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1.
The problem of makespan minimization on a flexible flow shop with k stages and m
s
machines at any stage proposed by Paternina-Arboleda et al. [Ann. Oper. Res. 164:29–40, 2008] was recently published in Annals of Operations Research journal to solve the flexible flow-shop scheduling problems. In
this work, some comments and suggestions are given to the paper. The comment is about the proposed mathematical formulation
and the modification of it is suggested. 相似文献
2.
Anis Rezgui 《Acta Appl Math》2005,89(1-3):271-286
In this work we study partial differential operators of infinite order on spaces of entire functions, generalizing some of
the results presented in [2] and [5] to the new spaces introduced in [3]. 相似文献
3.
Combinatorial Sublinear-Time Fourier Algorithms 总被引:1,自引:0,他引:1
M. A. Iwen 《Foundations of Computational Mathematics》2010,10(3):303-338
We study the problem of estimating the best k term Fourier representation for a given frequency sparse signal (i.e., vector) A of length N≫k. More explicitly, we investigate how to deterministically identify k of the largest magnitude frequencies of
[^(A)]\hat{\mathbf{A}}
, and estimate their coefficients, in polynomial(k,log N) time. Randomized sublinear-time algorithms which have a small (controllable) probability of failure for each processed signal
exist for solving this problem (Gilbert et al. in ACM STOC, pp. 152–161, 2002; Proceedings of SPIE Wavelets XI, 2005). In this paper we develop the first known deterministic sublinear-time sparse Fourier Transform algorithm which is guaranteed
to produce accurate results. As an added bonus, a simple relaxation of our deterministic Fourier result leads to a new Monte
Carlo Fourier algorithm with similar runtime/sampling bounds to the current best randomized Fourier method (Gilbert et al.
in Proceedings of SPIE Wavelets XI, 2005). Finally, the Fourier algorithm we develop here implies a simpler optimized version of the deterministic compressed sensing
method previously developed in (Iwen in Proc. of ACM-SIAM Symposium on Discrete Algorithms (SODA’08), 2008). 相似文献
4.
Xinmin Hou 《Graphs and Combinatorics》2011,27(6):865-869
Let k, h be positive integers with k ≤ h. A graph G is called a [k, h]-graph if k ≤ d(v) ≤ h for any v ? V(G){v \in V(G)}. Let G be a [k, h]-graph of order 2n such that k ≥ n. Hilton (J. Graph Theory 9:193–196, 1985) proved that G contains at least ?k/3?{\lfloor k/3\rfloor} disjoint perfect matchings if h = k. Hilton’s result had been improved by Zhang and Zhu (J. Combin. Theory, Series B, 56:74–89, 1992), they proved that G contains at least ?k/2?{\lfloor k/2\rfloor} disjoint perfect matchings if k = h. In this paper, we improve Hilton’s result from another direction, we prove that Hilton’s result is true for [k, k + 1]-graphs. Specifically, we prove that G contains at least
?\fracn3?+1+(k-n){\lfloor\frac{n}3\rfloor+1+(k-n)} disjoint perfect matchings if h = k + 1. 相似文献
5.
In this paper, we introduce the concept of feasible set for an equilibrium problem with a convex cone and generalize the notion
of a Z-function for bifunctions. Under suitable assumptions, we derive some equivalence results of equilibrium problems, least element
problems, and nonlinear programming problems. The results presented extend some results of [Riddell, R.C.: Equivalence of
nonlinear complementarity problems and least element problems in Banach lattices. Math. Oper. Res. 6, 462–474 (1981)] to equilibrium problems.
This work was supported by the National Natural Science Foundation of China (10671135) and Specialized Research Fund for the
Doctoral Program of Higher Education (20060610005) and the Educational Science Foundation of Chongqing (KJ051307). 相似文献
6.
We consider linear programming relaxations for the max cut problem in graphs, based on k-gonal inequalities. We show that the integrality ratio for random dense graphs is asymptotically 1+1/k and for random sparse graphs is at least 1+3/k. There are O(nk)k-gonal inequalities. These results generalize work by Poljak and Tuza, who gave similar results for k=3. 相似文献
7.
In a recent work, S. Cooper (J. Number Theory 103:135–162, [1988]) conjectured a formula for r
2k+1(p
2), the number of ways p
2 can be expressed as a sum of 2k+1 squares. Inspired by this conjecture, we obtain an explicit formula for r
2k+1(n
2),n≥1.
Dedicated to Srinivasa Ramanujan. 相似文献
8.
