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1.
On The Profinite Topology on a Free Group   总被引:3,自引:0,他引:3  
If F is a free abstract group, its profinite topology is thecoarsest topology making F into a topological group, such thatevery group homomorphism from F into a finite group is continuous.It was shown by M. Hall Jr that every finitely generated subgroupof F is closed in that topology. Let H1, H2, ..., Hn be finitelygenerated subgroups of F. J.-E. Pin and C. Reutenauer have conjecturedthat the product H1 H2 ... Hn is a closed set in the profinitetopology of F; also, they have shown that this conjecture impliesa conjecture of J. Rhodes on finite semigroups. In this paperwe give a positive answer to the conjecture of Pin and Reutenauer.Our method is based on the theory of profinite groups actingon graphs.  相似文献
2.
Parallel machine scheduling problems with a single server   总被引:3,自引:0,他引:3  
In this paper, we consider the problem of scheduling jobs on parallel machines with setup times. The setup has to be performed by a single server. The objective is to minimize the schedule length (makespan), as well as the forced idle time. The makespan problem is known to be NP-hard even for the case of two identical parallel machines. This paper presents a pseudopolynomial algorithm for the case of two machines when all setup times are equal to one. We also show that the more general problem with an arbitrary number of machines is unary NP-hard and analyze some list scheduling heuristics for this problem. The problem of minimizing the forced idle time is known to be unary NP-hard for the case of two machines and arbitrary setup and processing times. We prove unary NP-hardness of this problem even for the case of constant setup times. Moreover, some polynomially solvable cases are given.  相似文献
3.
The single machine batch scheduling problem to minimize the weighted number of late jobs is studied. In this problem,n jobs have to be processed on a single machine. Each job has a processing time, a due date and a weight. Jobs may be combined to form batches containing contiguously scheduled jobs. For each batch, a constant set-up time is needed before the first job of this batch is processed. The completion time of each job in the batch coincides with the completion time of the last job in this batch. A job is late if it is completed after its due date. A schedule specifies the sequence of jobs and the size of each batch, i.e. the number of jobs it contains. The objective is to find a schedule which minimizes the weighted number of late jobs. This problem isNP-hard even if all due dates are equal. For the general case, we present a dynamic programming algorithm which solves the problem with equal weights inO(n 3) time. We formulate a certain scaled problem and show that our dynamic programming algorithm applied to this scaled problem provides a fully polynomial approximation scheme for the original problem. Each algorithm of this scheme has a time requirement ofO(n 3/ +n 3 logn). A side result is anO(n logn) algorithm for the problem of minimizing the maximum weight of late jobs.Supported by INTAS Project 93-257.  相似文献
4.
A fully polynomial approximation scheme for the problem of scheduling n deteriorating jobs on a single machine to minimize makespan is presented. Each algorithm of the scheme runs in O(n 5 L 43) time, where L is the number of bits in the binary encoding of the largest numerical parameter in the input, and is required relative error. The idea behind the scheme is rather general and it can be used to develop fully polynomial approximation schemes for other combinatorial optimization problems. Main feature of the scheme is that it does not require any prior knowledge of lower and/or upper bounds on the value of optimal solutions.  相似文献
5.
A fully polynomial approximation scheme for the problem of scheduling n deteriorating jobs on a single machine to minimize makespan is presented. Each algorithm of the scheme runs in O(n 5 L 43) time, where L is the number of bits in the binary encoding of the largest numerical parameter in the input, and is required relative error. The idea behind the scheme is rather general and it can be used to develop fully polynomial approximation schemes for other combinatorial optimization problems. Main feature of the scheme is that it does not require any prior knowledge of lower and/or upper bounds on the value of optimal solutions.  相似文献
6.
