共查询到20条相似文献,搜索用时 0 毫秒
1.
O. N. German 《Mathematical Notes》2010,88(3-4):479-486
The validity of the Faugère criterion for the F5 algorithm is established. 相似文献
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Bernd Sturmfels 《Results in Mathematics》1989,15(3-4):351-360
Final polynomials and final syzygies provide an explicit representation of polynomial identities promised by Hilbert’s Nullstellensatz. Such representations have been studied independently by Bokowski [2,3,4] and Whiteley [23,24] to derive invariant algebraic proofs for statements in geometry. In the present paper we relate these methods to some recent developments in computational algebraic geometry. As the main new result we give an algorithm based on B. Buchberger’s Gröbner bases method for computing final polynomials and final syzygies over the complex numbers. Degree upper bound for final polynomials are derived from theorems of Lazard and Brownawell, and a topological criterion is proved for the existence of final syzygies. The second part of this paper is expository and discusses applications of our algorithm to real projective geometry, invariant theory and matrix theory. 相似文献
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William Bordeaux Montrieux 《Annales Henri Poincare》2011,12(1):173-204
We consider quite general differential operators on the circle with a small random lower order perturbation. We embrace two
points a view, the semiclassical and the high energy limits. We show (a) in the semiclassical limit, that the eigenvalues
inside a subdomain of the pseudospectrum are distributed according to a Weyl law with a probability close to 1, (b) that the
large eigenvalues obey a Weyl law almost surely. 相似文献
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Recently Dadush et al. (2017) have devised a polynomial submodular function minimization (SFM) algorithm based on their LP algorithm. In the present note we also show a weakly polynomial algorithm for SFM based on the recently developed linear programming feasibility algorithm of Chubanov (2017) to stimulate further research on SFM. 相似文献
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Mostafa Khorramizadeh Nezam Mahdavi-Amiri 《4OR: A Quarterly Journal of Operations Research》2011,9(2):159-173
Recently, we described a generalization of Rosser’s algorithm for a single linear Diophantine equation to an algorithm for solving systems of linear Diophantine equations. Here, we make use of the new formulation to present a new algorithm for solving rank one perturbed linear Diophantine systems, based on using Rosser’s approach. Finally, we compare the efficiency and effectiveness of our proposed algorithm with the algorithm proposed by Amini and Mahdavi-Amiri (Optim Methods Softw 21:819–831, 2006). 相似文献
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We prove an analogue of the Khinchin??s theorem for the Diophantine approximation by integer vectors lying on a quadratic variety. The proof is based on the study of a dynamical system on a homogeneous space of the orthogonal group. We show that in this system, generic trajectories of a certain geodesic flow visit a family of shrinking subsets infinitely often. 相似文献
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Jesús Guillera 《The Ramanujan Journal》2018,46(3):667-675
We show how to prove the examples of a paper by Chu and Zhang using the WZ algorithm. 相似文献
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Shiing-Shen Chern was an editor of our journal Results in Mathematics from 1984 to 2004, the year he passed away at Tianjin. This article honors one of the greatest mathematicians of the twentieth century, in particular remembering his studies at Hamburg University during the years 1934?C1936. This period strongly influenced his mathematical work and was decisive for his later career. We survey the situation of the Department of Mathematics there, Chern??s studies, his visits to Germany in later years, his honours and awards from German institutions, and finally exemplarily his influence on the next generations of Chinese mathematicians studying in Germany. 相似文献
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K. D. Shalbuzov V. V. Morozov 《Moscow University Computational Mathematics and Cybernetics》2012,36(1):1-7
The problem of constructing optimum cuts in the Gomory method for integer linear programming (ILP) problems is considered.
Algorithms for finding cuts are described, and their complexity is assessed. The modified Gomory algorithm is compared to
a standard Gomory algorithm. 相似文献
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Stuart James Hall 《Differential Geometry and its Applications》2011,29(3):426-432
This is a short note in which we show how to calculate the value of Perelman?s ν-functional for a variety of metrics. In particular we complete the calculation of values for the known 4-dimensional Einstein and shrinking Ricci soliton metrics. 相似文献
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Columns
Here’s to Your Health Assessing the seasonality of influenza 相似文献18.
Marco Squassina 《Journal of Fixed Point Theory and Applications》2011,10(1):191-195
For proper lower semicontinuous functionals bounded from below which do not increase upon polarization, an improved version of Ekeland’s variational principle can be formulated in Banach spaces, which provides almost symmetric points. 相似文献
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Dijkstra’s algorithm is a well-known algorithm for the single-source shortest path problem in a directed graph with nonnegative edge length. We discuss Dijkstra’s algorithm from the viewpoint of discrete convex analysis, where the concept of discrete convexity called L-convexity plays a central role. We observe first that the dual of the linear programming (LP) formulation of the shortest path problem can be seen as a special case of L-concave function maximization. We then point out that the steepest ascent algorithm for L-concave function maximization, when applied to the LP dual of the shortest path problem and implemented with some auxiliary variables, coincides exactly with Dijkstra’s algorithm. 相似文献
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This paper presents a new conversion technique of the standard linear programming problem into a homogenous form desired for the Karmarkar’s algorithm, where we employed the primal–dual method. The new converted linear programming problem provides initial basic feasible solution, simplex structure, and homogenous matrix. Apart from the transformation, Hooker’s method of projected direction is employed in the Karmarkar’s algorithm and the modified algorithm is presented. The modified algorithm has a faster convergence with a suitable choice of step size. 相似文献