Wear resistance of polyethylene

The effect of the molecular weight and branching of polyethylene on its wear resistance in direct contact with abrasive particles has been investigated. The abrasive wear resistance of the polyethylene increases with its molecular weight. Copolymers have better wear resistance than homopolymers."Plastolimer" Research and Production Association, Leningrad. Translated from Mekhanika Polimerov, No. 3, pp. 542–544, May–June, 1971.     

Wear resistance of metal polymer combinations

The possibilities of using polymer protectors in journal bearings are investigated, and the effects of operating conditions on the wear of metal/metal-polymer composition friction pairs are investigated.Mekhanika Polimerov, Vol. 2, No. 4, 580–584, 1966     

Wear resistance of filled epoxypolyamide composites in aggressive media

The authors investigate the influence of certain aggressive media (toxic chemicals) on the wear resistance of filled epoxypolyamide composites. The presence of toxic chemicals in the zone of friction causes a sharp fall in the wear of the polymers. The maximum wear resistance is displayed by epoxypolyamide composites filled with iron powder, cement, or graphite.     

Wear resistance of bodies protected by a thin composite coating

The mechanical contact interaction of bodies with a thin composite coating is investigated with account of wear. The thermal effects are not considered. The coating is modeled by a thin plate. Between the body and the coating is an interlayer, which is modeled by a Winkler body with one modulus of subgrade reaction. Under the action of a rigid stamp on the coating, the process of abrasive wear proceeds. The contact interaction of the coating with the base is described by using the model of an intermediate layer. To determine the stress-strain state of the coating, equations of the generalized theory of plates including the shear strains and the compression of normal are utilized. For the contact wear problem formulated, the basic integral equation with a Fredholm-type kernel is derived, and its solution algorithm is proposed. Numerical results are presented. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 319–330, May–June, 2006.     

Wear resistance of polymer coatings in relation to their physico-mechanical properties

The existence of a relationship was established between the wear resistance of polymer coatings and metal counterparts on one hand and their elastic moduli on the other; increasing the elasticity modulus of the polymer produces an increase in wear which is reduced by increasing the elastic modulus of the counterpart. It was shown that the wear resistance of polymer coatings depends on the type of hardener used and on the hardening conditions. An expression was derived which quantitatively relates the degree of wear of polymer coatings to their physical state (vitreous, highly-elastic, and visco-plastic).Mekhanika Polimerov, Vol. 2, No. 5, pp. 651–658, 1966     

Wear resistance of steel and brass in friction against filled polyethylene

The wear resistance of a shaft in friction against polyethylene filled with abrasive filler particles (fiberglass, SiO₂) has been investigated. Compositions containing fiberglass can be successfully employed in combination with steel, but are not recommended in combination with brass. Compositions containing SiO₂ cause considerable wear of the steel shaft.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 940–942, September–October, 1969.     

Effect of disperse mineral fillers on the strain-strength properties and crack resistance of cured polyesters

Conclusion The tendency of disperse mineral fillers toward aggregation, with the formation of a continuous framework of particles, when filler content is greater than the SCC is manifest in a sharp increase in the difference between the relative viscosity of polyester binder-pastes in the uncured state and the relative elastic modulus in the cured state. It is also manifest in an increase in the relative modulus and a reduction in crack growth energy in cured composites. In this case, there is an especially large increase in the size of the characteristic defect, which ultimately determines the reduction in the breaking stress. The modification of binder-pastes with surfactants increases filler dispersion and makes it possible to increase the strength of cured composites.Presented at the Sixth All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga, November, 1986).Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 819–824, September–October, 1987.     

Theory of compositions

A survey of papers on the theory of compositions and their application to the investigation of manifolds in spaces with fundamental groups is presented.Translated from Itogi Nauki i Tekhniki. Problemy Geometrii, Vol. 10, pp. 117–145, 1978.I thank Érnst Gergardovich Neifel'd, whose paper [12] stimulated much of this survey, and who, moreover, showed me inestimable help in the formulation of my paper. In particular, he wrote Sec. 17.     

