Dimension on Discrete Spaces

In this paper we develop some combinatorial models for continuous spaces. In this spirit we study the approximations of continuous spaces by graphs, molecular spaces and coordinate matrices. We define the dimension on a discrete space by means of axioms, and the axioms are based on an obvious geometrical background. This work presents some discrete models of n-dimensional Euclidean spaces, n-dimensional spheres, a torus and a projective plane. It explains how to construct new discrete spaces and describes in this connection several three-dimensional closed surfaces with some topological singularities It also analyzes the topology of (3+1)-spacetime. We are also discussing the question by R. Sorkin [19] about how to derive the system of simplicial complexes from a system of open covering of a topological space S.Comment: 16 pages, 8 figures, Latex. Figures are not included, available from the author upon request. Preprint SU-GP-93/1-1. To appear in "International Journal of Theoretical Physics

Phase transformation B1 to B2 in TiC, TiN, ZrC and ZrN under pressure

Phase stability of various phases of MX (M = Ti, Zr; X = C, N) at equilibrium and under pressure is examined based on first-principles calculations of the electronic and phonon structures. The results reveal that all B1 (NaCl-type) MX structures undergo a phase transition to the B2-structures under high pressure in agreement with the previous total-energy calculations. The B1-MX structures are dynamically stable under very high pressure (210-570 GPa). The pressure-induced B2 (CsCl-type) MC phases are dynamically unstable even at high pressures, and TiN and ZrN are found to crystallize with the B2-structure only at pressures above 55 GPa. The first-order B1-to-B2 phase transition in these nitrides is not related to the softening of phonon modes, and the dynamical instability of B2-MX is associated with a high density of states at the Fermi level.Comment: 9 pages, 4 figure

Training as a method of future psychologists’ moral values development

The article has the definition of moral values and moral values development (besides for better understanding of this definition we have analysed such notions as morality, values, development, values development).We have examined fundamental moral values of future psychologists and we describe the methods of training as a way of moral values development.В статье дается определение таким понятиям, как моральные ценности и развитие моральных ценностей (кроме того, для лучшего понимания сути данных понятий мы рассмотрели такие понятия: мораль, ценности, развитие, ценностное развитие). Также коротко рассматриваются основные моральные ценности будущих психологов и описываются методы тренинга как способа развития моральных ценностей

Cosmological scalar fields that mimic the ΛCDM\Lambda CDM cosmological model

We look for cosmologies with a scalar field (dark energy without cosmological constant), which mimic the standard $\Lambda CDM$ cosmological model yielding exactly the same large-scale geometry described by the evolution of the Hubble parameter (i.e. photometric distance and angular diameter distance as functions on $z$). Asymptotic behavior of the field solutions is studied in the case of spatially flat Universe with pressureless matter and separable scalar field Lagrangians (power-law kinetic term + power-law potential). Exact analytic solutions are found in some special cases. A number of models have the field solutions with infinite behavior in the past or even singular behavior at finite redshifts. We point out that introduction of the cosmological scalar field involves some degeneracy leading to lower precision in determination of $\Omega_m$. To remove this degeneracy additional information is needed beyond the data on large-scale geometry.Comment: VIII International Conference "Relativistic Astrophysics, Gravitation and Cosmology": May 21-23, 2008, Kyiv, Ukrain

Improving the assay-gravimetric method for determining the content of noble metals

The study considers the current state and problems of analytical control as the most important component of all stages of technology and production of noble metals. Based on the analysis carried out, a universal method for measuring the mass fraction of gold and silver in ores, products of their enrichment and metallurgical processing by the assay-gravimetric method was improved, and the optimal parameters for determining gold and silver were determined

Breeding value of potato hybrid clones from the VIR collection revealed in the environments of Kamchatka Territory

Background. Potato breeding involves planned artificial hybridization between previously selected parental lines. A way to make potato breeding more efficient is to use the diversity of the germplasm and broaden the gene pool of parental lines. Interspecific potato hybrids originated on the elite potato germplasm display a set of valuable traits. The current challenge is to assess the performance of potato hybrids under specific soil and climate conditions to clarify their breeding value.The objective of the study was to evaluate potato hybrids in the environments of Kamchatka Territory according to a set of traits, identify the best parental lines, develop new hybrid combinations, and select promising breeding material.Materials and methods. Eleven potato hybrids from VIR were studied over three years (2020–2022) in the fields of Kamchatka Research Institute of Agriculture. The hybrids were benchmarked against two reference potato cultivars, ‘Fresco’ and ‘Vulkan’, belonging to the early and mid-early maturity groups, respectively. Crosses between the hybrids and 28 potato cultivars were carried out in the greenhouse. The new hybrid material was tested in a preliminary trial nursery for yield and earliness.Results. Hybrid 117-2 was better in yield (899 g/plant) than cvs. ‘Vulkan’ and ‘Fresco’ (700–739 g/plant). Hybrids 94-5, 99-10- 1, 8-1-2004, 8-3-2004, 8-5-2004, 135-3-2005, 135-5-2005, 99-6-6, and 134-2-2006 in most traits matched the potato cultivars, manifesting good berry formation and seed setting when crossed. Out of 140 crosses between 11 hybrids and 28 cultivars, 35 crosses between 10 hybrids and 13 cultivars were successful. Most hybrids were effectively used in crossings as maternal forms.Conclusion. VIR’s hybrids 94-5, 8-1-2004, and 8-5-2004 proved the most promising as source material for the development of new early potatoes under the conditions of Kamchatka Territory

Percolation in Models of Thin Film Depositions

We have studied the percolation behaviour of deposits for different (2+1)-dimensional models of surface layer formation. The mixed model of deposition was used, where particles were deposited selectively according to the random (RD) and ballistic (BD) deposition rules. In the mixed one-component models with deposition of only conducting particles, the mean height of the percolation layer (measured in monolayers) grows continuously from 0.89832 for the pure RD model to 2.605 for the pure RD model, but the percolation transition belong to the same universality class, as in the 2- dimensional random percolation problem. In two- component models with deposition of conducting and isolating particles, the percolation layer height approaches infinity as concentration of the isolating particles becomes higher than some critical value. The crossover from 2d to 3d percolation was observed with increase of the percolation layer height.Comment: 4 pages, 5 figure

Gravitational Ionization: A Chaotic Net in the Kepler System

The long term nonlinear dynamics of a Keplerian binary system under the combined influences of gravitational radiation damping and external tidal perturbations is analyzed. Gravitational radiation reaction leads the binary system towards eventual collapse, while the external periodic perturbations could lead to the ionization of the system via Arnold diffusion. When these two opposing tendencies nearly balance each other, interesting chaotic behavior occurs that is briefly studied in this paper. It is possible to show that periodic orbits can exist in this system for sufficiently small damping. Moreover, we employ the method of averaging to investigate the phenomenon of capture into resonance.Comment: REVTEX Style, Submitte