Solution Of Problem Research Articles

Column generation based solution for bi-objective gate assignment problems

Column generation based solution for bi-objective gate assignment problems

A study on the fractional Black–Scholes option pricing model of the financial market via the Yang-Abdel-Aty-Cattani operator

PurposeFinancial mathematics is one of the most rapidly evolving fields in today’s banking and cooperative industries. In the current study, a new fractional differentiation operator with a nonsingular kernel based on the Robotnov fractional exponential function (RFEF) is considered for the Black–Scholes model, which is the most important model in finance. For simulations, homotopy perturbation and the Laplace transform are used and the obtained solutions are expressed in terms of the generalized Mittag-Leffler function (MLF).Design/methodology/approachThe homotopy perturbation method (HPM) with the help of the Laplace transform is presented here to check the behaviours of the solutions of the Black–Scholes model. HPM is well known for its accuracy and simplicity.FindingsIn this attempt, the exact solutions to a famous financial market problem, namely, the BS option pricing model, are obtained using homotopy perturbation and the LT method, where the fractional derivative is taken in a new YAC sense. We obtained solutions for each financial market problem in terms of the generalized Mittag-Leffler function.Originality/valueThe Black–Scholes model is presented using a new kind of operator, the Yang-Abdel-Aty-Cattani (YAC) operator. That is a new concept. The revised model is solved using a well-known semi-analytic technique, the homotopy perturbation method (HPM), with the help of the Laplace transform. Also, the obtained solutions are compared with the exact solutions to prove the effectiveness of the proposed work. The different characteristics of the solutions are investigated for different values of fractional-order derivatives.

TUTORIAL SUPPORT FOR THE DEVELOPMENT OF ENVIRONMENTAL COMPETENCE OF FUTURE SPECIALISTS IN SHIP NAVIGATION

The relevance of the study is determined by the fact that in modern society, one of the main ways to ensure sustainable development of society in the context of signs of environmental crisis is the formation of environmental competence, the inclusion of environmental safety factors in the context of professional training and formation of future specialists. The aim of the study is to identify and substantiate the most important aspects of tutor support for the formation of environmental competence of future specialists in ship navigation. Methods: theoretical methods of systematic analysis of philosophical, psychological and pedagogical literature to reveal the main provisions of the problem under study; analysis of current dissertation research; generalization and systematization to formulate own views on the problem of forming the environmental competence of future specialists in ship navigation. Results: various aspects of the concept of tutor support for the formation of environmental competence of future specialists in navigation are analyzed. The peculiarity of the study is the identification of innovative productive conditions and means of environmental education in higher education. Based on the idea of the need to organize purposeful environmental and vocational education, based on the use of active, practice-oriented teaching tools and technologies, the tutoring support is characterized, which allows the student to act as an initiative subject performing personally meaningful activities aimed at meaningful solution of ecological problems and improvement of the environment. The principles of the tutor form of interaction between teacher and student, the essence of the tutor's position and tutor support in the process of forming the environmental competence of future specialists in ship navigation are determined. Support, accompaniment, and facilitation are considered as effective forms of tutoring. Explaining the importance of openness of the educational and socio-cultural space within which the formation of environmental competence is carried out, the forms and technologies, as well as key aspects of tutoring support for the formation of environmental competence of future maritime transport specialists are listed. Conclusions: the prospects of using tutoring are due to the possibility of implementing a personal education strategy and the variability of using various resources of the socio-cultural environment based on the student's own potential and the content aspects of the main activity. The current ecological situation determines the need for a reasonable and responsible attitude to the environment. At the same time, the success of environmental protection and nature-transforming activities depends on the level of maturity of ecological thinking of specialists providing all spheres of life. The formation of high levels of environmental competence is the basis for the development of citizenship and patriotism, and therefore requires the search for effective approaches, forms and methods. Tutoring support in the framework of the formation of environmental competence of future maritime professionals allows to create optimal conditions for the actualization and development of a responsible and proactive attitude to the problems of preserving and improving the environment through a special emphasis on the manifestation of activity and initiative during professional activities to solve environmental problems and environmental protection, drawing up and implementing a personal trajectory of professional development of the student, development of the socio-cultural, communicative, leadership, and moral potential of the future specialist, which will allow the student to form his or her own environmental behavior model and effectively carry out professional activities based on the experience of solving environmental problems.