Reconstructing compositions

We consider the problem of reconstructing compositions of an integer from their subcompositions, which was raised by Raykova (albeit disguised as a question about layered permutations). We show that every composition w of n?3k+1 can be reconstructed from its set of k-deletions, i.e., the set of all compositions of n-k contained in w. As there are compositions of 3k with the same set of k-deletions, this result is best possible.     

Relaxation of polyvinylchloride compositions

The relaxation of polyvinyl chloride, stabilized by dibasic lead carbonate or lead stearate and plasticized by a small amount of diisooctyl phthalate, was investigated. It was found that the lead stabilizers and diisooctyl phthalate accelerate the relaxation processes in the polymer. There is a correlation between the rate of the relaxation processes and the glass-transition temperature.Higher Chemicotechnological Institute, Sofia. Translated from Mekhanika Polimerov, No. 5, pp. 916–919, September–October, 1972.     

Symmetrically constrained compositions

Given integers a ₁,a ₂,…,a _n , with a ₁+a ₂+???+a _n ≥1, a symmetrically constrained composition λ ₁+λ ₂+???+λ _n =M of M into n nonnegative parts is one that satisfies each of the n! constraints $\{\sum_{i=1}^{n}a_{i}\lambda_{\pi(i)}\geq 0:\pi \in S_{n}\}$ . We show how to compute the generating function of these compositions, combining methods from partition theory, permutation statistics, and lattice-point enumeration.     

n-Colour self-inverse compositions

MacMahon’s definition of self-inverse composition is extended ton-colour self-inverse composition. This introduces four new sequences which satisfy the same recurrence relation with different initial conditions like the famous Fibonacci and Lucas sequences. For these new sequences explicit formulas, recurrence relations, generating functions and a summation formula are obtained. Two new binomial identities with combinatorial meaning are also given.     

关于正整数有序分拆的一些恒等式和n-colour有序分拆的两个组合性质

研究了正整数的无序分拆与有序分拆的关系.给出了正整数的无序分拆与有序分拆的一些恒等式.并且利用菲波拉契数与正整数n分拆成不含分部量1的有序分拆数的关系给出了n-colour有序分拆的两个组合性质.     

Cyclic compositions and trisotopies

Cyclic compositions in the sense of Springer [T.A. Springer, Oktaven, Jordan-Algebren und Ausnahmegruppen, Universität Göttingen, 1963] and Knus, Merkurjev, Rost and Tignol [M.-A. Knus, A. Merkurjev, M. Rost, J.-P. Tignol, The Book of Involutions, Amer. Math. Soc. Colloq. Publ., vol. 44, Amer. Math. Soc., Providence, RI, 1998. With a preface in French by J. Tits] are investigated by means of cyclic trisotopies, a concept originally due to Albert [A.A. Albert, A construction of exceptional Jordan division algebras, Ann. of Math. (2) 67 (1958) 1–28]. Using the quadrupling of composition algebras, we enumerate cyclic trisotopies and compositions in a rational manner, i.e., without extending the base field. We relate cyclic trisotopies explicitly to simple associative algebras of degree 3 with involution and to the Tits process of cubic Jordan algebras.     

Factorizations of root-based polynomial compositions

Let denote the finite field of order q=p^r, p a prime and r a positive integer, and let f(x) and g(x) denote monic polynomials in of degrees m and n, respectively. Brawley and Carlitz (Discrete Math. 65 (1987) 115–139) introduce a general notion of root-based polynomial composition which they call the composed product and denote by fg. They prove that fg is irreducible over if and only if f and g are irreducible with gcd(m,n)=1. In this paper, we extend Brawley and Carlitz's work by examining polynomials which are composed products of irreducibles of non-coprime degrees. We give an upper bound on the number of distinct factors of fg, and we determine the possible degrees that the factors of fg can assume. We also determine when the bound on the number of factors of fg is met.     

Concave and convex compositions

In a previous work, concave compositions were defined with the restriction that there be essentially the same number of parts on each side of the minimal part. In this work, we drop that restriction, and, in addition, we consider convex compositions as well. We shall link the related generating functions to combinations of classical, false, or mock theta functions and other Appell–Lerch sums.