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Statical and dynamical two-dimensional models of a prismatic elastic shell are constructed. The existence and uniqueness of solutions of the corresponding boundary and initial boundary value problems are proved, the rate of approximation of the solution of a three-dimensional problem by the...
In the weighted Lebesgue space with variable exponent the boundedness of the Calderón–Zygmund operator is established. The variable exponent 𝑝(𝑥) is assumed to satisfy the logarithmic Dini condition and the exponent β of the power weight ρ (𝑥) = |𝑥 – 𝑥 0 | β is related only...
For the differential equation where 𝑝 𝑖 ∈ 𝐿 loc (𝑅 + ; 𝑅 + ), τ 𝑖 ∈ 𝐶(𝑅 + ; 𝑅 + ), τ 𝑖 (𝑡) ≤ 𝑡 for 𝑡 ∈ 𝑅 + , , optimal integral conditions for the oscillation of all solutions are established.
A theorem of S. Warschawski on the derivative of a holomorphic function mapping conformally the circle onto a simply-connected domain bounded by the piecewise-Lyapunov Jordan curve is extended to domains with a non-Jordan boundary having interior cusps of a certain type.
This is the sequel of a paper where we introduced an intrinsic ho-motopy theory and homotopy groups for simplicial complexes. We study here the relations of this homotopy theory with the well-known homology theory of simplicial complexes. Also, our investigation is aimed at applications in image...
Starting from the exponential, some classes of analytic functions of the derivative operator are studied, including pseudo-hyperbolic and pseudo-circular functions. Some formulas related to operational calculus are deduced, and the important role played in such a context by Hermite–Kampé de...
We say that a subset 𝑋 of the plane 𝐑 2 is an 𝑜𝑡-set if any three points of 𝑋 form an obtuse triangle. Some properties of 𝑜𝑡-sets are investigated. It is shown that no finite 𝑜𝑡-subset of 𝐑 2 is maximal, but there exists a countable maximal 𝑜𝑡-subset of 𝐑 2...
The Cauchy type singular integral equation is investigated when the line of integration is the union of a countable number of disconnected segments. The equation is equivalently reduced to an equation with double periodic kernel. Effective solutions having integrable singularities at the...
Two explicit guard functions 𝐾 𝑗 = 𝐾 𝑗 ( δ 𝑧 ), 𝑗 = 1, 2, are obtained, which depend on the distance δ 𝑧 between 𝑧 and the nearest point of the integer lattice in the complex plane, such that δ 𝑧 𝐾 1 ( δ 𝑧 ) ≤ | ॣ (𝑧)|𝑒 –π|𝑧| 2 /2 ≤ δ 𝑧...
We consider the vanishing problem for higher cohomology groups on certain infinite-dimensional complex spaces: good branched coverings of suitable projective spaces and subvarieties with a finite free resolution in a projective space P ( V ) (e.g. complete intersections or cones over...
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