L(d1, d2,..., dt)-Number λ(Cn; d1, d2,...,dt) of Cycles

An L(d1,d2,...,dt)-labeling of a graph G is a function f from its vertex set V(G) to the set {0, 1,..., k} for some positive integer k such that {f(x) - f(y)| ≥ di, if the distance between vertices x and y in G is equal to i for i = 1,2,...,t. The L(d1,d2,...,dt)-number λ(G;d1,d2,... ,dt) of G is the smallest integer number k such that G has an L(d1,d2,... ,dt)labeling with max{f(x)|x ∈ V(G)} = k. In this paper, we obtain the exact values for λ(Cn; 2, 2,1) and λ(Cn; 3, 2, 1), and present lower and upper bounds for λ(Cn; 2,..., 2,1,..., 1)     

Comment détecter le délit d'initiés?

This Note uses the enlargement of filiations for modelling the observation of a financial market by an insider trader. A characterization of admissible strategies and a criterium for optimization are given. Then a statistical test is proposed to test the unknown of the future against its knowledge.     

On 𝔬𝔰𝔭(1 | 2)-Relative Cohomology on S 1|1

We compute the second 𝔬𝔰𝔭(1 | 2) ?relative cohomology space of 𝒦(1) with coefficients in the module of λ-densities 𝔉_λ on S ^1|1. This result allows us to compute the second 𝔬𝔰𝔭(1 | 2) ?relative cohomology space of 𝒦(1) with coefficients in the Poisson superalgebra 𝒮𝒫. We explicitly give 2-cocycles spanning these cohomology spaces.     

Die Anzahl der primitiven Polytope im ℝ d mit 2d−2 Facetten

LetP ^d be ad-polytope and letN (P) be the set of outward normal vectors to its facets.P is said to be primitive if it has the property that there exists no polytopeQ withN(Q) N(P). In other words, removal of any facet ofP leaves an unbounded polyhedral set. The primitive polytopes withd+1 facets and with 2d facets are well known (they are the simplices and the parallelotopes), the primitive polytopes withd+2 and 2d–1 facets have also been classified. The present paper deals with primitive polytopes with 2d–2 facets.     

Dimension de la mesure d’équilibre d’applications méromorphes

The Journal of Geometric Analysis - Let ? be a dominating meromorphic self-map of a compact Kähler manifold. Assume that the topological degree of ? is larger than the other...     

Gelfand-Kirillov dimensions of the ℤ-graded oscillator representations of 𝔬(n,ℂ) and 𝔰𝔭(2n,ℂ)

In this paper, we give a method to compute the Gelfand–Kirillov dimensions of some polynomial–type weight modules. These modules are infinite-dimensional irreducible 𝔬(n,?)-modules and 𝔰𝔭(2n,?)-modules that appeared in the ?-graded oscillator generalizations of the classical theorem on harmonic polynomials established by Luo and Xu. We also found that some of these modules have the secondly minimal GK-dimension, and some of them have the larger GK-dimension than the maximal GK-dimension apearing in unitary highest-weight modules.     

Canonical forms of 2 × 2 × 2 and 2 × 2 × 2 × 2 arrays over 𝔽2 and 𝔽3

We consider arrays of size 2?×?2?×?2 and 2?×?2?×?2?×?2 over the fields with two and three elements. We use computer algebra to determine the canonical forms of these arrays with respect to the action of the semidirect product of general linear groups with the symmetric group. For each canonical form, we determine the size of its orbit and the rank of the arrays in its orbit.     

直径为d的超环面网的(d,2n)-控制数

ｎ维超环面网Ｃ（ｄ１ｄｄ２,…,ｄｎ）定义如下：顶点集为｛（ｘ１,…;ｘｎ）｜０≤ｘｉ＜ｄｉ（１≤ｉ≤ｎ）｝;每个顶点（ｘｌ,…,ｘｎ）与（ｘ１±１,ｘ２,…,ｘｎ）,（ｘ１,ｘ２±１,…,ｘｎ）,…;（ｘｌ,ｘ２,…,ｘｎ±１）这２ｎ个顶点相邻．（ｄ,ｍ）－控制数是用来刻画互连网络数据传输某种模式的一个新参数．本文证明了：当 ｄ＝ｄｉａｍ（Ｃ（ｄ１,ｄ２,…,ｄｎ））时,ｎ维超环面网Ｃ（ｄ１,ｄ２,…,ｄｎ）≠Ｃ（３,３,…,３）的（ｄ,２ｎ）－控制数为２（ｎ≥３,ｄｉ≥３,ｉ∈｛１,２,…,ｎ｝）．     

直径为d的超环面网的(d,2n)-控制数

n维超环面网C(dl,d2,…,dn)定义如下顶点集为{(x1,..,xn)|0≤xi<di(1≤i≤n)};每个顶点(xl,…,xn)与(x1±1,x2,…,xn),(xl,x2±1,…,xn),…,(x1,x2,….,xn±1)这2n个顶点相邻.(d,m)-控制数是用来刻画互连网络数据传输某种模式的一个新参数.本文证明了当d=diam(C(d1,d2,…,dn))时,n维超环面网C(d1,d2,…,dn)≠C(3,3,….,3)的(d,2n)控制数为2(n≥3,di≥3,i∈{1,2,…,n}.     

Produit d’inversions elliptiques ou hyperboliques

Let x and y be orthogonal coordinates of a point M (u = ax + iby or ax + ɛ by) of a plane where as x′ and y′ are orthogonal coordinates of a point M′(V = ax′ + iby′ or ax′ + ɛ by′) inverse of M in the elliptic hyperbolic inversion (k and k′ positive) designating the conjugate of v while i and ɛ are Clifford numbers such that i² = −1 and ɛ² = 1 (a and b are real). O is the origin of axises. Ox is the axis of inversions. We study particularly the product of two inversions.     

Some extensions of Rotfel’d theorem

We proved some inequalities for concave functions. Those inequalities complemented a theorem obtained by Lee. Finally, we partially solved an open problem proposed by Zhang P.     

A generalization of d’Alembert formula

In this paper we find a closed form of the solution for the factored inhomogeneous linear equation

一类裂变图的L(0,1,2 d,d,1)-标号数上界

将图的标号问题由每个顶点需要一个标号的情况推广到每个顶点需要多个标号的情况,给出裂变图的概念以及赋权图的L(0,1,2 d,d,1)-标号的概念,给出R-单位球图对应裂变图的L(0,1,2 d,d,1)-标号数的一个上界.     

Tilting bundles on orders on ℙd

We introduce a class of orders on ?^d called Geigle-Lenzing orders and show that they have tilting bundles. Moreover we show that their module categories are equivalent to the categories of coherent sheaves on Geigle- Lenzing projective spaces introduced in [HIMO].