Articles in "Mathematics"

Summary: In this work a nonlocal problem for the Laplace equation in an unbounded domain is considered. The notion of a strong solution of this problem is defined. Using the Fourier method, we prove the correct solvability of the considered problem in Sobolev spaces generated by a weighted mixed-norm. This problem in the classical formulation was previously considered by E. I. Moiseev [1]. The same type of problem was considered in the work of M. E. Lerner and O. A. Repin [2].

Summary: In this study, we examine cubic stochastic operators, which we will refer to as quasi-strictly non-Volterra cubic operators. Firstly, the definition of a quasi-strictly non-Volterra operator is provided, and the structure of an arbitrary quasi-strictly non- Volterra cubic operator on a two-dimensional simplex S2 is described. Secondly, the fixed and limit points of the quasi-strictly non-Volterra operator on S2 are investigated. It is proven that there exists a repelling unique fixed point.

Summary: In this study, we delve into the spectral properties of a pencil of nonself-adjoint second-order differential operators characterized by almost periodic potentials and impulse conditions. Such operators arise in various physical models, particularly in quantum mechanics, where they describe systems with discontinuities in their potentials or boundary conditions. Understanding the spectrum of these operators is crucial for comprehending the stability and dynamics of the associated physical systems. By investigating the spectral gaps and accumulation points we aim to contribute to the broader understanding of non-self-adjoint operator theory and its applications in mathematical physics.

Summary: Mixed problem for the fourth order ordinary differential equation with general boundary conditions is considered in present paper. Soluion of the problem is found by the residue method. According to the scheame of this method the mixed problem is divided by two auxiliary- specrtal and Cauchy problems. After researching these two problems, solution of the considering mixed problem is found by residue series. It is shown , that solution of considering mixed problem surround not only parabolic equations in the sense of Shilov, but also wider classes of equations.

Summary: This paper aims to study the risk situation of blockchain technology in interactive mobile hospitals. With the development of blockchain technology, interactive mobile hospitals have begun to use blockchain technology to empower technological capabilities in aspects such as diagnosis and treatment management, data security, and sharing. Firstly, by referring to relevant literature, this paper identifies that the existing risks include technical risks, privacy risks, compliance risks, management and operation risks, as well as cognitive and acceptance risks. Then, the entropy method is used to analyze the weights of these risks, and the fuzzy comprehensive evaluation (FCE) method is applied to calculate the risk levels. The calculation results show that the overall risk score of blockchain technology in interactive mobile hospitals is 63.3705, among which the technical risk score is 59.3491, the management and operation risk score is 59.8643, the privacy risk score is 65.8097, the compliance risk score is 64.1854, and the cognitive and acceptance risk score is 69.2427. This study conclusion is that the degree of risk of blockchain technology in interactive mobile hospitals is between general and high. Among them, technical risks and management and operation risks are between low and general, while privacy risks, compliance risks, and cognitive and acceptance risks are between general and high. Finally, this paper puts forward corresponding countermeasures and suggestions based on the risk conclusions. This paper hopes that the interactive mobile hospital industry can strengthen risk management in aspects such as enhancing technological research and development, protecting privacy, improving laws and regulations, optimizing management processes, and increasing the awareness of all parties so as to promote the healthy and stable development of the entire mobile medical industry.

Summary: Parcel delivery networks have grown rapidly during the last few years due to the intensive evolution of online marketplaces. We address the issue of managing the operation of a network’s pick-up point, including the selection of the warehouse’s capacity and the policy for accepting orders for delivery. The existence of the time lag between order placing and delivery to the pick-up point is accounted for via modeling the order’s processing as the service in the dual tandem queueing system. Distinguishing features of this tandem queue are the account of possible irregularity in order generation via consideration of the versatile Markov arrival process and the possibilities of batch transfer of the orders to the pick-up point, group withdrawal of orders there, and client no-show. To reduce the probability of an order rejection at the pick-up point due to the overflow of the warehouse, a threshold strategy of order admission at the first stage on a tandem is proposed. Under the fixed value of the threshold, tandem operation is described by the continuous-time multidimensional Markov chain with a block lower Hessenberg structure for the generator. Stationary performance measures of the tandem system are calculated. Numerical results highlight the dependence of these measures on the capacity of the warehouse and the admission threshold. The possibility of the use of the results for managerial goals is demonstrated. In particular, the results can be used for the optimal selection of the capacity of a warehouse and the policy of suspending order admission.

Summary: This work is dedicated to the impulsive Sturm - Liouville operator on the whole axis with complex almost periodic potentials and the discontinuous coefficient on the right – hand side. We investigated the main characteristics of the fundamental solutions of the Sturm – Liouville equation. From the impulsive condition we found the transfer matrix. Using the impulsive condition and transfer matrix, we constructed Green’s function and obtained the resolvent of the impulsive Sturm – Liouville operator. In future works, eigenvalues of the impulsive Sturm - Liouville operator will be investigated. The inverse problem will be formulated, a constructive procedure for the solution of the inverse problem will be provided.

Summary: The paper considers a boundary value problem generated by a differential diffusion equation and nonseparated boundary conditions. One of the boundary conditions contains a quadratic function of the spectral parameter. The multiplicity of eigenvalues of the boundary value problem under consideration is investigated. A criterion for the multiplicity of eigenvalues and zeros of the characteristic function of a boundary value problem is obtained.The found necessary and sufficient conditions are expressed through the values of the fundamental solutions of the diffusion equation and the coefficients of the boundary conditions. Note that the results obtained can be used in the study of direct and inverse problems of spectral analysis for various differential operators. These results also play an important role in studying the structure of the spectrum, in establishing the order of arrangement of eigenvalues of boundary value problems, and in finding sufficient conditions for the reconstruction of the corresponding problems.

Summary: In this article, the issue of controlling the movement of a hexacopter-type unman-ned aerial vehicle (UAV) along a route is investigated. The movement of the hexacopter is modeled as the movement of a rigid body, and in this process, the forces of gravity and aerodynamic resistance are taken into account. The spatial orientation of the hexacopter is expressed using quaternions. The movement route is considered as a broken line consisting of straight segments, and the parameters controlling its flight are determined when one of the hexacopter's motors is not working. Mathematical justification is provided for how the operational motors are controlled to continue the hexacopter's movement in its previous manner when one motor fails.

Summary: The paper examines different types of hypersingular integrals with the Cauchy kernel on a segment and a unit circle and defines them using specific methods. It presents more general definitions for one-dimensional hypersingular integrals with the Cauchy kernel based on Hadamard's integral in the sense of a finite part. The paper also establishes the existence theorems of these hypersingular integrals and formulas, which demonstrates the accuracy of the resulting integrals that are applied in various applications and engineering problem-solving. The proposed formulas are straightforward to calculate, making the new approximate method reliable and easy to apply and the obtained numerical results demonstrate the stability and efficiency of the approach.