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61.
A.R. Nazemi 《Communications in Nonlinear Science & Numerical Simulation》2012,17(4):1696-1705
This paper proposes a feedback neural network model for solving convex nonlinear programming (CNLP) problems. Under the condition that the objective function is convex and all constraint functions are strictly convex or that the objective function is strictly convex and the constraint function is convex, the proposed neural network is proved to be stable in the sense of Lyapunov and globally convergent to an exact optimal solution of the original problem. The validity and transient behavior of the neural network are demonstrated by using some examples. 相似文献
62.
63.
In this paper we lay the foundations for the study of permutation polytopes: the convex hull of a group of permutation matrices.We clarify the relevant notions of equivalence, prove a product theorem, and discuss centrally symmetric permutation polytopes. We provide a number of combinatorial properties of (faces of) permutation polytopes. As an application, we classify ?4-dimensional permutation polytopes and the corresponding permutation groups. Classification results and further examples are made available online.We conclude with several questions suggested by a general finiteness result. 相似文献
64.
65.
A digraph D is connected if the underlying undirected graph of D is connected. A subgraph H of an acyclic digraph D is convex if there is no directed path between vertices of H which contains an arc not in H. We find the minimum and maximum possible number of connected convex subgraphs in a connected acyclic digraph of order n. Connected convex subgraphs of connected acyclic digraphs are of interest in the area of modern embedded processors technology. 相似文献
66.
Andreas Tsanakas 《Insurance: Mathematics and Economics》2009,44(2):268-277
Convex risk measures were introduced by Deprez and Gerber [Deprez, O., Gerber, H.U., 1985. On convex principles of premium calculation. Insurance: Math. Econom. 4 (3), 179-189]. Here the problem of allocating risk capital to subportfolios is addressed, when convex risk measures are used. The Aumann-Shapley value is proposed as an appropriate allocation mechanism. Distortion-exponential measures are discussed extensively and explicit capital allocation formulas are obtained for the case that the risk measure belongs to this family. Finally the implications of capital allocation with a convex risk measure for the stability of portfolios are discussed. It is demonstrated that using a convex risk measure for capital allocation can produce an incentive for infinite fragmentation of portfolios. 相似文献
67.
Kazutoshi Ando 《Discrete Mathematics》2006,306(24):3181-3188
A pair (X,τ) of a finite set X and a closure operator τ:2X→2X is called a closure space. The class of closure spaces includes matroids as well as antimatroids. Associated with a closure space (X,τ), the extreme point operator ex:2X→2X is defined as ex(A)={p|p∈A,p∉τ(A-{p})}. We give characterizations of extreme point operators of closure spaces, matroids and antimatroids, respectively. 相似文献
68.
Christopher King 《Linear algebra and its applications》2006,413(1):24-35
The condition that a finite collection of stable matrices {A1, … , AM} has no common quadratic Lyapunov function (CQLF) is formulated as a hierarchy of singularity conditions for block matrices involving a number of unknown parameters. These conditions are applied to the case of two stable 3 × 3 matrices, where they are used to derive necessary and sufficient conditions for the non-existence of a CQLF. 相似文献
69.
Calculus has been witnessing fundamental changes in its curriculum, with an increased emphasis on visualization. This mode for representing mathematical concepts is gaining more strength due to the advances in computer technology and the development of dynamical mathematical software. This paper focuses on the understanding of the function and its derivative as viewed by students of a reformed Calculus 1 course offered in two experimental sections at the Lebanese American University in Beirut, Lebanon. Results have shown that the general approach adopted in the course proved to be unpopular for a great majority of the students, but rewarding for others. Interviews conducted with some students and a study of their performance on very specific exam questions reveal that for most students, the algebraic representation of a function still dominated their thinking; however, these students showed an almost complete understanding of the derivative, particularly the idea of the instantaneous rate of change and/or the slope of a curve at a given point. Furthermore, very few of these students referred to the mechanical methods for finding derivatives. 相似文献
70.
Hidetaka Hamada Tatsuhiro Honda Gabriela Kohr 《Journal of Mathematical Analysis and Applications》2006,317(1):302-319
Let B be the unit ball in Cn with respect to an arbitrary norm and let f(z,t) be a g-Loewner chain such that e−tf(z,t)−z has a zero of order k+1 at z=0. In this paper, we obtain growth and covering theorems for . Moreover, we consider coefficient bounds and examples of mappings in . 相似文献