This article is concerned with the study of the inverse problem of determining the difference kernel in a Volterra type integral term function in the third-order Moore–Gibson–Thompson (MGT) equation. First, the initial-boundary value problem is reduced to an equivalent problem. Using the Fourier spectral method, the equivalent problem is reduced to a system of integral equations. The existence and uniqueness of the solution to the integral equations are proved. The obtained solution to the integral equations of Volterra-type is also the unique solution to the equivalent problem. Based on the equivalence of the problems, the theorem of the existence and uniqueness of the classical solutions of the original inverse problem is proved. 

The review discusses two closely related problems: the solution of the Riemann boundary value problem for analytic functions and some of their generalizations in areas of the complex plane with non-rectifiable boundaries, and the construction of a generalization of the curvilinear integral to non-rectifiable curves that preserves properties important for complex analysis. This work reflects the current state of the issue, and many of the results presented in it were obtained quite recently. At the end of the article, readers are offered a number of unsolved problems, each of which can serve as a starting point for scientific research. 

In this work, in an unbounded domain, we prove the cof the problem with combined Tricomi and Frankl conditions on one boundary characteristic for one class of equations of mixed type. 

In the present paper we consider a 2 \times 2 operator matrix H. We construct an analog of the well-known Faddeev equation for the eigenvectors of H and study some important properties of this equation, related with the number of eigenvalues. In particular, the Birman–Schwinger principle for H is proven.

In this work, the problem of constructing optimal interpolation formulas is discussed. Here, first, an exact upper bound for the error of the interpolation formula in the Sobolev space is calculated. The existence and uniqueness of the optimal interpolation formula, which gives the smallest error, are proved. An algorithm for finding the coefficients of the optimal interpolation formula is given. By implementing this algorithm, the optimal coefficients are found. 

A new geometric necessary condition for regularity of a curved tree-web is found. A class of tree-webs from circles generalizing the regular tree-web of W. Blaschke from three elliptic bundles of circles with pairwise coinciding vertices is considered, and it is shown that only webs equivalent to the Blaschke web are regular in this class. 

This paper investigates conditions under which representability of each element a from the field P as the sum a = f + g, with f q1 = f, g q2 = g and q1, q2 are fixed integers >1, implies a similar representability of each square matrix over the field P. We propose a general approach to solving this problem. As an application we describe fields and commutative rings with 2 is a unit, over which each square matrix is the sum of two 4-potent matrices. 

The equivalence of the norms of deviations of the desired density of a body from operators such as finite density transformation with specially constructed elements and the Radon transformation from it is stated. It is shown how Computer Science, previously established in the theory of Computational (Numerical) diameter, immediately leads to non-trivial results in Computed Tomography.