Multiplicity of solutions for a nonlinear nonlocal problem with variable exponent

This work deals with a class of value problem involving the $p(x)$-biharmonic elliptic equation \begin{equation*} \begin{gathered} M_1(\int_{\Omega}\frac{1}{p(x)}|\Delta u|^{p(x)}dx)\Delta^2_{p(x)}u-M_2(\int_{\Omega}\frac{1}{p(x)}|\nabla u|^{p(x)}dx)\Delta_{p(x)}u=\lambda f(x,u)+\mu g(x,u) \quad\text{in }\Omega,\\ u=\Delta u=0,\quad x\in \partial \Omega, \end{gathered} \end{equation*} where $\Omega$ is a bounded domain in $\mathbb{R}^N,~N\geq1.$ with smooth boundary $\partial \Omega.$ Our technical method is based on a theorem obtained by B. Ricceri.

Analytical determination of a quasi-stationary electromagnetic field created by magnetic moments and eddy currents in conducting half-space

Aim. Study of the distribution of a three-dimensional alternating quasi-stationary electromagnetic field at the surface of conducting half-space with strong skin-effect, the source of which is an arbitrarily oriented magnetic moment. Methodology. The expressions for non-uniform electromagnetic field with strong skin effect are used for the analysis, which is based on the found exact analytical solution of the general three-dimensional problem and the use of expansion into asymptotic series with respect to a small parameter that is proportional to the ratio of the field penetration depth to the distance between the sources of the external field and the surface of body. Specific expressions at the surface are completely determined by the known field of external sources. In this work, the external magnetic moment field is used. Results. For strong skin effect, expressions for the electric and magnetic field strength are obtained separately for the components of the magnetic moment oriented perpendicularly and parallel to the flat surface between the dielectric and conducting areas. The features of the electromagnetic field distribution are analyzed depending on the value of introduced small parameter. The results are presented for the module and phase shift of the field strength with respect to the phase of the external field source. Originality. The expressions found for the electromagnetic field appear to be more general than the use of closed contours with alternating current, since they extend types of external field sources and allow the use of the superposition method instead of integration over the entire contour. Practical value. The found specific analytical expressions of the electromagnetic field at the surface for the external field of magnetic moments significantly simplify the solution of the problems, since they do not require additional solution of the field equations. References 20, figures 8.

Ground State Solutions for a Non-Local Type Problem in Fractional Orlicz Sobolev Spaces

In this paper, we study the following non-local problem in fractional Orlicz–Sobolev spaces: (−ΔΦ)su+V(x)a(|u|)u=f(x,u), x∈RN, where (−ΔΦ)s(s∈(0,1)) denotes the non-local and maybe non-homogeneous operator, the so-called fractional Φ-Laplacian. Without assuming the Ambrosetti–Rabinowitz type and the Nehari type conditions on the non-linearity f, we obtain the existence of ground state solutions for the above problem with periodic potential function V(x). The proof is based on a variant version of the mountain pass theorem and a Lions’ type result in fractional Orlicz–Sobolev spaces.

Разработка требований к одежде для женщин в до- и послеродовой период

This article describes the basic requirements and functions of household clothing for women during pregnancy and in the postpartum period. And also what requirements are given for designing such clothes. Imported clothing before and after the period in our country is sold at a high price and our women cannot afford to buy such expensive clothes. The establishment of the production of such special clothes in our republic using local resources would make their pains cheap, which would allow the solution of problems and increase the economy of our country.