Limit cycles of quadratic systems   总被引:2,自引:1,他引:1  
In this paper, the global qualitative analysis of planar quadratic dynamical systems is established and a new geometric approach to solving Hilbert’s Sixteenth Problem in this special case of polynomial systems is suggested. Using geometric properties of four field rotation parameters of a new canonical system which is constructed in this paper, we present a proof of our earlier conjecture that the maximum number of limit cycles in a quadratic system is equal to four and their only possible distribution is (3:1) [V.A. Gaiko, Global Bifurcation Theory and Hilbert’s Sixteenth Problem, Kluwer, Boston, 2003]. Besides, applying the Wintner–Perko termination principle for multiple limit cycles to our canonical system, we prove in a different way that a quadratic system has at most three limit cycles around a singular point (focus) and give another proof of the same conjecture.  相似文献
7.
We are concerned in this paper with the ideal structure of grouprings of infinite simple locally finite groups over fields ofcharacteristic zero, and its relation with certain subgroupsof the groups, called confined subgroups. The systematic studyof the ideals in these group rings was initiated by the secondauthor in[15], although some results had been obtained previously(see [3, 1]). Let G be an infinite simple locally finite groupand K a field of characteristic zero. It is expected that inmost cases, the group ring KG will have the smallest possiblenumber of ideals, namely three, (KG itself, {0} and the augmentationideal), and this has been verified in some cases. In some interestingcases, however, the situation is different, and there are moreideals. We mention in particular the infinite alternating groups[3] and the stable special linear groups [9], in which the ideallattice has been completely determined. The second author hasconjectured that the presence of ideals in KG, other than thethree unavoidable ones, is synonymous with the presence in thegroup of proper confined subgroups. Here a subgroup H of a locallyfinite group G is called confined, if there exists a finitesubgroup F of G such that HgF1 for all gG. This amounts to sayingthat F has no regular orbit in the permutation representationof G on the cosets of H.  相似文献
8.
Some Properties of Essential Spectra of a Positive Operator   总被引:1,自引:1,他引:0  
Egor A. Alekhno 《Positivity》2007,11(3):375-386
Let E be a Banach lattice, T be a bounded operator on E. The Weyl essential spectrum σew(T) of the operator T is a set , where is a set of all compact operators on E. In particular for a positive operator T next subsets of the spectrum
are introduced in the article. The conditions by which implies either or are investigated, where σef(T) is the Fredholm essential spectrum. By this reason, the relations between coefficients of the main part of the Laurent series of the resolvent R(., T) of a positive operator T around of the point λ  =  r(T) are studied. The example of a positive integral operator T : L1L which doesn’t dominate a non-zero compact operator, is adduced. Applications of results which are obtained, to the spectral theory of band irreducible operators, are given. Namely, the criteria when the operator inequalities 0 ≤ S < T imply the spectral radius inequality r(S) < r(T), are established, where T is a band irreducible abstract integral operator.  相似文献
9.
Many problems in physics and mathematics may be reduced to solving equations depending on a parameter. The justification of the existence of solutions to the equations and the sensitivity analysis may be conducted based on Implicit Function Theorem (IFT) under certain regularity assumptions. Provided the regularity assumptions do not hold, generalizations of IFT are needed in order to study solutions to the equations. The paper focuses on a particular generalization of IFT which is then applied to a parametric linear time-optimal control problem.  相似文献
10.
The following single machine scheduling problem is studied. A partition of a set of n jobs into g groups on the basis of group technology is given. The machine processes jobs of the same group contiguously, with a sequence independent setup time preceding the processing of each group. The setup times and the job processing times are controllable through the allocation of a continuously divisible or discrete resource to them. Each job uses the same amount of the resource. Each setup also uses the same amount of resource, which may be different from that for the jobs. Polynomial-time algorithms are constructed for variants of the problem of finding an optimal job sequence and resource values so as to minimize the total weighted job completion time, subject to given restrictions on resource consumption. The algorithms are based on a polynomial enumeration of the candidates for an optimal job sequence and solving the problem with a fixed job sequence by linear programming. This research was supported in part by The Hong Kong Polytechnic University under grant number G-T246 and the Research Grants Council of Hong Kong under grant number PolyU 5191/01E. In addition, the research of M.Y. Kovalyov was supported by INTAS under grant number 00-217.  相似文献
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