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91.
Akiko Takeda Katsuki Fujisawa Yusuke Fukaya Masakazu Kojima 《Journal of Global Optimization》2002,24(2):237-260
As computing resources continue to improve, global solutions for larger size quadrically constrained optimization problems become more achievable. In this paper, we focus on larger size problems and get accurate bounds for optimal values of such problems with the successive use of SDP relaxations on a parallel computing system called Ninf (Network-based Information Library for high performance computing). 相似文献
92.
In this paper, we study the existence of the uniformly minimum risk equivariant (UMRE) estimators of parameters in a class
of normal linear models, which include the normal variance components model, the growth curve model, the extended growth curve
model, and the seemingly unrelated regression equations model, and so on. The necessary and sufficient conditions are given
for the existence of UMRE estimators of the estimable linear functions of regression coefficients, the covariance matrixV and (trV)α, where α > 0 is known, in the models under an affine group of transformations for quadratic losses and matrix losses, respectively.
Under the (extended) growth curve model and the seemingly unrelated regression equations model, the conclusions given in literature
for estimating regression coefficients can be derived by applying the general results in this paper, and the sufficient conditions
for non-existence of UMRE estimators ofV and tr(V) are expanded to be necessary and sufficient conditions. In addition, the necessary and sufficient conditions that there
exist UMRE estimators of parameters in the variance components model are obtained for the first time. 相似文献
93.
Tim Van Voorhis 《Journal of Global Optimization》2002,24(3):349-370
Convex relaxations can be used to obtain lower bounds on the optimal objective function value of nonconvex quadratically constrained quadratic programs. However, for some problems, significantly better bounds can be obtained by minimizing the restricted Lagrangian function for a given estimate of the Lagrange multipliers. The difficulty in utilizing Lagrangian duality within a global optimization context is that the restricted Lagrangian is often nonconvex. Minimizing a convex underestimate of the restricted Lagrangian overcomes this difficulty and facilitates the use of Lagrangian duality within a global optimization framework. A branch-and-bound algorithm is presented that relies on these Lagrangian underestimates to provide lower bounds and on the interval Newton method to facilitate convergence in the neighborhood of the global solution. Computational results show that the algorithm compares favorably to the Reformulation–Linearization Technique for problems with a favorable structure. 相似文献
94.
Undominated d.c. Decompositions of Quadratic Functions and Applications to Branch-and-Bound Approaches 总被引:2,自引:0,他引:2
In this paper we analyze difference-of-convex (d.c.) decompositions for indefinite quadratic functions. Given a quadratic function, there are many possible ways to decompose it as a difference of two convex quadratic functions. Some decompositions are dominated, in the sense that other decompositions exist with a lower curvature. Obviously, undominated decompositions are of particular interest. We provide three different characterizations of such decompositions, and show that there is an infinity of undominated decompositions for indefinite quadratic functions. Moreover, two different procedures will be suggested to find an undominated decomposition starting from a generic one. Finally, we address applications where undominated d.c.d.s may be helpful: in particular, we show how to improve bounds in branch-and-bound procedures for quadratic optimization problems. 相似文献
95.
Adam B. Levy 《Mathematical Programming》2007,110(3):615-639
Numerical methods for solving constrained optimization problems need to incorporate the constraints in a manner that satisfies
essentially competing interests; the incorporation needs to be simple enough that the solution method is tractable, yet complex
enough to ensure the validity of the ultimate solution. We introduce a framework for constraint incorporation that identifies
a minimal acceptable level of complexity and defines two basic types of constraint incorporation which (with combinations)
cover nearly all popular numerical methods for constrained optimization, including trust region methods, penalty methods,
barrier methods, penalty-multiplier methods, and sequential quadratic programming methods. The broad application of our framework
relies on addition and chain rules for constraint incorporation which we develop here. 相似文献
96.
K. C. Kiwiel 《Journal of Optimization Theory and Applications》2007,134(3):549-554
We give a linear time algorithm for the continuous quadratic knapsack problem which is simpler than existing methods and competitive
in practice. Encouraging computational results are presented for large-scale problems.
The author thanks the Associate Editor and an anonymous referee for their helpful comments. 相似文献
97.
S. L. Skorokhodov D. V. Khristoforov 《Computational Mathematics and Mathematical Physics》2007,47(11):1802-1818
A method for computing the eigenvalues λ mn (b, c) and the eigenfunctions of the Coulomb spheroidal wave equation is proposed in the case of complex parameters b and c. The solution is represented as a combination of power series expansions that are then matched at a single point. An extensive numerical analysis shows that certain b s and c s are second-order branch points for λ mn (b, c) with different indices n 1 and n 2, so that the eigenvalues at these points are double. Padé approximants, quadratic Hermite-Padé approximants, the finite element method, and the generalized Newton method are used to compute the branch points b s and c s and the double eigenvalues to high accuracy. A large number of these singular points are calculated. 相似文献
98.
99.
Yang Li Zhang Qingling Liu Guoyi 《Annals of Differential Equations》2005,21(3):497-502
We discuss the delay dependent robust dissipative problem for a class of time-delay systems with nonlinear perturbations. And the sufficient conditions for the delay dependent robust dissipation and quadratic stability are given by the linear matrix inequalities (LMIs), then the time-delay bound and the delay dependent robust dissipative state feedback controller are presented. 相似文献
100.
In 1991, one of the authors showed the existence of quadratic transformations between the Painlevé VI equations with local monodromy differences (1/2, a, b, ±1/2) and (a, a, b, b). In the present paper we give concise forms of these transformations. They are related to the quadratic transformations obtained by Manin and Ramani–Grammaticos–Tamizhmani via Okamoto transformations. To avoid cumbersome expressions with differentiation, we use contiguous relations instead of the Okamoto transformations. The 1991 transformation is particularly important as it can be realized as a quadratic‐pull back transformation of isomonodromic Fuchsian equations. The new formulas are illustrated by derivation of explicit expressions for several complicated algebraic Painlevé VI functions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献