High Energy Solutions for p-Kirchhoff Elliptic Problems with Hardy–Littlewood–Sobolev Nonlinearity

This article deals with the study of the following Kirchhoff–Choquard problem: M∫RN|∇u|p(-Δp)u+V(x)|u|p-2u=∫RNF(u)(y)|x-y|μdyf(u),inRN,u>0,inRN,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\begin{array}{cc} \\displaystyle M\\left( \\, \\int \\limits _{{\\mathbb {R}}^N}|\ abla u|^p\\right) (-\\Delta _p) u + V(x)|u|^{p-2}u = \\left( \\, \\int \\limits _{{\\mathbb {R}}^N}\\frac{F(u)(y)}{|x-y|^{\\mu }}\\,dy \\right) f(u), \\;\\;\ ext {in} \\; {\\mathbb {R}}^N,\\\\ u > 0, \\;\\; \ ext {in} \\; {\\mathbb {R}}^N, \\end{array} \\end{aligned}$$\\end{document}where M models Kirchhoff-type nonlinear term of the form M(t)=a+btθ-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M(t) = a + bt^{\ heta -1}$$\\end{document}, where a,b>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a, b > 0$$\\end{document} are given constants; 1<p<N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1<p<N$$\\end{document}, Δp=div(|∇u|p-2∇u)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta _p = \ ext {div}(|\ abla u|^{p-2}\ abla u)$$\\end{document} is the p-Laplacian operator; potential V∈C2(RN)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$V \\in C^2({\\mathbb {R}}^N)$$\\end{document}; f is monotonic function with suitable growth conditions. We obtain the existence of a positive high energy solution for θ∈1,2N-μN-p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta \\in \\left[ 1, \\frac{2N-\\mu }{N-p}\\right) $$\\end{document} via the Pohožaev manifold and linking theorem. Apart from this, we also studied the radial symmetry of solutions of the associated limit problem.

Normalized homoclinic solutions of discrete nonlocal double phase problems

The aim of this paper is to discuss the existence of normalized solutions to the following nonlocal double phase problems driving by the discrete fractional Laplacian: [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] if [Formula: see text], [Formula: see text] if [Formula: see text], and [Formula: see text]([Formula: see text] or [Formula: see text], [Formula: see text] or [Formula: see text]) is the discrete fractional [Formula: see text]-Laplacian. By variational methods, we discuss the existence of non-negative normalized homoclinic solutions under the conditions that the nonlinear term satisfies sublinear growth or superlinear growth conditions. In particular, we establish the compactness of the associated energy functional of the problem without weights. Our paper is the first time to deal with the existence of normalized solutions for discrete double phase problems.

Special aspects of guarding and protecting sports facilities

Aim: The arrangement and organisation of sports events is a coordinated activity involving several organisations. The purpose of the research is to examine and reveal the special guarding and protection requirements of sports facilities and sports event venues. Methodology: After collecting and processing the reference literature, the Authors applied a qualitative method and focused on the methods and means of providing sports facilities, and looked for specifics from their own point of view. During the research, they used both empirical and logical methods. In order for the earned knowledge to contribute to the solution of practical problems, they chose the activity of practice-oriented research. Findings: Starting from the 1960s, and mainly from the 1980s, the arrangement and organisation of sports events is not just a professional sports issue. The capital injected by economic actors was aimed at organising family, cultural and entertainment events. As a result, unlike before, the sports facilities initially became multi-functional, and then the modern facilities became multi-functional venues. Due to its multi-functionality, special requirements for the security and protection of the venues and the facilities created in their surroundings, with different sports and economic purposes, have developed.

Special aspects of guarding and protecting sports facilities

Aim: The arrangement and organisation of sports events is a coordinated activity involving several organisations. The purpose of the research is to examine and reveal the special guarding and protection requirements of sports facilities and sports event venues. Methodology: After collecting and processing the reference literature, the Authors applied a qualitative method and focused on the methods and means of providing sports facilities, and looked for specifics from their own point of view. During the research, they used both empirical and logical methods. In order for the earned knowledge to contribute to the solution of practical problems, they chose the activity of practice-oriented research. Findings: Starting from the 1960s, and mainly from the 1980s, the arrangement and organisation of sports events is not just a professional sports issue. The capital injected by economic actors was aimed at organising family, cultural and entertainment events. As a result, unlike before, the sports facilities initially became multi-functional, and then the modern facilities became multi-functional venues. Due to its multi-functionality, special requirements for the security and protection of the venues and the facilities created in their surroundings, with different sports and economic purposes, have developed. Value: The basis of the security technology of sports facilities and the commercial, economic, entertainment, cultural and service units located in them is the security of objects, as well as personal and property security. Guarding and protecting the proper operation of the facilities is an organised and coordinated activity in the same way as in the case of sports events held in the facilities, but the method of implementation is not the same.

