A new heuristic algorithm solving the linear ordering problem

The linear ordering problem is an NP-hard combinatorial problem with a large number of applications. Contrary to another very popular problem from the same category, the traveling salesman problem, relatively little space in the literature has been devoted to the linear ordering problem so far. This is particularly true for the question of developing good heuristic algorithms solving this problem.In the paper we propose a new heuristic algorithm solving the linear ordering problem. In this algorithm we made use of the sorting through insertion pattern as well as of the operation of permutation reversal. The surprisingly positive effect of the reversal operation, justified in part theoretically and confirmed in computational examples, seems to be the result of a unique property of the problem, called in the paper the symmetry of the linear ordering problem. This property consists in the fact that if a given permutation is an optimal solution of the problem with the criterion function being maximized, then the reversed permutation is a solution of the problem with the same criterion function being minimized.     

The determination of environmental and industrial exposure to heavy metals based on the quantitative isolation of metallothionein from human fluids, with application of covalent affinity chromatography with thiol-disulphide interchange gel as a solid-phase extraction support

The aim of this study was to present a new analytical method for the quantitative determination of metallothionein (MT) proteins in human body fluids and tissues, in order to determine the level of environmental and industrial exposure to heavy metals. For MT isolation, covalent affinity chromatography with thiol-disulphide inter-change (CAC-TDI) was applied. Fundamentals of indirect determination of the contents of metallothionein proteins were worked out through estimation of the quantities of metals bound with metallothionein protein and adsorbed on covalent affinity chromatography gel as on solid-phase extraction support during separating process. The (CAC-TDI) gel, specially prepared, was used as a solid phase extraction support (SPE) for preconcentration of Hg-thionein (Hg-Th), Cd-thionein (Cd-Th), Zn-thionein (Zn-Th) and Cu-thionein (Cu-Th) proteins and Hg, Cd, Zn and Cu bonded with MTs from water, human fluids such as: urine, human plasma, breast milk and tissues homogenates.     

Cerium isotope partition in the HCl/TBP extraction system

The^142/140Ce unit separation factor (q) for Ce(III)-Ce(IV) exchange reaction in an extraction system containing Ce(IV) in tri-n-butyl phosphate (TBP) and Ce(III) in hydrochloric acid has been determined. The value of q was found to be 0.9996±0.0001 (2) in the 12M HCl/TBP extraction system. The properties of the extraction systems containing nitric and hydrochloric acids in regard to isotope partition have been discussed.     

On two methods of determining the ellipses and ellipsoids of positioning accuracy of robot manipulators

Summary When analysing the problem of the positioning accuracy of robot manipulators it is important to know how far random deviations of the hand may be from the desired position if the joint positioning errors possess a normal distribution. Two methods of determining the ellipses and ellipsoids of probability concentration are compared. The first of them is based on the standard procedure of the probability calculus. The second approximate method consists in finding at first the polygon or polyhedron of the positioning accuracy, and then in finding the ellipse or ellipsoid with principal axes and second order moments coinciding with those of the polygon or polyhedron, respectively. Examples of application demonstrate that these two methods give very close results.

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Zwei Methoden zur Bestimmung der Ellipsen und Ellipsoide der Positioniergenauigkeit von Handhabungsrobotern

Übersicht Bei der Untersuchung der Positioniergenauigkeit von Handhabungsrobotern ist es wichtig, die Größe zufälliger Abweichungen des Greifers von der erstrebten Position zu kennen, wenn die Lagefehler der Verbindungen eine Normalverteilung besitzen. Es werden zwei Methoden zur Bestimmung der Ellipsen bzw. Ellipsoide der Wahrscheinlichkeitsdichte verglichen. Die erste beruht auf dem Standardverfahren der Wahrscheinlichkeitsrechnung. Die zweite Näherungsmethode besteht darin, daß zunächst das Polygon bzw. Polyeder der Positioniergenauigkeit bestimmt wird und danach die Ellipse bzw. das Ellipsoid mit den Hauptachsen und Momenten zweiter Ordnung wie das Polygon oder Polyeder. Beispiele zeigen, daß beide Methoden zu sehr ähnlichen Ergebnissen führen.

     

Power series solutions to some nonlinear diffusion problems

In this paper power series solution to some nonlinear diffusion problems in semiconductor production are considered. The convergence proof for power series solutions is presented.This paper has been written when the first author was a Visiting Professor in the Universidad de Extremadura.     

Group theory and solutions of classical field theories with polynomial nonlinearities

In this paper we investigate a number of analytical solutions to the polynomial class of nonlinear Klein-Gordon equations in multidimensional spacetime. This is done in the context of classical ⁴ and ⁶ field theory, the former with and without the inclusion of an external force field conjugate to . Both massive (m0) and massless (m=0) cases are considered, as well as tachyonic solutions allowed (v>c). We first present a complete set of translationally invariant solutions for the ⁴ model and demonstrate the role of external force fields in altering the form of these solutions. Next, spherically symmetric solutions are discussed in both ⁴ and ⁶ cases since they provide the most realistic models of elementary particles.     

Pathwise global attractors for stationary random dynamical systems

Summary The asymptotic behaviour of random dynamical systems in Polish spaces is considered. Under the assumption of existence of a random compact absorbing set, assumption supposed to hold path by path, a candidate pathwise attractorA() is defined. The goal of the paper is to show that, in the case of stationary dynamical systems,A() attracts bounded sets, is measurable with respect to the -algebra of invariant sets, and is independent of when the system is ergodic. An application to a general class of Navier-Stokes type equations perturbed by a multiplicative ergodic real noise is discussed in detail.     

Further studies on the chemistry and structure of n-oxides of sparteine and its derivatives—V: Synthesis and structure of 2-phenylsparteine-n16-oxide,a new case of “sponge” proton

The synthesis of 2-phenylsparteine-N₁₆-oxide (7) and its perchlorate salt (7-H⁺) was carried out. On the basis of spectral data, and by comparison with appropriate sparteine-N-oxides, the mechanism of formation and the structures of the two new compounds were proposed. It was found, the basicity of the new N-oxide is unexpectedly high and comparable to the basicity of quaternary ammonium hydroxides. The structure and the strength of intramolecular H-bond in 7-H⁺ makes 7 an excellent “catcher” proton or specific ”sponge” proton.