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     

A Family of Semi-Regular Divisible Difference Sets

We give a construction of semi-regular divisible difference sets with parametersm = p2a(r–1)+2b (pr – 1)/(p – 1), n = pr, k = p(2a+1)(r–1)+2b (pr – 1)/(p – 1)1 = p(2a+1)(r–1)+2b (pr–1 – 1)/(p-1), 2 = p2(a+1)(r–1)–r+2b (pr – 1)/(p – 1)where p is a prime and r a + 1.     

On a Generalized Class of Minimax Inequalities

Some results on a generalized class of minimax inequalities based on the r–I–G–H-KKM mapping theorems in a G–H-space setting are presented. The r–I–G–H-KKM mappings represent a new class of KKM mappings in G–H-spaces as well as in the interval spaces.     

On the growth of entire solutions of algebraic differential equations

This is the opening memorial plenary lecture on memorial meeting in honor of Professor Shlomo Strelitz on Conference of Differential Equations and Complex Analysis, University of Haifa, Israel, December 2000. Shlomo Strelitz: 7.1.1923–27.9.1999, teached at Vilnius University 1946–1973, professor 1967–1973.__________Published in Lietuvos Matematikos Rinkinys, Vol. 45, No. 1, pp. 57–63, January–March, 2005.     

Generalized z-Distributions and Related Stochastic Processes

The class of generalized z–distributions is defined and their properties are investigated. Ornstein–Uhlenbeck–type and self–similar generalized z–processes are constructed and described. Esscher transforms of the generalized z–processes and the mixed generalized z–processes are characterized. Finally, construction and some properties of generalized z–diffusions are also discussed.     

The Maximal and Minimal Ranks of Some Expressions of Generalized Inverses of Matrices

In this paper, we first determine the maximal and minimal ranks of A — BXC with respect to X. Using those results, we then find the maximal and minimal ranks of the expressions AA^– — A^– A — BB^– A — AC^– C and B^– BA — ACC^– with respect to the choice of generalized inverses A^–, B^– and C^–. In particular, we consider the commutativity of A and A^–, A^k and A^–.The research of the author was supported in part by the Natural Sciences and Engineering Research Council of Canada.     

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.     

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.     

New Cyclic Difference Sets with Singer Parameters Constructed from d-Homogeneous Functions

In this paper, for a prime power q, new cyclic difference sets with Singer para- meters ((q ⁿ –1/q–1), (q ^n–1–1/q–1), (q ^n–2–1/q–1)) are constructed by using q-ary sequences (d-homogeneous functions) of period q ⁿ –1 and the generalization of GMW difference sets is proposed by combining the generation methods of d-form sequences and extended sequences. When q is a power of 3, new cyclic difference sets with Singer parameters ((q ⁿ –1/q–1), (q ^n–1–1/q–1), (q ^n–2–1/q–1)) are constructed from the ternary sequences of period q ⁿ –1 with ideal autocorrelation introduced by Helleseth, Kumar, and Martinsen.     

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.     

Über meromorphe Modifikationen

Ohne ZusammenfassungUnter dem gemeinsamen Titel Über meromorphe Modifikationen sind eine Reihe von Arbeiten erschienen, und zwar in der Mathematischen Zeitschrift: Teil I (§ 1–§ 3) Bd. 61, S. 206–234, Teil II (§ 4–§ 6) Bd. 61, S. 467–488, Teil III (§ 7–§ 9) Bd. 62, S. 189–210; in den Mathematischen Annalen: Teil IV (§ 10–§ 12) Bd. 130, S. 147–182. Die Literatur und eine ausführliche Einleitung findet sich in Teil I.     

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.     

Strength of boron fibers

The tensile and flexural strength and elastic properties of continuous boron fibers 95–105 µ in diameter obtained by depositing boron on a tungsten filament 10–12 µ in diameter have been investigated. The strength properties are primarily determined by the defects present at the boron sheath-core interface and for the fibers investigated have a limit of approximately 400 kgf/mm². Coarse surface or internal defects are capable of reducing the strength of the fibers to 200–250 kfg/mm².All-Union Scientific-Research Institute of Aviation Materials, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1126–1127, November–December, 1970.     

Solution of a problem of Ulam

In this paper we solve the following Ulam problem: “Give conditions in order for a linear mapping near an approximately linear mapping to exist” and establish results involving a product of powers of norms [[5.]; [5.]; [5.]]. There has been much activity on a similar “ -isometry” problem of Ulam [ [1.], 633–636; [2.], 263–277; [4.]]. This work represents an improvement and generalization of the work of [3.], 222–224].     

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.     

Superrigidity for homomorphisms into isometry groups of CAT(−1) spaces

CAT(–1) spaces are generalizations of manifolds with negative curvature. In this paper, we prove three types of rigidity results related to CAT(–1) spaces, namely the rigidity of the isometric actions on CAT(–1) spaces under the commensurability subgroups, the higher rank lattices and certain ergodic cocycles. The main idea for our approach relies on a study of the boundary theory we established for the general CAT(–1) spaces.     

Precise distribution properties of the van der Corput sequence and related sequences

The discrepancy is a quantitative measure for the irregularity of distribution of sequences in the unit interval. This article is devoted to the precise study of L_p–discrepancies of a special class of digital (0,1)–sequences containing especially the van der Corput sequence. We show that within this special class of digital (0,1)–sequences over ℤ₂ the van der Corput sequence is the worst distributed sequence with respect to L₂–discrepancy. Further we prove that the L_p–discrepancies of the van der Corput sequence satisfy a central limit theorem and we study the discrepancy function of (0,1)–sequences pointwise.     

Regularized Resolvent of Sums of Commuting Operators

For B ₁ and B ₂ commuting linear operators on a Banach space such that B ₁ generates a bounded strongly continuous semigroup and –B ₂ generates an exponentially decaying strongly continuous holomorphic semigroup, it is shown that (B ₁ – B ₂)^–1 B ₂ ^–r and (B ₁ – B ₂)^–1(–B ₁)^–r are bounded and everywhere defined, for any r > 0. Density of domains may also be removed. The results are applied to various abstract Cauchy problems.     

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.