Convergence of solutions of a one-phase Stefan problem with Neumann boundary data to a self-similar profile

We study a one-dimensional one-phase Stefan problem with a Neumann boundary condition on the fixed part of the boundary. We construct the unique self-similar solution, and show that starting from arbitrary initial data, solution orbits converge to the self-similar solution.

Prediction of monkeypox infection from clinical symptoms with adaptive artificial bee colony-based artificial neural network

AbstractIn 2022, the World Health Organization declared an outbreak of monkeypox, a viral zoonotic disease. With time, the number of infections with this disease began to increase in most countries. A human can contract monkeypox by direct contact with an infected human, or even by contact with animals. In this paper, a diagnostic model for early detection of monkeypox infection based on artificial intelligence methods is proposed. The proposed method is based on training the artificial neural network (ANN) with the adaptive artificial bee colony algorithm for the classification problem. In the study, the ABC algorithm was preferred instead of classical training algorithms for ANN because of its effectiveness in numerical optimization problem solutions. The ABC algorithm consists of food and limit parameters and three procedures: employed, onlooker and scout bee. In the algorithm standard, artificial onlooker bees are produced as much as the number of artificially employed bees and an equal number of limit values are assigned for all food sources. In the advanced adaptive design, different numbers of artificial onlooker bees are used in each cycle, and the limit numbers are updated. For effective exploitation, onlooker bees tend toward more successful solutions than the average fitness value of the solutions, and limit numbers are updated according to the fitness values of the solutions for efficient exploration. The performance of the proposed method was investigated on CEC 2019 test suites as examples of numerical optimization problems. Then, the system was trained and tested on a dataset representing the clinical symptoms of monkeypox infection. The dataset consists of 240 suspected cases, 120 of which are infected and 120 typical cases. The proposed model's results were compared with those of ten other machine learning models trained on the same dataset. The deep learning model achieved the best result with an accuracy of 75%. It was followed by the random forest model with an accuracy of 71.1%, while the proposed model came third with an accuracy of 71%.

The fractional analysis of thermo-elasticity coupled systems with non-linear and singular nature

It is mentioned that understanding linear and non-linear thermo-elasticity systems is important for understanding temperature, elasticity, stresses, and thermal conductivity. One of the most crucial aspects of the current research is the solution to these systems. The fractional form of several thermo-elastic systems is explored, and elegant solutions are provided. The solutions of fractional and integer thermo-elastic systems are further discussed using tables and diagrams. The closed contact between the LRPSM and exact solutions is displayed in the graphs. Plotting fractional problem solutions demonstrates their convergence towards integer-order problem solutions for suitable modeling. The tables confirm that greater precision is rapidly attained as the terms of the derived series solution increase. The faster convergence and stability of the suggested method support its modification for other fractional non-linear complex systems in nature.

Nonlocal boundary value problems for functional hybrid differential equations involving generalized w-Caputo fractional operator

In this manuscript , we establish the existence and uniqueness of solutions for boundary value problems of nonlinear hybrid fractional differential equations involving generalized $\omega-$Caputo fractional derivatives. The proofs are based on Krasnoselskii fixed point theorem and some basic concept of $\omega-$Caputo fractional analysis. As application, an nontrivial example is given in the last part of this paper to illustrate our theoretical results.

