# Alexander Georgievich LosevVolgograd State University · Faculty of Mathematics and Information Technology

Alexander Georgievich Losev

PhD

## About

61

Publications

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352

Citations

Introduction

Alexander Georgievich Losev currently works at the Faculty of Mathematics and Information Technology, Volgograd State University. Alexander does research in Hydrology, Hydrogeology and Climatology. Their most recent publication is 'Solvability of the Dirichlet Problem for the Poisson Equation on Some Noncompact Riemannian Manifolds'.

**Skills and Expertise**

## Publications

Publications (61)

Various classification algorithms used in the diagnosis of breast cancer based on microwave radiometry data are considered. In particular, their principles of operation and the possibility of substantiating diagnoses using numerical data are discussed. A substantiation algorithm based on decision trees and a naive Bayesian classifier is presented....

It is proved that the Liouville function associated with the semilinear equation $\Delta u -g(x,u)=0$ is identical to zero if and only if there is only a trivial bounded solution of the semilinear equation on non-compact Riemannian manifolds. This result generalizes the corresponding result of S.A. Korolkov for the case of the stationary Schrödinge...

We studied the possibility of using artificial intelligence (AI) passive microwave radiometry (MWR) for the diagnostics of venous diseases. MWR measures non-invasive microwave emission (internal temperature) from human body 4 cm deep. The method has been used for early diagnostics in cancer, back pain, brain, COVID-19 pneumonia, and other diseases....

This work was done with the aim of developing the fundamental breast cancer early differential diagnosis foundations based on modeling the spacetime temperature distribution using the microwave radiothermometry method and obtained data intelligent analysis. The article deals with the machine learning application in the microwave radiothermometry da...

We introduce the notion of an L-massive subset in a noncompact Riemannian
manifold and study properties of such subsets.
It is proved that a semilinear elliptic equation on a noncompact Riemannian
manifold has a nontrivial bounded solution if and only if there exists an
L-massive subset in this manifold.
A similar assertion is also proved for solut...

The global spread of severe acute respiratory syndrome coronavirus 2, which causes coronavirus disease 2019 (COVID-19), could be due to limited access to diagnostic tests and equipment. Currently, most diagnoses use the reverse transcription polymerase chain reaction (RT-PCR) and chest computed tomography (CT). However, challenges exist with CT use...

This work is devoted to the study of the dependence of the temperature fields of the mammary glands on external conditions and the parameters of the anamnesis, and preliminary examination of patients. As a result, it was possible to significantly improve the space of thermometric diagnostic signs intended for the intelligent system. The initial set...

Purpose: The paper is devoted to a creation of mathematical model of an artificial neural network for detection of breast cancer based on microwave radiothermometry and anamnesis. Design/Methodology/Approach: One of the most complex and urgent challenges of modern medicine is arranging of effective mammological screening. The solution to this probl...

This work was done with the aim of developing the fundamental breast cancer early differential diagnosis foundations based on modeling the space-time temperature distribution using the microwave radiothermometry method and obtained data intelligent analysis. The article deals with the machine learning application in the microwave radiothermometry d...

Microwave radiometry has seen its way in successful usage in medical applications. The focus here is its applicability in cancer detection and monitoring, specifically for breast cancer, as an additional and alternative tool. This is done by capturing the temperature of the skin and the internal tissue. However, the amount of data required by clini...

We study questions of existence and belonging to the
given functional class of solutions of the Laplace-Beltrami equations on a noncompact Riemannian manifold M with no boundary.
In the present work we suggest the concept of φ-equivalency in the
class of continuous functions and establish some interrelation between problems of existence of solution...

The method of microwave radiometry is one of the areas of medical diagnosis of breast cancer. It is based on analysis of the spatial distribution of internal and surface tissue temperatures, which are measured in the microwave (RTM) and infrared (IR) ranges. Complex mathematical and computer models describing complex physical and biological process...

