Heat and brine transport in porous media: the Oberbeck-Boussinesq approximation revisited

This paper discusses the Oberbeck-Boussinesq approximation for heat and solute transport in porous media. In this commonly used approximation all density variations are neglected except for the gravity term in Darcy’s law. However, in the limit of vanishing density differences this gravity term disappears as well. The main purpose of this paper is to give the correct limits in which the gravity term is retained, while other density effects can be neglected. We show that for isothermal brine transport, fluid volume changes can be neglected when a condition is fulfilled for a dimensionless number, which is independent of the density difference and specific discharge. For heat transfer an additional condition is required. One-dimensional examples of simultaneous heat and brine transport are given for which similarity solutions are constructed. These examples are included to elucidate the volume effects and the corresponding induced specific discharge variations. Finally, a two-dimensional example illustrates the relative effects of volume changes and gravity.     

On integral operators for certain classes of p-valent functions associated with generalized multiplier transformations

In this paper, we study new generalized integral operators for the classes of p-valent functions associated with generalized multiplier transformations.     

Biorthogonal Rational Functions and the Generalized Eigenvalue Problem

We present some general results concerning so-called biorthogonal polynomials of R_II type introduced by M. Ismail and D. Masson. These polynomials give rise to a pair of rational functions which are biorthogonal with respect to a linear functional. It is shown that these rational functions naturally appear as eigenvectors of the generalized eigenvalue problem for two arbitrary tri-diagonal matrices. We study spectral transformations of these functions leading to a rational modification of the linear functional. An analogue of the Christoffel–Darboux formula is obtained.     

Inorganic chemistry under high pressure

Abstract

In inorganic chemistry High Pressures can act as thermodynamic parameter and through the compression effect. Such effects can help the synthesis of new materials or induce specific properties. Such High Pressures studies are a great help for a better understanding of the chemical bonding and in field of resarches aimed at applications.     

Topotecan dynamics,tautomerism and reactivity—1H/13C NMR and ESI MS study

Topotecan (TPT) is in clinical use as an antitumor agent, hycamtin^?. Because of this, it requires both biologically and chemically useful information to be available. TPT acts by binding to the covalent complex formed by nicked DNA and topoisomerase I. This has a poisonous effect since inserted into the single‐strand nick and TPT inhibits its religation. We used NMR to trace TPT dynamics, tautomerism and solvolysis products in various solvents and conditions. Chemical stability was assessed in methanol and DMSO as compared to water, and the regioselectivity of the N‐ and O‐methylation was studied using various alkylating agents. The reaction products of quaternization of the nitrogen atom and methylation of the oxygen atom were characterized by means of ESI MS, ¹H/¹³C‐HMBC and ‐HSQCAD NMR. We have focused on the NMR characterization of TPT with an anticipation that its aggregation, tumbling properties and the intramolecular dipolar interactions will be a common feature for other compounds described in this article. These features can also be useful in tracing the interactions of this class of topoisomerase I (TopoI) poisons with DNA. Moreover, the results explained shed light on the recently disclosed problem of lack of stability of TPT in the heart tissue homogenate samples using the analytical assays developed for this class of compounds carried out in the presence of methanol. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamics of Triangular Transformations of Sequences over Finite Alphabets

Mathematical Notes -     

Multiperiodic multifractal martingale measures

A nonnegative 1-periodic multifractal measure on is obtained as infinite random product of harmonics of a 1-periodic function W(t). Such infinite products are statistically self-affine and generalize certain Riesz products with random phases. They are martingale structures, therefore converge. The criterion on W for nondegeneracy is provided. It differs completely from those for other known random measures constructed as martingale limits of multiplicative processes. In particular, it is very sensitive to small changes in W(t). When these infinite products are interpreted in the framework of thermodynamic formalism for random transformations, logW is a potential function when W>0. For regular enough potentials, in case of degeneracy, the natural normalization makes the sequence of measures converge. Moreover, this normalization is neutral for nondegenerate martingales. The multifractal analysis of the limit martingale measure is performed for a class of potential functions having a dense countable set of jump points.     

Squeezing and Quantum Canonical Transformations

In this paper we present an approach to quantum mechanical canonical transformations. Our main result is that time-dependent quantum canonical transformations can always be cast in the form of squeezing operators. We revise the main properties of these operators in regard to its Lie group properties, how two of them can be combined to yield another operator of the same class and how can also be decomposed and fragmented. In the second part of the paper we show how this procedure works extremely well for the time-dependent quantum harmonic oscillator. The issue of the systematic construction of quantum canonical transformations is also discussed along the lines of Dirac, Wigner, and Schwinger ideas and to the more recent work by Lee. The main conclusion is that the classical phase space transformation can be maintained in the operator formalism but the construction of the quantum canonical transformation is not clearly related to the classical generating function of a classical canonical transformation. We hereby propose the much more efficient method given by the squeezing operators. This method has also been proved to be very useful, by one of the authors, in the framework of the dynamical symmetries (Cerveró, J. M. (1999). International Journal of Theoretical Physics 38, 2095–2109).