On the Huang Class of Variable Metric Methods

Several authors have created one-parameter families of variable metric methods for function minimization. These families contain the methods known as Davidon–Fletcher–Powell, Broyden–Fletcher–Goldfarb–Shanno, and symmetric rank one. It is shown here that the same one-parameter families of methods are obtained from the Huang update by requiring the update to be symmetric.     

The effect of rate of deformation on the mechanical characteristics of plastics

An experimental investigation of the effect of the rate of deformation on the strength and modulus of elasticity of vinyl plastic and glass-reinforced laminate is described. It is established that when the rate of relative tensile deformation of vinyl plastic at 25°C is reduced from 2000×10^–6 sec^–1 to 5×10^–6 sec^–1, and that for glass-reinforced laminate from 1000×10^–6 sec^–1 to 1.3×10^–6 sec^–1, the decrease in the modulus of elasticity is about 40% and the decrease in ultimate strength 30 and 48%, as the case may be.Mekhanika polimerov, Vol. 1, No. 1, pp. 76–81, 1965     

On the number of relaxation regions in polyformaldehyde

The mechanical relaxation of a polyformaldehyde homopolymer free from surface grease and the additives normally used as stabilizers has been studied at a frequency of 10^–2 Hz in the temperature region 77–413°K. Six relaxation regions are observed on the curve of tangent of angle of mechanical losses as a function of temperature.T. G. Shevchenko Kiev State University. Translated from Mekhanika Polimerov, No. 5, pp. 925–927, September–October, 1973.     

Temperature dependence of the coefficient of friction of Ftorlon-graphite fiber

The reduced friction of Ftorlon (fluoroplastic) — graphite fiber against steel on the temperature interval 120–190°C is examined.Khmel'nitskii Technological Institute of Maintenance and Repairs. Translated from Mekhanika Polimerov, No. 6, pp. 1120–1121, November–December, 1973.     

On M. G. Krein's work in the theory of linear periodic Hamiltonian systems

We present basic ideas of the theory of linear periodic Hamiltonian systems.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, Nos. 1–2, pp. 128–144, January–February, 1994.     

Polymer fractography and fracture kinetics

The fractographic method makes it possible to determine the test temperature and time at which anomalies appear in the temperature-time dependence of the strength of polymethyl methacrylate and polycaprolactam by finding the conditions of disappearance of specular zones from the fracture surfaces of these polymers. For PMMA these values are –40°C and 10^–2 sec, for PCL –120°C and 10^–7 sec, respectively.For communication 1 see [2].Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 2, pp. 232–237, March–April, 1971.     

Static friction of metal - polymer pairs under vacuum conditions

The static friction of a series of polymer — steel friction pairs has been investigated as a function of the stationary contact time at temperatures from –150°C to +200°C. The experimental technique is described and the results of the experiments are evaluated.Novocherkassk Sergo Ordzhonikidze Polytechnic Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1065–1069, November–December, 1970.     

Variation of Curvatures of Subanalytic Spaces and Schläfli-Type Formulas

We prove a strong variational formula for Lipschitz–Killing curvaturesof subanalytic sets. As corollaries, we reprove the Chern–Gauss–Bonnettheorem and higher Schläfli formulas. The proof of the variationalformula uses normal cycles of subanalytic sets and a new method allowinga reduction from the difficult singular geometry to computations withdifferential forms.     

Experimental study of young's modulus of glass-plastics

The results of study of Young's modulus of glass-plastics in the 10^–1–10⁵-Hz frequency range are presented. A stepwise variation in the modulus, which governs the relaxation process corresponding to a low-temperature internal-friction peak in the filler, is obtained.Rybinsk Institute of Aircraft Technology. Translated from Mekhanika Polimerov, No. 6, pp. 1089–1091, November–December, 1975.     

Subrings of invariants of a finite group of automorphisms of a Jordan ring

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 1, pp. 207–211, January–February, 1991.     

