Matrices of completely Ramsey sets with infinitely many rows

The main result of the present article is the following: Let N be an infinite subset of , , and let be a matrix with infinitely many rows of completely Ramsey subsets of such that for every n, . Then there exist , a sequence of nonempty finite subsets of N, and an infinite subset T of such that for every infinite subset I of . We also give an application of this result to partitions of an uncountable analytic subset of a Polish space X into sets belonging to the σ‐algebra generated by the analytic subsets of X.     

Existence of infinitely many homoclinic orbits to Aubry sets for positive definite Lagrangian systems

In this paper, we study the problem of homoclinic orbits to Aubry sets for time-periodic positive definite Lagrangian systems. We show that there are infinitely many homoclinic orbits to some Aubry set under the conditions that the associated Mather set is uniquely ergodic and the first relative homology group of the projection of this Aubry set is nonzero.     

Toda flows with infinitely many variables

The Toda flow and related flows extend naturally to operators in Hilbert space and the purpose of this paper is to describe these flows and to analyse some of their special properties.     

Integrodifferential systems with infinitely many delays

Summary In this paper we consider the initial-value problems: (P ₁ )X(t)=(AX)(t) for t>0, X(0+)=I, X(t)=0 for t<0 and (P ₂ ) Y(t)=(QY)(t) for t>0, Y(0+)=I, Y(t)=0 for t<0, where A and Q are linear specified operators, I and0 — the identity and null matrices of order n, and X(t), Y(t) are unknown functions whose values are square matrices of order n. Sufficient conditions are established under which the problems (P ₁ ) and (P ₂ ) have the same unique solution, locally summable on the half-axis t ⩾0. Using this fact and some properties of the Laplace transform we find a new proof for the variation of constants formula given in[1, 2]. On the basis of this formula we derive certain results concerning a class of integrodifferential systems with infinite delay. Entrata in Redazione il 2 marzo 1977.     

Vector bundles with infinitely many souls

We construct the first examples of manifolds, the simplest one being , which admit infinitely many complete nonnegatively curved metrics with pairwise nonhomeomorphic souls.

     

Markets with countably infinitely many traders

In this paper we will show how to construct, in a canonical way, a continuous economy in the sense of R. J. Aumann [1]. This construction is based on W. Hildenbrand's [3] definition of “pure competition” for an exchange economy with countably infinitely many participants.     

Uniform subsmoothness and linear regularity for a collection of infinitely many closed sets

Motivated by the subsmoothness of a closed set introduced by Aussel et al. (2005) [8], we introduce and study the uniform subsmoothness of a collection of infinitely many closed subsets in a Banach space. Under the uniform subsmoothness assumption, we provide an interesting subdifferential formula on distance functions and consider uniform metric regularity for a kind of multifunctions frequently appearing in optimization and variational analysis. Different from the existing works, without the restriction of convexity, we consider several fundamental notions in optimization such as the linear regularity, CHIP, strong CHIP and property (G) for a collection of infinitely many closed sets. We establish relationships among these fundamental notions for an arbitrary collection of uniformly subsmooth closed sets. In particular, we extend duality characterizations of the linear regularity for a collection of closed convex sets to the nonconvex setting.     

Affine curves with infinitely many integral points

Let be an irreducible affine curve of (geometric) genus 0 defined by a finite family of polynomials having integer coefficients. In this note we give a necessary and sufficient condition for to possess infinitely many integer points, correcting a statement of J. H. Silverman (Theoret. Comput. Sci., 2000).

     

Risk-neutral valuation with infinitely many trading dates

The first Fundamental Theorem of Asset Pricing establishes the equivalence between the absence of arbitrage in financial markets and the existence of Equivalent Martingale Measures, if appropriate conditions hold. Since the theorem may fail when dealing with infinitely many trading dates, this paper draws on the A.A. Lyapunov Theorem in order to retrieve the equivalence for complete markets such that the Sharpe Ratio is adequately bounded.     

Three-bridge links with infinitely many three-bridge spheres

We construct infinitely many three-bridge links each of which admits infinitely many three-bridge spheres up to isotopy.     

On minimizing partitions with infinitely many components

It is known [8] that, wheng ∈L ⁿ (Ω) (Ω open and bounded inR ⁿ , with ≪regular≫ boundary∂Ω), any minimizer (K, w) of the functional among relatively closed subsetsC ofΩ and piecewise-constant functionsu onΩ/C, gives rise to a finite decomposition ofΩ/K. Here we exhibit a piecewise-constant functiong on the unit diskD ofR ², with radial symmetry, such thatg ∈L ^q (D) for all 1 ⩽q < 2 and the unique minimizer of F has infinitely many components. We also fill a gap occurred in the proof of Proposition 5.2 of [8].

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Sunto è noto [8] che quandog ∈L ⁿ (Ω (Ω aperto limitato diR ⁿ , con frontiera sufficientemente regolare) i minimi (K, w) del funzionale , doveC è relativamente chiuso in Ω eu è costante a tratti suΩ/C, danno luogo a decomposizioni finite diΩ/K. In questo lavoro mostriamo un controesempio relativo ad un datog ∈L ^q (D) per ogni 1 ⩽q < 2 (D è il disco unitario diR ²), a simmetria radiale e costante a tratti. Viene inoltre corretto un errore occorso nella dimostrazione della Prop. 5.2 di [8].

     

Quasi-isometries between groups with infinitely many ends

Let G, F be finitely generated groups with infinitely many ends and let? be graph of groups decompositions of F, G such that all edge groups are finite and all vertex groups have at most one end. We show that G, F are quasi-isometric if and only if every one-ended vertex group of is quasi-isometric to some one-ended vertex group of and every one-ended vertex group of is quasi-isometric to some one-ended vertex group of?. From our proof it also follows that if G is any finitely generated group, of order at least three, the groups: and are all quasi-isometric. Received: April 7, 2000; revised version: October 6, 2000     

On polling systems with infinitely many stations

The research was financially supported in part by the International Science Foundation (Grant NR8300) and the INTAS (Grant 93-820).