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71.
Recently Lexicographic Breadth First Search (LBFS) has received considerable attention and has often been employed in a multi-sweep fashion. One variant of LBFS called LBFS+ breaks ties by choosing the last vertex of the tied set in a previous LBFS. This has motivated the study of vertices that may appear last in an LBFS (called end-vertices). In this paper, we present various theoretical and algorithmic results concerning end-vertices. 相似文献
72.
The main result of the paper is a series of theorems, called here Infimum Principles. As applications, we derive some well-known
results related to fixed point, minimax, and equilibrium theorems including the Nash equilibrium theorem and Gale–Nikaido
theorem. Our study is based on and utilizes the techniques of simplicial structures and CO families. This approach enables
us to derive not only classical theorems but also stimulates new research.
相似文献
73.
Gábor Hetyei 《Journal of Combinatorial Theory, Series A》2008,115(4):569-592
We generalize the notion of the Tchebyshev transform of a graded poset to a triangulation of an arbitrary simplicial complex in such a way that, at the level of the associated F-polynomials j∑fj−1(j(x−1)/2), the triangulation induces taking the Tchebyshev transform of the first kind. We also present a related multiset of simplicial complexes whose association induces taking the Tchebyshev transform of the second kind. Using the reverse implication of a theorem by Schelin we observe that the Tchebyshev transforms of Schur stable polynomials with real coefficients have interlaced real roots in the interval (−1,1), and present ways to construct simplicial complexes with Schur stable F-polynomials. We show that the order complex of a Boolean algebra is Schur stable. Using and expanding the recently discovered relation between the derivative polynomials for tangent and secant and the Tchebyshev polynomials we prove that the roots of the corresponding pairs of derivative polynomials are all pure imaginary, of modulus at most one, and interlaced. 相似文献
74.
75.
76.
D. Reinelt P. Boltenhagen N. Rivier 《The European physical journal. E, Soft matter》2001,4(3):299-304
The “staircase” (2,1,1) foam structure in an ordered foam under expansion in a cylindrical tube and the structural transition
to the “bamboo” (1,1,0) structure are studied experimentally, analytically, and numerically using the Surface Evolver minimization
program. An analytical expression of the oblique interface in the (2,1,1) structure, a minimal surface, but curved by stretching
of the foam, is given as a classic example of singular perturbation (boundary layer) theory. The structural transition from
staircase structure to bamboo structure takes place at a considerable dilation. The transition is not due to an edge length
tending to zero continuously with dilation, but results from the equilibrium (2,1,1) solution losing its stability due to
a saddle node bifurcation.
Received 3 August 2000 相似文献
77.
Satoshi Murai 《Advances in Mathematics》2007,214(2):701-729
In 1988 Kalai constructed a large class of simplicial spheres, called squeezed spheres, and in 1991 presented a conjecture about generic initial ideals of Stanley-Reisner ideals of squeezed spheres. In the present paper this conjecture will be proved. In order to prove Kalai's conjecture, based on the fact that every squeezed (d−1)-sphere is the boundary of a certain d-ball, called a squeezed d-ball, generic initial ideals of Stanley-Reisner ideals of squeezed balls will be determined. In addition, generic initial ideals of exterior face ideals of squeezed balls are determined. On the other hand, we study the squeezing operation, which assigns to each Gorenstein* complex Γ having the weak Lefschetz property a squeezed sphere Sq(Γ), and show that this operation increases graded Betti numbers. 相似文献
78.
James W. Rogers Jr. 《Journal of Mathematical Analysis and Applications》2007,326(1):228-241
Various dynamic derivative formulae have been proposed in the development of a time scales calculus, with the goal of unifying continuous and discrete analysis. Recent discussions of combined dynamic derivatives, in particular the α? derivative defined as a linear combination of the Δ and the ∇ derivatives, have promised improved approximation formulae for computational applications. This paper presents an equivalent definition of the α? functions without reference to the existing Δ and ∇ derivatives, examines the status of the α? as a dynamic derivative and its properties relative to the Δ and ∇ derivatives, and compares data obtained using the various dynamic derivatives as approximation formulae in computational experiments. A α? integral case is investigated. 相似文献
79.
Satoshi Murai 《Discrete Mathematics》2007,307(14):1707-1721
Gil Kalai introduced the shifting-theoretic upper bound relation as a method to generalize the g-theorem for simplicial spheres by using algebraic shifting. We will study the connection between the shifting-theoretic upper bound relation and combinatorial shifting. Also, we will compute the exterior algebraic shifted complex of the boundary complex of the cyclic d-polytope as well as of a stacked d-polytope. It will turn out that, in both cases, the exterior algebraic shifted complex coincides with the symmetric algebraic shifted complex. 相似文献
80.
本文提出计算标准单纯形S″上连续自映射不动点的一种变维数重复开始不动点算法,证明了算法的可行性和有限步收敛性.一些数值试验结果表明新的不动点算法可以与三明治算法相媲美。 相似文献