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VARIABLE STEP-SIZE BDF3 METHOD FOR ALLEN-CAHN EQUATION

Journal of Computational mathematics 2024年第5期42卷 1380-1406页

作者： Minghua Chen Fan Yu Qingdong Zhang Zhimin Zhang School of Mathematics and Statistics Gansu Key Laboratory of Applied Mathematics and Complex SystemsLanzhou UniversityLanzhou 730000China Department of Mathematics Wayne State UniversityDetroitMI 48202USA

In this work,we analyze the three-step backward differentiation formula(BDF3)method for solving the Allen-Cahn equation on variable *** BDF2 method,the discrete orthogonal convolution(DOC)kernels are positive,the stability and convergence analysis are well established in[Liao and Zhang,***.,90(2021),1207–1226]and[Chen,Yu,and Zhang,arXiv:2108.02910,2021].However,the numerical analysis for BDF3 method with variable steps seems to be highly nontrivial due to the additional degrees of freedom and the non-positivity of DOC *** developing a novel spectral norm inequality,the unconditional stability and convergence are rigorously proved under the updated step ratio restriction rk:=τk/τk−1≤1.405 for BDF3 ***,numerical experiments are performed to illustrate the theoretical *** the best of our knowledge,this is the first theoretical analysis of variable steps BDF3 method for the Allen-Cahn equation.

关键词： Variable step-size BDF3 method Allen-Cahn equation Spectral norm inequality Stability and convergence analysis

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Enhancing photovoltaic energy forecasting:a progressive approach using wavelet packet decomposition

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Clean Energy 2024年第3期8卷 95-108页

作者： Khaled Ferkous Mawloud Guermoui Abderahmane Bellaour Tayeb boulmaiz Nadjem Bailek LMTESE Laboratory of Materials Technology of Energy Systems and EnvironmentUniversitéde Ghardaia47000Algeria Renewable Energy Applied Research Unit(URAER) Ghardaia47000Algeria Laboratory of Mathematics Modeling and Applications Department of Mathematics and Computer ScienceFaculty of Sciences and TechnologyAhmed Draia University of AdrarAdrar 01000Algeria

Accurate photovoltaic(PV)energy forecasting plays a crucial role in the efficient operation of PV power *** study presents a novel hybrid machine-learning(ML)model that combines Gaussian process regression with wavelet packet decomposition to forecast PV power half an hour *** proposed technique was applied to the PV energy database of a station located in Algeria and its performance was compared to that of traditional forecasting *** evaluations demonstrate the superiority of the proposed approach over conventional ML methods,including Gaussian process regression,extreme learning machines,artificial neural networks and support vector machines,across all *** proposed model exhibits lower normalized root mean square error(nRMSE)(2.116%)and root mean square error(RMSE)(208.233 kW)values,along with a higher coefficient of determination(R^(2))of 99.881%.Furthermore,the exceptional performance of the model is maintained even when tested with various prediction ***,as the forecast horizon extends from 1.5 to 5.5 hours,the prediction accuracy decreases,evident by the increase in the RMSE(710.839 kW)and nRMSE(7.276%),and a decrease in R2(98.462%).Comparative analysis with recent studies reveals that our approach consistently delivers competitive or superior *** study provides empirical evidence supporting the effectiveness of the proposed hybrid ML model,suggesting its potential as a reliable tool for enhancing PV power forecasting accuracy,thereby contributing to more efficient grid management.

关键词： short photovoltaic power forecasting wavelet packet decomposition sub-series reconstruction machine learning in energy forecasting sustainable power stations renewable energy

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Inertial Proximal ADMM for Separable Multi-Block Convex Optimizations and Compressive Affine Phase Retrieval

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Acta Mathematica Sinica,English Series 2023年第8期39卷 1459-1496页

作者： Peng LI Wen Gu CHEN Qi Yu SUN School of Mathematics and Statistics Gansu Key Laboratory of Applied Mathematics and Complex SystemsLanzhou UniversityLanzhou 730000P.R.China Graduate School China Academy of Engineering PhysicsBeijing 100088P.R.China Institute of Applied Physics and Computational Mathematics Beijing 100088P.R.China Department of Mathematics University of Central FloridaOrlandoFL 32816USA

Separable multi-block convex optimization problem appears in many mathematical and engineering *** the first part of this paper,we propose an inertial proximal ADMM to solve a linearly constrained separable multi-block convex optimization problem,and we show that the proposed inertial proximal ADMM has global convergence under mild assumptions on the regularization *** phase retrieval arises in holography,data separation and phaseless sampling,and it is also considered as a nonhomogeneous version of phase retrieval,which has received considerable attention in recent *** by convex relaxation of vector sparsity and matrix rank in compressive sensing and by phase lifting in phase retrieval,in the second part of this paper,we introduce a compressive affine phase retrieval via lifting approach to connect affine phase retrieval with multi-block convex optimization,and then based on the proposed inertial proximal ADMM for 3-block convex optimization,we propose an algorithm to recover sparse real signals from their(noisy)affine quadratic *** numerical simulations show that the proposed algorithm has satisfactory performance for affine phase retrieval of sparse real signals.

