Automorphisms of a rooted tree of countably infinite valency

Automorphisms of a rooted tree of infinite countable valency are studied. Two families of subgroups associated with growths of functions are introduced. This gives a classification of large sublattices of subgroups. Bibliography: 7 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 343, 2007, pp. 199–205.     

Remarks on the Analytic Centers of Convex Sets

In this paper we analyze properties of the analytic centers for perturbed convex problems. In particular we study the continuity of convex regions with respect to such characteristics as boundedness, full dimensionality and the existence of an analytic centre. Furthermore, we state the necessary and sufficient conditions for the existence of the analytic centre for possibly unbounded regions and we show that the analytic centre is identical for any minimal representation of the convex set. We are also concerned with the limiting behaviour of the central path as it approaches the set of optimal solutions of the problem.     

Thermal dehydration of some food products and kinetic parameters of this process

Metal poly(vinyl acetates) polymers were obtained by radical polymerization with azodiisobutyronitrile. The thermal stabilities of the metal polymers (M-PVAC) have been studied by thermogravimetry (TG) between 25 and 550°C under nitrogen flow. The decomposition temperature was obtained from the maximum of the first derivative from TG curve. The kinetic parameters of the thermal decomposition were determined by the Arrhenius equation. All these polymers degrade mainly in a single step with a very small second step, probably via a complex reaction. The kinetic data thus obtained show that the thermostabilities decrease in the order: Sb-PVA_c～Ge-PVA_c>Bi-PVA_c～Cd-PCA_c>Ag-PVA_c～PVA_c>Zn-PVA_c> Au-PVA_c>In-PVA_c>Sn-PVA_c>Ga-PVA_c>Pd-PVA_c. Again, the thermal stability is dependent upon the metal incorporated in the backbone polymer. They loose weight after 320°C. The order of reaction from the thermal decomposition of these metal polymers was found to be ?0.5 for the first step and 0 for the second. The pre-exponential factor, the reaction order and the activation energy of the decomposition for metal (PVA_c) have been determined in most of them.     

On extensions of the domain invariance theorem

If f maps continuously a compact subset X of Rⁿ into Rⁿ and x is a point whose distance from the boundary ∂X is greater than double diameter of the fibres of the points in f(∂X) then f(x) is in the interior of f(X). This theorem extends some results due to Borsuk and Sitnikov.     

On algebras with unique essentiallyn-ary operations

In this paper we characterize the class of algebras with one fundamental operation having for every nonnegative integern exactly one essentiallyn-ary polynomial.Presented by Joel Berman.     

Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence sequences

In this paper some decompositions of Cauchy polynomials, Ferrers-Jackson polynomials and polynomials of the form x ²ⁿ + y ²ⁿ , n ∈ ℕ, are studied. These decompositions are used to generate the identities for powers of Fibonacci and Lucas numbers as well as for powers of the so called conjugate recurrence sequences. Also, some new identities for Chebyshev polynomials of the first kind are presented here.     

Study of Amorphous Ferrimagnet Fe0.66Er0.19B0.15 by Means of Monochromatic Circularly Polarised Source

Properties of amorphous alloy Fe_0.66Er_0.19B_0.15 are reported. A reorientation of the Fe and Er magnetic moments during sample cooling through the compensation point in a large magnetic field is found by means of monochromatic circularly polarised radiation. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the stability of the polaron in one dimensional disordered systems

A one-dimensional disordered system of electrons described by a tight binding model interacting with vibrational degrees of freedom (in harmonic approximation) is considered. A stable configuration is determined by a numerical minimization of the total energy which is based on the adiabatic approximation. The behaviour of the electron density (charge density wave) and the density of states is analysed. The localization properties are investigated as well. In contrast to the corresponding disordered system with vanishing electron-phonon coupling the present model has an energy gap. The formation of the gap and the polaron band is shown to be quite different for both onsite and intersite types of coupling terms. For large disorder, the lattice distortion and the gap disappear if only the vibrational contribution to the intersite coupling is important. They increase, however, if only the vibrational contribution to the site energies is taken into account. In both cases the localization length decreases upon increasing the electron-phonon coupling energy. The results are discussed with respect to low dimensional organic materials and amorphous semiconductors.