Generalized Sasaki Projections and Riesz Ideals in Pseudoeffect Algebras

A noncommutative version of generalized Sasaki projections in pseudoeffect algebras is introduced. It is proved that an ideal in a pseudoeffect algebra is Riesz if and only if it is closed under the right and left Sasaki projections. In lattice ordered pseudoeffect algebras, it is shown that generalized Sasaki projections are one-element sets, and their explicit form is found. It is shown that if a supremum of a normal Riesz ideal in a lattice ordered pseudoeffect algebra exists, it is a central element. These results extend those obtained recently by Avallone and Vitolo for effect algebras.     

On an Embedding Criterion for Interpolation Spaces and Application to Indefinite Spectral Problems

An embedding criterion for interpolation spaces is formulated and applied to the study of the Riesz basis property in the L _2,g space of eigenfunctions of an indefinite Sturm–Liouville problem u=gu on the interval (-1,1) with the Dirichlet boundary conditions, provided that the function g(x) changes sign at the origin. In particular, the basis property criterion is established for an odd g(x). Some connections with stability in interpolation scales are discussed.     

A Fourier series formula for energy of measures with applications to Riesz products

In this paper we derive a formula relating the energy and the Fourier transform of a finite measure on the -dimensional torus which is similar to the well-known formula for measures on .

We apply the formula to obtain estimates on the Hausdorff dimension of Riesz product measures. These give improvements on the earlier, classical results which were based on completely different techniques.

     

Divergent Cesàro and Riesz means of Jacobi and Laguerre expansions

We show that for below certain critical indices there are functions whose Jacobi or Laguerre expansions have almost everywhere divergent Cesàro and Riesz means of order .

     

THE SPACE—FRACTIONAL TELEGRAPH EQUATION AND THE RELATED FRACTIONAL TELEGRAPH PROCESS

The space-fractional telegraph equation is analyzed and the Fourier transform of its fundamental solution is obtained and discussed.A symmetric process with discontinuous trajectories, whose transition function satisfies the space-fractional telegraph equation, is presented. Its limiting behaviour and the connection with symmetric stable processes is also examined.     

A capacitary weak type inequality for Sobolev functions and its applications

In this paper a capacitary weak type inequality for Sobolev functions is established and is applied to reprove some well-known results concerning Lebesgue points, Taylor expansions in the -sense, and the Lusin type approximation of Sobolev functions.

     

Molecular modeling, theoretical calculations and property evaluation of three muscarinic agonists. X-ray structures of LU 25-109 and WAL 2014

LU 25-109 (II) and WAL 2014 (talsaclidine, III) are two M1 muscarinic agonists chemically related to the natural substance arecoline (I). All these compounds have beneficial effects on memory and cognition in animals and humans, and they have been proposed in the treatment of Alzheimer's disease, but only III will likely find a place in therapy. In this work we have investigated the solid state structures of II and III, and the X-ray structures of the two molecules and of the parent compound I have been used to input a series of computational chemistry efforts.

In particular, the X-ray geometries have been manipulated to model 20 molecular structures (1–20) which have been submitted to ab initio, semiempirical quantum mechanics and molecular mechanics calculations. The conformational space accessible to the 20 structures has been assessed by means of potential energy maps. The reactivities of 1–20 have been estimated by examining at the graphics terminal the composition and the extension of the frontier orbitals (HOMOs and LUMOs) and of the molecular electrostatic potential. The information obtained has been interpreted to explain the different degrees of activity shown by I–III. Our data indicate that III has better in vivo activity for its intermediate size, less polar surface, conformational rigidity and orientation of reactive domains.     

Abstract Hardy-Sobolev spaces and interpolation

The purpose of this work is to describe an abstract theory of Hardy-Sobolev spaces on doubling Riemannian manifolds via an atomic decomposition. We study the real interpolation of these spaces with Sobolev spaces and finally give applications to Riesz inequalities.     

The pricing and optimal strategies of callable warrants

In this paper, we introduce a valuation model of callable warrants under a setting of the optimal stopping problem between the holder (investor) and the issuer (firm). A warrant is the right to purchase new shares at a predetermined price. When the new stocks are issued, the value of the stock is diluted. We consider the model taking the dilution into account. After identifying optimal policies for the issuer and the investor, we explore the analytical properties of the optimal exercise and call boundaries for the holder and the issuer, respectively. Furthermore, the value of such a callable warrant and the optimal critical prices are examined numerically using the binomial method.     

Ion-exchange resin decomposition in supercritical water

Abstract

Using supercritical water oxidation, the cation exchange resin was decomposed fast and completely to water, carbon dioxide and sulfuric acid. While the resin decomposition yield increased with the reaction time and the amount of hydrogen peroxide added as oxidizing agent, it was constant in the resin concentration from 0.14 to 1.9 dry resin weight percent to water. More than 99% of the cation exchange resin was decomposed with hydrogen peroxide added in the amount of 7 times the stoichiometric value at 673 K and 30MPa for 30 minutes of the reaction time. The cation exchange resin is decomposed through two main reaction pathways. One has a rate controlling intermediate such as acetic acid whose decomposition rate was very slow, and the other does not have stable intermediates. The decomposition of the acetic acid is a significant factor for the complete decomposition of the resin, although it does not dominate the whole resin decomposition. A simple kinetic model that estimates the resin decomposition yield was developed.