关键词： Inertial proximal ADMM separable multi-block convex optimization affine phase retrieval

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Wasserstein-1 Distance and Nonuniform Berry-Esseen Bound for a Supercritical Branching Process in a Random Environment

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Journal of Mathematical Research with Applications 2023年第6期43卷 737-753页

作者： Hao WU Xiequan FAN Zhiqiang GAO Yinna YE Center for Applied Mathematics Tianjin University School of Mathematics and Statistics Northeastern University at Qinhuangdao Laboratory of Mathematics and Complex Systems School of Mathematical SciencesBeijing Normal University Department of Applied Mathematics School of Mathematics and PhysicsXi'an Jiaotong-Liverpool University

Let（Z_n）n≥0be a supercritical branching process in an independent and identically distributed random environment. We establish an optimal convergence rate in the Wasserstein-1 distance for the process（Z_n）n≥0, which completes a result of Grama et al. [Stochastic ***., 2017, 127（4）: 1255–1281]. Moreover, an exponential nonuniform Berry-Esseen bound is also given. At last, some applications of the main results to the confidence interval estimation for the criticality parameter and the population size Z_n are discussed.

关键词： Branching processes Random environment Wasserstein-1 distance Nonuniform Berry-Esseen bounds

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On the Vortex Sheets of Compressible Flows

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Communications on applied mathematics and Computation 2023年第3期5卷 967-986页

作者： Robin Ming Chen Feimin Huang Dehua Wang Difan Yuan Department of Mathematics University of PittsburghPittsburghPA 15260USA School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China Institute of Applied Mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences Beijing Normal University and Laboratory of Mathematics and Complex SystemsMinistry of EducationBeijing 100875China

This paper provides a review of the recent results on the stability of vortex sheets in compressible *** sheets are contact discontinuities of the underlying *** vortex sheet problem is a free boundary problem with a characteristic boundary and is challenging in *** formulation of the vortex sheet problem will be *** linear stability and nonlinear stability for both the two-dimensional two-phase compressible flows and the two-dimensional elastic flows are *** linear stability of vortex sheets for the three-dimensional elastic flows is also *** difficulties of the vortex sheet problems and the ideas of proofs are discussed.

关键词： Vortex sheets Contact discontinuities Stability and instability Loss of derivatives Two-phase flows Elastic flows

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A Role of Diffusion of Adatoms Between Layers in Nano-Structured Thin Films Growth at Condensation 13

A Role of Diffusion of Adatoms Between Layers in Nano-Struct...

引用

13th IEEE International Conference on Nanomaterials: Applications and Properties, NAP 2023

作者： Dvornichenko, Alina Kharchenko, Vasyl Kharchenko, Dmitrii Sumy State University Dpt. Applied Mathematics and Modeling of Complex Systems Sumy Ukraine Institute of Applied Physics National Academy of Sciences of Ukraine Sumy State University Sumy Ukraine Institute of Applied Physics National Academy of Sciences of Ukraine Sumy Ukraine

ISBN: (纸本)9798350329087

We perform theoretical studies of the formation and growth of adsorbate surface structures during condensation from the gas phase in the framework of the reaction-diffusion model. We show that an increase in the vertical diffusion coefficient leads to a decrease in the concentration of the adsorbate on the first growing layer, the realization of first-order transitions and reversible processes of adsorbate ordering on the substrate. We demonstrate that in a limited range of values of the coefficient of vertical diffusion of adatoms between layers, its increase leads to a morphological transformation in the structure of the surface layer from separated holes in the adsorbate matrix (nano-holes) toward separated adsorbate structures on the substrate (nano-dots). © 2023 IEEE.

关键词： Surface morphology

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An Artificial Immune System Algorithm for the Permutation Flow Shop Scheduling Problem with Sequence Dependent Setup Times 10

An Artificial Immune System Algorithm for the Permutation Fl...

