Mean quadratic error of an estimate of splines of first order in a model of linear regression

We study the mean quadratic error of an estimate of splines of the first order, which is obtained by the method of least squares under the assumption that the data represents a superposition of proper values of a spline and a white noise. A quantitative formula for the quadratic mean error is found and its asymptotics is investigated.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 3, pp. 429–432, March, 1991.     

Sets of pairs of values omitted by univalent functions

This article proves covering theorems for classes of univalent functions that omit given pairs of values. In particular, a problem posed by D. A. Brannan [R. Zh. Mat. 1978, 2B63] is solved.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 185, pp. 140–145, 1990.     

Optimization problems of the stress-deformed state of thermoelastic shells

We discuss general questions about the choice of optimization criteria for the stressed state of thermoelastic shells taking account of the functional measures of the space-time variability of its characteristics. The efficiency of the proposed approach is illustrated using the example of the solution of a problem for an axisymmetrically heated cylindrical shell.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 11–18.     

采用级联原子滤光器的新型卫星激光链路系统研究

提出级联佛克脱型原子滤光器(Linked VADOF)的新构想。从理论上分析并计算了级联佛克脱型原子滤光器的透射谱。结果表明，级联佛克脱型原子滤光器将佛克脱型原子滤光器的多峰改造为单峰结构，具有比佛克脱型原子滤光器更窄的线宽和更高的噪声抑制比。将这种新型结构应用于激光信标锁频。该锁频方案提高了信标光频率的稳定性。在此基础上，给出了发射端采用级联佛克脱型原子滤光器锁频，接收端采用法拉第型原子滤光器(FADOF)滤光的新型卫星激光链路系统。外场初步联调实验表明了该系统的可行性。     

Electrochemically induced processes in the formation of phosphorus acid derivatives. 2. The role of polymerization processes in the electrosynthesis of the esters of phosphorus acids from white phosphorus

The mechanism of the electrosynthesis of phosphate esters from white phosphorus was investigated. It was shown that the reaction takes place by two paths, i.e., monomeric (with the participation of dissolved phosphorus) and polymeric (with the participation of phosphorus on the surface of an emulsion drop). It was established that in an alcohol solution of tetraethylammonium iodide the main part of the final product is formed through an intermediate polymeric compound. It was noticed that by studying the dynamics of the accumulation of the dissolved product during electrolysis it is possible to trace the mechanism of reaction of the phosphorus at the individual stages of the process.A. E. Arbuzov Institute of Organic and Physical Chemistry, Kazan' Scientific Center, Russian Academy of Sciences, 420028 Kazan'. V. I. Ul'yanov-Lenin Kazan' State University, 420028 Kazan'. Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 6, pp. 1328–1333, June, 1992.     

Stress concentration around a curvilinear hole in plates and shells

Azerbaidzhan Economic Institute, Baku. Translated from Prikladnaya Mekhanika, Vol. 27, No. 1, pp. 71–77, January, 1991.     

Effect of aging of the binder on the creep of polymer concrete

Two polyester concretes with diabase and marble fillers and aggregates are used as examples to illustrate the possibility of using a structural approach to evaluate the creep of the composite in the initial state and after preliminary aging under laboratory conditions for a period of 12–13 yrs. Experimental study of the creep of polymer concrete and its structural components (resin and binder) after preliminary aging at elevated temperatures (60, 90°) established that the change that occurs in viscoelastic compliance with aging conforms to the analogy principle with a reduction function that depends on aging temperature and time.Institute of Polymer Mechanics. Latvian Academy of Sciences Riga, Latvia. Central Laboratory of Physico-chemical Mechanics Sofia. Bulgaria. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 6, pp. 787–794, November–December, 1996.     

Statistical interpretation of the p-adic quantum field theory

A p-adic generalization of the frequency theory of probability is developed. Within the framework of this theory frequency meaning is imparted to probabilities belonging to the field of p-adic numbers. The Bargmann-Fock representation is constructed for the p-adic field theory. A frequency interpretation of quantum states in the Bargmann-Fock representation is proposed. The p-adic generalization is essentially an introduction of new quantum states which are meaningless from the point of view of the standard theory of probability based on Kolmogorov's axiomatics.Moscow Institute of Electronic Engineering. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 51–55, November, 1992.     

Power expansions for the self-similar solutions of the modified Sawada-Kotera equation

The fourth-order ordinary differential equation that defines the self-similar solutions of the Kaup—Kupershmidt and Sawada—Kotera equations is studied. This equation belongs to the class of fourth-order analogues of the Painlevé equations. All the power and non-power asymptotic forms and expansions near points z = 0, z = ∞ and near an arbitrary point z = z ₀ are found by means of power geometry methods. The exponential additions to the solutions of the studied equation are also determined.