We study 5-dimensional pseudo-Riemannian manifolds in the form of h-spaces H₃₂ of type {32}. A classification of h-spaces H₃₂,₂ is given according to (non-homothetic) Lie algebras of infinitesimal projective and affine transformations, all projectively mobile metrics are found and the dimensions, basis elements and structural equations of the maximal non-homothetic projective Lie algebras operating in them are indicated.

In this paper, we investigate large deviations of the local time of a self-similar Gaussian process called the generalized fractional Brownian motion process. This process, introduced by M. Zili [4] as an extension of the sub-fractional Brownian motion and fractional Brownian motion Gaussian processes, represents a significant breakthrough in stochastic processes. It provides a more flexible and robust approach to modeling natural phenomena and complex systems.

Our study starts by presenting large deviation estimates for the local time of this process. Additionally, we establish the law of iterated logarithm for the corresponding local time, further enhancing understanding of its behavior.

A homogeneous linear conjugation problem on a closed contour is considered for a three-dimensional piecewise analytic vector. To each of its solutions there corresponds a triple of functions that are the ratios of the boundary values on the contour of the respective components of this solution. Relations are given that connect the elements of the H-continuous matrix-function of the problem and ensure the existence of two of its solutions for which the corresponding components of the associated triples differ by rational factors, while the problem itself admits a closed-form solution.

In this paper, nonlinear stationary fractional-in-space differential equations with order 1 < α < 2 on a metric star graph with three finite bonds are considered. At the branching point of the star grap, the continuity condition for the weight is satisfied, and the generalized Kirchhoff rule is applied. They are found the exact solutions to nonlinear stationary fractional equations on the star graph. These solutions can be extended to star graphs with any number of bonds.

The paper examines the expansion of the strictly stable law for x ^ 0 and x ^ x in the case of extreme values of the asymmetry parameter. Asymptotic expansions of the probability density and distribution functions are obtained, as well as estimates of the residual terms of these expansions. Based on the obtained estimates of the residual terms, a criterion is presented that allows determining the coordinate region within which it is possible to use these asymptotic expansions. The presented calculations confirm the validity of the obtained expressions.

This article considers the inverse problem in the fractional wave equation with the Riemann-Louville derivative. In this case, the direct problem is an initial nonlocal boundary value problem for this equation with initial Cauchy type and nonlocal boundary conditions. As a redefinition condition, a nonlocal integral condition with respect to the direct solution of the problem is specified. Using the Fourier method, this problem is reduced to equivalent integral equations. Then, using the Mittag-Leffler function and the generalized singular Gronwall inequality, we obtain an a priori estimate of the solution in terms of the unknown coefficient, which we will need to investigate for the inverse problem. The inverse problem is reduced to the equivalent integral of a Volterra type equation. To solve this equation, the contraction mapping principle is used. Local existence and global uniqueness have been proven.

On a two-dimensional generalized hierarchical lattice, the distance between opposite vertices of a unit cell square differs from the distance between adjacent vertices and is a new parameter of the model. At each lattice vertex, the field is defined by a set of four components that are generators of the Grassmann algebra. The Gaussian part of the model is determined by a quadratic Hamiltonian which is invariant under the renormalization group transformation. The non-Gaussian part of the model is defined by a Grassmann-valued “free measure density”, whose sets of coefficients are treated as points in a two-dimensional projective plane. The renormalization group transformation in the space of these coefficients is a homogeneous transformation of degree 4 in the projective space. The commutation relation between the Fourier transform in the space of “densities” and the renormalization group transformation is investigated.

This paper investigates vertex processes of the convex hull generated by inhomogeneous Poisson point processes within a parabola in the plane. Using distribution laws and the conditional distribution of the vertex processes, a stationary Markov process is constructed to find an exact expression for the mathematical expectation of the part of the perimeter between the initial vertices of the convex hull.