Problem For Operator Research Articles

The Lp Minkowski type problem for a class of mixed Hessian quotient equations

Existence and uniqueness of the admissible solutions to the Lp Minkowski type problem for mixed Hessian operators are proved. By using the new phenomenon of “inverse convexity” of these operators, we show the existence of the geometric convex solutions by the Full Rank Theorem.

An iterative technique for solving split equality monotone variational inclusion and fixed point problems

Abstract The purpose of this paper is to introduce an iterative algorithm for approximating the solution of the split equality monotone variational inclusion problem (SEMVIP) for monotone operators, which is also a solution of the split equality fixed point problem (SEFPP) for strictly pseudocontractive maps in real Hilbert spaces. We establish the strong convergence of the sequence generated by our iterative algorithm. Our result complements and extends some related results in literature.

The four-state problem and convex integration for linear differential operators

We show that the four-state problem for general linear differential operators is flexible. The only flexibility result available in this context is the one for the five-state problem for the curl operator due to B. Kirchheim and D. Preiss, [27, Section 4.3], and its generalization [21]. To build our counterexample, we extend the convex integration method introduced by S. Müller and V. Šverák in [33] to linear operators that admit a potential, and we exploit the notion of largeTNconfiguration introduced by C. Förster and L. Székelyhidi in [21].

Short Proofs of Explicit Formulas to Boundary Value Problems for Polyharmonic Equations Satisfying Lopatinskii Conditions

This paper deals with Lopatinskii type boundary value problem (bvp) for the (poly) harmonic differential operators. In the case of Robin bvp for the Laplace equation in the ball B1 a Green function is constructed in the cases c>0, c∉−N, where c is the coefficient in front of u in the boundary condition ∂u∂n+cu=f. To do this a definite integral must be computed. The latter is possible in quadratures (elementary functions) in several special cases. The simple proof of the construction of the Green function is based on some solutions of the radial vector field equation Λu+cu=f. Elliptic boundary value problems for Δmu=0 in B1 are considered and solved in Theorem 2. The paper is illustrated by many examples of bvp for Δu=0, Δ2u=0 and Δ3u=0 in B1 as well as some additional results from the theory of spherical functions are proposed.

Inverse problem for a differential operator on a star-shaped graph with nonlocal matching condition

In this paper, we develop two approaches to investigation of inverse spectral problems for a new class of nonlocal operators on metric graphs. The Laplace differential operator is considered on a star-shaped graph with nonlocal integral matching condition. This operator is adjoint to the functional-differential operator with frozen argument at the central vertex of the graph. We study the inverse problem that consists in the recovery of the integral condition coefficients from the eigenvalues. We obtain the spectrum characterization, reconstruction algorithms, and prove the uniqueness of the inverse problem solution.

An algorithm based on an iterative optimal stopping method for Feller processes with applications to impulse control, perturbation, and possibly zero random discount problems

In this paper we present an iterative optimal stopping method for general optimal stopping problems for Feller processes. We show using an approximating scheme that the value function of an optimal stopping problem for some general operator is the unique viscosity solution to an Hamilton–Jacobi–Bellman equation (see for example Theorems 2.3 and 2.4). We apply our results to study impulse control problems for Feller–Markov processes and derive explicit solutions in the case of one dimensional regular Feller diffusion. We also use our result to study optimal stopping problems for both regime switching and semi-Markov processes and characterize their value functions as the limit of iterative optimal stopping problems (see Corollary 4.2 and Proposition 4.3 ). Finally, we examine optimal stopping problems for random (possibly zero) discount.

