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991.
Michael Doré 《Journal of Functional Analysis》2011,261(6):1674-1710
We show that any non-zero Banach space with a separable dual contains a totally disconnected, closed and bounded subset S of Hausdorff dimension 1 such that every Lipschitz function on the space is Fréchet differentiable somewhere in S. 相似文献
992.
We study the potential theory of a large class of infinite dimensional Lévy processes, including Brownian motion on abstract Wiener spaces. The key result is the construction of compact Lyapunov functions, i.e., excessive functions with compact level sets. Then many techniques from classical potential theory carry over to this infinite dimensional setting. Thus a number of potential theoretic properties and principles can be proved, answering long standing open problems even for the Brownian motion on abstract Wiener space, as, e.g., formulated by R. Carmona in 1980. In particular, we prove the analog of the known result, that the Cameron-Martin space is polar, in the Lévy case and apply the technique of controlled convergence to solve the Dirichlet problem with general (not necessarily continuous) boundary data. 相似文献
993.
Caishi Wang Yanchun Lu Huifang Chai 《Journal of Mathematical Analysis and Applications》2011,373(2):643-654
In this paper, we present an alternative approach to Privault's discrete-time chaotic calculus. Let Z be an appropriate stochastic process indexed by N (the set of nonnegative integers) and l2(Γ) the space of square summable functions defined on Γ (the finite power set of N). First we introduce a stochastic integral operator J with respect to Z, which, unlike discrete multiple Wiener integral operators, acts on l2(Γ). And then we show how to define the gradient and divergence by means of the operator J and the combinatorial properties of l2(Γ). We also prove in our setting the main results of the discrete-time chaotic calculus like the Clark formula, the integration by parts formula, etc. Finally we show an application of the gradient and divergence operators to quantum probability. 相似文献
994.
Recently, Barreira and Schmeling (2000) [1] and Chen and Xiong (1999) [2] have shown, that for self-similar measures satisfying the SSC the set of divergence points typically has the same Hausdorff dimension as the support K. It is natural to ask whether we obtain a similar result for self-similar measures satisfying the OSC. However, with only the OSC satisfied, we cannot do most of the work on a symbolic space and then transfer the results to the subsets of Rd, which makes things more difficult. In this paper, by the box-counting principle we show that the set of divergence points has still the same Hausdorff dimension as the support K for self-similar measures satisfying the OSC. 相似文献
995.
Felix Goldberg 《Linear algebra and its applications》2011,434(7):1656-1662
Let μ(G) and ω(G) be the Colin de Verdière and clique numbers of a graph G, respectively. It is well-known that μ(G)?ω(G)-1 for all graphs. Our main results include μ(G)?ω(G) for all chordal graphs; μ(G)?tw(G)+1 for all graphs (where tw is the tree-width), and a characterization of those split (⊆ chordal) graphs for which μ(G)=ω(G). The bound μ(G)?tw(G)+1 improves a result of Colin de Verdière by a factor of 2. 相似文献
996.
The paper studies differential equations of the form u′(x) = f(x, u(x), λ(x)), u(x0) = u0, where the right‐hand side is merely measurable in x. In particular sufficient conditions for the continuous and the differentiable dependence of solution u on the data and on the parameter λ are stated. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
997.
Viorel Vajaitu 《Mathematische Nachrichten》2011,284(4):560-565
We give examples of Stein domains D in C 2 such that C 2 ? D is either completely pluripolar or union of germs of (principal) hypersurfaces not intersecting D such that D fails to be meromorphically convex in C 2. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
998.
Hideaki Iiduka 《Applied mathematics and computation》2011,217(13):6315-6327
Many constrained sets in problems such as signal processing and optimal control can be represented as a fixed point set of a certain nonexpansive mapping, and a number of iterative algorithms have been presented for solving a convex optimization problem over a fixed point set. This paper presents a novel gradient method with a three-term conjugate gradient direction that is used to accelerate conjugate gradient methods for solving unconstrained optimization problems. It is guaranteed that the algorithm strongly converges to the solution to the problem under the standard assumptions. Numerical comparisons with the existing gradient methods demonstrate the effectiveness and fast convergence of this algorithm. 相似文献
999.
Miguel Ángel García-MarchFernando Giménez Francisco R. VillatoroJezabel Pérez Pedro Fernández de Córdoba 《Applied mathematics and computation》2011,217(18):7427-7431
A new and straightforward proof of the unisolvability of the problem of multivariate polynomial interpolation based on Coatmèlec configurations of nodes, a class of properly posed set of nodes defined by hyperplanes, is presented. The proof generalizes a previous one for the bivariate case and is based on a recursive reduction of the problem to simpler ones following the so-called Radon-Bézout process. 相似文献
1000.
Jonathan D. Hauenstein Andrew J. Sommese Charles W. Wampler 《Applied mathematics and computation》2011,218(4):1240-1246
A key step in the numerical computation of the irreducible decomposition of a polynomial system is the computation of a witness superset of the solution set. In many problems involving a solution set of a polynomial system, the witness superset contains all the needed information. Sommese and Wampler gave the first numerical method to compute witness supersets, based on dimension-by-dimension slicing of the solution set by generic linear spaces, followed later by the cascade homotopy of Sommese and Verschelde. Recently, the authors of this article introduced a new method, regeneration, to compute solution sets of polynomial systems. Tests showed that combining regeneration with the dimension-by-dimension algorithm was significantly faster than naively combining it with the cascade homotopy. However, in this article, we combine an appropriate randomization of the polynomial system with the regeneration technique to construct a new cascade of homotopies for computing witness supersets. Computational tests give strong evidence that regenerative cascade is superior in practice to previous methods. 相似文献