Stability and accuracy functions for a multicriteria Boolean linear programming problem with parameterized principle of optimality “from Condorcet to Pareto”

A multicriteria Boolean programming problem with linear cost functions in which initial coefficients of the cost functions are subject to perturbations is considered. For any optimal alternative, with respect to parameterized principle of optimality “from Condorcet to Pareto”, appropriate measures of the quality are introduced. These measures correspond to the so-called stability and accuracy functions defined earlier for optimal solutions of a generic multicriteria combinatorial optimization problem with Pareto and lexicographic optimality principles. Various properties of such functions are studied and maximum norms of perturbations for which an optimal alternative preserves its optimality are calculated. To illustrate the way how the stability and accuracy functions can be used as efficient tools for post-optimal analysis, an application from the voting theory is considered.     

Shear stress analysis in engineering beams using deplanation field of special 2-D finite elements

This paper deals with the 2-D finite element shear stress analysis in beams, loaded by bending with shear and St. Venant’s torsion. The properties of these finite elements, like stiffness matrices as well as load vectors, are derived on the basis of their axial nodal displacements, e.g. by warping field. Proposed finite elements enable stress analysis independently of both cross-sectional member shape and material properties. Stiffness matrices and load vectors are derived for several finite element types. Material is assumed to be isotropic and linear elastic. For justification of the proposed stress analysis procedure, some examples are presented.     

Dynamic Analysis of Human Gait Disorder and Metabolical Cost Estimation

For the design and improvement of orthotic and prosthetic devices the biomechanical effort is an important criterion to obtain a more comfortable and natural gait of humans with gait disorders. In the first part of the paper the inverse dynamic analysis based on measurements of the human gait for subjects with different kinds of disorders is presented. The second part is devoted to a method to estimate the energy expenditure for human motions. This approach allows the computation of metabolical cost for human locomotion using Hill-type muscle models.     

Gradient methods for multiple state optimal design problems

We optimise a distribution of two isotropic materials α I and β I (α < β) occupying the given body in R ^d . The optimality is described by an integral functional (cost) depending on temperatures u ₁, . . . , u _m of the body obtained for different source terms f ₁, . . . ,f _m with homogeneous Dirichlet boundary conditions. The relaxation of this optimal design problem with multiple state equations is needed, introducing the notion of composite materials as fine mixtures of different phases, mathematically described by the homogenisation theory. The necessary conditions of optimality are derived via the Gateaux derivative of the cost functional. Unfortunately, there could exist points in which necessary conditions of optimality do not give any information on the optimal design. In the case m < d we show that there exists an optimal design which is a rank-m sequential laminate with matrix material α I almost everywhere on Ω. Contrary to the optimality criteria method, which is commonly used for the numerical solution of optimal design problems (although it does not rely on a firm theory of convergence), this result enables us to effectively use classical gradient methods for minimising the cost functional.      

“Naturadeus”, a metaphor of the Perfect Diamond

In this essay, the author outlines his re-construction of Spinoza’s ontological monism by re-presenting the system of Ethica, ordine geometrico demonstrata, in an “intuitive” model of the Perfect Diamond, called NATURADEUS. So, for example, ordo et connexio idearum et rerum, is presented to the inner eye in the forms of two parallel structures, of rays and of facets within the NATURADEUS, respectively. The conceptual background of the proposed model is mostly analytic, the author essays to develop some ideas of Jonathan Bennett’s Spinoza’s metaphysics (especially “transattributive mode identity”), with strong emphasis on ethical issues of ontological monism or pantheism. This essay is written as a dialogue between master Bruno and his student John (physically absent at the moment). More philosophical dialogues of this kind can be found on the author’s web page and in his book Four Seasons (in Slovenian, 2002).     

The <Emphasis Type="Italic">D</Emphasis><Superscript>(−)</Superscript>-Center Energy Spectrum in the Quantum Narrowing in the Presence of a Longitudinal Magnetic Field

The dispersion equation for an electron localized at the D⁰-center in the quantum narrowing in the presence of a magnetic field longitudinal with respect to the axis of constriction is analytically derived within the model of zero-radius potential. It is found that a special feature of the electron spectrum in the quantum narrowing manifests itself in the dependence of the D(−)-state binding energy on the effective constriction length. The evolution of the D(−)-state binding energy with changes in the longitudinal magnetic-field strength is investigated and compared with the case of D(−)-states in quantum wires. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 23–27, June, 2005.     

