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STABILITY AND CONVERGENCE OF STEPSIZE-DEPENDENT LINEAR MULTISTEP METHODS FOR NONLINEAR DISSIPATIVE EVOLUTION EQUATIONS IN BANACH SPACE

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Journal of Computational mathematics 2024年第2期42卷 337-354页

作者： Wansheng Wang department of {1. Shanghai Normal UniversityShanghai 200234China

Stability and global error bounds are studied for a class of stepsize-dependent linear multistep methods for nonlinear evolution equations governed by ω-dissipative vector fields in Banach *** break through the order barrier p≤1.of unconditionally contractive linear multistep methods for dissipative systems,strongly dissipative systems are *** employing the error growth function of the methods,new contractivity and convergence results of stepsize-dependent linear multistep methods on infinite integration intervals are provided for strictly dissipative systems(ω<0)and strongly dissipative *** applications of the main results to several linear multistep methods,including the trapezoidal rule,are *** theoretical results are also illustrated by a set of numerical experiments.

关键词： Nonlinear evolution equation Linear multistep methods ω-dissipative operators Stability Convergence Banach space

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 {1. Guangdong University of EducationGuangzhou510303China department of {1. 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

QUASIPERIODICITY OF TRANSCENDENTAL MEROMORPHIC FUNCTIONS

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Acta Mathematica Scientia 2024年第1期44卷 161-172页

作者：刘新玲刘凯 Risto KORHONEN Galina FILIPUK department of {1. Nanchang UniversityNanchang330031China department of Physics and {1. University of Eastern FinlandP.O.Box 11180101JoensuuFinland Institute of mathematics Faculty of MathematicsInformatics and MechanicsUniversity of WarsawBanacha 202-097WarsawPoland

This paper is devoted to considering the quasiperiodicity of complex differential polynomials,complex difference polynomials and complex delay-differential polynomials of certain types,and to studying the similarities... 详细信息

关键词： quasiperiodicity meromorphic functions complex delay-differential polynomials Nevanlinna theory

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 {1. 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=1.skf(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

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 {1. University of Wisconsin-MadisonMadisonWI 53706USA department of {1. University of California-BerkeleyBerkeley CA 94720USA mathematics {1. 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

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 {1. Al Zaytoonah University of JordanAmman11733Jordan Nonlinear Dynamics Research Center(NDRC) Ajman UniversityAjman 346United Arab Emirates department of {1. Faculty of ScienceZarqa UniversityZarqa13110Jordan department of {1. Prince Sattam Bin Abdulaziz UniversityAlkharj11942Saudi Arabia department of {1. 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

Toeplitz Operators and Carleson Measures for Weighted Bergman Spaces Induced by Regular Weights

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Acta Mathematica Sinica,English Series 2024年第5期40卷 1345-1359页

作者： Jun Tao DU Song Xiao Hasi WULAN department of {1. Guangdong University of Petrochemical TechnologyMaoming 525000P.R.China department of {1. Shantou UniversityShantou 515063P.R.China

In this paper,we give a universal description of the boundedness and compactness of Toeplitz operator T_(μ)^(ω)between Bergman spaces A_(η)^(p)and A_(υ)^(q)whenμis a positive Borel measure,1.p,q<∞andω,η,υare regular *** using Khinchin’s inequality and Kahane’s inequality,we get a new characterization of the Carleson measure for Bergman spaces induced by regular weights.

关键词： Bergman space Carleson measure Toeplitz operator regular weight

Modeling Long- and Short-Term Service Recommendations with a Deep Multi-Interest Network for Edge Computing

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Tsinghua Science and Technology 2024年第1期29卷 86-98页

作者： Rui Yuan Shunmei Meng Ruihan Dou Xinna Wang department of Computer Science and Engineering Nanjing University of Science and TechnologyNanjing 210056China Faculty of mathematics University of WaterlooWaterloo N2L 3G1Canada

Edge computing platforms enable application developers and content providers to provide context-aware services(such as service recommendations)using real-time wireless access network *** to recommend the most suitable candidate from these numerous available services is an urgent ***-through rate(CTR)prediction is a core task of traditional service ***,many existing service recommender systems do not exploit user mobility for prediction,particularly in an edge computing *** this paper,we propose a model named long and short-term user preferences modeling with a multi-interest network based on user *** uses a logarithmic network to capture multiple interests in different fields,enriching the representations of user short-term *** terms of long-term preferences,users'comprehensive preferences are extracted in different periods and are fused using a nonlocal *** experiments on three datasets demonstrate that our model relying on user mobility can substantially improve the accuracy of service recommendation in edge computing compared with the state-of-the-art models.

关键词： recommender system logarithmic network nonlocal network

Enhanced entropy generation and heat transfer characteristics of magnetic nano-encapsulated phase change materials in latent heat thermal energy storage systems

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Applied mathematics and Mechanics(English Edition) 2024年第6期45卷 1051-1070页

作者： P.S.REDDY P.SREEDEVI department of {1. Rajeev Gandhi Memorial College of Engineering and TechnologyNandyal 518501India

The objective of the current study is to investigate the importance of entropy generation and thermal radiation on the patterns of velocity,isentropic lines,and temperature contours within a thermal energy storage device filled with magnetic nanoencapsulated phase change materials(NEPCMs).The versatile finite element method(FEM)is implemented to numerically solve the governing *** effects of various parameters,including the viscosity parameter,ranging from 1.to 3,the thermal conductivity parameter,ranging from 1.to 3,the Rayleigh parameter,ranging from 1.2 to 3×1.^(2),the radiation number,ranging from 0.1.to 0.5,the fusion temperature,ranging from 1.0 to 1.2,the volume fraction of NEPCMs,ranging from 2%to 6%,the Stefan number,ranging from 1.to 5,the magnetic number,ranging from 0.1.to 0.5,and the irreversibility parameter,ranging from 0.1.to 0.5,are examined in detail on the temperature contours,isentropic lines,heat capacity ratio,and velocity ***,the heat transfer rates at both the cold and hot walls are analyzed,and the findings are presented *** results indicate that the time taken by the NEPCMs to transition from solid to liquid is prolonged inside the chamber region as the fusion temperatureθf ***,the contours of the heat capacity ratio Cr decrease with the increase in the Stefan number Ste.

关键词： volume fraction of nano-encapsulated phase change material(NEPCM) radiation Stefan number heat capacity ratio entropy generation