Complex whitham deformations in problems with “integrable instability”

The focusing nonlinear Schrödinger equation with finite-density boundary conditions as |x| is considered. The asymptotic behavior of the solution ast is investigated by means of the complex theory of deformations of Whitham.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 3, pp. 393–419, September, 1995.     

On the Cohomology Sequence in a Semiabelian Category

In a semiabelian category, a strictly exact sequence 0ABC0 of cochain complexes gives rise to the cohomology sequence ...H ⁿ(A) H ⁿ(B) H ⁿ(C) H ⁿ⁺¹ (A) .... We study conditions for exactness of the homology sequence at a given term.     

On Galois representations arising from towers of coverings of P1\{0, 1, ∞}

Summary We propose a new way to describe, universally, thel-adic Galois representations associated to each almost pro-l tower of etale coverings ofP ¹\{0, 1, }. This generalizes our universal power series for Jacobi sums (cf. [I]) which arises from the tower of Fermat curves of degreel ⁿ (n), and contains the case of the tower of modular curves of level 2ml ⁿ (m: fixed,n) as another important special case. As a fundamental tool, we shall establish and use an almost pro-l version of the theorems of Blanchfield and of Lyndon in Fox free differential calculus.     

The Flooding Time in Random Graphs

Based on our analysis of the hopcount of the shortest path between two arbitrary nodes in the class G _p (N) of random graphs, the corresponding flooding time is investigated. The flooding time T _N (p) is the minimum time needed to reach all other nodes from one node. We show that, after scaling, the flooding time T _N (p) converges in distribution to the two-fold convolution ^(2*) of the Gumbel distribution function (z)=exp (–e ^–z ), when the link density p _N satisfies Np _N /(log N)³ if N .     

Surjectivity for Hamiltonian loop group spaces

Let G be a compact Lie group, and let LG denote the corresponding loop group. Let (X,) be a weakly symplectic Banach manifold. Consider a Hamiltonian action of LG on (X,), and assume that the moment map :XL ^* is proper. We consider the function ||²:X, and use a version of Morse theory to show that the inclusion map j:^-1(0)X induces a surjection j ^*:H _G ^*(X)H _G ^*(^-1(0)), in analogy with Kirwans surjectivity theorem in the finite-dimensional case. We also prove a version of this surjectivity theorem for quasi-Hamiltonian G-spaces.     

Infinitely divisible completely positive mappings

Summary We generalise the theory of infinitely divisible positive definite functions f:G on a group G to a theory of infinite divisibility for completely positive mappings : G() taking values in the algebra of bounded operators on some Hilbert space .We prove a structure theorem for normalised infinitely divisible completely positive mappings which shows that the mapping , its Stinespring representation and its Stinespring isometry are of type S (in the sense of Guichardet [Gui]). Furthermore, we prove that a completely positive mapping is infinitely divisible if and only if it is the exponential (as defined in this paper) of a hermitian conditionally completely positive mapping.     

The survival of the large dimensional basic contact process

Summary We consider the d-dimensional basic contact process obtaining the limit value of the probability of survival when d+, and showing that the finite dimensional distributions of the upper invariant measure become of the product form as d+.     

Nielsensche Realisierungssätze für Seifertfaserungen

Let M be a closed aspherical manifold and A a finite subgroup of the outer automorphism group Out ₁M of ₁M. A necessary (and in many cases also sufficient) condition for realising A by the induced action of an isomorphic group of homeomorphisms of M is the existence of an extension 1₁MEA1 to the abstract kernel (A,₁M, AOut ₁M). If the center of ₁M is nontrivial, this condition need not be fulfilled ([14]). We showed in [25] however that one can always find a surjection BA of a finite group B with abelian kernel such that there exists an extension to the abstract kernel (B,₁M,BAOut₁M), and one can try to realize B instead of A. The main result of the present paper is a characterisation of all such groups B (for a given A) which can be realized by a group of homeomorphisms. The class of manifolds considered here consists of certain Seifert fiber spaces in arbitrary dimensions but the main result is purely algebraic and can be applied to other classes of manifolds, for example to flat Riemannian manifolds.     

Liftungen von Tripeln

For triplesS andT in a categoryOl, J. Beck [1] has shown the equiva-lence of a distributive law 1:TSST with a lifting ofT into the category ofS-algebras. Now in this paper it is proved that such a di-ributive law is also equivalent with a lifting of S into the T-Kleisli-category. Distributive laws of mixed type are also considered. Each of the distributive laws GTTG and TGGT (with T a triple and G a cotriple inOl) produces a pair of dual liftings.     

