Class Of Problems Research Articles

An investigation of a new Lyapunov-type inequality for Katugampola–Hilfer fractional BVP with nonlocal and integral boundary conditions

In this manuscript, we focus our attention on investigating new Lyapunov-type inequalities (LTIs) for two classes of boundary value problems (BVPs) in the framework of Katugampola–Hilfer fractional derivatives, supplemented by nonlocal, integral, and mixed boundary conditions. The equivalent integral equations of the proposed Katugampola–Hilfer fractional BVPs are established in the context of Green functions. Also, the properties of these Green functions are proved. The LTIs are investigated as sufficient criteria for the existence and nonexistence of nontrivial solutions for the subjected problems. Our systems are more general than in the literature, as a consequence there are many new and known specific cases included. Finally, our results are applied for estimating eigenvalues of two given BVPs.

A study on a class of weighted elliptic problems with indefinite nonlinearities

In this work, we will study the existence of solutions for a class of problems involving the p-Laplacian operator with weight and a nonlinearity that changes sign in a domain Ω ⊂ R N with ∂ Ω smooth and N ≥ 3 . For this class of problems with subcritical growth, we can show the existence of two solutions, one nodal and one that does not change sign in Ω. To class with critical case, we prove the existence of nontrivial solution which does not change sign in Ω.

Leveraging decision diagrams to solve two-stage stochastic programs with binary recourse and logical linking constraints

We generalize an existing binary decision diagram-based (BDD-based) approach of Lozano and Smith (MP, 2022) to solve a special class of two-stage stochastic programs (2SPs) with binary recourse, where the first-stage decisions impact the second-stage constraints. First, we extend the second-stage problem to a more general setting where logical expressions of the first-stage solutions enforce constraints in the second stage. Then, as our primary contribution, we introduce a complementary problem, that appears more naturally for many of the same applications of the former approach, and a distinct BDD-based solution method, that is more efficient than the existing BDD-based approach on commonly applicable problem classes. In the novel problem, second-stage costs, rather than constraints, are impacted by expressions of the first-stage decisions. In both settings, we convexify the second-stage problems using BDDs and parameterize either the BDD arc costs or capacities with first-stage solutions. We extend this work by incorporating conditional value-at-risk and propose the first decomposition method for 2SP with binary recourse and a risk measure. We apply these methods to a novel stochastic problem, namely stochastic minimum dominating set problem, and present numerical results to support their effectiveness.

Metaheuristic Solutions to Order-of-Addition Design Problems

There is increasing recognition that the order of administration of drugs in drug combination studies can markedly affect the outcome. Similarly, manufactured products are often sequentially produced and the final quality frequently depends on the order of assembly. Order-of-addition designs account for the order of administration of the components, and they are quite prevalent, yet research in this area is quite limited. Because of the large dimension of such optimization problems, analytical approaches are invariably very limited and apply to simple setups only. Numerical approaches are also seriously underdeveloped. To this end, we employ two exemplary nature-inspired metaheuristic algorithms, Differential Evolution (DE) and Particle Swarm Optimization (PSO), to search for efficient order-of-addition designs for two classes of important inferential problems: (a) estimating parameters in an imprecisely specified model, and (b) constructing space-filling designs without specifying a model. We evaluate the capability of DE and PSO to solve the two classes of order-of-addition design problems and compare their performance with other algorithms that have been used to tackle somewhat similar problems. Using different criteria, we demonstrate that DE and PSO clearly outperform current algorithms by a wide margin. Supplementary materials containing codes to generate all results in this article are available online.

A METHOD FOR CONSTRUCTING DIGITAL SIGNATURE SCHEMES BASED ON NEW HARD PROBLEM ON THE ELLIPTIC CURVE

In this paper, the authors propose a solution to improve the secure of digital signature schemes, this solution is implemented on two levels of digital signature scheme construction. At the first level, the authors propose a new hard problem, this hard problem belongs to the class of hard problems for which there is currently no solution (except by “brute force attack" method). At the second level, the authors propose a method to construct new digital signature algorithms based on this hard problem.

On a class of fractional p (⋅,⋅)−Laplacian problems with sub-supercritical nonlinearities

This paper is devoted to study a class of nonlocal variable exponent problems involving fractional p (⋅,⋅)-Laplacian operator. Under appropriate conditions, some new results on the existence and nonexistence of solutions are established via variational approach and Pohozaev's fibering method.