On a quest of reverse translation

Explaining the emergence of life is perhaps central and the most challenging question in modern science. Within this area of research, the emergence and evolution of the genetic code is supposed to be a critical transition in the evolution of modern organisms. The canonical genetic code is one of the most dominant aspects of life on this planet, and thus studying its origin is critical to understanding the evolution of life, including life’s emergence. In this sense it is possible to view the ribosome as a digital-to-analogue information converter. Why the translation apparatus evolved, is one of the enduring mysteries of molecular biology. Assuming the hypothesis that during the emergence of life evolution had to first involve autocatalytic systems, which only subsequently acquired the capacity of genetic heredity, in the present article we discuss some aspects and causes of the possible emergence of digital, discrete information arising from analogue information realized in the intra- and inter-molecular interactions throughout molecular evolution. How such reverse translation was achieved at a molecular level is still unclear. The results of such debates and investigations might shift current biological paradigms and might also have a momentous significance for modern philosophy in understanding our place in the universe.     

A general variable neighborhood search variants for the travelling salesman problem with draft limits

In this paper, we present two general variable neighborhood search (GVNS) based variants for solving the traveling salesman problem with draft limits (TSPDL), a recent extension of the traveling salesman problem. TSPDL arises in the context of maritime transportation. It consists of finding optimal Hamiltonian tour for a given ship which has to visit and deliver products to a set of ports while respecting the draft limit constraints. The proposed methods combine ideas in sequential variable neighborhood descent within GVNS. They are tested on a set of benchmarks from the literature as well as on a new one generated by us. Computational experiments show remarkable efficiency and effectiveness of our new approach. Moreover, new set of benchmarks instances is generated.     

Wax treatment of wood slows photodegradation

Waxes and wax emulsions are one of the most important solutions for non-biocidal wood protection. Wax treated wood is designed for outdoor use, therefore it is of considerable importance to elucidate the influence of weathering on the photodegradation processes. It is presumed, that wax treatment will reduce water uptake and thus reduce or slow down photodegradation processes. In order to test this hypothesis, three types of wax emulsions at two different concentrations were vacuum impregnated into Norway spruce wood specimens: an emulsion of montan wax (LGE), an emulsion of polyethylene (WE1) and an emulsion of oxidized polyethylene (WE6) wax. The samples were exposed to artificial accelerated weathering (AAW) for 500 cycles. Before and after AAW colour, the contact angle of water and moisture content were determined. Chemical and morphological changes at exposed surfaces were also investigated with FTIR spectroscopy and SEM. In parallel, the uptake of wax emulsions and water into the axial surfaces of samples was determined with a tensiometer. The moisture content measurements showed that the best hydrophobic effect was achieved with LGE treated wood, where the lowest colour and FTIR changes were observed as well. These results were supported by tensiometer measurements as well. Presented data clearly showed that high loadings of waxes reduce or at least slow down weathering. Among tested waxes, montan wax was found the most effective.     

Theoretical study on transesterification in a combined process consisting of a reactive distillation column and a pervaporation unit

Steady state analysis of a combined hybrid process consisting of a reactive distillation column, pervaporation unit, and a distillation column is presented. This process configuration was first presented by Steinigeweg and Gmehling (2004) for the transesterification of methyl acetate and butanol to butyl acetate and methanol. This system is characteristic for its low reaction rate and complex phase equilibrium. Steinigeweg and Gmehling (2004) have shown that the combination of reactive distillation and pervaporation is favourable since conversions close to 100 % can be reached with a reasonable size of the reactive section in the reactive distillation column. The aim of this paper is to show that although high conversion can be achieved, very complicated steady state behaviour must be expected. The presented analysis is based on mathematical modelling of a process unit, where the steady-state analysis, including continuation and bifurcation analyses, was used. Multiple steady states were predicted for the studied system; three steady states with conversions higher than 98 %. However, not all predicted steady states met the maximal allowed temperature condition in the reactive section (catalyst maximal operation temperature of 393 K). The presence of multiple steady states reduces the operability and controllability of the reactive distillation column during its start-up and during the occurrence of any variation of operating parameters because the system can be shifted from one steady state to another one (concurrent exceeding the maximal allowed temperature) with unwanted consequences, e.g. production loss. Therefore, design and subsequent operation of such a complicated system is an ambitious task requiring knowledge of any possible system behaviour.