Linear Balanceable and Subcubic Balanceable Graphs*

In Math Program 55(1992), 129–168, Conforti and Rao conjectured that every balanced bipartite graph contains an edge that is not the unique chord of a cycle. We prove this conjecture for balanced bipartite graphs that do not contain a cycle of length 4 (also known as linear balanced bipartite graphs), and for balanced bipartite graphs whose maximum degree is at most 3. We in fact obtain results for more general classes, namely linear balanceable and subcubic balanceable graphs. Additionally, we prove that cubic balanced graphs contain a pair of twins, a result that was conjectured by Morris, Spiga, and Webb in ( Discrete Math 310(2010), 3228–3235).     

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.     

Retention of lysozyme activity by physical immobilization in nanocellulose aerogels and antibacterial effects

Aerogels prepared from aqueous dispersions of anionic and cationic cellulose nanofibrils (CNFs) were investigated as solid supports for enzymes and silver nanoparticles and to elicit a sustained antibacterial effect. The imparted stabilization in dry conditions was studied with aerogels that were cast after mixing the enzymes with CNFs followed by dehydration (freeze-drying). The activity of lysozyme immobilized in the given CNF system was analyzed upon storage in liquid and air media. In contrast with aqueous solutions of free, unbound enzyme, which lost activity after the first day, the enzyme immobilized physically in unmodified and cationic CNF presented better stability (activity for a longer time). However, the enzyme activity was reduced in the case of anionic CNF, which was prepared by TEMPO-mediated oxidation (TO-CNF). Both humidity and temperature reduced the stability of the enzyme immobilized in the respective CNF aerogel. The antibacterial activity of CNF aerogels carrying lysozyme was also tested against gram-negative and gram-positive bacteria. The results were compared with those obtained from CNF systems loaded with silver nanoparticles (AgNP) after in situ synthesis via UV reduction. Storage in cold or dry conditions preserved the activity and antibacterial performance of enzyme-loaded CNF aerogels. As expected, the lysozyme-containing aerogels showed lower inhibition than the AgNP-containing aerogel. In this latter case, the antibacterial activity depended on the concentration and size of the nanoparticles. Compared to unmodified CNF and TO-CNF, the aerogels prepared with cationic CNF, loaded with either lysozyme or AgNPs, showed remarkably better antibacterial activity. Similar experiments were conducted with horseradish peroxidase, which confirmed, to different degrees, the observations derived from the lysozyme systems. Overall, the results indicate that non-toxic and biodegradable CNF is a suitable support for bio-active materials and is effective in protecting and retaining enzymatic and antibacterial activities.     

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.