Problem For Operator Research Articles

Modified Tseng Method for Solving Pseudomonotone Variational Inequality Problem in Banach Spaces

This article examines the process for solving the fixed-point problem of Bregman strongly nonexpansive mapping as well as the variational inequality problem of the pseudomonotone operator. Within the context of p-uniformly convex real Banach spaces that are also uniformly smooth, we introduce a modified Halpern iterative technique combined with an inertial approach and Tseng methods for finding a common solution of the fixed-point problem of Bregman strongly nonexpansive mapping and the pseudomonotone variational inequality problem. Using our iterative approach, we develop a strong convergence result for approximating the solution of the aforementioned problems. We also discuss some consequences of our major finding. The results presented in this paper complement and build upon many relevant discoveries in the literature.

Inverse spectral problems for Dirac-type operators with global delay on a star graph

Inverse spectral problems for Dirac-type operators with global delay on a star graph

Solvability of the inverse spectral problem for Sturm-Liouville operator with spectral parameter in the boundary condition

This paper deals with an inverse problem for the Sturm-Liouville operator with non-separated boundary conditions, one of which linearly depends on a spectral parameter. Uniqueness theorem is proved, solution algorithm is constructed and sufficient conditions for solvability of inverse problem are obtained. As spectral data, we only use the spectrum of one boundary value problem and some sequence of signs, and some number.

Direct and inverse resonance problems for the massless Dirac operator on the half line

For the direct problem, we give the asymptotic distribution of the resonances in the complex plane. For the inverse problem, we prove several uniqueness theorems of recovering the potential on the whole interval from partial resonances and the information of the potential on a subinterval.

Sturm–Liouville Problem for a One-Dimensional Thermoelastic Operator in Cartesian, Cylindrical, and Spherical Coordinate Systems

Sturm–Liouville Problem for a One-Dimensional Thermoelastic Operator in Cartesian, Cylindrical, and Spherical Coordinate Systems

Inverse problems for Dirac operators with constant delay less than half of the interval

In this work, we consider Dirac-type operators with a constant delay of less than half of the interval and not less than two-fifths of the interval. For our considered Dirac-type operators, two inverse spectral problems are studied. Specifically, reconstruction of two complex L2-potentials is studied from complete spectra of two boundary value problems with one common boundary condition y1(0) = 0 or y2(0) = 0. We give answers to the full range of questions usually raised in the inverse spectral theory. That is, we give uniqueness, necessary and sufficient conditions of the solvability, reconstruction algorithm and uniform stability for our considered inverse problems.

Boundary Value Problem of Nonlinear Fractional Differential Equations of Mixed Volterra-Fredohlm Integral Equations in Banach Space

This paper is dedicated to study the existence and uniqueness of solutions for a boundary value problem of nonlinear fractional differential equations of mixed Volterra-Fredohlm integral equations in Banach space, the recent researches considered the study of differential equations of mixed Volterra-Fredholm integral equations with classical order and the study of existence and uniqueness of solutions using approched numerical methodes, the objective of this paper is the study of the existence and uniqueness of fractional order of differential equations with mixed Volterra-Fredholm integral equations using fixed point theory. This work have two important results, the first result was the discussion of the existence of solutions using the Krasnoselskii fixed point theorem after transforming the problem into integral equation firstly then into operator problem suitable for the fixed point theory. The second result will be the existence and uniqueness of solution, this result was obtained by the use of Banach fixed point theorem after the same transformation used in the first one. This work give as conclusion that the boundary value problem of nonlinear fractional differential equations of mixed Volterra-Fredholm integral equation has a unique solution in Banach space. Finally, this work was ended with an example to illustrate the results obtained.

Incomplete inverse problem for Dirac operator with constant delay

In this work, we consider Dirac-type operators with a constant delay less than two-fifths of the interval and not less than one-third of the interval. For our considered Dirac-type operators, an incomplete inverse spectral problem is studied. Specifically, when two complex potentials are known a priori on a certain subinterval, reconstruction of the two potentials on the entire interval is studied from complete spectra of two boundary value problems with one common boundary condition. The uniqueness of the solution of the inverse problem is proved. A constructive method is developed for the solution of the inverse problem.

On the Links between Miura Transformations of Bogoyavlensky Lattices and Inverse Spectral Problems for Band Operators

We consider semi-infinite and finite Bogoyavlensky lattices$$\overset\cdot a_i =a_i\left(\prod_{j=1}^{p}a_{i+j}-\prod_{j=1}^{p}a_{i-j}\right),$$$$\overset\cdot b_i = b_i\left(\sum_{j=1}^{p}b_{i+j}-\sum_{j=1}^{p}b_{i-j}\right),$$for some $p\ge 1$, and Miura-like transformations between these systems, defined for $p\ge 2$. Both lattices are integrable (via Lax pair formalism) by the inverse spectral problem method for band operators, i.e., operators generated by band matrices. The key role in this method is played by the moments of the Weyl matrix of the corresponding band operator and their evolution in time. We find a description of the above-mentioned transformations in terms of these moments and apply this result to study finite Bogoyavlensky lattices and, in particular, their first integrals.

The Condition of Decreased Eye Vision (Myopia) in Production Operators in The Workplace Impact on The Quality of Production Results

Myopia or nearsightedness is a vision condition that cannot see distant objects clearly. This condition is increasingly common around the world, including in Indonesia. In the workplace, myopia can be a problem for production operators who need sharp vision to perform their tasks well. The purpose of this study was to determine the condition of decreased eye vision (myopia) in production operators in the workplace and its impact on the quality of production results. This research uses qualitative research methods. The data collection technique in this research is by literature study. The data that has been collected is then processed through three stages, namely data reduction, data presentation and conclusion drawing. The results showed that operators suffering from myopia can experience a decrease in production output for three main reasons, including myopia sufferers tend to have difficulty seeing details that can affect the accuracy and quality of work, myopia conditions can cause eye fatigue which can reduce the efficiency and productivity of operators in carrying out production tasks and myopia can cause discomfort in physical members, such as the neck, shoulders and back, due to improper posture during work. In addition, myopia can also increase the risk of work accidents due to impaired vision.

