An Improved Interval Linearization for Solving Nonlinear Problems

Let f(x) denote a system of n nonlinear functions in m variables, m≥n. Recently, a linearization of f(x) in a box x has been suggested in the form L(x)=Ax+b where A is a real n×m matrix and b is an interval n-dimensional vector. Here, an improved linearization L(x,y)=Ax+By+b, x∈x, y∈y is proposed where y is a p-dimensional vector belonging to the interval vector y while A and B are real matrices of appropriate dimensions and b is a real vector. The new linearization can be employed in solving various nonlinear problems: global solution of nonlinear systems, bounding the solution set of underdetermined systems of equations or systems of equalities and inequalities, global optimization. Numerical examples illustrating the superiority of L(x,y)=Ax+By+b over L(x)=Ax+b have been solved for the case where the problem is the global solution of a system of nonlinear equations (n=m).     

The nature of the salt error in the Sn(II)-reduced molybdenum blue reaction for determination of dissolved reactive phosphorus in saline waters

Sn(II) is a well-known reductant used in the formation of phosphomolybdenum blue for the determination of dissolved reactive phosphorus (DRP) in waters because it provides rapid and quantitative reduction. However, in saline waters, this method suffers from a salt error which causes a significant decrease in sensitivity. This phenomenon has never been adequately explained in the literature. The Murphy and Riley method, which uses Sb(III) and ascorbic acid for the reduction step, is preferred for DRP determination in saline waters because it is unaffected by salinity, but it exhibits a sensitivity approximately 30% lower than that when Sn(II) is used as the reductant without Cl⁻ interference. This study investigates the processes causing the salt error and possible ways of minimizing it, so that the benefits of Sn(II) reduction on the molybdenum blue reaction rate and sensitivity may be exploited in the determination of low levels of DRP in marine and estuarine waters. It has been established that the salt error is caused by the formation of Sn(IV) chloro-complexes which compete with the formation of Sn(IV)-substituted phosphomolybdenum blue, forcing the reaction to proceed via the much slower, less favourable process of direct reduction that occurs in methods using organic reductants such as ascorbic acid.     

Nonstandard methods for the convective‐dispersive transport equation with nonlinear reactions

A new nonstandard Eulerian‐Lagrangian method is constructed for the one‐dimensional, transient convective‐dispersive transport equation with nonlinear reaction terms. An “exact” difference scheme is applied to the convection‐reaction part of the equation to produce a semi‐discrete approximation with zero local truncation errors with respect to time. The spatial derivatives involved in the remaining dispersion term are then approximated using standard numerical methods. This approach leads to significant, qualitative improvements in the behavior of the numerical solution. It suppresses the numerical instabilities that arise from the incorrect modeling of derivatives and nonlinear reaction terms. Numerical experiments demonstrate the scheme's ability to model convection‐dominated, reactive transport problems. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 617–624, 1999     

Locomotion based on the control of the shape of magnetic fluid surfaces and of magnetizable media

The realization of locomotion based on the deformation of a free surface of a magnetic fluid layer in a traveling magnetic field is studied. A plane flow of an incompressible viscous magnetic fluid layer on a horizontal surface in a nonuniform magnetic field and a plane two-layers flow of incompressible viscous magnetic fluids between two parallel solid planes in a magnetic field is considered. Also the flow of an incompressible viscous magnetic fluid layer on a cylinder in a nonuniform magnetic field is an object of investigation. The deformation and the motion of a body made by a magnetizable polymer in an alternating magnetic field are experimentally studied. The cylindrical body (worm) which is located in a cylindrical tube is analyzed. These effects can be used in designing autonomous mobile robots without a hard cover. Such robots can be employed in clinical practice and biological investigations. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

End effects in flow-analysis and process systems

The “end effects” in flow-analysis and process systems are investigated theoretically on the basis of the axially-dispersed plug-flow model. Three-section systems consisting of reactor, fore- or after-section and additional section are used. In the additional section back-mix flow is assumed to exist. The corresponding Peclet number has been found to be 0.01. The difference between the system responses to a delta-function input signal for finite and infinite length of the fore- or after-section is studied. Both the statistical moments of the system responses and the actual response curves are used for that purpose. The results can be used to evaluate the length of the fore- and after-sections needed in real flow-analysis and process systems in order that the phenomena taking place downstream or upstream of these two sections, respectively, will not play an important role in the system response.     

