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arXiv 2021年

作者： Tynda, Aleksandr Noeiaghdam, Samad Sidorov, Denis Higher and Applied Mathematics Department Penza State University Penza440026 Russia Industrial Mathematics Laboratory Baikal School of BRICS Irkutsk National Research Technical University Irkutsk664074 Russia Department of Applied Mathematics and Programming South Ural State University Lenin prospect 76 Chelyabinsk454080 Russia Energy Systems Institute Siberian Branch of Russian Academy of Science Irkutsk664033 Russia Institute of Mathematics and Information Technologies Irkutsk State University Irkutsk664025 Russia

The polynomial spline collocation method is proposed for solution of Volterra integral equations of the first kind with special piecewise continuous kernels. The Gauss-type quadrature formula is used to approximate integrals during the discretization of the proposed projection method. The estimate of accuracy of approximate solution is obtained. Stochastic arithmetics is also used based on the Contrôle et Estimation Stochastique des Arrondis de Calculs (CESTAC) method and the Control of Accuracy and Debugging for Numerical Applications (CADNA) library. Applying this approach it is possible to find optimal parameters of the projective method. The numerical examples are included to illustrate the efficiency of proposed novel collocation *** Codes 45H05, 65R20 © 2021, CC BY.

关键词： Integral equations

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Optimum Production for a heaped stock dependent breakable item through variational principle

arXiv

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arXiv 2020年

作者： Roul, J.N. Maity, K. Kar, S. Maiti, M. Patha Bhavana Visva-Bharati SantiniketanWest Bengal731235 India Department of Mathematics Mugberia Gangadhar Mahavidyalaya Bhupatinagar Purba MedinipurW.B.721425 India Department of Mathematics National Institute of Technology DurgapurW.B.713209 India Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University MidnaporeW.B.711201 India

Breakability rate of fragile item depends on the accumulated stress of heaped stock level. So breakablility rate can be considered as dependent parameter of stock variable. The unit production cost is a function of production rate and also dependent on raw material cost, development cost and wear-tear cost. The holding cost is assumed to be non-linear, dependent on time. Here optimal control problem for a fragile item under finite time horizon is considered. The profit function which consists of revenue, production and holding costs is formulated as a Fixed-Final Time and Fixed State System(cf. Naidu (2000)[8]) optimal control problem with finite time horizon. Here production rate is unknown and considered as a control variable and stock level is taken as a state variable. It is formulated to optimize the production rate so that total profit is maximum. As particular cases, models are evaluated with and without breakability. The models are solved by using conventional Variational Principle along with the non-linear optimization technique-Generalised Reduced Gradient Method (LINGO 12.0). The optimum results are illustrated both numerically and graphically. Some sensitivity analysis on breakability coefficient are presented. Copyright © 2020, The Authors. All rights reserved.

关键词： Optimal control systems

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Some remarks on smooth mappings of Hilbert and Banach spaces and their local convexity property

arXiv

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arXiv 2021年

作者： Prykarpatskyy, Yarema A. Pukach, Petro Y. Vovk, Myroslava I. Greguš, Michal Department of Applied Mathematics University of Agriculture in Krakow Al. Mickiewicza 21 Krakow31-120 Poland Institute of Mathematics of NAS of Ukraine 3 Tereschenkivska st. Kyiv 401024 Ukraine Department of Computational Mathematics and Programming Institute of Applied Mathematics and Fundamental Sciences Lviv Polytechnic National University 12 Bandera Str. Lviv79013 Ukraine Department of Mathematics Institute of Applied Mathematics and Fundamental Sciences Lviv Polytechnic National University 12 Bandera Str. Lviv79013 Ukraine Department of Information Systems Faculty of Management Comenius University in Bratislava Odbojarov 10 Bratislava 2582005 Slovakia

We analyze smooth nonlinear mappings for Hilbert and Banach spaces that carry small balls to convex sets, provided that the radius of the balls is small enough. Being focused on the study of new and mild sufficient conditions for a nonlinear mapping of Hilbert and Banach spaces to be locally convex, we address a suitably reformulated local convexity problem analyzed within the Leray-Schauder homotopy method approach for Hilbert speces, and within the Lipscitz smoothness condition both for Hilbert and Banach spaces. Some of the results presented in the work prove to be interesting and novel even for finite-dimensional problems. Open problems related to the local convexity property for nonlinear mapping of Banach spaces are also *** Codes 46B20, 49J50, 52A41, 58C20 © 2021, CC BY.

关键词： Banach spaces

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Evolutionary Algorithm for Calculating the Optimal Temperature Regime of the Catalytic Process

Evolutionary Algorithm for Calculating the Optimal Temperatu...

