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81.
In this work, we implemented and compared two different methods to impose the rigid‐body motion constraint on a solid particle moving inside a fluid. We consider a fictitious domain method to easily manage the particle motion. As the solid as well as the fluid inertia are neglected, the particle can be discretized through its boundary only. The rigid‐body motion is imposed via Lagrange multipliers on the boundary. In the first method, such constraints are imposed in discrete points on the boundary (collocation), whereas in the second the constraint is imposed in a weak way on elements dividing the particle surface. Two test problems, that is, a spherical and an ellipsoidal particle in a sheared Newtonian fluid, are chosen to compare the methods. In both cases, the analysis is carried out in 2D as well as in 3D. The results show that for the collocation method an optimal number of collocation points exist leading to the smallest error. However, small variations in the optimal value can generate large deviations. In the weak implementation, the error is only mildly affected by the number of elements used to discretize the particle boundary and by the Lagrange multiplier's interpolation space. A further analysis is carried out to study the effect of an approximated integration of weak constraints. A comparison between the two methods showed that the same accuracy can be achieved by using less constraints if the weak discretization is used. Finally, the rigid‐body motion imposed via weak constraints leads to better conditioned linear systems. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
82.
83.
J. Barral M. -O. Coppens B. B. Mandelbrot 《Journal de Mathématiques Pures et Appliquées》2003,82(12):1555-1589
A nonnegative 1-periodic multifractal measure on
is obtained as infinite random product of harmonics of a 1-periodic function W(t). Such infinite products are statistically self-affine and generalize certain Riesz products with random phases. They are martingale structures, therefore converge. The criterion on W for nondegeneracy is provided. It differs completely from those for other known random measures constructed as martingale limits of multiplicative processes. In particular, it is very sensitive to small changes in W(t). When these infinite products are interpreted in the framework of thermodynamic formalism for random transformations, logW is a potential function when W>0. For regular enough potentials, in case of degeneracy, the natural normalization makes the sequence of measures converge. Moreover, this normalization is neutral for nondegenerate martingales. The multifractal analysis of the limit martingale measure is performed for a class of potential functions having a dense countable set of jump points. 相似文献
84.
Bilevel programming problems are hierarchical optimization problems where in the upper level problem a function is minimized
subject to the graph of the solution set mapping of the lower level problem. In this paper necessary optimality conditions
for such problems are derived using the notion of a convexificator by Luc and Jeyakumar. Convexificators are subsets of many
other generalized derivatives. Hence, our optimality conditions are stronger than those using e.g., the generalized derivative
due to Clarke or Michel-Penot. Using a certain regularity condition Karush-Kuhn-Tucker conditions are obtained.
相似文献
85.
David E. Edmunds Bohumí r Opic 《Proceedings of the American Mathematical Society》2003,131(3):745-754
We give new characterizations of Lorentz spaces by means of certain quasi-norms which are shown to be equivalent to the classical ones.
86.
Silvia Bonettini Emanuele Galligani Valeria Ruggiero 《Computational Optimization and Applications》2007,37(1):1-34
This paper deals with the solution of nonlinear programming problems arising from elliptic control problems by an interior
point scheme. At each step of the scheme, we have to solve a large scale symmetric and indefinite system; inner iterative
solvers, with an adaptive stopping rule, can be used in order to avoid unnecessary inner iterations, especially when the current
outer iterate is far from the solution.
In this work, we analyse the method of multipliers and the preconditioned conjugate gradient method as inner solvers for interior
point schemes. We discuss the convergence of the whole approach, the implementation details and report the results of numerical
experimentation on a set of large scale test problems arising from the discretization of elliptic control problems. A comparison
with other interior point codes is also reported.
This research was supported by the Italian Ministry for Education, University and Research (MIUR) projects: FIRB Project:
“Parallel Nonlinear Numerical Optimization PN
2
O” (grant n. RBAU01JYPN, ) and COFIN/PRIN04 Project “Numerical Methods and Mathematical Software for Applications” (grant n. 2004012559, ). 相似文献
87.
Björn Gustafsson Mihai Putinar 《Journal of Mathematical Analysis and Applications》2007,328(2):995-1006
The analytic continuation of the exponential transform of a domain in Rn is proved under some global geometric assumptions on the boundary. Two approximation schemes of the continued transform (one based on a Taylor series truncation, the other on a global eigenfunction expansion) are also discussed. 相似文献
88.
Constraint qualifications in multiobjective optimization problems: Differentiable case 总被引:7,自引:0,他引:7
T. Maeda 《Journal of Optimization Theory and Applications》1994,80(3):483-500
In this paper, we are concerned with a multiobjective optimization problem with inequality constraints. We introduce a constraint qualification and derive the Kuhn-Tucker type necessary conditions for efficiency. Moreover, we give conditions which ensure the constraint qualification.This work was done while the author was visiting the University of California, Berkeley, California. 相似文献
89.
Alexander Shapiro 《Annals of Operations Research》1991,30(1):169-186
In this paper we discuss a general approach to studying asymptotic properties of statistical estimators in stochastic programming. The approach is based on an extended delta method and appears to be particularly suitable for deriving asymptotics of the optimal value of stochastic programs. Asymptotic analysis of the optimal value will be presented in detail. Asymptotic properties of the corresponding optimal solutions are briefly discussed. 相似文献
90.
Liu Yongping 《数学年刊B辑(英文版)》1995,16(3):351-360
AVERAGE σ-K WIDTH OF CLASS OF L_p(R~n)IN L_q(R~n)AVERAGEσ-KWIDTHOFCLASSOFL_p(R~n)INL_q(R~n)¥LIUYONGPINGAbstract:Theaverageσ-Kwidt... 相似文献