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Semi-derived Ringel-Hall algebras and Hall algebras of odd-periodic relative derived categories

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Science China mathematics 2024年第8期67卷 1735-1760页

作者： Ji Lin Liangang Peng department of mathematics and Statistics Fuyang Normal UniversityFuyang 236037China School of mathematics Sichuan UniversityChengdu 610064China

Let t be a positive integer and A be a hereditary abelian category satisfying some finiteness *** define the semi-derived Ringel-Hall algebra of A from the category C_(Z/t)(A)of Z/t-graded complexes and obtain a natural basis of the semi-derived Ringel-Hall ***,we describe the semiderived Ringel-Hall algebra by the generators and defining *** particular,if t is an odd integer,we show an embedding of the derived Hall algebra of the odd-periodic relative derived category in the extended semi-derived Ringel-Hall algebra.

关键词： hereditary abelian categories the categories of Z/t-graded complexes semi-derived Ringel-Hall algebras derived Hall algebras

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A REFINEMENT OF THE SCHWARZ-PICK ESTIMATES AND THE CARATHéODORY METRIC IN SEVERAL COMPLEX VARIABLES

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Acta Mathematica Scientia 2024年第4期44卷 1337-1346页

作者： Xiaosong LIU Taishun LIU School of mathematics and Statistics Lingnan Normal UniversityZhanjiang 524048China department of mathematics Huzhou UniversityHuzhou 313000China

In this article,we first establish an asymptotically sharp result on the higher order Fréchet derivatives for bounded holomorphic mappings f(x)=f(0)+∞∑s=1Dskf(0)(x^(sk))/(sk)!:B_(X)→B_(Y),where B_X is the unit ball of *** next give a sharp result on the first order Fréchet derivative for bounded holomorphic mappings F(X)=F(0+)∞∑s=KD^(s)f(0)(x^(8)/s!):B_(X)→B_(Y),where B_(X)is the unit ball of *** results that we derive include some results in several complex variables,and extend the classical result in one complex variable to several complex variables.

关键词： refined Schwarz-Pick estimate bounded holomorphic mapping Carathéodory metric first order Fréchet derivative higher order Fréchet derivatives

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

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

THE ASYMPTOTIC BEHAVIOR AND OSCILLATION FOR A CLASS OF THIRD-ORDER NONLINEAR DELAY DYNAMIC EQUATIONS

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Acta Mathematica Scientia 2024年第3期44卷 925-946页

作者：黄先勇邓勋环王其如 department of mathematics Guangdong University of EducationGuangzhou510303China department of mathematics College of Medical Information EngineeringGuangdong Pharmaceutical UniversityGuangzhou510006China School of mathematics Sun Yat-sen UniversityGuangzhou510275China

In this paper,we consider a class of third-order nonlinear delay dynamic ***,we establish a Kiguradze-type lemma and some useful ***,we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to ***,we obtain new oscillation criteria by employing the Potzsche chain ***,using the generalized Riccati transformation technique and averaging method,we establish the Philos-type oscillation ***,the integral value of the Philos-type oscillation criteria,which guarantees that all unbounded solutions oscillate,is greater than θ_(4)(t_(1),T).The results of Theorem 3.5 and Remark 3.6 are ***,we offer four examples to illustrate our results.

关键词： nonlinear delay dynamic equations nonoscillation asymptotic behavior Philostype oscillation criteria generalized Riccati transformation

A REDUCED ORDER SCHWARZ METHOD FOR NONLINEAR MULTISCALE ELLIPTIC EQUATIONS BASED ON TWO-LAYER NEURAL NETWORKS

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Journal of Computational mathematics 2024年第2期42卷 570-596页

作者： Shi Chen Zhiyan Ding Qin Li Stephen J.Wright mathematics department University of Wisconsin-MadisonMadisonWI 53706USA department of mathematics University of California-BerkeleyBerkeley CA 94720USA mathematics department and Discovery Institute University of Wisconsin-Madison MadisonWI 53706USA Computer Sciences department University of WisconsinMadisonWI 53706USA

Neural networks are powerful tools for approximating high dimensional data that have been used in many contexts,including solution of partial differential equations(PDEs).We describe a solver for multiscale fully nonlinear elliptic equations that makes use of domain decomposition,an accelerated Schwarz framework,and two-layer neural networks to approximate the boundary-to-boundarymap for the subdomains,which is the key step in the Schwarz ***,the boundary-to-boundary map requires solution of boundary-value elliptic problems on each *** leveraging the compressibility of multiscale problems,our approach trains the neural network offline to serve as a surrogate for the usual implementation of the boundary-to-boundary *** method is applied to a multiscale semilinear elliptic equation and a multiscale p-Laplace *** both cases we demonstrate significant improvement in efficiency as well as good accuracy and generalization performance.

