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We propose a modification of the algorithm aimed at the construction of analytic solutions of plane axisymmetric problems of elasticity and thermoelasticity in stresses for solid cylinders formed by radially inhomogeneous coaxial layers. Unlike the original approach based on the application of the method of direct integration and the procedure of generalized differentiation, the proposed modification makes it possible to formulate and solve the governing equations of problems of this kind in terms of the classical derivatives with respect to the radial coordinate. In this way, we simplify the procedure of construction of iterated integral kernels of the resolvent solution of the governing integral equation of continuity to which the solution of the analyzed problems is reduced by the method of direct integration. [ABSTRACT FROM AUTHOR]

In this paper, for the mapping of a sphere into a compact orientable manifold Sn → M, n ≥ 1, we solve the problem of determining whether it represents a nontrivial element in the homotopy group of the manifold πn(M). For this purpose, we consistently use the theory of iterated integrals developed by Chen. It should be noted that the iterated integrals as repeated integration were previously meaningfully used by Lappo-Danilevsky to represent solutions of systems of linear differential equations and by Whitehead for the analytical description of the Hopf invariant for mappings f : S2n−1 → Sn, n ≥ 2. We give a brief description of Chen's theory representing Whitehead's and Haefliger's formulas for the Hopf invariant and generalized Hopf invariant. Examples of calculating these invariants using the technique of iterated integrals are given. Further, it is shown how one can detect any element of the fundamental group of a Riemann surface using iterated integrals of holomorphic forms. This required to prove that the intersection of the terms of the lower central series of the fundamental group of a Riemann surface is a unit group. [ABSTRACT FROM AUTHOR]

We study the homotopic classifications of maps from circles and spheres to manifolds and compare the classical approach to define the Hopf invariant with the approach based on Chen's iterated integrals. Bibliography: 5 titles. [ABSTRACT FROM AUTHOR]

We study empirical semi-parametric Bayesian estimates of exponential functionals in the model of competing risks. For these estimates we establish the properties of the uniform strong consistency and iterated logarithm type laws. [ABSTRACT FROM AUTHOR]

This article deals with the study of asymptotic properties of a nonparametric kernel estimator of a characteristic function. Uniformly strong consistency of kernel estimator with fixed and expanding interval is established. The law of iterated logarithm type is also proved. [ABSTRACT FROM AUTHOR]