Effect of internal stresses on the wear resistance of epoxy coatings

The results of wear tests on ED-5 epoxy coatings are used to derive a relation between internal stresses, modulus of elasticity, and wear resistance. During wear the internal tensile stresses diminish, the rate of decrease depending on the initial stress state, the material of the abrading body, and the test conditions. The thickness of the coating affects wear resistance up to a certain value; for ED-5 the limiting thickness is 500 microns.Mekhanika Polimerov, Vol. 1, No. 2, pp. 123–128, 1965     

Effect of character of counterbody roughness on the wear resistance of composites based on polyethylene

Conclusions 1. The magnitude of the mean-square deviation in heights of irregularities is not a comprehensive characteristic of the starting roughness of the counterbody for evaluating the wear of polymeric composites. The characteristic of the steel counterbody surface in magnitude of the mean radius of curvature of the peaks of the irregularities is very important.2. On the basis of a study of profilograms of the friction surfaces and results obtained in a study of the wear of composites containing fillers of various hardnesses and dispersities which have been presented in this and preceding articles [3], it has been shown that the presence of filler particles leads to a significant change in the profile of the surface of the steel counterbody (peaks of irregularities are smoothed out, and the mean radius of curvature of the peaks of irregularities increases considerably, by a factor of severalfold). The harder the filler and the coarser the filler particles of a given type, the faster an optimum roughness is created, which ensures the lowest wear of the composite.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 479–485, May–June, 1977.     

On the combinatorics of the number of even parts in all partitions with distinct parts

The Ramanujan Journal - Recently, Andrews and Merca obtained two identities concerning the number of even parts in all partitions of n into distinct parts. In this paper, we provide bijective...     

On the wear of brake pads

Within measurements of brake pads on the IDS high load Tribometer, the wear of pads was investigated by a new non-contact wear measurement under low normal pressures and low temperatures. The first results show that the wear of the pad in the sliding friction is nearly proportional to the friction work, and inversely proportional to the shear strength. The results are also interpreted by the adhesion theory of friction and Archard's equation. On the basis of further interpretations of shear strength and extension of adhesion theory of friction, the wear is derived as a piecewise linear function, which can evaluate explicitly the effect factors of wear and relative correlations at different pressures and different temperatures. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Increasing the convergence rate of series

This paper deals with the question of obtaining from the sequence {s_n} of partial sums of a convergent series s a new sequence {t_n} which converges to the same limit s as s_n, but more rapidly. When the general term u_n of the series s possesses certain types of expansion involving inverse powers of n, it is shown how t_n is obtained by adding a fixed number of terms to s_n. When the series s is convergent, these terms tend to zero as n tends to infinity, but they are such as to make t_n much more rapidly convergent to s—in fact we can make the convergence rate as great as we wish. Explicit general formulas are obtained for a wide range of important series.     

Increasing the security of hash functions

In this paper, we introduce a solution for ensuring data integrity using cryptographic one-way hash functions. The cryptographic security of such hash functions was estimated by us in detail for different kinds of attacks. We propose several new schemes for increasing the security of one-way hash functions without reformation of its internal algorithms. Also we outline schemes with the best speed and security level. We show that the Schneier method of suffix superposition has a serious drawback. In this article, we also suggest the method of constructing collision resistant one-way hash functions from standard well-known hash functions. Therefore, the proposed schemas can be used to upgrade the majority of cryptographic one-way functions, such as MD4, MD5, RIPEMD, SHA, GOST 34 11-94.     

Increasing the applicability of Steffensen's method

We present an original alternative to the majorant principle of Kantorovich to study the semilocal convergence of Steffensen's method when it is applied to solve nonlinear systems which are differentiable. This alternative allows choosing starting points from which the convergence of Steffensen's method is guaranteed, but it is not from the majorant principle. Moreover, this study extends the applicability of Steffensen's method to the solution of nonlinear systems which are nondifferentiable and improves a previous result given by the authors.     

On the imaginary parts of chromatic roots

While much attention has been directed to the maximum modulus and maximum real part of chromatic roots of graphs of order $n$ (ie, with $n$ vertices), relatively little is known about the maximum imaginary part of such graphs. We prove that the maximum imaginary part can grow linearly in the order of the graph. We also show that for any fixed $\text{◂+▸}p\in \left(0,1\right)$, almost every random graph $G$ in the Erdös-Rényi model has a nonreal root.     

Estimates of the averaged sums of fractional parts

We establish asymptotically sharp estimates for the sums of the inverses (and more general sums) of the fractional parts {iθ} of irrational numbers θ, depending on the arithmetical characteristics of the numbers θ.     

Increasing the Weight of Minimum Spanning Trees

The problems of computing the maximum increase in the weight of the minimum spanning trees of a graph caused by the removal of a given number of edges, or by finite increases in the weights of the edges, are investigated. For the case of edge removals, the problem is shown to be NP-hard and an Ω(1/log k)-approximation algorithm is presented for it, where (input parameter) k > 1 is the number of edges to be removed. The second problem is studied, assuming that the increase in the weight of an edge has an associated cost proportional to the magnitude of the change. An O(n³m² log(n²/m)) time algorithm is presented to solve it.     

Increasing the optical anisotropy of polyethylene spherulites

The authors show that in some cases chemical modification leads to an increase in the optical anisotropy of polyethylene spherulites; this phenomenon can be used to obtain additional information on the structure and growth of the spherulites.Institute of the Mechanics of Metal-Polymer Systems, Academy of Sciences of the Belorussian SSR, Gomel'. Translated from Mekhanika Polimerov, No. 2, pp. 343–344, March–April, 1974.