Abstract In this paper we are interested in Riesz basisness of root functions of the non-selfadjoint a discontinuous Sturm–Liouville operator with periodic boundary condition which are not strong regular and with conjugate conditions. Here we assume that the potentials are complex valued and continuously differentiable functions. One of conjugate conditions have different finite one-sided limits at

Abstract In investigation of boundary-value problems for certain partial differential equations arising in applied mathematics, we often need to study the solution of a system of partial differential equations satisfied by hypergeometric functions and find explicit linearly independent solutions for the system. In this investigation, we construct special solutions for a certain class of degenerating

Abstract In this research work, for a third-order elliptic-hyperbolic type equation, a method for studying a nonlocal boundary-value problem by solving the inverse problem for a second-order mixed elliptic-hyperbolic type equation with an unknown right-hand side was proposed. A new extremume principle for a third-order equation was developed, and with the help of which the uniqueness of the problem

Abstract The work is devoted to the construction of the asymptotics of the solution of a singularly perturbed system of equations of parabolic type, in the case when the limit equation has a regular singularity as the small parameter tends to zero. The asymptotics of the solution of such problems contains, along with parabolic boundary layer functions, and power boundary layer functions.

Abstract We study a regularization of linear Volterra integral equation of the first kind with differentiable kernel degenerated at the initial point or at the end point of the interval on the diagonal. Accordingly, in the first case, the kernel on the diagonal is a non-decreasing function, in the second case, a non-increasing function. Regularizing Lavrentiev’s type operator is constructed that preserves

Abstract Boundary-value problems for loaded equations in the plane in the case of loaded parts consist of traces of an unknown solution or its first normal derivatives, are well studied. The multidimensional loaded differential equations are relatively less investigated. Moveover, when the loaded part consists of not only the traces of the solution or its first normal derivatives, but also second derivatives

Abstract In the three-dimensional domain a Boussinesq type nonlinear partial integro-differential equation of the fourth order with a degenerate kernel, integral form conditions, spectral parameters and reflecting argument is considered. The solution of this partial integro-differential equation is studied in the class of generality functions. The method of separation of variables and the method of

Abstract For a mixed-type equation of the second kind with a singular coefficient by the spectral expansions uniqueness criterion is installed for solving the first boundary-value problem. The solution was constructed as the sum of a Fourier–Bessel series. In justifying the uniform convergence appeared the problem of small denominators. In connection with this evaluation is set on a small separation

Abstract We consider a three-dimensional elliptic equation with two singular coefficients, for which a nonlocal problem is studied in a semi-infinite parallelepiped. The study of the problem is carried out using the method of separation of Fourier variables and spectral analysis. For the problem posed, using the Fourier method, two one-dimensional spectral problems are obtained. Based on the completeness

Abstract An investigation of applied problems related to heat conduction and dynamics, electromagnetic oscillations and aerodynamics, quantum mechanics and potential theory leads to the study of various hypergeometric functions. The great success of the theory of hypergeometric functions in one variable has stimulated the development of corresponding theory in two and more variables. In the theory

Abstract The questions of weakly generalized solvability of a nonlinear inverse problem in nonlinear optimal control of thermal processes for a parabolic differential equation are studied. The parabolic equation is considered under initial and boundary conditions. To determine the recovery function, a nonlocal integral condition is specified. Moreover, the recovery function nonlinearly enters into

Abstract The aim of the research is the development of the asymptotic method of boundary functions to Robin problem for a ring with regularly singular boundary. This work is devoted to constructing complete asymptotic expansions of the solutions of Robin problem for singular perturbed inhomogeneous linear second order elliptic equation with regularly singular boundary. Singularities of the equation:

Abstract The Cauchy problem for an iterated generalized two-axially symmetric equation of hyperbolic type is investigated. Unlike traditional methods, the generalized Erdélyi–Kober operator of fractional order is applied to solve the problem. The application of this operator allows us to reduce the equations with the lowest term and with the singular Bessel operator acting in one of the variables to

Abstract In the work Tricomi problem was investigated for a parabolic-hyperbolic type equation in a mixed domain. If the parabolic degeneration line is a characteristic of a hyperbolic equation, then Tricomi problem for considered equation will not be uniquely solvable. Therefore, another formulation of Tricomi problem was proposed which the gluing condition is given as in [1, 2]. To study Tricomi

Abstract The peridinamics theory, proposed by Silling in 2000, is a nonlocal theory of continuum mechanics based on an integro-differential equation without spatial derivatives and may cope with discontinuous displacement fields commonly occurring in fracture mechanics. Instead of spatial differential operators, integration over differences of the displacement field is used to describe the existing

Abstract The article studies the asymptotic behavior of the solutions of a singularly perturbed three boundary value problems on an interval. The object of the study is a linear inhomogeneous ordinary differential equation of the second order with a small parameter with the highest derivative of the unknown function. The singularities of the problem are that the small parameter is found at the highest

It is found the spectrum of a singular integral operator on the compound contour with elliptic function in the kernel. Explicit solution of the corresponding singular integral equation is constructed by applying its reduction to the boundary value problem on the Riemann surface.

This paper is devoted to study of the relationship between M-orthogonality and orthogonality in the sense of SFS-spaces in dual space. A geometric characterization of geometric tripotents in reflexive complex SFS-spaces is given.

A motif is a pair of subsequences of a longer time series, which are very similar to each other. Motif discovery is applied in a wide range of subject areas involving time series: medicine, biology, entertainment, weather prediction, and others. In this paper, we propose a novel parallel algorithm for motif discovery using Intel MIC (Many Integrated Core) accelerators in the case when time series fit

The paper deals with the normal extensions of cancellative commutative semigroups and the Toeplitz algebras for those semigroups. By the Toeplitz algebra for a semigroup S one means the reduced semigroup C*-algebra C*r(S). We study the normal extensions of cancellative commutative semigroups by the additive group ℤn of integers modulo n. Moreover, we assume that such an extension is generated by one