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1.

Augmenting forests to meet odd diameter requirements

**总被引：1，自引：0，他引：1**Given a graph

*G*=(*V*,*E*) and an integer*D*≥1, we consider the problem of augmenting*G*by the smallest number of new edges so that the diameter becomes at most*D*. It is known that no constant approximation algorithms to this problem with an arbitrary graph*G*can be obtained unless*P*=*N**P*. For a forest*G*and an odd*D*≥3, it was open whether the problem is approximable within a constant factor. In this paper, we give the first constant factor approximation algorithm to the problem with a forest*G*and an odd*D*; our algorithm delivers an 8-approximate solution in*O*(|*V*|^{3}) time. We also show that a 4-approximate solution to the problem with a forest*G*and an odd*D*can be obtained in linear time if the augmented graph is additionally required to be biconnected. 相似文献2.

On a synchronization queue with two finite buffers

**总被引：1，自引：0，他引：1**In this paper, we consider a synchronization queue (or synchronization node) consisting of two buffers with finite capacities.
One stream of tokens arriving at the system forms a Poisson process and the other forms a PH-renewal process. The tokens are
held in the buffers until one is available from each flow, and then a group-token is instantaneously released as a synchronized
departure. We show that the output stream of a synchronization queue is a Markov renewal process, and that the time between
consecutive departures has a phase type distribution. Thus, we obtain the throughput of this synchronization queue and the
loss probabilities of each type of tokens. Moreover, we consider an extended synchronization model with two Poisson streams
where a departing group-token consists of several tokens in each buffer.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献

3.

A conflict-avoiding code of length

*n*and weight*k*is defined as a set of binary vectors, called codewords, all of Hamming weight*k*such that the distance of arbitrary cyclic shifts of two distinct codewords in*C*is at least 2*k*−2. In this paper, we obtain direct constructions for optimal conflict-avoiding codes of length*n*= 16*m*and weight 3 for any*m*by utilizing Skolem type sequences. We also show that for the case*n*= 16*m*+ 8 Skolem type sequences can give more concise constructions than the ones obtained earlier by Jimbo et al. 相似文献4.

We look at the computational complexity of 2-dimensional geometric optimization problems on a finite point set with respect to the number of inner points (that is, points in the interior of the convex hull). As a case study, we consider the minimum weight triangulation problem. Finding a minimum weight triangulation for a set of

*n*points in the plane is not known to be NP-hard nor solvable in polynomial time, but when the points are in convex position, the problem can be solved in O(*n*^{3}) time by dynamic programming. We extend the dynamic programming approach to the general problem and describe an exact algorithm which runs in O(6^{k}*n*^{5}log*n*) time where*n*is the total number of input points and*k*is the number of inner points. If*k*is taken as a parameter, this is a fixed-parameter algorithm. It also shows that the problem can be solved in polynomial time if*k*=O(log*n*). In fact, the algorithm works not only for convex polygons, but also for simple polygons with*k*inner points. 相似文献5.

Let and be finite groups that have a common central -subgroup for a prime number , and let and respectively be -blocks of and induced by -blocks and respectively of and , both of which have the same defect group. We prove that if and are Morita equivalent via a certain special -bimodule, then such a Morita equivalence lifts to a Morita equivalence between and .

6.

This article considers an opportunity-based age replacement model with different intensity rates. Most of the articles suppose that opportunities are generated according to a homogeneous Poisson process, where the intensity rate does not change with time. However, social, economical, and physical environments can change the intensity rate. We suppose the intensity rate changes at specific age. The occurrence of opportunities is independent to the failure of a component. Pre ventive replacement is carried out at the first opportunity after age

*T*. If the component breaks down then it is replaced immediately. We derive the expected cost per unit time for an infinite time horizon. An optimal policy to minimize the expected cost per unit time is derived. Finally, numerical examples are given. 相似文献7.

FADEC (full authority digital engine control) is widely adopted for gas turbine engine controllers. The advancement of microelectronics produces high speed general purpose programmable logic controllers (PLC) with low price. When they are adopted for FADEC, we can expect high cost performance engine controllers. However, these PLCs were originally developed for ordinary industrial machinery controllers and PLC makers prohibited their use as gas turbine controllers because of their low reliability. Engine makers should give some measures to hold enough reliability when they apply PLCs for FADEC. In this paper, a FADEC is self-diagnosed at the

*n*^{th}control calculations. Introducing an expected cost until self-diagnosis and an expected cost per unit time, optimal policies which minimize them are discussed. Numerical examples are finally given. 相似文献8.

This paper considers a communication system which consists of many processors and studies the problem for improving its reliability by adopting the recovery techniques of checkpoint and rollback. When either processor failure or communication error has occurred, the rollback recovery for processors associated with such an event is executed to the most recent checkpoint, and so, a consistent state in the whole system is maintained. The stochastic model with the above recovery techniques is formulated, using the theory of Markov renewal processes. The mean time to take checkpoint and the expected numbers of rollback recovery caused by processor failures and communication errors are derived. Further, an optimal checkpointing interval which minimizes the expected cost is analytically discussed. 相似文献

9.

Naohiro Suzuki 《Proceedings of the American Mathematical Society》2000,128(3):819-825

We consider the Dirac operators with electromagnetic fields on 2-dimensional Euclidean space. We offer the sufficient conditions for electromagnetic fields that the associated Dirac operator has only discrete spectrum.

10.

In this paper we show the uniform or mean convergence of Hermite–Fejér interpolation polynomials of higher order based at the zeros of orthonormal polynomials with the typical Freud weight. 相似文献