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Advances in Applied mathematics and Mechanics 2024年第1期16卷 237-252页

作者： Alexey Shcheglov Jingzhi Li Chao Wang Alexander Ilin Ye Zhang Faculty of computational mathematics and cybernetics Shenzhen MSU-BIT UniversityShenzhenGuangdong 518172China Faculty of computational mathematics and cybernetics Lomonosov Moscow State UniversityMoscowRussia department of mathematics&National Center for Applied mathematics Shenzhen&SUSTech International Center for mathematics Southern University of Science and TechnologyShenzhenGuangdong 518055China School of mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China

This study addresses the parameter identification problem in a system of time-dependent quasi-linear partial differential equations(PDEs).Using the integral equation method,we prove the uniqueness of the inverse problem in nonlinear ***,using the method of successive approximations,we develop a novel iterative algorithm to estimate sorption *** stability results of the algorithm are proven under both a priori and a posteriori stopping rules.A numerical example is given to show the efficiency and robustness of the proposed new approach.

关键词： Inverse problem quasi-linear dynamic model uniqueness method of successive approximations stability

Investigation of coupling effect on the evolution of Richtmyer-Meshkov instability at double heavy square bubbles

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Science China(Physics,Mechanics & Astronomy) 2024年第1期67卷 52-70页

作者： Satyvir Singh Dhouha Taib Jalleli Applied and computational mathematics RWTH Aachen UniversityAachen 52056Germany department of mathematics Graphic Era Deemed to be UniversityDehradun 244712India mathematics department University College in DarbJazan UniversityAbu As Sadad 89653Saudi Arabia

This study investigates numerically the coupling effect on the evolution of Richtmyer-Meshkov instability at double heavy square *** scenarios are considered,each with varying initial separations S/L(where L demotes the side length of the square)ranging from 0.125 to *** are filled with SF6gas,and are enclosed by *** simulations of shock-induced multispecies flow are performed by solving the two-dimensional compressible Euler equations with a higher-order explicit modal discontinuous Galerkin *** simulations demonstrate that the flow morphology resulting from the coupling effect is highly dependent on the separation between two *** the separation is large,the squares experience a weaker coupling effect and evolve ***,as the separation reduces,the coupling effect manifests earlier in the interaction and becomes more *** a result,this phenomenon greatly intensifies the motion of inner upstream/downstream vortex rings towards the symmetry axis,leading to the emergence of multiple jets such as the twisted downward,upward,and coupled jets.A thorough exploration of the coupling effect of double squares is conducted by analyzing the vorticity ***,a significant quantity of vorticity is produced along the squares interface for smaller ***,these coupling effects result in various interface features(upstream/downstream movement,and height/width evolution),and temporal variations of various spatially integrated ***,the analysis of the flow structure also considers the interaction between two more flow parameters,the Mach and Atwood numbers,in order to evaluate the coupling effects.

关键词： RM instability shock wave double square bubbles coupling effect

Research on Multi-Scale Feature Fusion Network Algorithm Based on Brain Tumor Medical Image Classification

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Computers, Materials & Continua 2024年第6期79卷 5313-5333页

作者： Yuting Zhou Xuemei Yang Junping Yin Shiqi Liu Graduate School China Academy of Engineering PhysicsBeijing100000China department of computational mathematics Beijing Institute of Applied Physics and Computational MathematicsBeijing100000China National Key Laboratory of computational Physics Beijing100088China Shanghai Zhangjiang Institute of mathematics Shanghai201203China

Gliomas have the highest mortality rate of all brain *** classifying the glioma risk period can help doctors make reasonable treatment plans and improve patients’survival *** paper proposes a hierarchical multi-scale attention feature fusion medical image classification network(HMAC-Net),which effectively combines global features and local *** network framework consists of three parallel layers:The global feature extraction layer,the local feature extraction layer,and the multi-scale feature fusion layer.A linear sparse attention mechanism is designed in the global feature extraction layer to reduce information *** the local feature extraction layer,a bilateral local attention mechanism is introduced to improve the extraction of relevant information between adjacent *** the multi-scale feature fusion layer,a channel fusion block combining convolutional attention mechanism and residual inverse multi-layer perceptron is proposed to prevent gradient disappearance and network degradation and improve feature representation *** double-branch iterative multi-scale classification block is used to improve the classification *** the brain glioma risk grading dataset,the results of the ablation experiment and comparison experiment show that the proposed HMAC-Net has the best performance in both qualitative analysis of heat maps and quantitative analysis of evaluation *** the dataset of skin cancer classification,the generalization experiment results show that the proposed HMAC-Net has a good generalization effect.