S472 Clinical Adverse Events Associated With Esophageal Stents: A MAUDE Database Analysis

Introduction: Esophageal stents are widely utilized for the treatment of benign and malignant obstructions. However, associated procedural complications are not well described. We aim to investigate post Food and Drug Administration (FDA) approval outcomes associated with esophageal stents. Methods: We analyzed post-marketing surveillance data on esophageal stents from the FDA Manufacturer and User Facility Device Experience (MAUDE) database from January 2015 to December 2021 to report device-related injuries and modes of failure. This database is an open-access platform that receives device reports from mandatory sources, including manufacturers and facilities, as well as, voluntary sources such as healthcare professionals, patients and consumers. These reports allow the FDA to monitor device performance and device-related safety concerns. Results: During the study period, approximately 899 reported cases with 1312 device issues and 303 patient complications were examined. Reported cases included Ultraflex stent (n= 275, 30.6%), Wallflex stent (n= 210, 23.4%), Covered NITI-S stent (n= 144, 16.0%), and Evolution Partially Covered stent (n= 98, 10.9%). The most reported device issues were due to activation, position, or separation failure (n= 597, 45.5%), followed by migration or expulsion of device (n= 120, 9.1%), break (n= 96, 7.3%), difficulty to remove (n= 43, 3.3%), and material deformation (n= 41, 3.1%). A number of reports described an unclassified adverse event without specifying device or operator problem (n= 100, 7.6 %). The most reported patient adverse events were dysphagia or odynophagia (n= 29, 9,6%), followed by death (n= 24, 7.9%), hemorrhage (n= 22, 7.3%), obstruction or occlusion (n= 22, 7.3%), and perforation (n= 17, 5.6%). Conclusion: Our analysis of the FDA MAUDE database revealed a predominance of reported device complications related to activation, positioning, and separation difficulties. Dysphagia or odynophagia represented the most commonly reported patient complication. This database has notable limitations, including limited information on patient comorbidities, detailed endoscopy reports, an absence of operator experience and total volume of procedures performed in the United States. This study provides insight into the most commonly reported complications of esophageal stents that will help inform the risk/benefit conversation with patients and may lead to a more detailed approach on how to mitigate and manage complications.

A modified Mann algorithm for the general split problem of demicontractive operators

This work proposes a novel method for solving the general split common fixed point problem of demicontractive operators in the framework of real Hilbert spaces. Our proposed technique is principally based on the Mann algorithm. The proof of the weak convergence theorem is additionally established under some particular conditions. We subsequently verify the convergence of our algorithm via numerical examples.

A CABINE DOS Can the tractor's cabin allow the noise at the operator's station?PODE ATENUAR O RUÍDO NO POSTO DO OPERADOR?

Constant exposure to high noise levels can cause health problems for agricultural machinery operators. Machines equipped with closed cabs can attenuate noise and preserve the operator from an unhealthy condition. Some studies show that in cabin tractors it is possible to renounce the use of hearing protection, however indoor equipment and air conditioning can reach high levels of noise, which need to be further investigated. The present study aimed to evaluate the noise emitted by a cabined agricultural tractor, in different points, inside and outside cabin, in the engine rotations of 800rpm, 2180rpm and 2500rpm. In each reading, 100 noise intensity values were automatically collected, over two minutes with the aid of a digital decibel meter device. The results were compared with the levels assumed by Annex 1 of the regulatory Brazilian standard NR 15, and it was found that the cabin was able to isolate the noise emitted by the engine and its external components in 15%, however, the internal noise reached 81dB(A). The cabin can attenuate external noise and offer a healthy working environment, however, in long working hours it is recommended to use personal protective equipment such as ear protectors.

Bounds for eigenfunctions of the Neumann p-Laplacian on noncompact Riemannian manifolds

Abstract Eigenvalue problems for the p-Laplace operator in domains with finite volume, on noncompact Riemannian manifolds, are considered. If the domain does not coincide with the whole manifold, Neumann boundary conditions are imposed. Sharp assumptions ensuring L q {L^{q}} - or L ∞ {L^{\infty}} -bounds for eigenfunctions are offered either in terms of the isoperimetric function or of the isocapacitary function of the domain.