Sequences of nodal solutions for critical double phase problems with variable exponents

In this paper, we study a double phase problem with both variable exponents. Such problem has a reaction consisting of a Carathéodory perturbation defined only locally and of a critical term. The presence of the critical term does not permit to use results of the critical point theory for the corresponding energy functional. Consequently, using suitable cut-off functions and truncation techniques we focus on an auxiliary coercive problem on which, differently from our main problem, we can act with variational tools. In this way, we are able to produce a sequence of sign-changing solutions to our main problem converging to 0 in L∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^{\\infty }$$\\end{document} and in the Musielak–Orlicz Sobolev space.

Multi-objective optimization for low hydrogen consumption and long useful life in fuel cell emergency power supply systems

The power system using hydrogen fuel cells (FCs) as the primary energy source holds significant potential for applications in emergency fields such as post-disaster relief and outdoor power supply. The operational environment of the FC emergency power supply system (FCEPSS) is challenging, with long continuous operation time, difficulties in hydrogen supply, high maintenance costs, and, accordingly, requirements for hydrogen consumption and useful life of FCs are heightened. Hence, this paper proposes a multi-objective energy management strategy (EMS) for FCEPSS. First, the structure of FCEPSS is designed based on the demand analysis in emergency scenarios. Then, the hydrogen consumption and life degradation models of FCEPSS are established. Aiming at the multi-objective optimization problem of minimizing hydrogen consumption and life degradation value in the FCEPSS, an improved multi-objective optimization algorithm is proposed. This paper converts complex constraints into the penalty term and incorporates it as one of the objectives, constructing a three-objective optimization model. To enhance the solution of multi-objective optimization problems, an improved strategy based on relaxation-tightening and three-objective sorting is proposed. Combining the fast non-dominated sorting genetic algorithm-II and the above improved strategy, an improved multi-objective optimization algorithm (IMOOA) is constructed. In the simulation, the advantages of the proposed IMOOA algorithm are verified. In the experimental part, compared with the logical threshold strategy, the proposed strategy saves 0.60% of hydrogen consumption and reduces 5.65% of life degradation within 24 h, respectively. Finally, the superiority of the multi-objective EMS utilizing the IMOOA is demonstrated.

FairSNA: Algorithmic Fairness in Social Network Analysis

In recent years, designing fairness-aware methods has received much attention in various domains, including machine learning, natural language processing, and information retrieval. However, in social network analysis (SNA), designing fairness-aware methods for various research problems by considering structural bias and inequalities of large-scale social networks has not received much attention. In this work, we highlight how the structural bias of social networks impacts the fairness of different SNA methods. We further discuss fairness aspects that should be considered while proposing network structure-based solutions for different SNA problems, such as link prediction, influence maximization, centrality ranking, and community detection. This survey-cum-vision clearly highlights that very few works have considered fairness and bias while proposing solutions; even these works are mainly focused on some research topics, such as link prediction, influence maximization, and PageRank. However, fairness has not yet been addressed for other research topics, such as influence blocking and community detection. We review the state of the art for different research topics in SNA, including the considered fairness constraints, their limitations, and our vision. This survey also covers evaluation metrics, available datasets and synthetic network generating models used in such studies. Finally, we highlight various open research directions that require researchers’ attention to bridge the gap between fairness and SNA.

LYAPUNOV-TYPE INEQUALITY FOR CERTAIN HALF-LINEAR LOCAL FRACTIONAL ORDINARY DIFFERENTIAL EQUATIONS

In this paper, we establish a Lyapunov-type inequality for the half-linear local fractional ordinary differential equation based on the formulation of the local fractional derivative. In addition, we apply the inequality to investigate the non-existence and uniqueness of solutions for related homogeneous and non-homogeneous local fractional boundary value problems.

The non-homogeneous Cauchy problem of semigroup of linear operators

This paper presents the results of ω-order reversing partial contraction mapping generated by the non-homogeneous Cauchy problem. We investigated several concepts of solution for non-homogeneous Cauchy problem where an analysis was arrived out on the relationship between C' strong and respectively C0-solution. We showed that Z is the infinitesimal generator of a C0-semigroup of contractions. Finally, we obtained that the problem has a unique classical solution and f, a member of L1(a,b; X) is continuous on (a,b).