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Journal of applied and Numerical Optimization 2024年第2期6卷 291-320页

作者： DE MARCHI, Alberto Institute of Applied Mathematics and Scientific Computing Department of Aerospace Engineering University of the Bundeswehr Munich Neubiberg85577 Germany

Generalized nonlinear programming is considered without any convexity assumption, capturing a variety of problems that include nonsmooth objectives, combinatorial structures, and set-membership nonlinear constraints. We extend the augmented Lagrangian framework to this broad problem class, preserving an implicit formulation and introducing auxiliary variables merely as a formal device. This, however, gives rise to a generalized augmented Lagrangian function that lacks regularity. Based on parametric optimization, we develop a tailored stationarity concept to better qualify the iterates, generated as approximate solutions to a sequence of subproblems. Using this variational characterization and the lifted representation, asymptotic properties and convergence guarantees are established for a safeguarded augmented Lagrangian scheme. Numerical examples showcase the modelling versatility gained by dropping convexity assumptions and the practical benefits of the advocated implicit approach. © 2024 Journal of applied and Numerial Optimization.

关键词： Optimization algorithms

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A semi-analytical solution approach for fuzzy fractional acoustic waves equations using the Atangana Baleanu Caputo fractional operator

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Soft computing 2024年第17-18期28卷 9307-9315页

作者： Ghazouani, Aziz El Elomari, M’hamed Melliani, Said Laboratory of Applied Mathematics and Scientific Computing Department and Organization Sultan Moulay Slimane University Beni Mellal23000 Morocco

In this paper, we investigate the approximate solutions for the fractional fuzzy acoustic wave equations. We use the Laplace transform and an iterative technique with the fractional Atangana–Baleanu–Caputo operator to archive the series form results for the mains equations, and the expected outcomes of the suggested kinds were calculated. Finally, numerical examples are presented to show the usability of our major results. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.

关键词： Laplace transforms

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Innovative Study on Complex Fuzzy Soft Graph and its Properties

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IAENG International Journal of applied mathematics 2024年第10期54卷 2041-2048页

作者： Suresh, R. Veeramani, V. Thamizharasi, R. Department of Mathematics SRM Institute of Science and Technology Tamilnadu Tiruchirappalli India Mathematics and Computing Skills Unit Preparatory Studies Centre University of Technology and Applied Sciences Salalah Oman Department of Mathematics Saveetha Engineering College Tamilnadu Chennai India

This study aims to present complex fuzzy soft graphs (cfsg). We also obtain regular cfsg, strong cfsg, spanning cfsg, and complex fuzzy soft graph (cfsg) along with the definitions of the cfsg ‘s for path, bridge, strength, regular order and size. Furthermore, examples are provided for the union, intersection, complement, and Cartesian product of the cfsg procedures. This study also addresses the potential applications of the cfsg and energy of the cfsg. © (2024), (International Association of Engineers). All rights reserved.

关键词： Fuzzy sets

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Strategic Defense Post Allocation Using the Corona Cover Set for Enhanced Military Zone Security 1

Strategic Defense Post Allocation Using the Corona Cover Set...

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1st International Conference for Women in computing, InCoWoCo 2024

作者： Niveditha, P. Mahadevan, G. Sivagnanam, C. Department of Mathematics Tamilnadu Gandhigram India University of Technology and Applied Sciences-Sur Mathematics and Computing Skills Unit Oman

ISBN: (纸本)9798331518943

Defense forces are vital for national safety, peace-keeping, disaster response, and economic support. They require strong support systems, medical access, rapid deployment, and effective command centers to operate efficiently. Proper placement and a well-structured defense strategy focusing on sustainability and readiness are essential for ensuring safety and stability for both military and civilians. Recently G. Mahadevan *** established the concept of Corona covering number of a graph and obtained many results. A vertex cover set $S\subseteq V(G)$ is a corona cover set if every vertex $v\in S$ such that $d_{\langle S\rangle}(v)=1$ or there exist a vertex $u\in S$ with $d_{\langle S\rangle}(u)=1$ and $uv\in E$. The least cardinality of a corona cover set is the corona covering number of a graph and it is expressed as $\tau_{C}(G)$. In this article, the investigation of corona covering number in the strategic placement of defense posts within military zones, aiming to enhance operational efficiency and effectively deter unauthorized incursions has been attained. © 2024 IEEE.