The weighted Kato square root problem of elliptic operators having a BMO anti-symmetric part

The weighted Kato square root problem of elliptic operators having a BMO anti-symmetric part

Obstacle Problems for Integro-Differential Operators with Partially Vanishing Kernels

Obstacle Problems for Integro-Differential Operators with Partially Vanishing Kernels

Inverse problems for real principal type operators

abstract: We consider inverse boundary value problems for general real principal type differential operators. The first results state that the Cauchy data set uniquely determines the scattering relation of the operator and bicharacteristic ray transforms of lower order coefficients. We also give two different boundary determination methods for general operators, and prove global uniqueness results for determining coefficients in nonlinear real principal type equations. The article presents a unified approach for treating inverse boundary problems for transport and wave equations, and highlights the role of propagation of singularities in the solution of related inverse problems.

Digital Twin Learning Ecosystem: A cyber–physical framework to integrate human-machine knowledge in traditional manufacturing

As Industry 4.0 enablers, digital twins of manufacturing systems have led to multiple interaction levels among processes, systems, and workers across the factory. However, open issues still exist when addressing cyber–physical convergence in traditional manufacturing small and medium-sized enterprises. The problem for both traditional operators and the existing infrastructure is how to adapt knowledge to the increasing business needs of manufacturing plants that demand high efficiency, while reducing production costs. In this paper, a framework that implements the novel concept of Digital Twin Learning Ecosystem in traditional manufacturing is presented. The objective is to facilitate the integration of human-machine knowledge in different industrial cyber–physical contexts and eliminate existing technological and workforce barriers. This adaptive approach is particularly important in meeting the requirements to help small and medium-sized enterprises build their own interconnected Digital Twin Learning Ecosystem. The contribution of this work lies in a single digital twin learning framework for different traditional manufacturing scenarios that can work from scratch using a light infrastructure, reusing the knowledge and common condition-based methods well-known by skilled workers to rapidly and flexibly integrate existing legacy resources in a non-intrusive manner. The solution was tested using real data from a milling machine and a currently operating induction furnace with a maximum power of 12 MW in a foundry plant. In both cases, the proposed solution proved its benefits: first, by providing augmented methods for maintenance operations on the milling machine and second, by improving the power efficiency of the induction furnace by approximately 9 percent.

Polyanalytic Neumann-n problem in the unit disk

An iterated Neumann boundary value problem for the polyanalytic operator is investigated in the unit disc of the complex plane. Although this problem can be treated for domains in the complex plane having a harmonic Green function, the unit disk is particularly interesting as it is the origin of complex boundary value problems and the prototype of simply connected domains. Moreover, the resulting formulas for solutions and for solvability conditions are expressed by integral formulas with explicit kernels. By the way, the result verifies the findings for domains with harmonic Green function.

Асимптотика Сеге для системы Анжелеско

We discuss opportunity for extension the strong asymptotics (Szego asymptotics) for more wide class of the sequences of multiple orthogonal polynomials with respect to the system of weights supported by the non-intersecting intervals (Angelesco system). The interest for limiting properties of these polynomials, when their multi-index tends monotonically to in_nity (along of the edges of p-dimensional lattice) has appeared recently, in onnection with spectral problems for the discrete Schrodinger operator (multidimensional Jacobi matrix) on the graph-trees.

INVERSE SPECTRAL PROBLEM FOR THE DIRAC OPERATOR ON A STAR GRAPH

Abstract. The paper discusses the inverse spectral problem for the Dirac operator on a star graph, interpreting the problem as a study of the operator on a non-compact graph.

On solvability of some inverse problems for a nonlocal fourth-order parabolic equation with multiple involution

<abstract><p>In this paper, the solvability of some inverse problems for a nonlocal analogue of a fourth-order parabolic equation was studied. For this purpose, a nonlocal analogue of the biharmonic operator was introduced. When defining this operator, transformations of the involution type were used. In a parallelepiped, the eigenfunctions and eigenvalues of the Dirichlet type problem for a nonlocal biharmonic operator were studied. The eigenfunctions and eigenvalues for this problem were constructed explicitly and the completeness of the system of eigenfunctions was proved. Two types of inverse problems on finding a solution to the equation and its righthand side were studied. In the two problems, both of the righthand terms depending on the spatial variable and the temporal variable were obtained by using the Fourier variable separation method or reducing it to an integral equation. The theorems for the existence and uniqueness of the solution were proved.</p></abstract>

On the Inverse Spectral Problem for the One-dimensional Stark Operator on the Semiaxis

On the Inverse Spectral Problem for the One-dimensional Stark Operator on the Semiaxis

Modified mildly inertial subgradient extragradient method for solving pseudomonotone equilibrium problems and nonexpansive fixed point problems

<abstract><p>This paper presents and examines a newly improved linear technique for solving the equilibrium problem of a pseudomonotone operator and the fixed point problem of a nonexpansive mapping within a real Hilbert space framework. The technique relies two modified mildly inertial methods and the subgradient extragradient approach. In addition, it can be viewed as an advancement over the previously known inertial subgradient extragradient approach. Based on common assumptions, the algorithm's weak convergence has been established. Finally, in order to confirm the efficiency and benefit of the proposed algorithm, we present a few numerical experiments.</p></abstract>