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1.
Multivariate Birkhoff interpolation problem has many important applications, such as in finite element method. In this paper two algorithms are given to compute the basis of the minimal interpolation space and the lower interpolation space respectively for an arbitrary given node set and the corresponding interpolation conditions on each node. We can get the monomial basis, Newton-type basis as well as Lagrange-type basis. The interpolation polynomial can be derived from the basis directly.  相似文献   

2.
Tracing back from Charnes et al. [9] many approaches have been proposed to extend the DEA production model to non-convex technologies. The FDH method were introduced by Deprins et al. [13] and it only assumes a free disposal assumption of the technology. This paper, continues further an earlier work by Briec and Horvath [7]. Among other things, a new class of semilattice production technologies is introduced. Duality results as well as computational issues are proposed.  相似文献   

3.
In this paper, the geometric meaning of (α,β)-norms is made clear. On this basis, a new class of Finsler metrics called general (α,β)-metrics are introduced, which are defined by a Riemannian metric and a 1-form. These metrics not only generalize (α,β)-metrics naturally, but also include some metrics structured by R. Bryant. The spray coefficients formula of some kinds of general (α,β)-metrics is given and the projective flatness is also discussed.  相似文献   

4.
We introduce new families of orthogonal polynomials HD,n, motivated by the non-equilibrium evolution of a quantum Brownian particle (qBp). The HD,n’s generalize non-trivially the standard Hermite polynomials, employed for classical Brownian motion. We treat several models (labelled by D) for a non-equilibrium qBp, by means of the Wigner function W, in the presence of a “heat bath” at thermal equilibrium, with and without ab initio friction. For long times (for a suitable class of initial conditions), the non-equilibrium Wigner function W should approach, in some sense, the (time-independent) equilibrium Wigner function Weq,D, which describes the thermal equilibrium of the qBp with the “heat bath” and plays a central role. Weq,D is chosen to be the weight function which orthogonalizes the HD,n’s. New results on Weq,D and on the HD,n’s are reported. We justify the key role of the HD,n’s as follows. Using the HD,n’s, moments Weq,D,n and Wn are introduced for Weq,D and W, respectively. At equilibrium, all moments Weq,D,n except the lowest one (Weq,D,0) vanish identically. Off-equilibrium, one expects that, for long times (for suitable initial conditions): (i) all non-equilibrium moments Wn (except the lowest moment W0), will approach zero, while (ii) the lowest non-equilibrium moment W0 will tend to Weq,D,0(≠0). To complete the justification, we outline how the approximate long-time non-equilibrium theories determined by W0 for the different models (D) yield Smoluchowski equations and irreversible evolutions of the qBp towards thermal equilibrium.  相似文献   

5.
6.
This paper determines the mean waiting times for a single server multi-class queueing model with Poisson arrivals and relative priorities. If the server becomes idle, the probability that the next job is from class-i is proportional to the product between the number of class-i jobs present and their priority parameter.  相似文献   

7.
We present an iteration method for the polynomial approximation of rational Bézier curves. Starting with an initial Bézier curve, we adjust its control points gradually by the scheme of weighted progressive iteration approximations. The Lp-error calculated by the trapezoidal rule using sampled points is used to guide the iteration approximation. We reduce the Lp-error by a predefined factor at every iteration so as to obtain the best approximation with a minimum error. Numerical examples demonstrate the fast convergence of our method and indicate that results obtained using the L1-error criterion are better than those obtained using the L2-error and L-error criteria.  相似文献   

8.
This paper studies low-regularity solutions of the periodic general Degasperis-Procesi equation with an initial value. The existence and the uniqueness of solutions are proved. The results are illustrated by considering the periodic peakons of the periodic general Degasperis-Procesi equation.  相似文献   

9.
The problem addressed in this paper is to compare the minimum cost of the two randomized control policies in the M/G/1 queueing system with an unreliable server, a second optional service, and general startup times. All arrived customers demand the first required service, and only some of the arrived customers demand a second optional service. The server needs a startup time before providing the first required service until the system becomes empty. After all customers are served in the queue, the server immediately takes a vacation and the system operates the (T, p)-policy or (p, N)-policy. For those two policies, the expected cost functions are established to determine the joint optimal threshold values of (T, p) and (p, N), respectively. In addition, we obtain the explicit closed form of the joint optimal solutions for those two policies. Based on the minimal cost, we show that the optimal (p, N)-policy indeed outperforms the optimal (T, p)-policy. Numerical examples are also presented for illustrative purposes.  相似文献   

10.
Given an edge- or vertex-weighted graph or digraph and a list of source-sink pairs, the minimum multicut problem consists in selecting a minimum weight set of edges or vertices whose removal leaves no path from each source to the corresponding sink. This is a classical NP-hard problem, and we show that the edge version becomes tractable in bounded tree-width graphs if the number of source-sink pairs is fixed, but remains NP-hard in directed acyclic graphs and APX-hard in bounded tree-width and bounded degree unweighted digraphs. The vertex version, although tractable in trees, is proved to be NP-hard in unweighted cacti of bounded degree and bounded path-width.  相似文献   

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