The elementary diagram of a trivial,weakly minimal structure is near model complete

We prove that if M is any model of a trivial, weakly minimal theory, then the elementary diagram T(M) eliminates quantifiers down to Boolean combinations of certain existential formulas. M. C. Laskowski has been partially supported by NSF grant DMS-0600217.     

Semifree actions of free groups

We study countable universes similar to a free action of a group G. It turns out that this is equivalent to the study of free semi-actions of G, with two universes being transformable iff one corresponding free semi-action can be obtained from the other by a finite alteration. In the case of a free group G (in finitely many or countably many generators), a classification is given. Research partially supported by a DAAD Doktorandenstipendium D/02/02345.     

Non-Axiomatizability of the amalgamation class of modular lattice varieties

We prove that if v is the variety generated by a finite modular lattice, then v is not an elementary class. We also consider the same question for the variety generated by N ₅.Research partially supported by National Science Foundation grant DMS-8701643.     

On the distribution of imaginary parts of zeros of the Riemann zeta function,II

We continue our investigation of the distribution of the fractional parts of αγ, where α is a fixed non-zero real number and γ runs over the imaginary parts of the non-trivial zeros of the Riemann zeta function. We establish some connections to Montgomery’s pair correlation function and the distribution of primes in short intervals. We also discuss analogous results for a more general L-function. The first author is supported by National Science Foundation Grant DMS-0555367. The second author is partially supported by the National Science Foundation and the American Institute of Mathematics (AIM). The third author is supported by National Science Foundation Grant DMS-0456615.     

A Generalization of the Hutchinson Measure

The Hutchinson measure is the invariant measure associated with an iterated function system with probabilities. Generalized iterated function systems (GIFS) are generalizations of iterated function systems which are obtained by considering contractions from X × X to X, rather than contractions from a metric space X to itself. Along the lines of this generalization we consider GIFS with probabilities. In this paper we prove the existence of an analogue of Hutchinson measure associated with a GIFS with probabilities and present some of its properties. The work was supported by CNCSIS grant 8A;1067/2006.     

Bounded characteristic functions and models for noncontractive sequences of operators

The Sz.-Nagy-FoiaŞ functional model for completely non-unitary contractions is extended to completely non-coisometric sequences of bounded operatorsT = (T₁,...,T _d) (d finite or infinite) on a Hilbert space, with bounded characteristic functions. For this class of sequences, it is shown that the characteristic function θ_T is a complete unitary invariant. We obtain, as the main result, necessary and sufficient conditions for a bounded multi-analytic operator on Fock spaces to coincide with the characteristic function associated with a completely non-coisometric sequence of bounded operators on a Hilbert space. Research supported in part by a COBASE grant from the National Research Council. The first author was partially supported by a grant from Ministerul Educaţiei Şi Cercetarii. The second author was partially supported by a National Science Foundation grant.     

On the first homology of automorphism groups of manifolds with geometric structures

Hermann and Thurston proved that the group of diffeomorphisms with compact support of a smooth manifold M which are isotopic to the identity is a perfect group. We consider the case where M has a geometric structure. In this paper we shall survey on the recent results of the first homology of the diffeomorphism groups which preserve a smooth G-action or a foliated structure on M. We also work in Lipschitz category. This research was partially supported by Grant-in-Aid for Scientific Research (No. 16540058), Japan Society for the Promotion of Science. This research was partially supported by Grant-in-Aid for Scientific Research (No. 14540093), Japan Society for the Promotion of Science.     

Typical convex program is very well posed

In this paper we consider the collection of convex programming problems with inequality and equality constraints, in which every problem of the collection is obtained by linear perturbations of the cost function and right-hand side perturbation of the constraints, while the ``core' cost function and the left-hand side constraint functions are kept fixed. The main result shows that the set of the problems which are not well-posed is σ-porous in a certain strong sense. Our results concern both the infinite and finite dimensional case. In the last case the conclusions are significantly sharper. Research of A. Ioffe was supported in part by the US-Israel Binational Fund under the grant 2000157. research of R. E. Lucchetti was partially supported by Ministero dell'Istruzione, dell'Università e della Ricerca (COFIN 2001).     

Vectorization hierarchies of some graph quantifiers

We give a sufficient condition for the inexpressibility of the k-th extended vectorization of a generalized quantifier in , the extension of first-order logic by all k-ary quantifiers. The condition is based on a model construction which, given two -equivalent models with certain additional structure, yields a pair of -equivalent models. We also consider some applications of this condition to quantifiers that correspond to graph properties, such as connectivity and planarity. Received: 15 October 1996     

Multipeak solutions for some singularly perturbed nonlinear elliptic problems on Riemannian manifolds

Given (M, g) a smooth compact Riemannian N-manifold, we prove that for any fixed positive integer K the problem

A theory of recursive dimension for ordered sets

The classical theorem of R. P. Dilworth asserts that a partially ordered set of width n can be partitioned into n chains. Dilworth's theorem plays a central role in the dimension theory of partially ordered sets since chain partitions can be used to provide embeddings of partially ordered sets in the Cartesian product of chains. In particular, the dimension of a partially-ordered set never exceeds its width. In this paper, we consider analogous problems in the setting of recursive combinatorics where it is required that the partially ordered set and any associated partition or embedding be described by recursive functions. We establish several theorems providing upper bounds on the recursive dimension of a partially ordered set in terms of its width. The proofs are highly combinatorial in nature and involve a detailed analysis of a 2-person game in which one person builds a partially ordered set one point at a time and the other builds the partition or embedding.This paper was prepared while the authors were supported, in part, by NSF grant ISP-80-11451. In addition, the second author received support under NSF grant MCS-80-01778 and the third author received support under NSF grant MCS-82-02172.     

