Structure of water: Short-ranged versus long-ranged forces

By transforming a realistic water-water potential separately into long-ranged and short-ranged systems and using computer simulations it is shown that the structure of water is determined primarily by short-ranged (both repulsive and attractive) forces. An extended primitive model of water is then shown to provide both the spatial and orientational arrangement of water molecules in the liquid phase in semi-quantitative agreement with diffraction experiments. Practical importance of this finding is exemplified by formulating a perturbation expansion about the primitive model reference and its individual steps are analyzed with respect to their implementation. This work was supported by the Grant Agency of the Czech Republic (Grant No. 203/96/0585) and by the Grant Agency of the Academy of Sciences of the Czech Republic (Grant No. A-4072607).     

The G/M/1 queue revisited

The G/M/1 queue is one of the classical models of queueing theory. The goal of this paper is two-fold: (a) To introduce new derivations of some well-known results, and (b) to present some new results for the G/M/1 queue and its variants. In particular, we pay attention to the G/M/1 queue with a set-up time at the start of each busy period, and the G/M/1 queue with exceptional first service. Dedicated to Arie Hordijk on his 65th birthday, in friendship and admiration.     

Dimensional reduction for Helmholtz's equation on a bounded domain

Summary. The dimensional reduction method for solving boundary value problems of Helmholtz's equation in domain by replacing them with systems of equations in dimensional space are investigated. It is proved that the existence and uniqueness for the exact solution and the dimensionally reduced solution of the boundary value problem if the input data on the faces are in some class of functions. In addition, the difference between and in is estimated as and are fixed. Finally, some numerical experiments in a domain are given in order to compare theretical results. Received April 2, 1996 / Revised version received July 30, 1990     

Comparison theorems for weak splittings of bounded operators

Summary Comparison theorems for weak splittings of bounded operators are presented. These theorems extend the classical comparison theorem for regular splittings of matrices by Varga, the less known result by Wonicki, and the recent results for regular and weak regular splittings of matrices by Neumann and Plemmons, Elsner, and Lanzkron, Rose and Szyld. The hypotheses of the theorems presented here are weaker and the theorems hold for general Banach spaces and rather general cones. Hypotheses are given which provide strict inequalities for the comparisons. It is also shown that the comparison theorem by Alefeld and Volkmann applies exclusively to monotone sequences of iterates and is not equivalent to the comparison of the spectral radius of the iteration operators.This work was supported by the National Science Foundation grants DMS-8807338 and INT-8918502     

On the solution of singular linear systems of algebraic equations by semiiterative methods

Summary For a square matrixT ^n,n , where (I–T) is possibly singular, we investigate the solution of the linear fixed point problemx=T x+c by applying semiiterative methods (SIM's) to the basic iterationx ₀ ⁿ ,x _k T c _k–1+c(k1). Such problems arise if one splits the coefficient matrix of a linear systemA x=b of algebraic equations according toA=M–N (M nonsingular) which leads tox=M ^–1 N x+M ^–1 bT x+c. Even ifx=T x+c is consistent there are cases where the basic iteration fails to converge, namely ifT possesses eigenvalues 1 with ||1, or if =1 is an eigenvalue ofT with nonlinear elementary divisors. In these cases — and also ifx=T x+c is incompatible — we derive necessary and sufficient conditions implying that a SIM tends to a vector which can be described in terms of the Drazin inverse of (I–T). We further give conditions under which is a solution or a least squares solution of (I–T)x=c.Research supported in part by the Alexander von Humboldt-Stiftung     

Excitation functions for some output channels following the p +55Mn interaction atE p=1·3–2·0 MeV

Excitation functions for the⁵⁵Mn(p, p )⁵⁵Mn,⁵⁵Mn(p, n )⁵⁵Fe and⁵⁵Mn(p, )⁵⁶Fe reactions are studied for proton beam energyE _p=1·3–2 MeV. The excitation functions are established from yield functions for -rays emitted from the first excited states of final nuclei. Many resonances are observed and competition of their decay into all three output channels is analysed. Spin-parity assignment for some resonant states in the⁵⁶Fe compound nucleus is deduced.Participated partly in the course of his work on a Thesis.The authors wish to thank the staff of the Van de Graaff accelerator at Charles University in Prague for the efficient operation of the machine and dr. I. Wilhelm for the valuable technical help in the early period of the experimental work. One of us (N. A. N.) acknowledges the staff of the Dept. of Nuclear Physics of Charles University in Prague for the excellent working conditions.     

