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971.
The purpose of this paper is to extend a family of variable metric methods, of which the BFGS algorithm (Ref. 1) is a member, into function space, in particular, for the solution of unconstrained optimal control problems. An inexact one-dimensional minimization as suggested by Fletcher (ref. 2) is used. It is shown that, with this stepsize rule and under some mild assumptions, the sequence constructed by this family of methods converges superlinearly for a strictly convex functional defined on a suitable Banach space. This result is shown to remain valid on a Hilbert space and on a Euclidean space under more relaxed assumptions. The BFGS method without line searches is used to solve several standard numerical examples, and excellent performance is observed.This work was supported by the Consejo Nacional de Ciencia y Tecnologia de Mexico, and by the National Research Council of Canada, Grant No. A-8835. The authors are indebted to Dr. C. Charalambous for suggesting the topic and stimulating discussions. 相似文献
972.
973.
974.
B. R. Barmish 《Journal of Optimization Theory and Applications》1978,26(3):379-394
S is taken to be a dynamical system (described by Banach space operators) whose outputy we wish to regulate. The structural complexity ofS (nonlinearities, distributed parameters, etc.) forces us to design a controller forS using an approximate modelM ofS. A convex error bound ? describes the accuracy of the approximation ofS byM. For a prescribed target setY t , we considered the problem of driving the output ofS toY t subject to worst possible error excursions betweenM andS. The notion of areconstructed support function is instrumental to the derivation of the main result, Theorem 6.1, which we can paraphrase as follows. IfM is linear (S need not be), then we can describe a finite-dimensional convex programming Problem (P), whose solution tells us whether or notY t is reachable. Theorem 6.1 is then specialized to differential systems approximated in the norm. The computation of numerical solutions is also discussed. 相似文献
975.
Eiichi Bannai 《Journal of Algebraic Combinatorics》1993,2(4):327-344
We introduce the concept of fusion algebras at algebraic level, as a purely algebraic concept for the fusion algebras which appear in conformal field theory in mathematical physics. We first discuss the connection between fusion algebras at algebraic level and character algebras, a purely algebraic concept for Bose-Mesner algebras of association schemes. Through this correspondence, we establish the condition when the matrix S of a fusion algebra at algebraic level is unitary or symmetric. We construct integral fusion algebras at algebraic level, from association schemes, in particular from group association schemes, whose matrix S is unitary and symmetric. Finally, we consider whether the modular invariance property is satisfied or not, namely whether there exists a diagonal matrix T satisfying the condition (ST)3 = S
2. We prove that this property does not hold for some integral fusion algebras at algebraic level coming from the group association scheme of certain groups of order 64, and we also prove that the (nonintegral) fusion algebra at algebraic level obtained from the Hamming association scheme H(d, q) has the modular invariance property. 相似文献
976.
杜芹香 《宁波大学学报(理工版)》1998,(1)
提出了测度空间(XA,)中测度稠密性和测度半稠密性的两个概念,在给定条件下证明了集代数FA在(F)中的测度稠密性及半集代数SA在(S)中的测度半稠密性;并将所得结果应用于线性赋范空间[a,b]的可分性的证明。 相似文献
977.
A short review about nonassociative algebraic systems (mainly nonassociative algebras) and their physical applications is presented. We begin with some motivations, then we give a brief historical overview about the formation and development of the concept of hypercomplex number system and about some earlier applications. The main directions discussed are the octonionic, Lie-admissible, and quasigroup approaches. Also, some problems investigated in Tartu, the octonionic approach, Moufang–Mal'tsev symmetry, and associator quantization are discussed. This review does not pretend to be complete as the accent is placed on ideas and not on the techniques, also the references are quite sporadic (there are many authors and results mentioned in the text without references). 相似文献
978.
979.
Edward Ames 《Mathematical Social Sciences》1983,6(2):247-260
It is shown that the economic adjustment mechanism developed by Hurwicz and his associates has the structure of automata. It is then shown that certain price adjustment mechanisms, having an acceptability condition, impose a group structure upon the automaton. This condition is a bilinear invariance implied by a budget constraint. Then the automaton is defined by a subgroup, depending on agents' tastes, technologies and strategies, and by the representations of the subgroup imposed by the automaton. 相似文献
980.