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Science China mathematics 2024年第9期67卷 2171-2194页

作者： Chuanjun Chen Xiaofeng Yang School of mathematics and information sciences Yantai UniversityYantai 264005China department of mathematics University of South CarolinaColumbiaSC 29208USA

In this paper,an efficient fully-decoupled and fully-discrete numerical scheme with second-order temporal accuracy is developed to solve the incompressible hydrodynamically coupled Cahn-Hilliard model for simulating the two-phase fluid flow *** scheme is developed by combining the finite element method for spatial discretization and several effective time marching approaches,including the pressure-correction projection method for dealing with fluid equations and the explicit-invariant energy quadratization(explicit-IEQ)approach for dealing with coupled nonlinear *** obtained scheme is very efficient since it only needs to solve several decoupled,linear elliptic equations with constant coefficients at each time *** also strictly prove the solvability and unconditional energy stability of the scheme,and verify the accuracy and stability of the scheme through plenty of numerical examples.

关键词： finite element method decoupled scheme two-phase fow Cahn-Hilliard equation Navier-Stokes equations energystability

Density peak clustering using tensor network

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Science China(information sciences) 2024年第3期67卷 321-322页

作者： Xiao SHI Yun SHANG Institute of mathematics Academy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical sciences University of Chinese Academy of Sciences National Center for mathematics and Interdisciplinary sciences Key Laboratory of ManagementDecision and Information SystemsAcademy of Mathematics and Systems ScienceChinese Academy of Sciences

Tensor networks have been a powerful tool in simulating many-body physics and have recently gained recognition in the machine learning community due to their remarkable representation capabilities. However, using tens... 详细信息

关键词： Tensors

UNIFORM SUPERCONVERGENCE ANALYSIS OF A TWO-GRID MIXED FINITE ELEMENT METHOD FOR THE TIME-DEPENDENT BI-WAVE PROBLEM MODELING D-WAVE SUPERCONDUCTORS

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Journal of Computational mathematics 2024年第2期42卷 415-431页

作者： Yanmi Wu Dongyang Shi PLA information Engineering University Zhengzhou 450001China School of mathematics and information sciences Yantai UniversityYantai 264005China

In this paper,a two-grid mixed finite element method(MFEM)of implicit Backward Euler(BE)formula is presented for the fourth order time-dependent singularly perturbed Bi-wave problem for d-wave superconductors by the nonconforming EQ_(1)^(rot) *** this approach,the original nonlinear system is solved on the coarse mesh through the Newton iteration method,and then the linear system is computed on the fine mesh with Taylor’s *** on the high accuracy results of the chosen element,the uniform superclose and superconvergent estimates in the broken H^(1)-norm are derived,which are independent of the negative powers of the perturbation parameter appeared in the considered *** results illustrate that the computing cost of the proposed two-grid method is much less than that of the conventional Galerkin MFEM without loss of accuracy.

关键词： Time-dependent Bi-wave problem Two-grid mixed finite element method Uniform superclose and superconvergent estimates

Non-thermal atmospheric-pressure positive pulsating corona discharge in degradation of textile dye Reactive Blue 19 enhanced by Bi_(2)O_(3) catalyst

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Plasma Science and Technology 2024年第2期26卷 104-113页

作者： Milica PETROVIC Dragan RADIVOJEVIC Sasa RANCEV Nena VELINOV Milos KOSTIC Danijela BOJIC Aleksandar BOJIC department of Chemistry Faculty of Sciences and MathematicsUniversity of NisNis 18000Serbia department of Physics Faculty of Sciences and MathematicsUniversity of NisNis 18000Serbia

In this work,monoclinic Bi_(2)O_(3) was applied for the first time,to the best of our knowledge,as a catalyst in the process of dye degradation by a non-thermal atmospheric-pressure positive pulsating corona *** research focused on the interaction of the plasma-generated species and the catalyst,as well as the role of the catalyst in the degradation *** decomposition of the anthraquinone reactive dye Reactive Blue 19(RB 19) was performed in a selfmade reactor ***_(2)O_(3) was prepared by electrodeposition followed by thermal treatment,and characterized by x-ray diffraction,scanning electron microscopy and energy-dispersive xray *** was observed that the catalyst promoted decomposition of plasma-generated H_(2)O_(2) into ·OH radicals,the principal dye-degrading reagent,which further attacked the dye *** catalyst improved the decolorization rate by 2.5 times,the energy yield by 93.4%and total organic carbon removal by 7.1%.Excitation of the catalyst mostly occurred through strikes by plasma-generated reactive ions and radical species from the air,accelerated by the electric field,as well as by fast electrons with an energy of up to 15 eV generated by the streamers reaching the liquid *** strikes transferred the energy to the catalyst and created the electrons and holes,which further reacted with H_(2)O_(2) and water,producing ·OH *** was indentified as the primary role of the catalyst in this *** reactions followed pseudo first-order *** of H_(2)O_(2) and the dye degradation rate increased with increase in the input *** optimal catalyst dose was 500 mg·dm^(-3).The decolorization rate was a little lower in river water compared with that in deionized water due to the side reactions of ·OH radicals with organic matter and inorganic ions dissolved in the river water.

