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Abstract: The regularized asymptotics of the solution of the first boundary-value problem for a two-dimensional differential equation of parabolic type is constructed in the case where the phase derivative vanishes at a single point. It is shown that angular and multidimensional boundary-layer functions appear in problems of this kind parallel with other types of boundary layers. PubDate: 2022-08-11

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Abstract: We perform the structural analysis of C*-subalgebras of the Toeplitz algebra that are generated by inverse subsemigroups of a bicyclic semigroup. We construct a category of the sets of natural numbers of length k < m and associate each set with a certain C*-algebra. As a result, we obtain a category of C*-algebras. The existence of a functor between these categories is proved. In particular, we establish the conditions under which the category of C*-algebras turns into a bundle of C*-algebras. PubDate: 2022-08-11

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Abstract: We consider the problem of equivalence of matrices in the ring M(n, R) and its subrings of block triangular matrices MBT (n1, . . . , nk, R) and block diagonal matrices MBD (n1, . . . , nk, R), where R is a commutative domain of principal ideals, and investigate the relationships between these equivalences. Under the condition that the block triangular matrices are block diagonalizable, i.e., equivalent to their main block diagonals, we show that these matrices are equivalent in the subring MBT (n1, . . . , nk, R) of block triangular matrices if and only if their main diagonals are equivalent in the subring MBD (n1, . . . , nk, R) of block diagonal matrices, i.e., the corresponding diagonal blocks of these matrices are equivalent. We also prove that if block triangular matrices A and B with Smith normal forms S(A) = S(B) are equivalent to the Smith normal forms in the subring MBT (n1, . . . , nk, R), then these matrices are equivalent in the subring MBT (n1, . . . , nk, R). PubDate: 2022-08-11

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Abstract: We find periodic solutions of the d-dimensional (d = 1, 2, 3) Coulomb equations of motion for three identical negative point charges in the field of four identical positive point charges fixed at the vertices of a rectangle. Systems of this kind possess equilibrium configurations. Periodic solutions are obtained with the help of the Lyapunov central theorem. PubDate: 2022-08-11

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Abstract: For systems of non-Lipschitz differential equations, we establish conditions for the existence of invariant sets. To obtain this result, we apply the Green–Samoilenko function and the corresponding operator. PubDate: 2022-08-11

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Abstract: Let V be a vector space over a field and let T(V) denote the semigroup of all linear transformations from V into V. For a fixed subspace W of V, let F(V,W) be the subsemigroup of T(V ) formed by all linear transformations α from V into W such that V α ⊆ W α. We prove that any regular semigroup S can be embedded in F(V,W) with dim(V) = S1 and dim(W) = S , and determine all maximal subsemigroups of F(V,W) in the case where W is a finite-dimensional subspace of V over a finite field. PubDate: 2022-08-11

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Abstract: We obtain new recurrence relations, an explicit formula, and convolution identities for higher-order geometric polynomials. These relations generalize known results for geometric polynomials and lead to congruences for higher-order geometric polynomials and, in particular, for p-Bernoulli numbers. PubDate: 2022-08-11

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Abstract: We study the existence result for a unilateral problem $$ Au-\operatorname{div}\left(\Phi \left(x,u\right)\right)+H\left(x,u,\nabla u\right)=\mu, $$ where Au = − div(a(x, u, ∇u)) is a Leray–Lions operator defined in the Sobolev–Orlicz space \( D(A)\subset {W}_0^1{L}_M\left(\Omega \right)+{W}^{-1}{E}_{\overline{M}}\left(\Omega \right) \) , where M and \( \overline{M} \) are two complementary N-functions. The first and second lower terms Φ and H satisfy solely the growth condition and an arbitrary sign condition and, moreover, u ≥ ζ, where ζ is a measurable function. PubDate: 2022-08-11

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Abstract: We consider a class of generalized convex sets in the real plane known as weakly 1-convex sets. For a set in the real Euclidean space ℝn, n ≥ 2, we say that a point of the complement of this set to the entire space ℝn is an m-nonconvexity point of the set, \( m=\overline{1,n-1} \) , if any m-dimensional plane passing through this point crosses the indicated set. An open set in the space ℝn, n ≥ 2, is called weakly m-convex, \( m=\overline{1,n-1} \) , if its boundary does not contain any m-nonconvexity points of the set. Moreover, in the class of open weakly 1-convex sets in the plane, we select a subclass of sets with finitely many connected components and a nonempty set of 1-nonconvexity points. We mainly analyze the properties of the set of 1-nonconvexity points for the sets from the indicated subclass. In particular, for any set in this subclass, it is proved that the set of its 1-nonconvexity points is open, that any connected component of the set of its 1-nonconvexity points is the interior of a convex polygon, and that, for any convex polygon, there exists a set from the indicated subclass such that its set of 1-nonconvexity points coincides with the interior of a polygon. PubDate: 2022-08-11