An Existential Divisibility Lemma for Global Fields

We generalize the Existential Divisibility Lemma by Th. Pheidas [7] to all global fields K of characteristic not 2, and for all sets of primes that are inert in a quadratic extension L of K. We also remove the conditions in real and ramifying primes, which were present in Pheidas’ version. As a Corollary, we recover the known fact that the set of integral elements at a prime in a global field is existentially definable. The first author is a Research Assistant of the Research Foundation – Flanders (FWO – Vlaanderen). Work partially supported by the European Community’s Human Potential Programme under contract HPRN-CT-2002-00287.     

Exponential attractors for a class of reaction-diffusion problems with time delays

We consider a reaction-diffusion system subject to homogeneous Neumann boundary conditions on a given bounded domain. The reaction term depends on the population densities as well as on their past histories in a very general way. This class of systems is widely used in population dynamics modelling. Due to its generality, the longtime behavior of the solutions can display a certain complexity. Here we prove a qualitative result which can be considered as a common denominator of a large family of specific models. More precisely, we demonstrate the existence of an exponential attractor, provided that a bounded invariant region exists and the past history decays exponentially fast. This result will be achieved by means of a suitable adaptation of the l-trajectory method coming back to the seminal paper of Málek and Nečas. The first author was partially supported by the Italian PRIN 2006 research project Problemi a frontiera libera, transizioni di fase e modelli di isteresi. The second author was supported by the research project MŠM 0021620839 and by the project LC06052 (Jindřich Nečas Center for Mathematical Modeling).     

Imaginaries in Boolean algebras

Given an infinite Boolean algebra B, we find a natural class of $\varnothing$‐definable equivalence relations $\mathcal {E}_{B}$ such that every imaginary element from B^eq is interdefinable with an element from a sort determined by some equivalence relation from $\mathcal {E}_{B}$. It follows that B together with the family of sorts determined by $\mathcal {E}_{B}$ admits elimination of imaginaries in a suitable multisorted language. The paper generalizes author's earlier results concerning definable equivalence relations and weak elimination of imaginaries for Boolean algebras, obtained in 10 .     

Boundary Harnack Principle for <Emphasis Type="Italic">p</Emphasis>-harmonic Functions in Smooth Euclidean Domains

We establish a scale-invariant version of the boundary Harnack principle for p-harmonic functions in Euclidean C ^1,1-domains and obtain estimates for the decay rates of positive p-harmonic functions vanishing on a segment of the boundary in terms of the distance to the boundary. We use these estimates to study the behavior of conformal Martin kernel functions and positive p-superharmonic functions near the boundary of the domain. H. A. was partially supported by Grant-in-Aid for (B) (2) (No. 15340046) Japan Society for the Promotion of Science. N. S. was partially supported by NSF grant DMS-0355027. X. Z. was partially supported by the Taft foundation.     

Motives of some Fano varieties

We study the Fano varieties of projective k-planes lying in hypersurfaces and investigate the associated motives. The first author is partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada. The second author is partially supported by TüBİTAK-BDP funds and Bilkent University research development funds.     

Global existence and exponential stability for the micropolar fluid system

We consider the micropolar fluid system in a bounded domain of

Topological André-Quillen homology for cellular commutative S-algebras

Topological André-Quillen homology for commutative S-algebras was introduced by Basterra following work of Kriz, and has been intensively studied by several authors. In this paper we discuss it as a homology theory on CW commutative S-algebras and apply it to obtain results on minimal atomic p-local S-algebras which generalise those of Baker and May for p-local spectra and simply connected spaces. We exhibit some new examples of minimal atomic commutative S-algebras. A. Baker was partially supported by a YFF Norwegian Research Council grant while at the University of Oslo in 2007–8, a Carnegie Trust for the Universities of Scotland grant, and Intas grants 03-51-3251 and 06-1000017-8609. H. Gilmour was supported by an EPSRC studentship. P. Reinhard was supported by an ORS grant. We would like to thank M. Basterra, P. Kropholler, M. Mandell, P. May, B. Richter, J. Rognes and S. Sagave for numerous helpful comments. We are also very grateful to the referee for encouraging us to rethink significantly issues of notation and structure, thus improving the structure of the paper.     

Compactification and maximal diameter theorem for noncompact manifolds with radial curvature bounded below

Let M be a complete open n-manifold with a base point p, at which the radial sectional curvature along every minimizing geodesic emanating from p is bounded below by the radial curvature function of a model surface. We discuss the maximal diameter theorem for the compactification of M by attaching the ideal boundary. Under certain conditions we prove that p becomes a pole and that M is isometric to the n-model. Received: 24 September 2000; in final form: 21 November 2001 / Published online: 17 June 2002 Dedicated to Professor Su Bu-Chin on the occasion of his one hundredth birthday The work of the first author was partially supported by the Grant-in-Aid for Scientific Research, No. 12440021 and for Exploratory Research, No. 13874012     

On integrability in the LIL for degenerateU-statistics

It is shown by example that square integrability of the kennelh of a completely degenerateU-statistic is not a necessary condition for the law of the iterated logarithm to hold. Necessary integrability conditions are given onh which are in a sense the strongest possible. Sufficient conditions for a degenerateU-statistic of order 2 to satisfy the LIL, weaker than square integrability of the kernel, are also given.Research partially supported by NSF Grant No. DMS-93-00725. Part of this author's work was done at the University of Bielefeld, supported by the Deutsche Forschungsgemeinshaft, Sonderforschungbereich 343, Diskrete Structuren in der Mathematik.Research partially supported by the Army Research Office and the National Security Agency.