Exact estimations of dimensions of spaces of bounded solutions of stationary Schrodinger equation with finite Dirichlet integral in terms of massive sets are obtained. It is proved that dimension of spaces of bounded solutions of this equation is not less than number of disjoint qD-massive subsets of manifold. This paper partly extends, the results...

The method of microwave radiometry is one of the areas of medical diagnosis of breast cancer. It is based on analysis of the spatial distribution of internal and surface tissue temperatures, which are measured in the microwave (RTM) and infrared (IR) ranges. Complex mathematical and computer models describing complex physical and biological process...

We study questions of existence and belonging to a given functional class of solutions of the inhomogeneous elliptic equations Δu - c(x)u = g(x), where c(x) ≥ 0, g(x) are Hölder fuctions on a noncompact Riemannian manifold M without boundary. In this work we develop an approach to evaluation of solutions to boundary-value problems for linear and qu...

The behavior of solutions of the Poisson equation on noncompact Riemannian manifolds of a special form is studied. Sharp conditions for the unique solvability of the Dirichlet problem on the reconstruction of solutions of the Poisson equation from continuous boundary data at infinity are found.

В работе найдены условия выполнения теорем типа Лиувилля о тривиальности ограниченных решений эллиптического неравенства специального вида, а также стационарного уравнения Гинзбурга-Ландау на некомпактных сферически-симметричных римановых многообразиях. Библиография: 14 названий.

In this paper, we obtain conditions for the validity of Liouville-type theorems on the triviality of bounded solutions of an elliptic inequality of special form as well as of the stationary Ginzburg–Landau equation for noncompact spherically symmetric Riemannian manifolds.

The results of the numerical simulations of the dynamics of shallow waters for Volga-Akhtuba Floodplain are discussed. The mathematical model is based on the system of Saint-Venant equations. Numerical solution applies a combined Lagrangian-Eulerian (cSPH-TVD) algorithm. We have investigated the features of the spring flood in 2011 and found the in...

We study L-harmonic functions (solutions of the stationary Schrödinger equation) on arbitrary noncompact Riemannian manifolds with finitely many ends. We establish some existence and uniqueness results, and obtain sharp dimension estimates for L-harmonic functions on such manifolds.

In this paper, we consider the generalized solutions of the inequality
$$ - div(A(x,u,\nabla u)\nabla u) \geqslant F(x,u,\nabla u)u^q , q > 1,$$
on noncompact Riemannian manifolds. We obtain sufficient conditions for the validity of Liouville’s theorem on the triviality of the positive solutions of the inequality under consideration. We also obt...

In this paper, we consider the generalized solutions of the inequality
$ - div(A(x,u,\nabla u)\nabla u) \geqslant F(x,u,\nabla u)u^q , q > 1,$ - div(A(x,u,\nabla u)\nabla u) \geqslant F(x,u,\nabla u)u^q , q > 1,
on noncompact Riemannian manifolds. We obtain sufficient conditions for the validity of Liouville’s theorem on the triviality
of the po...

We study questions of existence and membership to a given func- tional class of unbounded solutions of the stationary Schrodinger equation u cu = 0, where c is a smooth non-negative function on a non-compact Riemannian manifold M without boundary. We establish some interrelation between problems of existence of solutions of this equation on M and o...

In the paper we consider solutions of the equation ds 2 -c(x)u = 0, c(x) ≥ 0, on complete Riemannian manifolds constituted as follows: the exterior of some compact set is isometric to the direct product of the semiaxis by some compact manifold with the metric ds 2 = h 2 (r) dr 2 + g 2 (r) do 2 . Necessary and sufficient conditions under which bound...

The properties of bounded solutions of elliptic partial differential equations are studied on the Riemannian manifolds of a certain type. The exact condition of solvability of the Dirichlet problem at infinity is proved. Also the condition of existence of the limit at infinity of bounded solutions and the condition of validity of the Liouville theo...

In this paper we study the behavior of bounded harmonic functions on complete Riemannian manifolds (of a certain special type)
depending on the geometry of the manifold.