Critical perturbations for second-order elliptic operators, I: Square function bounds for layer potentials

This is the first part of a series of two papers where we study perturbations of divergence form second order elliptic operators $-\mathop{\operatorname{div}} A \nabla$ by first and zero order terms, whose coefficients lie in critical spaces, via the method of layer potentials. In particular, we show that the $L^2$ well-posedness of the Dirichlet, Neumann and Regularity problems for complex Hermitian, block form, or constant-coefficient divergence form elliptic operators in the upper half-space are all stable under such perturbations. For instance, this allows us to claim the first results in the setting of an unbounded domain concerning the solvability of boundary value problems for the magnetic Schr\"odinger operator $-(\nabla-i{\bf a})^2+V$ when the magnetic potential ${\bf a}$ and the electric potential $V$ are accordingly small in the norm of a scale-invariant Lebesgue space. In the present paper, we establish $L^2$ control of the square function via a vector-valued $Tb$ theorem and abstract layer potentials, and use these square function bounds to obtain uniform slice bounds for solutions. The existence and uniqueness of solutions, as well as bounds for the non-tangential maximal operator, are considered in the upcoming paper.

Closed range Volterra-type integral operators and dynamical sampling

We solve the closed range problem for Volterra-type integral operator on Fock spaces. Several applications of the result related to the operators invertibility, Fredholm, and dynamical sampling structures from frame perspectives are provided. We further prove a bounded Volterra-type integral operator preserves no frame property. On the contrary, the adjoint operator preserves frame if and only if it is noncompact but fails to preserve both tight frames and Riesz basis.

A model and a numerical scheme for the description of distribution and abundance of individuals.

We introduce a model in the context of ecology that can be used to describe the distribution and abundance of individuals when data from field work is extremely limited (for example, in the case of endangered species). Our procedure is based on an intuitive understanding of the physical properties of phenomena. The idea is that individuals have the tendency to be attracted (or repulsed) to certain properties of the environment. At the same time, they are spread in such a way that if there is no reason for them to be in some specific locations, then they are uniformly distributed throughout the region. Our model draws from quantum mechanics, by using quantum Hamiltonians in the context of classical statistical mechanics. The equilibrium between the spreading and the attractive (or repulsive) forces determines the behavior of the species that we model, and this is expressed in terms of a global control problem of an energy operator which is the sum of a kinetic term (spreading) and a potential (attraction or repulsion). We focus on the full probability measure and a global control of the model (instead of looking at conditional measures that generate a global measure). Furthermore, we propose a numerical solution to this global control problem that overcomes the well-known major difficulty of Gibbs sampling (annealing) which is the fact that a global control is hardly reachable when the number of variables is large (the algorithms get stuck in non-optimal states).

Proposal and Simulation with NS3 of a New offloading Algorithm between LTE/LTE-Advanced and Wi-Fi

The field of mobile telecommunications is an integral part of our society. In the wake of IT, it is implemented and used in all areas of society. This deep anchoring, which mobile networks use today, poses significant problems for operators in terms of speed, capacity demands and customer satisfaction, particularly for the quality of services, but also in terms of profitability and cost of services investments. Reports from Ericsson and Cisco which are representative bases for calculating world total data traffic in cellular mobile networks predict that the number of devices connected to IP networks will be more than three times the global population by 2023. There will be 3.6 networked devices per capita by 2023, up from 2.4 networked devices per capita in 2018. There will be 29.3 billion networked devices by 2023, up from 18.4 billion in 2018. To answer these challenges, two choices are offered to the operators the evolution of the standards or the interconnection of several networks. In this order of idea, we carried out an 4G/4G+ -Wi-Fi offloading simulation algorithm. It was up to us to design an offloading algorithm and then to simulate through a dedicated environment in a scenario allowing to implement it. To achieve this, it was first necessary for us to understand the concept of mobile data offload, to know the types of mobile data offload and to choose one on which the present work will be based. Later we carried out an analysis of the existing data offload algorithms to be able to bring out the limits. From these limits we have designed and proposed a new traffic offloading algorithm with a different approach compared to the existing one studied in the literature. After all this, we have developed and simulated a scenario comprising a 3GPP network in this case the 4G + network, a non 3GPP network in this case the WiFi network, and we have implemented our algorithm via NS3 network simulation software. With this work, we have proposed a solution to overcome an investment deemed expensive to deploy 5G in Africa.

