed circulant graph. Let
and
be the numbers of spanning trees and of Eulerian trails, respectively. Then
Furthermore, their line digraph and iterations are dealt with and similar results are obtained for undirected circulant graphs.
Project partially supported by the National Natural Science Foundation of China (Grant No. 69673042) and by Hong Kong CERG
(HKUST652/95E). 相似文献
87.
Matthias Kriesell 《Graphs and Combinatorics》2002,18(3):565-571
A. Saito conjectured that every finite 3-connected line graph of diameter at most 3 is hamiltonian unless it is the line
graph of a graph obtained from the Petersen graph by adding at least one pendant edge to each of its vertices. Here we shall
see that a line graph of connectivity 3 and diameter at most 3 has a hamiltonian path.
Received: May 31, 2000 Final version received: August 17, 2001
RID="*"
ID="*" This work has partially been supported by DIMATIA, Grant 201/99/0242, Grant Agency of the Czech Republic
AMS subject classification: 05C45, 05C40 相似文献
88.
Peter S. Albin 《Mathematical Social Sciences》1980,1(1):101-129
This paper presents methodology which permits the complete ranking of nondirected graphs (NDG's) on an attribute labelled ‘complexity.’ The technique applies to both small and large systems as might arise in studies of group or organization behavior. The methodology extends to cover the complexity of directed graphs (DG's) and permits the detailed specification of individual and group behavior.For the NDG an abstract automaton representing the participants' interaction or communications function is sited at each node. Each automaton is constructed so its internal complexity is sufficient to realize the minimal social action (e.g. transmission of a rumor and the path followed by the rumor) within the framework of the NDG. It is shown that the complexity of each node automaton depends upon the order of the graph, the degree of the node and the longest path parameter of the graph. The combined complexity of node automata constitutes the complexity of the NDG. The complexity of a DG is specified as a composition of complexities computed for the associated NDG and logical devices which produce the observed behavior. Illustrative examples pertaining to the committee-subcommittee problem and to organizational structures are presented. 相似文献
89.
Mark N.?Ellingham Herbert?Fleischner Martin?KocholEmail author Emanuel?Wenger 《Graphs and Combinatorics》2004,20(4):443-446
By a hole graph we mean a 2-connected planar graph where no two nontriangular faces have a vertex in common. We give necessary and sufficient conditions for a hole graph to be 3-colorable.Acknowledgments. This paper was prepared in framework of the exchange program between the Austrian and Slovak Academies of Sciences. The third author was active at Department of Mathematics, Vanderbilt University and Fakulta prírodných vied, ilinská univerzita v iline.Mathematics Subject Classification (1991): 05C15 相似文献
90.
Dan Archdeacon Joan Hutchinson Atsuhiro Nakamoto Seiya Negam Katsuhiro Ota 《Journal of Graph Theory》2001,37(2):100-114
It has been shown that every quadrangulation on any nonspherical orientable closed surface with a sufficiently large representativity has chromatic number at most 3. In this paper, we show that a quadrangulation G on a nonorientable closed surface Nk has chromatic number at least 4 if G has a cycle of odd length which cuts open Nk into an orientable surface. Moreover, we characterize the quadrangulations on the torus and the Klein bottle with chromatic number exactly 3. By our characterization, we prove that every quadrangulation on the torus with representativity at least 9 has chromatic number at most 3, and that a quadrangulation on the Klein bottle with representativity at least 7 has chromatic number at most 3 if a cycle cutting open the Klein bottle into an annulus has even length. As an application of our theory, we prove that every nonorientable closed surface Nk admits an eulerian triangulation with chromatic number at least 5 which has arbitrarily large representativity. © 2001 John Wiley & Sons, Inc. J Graph Theory 37: 100–114, 2001 相似文献