Asymptotics of Intersection Local Time for Diffusion Processes

In the paper, we investigate the intersection local time for two correlated Brownian motions on the plane that form a diffusion process in ?⁴ associated with a divergence-form generator. Using Gaussian heat kernel bounds, we prove the existence of intersection local time for these Brownian motions, obtain estimates of its moments, and establish the law of iterated logarithm for it.

     

Polymerization of 3‐ethynylthiophene with homogeneous and heterogeneous Rh catalysts

3‐Ethynylthiophene (3ETh) was polymerized with Rh(I) complexes: [Rh(cod)acac], [Rh(nbd)acac], [Rh(cod)Cl]₂, and [Rh(nbd)Cl]₂ (cod is η²:η²‐cycloocta‐1,5‐diene and nbd η²:η²‐norborna‐2,5‐diene), used as homogeneous catalysts and with the last two complexes anchored on mesoporous polybenzimidazole (PBI) beads: [Rh(cod)Cl]₂/PBI and [Rh(nbd)Cl]₂/PBI used as heterogeneous catalysts. All tested catalyst systems give high‐cis poly(3ETh). In situ NMR study of homogeneous polymerizations induced with [Rh(cod)acac] and [Rh(nbd)acac] complexes has revealed: (i) a transformation of acac ligands into free acetylacetone (Hacac) occurring since the early stage of polymerization, which suggests that this reaction is part of the initiation, (ii) that the initiation is rather slow in both of these polymerization systems, and (iii) a release of cod ligand from [Rh(cod)acac] complex but no release of nbd ligand from [Rh(nbd)acac] complex during the polymerization. The stability of diene ligand binding to Rh‐atom in [Rh(diene)acac] catalysts remarkably affects only the molecular weight but not the yield of poly(3ETh). The heterogeneous catalyst systems also provide high‐cis poly(3ETh), which is of very low contamination with catalyst residues since a leaching of anchored Rh complexes is negligible. The course of heterogeneous polymerizations is somewhat affected by limitations arising from the diffusion of monomer inside catalyst beads. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2776–2787, 2008     

Playfulness: A Motivator in Elementary Science Teacher Preparation

Research suggests that teacher preparation courses should model hands-on activities promoting positive attitudes toward science. This study investigated the qualities of activities in a field-based science methods course that motivate preservice elementary teachers to implement them in their own classrooms. Ratings of the activities as fun, interesting, and having a high potential for learning were highly correlated, and the preservice teachers predicted that they would more likely implement activities they rated high on these qualities. A comparison of activities ranked high and low in fun suggests that activities ranked high tended to be exploratory in nature, taught process skills in context, enabled the preservice teachers to experience something new in a nonthreatening way, and promoted social interactions. ¹     

Tomographic characteristics of spin states

Spin states are studied in the tomographic-probability representation. The standard probability distribution of spin projection onto a direction in space is used instead of the spinor or the density matrix to identify the quantum state. The Shannon entropy and information are associated with the spin tomographic probability. A short review of the probability-theory notions is presented. Analysis of tomographic entropy and tomographic information for the Werner state is considered. The probability representation is used to describe a spin-3/2 particle and two qubits. The connection of tomographic entropy with the von Neumann entropy is discussed.     

Design and Implementation of a Composite Performance Evaluation Model for Heterogeneous Network Management Applications

This article examines the place of analytical models in realtime performance management applications. The main objectives are to define, specify and implement a system based on a composite model that provides the optimal software environment for performance analysis and tuning of heterogeneous networks.     

Matrix realizations of littlewood—richardson sequences

In this paper we consider the problem of characterizing the invariant factors of three matrices AB, and C, such that AB — C Our matrices have entries over a principal ideal domain or over a local domain. In Section 2 we show that this problem is localizablc

The above problem lias a well-known solution in terms of Littlewood-Richardson sequences. We introduce the concept of a matrix realization of a Littlewood-Richardson sequence. The main result is an explicit construction of a sequence of matrices which realizes a previously given Littlewood Richardson sequence. Our methods offer a matrix theoretical proof of a well-known result of T, Klein on extensions of p-modules.     

Study of the TCP Dynamics over Wireless Networks with Micromobility Support Using the ns Simulator

Several IP micro-mobility protocols have been proposed to enhance the performance of Mobile IP in an environment with frequent handoffs. In this paper we make a detailed study of how some of these protocols namely Cellular IP, HAWAII and Hierarchical Mobile IP affect the behavior of TCP and their interaction with the MAC layer. The aim of the paper is to investigate the impact of handoffs on TCP by means of simulation traces that show the evolution of segments and acknowledgments during handoffs.