We study the Lov¶ asz extension b v for cooperative games v by using the marginal worth vectors and the dividends. First, we prove that the marginal worth vector aC with respect to an x-compatible ordering C satis ̄es, for supermodular games, b v(x) = min fhx; yi : y 2 Core(v)g = ­x; aC® : Next, we obtain the following characterization of the utility function of a market game: The utility functi...

We introduce a new inductive approach to the lace expansion and apply it to prove Gaussian behaviour for the weakly self avoiding walk on Zd where loops of length m are penalised by a factor e m p when d p d p d In particular we derive results rst obtained by Brydges and Spencer and revisited by other authors for the case d p In addition we prove a local central limit theorem with the exception...

Fixes are presented for the solution errors (`pressure oscillations') that may occur near twouid interfaces when applying a capturing method. The xes are analyzed and tested. For twouid ows with arbitrarily large density ratios, a variant of the ghostuid method appears to be a perfect remedy. Results are presented for compressible water-air ows. The results are promising for a further elaborati...

Iterative methods for nite-dimensional inclusions which arise in applying a nite-element or a nite-di erence method to approximate state-constrained optimal control problems have been investigated. Speci cally, problems of control on the righthand side of linear elliptic boundary value problems and observation in the entire domain have been considered. The convergence and the rate of convergenc...

It is well known that if D is a bounded derivation on a Banach algebra A and if s is an element of A satisfying [s; Ds] = 0 then Ds must be quasinilpotent. The unbounded Kleinecke-Shirokov conjecture states that the same result holds even if D is unbounded. As yet, the conjecture has neither been proved nor has a case been found where it fails. If there is a counterexample we obtain a further r...

In this paper we extend the niteness result on the p-primary torsion subgroup in the Chow group of zero cycles on the selfproduct of a semistable elliptic curve obtained in joint work with S. Saito to primes p dividing the conductor. On the way we show the niteness of the Selmer group associated to the symmetric square of the elliptic curve for those primes. The proof uses p-adic techniques, in...

Let f denotes the space of almost convergent sequences, and f̂ also be the domain of the generalized di erence matrix B(r, s) in the sequence space f . The present paper is devoted to studing on the sequence spaces f̂ and f̂ s. Furthermore, the βand γ-duals of the space f̂ are determined. Finally, the classes (f̂ : μ) and (μ : f̂) of in nite matrices are characterized and the characterizations of som...

We study some classes of generalized convex functions, using a generalized di¤erential approach. By this we mean a set-valued mapping which stands either for a derivative, a subdi¤erential or a pseudodi¤erential in the sense of Jeyakumar and Luc. We establish some links between the corresponding classes of pseudoconvex, quasiconvex and another class of generalized convex functions we introduced...

In this paper we investigate the compressible Navier-Stokes-Cahn-Hilliard equations (the so-called NSCH model) derived by Lowengrub and Truskinowsky. This model describes the ow of a binary compressible mixture; the uids are supposed to be macroscopically immiscible, but partial mixing is permitted leading to narrow transition layers. The internal structure and macroscopic dynamics of these lay...

The use of interval judgment in the analytical hierarchy process, called Interval Analytic Hierarchy Process (IAHP), has begun to grow in many decision making environments, providing an e ective means of modeling the presence of uncertainty in a decision makers judgment or representing comparisons in group decision making. Linear programming method can be used for generating weights in that sit...