Chaobao Huang Martin Stynes 《Numerical Methods for Partial Differential Equations》2019,35(6):2076-2090
A time‐fractional reaction–diffusion initial‐boundary value problem with periodic boundary condition is considered on Q ? Ω × [0, T] , where Ω is the interval [0, l] . Typical solutions of such problem have a weak singularity at the initial time t = 0. The numerical method of the paper uses a direct discontinuous Galerkin (DDG) finite element method in space on a uniform mesh, with piecewise polynomials of degree k ≥ 2 . In the temporal direction we use the L1 approximation of the Caputo derivative on a suitably graded mesh. We prove that at each time level of the mesh, our L1‐DDG solution is superconvergent of order k + 2 in L2(Ω) to a particular projection of the exact solution. Moreover, the L1‐DDG solution achieves superconvergence of order (k + 2) in a discrete L2(Q) norm computed at the Lobatto points, and order (k + 1) superconvergence in a discrete H1(Q) seminorm at the Gauss points; numerical results show that these estimates are sharp. 相似文献
9.
It is shown that a variety generated by a nilpotent A-loop has a decidable equational (quasiequational ) theory. Thereby the question posed by A. I. Mal’tsev in [6] is answered in the negative, and moreover, a finitely presented nilpotent A-loop has a decidable word problem. 相似文献
10.
For stable FIFO GI/GI/s queues, s ≥ 2, we show that finite (k+1)st moment of service time, S, is not in general necessary for finite kth moment of steady-state customer delay, D, thus weakening some classical conditions of Kiefer and Wolfowitz (1956). Further, we demonstrate that the conditions required
for E[D
k]<∞ are closely related to the magnitude of traffic intensity ρ (defined to be the ratio of the expected service time to the
expected interarrival time). In particular, if ρ is less than the integer part of s/2, then E[D] < ∞ if E[S3/2]<∞, and E[Dk]<∞ if E[Sk]<∞, k≥ 2. On the other hand, if s-1 < ρ < s, then E[Dk]<∞ if and only if E[Sk+1]<∞, k ≥ 1. Our method of proof involves three key elements: a novel recursion for delay which reduces the problem to that of a
reflected random walk with dependent increments, a new theorem for proving the existence of finite moments of the steady-state
distribution of reflected random walks with stationary increments, and use of the classic Kiefer and Wolfowitz conditions.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
11.
In this paper we consider basis function methods for solving the problem of interpolating data over distinct points on the unit circle. In the special case where the points are equally spaced we can appeal to the theory of circulant matrices which enables an investigation into the stability and accuracy of the method. This work is a further extension and application of the research of Cheney, Light and Xu ([W.A. Light and E.W. Cheney, J. Math. Anal. Appl., 168:110–130, 1992] and [Y. Xu and E.W. Cheney, Computers Math. Applic., 24:201–215, 1992]) from the early nineties. 相似文献
12.
The optimal k-restricted 2-factor problem consists of finding, in a complete undirected graph K
n
, a minimum cost 2-factor (subgraph having degree 2 at every node) with all components having more than k nodes. The problem is a relaxation of the well-known symmetric travelling salesman problem, and is equivalent to it when
≤k≤n−1. We study the k-restricted 2-factor polytope. We present a large class of valid inequalities, called bipartition inequalities, and describe
some of their properties; some of these results are new even for the travelling salesman polytope. For the case k=3, the triangle-free 2-factor polytope, we derive a necessary and sufficient condition for such inequalities to be facet
inducing.
Received March 4, 1997 / Revised version received September 7, 1998?Published online November 9, 1999 相似文献
13.
Robert B. Ellis Vadim Ponomarenko Catherine H. Yan 《Journal of Combinatorial Theory, Series A》2005,112(2):328-336
The q-round Rényi–Ulam pathological liar game with k lies on the set [n]{1,…,n} is a 2-player perfect information zero sum game. In each round Paul chooses a subset A[n] and Carole either assigns 1 lie to each element of A or to each element of [n]A. Paul wins if after q rounds there is at least one element with k or fewer lies. The game is dual to the original Rényi–Ulam liar game for which the winning condition is that at most one element has k or fewer lies. Define to be the minimum n such that Paul can win the q-round pathological liar game with k lies and initial set [n]. For fixed k we prove that is within an absolute constant (depending only on k) of the sphere bound, ; this is already known to hold for the original Rényi–Ulam liar game due to a result of J. Spencer. 相似文献
14.
Let k be a field of characteristic 0 and let [`(k)] \bar{k} be a fixed algebraic closure of k. Let X be a smooth geometrically integral k-variety; we set [`(X)] = X ×k[`(k)] \bar{X} = X{ \times_k}\bar{k} and denote by [`(X)] \bar{X} . In [BvH2] we defined the extended Picard complex of X as the complex of Gal( [`(k)]