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91.
We prove a general embedding theorem for Sobolev spaces on open manifolds of bounded geometry and infer from this the module structure theorem. Thereafter we apply this to weighted Sobolev spaces. 相似文献
92.
R. S. Ismagilov 《Mathematical Notes》1997,62(2):186-197
We present simple proofs of the possibility of embedding ultrametric spaces in Hilbert spaces. The main part of the paper
deals with ultrametric spaces that we call totally infinite spaces. Related Hilbert spaces, automorphisms of totally infinite
spaces, and the corresponding linear operators are considered.
Transplated fromMatematicheskie Zametki, Vol. 62, No. 2, pp. 223–237, August, 1997.
Translated by V. E. Nazaikinskii 相似文献
93.
We consider some Sobolev-type spaces and obtain a necessary and sufficient condition for their embedding in a Lebesgue space. 相似文献
94.
Howel Tong 《应用数学学报(英文版)》2002,18(2):177-184
Abstract I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five majorareas of development. These areas include the interface between nonlinear time series analysis and chaos,thenonparametric/semiparametric approach,nonlinear state space modelling,financial time series and nonlinearmodelling of panels of time series. 相似文献
95.
We present a method for simultaneous three-dimensional (3D) structure generation and pharmacophore-based alignment using a self-organizing algorithm called Stochastic Proximity Embedding (SPE). Current flexible molecular alignment methods either start from a single low-energy structure for each molecule and tweak bonds or torsion angles, or choose from multiple conformations of each molecule. Methods that generate structures and align them iteratively (e.g., genetic algorithms) are often slow. In earlier work, we used SPE to generate good-quality 3D conformations by iteratively adjusting pairwise distances between atoms based on a set of geometric rules, and showed that it samples conformational space better and runs faster than earlier programs. In this work, we run SPE on the entire ensemble of molecules to be aligned. Additional information about which atoms or groups of atoms in each molecule correspond to points in the pharmacophore can come from an automatically generated hypothesis or be specified manually. We add distance terms to SPE to bring pharmacophore points from different molecules closer in space, and also to line up normal/direction vectors associated with these points. We also permit pharmacophore points to be constrained to lie near external coordinates from a binding site. The aligned 3D molecular structures are nearly correct if the pharmacophore hypothesis is chemically feasible; postprocessing by minimization of suitable distance and energy functions further improves the structures and weeds out infeasible hypotheses. The method can be used to test 3D pharmacophores for a diverse set of active ligands, starting from only a hypothesis about corresponding atoms or groups. 相似文献
96.
以3-脲丙基三甲氧基硅烷为偶联剂,制备了一种新型极性脲丙基-C30(TPU-C30)反相色谱固定相。采用扫描电子显微镜、元素分析、红外光谱和热分析等对该固定相进行表征。结果表明,TPU-C30固定相已成功制备,连续制备3次固定相,其元素含量的相对偏差均小于5%,说明该合成工艺重复性良好。以不同极性、位置异构、碱性化合物为溶质探针,以传统的C18色谱柱与C30色谱柱为参比,对制备的固定相的色谱性能进行了研究。研究结果表明,TPU-C30固定相具有不同于传统C18柱、C30柱的选择性和更优的择形性,明显改善了碱性物质的峰形,其具有广阔的应用空间。 相似文献
97.
We introduce an impartial combinatorial game on Steiner triple systems called Next One to Fill Is the Loser (Nofil ). Players move alternately, choosing points of the triple system. If a player is forced to fill a block on their turn, they lose. By computing nim-values, we determine optimal strategies for Nofil on all Steiner triple systems up to order 15 and a sampling for orders 19, 21 and 25. The game Nofil can be thought of in terms of play on a corresponding hypergraph which will become a graph during play. At that point Nofil is equivalent to playing the game Node Kayles on the graph. We prove necessary conditions and sufficient conditions for a graph to reached playing Nofil. We conclude that the complexity of determining the outcome of the game Nofil on Steiner triple systems is PSPACE-complete for randomized reductions. 相似文献
98.
Understanding self‐assembling peptides becomes essential in nanotechnology, thereby providing a bottom‐up method for fabrication of nanostructures. Diphenylalanine constitutes an outstanding building block that can be assembled into various nanostructures, including two‐dimensional bilayers or nanotubes, exhibiting superb mechanical properties. It is known that the effect of the ions is critical in conformational and chemical interactions of bilayers or membranes. In this study, we analyzed the effect of sodium chloride on diphenylalanine bilayer using coarse‐grained molecular dynamics simulations, and calculated the bending Young's modulus and the torsional modulus by applying normal modal analysis using an elastic network model. The results showed that sodium chloride dramatically increases the assembling efficiency and stability, thereby promising to allow the precise design and control of the fabrication process and properties of bio‐inspired materials. © 2016 Wiley Periodicals, Inc. 相似文献
99.
In this article, we review a construction in the complex geometry often known as the Penrose transform. We then present two
new applications of this transform. One concerns the construction of symmetries of the massless field equations from mathematical
physics. The other concerns obstructions to the embedding of CR structures on the three-sphere.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
100.
Book embedding of graphs is one of the graph layout problem. It is useful for the multiprocessor network layout or the fault-tolerant processor arrays. We show that the trivalent Cayley graphs proposed by Vadapalli and Srimani can be embedded in five pages, and show some additional results on cube-connected cycles. 相似文献