关键词： corona RB 19 Bi_(2)O_(3) catalyst degradation

Global Spherically Symmetric Solutions for a Coupled Compressible Navier–Stokes/Allen–Cahn System

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Acta Mathematica Sinica,English Series 2024年第8期40卷 2037-2064页

作者： Chang Ming SONG Jian Lin ZHANG Yuan Yuan WANG department of Applied mathematics School of Mathematics and Information ScienceZhongyuan University of TechnologyZhengzhou 450007P.R.China

In this paper,we consider the global spherically symmetric solutions for the initial boundary value problem of a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of two-phase viscous compressible *** prove the existence and uniqueness of global classical solution,weak solution and strong solution under the assumption of spherically symmetry condition for initial dataρ0 without vacuum state.

关键词： Diffuse interface model global solutions Navier-Stokes equations Allen-Cahn equation spherically symmetry

A Hybrid SIR-Fuzzy Model for Epidemic Dynamics:A Numerical Study

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Computer Modeling in Engineering & sciences 2024年第6期139卷 3417-3434页

作者： Muhammad Shoaib Arif Kamaleldin Abodayeh Yasir Nawaz department of mathematics and sciences College of Humanities and SciencesPrince Sultan UniversityRiyadh11586Saudi Arabia department of mathematics Air UniversityIslamabad44000Pakistan

This study focuses on the urgent requirement for improved accuracy in diseasemodeling by introducing a newcomputational framework called the Hybrid SIR-Fuzzy *** integrating the traditional Susceptible-Infectious-Recovered(SIR)modelwith fuzzy logic,ourmethod effectively addresses the complex nature of epidemic dynamics by accurately accounting for uncertainties and imprecisions in both data and model *** main aim of this research is to provide a model for disease transmission using fuzzy theory,which can successfully address uncertainty in mathematical *** main emphasis is on the imprecise transmission rate parameter,utilizing a three-part description of its membership *** enhances the representation of disease processes with greater complexity and tackles the difficulties related to quantifying uncertainty in mathematical *** investigate equilibrium points for three separate scenarios and perform a comprehensive sensitivity analysis,providing insight into the complex correlation betweenmodel parameters and epidemic *** order to facilitate a quantitative analysis of the fuzzy model,we propose the implementation of a resilient numerical *** convergence study of the scheme demonstrates its trustworthiness,providing a conditionally positive solution,which represents a significant improvement compared to current forward Euler *** numerical findings demonstrate themodel’s effectiveness in accurately representing the dynamics of disease ***,when the mortality coefficient rises,both the susceptible and infected populations decrease,highlighting the model’s sensitivity to important epidemiological ***,there is a direct relationship between higher Holling type rate values and a decrease in the number of individuals who are infected,as well as an increase in the number of susceptible *** correlation offers a significant understanding of how many elements affect the con

关键词： Fuzzy-based model sensitivity equilibriumpoints proposed numerical scheme convergence and stability analysis

Noncommutative analysis of Hermite expansions

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Science China mathematics 2024年第10期67卷 2331-2356页

作者： Bang Xu department of mathematics University of Houston department of Mathematical sciences Seoul National University

This paper is devoted to the study of semi-commutative harmonic analysis associated with Hermite semigroups. In the first part, we establish the noncommutative maximal inequalities for Bochner-Riesz means associated with Hermite operators and then obtain the corresponding pointwise convergence theorems. In particular, we develop a noncommutative version of Stein's theorem of Bochner-Riesz means for Hermite operators. In the second part, we investigate two noncommutative multiplier theorems. Our approach in this part relies on a noncommutative analog of the classical Littlewood-Paley-Stein theory associated with Hermite semigroups.

