Stochastic flows on a countable set: Convergence in distribution

Consider a sequenceF ₁,F ₂,... of i.i.d. random transformations from a countable setV toV. Such a sequence describes a discrete-time stochastic flow onV, in which the position at timen of a particle that started at sitex isM _n(x), whereM _n =F _n F _n–1 F ₁. We give conditions on the law ofF ₁ for the sequence (M _n) to be tight, and describe the possible limiting law. an example called the block charge model is introduced. The results can be formulated as a statement about the convergence in distribution of products of infinite-dimensional random stochastic matrices. In practical terms, they describe the possible equilibria for random motions of systems of particles on a countable set, without births or deaths, where each site may be occupied by any number of particles, and all particles at a particular site move together.     

More on limit theorems for iterates of probability measures on semigroups and groups

Summary In this paper, we continue earlier works of one of the authors on vague convergence of the sequence _k,n= _k+1 *...* _n, where _n is a sequence of probability measures on semigroups or groups. Typical results in this paper are: Theorem. Let S be a locally compact noncompact second countable group such that being the support of a probability measure on S. Suppose there exists an open set V with compact closure such that x ^–1 Vx=V for every xS. Then for all compact sets K, sup{ ⁿ (Kx): xS0 as n. Theorem. Let S be an at most countable discrete group. Let _n be a sequence of probability measures on S. Then for all nonnegative integers k, the sequence _k,n converges vaguely to some probability measure if and only if there exists a finite subgroup G such that the series and for any proper subgroup G of G and any choice of elements g_n in S, the series . A sufficient condition for the vague convergence of the sequence _k,n to a probability measure is that (i) there exists a finite subgroup G such that and (ii) _n(e)>s>0 for all n, e being the identity.The author was supported by NSF grant MCS77-03639     

Isolation and purification of a vertebral hemoglobin,the chicken hemoglobin,and its interaction with copperglutathione complex

Hemoglobin was isolated from chicken blood and purified by biochemical methods.This hemoglobin was allowed to interact with copperglutathione (CuGSH) and the interaction pattern was monitored by spectrophotometric and spectrofluorimetric techniques. The interaction ratio was found to be 1:0.7 in both the cases. The equilibrium constant data suggested associative binding and a fluorimetric study revealed that such association occurred around tryptophan residues of hemoglobin.     

Concentration functions and a class of non-compact groups

Mathematische Annalen -     

On the limit of the convolution iterates of a probability measure on n × n stochastic matrices

This article initiates a detailed analysis of the spectral representation for the ground state representation of the infinite one-dimensional Heisenberg ferromagnet. Here, we obtain explicit expressions for the infinite volume (weak) limits of the projections constructed from Bethe's eigenfunctions for the finite volume Heisenberg Hamiltonians. Assuming the limits are projections, we establish various spectral properties for the Hamiltonian restricted to the corresponding subspaces.     

Synthesis, structural characterization and catalytic activity of a multifunctional enzyme mimetic oxoperoxovanadium(V) complex

The synthesis and structural characterization of a novel oxoperoxovanadium(V) complex [VO(O(2))(PAH)(phen)] containing the ligands 2-phenylacetohydroxamic acid (PAHH) and 1,10-phenanthroline (phen) has been accomplished. The oxoperoxovanadium(V) complex was found to mimic both vanadate-dependent haloperoxidase (VHPO) activity as well as nuclease activity through effective interaction with DNA. The complex is the first example of a structurally characterized stable oxoperoxovanadium(V) complex with a coordinated bi-dentate hydroximate moiety (-CONHO(-)) from 2-phenylacetohydroximate (PAH). The oxoperoxovanadium(V) complex has been used as catalyst for the peroxidative bromination reaction of some unsaturated alcohols (e.g. 4-pentene-1-ol, 1-octene-3-ol and 9-decene-1-ol) in the presence of H(2)O(2) and KBr. The catalytic products have been characterized by GC-MS analysis and spectrophotometric methods. The DNA binding of this complex has been established with CT DNA whereas the DNA cleavage was demonstrated with plasmid DNA. The interactions of the complex with DNA have been monitored by electronic absorption and fluorescence emission spectroscopy. Viscometric measurements suggest that the compound is a DNA intercalator. The nuclease activity of this complex was confirmed by gel electrophoresis studies.     

Convolution products of nonidentical distributions on a topological semigroup

In this paper we present a number of sufficient conditions on a sequence of probability measuresµ _n on a locally compact (second countable) Hausdorff topological semigroupS that guarantee the weak convergence of the sequence of convolution productsµ _k,n µ _{k + 1} *···*µ _n (k), asn, for allk0.