Effect of Gd-Mn exchange on phase transitions in GdMn<Subscript>2</Subscript>O<Subscript>5</Subscript> induced by a strong magnetic field

Complex studies of the magnetic, magnetoelectric, and magnetoelastic properties of GdMn₂O₅ single crystals in strong pulsed magnetic fields are carried out in order to obtain additional indirect information on the character of the rare-earth and manganese spin ordering. It is shown that magnetic ordering of Gd³⁺ spins affects the manganese sublattice spin orientation and initiates new magnetic phase transitions. The observed magnetoelectric properties of the GdMn₂O₅ system are interpreted in terms of the theory of phase transitions.     

Phase dynamics of a relativistic electron driven by the potential field of a wave packet: Poincaré transformation dynamics

We investigate the Poincaré transformation dynamics describing the stochastic motion of a relativistic electron in the regular electrostatic field of a wave packet. The conditions of local instability of the phase trajectories are determined: it is shown that the system is a structurally stable Y system with an attracting set of the hyperbolic type. The relationship between the dynamics at the strange attractor characterized by Lyapunov indices and its statistical structure described by the Kolmogorov entropy is discussed. The fractal dimension of the phase space of the system is determined. The results of a numerical simulation of the effect are presented and discussed. Altai State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 15–20, June, 1998.     

On the Theory of Heat Conductivity, Electrical Conductivity, and Hydraulic Conductivity of Polydisperse Polyhedral Foams and Highly Concentrated Emulsions

Rigorous formulas for the heat conductivity, electrical conductivity, and hydraulic conductivity of polydisperse polyhedral foams and highly concentrated emulsions are derived on the basis of the ideas recently formulated by one of the authors, with the structure of Plateau borders and films represented in the form of hierarchic series.     

Strong approximation by Fourier series and differentiability properties of functions

ПустьΦ —N-функция Юнг а со свойствами $$\Phi (x)x^{ - 1} \downarrow 0, \exists \alpha > 1 \Phi (x)x^{ - \alpha } \uparrow (x \downarrow 0),$$ илиΦ(х)=х, {λ_k} — положи тельная, неубывающая последовательность и $$S_\Phi \{ \lambda \} = \left\{ {f:\left\| {\sum\limits_{k = 0}^\infty \Phi (\lambda _k |f - s_k |)} \right\|_\infty< \infty } \right\}.$$ В работе найдены необ ходимые и достаточны е условия для вложений $$S_\Phi \{ \lambda \} \subset W^r F(r \geqq 0),$$ , гдеF=C, L ^∞, Lip α (0<α≦1). С этой то чки зрения рассматриваются и др угие классы (например, \(W^r H^\omega ,\tilde W^r F\) ).     

FPGA-Implemented Fractal Decoder with Forward Error Correction in Short-Reach Optical Interconnects

Forward error correction (FEC) codes combined with high-order modulator formats, i.e., coded modulation (CM), are essential in optical communication networks to achieve highly efficient and reliable communication. The task of providing additional error control in the design of CM systems with high-performance requirements remains urgent. As an additional control of CM systems, we propose to use indivisible error detection codes based on a positional number system. In this work, we evaluated the indivisible code using the average probability method (APM) for the binary symmetric channel (BSC), which has the simplicity, versatility and reliability of the estimate, which is close to reality. The APM allows for evaluation and compares indivisible codes according to parameters of correct transmission, and detectable and undetectable errors. Indivisible codes allow for the end-to-end (E2E) control of the transmission and processing of information in digital systems and design devices with a regular structure and high speed. This study researched a fractal decoder device for additional error control, implemented in field-programmable gate array (FPGA) software with FEC for short-reach optical interconnects with multilevel pulse amplitude (PAM-M) modulated with Gray code mapping. Indivisible codes with natural redundancy require far fewer hardware costs to develop and implement encoding and decoding devices with a sufficiently high error detection efficiency. We achieved a reduction in hardware costs for a fractal decoder by using the fractal property of the indivisible code from 10% to 30% for different n while receiving the reciprocal of the golden ratio.     

Infrared sensitivity of unstable vacua

We discover that some unstable vacua have long memory. By that we mean that even in the theories containing only massive particles, there are correllators and expectation values which grow with time. We examine the cases of instabilities caused by the constant electric fields, expanding and contracting universes and, most importantly, the global de Sitter space. In the last case the interaction leads to a remarkable UV/IR mixing and to a large back reaction. This gives reasons to believe that the cosmological constant problem could be resolved by the infrared physics.     

Study of thermohumid aging of aircraft fiberglass plastic

The thermohumid aging of aircraft fiberglass plastic over 5.5 years is studied. It is shown that, under conditions that simulate a tropical climate, the controlled parameters (maximal water saturation, moisture diffusion coefficient, shear modulus along the sheet plane) vary to the greatest extent after 1 year of aging, after which they stabilize. The molding conditions under which fiberglass plastic preserves high parameters under long-term exposure to a moist environment are determined.     

On diameter perfect constant-weight ternary codes

From cosets of binary Hamming codes we construct diameter perfect constant-weight ternary codes with weight n-1 (where n is the code length) and distances 3 and 5. The class of distance 5 codes has parameters unknown before.