关键词： noncommutative $L_{p}$-spaces Hermite semigroup maximal inequalities pointwise convergence multipliers

Compound Product of Hypermatrices

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Journal of Systems Science & Complexity 2024年第1期37卷 169-183页

作者： CHENG Daizhan MENG Min ZHANG Xiao JI Zhengping Key Laboratory of Systems and Control Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China department of Control Science and Engineering School of Electronics and Information EngineeringTongji UniversityShanghai 201210China National Center for mathematics and Interdisciplinary sciences Chinese Academy of SciencesBeijing 100190China School of Mathematical sciences University of Chinese Academy of SciencesBeijing 100149China.

The semi-tensor product(STP)of matrices is generalized to multidimensional arrays,called the compound product of *** product is first defined for three-dimensional hypermatrices with compatible orders and then extended to general *** different types of hyperdeterminants are introduced and certain properties are *** Lie groups and Lie algebras corresponding to the hypermatrix products are ***,these results are applied to dynamical systems.

关键词： Compound semi-tensor product hyperdeterminants hypereigenvalues and hypereigenvectors hypergeneral linear groups hypermatrices.

Optimal regularity of positive solutions of the Hénon-Hardy equation and related equations

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Science China mathematics 2024年第10期67卷 2283-2302页

作者： Zongming Guo Fangshu Wan College of mathematics and information Science Henan Normal University School of Mathematical sciences University of Science and Technology of China School of Mathematical sciences Anhui University

We present a new method to determine the optimal regularity of positive solutions u∈C4（Ω{0}）∩C0■ of the Hénon-Hardy equation,i.e.,■ where Ω■RN（N≥4） is a bounded smooth domain with 0∈Ω,α>-4,and p∈*** is clear that 0 is an isolated singular point of solutions of（0.1） and the optimal regularity of u in Ω relies on the parameter α.It is also important to see that the regularity of u at x=0 determines the regularity of u in Ω.We first establish asymptotic expansions up to arbitrary orders at x=0 of prescribed positive solutions u ∈C4（Ω{0}） ∩ C0（Ω）of（0.1）.Then we show that the regularity at x=0 of each positive solution u of（0.1） can be determined by some terms in asymptotic expansions of the related positive radial solution of the equation（0.1） with Ω=B,where B is the unit ball of *** main idea works for more general equations with singular weights.

关键词： Hénon-Hardy equation positive solutions optimal regularity singular point asymptotic expansions

Mixed convectional and chemical reactive flow of nanofluid with slanted MHD on moving permeable stretching/shrinking sheet through nonlinear radiation,energy omission

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Chinese Physics B 2024年第5期33卷 193-202页

作者： Saleem Nasir Sekson Sirisubtawee Pongpol Juntharee Taza Gul department of mathematics Faculty of Applied ScienceKing Mongkut's University of Technology North BangkokBangkok 10800Thailand department of mathematics City University of Science and Information TechnologyPeshawarPakistan

Hybrid nanofluids are remarkable functioning liquids that are intended to reduce the energy loss while maximizing the heat *** the involvement of suction and nonlinear thermal radiation effects,this study attempted to explore the energy transmission features of the inclined magnetohydrodynamic(MHD)stagnation flow of CNTs-hybrid nanofluid across the nonlinear permeable stretching or shrinking *** work also included some noteworthy features like chemical reactions,variable molecular diffusivity,quadratic convection,viscous dissipation,velocity slip and heat omission *** appropriate similarity components,the model equations were modified to ODEs and computed by using the HAM *** impact of various relevant flow characteristics on movement,heat and concentration profiles was investigated and plotted on a *** various model factors,the significance of drag friction,heat and mass transfer rate were also computed in tabular and graphical *** leads to the conclusion that such factors have a considerable impact on the dynamics of fluid as well as other engineering measurements of ***,viscous forces are dominated by increasing the values ofλ_(p),δ_(m)andδ_(q),and as a result,F(ξ)accelerates while the opposite trend is observed for M andφ.The drag friction is boosted by the augmentation M,λ_(p)andφ,but the rate of heat transfer *** to our findings,hybrid nanoliquid effects dominate that of ordinary nanofluid in terms of F(ξ),Θ(ξ)andφ(ξ)*** HAM and the numerical technique(shooting method)were found to be in good agreement.

关键词： hybrid nanofluid(SWCNT+MWCNT/H_(2)O) velocity slip conditions nonlinear thermal radiation exponential stretching/shrinking sheet inclined magnetohydrodynamic(MHD)stagnation flow