Proximal Gradient Method with Extrapolation and Line Search for a Class of Non-convex and Non-smooth Problems

Proximal Gradient Method with Extrapolation and Line Search for a Class of Non-convex and Non-smooth Problems

MATHEMATICAL MODELS AND METHODS OF COORDINATED PLANNING

Modern processes of globalization and economic competition require a significant increase in the requirements for the professional degree of top-level managers who manage the activities of international corporations, regional economies, branch ministries, etc. Their efficient operation is impossible without the use of basic scientific developments and appropriate software which implement the main qualitative law of complex organizational and production systems management: the law of coordinated management (planning), when management decisions at the top level take into account interests that may not coincide, or even be antagonistic in organizational and production subsystems connected by a certain structure of mutual relations within a single organizational and production complex system. In this work, we consider a two-level organizational and production system, which in terms of the generally known theory of active systems is defined as “decision-making center → elements (of an organizational and production subsystem)”. We consider formal models of elements of two classes, linear continuous and discrete, aggregated production models which belong to the same class of NP-hard single-stage scheduling problems. For both types of element models, we give compromise criteria and corresponding methods of constructing compromise solutions based on the results of Prof. A. A. Pavlov for multi-objective linear programming, as a result of his theoretical research for discrete optimization problems under uncertainty, and the theory of PSC-algorithms created by him and his students, that is, algorithms containing polynomial complexity subalgorithms for constructing feasible solutions that satisfy theoretically substantiated sufficient signs of optimality. In this work, we use the PSC-algorithm for the NP-hard scheduling problem “Minimization of the total weighted completion time of jobs on a single machine with precedence relations given by a directed acyclic graph”.

Inverse Optimization: Theory and Applications

A Review of Inverse Optimization In recent years, there has been an explosion of interest in the mathematics and applications of inverse optimization. Unlike traditional optimization, which seeks to compute optimal decisions given an objective and constraints, inverse optimization takes decisions as input and determines an objective and/or constraints that render these decisions approximately or exactly optimal. In “Inverse Optimization: Theory and Applications,” Chan, Rafid, and Zhu provide a comprehensive review of both the methodological and application-oriented literature. Specifically, the authors consolidate various model properties, reformulation techniques, and computational methods of different classes of inverse optimization problems. The authors also review a wide range of application areas that include, but are not limited to, transportation, logistics, healthcare, and energy systems. The paper concludes with several major directions for future research.

Reaction–diffusion systems with nonlinear sources of different intensity in the case of a multiple root without quasimonotonicity condition

We consider a boundary value problem for a singularly perturbed system of two second-order ordinary differential equations with different powers of a small parameter at the second derivatives without requiring the right-hand sides to be quasimonotonic. The specific feature of the problem is that one of the two equations in the degenerate system has a double root. It is proved that for sufficiently small values of a small parameter, the problem has a solution of the boundary layer type. A condition is obtained that replaces the quasimonotonicity condition and expands the class of problems to which the results of the work are applicable.

Heuristics for online three-dimensional packing problems and algorithm selection framework for semi-online with full look-ahead

In online three-dimensional packing problems (3D-PPs), unlike offline problems, items arrive sequentially and require immediate packing decisions without any information about the quantities and sizes of the items to come. Heuristic methods are of great importance in solving online problems to find good solutions in a reasonable amount of time. However, the literature on heuristics for online problems is sparse. As our first contribution, we developed a pool of heuristics applicable to online 3D-PPs with complementary performance on different sets of instances. Computational results showed that in terms of the number of used bins, in all problem instances, at least one of our heuristics had a better or equal performance compared to existing heuristics in the literature. The developed heuristics are also fully applicable to an intermediate class between offline and online problems, referred to in this paper as a specific type of “semi-online with full look-ahead”, which has several practical applications. In this class, as in offline problems, complete information about all items is known in advance (i.e., full look-ahead); however, due to time or space constraints, as in online problems, items should be packed immediately in the order of their arrival. As our second contribution, we presented an algorithm selection framework, building on developed heuristics and utilizing prior information about items in this specific class of problems. We used supervised machine learning techniques to find the relationship between the features of problem instances and the performance of heuristics and to build a prediction model. The results indicate an 88% accuracy in predicting (identifying) the most promising heuristic(s) for solving any new instance from this class of problems.

A weak solution to a Kirkoff type problem with discontinuous nonlinearities

This paper is devoted to the study of a class of Kirchhoff-type problems with discontinuous nonlinearities with Neumann boundary data. Here,
 by employing the topological degree methods for the abstract Hammerstein equation, we establish the existence of at least one solution.

Existence and stability results for implicit impulsive convex combined Caputo fractional differential equations

This paper deals with the existence and uniqueness results for a class of impulsive implicit fractional initial value problems of the convex combined Caputo fractional derivative. The arguments are based on Banach's contraction principle, Schauder's and Mönch's fixed point theorems. We will also establish the Ulam stability and give some examples to illustrate our results.