The Cheeger cut and Cheeger problem in metric graphs

For discrete weighted graphs there is sufficient literature about the Cheeger cut and the Cheeger problem, but for metric graphs there are few results about these problems. Our aim is to study the Cheeger cut and the Cheeger problem in metric graphs. For that, we use the concept of total variation and perimeter in metric graphs introduced in Mazón (Math Eng 5(1):1–38, 2023. https://doi.org/10.3934/mine.2023009), which takes into account the jumps at the vertices of the functions of bounded variation. Moreover, we study the eigenvalue problem for the minus 1-Laplacian operator in metric graphs, whereby we give a method to solve the optimal Cheeger cut problem.

Optimal operation of virtual power plants with shared energy storage

AbstractThe emergence of the shared energy storage mode provides a solution for promoting renewable energy utilization. However, how establishing a multi‐agent optimal operation model in dealing with benefit distribution under the shared energy storage is still a challenge. Considering the multi‐agent integrated virtual power plant (VPP) taking part in the electricity market, an energy trading model based on the sharing mechanism is proposed to explore the effect of the shared energy storage on multiple virtual power plants (MVPPs). To analyse the relationship among MVPPs in the shared energy storage system (SESS), a game‐theoretic method is introduced to simulate the bidding behaviour of VPP. Furthermore, the benefit distribution problem of the virtual power plant operator (VPPO) is formulated based on the Nash bargaining theory. In the case study, the proposed method is conducted in four VPPs with different resource endowments in terms of techno‐economic and operation efficiency. Results verify that the multiple virtual power plants with a shared energy storage system interconnection system based on the sharing mechanism not only can achieve a win‐win situation between the VPPO and the SESS on an operation cost but also obtain the optimal allocation scheme and improves the operation efficiency of the VPPs.

The existence and uniqueness result of entropy solutions for a p(·)-Laplace operator problem in weighted Sobolev spaces

The paper is concerned with the existence and uniqueness result of entropy solutions for a degenerate elliptic p(·)-Laplacian problem by using the regularization approach and theory of weighted Sobolev spaces with variable exponents.

Well-posedness of Tricomi–Gellerstedt–Keldysh-type fractional elliptic problems

We study Tricomi–Gellerstedt–Keldysh-type fractional elliptic equations and obtain results on the well-posedness of fractional elliptic boundary value problems for general positive operators with discrete spectrum and for Fourier multipliers with positive symbols. As examples, we discuss results in half-cylinder, star-shaped graph, half-space and other domains.

The numerical solution of inverse nodal problem for integro-differential operator by Legendre wavelet method

In this study, integro-differential equation under separated boundary conditions is considered. In fact, we study the inverse nodal problem, which includes differential part of Sturm–Liouville equation and Volterra type integral to obtain approximative solutions by Legendre polynomials. And, we use Legendre wavelets method to solve these types of problems. In addition, we present the error bound of for continuous derivatives with its approximative solution. Once and for all, the strength of the method can be seen in a few examples.

Boundary regularity of mixed local-nonlocal operators and its application

Let $$\Omega$$ be a bounded $$C^2$$ domain in $${\mathbb {R}^{n}}$$ and $$u\in C({\mathbb {R}^{n}})$$ solves $$\begin{aligned} \begin{aligned} \Delta u + a Iu + C_0|Du| \ge -K\quad \text {in}\; \Omega , \quad \Delta u + a Iu - C_0|Du|\le K \quad \text {in}\; \Omega , \quad u=0\quad \text {in}\; \Omega ^c, \end{aligned} \end{aligned}$$ in the viscosity sense, where $$0\le a\le A_0$$ , $$C_0, K\ge 0$$ , and I is a suitable nonlocal operator. We show that $$u/\delta$$ is in $$C^{\upkappa }(\bar{\Omega })$$ for some $$\upkappa \in (0,1)$$ , where $$\delta (x)=\mathop {\mathrm {dist}}\limits (x, \Omega ^c)$$ . Using this result, we also establish that $$u\in C^{1, \gamma }(\bar{\Omega })$$ . Finally, we apply these results to study an overdetermined problem for mixed local-nonlocal operators.