Analysis of the Heat-Insulating Materials Properties for Pipeline Fittings

A relationship for the determination of the optimal thickness of heat insulation for line systems is developed. Experimental findings concerning the heat-insulation properties of liquid-ceramic heat-insulation materials are given for valves.     

Observation of an intermediate phase in the K<Subscript>3</Subscript>Na(CrO<Subscript>4</Subscript>)<Subscript>2</Subscript> ferroelastic by Raman scattering

This paper reports on the first study in K₃Na(CrO₄)₂ crystals of Raman spectra within a broad temperature interval of 4–300 K. The study has revealed significant variations in the intensity and shape of the Raman lines at T = 150 K; a group theory analysis has revealed that the structural phase transition in this ferroelastic proceeds in two stages through an intermediate phase: \(P\bar 3m1 \to C2/m \to C2/c\).     

Steady streaming around a spherical drop displaced from the velocity antinode in an acoustic levitation field

The steady (acoustic) streaming associated with a sphericaldrop displaced from the velocity antinode of a standing waveis studied. The ratio of the particle size to the acoustic wavelengthis treated as small but non-zero, and the solution is developedin the form of a two-term expansion in terms of the correspondingsmallness parameter. The drop viscosity is assumed to be muchhigher than that of the surrounding fluid, which is the casefor a drop in a gas medium. There are essentially three distinctregions where the steady streaming flow is analysed: insidethe drop (internal circulation), in the Stokes shear-wave layerat the surface on the gas side, and the gas outside the Stokeslayer (the outer streaming region). Solutions for the internalcirculation and the outer streaming are obtained in the limitof small Reynolds number. Despite the gas-to-liquid viscosity ratio being small, the outerstreaming may be dramatically affected by the fact that thesphere is liquid as opposed to solid. The parameter that measuresthe effect of liquidity is essentially the viscosity ratio dividedby the relative (to the particle size) thickness of the Stokeslayer. The case of a solid sphere is recovered by letting thisparameter go to zero.     

Classifying Descents According to Parity

In this paper we refine the well-known permutation statistic “descent” by fixing parity of (exactly) one of the descent’s numbers. We provide explicit formulas for the distribution of these (four) new statistics. We use certain differential operators to obtain the formulas. Moreover, we discuss connection of our new statistics to the Genocchi numbers. We also provide bijective proofs of some of our results. Received September 7, 2005     

Kinetics of Lead Sulfide Precipitation from Citrate Solutions of Thiourea

The kinetics of lead sulfide precipitation with thiourea from alkaline solutions at 30, 40, and 50°C under conditions of spontaneous nucleation of the solid phase in the solution bulk was studied.     

Kinetics of Cadmium Sulfide Precipitation from Aqueous Thiourea Solutions

Kinetics of cadmium sulfide precipitation with thiourea from solutions of cadmium(II) ammine complexes under conditions of spontaneous nucleation of the solid phase in the bulk of solution was studied.     

Simulation of Topological Field Theories¶by Quantum Computers

Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering, the most abstract reaches of theoretical physics has spawned “topological models” having a finite dimensional internal state space with no natural tensor product structure and in which the evolution of the state is discrete, H≡ 0. These are called topological quantum field theories (TQFTs). These exotic physical systems are proved to be efficiently simulated on a quantum computer. The conclusion is two-fold: 1. TQFTs cannot be used to define a model of computation stronger than the usual quantum model “BQP”. 2. TQFTs provide a radically different way of looking at quantum computation. The rich mathematical structure of TQFTs might suggest a new quantum algorithm. Received: 4 May 2001 / Accepted: 16 January 2002     

Transformations RS42(3) of the Ranks ≤ 4¶and Algebraic Solutions of the Sixth Painlevé Equation

Compositions of rational transformations of independent variables of linear matrix ordinary differential equations (ODEs) with the Schlesinger transformations (RS-transformations) are used to construct algebraic solutions of the sixth Painlevé equation. RS-Transformations of the ranks 3 and 4 of 2 × 2 matrix Fuchsian ODEs with 3 singular points into analogous ODE with 4 singular points are classified. Received: 17 August 2001 / Accepted: 14 February 2002     

Multi-avoidance of generalised patterns

Recently, Babson and Steingrímsson introduced generalised permutation patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. We investigate simultaneous avoidance of two or more 3-patterns without internal dashes, that is, where the pattern corresponds to a contiguous subword in a permutation.