A Methodological Approach to the Simulation of a Ship’s Electric Power System

Modern ships are complex energy systems containing a large number of different elements. Each of these elements is simulated separately. Since all these models form a single system (ship), they are interdependent. The operating modes of some systems influence others, but at the same time, the work of all the systems should be aimed at fulfilling the basic functions of the ship. The work proposes a methodological approach to combining various systems of ships into a single complex model. This model allows combining models of ship systems of various levels (microlevel, macrolevel, metalevel, megalevel). The work provides examples of models of such multi-level energy systems. These are energy systems composed of an electric generator, a diesel engine, a propeller shaft, and algorithms used for operating the common parts of the ship’s electric power system and a piston wear process. Analytical, structural, numerical, and object-oriented models were made for these objects. Each of these particular models describes a limited class of problems, has characteristic properties, and a mathematical structure. The work shows how particular models can be interconnected using a set-theoretic description. Particular models are combined into macrolevel models, whose output parameters are quantities that are by no means related. The macrolevel models are interrelated using control models. Control models belong to the metalevel and allow for assigning settings and response thresholds to algorithms used in automation systems. Such a model (megalevel model) allows, ultimately, investigating the dynamics of the entire system as a whole and managing it.

Eview: an open source software for converting and visualizing of multichannel electrophysiological signals

BACKGROUND: Methods and tools for operating with multichannel electrophysiological signals need to develop and correspond to the speed of data traffic in contemporary experiments. Analyzing and visualizing experimental data with minimal delay and with minimized experimenter effort is a pressing task in the field of neurobiology and requires the use of complex approaches specifically selected for each specific type of experiment. Creating open-source programs that can be promptly adapted for different tasks is one of the approaches that provide the ability to perform complex scientific experiments with high quality. AIM: This work is aimed at creating open-source software for analytical and visualization support of neurobiological experiments. METHODS: Software development was performed in MATLAB environment. The program is built on a modular principle and includes an intuitive graphical interface that facilitates control of the signal processing and display. RESULTS: A software tool was created that allows to optimize and accelerate various stages of electrophysiological research, including preliminary analysis of the quality of the experiment being prepared, in-depth analysis of recorded signals, and preparation of illustrative material for publications. CONCLUSION: The resulting program has a number of advantages in comparison with similar products in terms of versatility, speed, and availability, and can be used to solve a wide class of research problems.

On ellipticity of operators with shear mappings

The nonlocal boundary value problems are considered, in which the main operator and the operators in the boundary conditions include the differential operators and twisting operators. The de nition of the trajectory symbols for this class of problems is given. We show that the elliptic problems de ne the Fredholm operators in the corresponding Sobolev spaces. The ellipticity condition of such nonlocal boundary value problem is given.

K voprosu o chislennom reshenii nekonservativnykh giperbolicheskikh sistem uravneniy

Issues related to the lack of convergence in the application of formally path-conservative difference schemes for solving nonconservative hyperbolic systems of equations are numerically investigated. This problem is central in constructing well-posed difference schemes for solving this class of problems. The basic concepts of the theory of nonconservative hyperbolic systems of equations and the corresponding problems of constructing difference schemes for their solution are outlined. A variant of the HLL method is proposed that allows using an arbitrary explicitly specified path. For a model system of Burgers equations, the shock adiabates and paths corresponding to the viscous regularization of a system of a given form are explicitly calculated. The reasons for the lack of convergence of numerical solutions of exact ones in the case of incorrect application of the corresponding algorithms are analyzed. It is shown that, at least in the particular case considered, a variant of the HLL method that is formally conservative along the way gives the correct solution of the problem.

Fredholm Integral Equation for Problems of Acoustic Scattering by Three-Dimensional Transparent Structures

We consider the differential and integral statements of problems of acoustic scattering by three-dimensional bounded transparent structures described by an integral equation. The results of the numerical solution of the integral equation describing the class of problems under consideration are presented. A theorem on existence and uniqueness of the solution is proved.

On a New Class of Impulsive η-Hilfer Fractional Volterra-Fredholm Integro-Differential Equations

This work addresses the idea of the uniqueness and existence results for a class of boundary value problems (BVPs) for implicit Volterra-Fredholm integro-differential equations (V-FIDEs) with fractional η-Hilfer nonlinear equations and multi-point fractional boundary non-instantaneous conditions. The conclusions are confirmed by the fixed point of Krasnoselskii's theorem and the Banach contraction principle. Finally, a concrete example is given to illustrate our main conclusions.

Convexificators for nonconvex multiobjective optimization problems with uncertain data: robust optimality and duality

In this paper, we investigate robust optimality conditions and duality for a class of nonconvex multiobjective optimization problems with uncertain data in the worst case by the upper semi-regular convexificator. The Fermat principle for a locally Lipschitz function is presented in terms of the upper semi-regular convexificator. We establish robust necessary optimality conditions of the Fritz-John type and KKT type for the uncertain nonconvex multiobjective optimization problems. In addition, robust sufficient optimality conditions as well as saddle point conditions are derived under the generalized ∂ ˆ ∗ -pseudoquasiconvexity and generalized convexity, respectively. The robust duality relations between the original problem and its mixed robust dual problem are obtained under a generalized pseudoconvexity assumption.