Recurrence of sums of multiple markov sequences

Ad-dimensional random walk on a lattice is studied in which each step is bounded, and may depend on the previousm steps. It is proved that if trivial cases are excluded, there are no recurrent points ford≧3, and conditions are given for the existence of sets, recurrent conditional on the firstm steps, ford=1, 2.     

Naturally ordered transformation semigroups

The full transformation semigroup (T _x o) on the setX is studied with respect to the natural partial order which is defined on any regular semigruop. A characterization of this ordering in terms of images and kernels is given, the maximal and minimal elements are determined and the covering elements are described. Lower and upper bounds for two transformations are studied and necessary as well as sufficient conditions for their existence are gieven.     

Multistability of neural networks with discontinuous activation function

In this paper, the multistability is studied for two-dimensional neural networks with multilevel activation functions. And it is showed that the system has n² isolated equilibrium points which are locally exponentially stable, where the activation function has n segments. Furthermore, evoked by periodic external input, n² periodic orbits which are locally exponentially attractive, can be found. And these results are extended to k-neuron networks, which is really enlarge the capacity of the associative memories. Examples and simulation results are used to illustrate the theory.     

The connected components of the closed support of super Brownian motion

Summary The closed support of super Brownian motion inR ^d is studied. It is shown that at a fixed timet>0 the mass of the process is located in connected components which are single points.     

Meromorphic Factorization Revisited and Application to Some Groups of Matrix Functions

Some properties and applications of meromorphic factorization of matrix functions are studied. It is shown that a meromorphic factorization of a matrix function G allows one to characterize the kernel of the Toeplitz operator with symbol G without actually having to previously obtain a Wiener–Hopf factorization. A method to turn a meromorphic factorization into a Wiener–Hopf one which avoids having to factorize a rational matrix that appears, in general, when each meromorphic factor is treated separately, is also presented. The results are applied to some classes of matrix functions for which the existence of a canonical factorization is studied and the factors of a Wiener–Hopf factorization are explicitly determined. Submitted: April 15, 2007. Revised: October 26, 2007. Accepted: December 12, 2007.     

An Analog of the Milnor Group of a Link in the Higher-Dimensional Link Theory

Singular links consisting of several k-spheres and a p-sphere in the (2k+1)-sphere are studied. For k>1, a theory of such singular links is constructed, which is parallel to J. Milnor's theory of one-dimensional links. Bibliography: 14 titles.     

Totally Permutable Products of Finite Groups Satisfying SC or PST

Finite groups G=AB factorized by two subgroups A and B such that every subgroup of A permutes with every subgroup of B are studied in this paper. The behaviour of such products with respect to the class of finite groups in which Sylow-permutability is transitive is analyzed.     

On averaging of rearrangement invariant ideals of the space L<Superscript>1</Superscript> (Ω, Σ, μ) by non-atomic <Emphasis Type="Italic">σ</Emphasis>-subalgebras of Σ

The problem of averaging = into mapping) is studied for conditional expectation operators which are considered on rearrangement invariant order ideals of measurable functions given on non-atomic probability supports.     

Special conformal mappings in the general theory of relativity

Some special conformal mappings of relativistic spaces are studied. The amount of arbitrariness with which one can describe a nontrivial special conformai mapping is determined. Necessary and sufficient conditions are found under which a space-timeV admits a special conformal mapping to space-time ¯V in which the metric tensor of bothV and ¯V satisfy the Einstein equations with the energy-momentum tensor of an ideal fluid having a geodesic velocity field.It is proved that such spaces are spaces of standard cosmological models.Translated from Ukrainskií Geometricheskií Sbornik, Issue 28, 1985, pp. 43–50.     

The dynamics of marginal equilibria

Suppose F is a real-valued function defined on ^m. The dynamics of the system which is obtained by minimizing F by one (real) component at a time is studied. Two distinct cases arise depending upon whether F is C¹ or not. Thus when F ε C², the dynamical system obtained may be studied in terms of iterations of a C² local diffeomorphism. In particular when F is a Morse function, the system will converge to a minimum of F. However, when F is not C¹, but convex and suitably approximable, then the system exhibits a notion of turbulence which leads to orbits terminating at trapping points. These are not minima of F but are fixed points of the system.     