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International Conference on Control Systems, Mathematical Modelling, Automation and Energy Efficiency (SUMMA)

作者： Evgenia Antipina Svetlana Mustafina Andrey Antipin Department of Scientific Research Ufa University of Science and Technology Ufa Russia Faculty of Mathematics and Information Technologies Ufa University of Science and Technology Ufa Russia Department of Applied Informatics and Programming Sterlitamak Branch of Ufa University of Science and Technology Sterlitamak Russia

The paper formulates an algorithm for searching the optimal temperature regime of the catalytic process in an ideal mixing reactor. The problem of optimal control of the catalytic process is formulated in a general form. To find its numerical solution, an algorithm based on the method of differential evolution is described. The algorithm allows to obtain an approximate solution of the optimization problem in a time acceptable from the practical point of view. A computational experiment for the dimerization process of alphamethylstyrene is carried out. The optimal temperature profile for achieving the maximum yield of reaction products – linear dimers – is obtained.

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Evaluating carbon cap and trade policy effects on a multi-period bi-objective closed-loop supply chain in retail management under mixed uncertainty: Towards greener horizons

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Expert Systems with Applications 2024年 250卷

作者： Bhunia, Satyajit Das, Soumen Kumar Jablonsky, Josef Roy, Sankar Kumar Department of Pure and Applied Science Midnapore City College Kuturia West Bengal Bhadutala721129 India Department of Industrial Management National Taiwan University of Science and Technology Taipei Taiwan Department of Econometrics Faculty of Informatics and Statistics Prague University of Economics and Business Praha 3 Prague Czech Republic Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University West Bengal Midnapore721102 India

In response to the growing imperative of addressing environmental concerns and aligning with governmental regulations in supply chain management, this study navigates the optimization landscape of closed-loop supply chains through the lens of carbon cap and trade policy. The optimization model aims to account for the impact of consumer demands, distribution networks, and retail operations on the overall closed-loop supply chain dynamics. The innovative approach introduces an optimization model designed to grapple with the challenges posed by imprecise information within an intuitionistic type-2 fuzzy framework. The bi-objective mixed-integer model integrates pivotal objectives, including carbon emissions reduction, total cost minimization, and trade policy compliance. For a nuanced comprehension of the proposed model, we present three numerical examples, offering clarity on its complexities. Following this, a sensitivity analysis visually depicts the impact of fluctuations in demand and capacity on the defined objective functions. Furthermore, these conclusions unveil promising avenues for future research and exploration within the ambit of this study. © 2024 Elsevier Ltd

关键词： Multiobjective optimization

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Numerical solution of fractional Fredholm integro-differential equations by spectral method with fractional basis functions

arXiv

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arXiv 2022年

作者： Talaei, Younes Noeiaghdam, Samad Hosseinzadeh, Hasan Faculty of Mathematical Sciences University of Tabriz Tabriz Iran Industrial Mathematics Laboratory Baikal School of BRICS Irkutsk National Research Technical University Irkutsk664074 Russia Department of Applied Mathematics and Programming South Ural State University Lenin prospect 76 Chelyabinsk454080 Russia Department of Mathematics Ardabil Branch Islamic Azad University Ardabil*** Iran

This paper presents an efficient spectral method for solving the fractional Fredholm integro-differential equations. The non-smoothness of the solutions to such problems leads to the performance of spectral methods based on the classical polynomials such as Chebyshev, Legendre, Laguerre, etc, with a low order of convergence. For this reason, the development of classic numerical methods to solve such problems becomes a challenging issue. Since the non-smooth solutions have the same asymptotic behavior with polynomials of fractional powers, therefore, fractional basis functions are the best candidate to overcome the drawbacks of the accuracy of the spectral methods. On the other hand, the fractional integration of the fractional polynomials functions is in the class of fractional polynomials and this is one of the main advantages of using the fractional basis functions. In this paper, an implicit spectral collocation method based on the fractional Chelyshkov basis functions is introduced. The framework of the method is to reduce the problem into a nonlinear system of equations utilizing the spectral collocation method along with the fractional operational integration matrix. The obtained algebraic system is solved using Newton’s iterative method. Convergence analysis of the method is studied. The numerical examples show the efficiency of the method on the problems with smooth and non-smooth solutions in comparison with other existing *** Codes 65N35, 47G20, 35R11, 42C10 Copyright © 2022, The Authors. All rights reserved.

关键词： Polynomials

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Sports programming as a Tool for Regional Development of the Digital Industry and Higher Education

Sports Programming as a Tool for Regional Development of the...

