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111.
112.
V. N. Sudakov 《Journal of Mathematical Sciences》2009,163(4):430-445
The notion of “Gaussian Lebesgue–Rokhlin space” is introduced. The definition is canonical, i.e., is given without use of
topological and others irrelevant mathematical structures. The object under discussion completes the category of finite-dimensional
Gaussian vector spaces. Some nontrivial examples are considered and historical comments are given. Bibliography: 30 titles. 相似文献
113.
114.
Benny Sudakov 《Random Structures and Algorithms》2005,26(3):253-265
In this paper we present three Ramsey‐type results, which we derive from a simple and yet powerful lemma, proved using probabilistic arguments. Let 3 ≤ r < s be fixed integers and let G be a graph on n vertices not containing a complete graph Ks on s vertices. More than 40 years ago Erd?s and Rogers posed the problem of estimating the maximum size of a subset of G without a copy of the complete graph Kr. Our first result provides a new lower bound for this problem, which improves previous results of various researchers. It also allows us to solve some special cases of a closely related question posed by Erd?s. For two graphs G and H, the Ramsey number R(G, H) is the minimum integer N such that any red‐blue coloring of the edges of the complete graph KN, contains either a red copy of G or a blue copy of H. The book with n pages is the graph Bn consisting of n triangles sharing one edge. Here we study the book‐complete graph Ramsey numbers and show that R(Bn, Kn) ≤ O(n3/log3/2n), improving the bound of Li and Rousseau. Finally, motivated by a question of Erd?s, Hajnal, Simonovits, Sós, and Szemerédi, we obtain for all 0 < δ < 2/3 an estimate on the number of edges in a K4‐free graph of order n which has no independent set of size n1‐δ. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2005 相似文献
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A new phase-shifting interferometric technique that uses an unknown phase step is described in which the phase step is determined by use of an algorithm called Probabilistic Global Search Lausanne (PGSL). One of the main sources of error in phase stepping is piezoelectric device (PZT) nonlinearity. The PGSL algorithm identifies the characteristics of the response of the PZT to the applied voltage through matching predicted and measured responses. The unknown phase step is also calculated with 0.097% error. This approach overcomes the limitations of existing techniques to determine unknown phase steps. Linear regression is subsequently applied for interference phase determination. 相似文献
117.
118.
We study the relation between stochastic and continuous transport-limited growth models. We derive a nonlinear integro-differential equation for the average shape of stochastic aggregates, whose mean-field approximation is the corresponding continuous equation. Focusing on the advection-diffusion-limited aggregation (ADLA) model, we show that the average shape of the stochastic growth is similar, but not identical, to the corresponding continuous dynamics. Similar results should apply to DLA, thus explaining the known discrepancies between average DLA shapes and viscous fingers in a channel geometry. 相似文献
119.
Let PG2(2) be the Fano plane, i. e., the unique hypergraph with 7 triples on 7 vertices in which every pair of vertices is contained
in a unique triple. In this paper we prove that for sufficiently large n, the maximum number of edges in a 3-uniform hypergraph on n vertices not containing a Fano plane is
Moreover, the only extremal configuration can be obtained by partitioning an n-element set into two almost equal parts, and taking all the triples that intersect both of them. This extends an earlier
result of de Caen and Füredi, and proves an old conjecture of V. Sós. In addition, we also prove a stability result for the
Fano plane, which says that a 3-uniform hypergraph with density close to 3/4 and no Fano plane is approximately 2-colorable.
* Research supported in part by NSF grant DMS-0106589. 相似文献
120.
This paper outlines a method that has been implemented to predict and measure the acoustic radiation generated by ultrasonic transducers operating into air in continuous wave mode. Commencing with both arbitrary surface displacement data and radiating aperture, the transmitted pressure beam profile is obtained and includes simulation of propagation channel attenuation and where necessary, the directional response of any ultrasonic receiver. The surface displacement data may be derived directly, from laser measurement of the vibrating surface, or indirectly, from finite element modeling of the transducer configuration. To validate the approach and to provide experimental measurement of transducer beam profiles, a vibration-free, draft-proof scanning system that has been installed within an environmentally controlled laboratory is described. A comparison of experimental and simulated results for piezoelectric composite, piezoelectric polymer, and electrostatic transducers is then presented to demonstrate some quite different airborne ultrasonic beam-profile characteristics. Good agreement between theory and experiment is obtained. The results are compared with those expected from a classical aperture diffraction approach and the reasons for any significant differences are explained. 相似文献