The functional equation of multiplicative derivation is superstable on standard operator algebras

LetX be a real or complex infinite dimensional Banach space andA a standard operator algebra onX. Denote byB(X) the algebra of all bounded linear operators onX. Let : _{+ +} be a function with the property lim _t (t)t ^–1=0. Assume that a mappingD:A B(X) satisfies D(AB)–AD(B)–D(A)B<(A B) for all operatorsA, B D (no linearity or continuity ofD is assumed). ThenD is of the formD(A)=AT–TA for someTB(X).This work was supported by the Research Council of Slovenia     

Lower functions for asymmetric Lévy processes

Summary Let {X _t } be a ¹ process with stationary independent increments and its Lévy measurev be given byv{yy>x}=x ^–L ₁ (x), v{yy<–x}=x ^–L ₂ (x) whereL ₁,L ₂ are slowly varying at 0 and and 0<1. We construct two types of a nondecreasing functionh(t) depending on 0<<1 or =1 such that lim inf a.s. ast 0 andt for some positive finite constantC.This research is partialy supported by a grant from Korea University     

Rates of convergence and optimal spectral bandwidth for long range dependence

Summary For a realization of lengthn from a covariance stationary discrete time process with spectral density which behaves like ^1–2H as 0+ for 1/2<H<1 (apart from a slowly varying factor which may be of unknown form), we consider a discrete average of the periodogram across the frequencies 2j/n,j=1,..., m, wherem andm/n0 asn. We study the rate of convergence of an analogue of the mean squared error of smooth spectral density estimates, and deduce an optimal choice ofm.     

K-Theory of the Commutator Ideal

We consider for unital c ^*-algebras the short exact sequence 0 I A * _C B A _max B 0and give an explicit formula for the boundary map for separable C ^*-algebras for which the Künneth formula for tensor products holds without Tor-terms. In the course of the article, we study the similar case of an ideal concerning one-relator groups.     

Isolated points in duals of certain locally compact groups

Summary LetG be a separable locally compact group with dual space. consists of all equivalence classes of irreducible unitary representations ofG, and is endowed with the Fell-topology. We study the topological properties in of the square-integrable representations ofG. [ is square-integrable provided there is a coordinate functiong((g)v, v),gG, for which is inL ²(G) w.r.t. left Haar measure onG.]SupposeG contains an open normal subgroupN of the formeKN ⁿ e whereK is compact. (All groups with a compact invariant neighborhood of the identity, [IN] groups, satisfy this condition.) In this case we show that if is square-integrable then {} is an open point of.Finally, our techniques are used to prove this result for arbitrary (non connected) nilpotent Lie groups.     

Partially ordered permutation groups

In this note we discuss permutation groups (G, ) in which the set admits aG-invariant order. By aG-invariant partial order (G-partial order) we mean a partial order < of such that < implies g<g, for all and in andg inG. If the set admits aG-partial order which is a total order, then (G, ) is an O-permutation group (orderable permutation group).The main concern of this paper is the development of a foundation for partially ordered permutation groups analogous to the existing one for partially ordered groups, as found in Fuchs [2].     

On the two-gap elliptic potentials

The-parametrized family of two-gap elliptic potentials is constructed so that (i) 0<<1, (ii) for rational values of such potentials are elliptic (i.e., double-periodic), (iii) within the limit0 this family degenerates to the soliton potential, (iv) within the limit1 this family degenerates to the one-gap Lamé potential.Dedicated to the memory of J.-L. Verdier     

The size Ramsey number

Let denote the class of all graphsG which satisfyG(G ₁,G ₂). As a way of measuring minimality for members of, we define thesize Ramsey number (G ₁,G ₂) by.We then investigate various questions concerned with the asymptotic behaviour of.     

The probability of generating a finite simple group

We show that two random elements of a finite simple groupG generateG with probability 1 as |G| . This settles a conjecture of Dixon.     

Ultrafilters and Decompositions of Abelian Groups

We prove that every PS-ultrafilter on a group without second-order elements is a Ramsey ultrafilter. For an arbitrary PS-ultrafilter on a countable group G, we construct a mapping f: G such that f() is a P-point in the space *. We determine a new class of subselective ultrafilters, which is considerably wider than the class of PS-ultrafilters.