Vibrational Spectra of 4-Benzoylpiridine and the 18O Substituted Derivative

Abstract

Infrared and Raman spectra of 4-benzoylpiridine (4BP) and its ¹⁸O substituted derivative have been recorded in the solid and in the molten state. Polarized Raman spectra in the molten state have also been measured. The assignment of the vibrational bands is performed on the basis of isotopic shifts, group vibrational concept and polarization features of the normal modes. The previous assignment of the in- and out-of-plane deformations of the carbonyl group and the fundamentals below 700 cm^?1 are questioned and corrected.     

The Vibrational Spectra of 9-Fluorenone and Some of Its Isotopic Isomers

Abstract

Vibrational spectra of 9-Fluorenone, 9-Fluorenone-¹⁸O and 9-Fluorenone-d₈ have been recorded in the solid state and solutions in the infrared and (4000–100 cm^?1) and in the Raman (4000–50 cm^?1). Differential infrared linear dichroic spectra have also been measured. The assignment of the vibrational bands is performed using the group vibrational concept, isotopic shifts and polarization features of the normal modes.     

Molecular dynamics approach to water structure of H(II) mesophase of monoolein

The goal of the present work is to study theoretically the structure of water inside the water cylinder of the inverse hexagonal mesophase (H(II)) of glyceryl monooleate (monoolein, GMO), using the method of molecular dynamics. To simplify the computational model, a fixed structure of the GMO tube is maintained. The non-standard cylindrical geometry of the system required the development and application of a novel method for obtaining the starting distribution of water molecules. A predictor-corrector schema is employed for generation of the initial density of water. Molecular dynamics calculations are performed at constant volume and temperature (NVT ensemble) with 1D periodic boundary conditions applied. During the simulations the lipid structure is kept fixed, while the dynamics of water is unrestrained. Distribution of hydrogen bonds and density as well as radial distribution of water molecules across the water cylinder show the presence of water structure deep in the cylinder (about 6 ? below the GMO heads). The obtained results may help understanding the role of water structure in the processes of insertion of external molecules inside the GMO∕water system. The present work has a semi-quantitative character and it should be considered as the initial stage of more comprehensive future theoretical studies.     

A simple strategy for varying the restart parameter in GMRES()

When solving a system of linear equations with the restarted GMRES method, a fixed restart parameter is typically chosen. We present numerical experiments that demonstrate the beneficial effects of changing the value of the restart parameter in each restart cycle on the total time to solution. We propose a simple strategy for varying the restart parameter and provide some heuristic explanations for its effectiveness based on analysis of the symmetric case.     

The effect of the counter anion on the transport of thiourea in a PVC-based polymer inclusion membrane using Capriquat as carrier

This paper describes the effect of four counter anions (CH₃COO⁻, Cl⁻, NO₃⁻, ClO₄⁻) of the trioctylmethylammonium (TOMA) cation on the rate of solvent extraction of thiourea and its transport across poly(vinyl chloride) (PVC)-based polymer inclusion membranes (PIMs). The membranes also contained 2-nitrophenyl octyl ether (NPOE) as the plasticizer while chloroform was used as diluent in the solvent extraction studies. It is demonstrated that the counter anion affects substantially the rate of membrane transport and the degree of extraction follows the order: CH₃COO⁻ > Cl⁻ > NO₃⁻ ? ClO₄⁻. The transport rate is negligible for the perchlorate anion. This order is consistent with thiourea interacting with the counter anion through hydrogen bonding to form a heteroconjugate anion.