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Abstract: We prove the existence of a close relationship between the generalized central series of Leibniz algebras. We also prove some analogs of the classical Schur and Baer group-theoretic theorems for Leibniz algebras. PubDate: 2022-08-11

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Abstract: Let G be a finite group. We say that an element g of G is a vanishing element if there exists an irreducible complex character ðœ’ of G such that (g) = 0. Ghasemabadi, Iranmanesh, and Mavadatpour (2015) made the following conjecture: Let G be a finite group and let M be a finite non-Abelian simple group such that Vo(G) = Vo(M) and G = M . Then G ≅ M. We give an affirmative answer to this conjecture for M = 2Dr+1(2), where r = 2n − 1 ≥ 3 and either 2r + 1 or 2r+1 + 1 is a prime number, and M = 2Dr(3), where r = 2n + 1 ≥ 5 and either (3r−1 + 1)/2 or (3r + 1)/4 is prime. PubDate: 2022-08-08

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Abstract: We prove a generalized Picone-type identity for the Finsler p-Laplacian and use it to establish qualitative results for some boundary-value problems involving the Finsler p-Laplacian. PubDate: 2022-08-08

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Abstract: Generalized Clifford algebras are constructed by various methods and have some applications in mathematics and physics. We introduce a new type of generalized Clifford algebra such that all components of a monogenic function are solutions of an elliptic partial differential equation. One of our aims is to cover more partial differential equations within the framework of Clifford analysis. We prove some Cauchy integral representation formulas for monogenic functions in these cases. PubDate: 2022-08-06

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Abstract: We find the radii of starlikeness and convexity of the derivatives of Bessel function for three different kinds of normalization. The key tools in the proof of our main results are the Mittag-Leffler expansion for the nth derivative of the Bessel function and the properties of its real zeros. In addition, by using the Euler–Rayleigh inequalities we obtain some tight lower and upper bounds for the radii of starlikeness and convexity of order zero for the normalized nth derivative of the Bessel function. As the main results of our investigations, we can mention natural extensions of some known results for the classical Bessel functions of the first kind. PubDate: 2022-08-06

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Abstract: For \( \left\{\overset{\sim }{p};\overrightarrow{h}\right\} \) -parabolic equations with continuous coefficients, we study the problem of finding classical solutions satisfying modified initial conditions with generalized data in the form of Gelfand- and Shilovtype distributions. This condition linearly combines the values of the solution at the initial time and at a certain intermediate time point. We establish the conditions for the correct solvability of this problem and deduce the formula for its solution. By using the obtained results, we solve the corresponding problem with impulsive action. PubDate: 2022-08-06

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Abstract: We study the problem of existence and uniqueness of a bounded solution to a difference equation of the first order with constant operator coefficient in a Banach space. We establish necessary and sufficient conditions for the case where the initial condition and the input sequence belong to certain subspaces. These results are applied to the case of difference equations with a jump of the operator coefficient and difference equations of higher orders. PubDate: 2022-08-06

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Abstract: We establish necessary and sufficient conditions for autonomous nonlinear differential operators defined in the space of functions bounded and continuous on the axis to be C1-diffeomorphisms. PubDate: 2022-08-06

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Abstract: We study a subclass of bi-starlike functions and obtain, for the first time, the initial seven Taylor– Maclaurin coefficient estimates a2 , a3 , . . . , a7 for functions from a subclass of the function class Σ. Some new or known consequences of the accumulated results are also pointed out. PubDate: 2022-08-06

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Abstract: We study the properties of the systems of polynomials of complex variable represented in the form of contour integrals with kernel functions analytic at infinity. We formulate the conditions for the existence of functions associated with these polynomials and sufficient conditions for the expansion of analytic functions in series in these polynomials. The accumulated results can be used to find the expansions of functions in series in the classical orthogonal polynomials in complex domains, the integral representations for some of these polynomials, the dependences of monomials zn of these polynomials, and other relations. PubDate: 2022-08-06

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Abstract: We apply the method of inverse spectral problem to find the solution to the Cauchy problem for a modified Korteweg–de-Vries equation (mKdV) in the class of periodic infinite-gap functions. A simple procedure is proposed for the derivation of the Dubrovin system of differential equations. We prove the solvability of the Cauchy problem for an infinite system of Dubrovin differential equations in the class of five times continuously differentiable periodic infinite-gap functions. It is shown that the sum of a uniformly convergent function series constructed from the solutions of the infinite system of Dubrovin equations and the formulas for the first trace satisfy the mKdV equation. Moreover, it is proved that: (i) if the initial function is a real π-periodic analytic function, then the solution of the Cauchy problem for the mKdV equation with loaded term is also a real analytic function with respect to the variable x; (ii) if the number \( \frac{\pi }{2} \) is a period (antiperiod) of the original function, then \( \frac{\pi }{2} \) is also a period (antiperiod) in the variable x of the solution to the Cauchy problem for the mKdV equation with loaded term. PubDate: 2022-08-06