M. G. Krein's ideas in the theory of orthogonal polynomials

This is a survey of M. G. Krein's ideas in the theory of orthogonal polynomials.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, Nos. 1–2, pp. 76–86, January–February, 1994.     

Mass-spectrometric investigation of solid lubricating coatings subjected to friction in a deep vacuum

The life of solid lubricating coatings of the VNII NP type, based on molybdenum disulfides and various binders, has been experimentally investigated under deep vacuum conditions (10^–8–5 · 10^–9 torr) together with the composition of the gas released in the friction process. It is shown that both under atmospheric conditions and in a deep vacuum the life of the coatings depends on the chemical nature of the film-former. The depth of the vacuum also has an important influence on the life of the coatings, both the mechanism and the end result of this effect depending to a large extent on the physicochemical properties of the bind. On the interval 10^–1–10^–2 torr there is a sudden change in the life of the coating.Physicotechnical Institute of Low Temperatures, Academy of Sciences of the Ukrainian SSR, Khar'kov. Translated from Mekhanika Polimerov, No. 6, pp. 1070–1075, November–December, 1970.     

Quality properties of solutions of diffenetial inequalities of a special form

Volgograd. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 33, No. 3, pp. 78–90, May–June, 1992.     

Supremum of an even moment of sums of independent random variables

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 1, pp. 171–173, January–February, 1991.     

Axiomatizability and completeness of some classes of s-polygons

Translated from Algebra i Logika, Vol. 30, No. 5, pp. 583–594, September–October, 1991.     

The metatheory of sets

Translated from Algebra i Logika, Vol. 30, No. 6, pp. 671–692, November–December, 1991.     

On the existence of certain cyclic difference families and difference matrices

A theorem is proved to the effect that if there exists a BIB-schema with parameters (p^m–1,k, k–1), where k¦(p^m–1), p is prime, and m is a natural number, then there exists a BIB-schema (p^mn–1),k, k–1). A consequence is the existnece of a cyclic BIB-schema (p^mn–1, p^m–1, p^m–2) (p^m–1 is prime) that specifies each ordered pair of difference elements at any distance = 1, 2, ..., p^m–2 (cyclically) precisely once. Recursive theorems on the existence of difference matrices and (v, k, k)-difference families in the group Z_v of residue classes mod v are proved, along with a theorem on difference families in an additive abelian group.Translated from Matematicheskie Zametki, Vol. 52, No. 1, pp. 114–119, July, 1992.     

Effect of temperature on the mechanical properties of boron fibers

The effect of exposure to temperatures on the interval 20–600°C for up to 1000 h on the physicomechanical properties of boron fibers at room temperature has been investigated. Prolonged exposure to temperatures up to 200°C does not have much effect on the mechanical characteristics of the fibers, whereas heating for one hour at 300–350°C increases the strength of the fibers by 10–12%.All-Union Scientific Research Institute of Aviation Materials, Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 329–332, March–April, 1971.     

Dynamic Robust Output Min–Max Control for Discrete Uncertain Systems

Min–max control is a robust control, which guarantees stability in the presence of matched uncertainties. The basic min–max control is a static state feedback law. Recently, the applicability conditions of discrete static min–max control through the output have been derived. In this paper, the results for output static min–max control are further extended to a class of output dynamic min–max controllers, and a general parametrization of all such controllers is derived. The dynamic output min–max control is shown to exist in many circumstances under which the output static min–max control does not exist, and usually allows for broader bounds on uncertainties. Another family of robust output min–max controllers, constructed from an asymptotic observer which is insensitive to uncertainties and a state min–max control, is derived. The latter is shown to be a particular case of the dynamic min–max control when the nominal system has no zeros at the origin. In the case where the insensitive observer exists, it is shown that the observer-controller has the same stability properties as those of the full state feedback min–max control.     

Generalizations of purity

Translated from Algebra i Logika, Vol. 30, No. 4, pp. 432–456, July–August, 1991.