关键词： Medical image classification feature fusion transformer

Sparse-Grid Implementation of Fixed-Point Fast Sweeping WENO Schemes for Eikonal Equations

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Communications on Applied mathematics and Computation 2024年第1期6卷 3-29页

作者： Zachary M.Miksis Yong-Tao Zhang department of Applied and computational mathematics and Statistics University of Notre DameNotre DameIN46556USA

Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady-state solutions of hyperbolic partial differential equations(PDEs).As other types of fast sweeping schemes,fixed-point fast sweeping methods use the Gauss-Seidel iterations and alternating sweeping strategy to cover characteristics of hyperbolic PDEs in a certain direction simultaneously in each sweeping *** resulting iterative schemes have a fast convergence rate to steady-state ***,an advantage of fixed-point fast sweeping methods over other types of fast sweeping methods is that they are explicit and do not involve the inverse operation of any nonlinear local ***,they are robust and flexible,and have been combined with high-order accurate weighted essentially non-oscillatory(WENO)schemes to solve various hyperbolic PDEs in the *** multidimensional nonlinear problems,high-order fixed-point fast sweeping WENO methods still require quite a large amount of computational *** this technical note,we apply sparse-grid techniques,an effective approximation tool for multidimensional problems,to fixed-point fast sweeping WENO methods for reducing their computational ***,we focus on fixed-point fast sweeping WENO schemes with third-order accuracy(Zhang et al.2006[41]),for solving Eikonal equations,an important class of static Hamilton-Jacobi(H-J)*** experiments on solving multidimensional Eikonal equations and a more general static H-J equation are performed to show that the sparse-grid computations of the fixed-point fast sweeping WENO schemes achieve large savings of CPU times on refined meshes,and at the same time maintain comparable accuracy and resolution with those on corresponding regular single grids.

关键词： Fixed-point fast sweeping methods Weighted essentially non-oscillatory(WENO)schemes Sparse grids Static Hamilton-Jacobi(H-J)equations Eikonal equations

Pricing Binary Variables of System-wide Constraints for Power System Optimization

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CSEE Journal of Power and Energy Systems 2024年第3期10卷 1131-1144页

作者： Jiaxun Li Wei Lin Zhifang Yang Mikhail Davidson State Key Laboratory of Power Transmission Equipment and System Security and New Technology College of Electrical EngineeringChongqing UniversityChongqing 400030China department of Electrical Engineering The Hong Kong Polytechnic UniversityHong Kong SAR 999077China Faculty of computational mathematics and cybernetics Moscow State UniversityMoscow 119991Russia IEEE

With the trend of multiple energies or flexible demand in power systems,binary variables appear in systemwide constraints,which are the foundation of marginal pricing currently in *** appropriate pricing method incentivizes compliance of market participants;otherwise,compliance can be incentivized by paying discriminatory uplift payments which jeopardize transparency of *** paper proposes two theorems to examine whether the binary variables brought by multiple energies and flexible demand will impact compliance under marginal *** first theorem shows sufficient conditions with which marginal pricing with fixed binary variables incentivizes compliance,while the second theorem shows sufficient conditions to require uplift *** improve transparency by reducing uplift payments under cases which fall into the second theorem,this paper further proposes a pricing method by combining 1)designed constraints to price binary variables in system-wide constraints,and 2)convex hull pricing to price binary variables in private *** of the proposed theorems and pricing method is verified in an electricity-gas case(consisting of the IEEE 30-bus system and the NGS 10-node system)and the IEEE 118-bus test system.

关键词： Binary variables impact analysis pricing under non-convexities

Adaptive Sparse Grid Discontinuous Galerkin Method:Review and Software Implementation

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Communications on Applied mathematics and Computation 2024年第1期6卷 501-532页

作者： Juntao Huang Wei Guo Yingda Cheng department of mathematics and Statistics Texas Tech UniversityLubbockTX79409USA department of computational mathematics Science and EngineeringMichigan State UniversityEast LansingMI48824USA department of mathematics Michigan State UniversityEast LansingMI48824USA

This paper reviews the adaptive sparse grid discontinuous Galerkin(aSG-DG)method for computing high dimensional partial differential equations(PDEs)and its software *** C++software package called AdaM-DG,implementing the aSG-DG method,is available on GitHub at https://***/JuntaoHuang/*** package is capable of treating a large class of high dimensional linear and nonlinear *** review the essential components of the algorithm and the functionality of the software,including the multiwavelets used,assembling of bilinear operators,fast matrix-vector product for data with hierarchical *** further demonstrate the performance of the package by reporting the numerical error and the CPU cost for several benchmark tests,including linear transport equations,wave equations,and Hamilton-Jacobi(HJ)equations.

