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THE LIMIT CYCLE BIFURCATIONS OF A WHIRLING PENDULUM WITH PIECEWISE SMOOTH PERTURBATIONS

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Acta Mathematica Scientia 2024年第3期44卷 1115-1144页

作者：杨纪华 School of mathematics and Computer Science Ningxia Normal UniversityGuyuan756000China Ningxia Basic Science research center of mathematics Yinchuan750000China

This paper deals with the problem of limit cycles for the whirling pendulum equation x=y,y=sin x(cosx-r)under piecewise smooth perturbations of polynomials of cos x,sin x and y of degree n with the switching line x=*** upper bounds of the number of limit cycles in both the oscillatory and the rotary regions are obtained using the Picard-Fuchs equations,which the generating functions of the associated first order Melnikov functions ***,the exact bound of a special case is given using the Chebyshev *** the end,some numerical simulations are given to illustrate the existence of limit cycles.

关键词： whirling pendulum limit cycle Melnikov function Picard-Fuchs equation Chebyshev system

Dynamics and synchronization of neural models with memristive membranes under energy coupling

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Chinese Physics B 2024年第5期33卷 316-322页

作者：万婧玥吴富强马军汪文帅 School of mathematics and Statistics Ningxia UniversityYinchuan 750021China Ningxia Basic Science research center of mathematics Ningxia UniversityYinchuan 750021China Department of Physics Lanzhou University of TechnologyLanzhou 730050China

Dynamical modeling of neural systems plays an important role in explaining and predicting some features of biophysical *** electrophysiological environment inside and outside of the nerve cell is *** to the continuous and periodical properties of electromagnetic fields in the cell during its operation,electronic components involving two capacitors and a memristor are effective in mimicking these physical *** this paper,a neural circuit is reconstructed by two capacitors connected by a memristor with periodical *** is found that the memristive neural circuit can present abundant firing patterns without *** Hamilton energy function is deduced using the Helmholtz ***,a neuronal network consisting of memristive neurons is proposed by introducing energy *** controllability and flexibility of parameters give the model the ability to describe the dynamics and synchronization behavior of the system.

关键词： memristor neuronal model energy synchronization

Signifying quantum uncertainty relations by optimal observable sets and the tightest uncertainty constants

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Science China(Physics,Mechanics & Astronomy) 2024年第9期Mechanics & Astronomy) .卷 47-54页

作者： Xiao-Bin Liang Bo Li Shao-Ming Fei School of mathematics and Computer Science Shangrao Normal University Quantum Information research center Shangrao Normal University School of Mathematical Sciences Capital Normal University

Quantum uncertainty relations constrain the precision of measurements across multiple non-commuting quantum mechanical observables. Here, we introduce the concept of optimal observable sets and define the tightest uncertainty constants to accurately describe these measurement uncertainties. For any quantum state, we establish optimal sets of three observables for both product and summation forms of uncertainty relations, and analytically derive the corresponding tightest uncertainty constants. We demonstrate that the optimality of these sets remains consistent regardless of the uncertainty relation form. Furthermore, the existence of the tightest constants excludes the validity of standard real quantum mechanics, underscoring the essential role of complex numbers in this field. Additionally, our findings resolve the conjecture posed in [Phys. Rev. Lett. 118, 180402(2017)],offering novel insights and potential applications in understanding preparation uncertainties.

关键词： uncertainty relation the tightest uncertainty constants optimal observable sets

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Image Splicing Forgery Detection Using Feature-Based of Sonine Functions and Deep Features

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Computers, Materials & Continua 2024年第1期78卷 795-810页

作者： Ala’a R.Al-Shamasneh Rabha W.Ibrahim Department of Computer Science College of Computer&Information SciencesPrince Sultan UniversityRiyadh11586Saudi Arabia Department of Computer Science and mathematics Lebanese American UniversityBeirut11022801Lebanon Department of mathematics Mathematics Research CenterNear East UniversityNicosia99138Turkey Information and Communication Technology research Group Scientific Research CenterAlayen UniversityDhi Qar64001Iraq

