Synthesis of Phosphorus Containing Polymers by Phase Transfer Catalysis (PTC). I. Comparative Study between Liquid-Liquid and Liquid-Vapor Systems

Abstract

Polyphosphonates were synthesized by interfacial alkaline polycondensation of bispheml A (BA) with phenyldichlorophosphonate (PPD) and cyclohexyl-dichlorophosphonate (CPD) in liquid-liquid[1] (1–1) and Iiquid-vapoR[2] (I-v) systems.     

Optical Rotatory Dispersion of Poly(propylene oxide) in Benzene Solution Determined from Channeled Spectra

The proposed method of channeled spectrum employs the recorded channeled spectrum of an optical active polymer solution placed between two crossed polarizers. The approach allows the evaluation of the optical rotatory dispersion of poly(propylene oxide) in benzene. The specific rotation, circular birefringence, and dispersion parameter depend on the wavelengths of the maxima and minima from the channeled spectrum.     

SOBP forming for carbon therapy

A ridge carbon beam filter for Spreading Out the Bragg Peak (SOBP) up to 20 mm in the targeted area has been designed and experimentally tested. The instrument was constructed of Plexiglas with a density of 1.165 g/cm³ and has a “teeth” structure with a period of 2.5 mm. The design is based on a simple analytical model and detailed GEANT4 Monte Carlo simulations. In-beam test measurements were performed with a 500-MeV/u ¹²C beam at the Nuclotron facility of the Joint Institute for Nuclear Research (JINR) in Dubna. The filter can be used as a static device positioned in front of patients undergoing carbon therapy.     

A Multiplicity Result for an Elliptic Anisotropic Differential Inclusion Involving Variable Exponents

In this paper we are concerned with the study of a class of quasilinear elliptic differential inclusions involving the anisotropic $\overrightarrow {p}(\cdot)$ -Laplace operator, on a bounded open subset of ${\mathbb R}^n$ which has a smooth boundary. The abstract framework required to study this kind of differential inclusions lies at the interface of three important branches in analysis: nonsmooth analysis, the variable exponent Lebesgue–Sobolev spaces theory and the anisotropic Sobolev spaces theory. Using the concept of nonsmooth critical point we are able to prove that our problem admits at least two non-trivial weak solutions.     

A perturbation result for q-open quotient morphisms in normed spaces and applications to linear relations

Using some techniques of perturbation theory for quotient morphisms between Banach spaces we obtain necessary and sufficient conditions for the stability of the topological index of a q-open quotient morphism under small (with respect to the gap topology) perturbations with quotient morphisms. As an application we obtain necessary and sufficient conditions for the stability of the topological index of an open linear relation with closed multivalued part between normed spaces under small perturbations with linear relations.     

On Confining Potentials and Essential Self-Adjointness for Schrödinger Operators on Bounded Domains in {\mathbb{R}}^n

Let Ω be a bounded domain in with C²-smooth boundary, , of co-dimension 1, and let be a Schr?dinger operator on Ω with potential . We seek the weakest conditions we can find on the rate of growth of the potential V close to the boundary which guarantee essential self-adjointness of H on . As a special case of an abstract condition, we add optimal logarithmic type corrections to the known condition where . More precisely, we show that if, as x approaches ,

The Faraday effect revisited: Thermodynamic limit

This paper is the second in a series revisiting the (effect of) Faraday rotation. We formulate and prove the thermodynamic limit for the transverse electric conductivity of Bloch electrons, as well as for the Verdet constant. The main mathematical tool is a regularized magnetic and geometric perturbation theory combined with elliptic regularity and Agmon-Combes-Thomas uniform exponential decay estimates.     

Approximations to mild solutions of stochastic semilinear equations with non-Lipschitz coefficients

In the present paper, using a Picard Type method of approximation, we investigate the global existence of mild solutions for a class of Ito Type stochastic differential equations whose coefficients satisfy conditions more general than the Lipschitz and linear growth ones.     

Characterization of Dirichlet Forms by their Excessive and Co–Excessive Elements

It is proved that if S, T are two elliptic Dirichlet operators on an ordered Hilbert space such that the excessive (resp. coexcessive) elements with respect to S and T are the same then there exists > 0 with T = S. Particularly if , are two elliptic Dirichlet forms on L² ( ) having the same domain of definition and the same -excessive (resp. -coexcessive) elements for any > 0 then = .