关键词： Adaptive sparse grid Discontinuous Galerkin High dimensional partial differential equation Software development

An Accelerated Proximal Gradient Algorithm for Hankel Tensor Completion

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Journal of the Operations Research Society of China 2024年第2期12卷 461-477页

作者： Chuan-Long Wang Xiong-Wei Guo Xi-Hong Yan Key Laboratory of Engineering and computational Science Shanxi Provincial Department of EducationJinzhong 030619ShanxiChina department of mathematics Taiyuan Normal UniversityJinzhong 030619ShanxiChina

In this paper,an accelerated proximal gradient algorithm is proposed for Hankel tensor completion *** our method,the iterative completion tensors generated by the new algorithm keep Hankel structure based on projection on the Hankel tensor ***,due to the special properties of Hankel structure,using the fast singular value thresholding operator of the mode-s unfolding of a Hankel tensor can decrease the computational ***,the convergence of the new algorithm is discussed under some reasonable ***,the numerical experiments show the effectiveness of the proposed algorithm.

关键词： Hankel tensor Tensor completion Accelerated proximal gradient algorithm

Detecting Malicious Uniform Resource Locators Using an Applied Intelligence Framework

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Computers, Materials & Continua 2024年第6期79卷 3827-3853页

作者： Simona-Vasilica Oprea Adela Bara department of Economic Informatics and cybernetics Bucharest University of Economic StudiesBucharest010572Romania

The potential of text analytics is revealed by Machine Learning(ML)and Natural Language Processing(NLP)*** this paper,we propose an NLP framework that is applied to multiple datasets to detect malicious Uniform Resource Locators(URLs).Three categories of features,both ML and Deep Learning(DL)algorithms and a ranking schema are included in the proposed *** apply frequency and prediction-based embeddings,such as hash vectorizer,Term Frequency-Inverse Dense Frequency(TF-IDF)and predictors,word to vector-word2vec(continuous bag of words,skip-gram)from Google,to extract features from ***,we apply more state-of-the-art methods to create vectorized features,such as ***,feature engineering that is specific to URL structure is deployed to detect scams and other *** framework assessment,four ranking indicators are weighted:computational time and performance as accuracy,F1 score and type error *** the computational time,we propose a new metric-Feature Building Time(FBT)as the cutting-edge feature builders(like doc2vec or GloVe)require more *** applying the proposed assessment step,the skip-gram algorithm of word2vec surpasses other feature builders in ***,eXtreme Gradient Boost(XGB)outperforms other *** this setup,we attain an accuracy of 99.5%and an F1 score of 0.99.

关键词： Detecting malicious URL classifiers text to feature deep learning ranking algorithms feature building time

On Some Properties of Graph of Prefix Code

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Journal of Applied mathematics and Physics 2024年第4期12卷 1571-1581页

作者： Nikolai I. Krainiukov Mikhail E. Abramyan Boris F. Melnikov Faculty of computational mathematics and cybernetics Shenzhen MSU-BIT University Shenzhen China department of Algebra and Discrete mathematics Southern Federal University Rostov-on-Don Russian Federation

We investigate decomposition of codes and finite languages. A prime decomposition is a decomposition of a code or languages into a concatenation of nontrivial prime codes or languages. A code is prime if it cannot be decomposed into at least two nontrivial codes as the same for the languages. In the paper, a linear time algorithm is designed, which finds the prime decomposition. If codes or finite languages are presented as given by its minimal deterministic automaton, then from the point of view of abstract algebra and graph theory, this automaton has special properties. The study was conducted using system for computational Discrete Algebra GAP. .

关键词： Finite Languages Minimal Deterministic Automata Concatenation Codes Graph of Automaton Free Algebra

On the “Onion Husk” Algorithm for Approximate Solution of the Traveling Salesman Problem

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Journal of Applied mathematics and Physics 2024年第4期12卷 1557-1570页

作者： Mikhail E. Abramyan Nikolai I. Krainiukov Boris F. Melnikov Faculty of computational mathematics and cybernetics Shenzhen MSU-BIT University Shenzhen China department of Algebra and Discrete mathematics Southern Federal University Rostov-on-Don Russian Federation

The paper describes some implementation aspects of an algorithm for approximate solution of the traveling salesman problem based on the construction of convex closed contours on the initial set of points (“cities”) and their subsequent combination into a closed path (the so-called contour algorithm or “onion husk” algorithm). A number of heuristics related to the different stages of the algorithm are considered, and various variants of the algorithm based on these heuristics are analyzed. Sets of randomly generated points of different sizes (from 4 to 90 and from 500 to 10,000) were used to test the algorithms. The numerical results obtained are compared with the results of two well-known combinatorial optimization algorithms, namely the algorithm based on the branch and bound method and the simulated annealing algorithm. .

关键词： Branch and Bound Method Contour Algorithm “Onion Husk” Algorithm Simulated Annealing Method Traveling Salesman Problem