关键词： Disasters

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A Polynomial Time Algorithm for Steiner Tree When Terminals Avoid a Rooted K4-Minor 19

A Polynomial Time Algorithm for Steiner Tree When Terminals ...

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19th International Symposium on Parameterized and Exact Computation, IPEC 2024

作者： Groenland, Carla Nederlof, Jesper Koana, Tomohiro Delft Institute of Applied Mathematics Netherlands Department of Information and Computing Sciences Utrecht University Netherlands

ISBN: (纸本)9783959773539

We study a special case of the Steiner Tree problem in which the input graph does not have a minor model of a complete graph on 4 vertices for which all branch sets contain a terminal. We show that this problem can be solved in O(n4) time, where n denotes the number of vertices in the input graph. This generalizes a seminal paper by Erickson et al. [Math. Oper. Res., 1987] that solves Steiner tree on planar graphs with all terminals on one face in polynomial time. © Carla Groenland, Jesper Nederlof, and Tomohiro Koana.

关键词： Trees (mathematics)

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Chemical Reaction and Viscous Dissipative Effects on Buongiorno’s Nanofluid Model Past an Inclined Plane: A Numerical Investigation

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International Journal of applied and Computational mathematics 2024年第2期10卷 1-20页

作者： Reddy, Ramesh Gaffar, S. Abdul Department of Mathematics Madanapalle Institute of Technology & amp Preparatory Studies Center Mathematics and Computing Skills Unit University of Technology and Applied Sciences Salalah Oman

The use of nanofluid in thermal applications dramatically enhanced the pattern of heat and mass transmission, which is essential in numerous engineering and industrial areas. Numerous innovative applications in solar energy and thermal engineering can be attributed to the consideration of nanofluid. Additionally, motile microorganisms, which have applications in enzymes, bioengineering, biomedicine, biofuels and petroleum sciences, perfectly improve the stability of nanofluid. The study of nanofluid has several dynamic applications in renewable energy and thermodynamic engineering problems. The aim of this paper is to discuss the chemical viscous dissipative transport of Buongiorno’s nanofluid across an inclined plane, considering Brownian movement and thermophoresis effects. The governing equations and the associated boundary conditions are normalized using the non-similarity transformation approach. The key variables and corresponding non-similarity solutions are provided to summarize the transpiration parameters. The Keller’s Box method is used to obtain the mathematical solutions. The numerical findings are given for various thermos-physical parameter values both physically and quantitatively. The graphical effects of various thermos-physical factors on momentum, energy, nanoparticle volume fraction concentration, shear stress rate, heat and mass transfer rates are examined and well discussed. The results show strong associations when compared to previously published literature. A slight increase in velocity with a rise in Kr values. Whereas, a slight decrease in temperature with an increase in Kr values and a strong decrease in nanoparticle volume fraction concentration with an increase in Kr values. A significant increase in velocity and temperature is seen with an increase in Ec and Nb values while nanoparticle volume fraction concentration is seen to decrease slightly. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2024.

关键词： Chemical reaction Heat transfer rate Keller’s box technique Mass transfer rate Nanofluid Skin friction Viscous dissipation

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The Hadamard ψ-Caputo tempered fractional derivative in various types of fuzzy fractional differential equations

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Soft computing 2024年第17-18期28卷 9253-9270页

作者： Amir, Fouad Ibrahim Abdou Moussaoui, Abdelhamid Shafqat, Ramsha El Omari, M’hamed Melliani, Said Laboratory of Applied Mathematics and Scientific Computing Sultan Moulay Slimane University P.O. Box 523 Beni Mellal23000 Morocco Department of Mathematics and Statistics The University of Lahore Sargodha40100 Pakistan

Different types of fractional calculus have been defined, grouped into categories based on their properties. Two types particularly studied are Hadamard-type fractional calculus and tempered fractional calculus. This paper establishes a connection between these two types by expressing one in terms of the other, using the theory of fuzzy fractional calculus with respect to functions. By naturally extending this connection, a generalization is developed that unifies several existing fractional operators, including Riemann–Liouville, Caputo, ψ-Caputo, classical Hadamard, Hadamard-type, tempered, and all these operators considered with respect to functions via the Hadamard ψ-Caputo tempered fractional derivative (CTFD) using the Mittag-Leffler function. In addition, we explore the Cauchy problem for fuzzy fractional differential equations (FDEs) with this kind of derivative and demonstrate various results of existence and uniqueness using fixed-point theorems of Krasnoselskii, Schaüder’s, and Banach. Applications further serve as proof of the utility of our findings, which converge, expand, and generalize several previously reported results in research. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.