关键词： Nonlinear homogenization Multiscale elliptic problem Neural networks Do-main decomposition

Nuclearity and Finite-Representability in the System of Completely Integral Mapping Spaces

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Acta Mathematica Sinica,English Series 2024年第5期40卷 1197-1214页

作者： Zhe DONG Ji Cheng TAO Ya Fei ZHAO department of mathematics Zhejiang UniversityHangzhou 310027P.R.China department of mathematics China Jiliang UniversityHangzhou 310018P.R.China department of mathematics Zhejiang International Studies UniversityHangzhou 310023P.R.China

In this paper,we investigate local properties in the system of completely integral mapping *** introduce notions of injectivity,local reflexivity,exactness,nuclearity,finite-represent ability and WEP in the system of completely integral mapping *** we obtain that any finite-dimensional operator space is injective in the system of completely integral mapping *** we prove that C is the unique nuclear operator space and the unique exact operator space in this *** also show that C is the unique operator space which is finitely representable in{T_(n)}n∈Nin this *** corollaries,Kirchberg’s conjecture and QWEP conjecture in the system of completely integral mapping spaces are false.

关键词： Completely integral mapping space injectivity exactness nuclearity finite-representability WEP

Composite Fractional Trapezoidal Rule with Romberg Integration

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Computer Modeling in Engineering & Sciences 2024年第9期140卷 2729-2745页

作者： Iqbal M.Batiha Rania Saadeh Iqbal H.Jebril Ahmad Qazza Abeer A.Al-Nana Shaher Momani department of mathematics Al Zaytoonah University of JordanAmman11733Jordan Nonlinear Dynamics Research Center(NDRC) Ajman UniversityAjman 346United Arab Emirates department of mathematics Faculty of ScienceZarqa UniversityZarqa13110Jordan department of mathematics Prince Sattam Bin Abdulaziz UniversityAlkharj11942Saudi Arabia department of mathematics The University of JordanAmman11942Jordan

The aim of this research is to demonstrate a novel scheme for approximating the Riemann-Liouville fractional integral *** would be achieved by first establishing a fractional-order version of the 2-point Trapezoidal rule and then by proposing another fractional-order version of the(n+1)-composite Trapezoidal *** particular,the so-called divided-difference formula is typically employed to derive the 2-point Trapezoidal rule,which has accordingly been used to derive a more accurate fractional-order formula called the(n+1)-composite Trapezoidal ***,in order to increase the accuracy of the proposed approximations by reducing the true errors,we incorporate the so-called Romberg integration,which is an extrapolation formula of the Trapezoidal rule for integration,into our proposed *** numerical examples are provided and compared with a modern definition of the Riemann-Liouville fractional integral operator to illustrate the efficacy of our scheme.

关键词： Composite fractional Trapezoidal rule Romberg integration

Feedback Mechanism-driven Mutation Reptile Search Algorithm for Optimizing Interpolation Developable Surfaces

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Journal of Bionic Engineering 2024年第1期21卷 527-571页

作者： Gang Hu Jiao Wang Xiaoni Zhu Muhammad Abbas department of Applied mathematics Xi'an University of TechnologyXi'an 710054China School of Mechanical and Precision Instrument Engineering Xi'an University of TechnologyXi'an 710048China department of mathematics University of SargodhaSargodha 40100Pakistan

Curvature lines are special and important curves on *** is of great significance to construct developable surface interpolated on curvature lines in engineering *** this paper,the shape optimization of generalized cubic ball developable surface interpolated on the curvature line is studied by using the improved reptile search ***,based on the curvature line of generalized cubic ball curve with shape adjustable,this paper gives the construction method of SGC-Ball developable surface interpolated on the ***,the feedback mechanism,adaptive parameters and mutation strategy are introduced into the reptile search algorithm,and the Feedback mechanism-driven improved reptile search algorithm effectively improves the solving *** IEEE congress on evolutionary computation 2014,2017,2019 and four engineering design problems,the feedback mechanism-driven improved reptile search algorithm is compared with other representative methods,and the result indicates that the solution performance of the feedback mechanism-driven improved reptile search algorithm is *** last,taking the minimum energy as the evaluation index,the shape optimization model of SGC-Ball interpolation developable surface is *** developable surface with the minimum energy is achieved with the help of the feedback mechanism-driven improved reptile search algorithm,and the comparison experiment verifies the superiority of the feedback mechanism-driven improved reptile search algorithm for the shape optimization problem.

关键词： Reptile search algorithm Feedback mechanism Adaptive parameter Mutation strategy SGC-Ball interpolation developable surface Shape optimization