The growing prevalence of fake images on the Internet and social media makes image integrity verification a crucial research *** of the most popular methods for manipulating digital images is image splicing,which involves copying a specific area from one image and pasting it into *** were made to mitigate the effects of image splicing,which continues to be a significant research *** study proposes a new splicing detectionmodel,combining Sonine functions-derived convex-based features and deep *** stages make up the proposed *** first step entails feature extraction,then classification using the“support vector machine”(SVM)to differentiate authentic and spliced *** proposed Sonine functions-based feature extraction model reveals the spliced texture details by extracting some clues about the probability of image *** proposed model achieved an accuracy of 98.93% when tested with the CASIA V2.0 dataset“Chinese Academy of Sciences,Institute of Automation”which is a publicly available dataset for forgery *** experimental results show that,for image splicing forgery detection,the proposed Sonine functions-derived convex-based features and deep features outperform state-of-the-art techniques in terms of accuracy,precision,and ***,the obtained detection accuracy attests to the benefit of using the Sonine functions alongside deep feature *** the regions or locations where image tampering has taken place is limited by the *** research will need to look into advanced image analysis techniques that can offer a higher degree of accuracy in identifying and localizing tampering regions.

关键词： Image forgery image splicing deep learning Sonine functions

Second-order error analysis of the averaged L1 scheme L1 for time-fractional initial-value and subdiffusion problems

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Science China mathematics 2024年第7期67卷 1641-1664页

作者： Jinye Shen Fanhai Zeng Martin Stynes School of mathematics Southwestern University of Finance and EconomicsChengdu611130China School of mathematics Shandong UniversityJinan250100China Applied and Computational mathematics Division Beijing Computational Science Research CenterBeijing100193China

Fractional initial-value problems(IVPs) and time-fractional initial-boundary value problems(IBVPs), each with a Caputo temporal derivative of order α ∈(0, 1), are considered. An averaged variant of the well-known L1 scheme is proved to be O(N^(-2)) convergent for IVPs on suitably graded meshes with N points, thereby improving the O(N^(-(2-α))) convergence rate of the standard L1 scheme. The analysis relies on a delicate decomposition of the temporal truncation error that yields a sharp dependence of the order of convergence on the degree of mesh grading used. This averaged L1 scheme can be combined with a finite difference or piecewise linear finite element discretization in space for IBVPs, and under a restriction on the temporal mesh width, one gets again O(N^(-2)) convergence in time, together with O(h^(2)) convergence in space,where h is the spatial mesh width. Numerical experiments support our results.

关键词： time-fractional subdiffusion averaged L1 scheme

Transfer of Highest Weight Modules and Small Unipotent Representations

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Acta Mathematica Sinica,English Series 2024年第3期40卷 772-791页

作者： Hai An HE Jing Song HUANG Kayue Daniel WONG Department of mathematics College of SciencesShanghai UniversityShanghai 200444P.R.China Newtouch center for mathematics of Shanghai university Shanghai 200444P.R.China mathematics research center School of Science and EngineeringThe Chinese University of Hong KongShenzhen 518172P.R.China

We study the transfer between small special unipotent representations for all equal rank real forms of type E_(6) and E_(7). As a consequence, one can verify these modules are unitarity using the results of Wallach an... 详细信息

关键词： Unipotent representations Wallach representations Transfer of unitary modules

A Novel Fractional Dengue Transmission Model in the Presence of Wolbachia Using Stochastic Based Artificial Neural Network

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Computer Modeling in Engineering & Sciences 2024年第5期139卷 1217-1238页

作者： Zeshan Faiz Iftikhar Ahmed Dumitru Baleanu Shumaila Javeed Department of mathematics COMSATS University IslamabadIslamabad45550Pakistan Department of mathematics Cankaya UniversityAnkara06790Turkey Institute of Space Sciences Magurele-Bucharest077125Romania Department of Medical research China Medical University HospitalChina Medical UniversityTaichung40402Taiwan Department of Computer Science and mathematics Lebanese American UniversityBeirut135053Lebanon Department of mathematics Mathematics Research CenterNear East UniversityNicosia/Mersin99138Turkey