关键词： Fixed point arithmetic

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STABILITY ANALYSIS OF A COUPLE-STRESS FLUID WITH VARIABLE GRAVITY IN A POROUS MEDIUM FOR DIFFERENT CONDUCTING BOUNDARIES

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Special Topics and Reviews in Porous Media 2024年第6期15卷 47-59页

作者： Choudhary, Shalu Devi, Reeta Mahajan, Amit Sunil Department of Mathematics Uttaranchal University Uttarakhand Dehradun248007 India Department of Mathematics Govt. Post Degree College Nagrota Bagwan H.P. Kangra176047 India Department of Applied Sciences NIT Delhi 110036 India Department of Mathematics and Scientific Computing NIT Hamirpur 177005 India

Models with higher order gradient terms are of considerable interest in modeling the transporting of biofluids in biological systems. A horizontal layer of couple stress fluid is considered to model a system with a variable gravity field and conducting boundaries. The stability of the nonlinear model is analyzed by applying the energy technique and calculating the values of Rayleigh numbers (critical) numerically using the Galerkin technique for rigid-rigid, rigid-free, and free-free boundary conditions. It is observed that the increase in values of Brinkman number and couple stress parameter stabilizes the model. However, the critical values of the Rayleigh number are greatly influenced by the gravity variation models. The results suggests that the stability of the fluids with higher order stress contribution is highly influenced by varying gravity conditions, such as in space. © 2024 by Begell House, Inc.

关键词： Rayleigh number

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Efficient Real-Time Obstacle Avoidance Using Multi-Objective Nonlinear Model Predictive Control and Semi-Smooth Newton Method 10

Efficient Real-Time Obstacle Avoidance Using Multi-Objective...

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10th International Conference on Vehicle Technology and Intelligent Transport Systems, VEHITS 2024

作者： Emam, Mostafa Rottmann, Thomas Gerdts, Matthias Department of Aerospace Engineering Institute of Applied Mathematics and Scientific Computing University of the Bundeswehr Munich Neubiberg85579 Germany

ISBN: (纸本)9789897587030

This work discusses the theory and methodology of applying Nonlinear Model Predictive Control (NMPC) in an efficient manner to achieve real-time path planning and obstacle avoidance for autonomous vehicles. First, we explain the optimization problem formulation and the numerical solution approach using a semi-smooth Newton method adapted for nonlinear problems. Then, an MPC path planning problem is described in terms of the vehicle model, the controller design, and the mathematical representation of obstacles as proper system constraints. Afterwards, the developed controller is numerically evaluated for different vehicle models in a simulated environment to dynamically assess its flexibility and real-time performance, which serves as a prerequisite to deferred real-life testing. Copyright © 2024 by SCITEPRESS - Science and Technology Publications, Lda.

关键词： Motion planning

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Network Malaria Model on Account of Wide Communication 2

Network Malaria Model on Account of Wide Communication

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2nd IEEE International Conference on IoT, Communication and Automation Technology, ICICAT 2024

作者： Tripathi, Padmaja Chandra, Harish Ramkeval Madan Mohan Malviya University of Technology Department of Mathematics and Scientific Computing Gorakhpur273010 India MJP Rohilkhand University Department of Applied Mathematics Bareilly India

ISBN: (纸本)9798350368109

Diseases caused by parasites proliferate quickly over the globe. As a result, their control intervention needs to be swift and comprehensive. Preventing chronic diseases can be accomplished by using multi-modal communication to attract attention and enhance awareness. This study presents a nonlinear dynamical model to evaluate the impact of media knowledge on the dissemination of illnesses carried by vectors. In this research, we propose a network model for wide-area multi-media communication. Positiveness, simple reproduction number equilibria, numerical simulation, and a fitted model using Delhi malaria data are used to analyze the mathematical model. An informed community makes it more difficult for disease to spread. Constant multi-media efforts combined with quick communication can effectively eradicate the illness. © 2024 IEEE.

关键词： Malaria network model social media stability

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