The normal form of germs of four-dimensional real submanifolds in ℂ n at generic ℝℂ-singular points

Mathematical Notes -     

The stress-strain state of anisotropic rock

We use integrals of Cauchy type and the complex potentials of S. G. Lekhnitskii to solve the problem of the stress-strain state of a piecewise-homogeneous anisotropic rock during the working of a horizontal seam of mineral. We study the stress distribution in the deloaded zones. Three figures, 1 table. Bibliography: 4 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 27, 1997, pp. 81–86.     

Statistical hydrodynamics of magnetic fluids. I. the nonequilibrium statistical operator method

The Zubarev nonequilibrium statistical operator is used to describe the generalized hydrodynamic state of a magnetic fluid in an external magnetic field. The magnetic fluid is modeled with “liquid-state” and “magnetic” subsystems described using the classical and quantum statistics methods respectively. Equations of the generalized statistical hydrodynamics for a magnetic fluid in a nonhomogeneous external magnetic field with the Heisenberg spin interaction are derived for “liquid-state” and “magnetic” subsystems characterized by different nonequilibrium temperatures. These equations can be used to describe both the weakly and strongly nonequilibrium states. Some limiting cases are analyzed in which the variables of one of the subsystems can be formally neglected. Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. 115, No. 1, pp. 132–153, April, 1998.     

Records in the Fα-scheme. II. Limit laws

Limit theorems for the number of records in a sequence of independent nonidentically distributed random variables are obtained. A generalization of the so-called F^α-scheme is given. Bibliography: 4 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 216, 1994, pp. 42–51. Translated by A. Sudakov.     

Isolation of acetic acid-tolerant Baker’s yeast variants in a turbidostat

A commercial baker’s yeast was subjected to selection in a continuous turbidostat cultivation with increasing concentration of acetic acid. The final acetic acid content in fresh medium was 0.6% or 0.8% v/v. Two of seven selected variants were stable over 15 sequential shake flask cultivations without selection pressure. After laboratory scale production of baker’s yeast, one of the variants also showed increased acetic acid tolerance in sour dough. The overall raising power (mL CO₂/h) in sour dough was improved 36%.     

Kinetics of the reactions of the IO radical with dimethyl sulfide,methanethiol, ethylene,and propylene

The reactions of IO radicals with CH₃SCH₃, CH₃SH, C₂H₄, and C₃H₆ have been studied using the discharge flow method with direct detection of IO radicals by mass spectrometry. The absolute rate constants obtained at 298 K are the following: IO + CH₃SCH₃ → products (1): k₁ = (1.5 ± 0.2) × 10^?14; IO + CH₃SH → products (2): k₂ = (6.6 ± 1.3) × 10^?16; IO + C₂H₄ →products (3): k₃ < 2 × 10^?16; IO + C₃H₆ → products (4): k₄ < 2 × 10^?16 (units are cm³ molecule^?1 s^?1). CH₃S(O)CH₃ and HOI were found as products of reactions (1) and (2), respectively. The present lower value of k₁ compared to our previous determination is discussed.     

351 nm, 0.7 ns laser damage thresholds of monomeric liquid-crystalline systems

The 351 nm laser-damage thresholds (at 0.7 nm pulse length) of monomeric liquid crystals are reported and results from aromatic-core samples are compared with those from fully saturated systems. The role of π-electron conjugation is examined and identified as the key cause for laser damage. For UV laser compatibility of devices, the damage behaviour of an alignment-layer polymer (nylon 6/6) was also investigated.     

Optimality conditions in a resource allocation problem

Translated from Vychislitel'nye Kompleksy i Modelirovanie Slozhnykh Sistem, pp. 138–141, Moscow State University, 1989.