The purpose of this research work is to investigate the numerical solutions of the fractional dengue transmission model(FDTM)in the presence of Wolbachia using the stochastic-based Levenberg-Marquardt neural network(LM-NN)*** fractional dengue transmission model(FDTM)consists of 12 *** human population is divided into four compartments;susceptible humans(S_(h)),exposed humans(E_(h)),infectious humans(I_(h)),and recovered humans(R_(h)).Wolbachia-infected and Wolbachia-uninfected mosquito population is also divided into four compartments:aquatic(eggs,larvae,pupae),susceptible,exposed,and *** investigated three different cases of vertical transmission probability(η),namely when Wolbachia-free mosquitoes persist only(η=0.6),when both types of mosquitoes persist(η=0.8),and when Wolbachia-carrying mosquitoes persist only(η=1).The objective of this study is to investigate the effectiveness of Wolbachia in reducing dengue and presenting the numerical results by using the stochastic structure LM-NN approach with 10 hidden layers of neurons for three different cases of the fractional order derivatives(α=0.4,0.6,0.8).LM-NN approach includes a training,validation,and testing procedure to minimize the mean square error(MSE)values using the reference dataset(obtained by solving the model using the Adams-Bashforth-Moulton method(ABM).The distribution of data is 80% data for training,10% for validation,and,10% for testing purpose)results.A comprehensive investigation is accessible to observe the competence,precision,capacity,and efficiency of the suggested LM-NN approach by executing the MSE,state transitions findings,and regression *** effectiveness of the LM-NN approach for solving the FDTM is demonstrated by the overlap of the findings with trustworthy measures,which achieves a precision of up to 10^(-4).

关键词： Wolbachia dengue neural network vertical transmission mean square error Levenberg-Marquardt

Thermal analysis of the Rindler-Schwarzschild black hole via corrected entropy

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Communications in Theoretical Physics 2024年第9期76卷 97-108页

作者： Allah Ditta Xia Tiecheng Riasat Ali Ali ?vgün Department of mathematics Shanghai University and Newtouch Center for Mathematics of Shanghai University Physics Department Eastern Mediterranean University

In this study, we investigate the thermodynamic characteristics of the Rindler–Schwarzschild black hole solution. Our analysis encompasses the examination of energy emission, Gibbs free energy, and thermal fluctuations. We calculate various quantities such as the Hawking temperature, geometric mass, and heat capacity to assess the local and global thermodynamic stability. The temperature of the black hole is determined using the first law of thermodynamics,while the energy emission rate is evaluated as well. By computing the Gibbs free energy, we explore the phase transition behavior exhibited by Rindler–Schwarzschild black hole,specifically examining the swallowing tails. Moreover, we derive the corrected entropy to investigate the influence of thermal fluctuations on small and large black holes. Notably, we compare the impact of correction terms on the thermodynamic system by comparing the results obtained for large black holes and small black holes.

关键词： black holes energy emission Gibbs free energy heat capacity Rindler-Schwarzschild black hole thermal fluctuations thermodynamics

The KAM theorem on the modulus of continuity about parameters

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Science China mathematics 2024年第3期67卷 577-592页

作者： Zhicheng Tong Jiayin Du Yong Li School of mathematics Jilin UniversityChangchun 130012China Institute of mathematics Jilin UniversityChangchun 130012China School of mathematics and Statistics Center for Mathematics and Interdisciplinary SciencesNortheast Normal UniversityChangchun 130024China

In this paper,we study the Hamiltonian systems H(y,x,ξ,ε)=〈ω(ξ),y〉+εP(y,x,ξ,ε),where ω and P are continuous about ξ.We prove that persistent invariant tori possess the same frequency as the unperturbed tori,under a certain transversality condition and a weak convexity condition for the frequency mapping ω.As a direct application,we prove a Kolmogorov-Arnold-Moser(KAM) theorem when the perturbation P holds arbitrary Holder continuity with respect to the parameter ξ.The infinite-dimensional case is also *** our knowledge,this is the first approach to the systems with the only continuity in the parameter beyond H?lder's type.

关键词： Hamiltonian systems invariant tori frequency-preserving weak regularity

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