Stability and distribution constants of thallium(I) dithiocarbamates

Stability and distribution constants of thallium(I) chelates with diethyl-(I), pyrrolidine- (II), piperidine- (III), phenylethyl- (IV) and methylphenylethyldithiocarbamate (V) have been radiometrically determined using ion-exchange and solvent extraction methods. Stability constants of individual chelates do not change considerably, however, the distribution constants of neutral chelates increase in the order II<IV<IIII<V.     

Banana-shaped molecules peculiarly oriented in a magnetic field: (2)H NMR spectroscopy and quantum mechanical calculations.

The orientational properties of the banana-shaped liquid crystal 4-chloro-1,3-phenylenebis{4-[4'-(10-undecenyloxy)]benzoyloxy} benzoate (ClPbis11BB) are reported in the nematic phase under the effect of an external magnetic field. A new hypothesis, which states that the central ring of the aromatic core is oriented perpendicularly to the external magnetic field, is proposed. In support of this hypothesis, a series of studies based on (2)H NMR spectroscopy, both in the bulk and in solution, are discussed. (2)H NMR measurements on three selectively deuterium-labelled isotopomers are presented, together with DFT results from B3LYP/cc-pvDz calculations performed on the aromatic core. The rather flat shape of the investigated intramolecular energy surface allows for several different conformations to be populated, the computed magnetic susceptibilities of which are consistent with the proposed hypothesis of peculiar orientation of banana-shaped molecules. Moreover, the orientation of the magnetic susceptibility tensor is shown to be strongly dependent on the internal conformation of the banana-shaped molecules.     

Physico-chemical characterization of nanofiltration membranes.

This study presents a methodology for an in-depth characterization of six representative commercial nanofiltration membranes. Laboratory-made polyethersulfone membranes are included for reference. Besides the physical characterization [molecular weight cut-off (MWCO), surface charge, roughness and hydrophobicity], the membranes are also studied for their chemical composition [attenuated total reflectance Fourier spectroscopy (ATR-FTIR) and X-ray photoelectron spectroscopy (XPS)] and porosity [positron annihilation spectroscopy (PAS)]. The chemical characterization indicates that all membranes are composed of at least two different layers. The presence of an additional third layer is proved and studied for membranes with a polyamide top layer. PAS experiments, in combination with FIB (focused ion beam) images, show that these membranes also have a thinner and a less porous skin layer (upper part of the top layer). In the skin layer, two different pore sizes are observed for all commercial membranes: a pore size of 1.25-1.55 angstroms as well as a pore size of 3.20-3.95 angstroms (both depending on the membrane type). Thus, the pore size distribution in nanofiltration membranes is bimodal, in contrast to the generally accepted log-normal distribution. Although the pore sizes are rather similar for all commercial membranes, their pore volume fraction and hence their porosity differ significantly.     

A mathematical evaluation of dose-dependent PpIX fluorescence kinetics in vivo

The in vivo pharmacokinetics of protoporphyrin IX (PpIX) after administration of 5-aminolevulinic acid (ALA) cannot be described accurately by mathematical models using first-order rate processes. We have replaced first-order reaction rates by dose-dependent (Michaelis-Menten [MM]) reaction rates in a mathematical compartment model. Different combinations of first-order and dose-dependent reaction rates were evaluated to see which one would improve the goodness-of-fit to experimentally determined in vivo PpIX fluorescence kinetics as a function of concentration. The mathematical models that were evaluated are all based on a three-compartment model for drug distribution, conversion to PpIX and subsequent conversion to heme. Implementation of dose-dependent reaction rates improved the goodness-of-fit and enabled interpolation to other drug doses. For most data sets the time constant for delivery to the target cells turned out to be dose dependent. For all data sets the use of MM rates for the conversion of ALA to PpIX yielded better fits. The clearance of PpIX turned out to be a first-order process for all doses and types of administration. Fluorescence curves measured on a specific tissue type but obtained in different studies with different measurement techniques could be described with a single set of parameters.