Variational Derivative for Buckling Loads of Beams and Frames

The finite-difference method is a numerical technique for obtaining approximate solutions to differential equations. The main objective of the present study is to give a new aspect to the finite-difference method by using a variational derivative. By applying this formulation, accurate values of the buckling loads of beams and frames with various end supports are obtained. The performance of this formulation is verified by comparison with numerical examples in the literature __________ Published in Prikladnaya Mekhanika, Vol. 41, No. 7, pp. 139–144, July 2005.     

Monotone Nonincreasing Random Fields on Partially Ordered Sets. I

For an arbitrary poset H and measure ρ on H × _R (where _R is the real axis), we construct a monotone decreasing stochastic field η_ρ and compute its finite-dimensional distributions. In the case where H is a Λ-semilattice and the measure ρ satisfies additional conditions, we compute various characteristics of the field η_ρ such as the expectation of the field value at a point, variance of the field value at a point, and correlation function of the field. The described construction of random fields gives a new method for constructing positive definite functions on posets. Bibliography: 6 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 301, 2003, pp. 92–143.     

Dielectric investigations of associate formation process in thin nitrobenzene interlayers formed between metal substrates

Studies of thickness and temperature dependencies of the dielectric susceptibility of nitrobenzene interlayers formed on conductive substrates were carried out. The obtained data were processed under the assumption of the existence of dimers (with opposite directions of molecular dipole moments) in orientationally ordered wall-adjacent layers. The results were treated on the basis of Lifshits theory.     

Ac behaviour and phase transition in PLZT 6/80/20 ferroelectric ceramics

The Ac behaviour of PLZT 6/80/20 ferroelectric ceramics was analyzed around and above the phase transition. Two relaxation processes are identified, showing that the so-called ‘universal relaxation law’ holds for the ceramics. A critical point in the values of the Ac conductivity, around the temperature corresponding to the maximum of the dielectric losses, is observed below the transition temperature due to the relaxor behaviour. The frequency dependence of the Ac conductivity at various temperatures and the hysteresis loops show classical relaxor behaviour with a diffuse phase transition.     

The thermodynamic properties of Ln2BaO4 (Ln = Sm, Dy, Ho)

The thermodynamic properties of the Ln₂BaO₄ phases (Ln = Dy, Ho, Sm) were studied by the electromotive force method with a fluoride electrolyte (890–1180 K), solution calorimetry in 1.07 N hydrochloric acid at 298.15 K, and differential scanning calorimetry (298–860 K). The experimental data were jointly processed, and the thermodynamic functions of the compounds over the temperature range 298–1200 K were calculated.