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10th International Conference on Optimization and Applications, ICOA 2024

作者： Mesmar, Khadija Lebbar, Maria Aqil, Said Asebriy, Zahra Allali, Karam National School of Mines of Rabat Rosdm Research Team Lmaid Laboratory of Applied Mathematics and Business Intelligence Rabat Morocco Ensam Casablanca Hassan Ii University Laboratory Artificial Intelligence and Complex Systems Engineering Casablanca Morocco Est Essaouira Cadi Ayyad University Laboratory mathematics Computer sciences and modeling of complex systems Essaouira Morocco Fst Mohammadia Hassan Ii University Laboratory of Mathematics Computer Science and Applications Mohammadia Morocco

ISBN: (纸本)9798350387353

This paper is concerned with a set of independent jobs in a permutation flow shop that have setup times on a set of machines. The M-IAIS algorithm, which is based on immunoglobulins and has been modified, is designed to reduce the makespan. A unique procedure known as B cell repertoire updating, which comprises size C of jobs that are taken out of the sequence and reinserted into all possible positions of the remaining sequences of jobs, has an impact on the M-IAIS algorithm's performance. To increase the convergence velocity, three iterations of the algorithm are suggested. Thorough testing was done, and the three versions' performances on a set (benchmark) are compared. Problem instances are described in Sistemas de Optimizacion Aplicada (http://***/problem-instances) In the paper, percentage deviation is considered to evaluate the performance of the proposed algorithms. Furthermore, the ensuing outcomes demonstrate its suitability for addressing for the Permutation Flow Shop Scheduling Problem with Sequence Dependent Setup Times. © 2024 IEEE.

关键词： Scheduling algorithms

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A Markovian Queueing Model for Telecommunications Support Center with Breakdowns and Vacation Periods

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Operations Research Forum 2024年第1期5卷 22页

作者： Chettouf, Anis Bouchentouf, Amina Angelika Boualem, Mohamed Department of Mathematics Applied Mathematics Laboratory (LMA) University of Bejaia Bejaia 06000 Algeria Laboratory of Mathematics Djillali Liabes University of Sidi Bel Abbes Sidi Bel Abbes 22000 Algeria Research Unit LaMOS (Modeling and Optimization of Systems) Faculty of Technology University of Bejaia Bejaia 06000 Algeria

This paper presents an in-depth analysis of an infinite-space single-server Markovian queueing model for a customer support center that incorporates working breakdowns, repairs, balking, and reneging, along with both single and multiple vacation policies. Additionally, we consider the scenario where the server must wait for a random period before going on vacation. By employing the matrix-geometric method, we determine the steady-state probabilities of the system and derive essential performance measures. We construct an expected cost function and formulate an optimization problem to minimize the cost, using the direct search method to find the optimal service rates during working breakdown and busy periods. To demonstrate the model’s usefulness, the results are complemented with numerical illustrations and sensitivity analysis. This work thus enables improved decision-making and resource management in customer support centers by deepening our understanding of their dynamics. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.

关键词： 60K25 68M20 90B22 Cost optimization Customer support center Impatience Matrix method Queueing models Vacation

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Vulnerability of multilayer network systems to system-wide lesions

arXiv

引用

arXiv 2025年

作者： Polishchuk, Olexandr Polishchuk, Dmytro Laboratory of Modeling and Optimization of Complex Systems Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine Lviv Ukraine

On the basis of structural and flow models of multilayer network system (MLNS), the main structural and functional importance indicators of separate layers in the process of intersystem interactions are calculated. With the help of influence and betweenness parameters of separate layers, their role as generators, final receivers and transitors of intersystem flows is determined. Using the introduced importance indicators, effective scenarios of system-wide targeted attacks on MLNS are developed. The problem of the scale of targeted attacks and non-target lesions consequences for the network system (NS) and determination of its protection and sensitivity to various negative influences is analyzed. The advantages of flow-based approach over the structural ones during the study of vulnerability of NS and MLNS to heterogeneous internal and external negative influences are shown. © 2025, CC BY.

关键词： Multilayers

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Structural and flow approaches to complex network systems lesions scale analysis

arXiv

引用

arXiv 2024年

作者： Polishchuk, Olexandr Laboratory of Modeling and Optimization of Complex Systems Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine Lviv Ukraine

A comparative analysis of structural and flow approaches to analysis of vulnerability of complex network systems (NS) from targeted attacks and non-target lesions of various types was carried out. Typical structural and functional scenarios of successive targeted attacks on the most important by certain characteristics system elements were considered, and scenarios of simultaneous group attacks on the most significant NS's components were proposed. The problem of system lesions scale from heterogeneous negative impacts was investigated and it was confirmed that the flow approach allows us to obtain a much more realistic picture of consequences of such lesions. It is shown that scenarios of group targeted attacks built on the basis of the NC flow model are more optimal from the point of view of choosing attack targets than structural ones. © 2024, CC BY.

关键词： complex networks

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