Game sentences and ultrapowers

We prove that if is a model of size at most [kappa], λ^[kappa] = λ, and a game sentence of length 2^λ is true in a 2^λ-saturated model ≡ , then player has a winning strategy for a related game in some ultrapower Π_D of . The moves in the new game are taken in the cartesian power ^λA, and the ultrafilter D over λ must be chosen after the game is played. By taking advantage of the expressive power of game sentences, we obtain several applications showing the existence of ultrapowers with certain properties. In each case, it was previously known that such ultrapowers exist under the assumption of the GCH, and we get them without the GCH.     

Banach ultrapowers and multivalued nonexpansive mappings

The Banach ultrapower construction is applied in fixed point theory for multivalued mappings. We introduce the notion of ultra-asymptotic centers and use it to remove the separability assumption from the results of Domínguez Benavides, Lorenzo Ramírez (2004) and Dhompongsa, Kaewcharoen, Kaewkhao (2006).     

Normed lattices with discrete ultrapowers

The paper is devoted to investigations of the order structure of ultrapowers. A characterization of discrete normed lattices, all of whose ultrapowers are discrete, is presented (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

迭代Brown运动的一个Chung型重对数律

X及Y分别为Rd1及Rd2中的相互独立的标准Brown运动,满足X（0）=Y（0）=0．定义,称为一个迭代Brown运动．本文给出了关于Zd1,d2的一个Chung型重对数律．     

Iterated Galerkin versus Iterated Collocation for Integral Equations of the Second Kind

We consider the numerical solution of one-dimensional Fredholmintegral equations of the second kind by the Galerkin and collocationmethods and their iterated variants, using spline bases. Inparticular, we state and prove new superconvergence resultsfor the iterated solutions, under general smoothness requirementson the kernel and solution. We find that the smoothness requirementsfor the iterated collocation method are more stringent thanthose for the iterated Galerkin method, and show by examplethat these more stringent smoothness conditions are in a certainsense necessary. In the light of these results the Galerkinand collocation schernes are compared.     

Iterated greedy for the maximum diversity problem

The problem of choosing a subset of elements with maximum diversity from a given set is known as the maximum diversity problem. Many algorithms and methods have been proposed for this hard combinatorial problem, including several highly sophisticated procedures. By contrast, in this paper we present a simple iterated greedy metaheuristic that generates a sequence of solutions by iterating over a greedy construction heuristic using destruction and construction phases. Extensive computational experiments reveal that the proposed algorithm is highly effective as compared to the best-so-far metaheuristics for the problem under consideration.     

Generalized Prikry forcing and iteration of generic ultrapowers

It is known that there is a close relation between Prikry forcing and the iteration of ultrapowers: If U is a normal ultrafilter on a measurable cardinal κ and 〈M_n, j_m,n | m ≤ n ≤ ω〉 is the iteration of ultrapowers of V by U, then the sequence of critical points 〈j_0,n(κ) | n ∈ ω〉 is a Prikry generic sequence over M_ω. In this paper we generalize this for normal precipitous filters. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structure of ultrapowers on abelian groups over ω

Translated from Matematicheskie Zametki, Vol. 51, No. 2, pp. 40–45, February, 1992.     

Every two elementarily equivalent models have isomorphic ultrapowers

We prove (without G.C.H.) that every two elementarily equivalent models have isomorphic ultrapowers, and some related results. The preparation of this paper was supported in Part by NSF Grant GP-22937.     

几类微分方程解的迭代增长级数与零点迭代收敛指数

本文研究了几类微分方程解的迭代增长级及零点迭代收敛指数．     

Iterated tabu search for the car sequencing problem

This paper introduces an iterated tabu search heuristic for the daily car sequencing problem in which a set of cars must be sequenced so as to satisfy requirements from the paint shop and the assembly line. The iterated tabu search heuristic combines a classical tabu search with perturbation operators that help escape from local optima. The resulting heuristic is flexible, easy to implement, and fast. It has produced very good results on a set of test instances provided by the French car manufacturer Renault.     

Iterated local search for the quadratic assignment problem

Iterated local search (ILS) is a simple and powerful stochastic local search method. This article presents and analyzes the application of ILS to the quadratic assignment problem (QAP). We justify the potential usefulness of an ILS approach to this problem by an analysis of the QAP search space. However, an analysis of the run-time behavior of a basic ILS algorithm reveals a stagnation behavior which strongly compromises its performance. To avoid this stagnation behavior, we enhance the ILS algorithm using acceptance criteria that allow moves to worse local optima and we propose population-based ILS extensions. An experimental evaluation of the enhanced ILS algorithms shows their excellent performance when compared to other state-of-the-art algorithms for the QAP.     

Iterated homotopy fixed points for the Lubin-Tate spectrum

When G is a profinite group and H and K are closed subgroups, with H normal in K, it is not known, in general, how to form the iterated homotopy fixed point spectrum (ZhH)^hK/H, where Z is a continuous G-spectrum and all group actions are to be continuous. However, we show that, if G=Gn, the extended Morava stabilizer group, and , where is Bousfield localization with respect to Morava K-theory, En is the Lubin-Tate spectrum, and X is any spectrum with trivial Gn-action, then the iterated homotopy fixed point spectrum can always be constructed. Also, we show that is just , extending a result of Devinatz and Hopkins.