— In this paper, building among others on earlier works by U. Krause and C. Zahlten (dealing with the case of cyclic groups), we obtain a new upper bound for the little cross number valid in the general case of arbitrary finite Abelian groups. Given a finite Abelian group, this upper bound appears to depend only on the rank and on the number of distinct prime divisors of the exponent. The main ...

We prove that χ(G) ≤ max { ω(G),∆2(G), 5 6 (∆(G) + 1) } for every graph G with ∆(G) ≥ 3. Here ∆2 is the parameter introduced by Stacho that gives the largest degree that a vertex v can have subject to the condition that v is adjacent to a vertex whose degree is at least as large as its own. This upper bound generalizes both Brooks’ Theorem and the Ore-degree version of Brooks’ Theorem.

We pursue a general theory of quantum games. We show that quantum games are more efficient than classical games, and provide a saturated upper bound for this efficiency. We also demonstrate how quantum games may be viewed simultaneously as both a generalized and yet restricted version of the corresponding classical games. We also deduce the quantum version of the Minimax Theorem and the Nash Eq...

This is easy for p 3, true but difficult for p=4 and 5 (in both cases [9, 6] it is equivalent to the four-colour theorem [1, 2, 7]), and open for p 6. It is therefore of interest to examine weakenings of (1.1). If G has no Kp+1 minor, the best upper bound known on its chromatic number is O( p(log p) ). This follows easily from the following theorem of Kostochka [5] or Thomason [8]. Article No. ...

Let K be a number field and A an abelian variety over K. The K-rational points of A are known to constitute a finitely generated abelian group (Mordell-Weil theorem). The problem studied in this paper is to find an explicit upper bound for the rank r of its free part in terms of other invariants of A/K. This is achieved by a close inspection of the classical proof of the so-called ‘weak Mordell...

Here a posteriori error estimate for the numerical solution of nonlinear Voltena- Hammerstein equations is given. We present an error upper bound for nonlinear Voltena-Hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of Brunner for these problems (the implicitly linear collocation method)...

BGP allows routers to use general preference policies for route selection. This paper studies the impact of these policies on convergence time. We first describe a real-time model of BGP. We then state and prove a general theorem providing an upper bound on convergence time. Finally, we show how to the use the theorem to prove convergence and estimate convergence time in three case studies.

In this paper, we study semi-infinite systems of Linear Matrix Inequalities which are generically NP-hard. For these systems, we introduce computationally tractable approximations and derive quantitative guarantees of their quality. As applications, we discuss the problem of maximizing a Hermitian quadratic form over the complex unit cube and the problem of bounding the complex structured singu...

Analogies between the Nevanlinna theory and the theory of heights in number theory have motivated to the determination the precise error term of the second fundamental theorem of the Nevanlinna theory. The Nevanlinna secondary deeciency, introduced by P.M. Wong, gives the error term in a certain sense. We rst prove that, from a topological point of view, almost all meromorphic functions have se...

We pursue a general theory of quantum games. We show that quantum games are more efficient than classical games, and provide a saturated upper bound for this efficiency. We demonstrate that the set of finite classical games is a strict subset of the set of finite quantum games. We also deduce the quantum version of the Minimax Theorem and the Nash Equilibrium Theorem. [email protected] n....