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Technology Enhanced Learning in Higher Education (TELE), International Conference on

作者： Alexander Galkin Artem Miroshnikov Daniil Sapronov Elena Skarzhinskaya Faculty of Automation and Computer Science Lipetsk State Technical University Lipetsk Russia Department of Applied Mathematics Lipetsk State Technical University Lipetsk Russia Lipetsk branch of the Russian Federation of Sports Programming Lipetsk Russia Department of Cybersport Moscow Financial and Industrial University “Synergy” Moscow Russia

ISBN: (数字)9798350353532

ISBN: (纸本)9798350353549

Abstract-The article presents the history of the development of sports programming as a sport in Russia. The main stages of the formation of the legislative basis for this sport are given. The rationale and description of the process of training athletes in higher education institutions are given - possible traj ectories in the disciplines of “algorithmic programming” and “product programming”, the influence of the development of sports programming on improving the quality of IT education. As an example, the organization of training students in the discipline of “algorithmic programming” at the Lipetsk State Technical University is given. The activities of the Lipetsk regional branch of the All- Russian Sports Federation to popularize this sport including among students are also described.

关键词： Training Industries Organizations History programming profession Sports

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Correction to: Estimation of most effected cycles and busiest network route based on complexity function of graph in fuzzy environment

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Artificial Intelligence Review 2023年第12期56卷 15567-15567页

作者： Ghorai, Ganesh Poulik, Soumitra Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Midnapore India

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A multiobjective multi-item inventory control problem in fuzzy-rough environment using soft computing techniques

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Advances in Decision Sciences 2014年第unknown期2014卷 1-13页

作者： Jana, Dipak Kumar Maity, K. Maiti, M. Roy, T.K. Department of Engineering Science Haldia Institute of Technology Haldia West Bengal 721657 India Department of Mathematics Mugberia Gangadhar Mahavidyalaya Mugberia Purba Medinipur West Bengal 721425 India Department of Applied Mathematics with Oceanology and Computer Programming Vidyasagar University Medinipur West Bengal 721 102 India Department of Mathematics Bengal Engineering and Science University Shibpur Howrah West Bengal 711103 India

The optimal production and advertising policies for an inventory control system of multi-item multiobjective problem under a single management are formulated as an optimal control problem with resource constraints under inflation and discounting in fuzzy rough (Fu-Ro) environment. The objectives and constraints in Fu-Ro are made deterministic using fuzzy rough expected values method (EVM). Here, the production and advertisement rates are unknown and considered as control (decision) variables. The production, advertisement, and demand rates are functions of time t. Maximization of the total proceed from perfect and imperfect units and minimization of the total cost consisting of production, holding, and advertisement costs are formulated as optimal control problems and solved directly using multiobjective genetic algorithm (MOGA). In another method for solution, membership functions of the objectives are derived and the multi-objective problems are transformed to a single objective by the convex combination of the membership functions and then the problem is solved by generalized reduced gradient (GRG) method. Finally, numerical experiment and graphical representation are provided to illustrate the system. © 2014 Dipak Kumar Jana et al.

关键词： INVENTORY control EXPECTED returns OPTIMAL control theory SOFT computing FUZZY sets GENETIC algorithms

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Sentiment Analysis Technology of English Newspapers Quotes Based on Neural Network as Public Opinion Influences Identification Tool

Sentiment Analysis Technology of English Newspapers Quotes B...

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International Computer Sciences and Information Technologies (CSIT)

作者： Serhii Voloshyn Victoria Vysotska Oksana Markiv Ivan Dyyak Ihor Budz Vadim Schuchmann Information Systems and Networks Department Lviv Polytechnic National University Lviv Ukraine Lviv Polytechnic National University Lviv Ukraine Osnabrück University Osnabrück Germany Applied Mathematics Department Ivan Franko National University of Lviv Lviv Ukraine Computational Mathematics and Programming Department Lviv Polytechnic National University Lviv Ukraine Software Engineering Department West Ukrainian National University Ternopil Ukraine

ISBN: (纸本)9798350334326

This article dwells upon research concerning human language processing techniques, namely emotion analysis, conducted to identify emotions of author quotations in English newspaper articles. The publication describes general information about human language processing, brief description of analogues based on machine learning and neural network to analyse emotions in text. The main goal is to develop intelligent system for sentiment analysis of English language quotations and keywords identification that influences public opinion. The article describes sequence of program actions and tools that have been used. Then, statistics of tasks performed by neural networks with various functions of activators have been described. In the publication, product demo version has been described, and primary usage scenario has been depicted. In the end, research results have been summarised.

关键词： Training Sentiment analysis Vocabulary Dictionaries Mood Neural networks Text categorization

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