Upper and lower bounds for the fixed spectrum frequency assignment problem

A survey of the results described in the authors PhD thesis (Montemanni 2001) is presented. The thesis, which was supervised by Prof. Derek H. Smith and Dr. Stuart M. Allen, has been defended in January 2002 at the University of Glamorgan (U.K.). The thesis proposes new heuristic algorithms, based on well-known meta-heuristic paradigms, and new lower bounding techniques, based on linear programming, for the fixed spectrum frequency assignment problem.Received: May 2003, Revised: May 2003, AMS classification: 90C27, 90C59,05C90, 90C05Roberto Montemanni: Present address: Istituto Dalle Molle di Studi sullIntelligenza Artificiale (IDSIA), Galleria 2, 6928 Manno-Lugano, Switzerland (e-mail: roberto@idsia.ch)     

Fixed points of asymptotic contractions

Let be a contractive gauge function in the sense that φ is continuous, φ(s)<s for s>0, and if f:M→M satisfies d(f(x),f(y))?φ(d(x,y)) for all x,y in a complete metric space (M,d), then f always has a unique fixed point. It is proved that if T:M→M satisfies

     

具超前变元的二阶微分方程三点边值问题的正解

§ 1　 IntroductionRecently,certain three-point boundary value problems for nonlinear ordinarydifferential equations have been studied by many authors[1— 6] .However,few papers havebeen published on the same problems for nonlinear functional differential equations.In thispaper,we are concerned with the following second order differential equation with anadvanced argumentu″(t) +λa(t) f(u(h(t) ) ) =0 ,t∈ (0 ,1 ) (1 .1 )with the three-point boundary conditionsu(0 ) =0 ,αu(η) =u(1 ) ,(1 .2 )…     

On Vector Quasi-Equilibrium Problems with Set-Valued Maps

In this paper, we introduce a new class of vector quasi-equilibrium problems with set-valued maps. Almost all the vector equilibrium models of the Blum-Oettli type in the literature are special cases of our new class of equilibrium problems under consideration. Moreover, a number of C-diagonal quasiconvexity properties are proposed for set-valued maps, which are natural generalizations of the -diagonal quasiconvexity for real functions. Together with an application of continuous selection and fixed-point theorems, these conditions enable us to prove unified existence results of solutions for such vector equilibrium problems.     

AFPP vs FPP

The main theme of this paper is that almost fixed point properties of discrete structures and fixed point properties of (topological) spaces are interdeducible via a suitable category which contains both graphs and spaces as objects. To carry out the program, we have to consider (almost) fixed points of multifunctions, and for this we need a preliminary discussion of power structures for graphs and simplicial complexes. Specific applications developed are: a digital convexity (discrete) version of Kakutani's fixed point theorem for convex-valued multifunctions; and fixed point properties of dendrites in terms of those of finite discrete trees.     

On nonoscillatory solutions of differential inclusions

This paper introduces a nonoscillatory theory for differential inclusions based on fixed point theory for multivalued maps.

     

Ergodic-theoretic properties of certain Bernoulli convolutions

The aim of this paper is to prove some fixed point theorems which generalize well known basic fixed point principles of nonlinear functional analysis. Moreover, we investigate the class of mappings f: X→ X, where X is a Banach space, for which one of the main conditions in the metric fixed point theory, namely the condition (1), is satisfied. We obtain essential applications of this fact. All our results are illustrated by suitable examples. This revised version was published online in June 2006 with corrections to the Cover Date.     

Edgeworth Expansion of Densities of Order Statistics with Fixed Rank

We give an Edgeworth expansion for densities of order statistics with fixed rank k.The Edgeworth expansion for densities of extreme values is then obtained as a special case k=1.     

A non-conforming finite element method with anisotropic mesh grading for the Stokes problem in domains with edges

The solution of the Stokes problem in three-dimensional domainswith edges has anisotropic singular behaviour which is treatednumerically by using anisotropic finite element meshes. Thevelocity is approximated by Crouzeix–Raviart (nonconformingP₁ ) elements and the pressure by piecewise constants. Thismethod is stable for general meshes (without minimal or maximalangle condition). Denoting by N_e the number of elements in themesh, the interpolation and consistency errors are of the optimalorder h N_e^–1/3 which is proved for tensor product meshes.As a by-product, we analyse also nonconforming prismatic elementswith P₁ [oplus ] span {x₃²} as the local space for the velocitywhere x₃ is the direction of the edge.