Quasivarieties of distributivep-algebras

A counterexample is given to show that not all quasivarieties of distributivep-algebra lie between two consecutive varieties. It is shown that there are no strict relatively congruence distributive quasivarieties of distributivep-algebras. The relative congruence extension property in the class of distributivep-algebras is studied. It is proved that only quasivarieties which are varieties possess this property.Presented by J. Berman.This research is part of the author's dissertation done at Iowa State University under the supervision of Dr. Clifford Bergman.     

q-analogs of harmonic oscillators and related rings

A ringH _q which is aq-analog of the universal enveloping algebra of the Heisenberg Lie algebraU(h) is constructed, and its ring theoretic properties are studied. It is shown thatH _q has a factor ringA _q which is a simple domain with properties that are compared to the Weyl algebra. A secondq-analogH _q ofU(h) is constructed, andH _q is shown to be a primitive ring.     

Totally Permutable Products of Finite Groups Satisfying SC or PST

Finite groups G=AB factorized by two subgroups A and B such that every subgroup of A permutes with every subgroup of B are studied in this paper. The behaviour of such products with respect to the class of finite groups in which Sylow-permutability is transitive is analyzed.     

Translations and semi-translations in infinite graphs

A self-contraction of an infinite graph is translating if it stabilizes no non-empty finite set of vertices. To each translating self-contractionf of a graph G is associated a particular end ofG, which is called the direction off. This generalizes the concept of direction of a translation (translating automorphism) defined and studied by Halin [5]. In this paper several properties of translating self-contractions are studied, with an emphasis to self-contractions of non-locally finite graphs.     

Semiovals contained in the union of three concurrent lines

Semiovals which are contained in the union of three concurrent lines are studied. The notion of a strong semioval is introduced, and a complete classification of these objects in PG(2,p) and PG(2,p²), p an odd prime, is given. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 491–501, 2007     

On a multi-channel change-point problem

A continuous change-point problem is studied in which N independent diffusion processes X _j are observed. Each process X _j is associated with a “channel”, each has an unknown piecewise constant drift and the unit diffusion coefficient. All the channels are connected only by a common change-point of drift. As the result, a change-point problem is defined in which the unknown and unidentifiable drift forms a 2N-dimensional nuisance parameter. The asymptotics of the minimax rate in estimating the change-point is studied as N → ∞. This rate is compared with the case of the known drift. This problem is a special case of an open change-point detection problem in the high-dimensional diffusion with nonparametric drift.      

Properties of a Time-Dependent Nonlinear Viscous Critical Layer

The time-dependent, nonlinear, viscous critical-layer problem posed by Gajjar and Smith is studied analytically and numerically, for various values of the time-dependence parameter µ and the viscous parameter γ_c, to help to complete the understanding of the solution. The analysis concerns the nearly inviscid limit γ_c → 0 which corresponds to increasing disturbance amplitude, other limits for weaker disturbances having been studied previously. On the numerical side, computational results obtained for order-1 values of µ, γ_c are described and are compared with analytical predictions. Particular attention is given to the phase shift produced across the critical layer.     

On some property of an irreducible subalgebra of the general linear Lie algebra gl(n,R)

Summary A subalgebrag ofgl(n, R) which admits no proper invariant subspace in Rⁿ and contains a subalgebra of a special kind is studied. It is concluded that only four cases are possible if n is even, and only two if n is odd. To Enrico Bompiani on his scientific Jubilee     

Geometrization of Dehn Twist Tori of a Surface with Infinite Genus

The conditions under which an infinite three-dimensional graph manifold M carries a metric of nonpositive bounded curvature (an NPC-metric) having finite volume are studied. A complete list of all such manifolds is obtained in the case where M is the mapping torus of a collection of Dehn twists on a surface of infinite genus and the graph of M is linear (i.e., homeomorphic to a line or a ray). Bibliography: 4 titles.