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A numerical analysis is made of the joint effect of two factors of asymmetry-ellipticity and eccentricity-on the stress distribution near a free hole in a spherical shell. The nature of deformation is determined by the predominant factor. Whether there are "fixed" points on the graphs of stress distribution around a small hole at which they intersect depends on how rigidly the outer edge is fixed. As the rigidity of fixation is increased, the points smear Introduction. The asymmetric stress-strain state (SSS) near curvilinear holes (cutouts) in isotropic [4,6,9,10] and composite [4,5,8,11] plates and shells is of theoretical and practical interest: the results of a stress-strain analysis would allow us to evaluate the stress and strain of various thin-walled structural members under various kinds of loads.Numerical stress-strain analyses were performed mainly for thin-walled spherical caps with a central elliptical hole [4,5,8,10,11].As pointed out in [1,7], in the off-center case, numerical results are mainly available only for a circular hole, with the emphasis being on the stress distribution around the bridge between the outer and inner edges, which does not give an accurate account of the maximum stresses. Most publications employ special orthogonal coordinate frames and address simply connected stress-concentration problems for elastic isotropic shells. Such problems for elastoplastic shells were analyzed in [6, 10] and for shells made of nonlinear elastic composites in [8].Note that the paper [5], where the SSS of elastic orthotropic laminates with an elliptic hole was analyzed, gives specific results only for a special case (a circular hole).Specific simply and doubly connected problems for spherical shells with a central circular hole or with two circular holes were solved in [6].We will examine the joint effect of two factors of asymmetry (ellipticity and eccentricity) on the SSS only for a rigidly fixed shell with finite mechanical and geometrical parameters.Nowadays, stress-strain studies of doubly and multiply connected thin-walled structural members are of interest. The same applies to the stress-strain analysis of spherical shells (bottoms). We will discuss below results from a stress-strain analysis of elastic isotropic spherical shells with an off-center curvilinear (elliptical or circular) hole.1. Problem Formulation. Let us consider a thin isotropic nonclosed spherical shell of radius R and thickness h with an off-center [7] curvilinear (elliptical, circular) hole. The shell is a doubly connected domain (Fig. 1); its boundaries are the outer and inner edges of the shell. The shell is subjected to surface forces { } { , , } p p p p T = 1 2 3 . The inner boundary can be free, fixed,

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A new integral equation that describes the behavior of the momentum space wave function for the one-dimensional Coulomb potential is proposed. The obtained result turned out to be a homogeneous Fredholm integral equation of the second kind and a singular integral equation, because its kernel has a singularity at some point in the momentum space. A nontriviality of the method of solving this singular integral equation lies in the application of the integral representation for its integral kernel. The technique applied in this paper made it possible to show that the wave function in the momentum representation is simultaneously a solution of the homogeneous Fredholm integral equation of the second kind and of the linear Volterra integral equation of the second kind. 
Since a linear Volterra integral equation of the second kind was easily transformed into a second order linear
inhomogeneous differential equation with constant coefficients, the eigenfunctions and eigenvalues in the one-dimensional Coulomb problem were found without any difficulties. Such a circumstance may indicate the validity of the new integral equation and the proposed method of its solving.