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Communications in Theoretical Physics 2025年第1期77卷 11-22页

作者： Yusry O El-Dib Department of mathematics Faculty of EducationAin Shams UniversityRoxyCairoEgypt

The damped Helmholtz-Duffing oscillator is a topic of great interest in many different fields of study due to its complex *** transitioning from conventional continuous differential equations to their fractal counterparts,one gains insights into the system's response under new mathematical *** paper presents a novel method for converting standard continuous differential equations into their fractal *** conversion occurs after the nonlinear system is transformed into its linear *** analyses show that there are several resonance sites in the fractal system,which differ from the one resonance point found in the continuous *** important finding is that the fractal system loses some of its stabilizing power when decaying behavior is transformed into a diffuse ***,a decrease in the fractal order in resonance settings shows a stabilizing impact,highlighting the dynamics'complexity inside fractal *** endeavor to convert to fractals is a revolutionary technique that is being employed for the first time.

关键词： nonlinear oscillations Helmholtz-Duffing oscillator forced with delay effect non-perturbative methodology stability outlines new perspectives on transferal to fractal space modeling

On Sawada-Kotera and Kaup-Kuperschmidt integrable systems

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Communications in Theoretical Physics 2025年第2期77卷 21-29页

作者： Metin Gürses Aslı Pekcan Department of mathematics Faculty of Science Bilkent University06800 AnkaraTurkey Department of mathematics Faculty of Science Hacettepe University06800 AnkaraTurkey

To obtain new integrable nonlinear differential equations there are some well-known methods such as Lax equations with different Lax *** are also some other methods that are based on integrable scalar nonlinear partial differential *** show that some systems of integrable equations published recently are the M_(2)-extension of integrable such scalar *** illustration,we give Korteweg-de Vries,Kaup-Kupershmidt,and SawadaKotera equations as *** the use of such an extension of integrable scalar equations,we obtain some new integrable systems with recursion *** also give the soliton solutions of the systems and integrable standard nonlocal and shifted nonlocal reductions of these systems.

关键词： M_(2)-extension recursion operator nonlocal reductions Hirota bilinear form soliton solutions

Large Deviations for a Critical Galton-Watson Branching Process

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Acta Mathematicae Applicatae Sinica 2025年第2期41卷 456-478页

作者： Dou-dou LI Wan-lin SHI Mei ZHANG College of Statistics and Data science Faculty of Science Beijing University of Technology Department of mathematics and Physics North China Electric Power University Laboratory of mathematics and Complex Systems(Ministry of education) School of Mathematical SciencesBeijing Normal University

In this paper, a critical Galton-Watson branching process {Z_n} is considered. Large deviation rates of ■ are obtained, where {Xi, i ≥ 1} is a sequence of independent and identically distributed random variables and X1is in the domain of attraction of an α-stable law with α ∈（0, 2）. One shall see that the convergence rate is determined by the tail index of X1and the variance of Z1. Our results can be compared with those ones of the supercritical case.

关键词： 60F10 60J80 branching process critical large deviation α-stable

Transport mechanism in chemically reactive hybrid nanofluid flow containing gyrotactic micro-organisms over a curved oscillatory surface

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Applied mathematics and Mechanics(English Edition) 2025年第1期46卷 177-192页

作者： M.NAVEED M.IMRAN T.ASGHAR Z.ABBAS Department of mathematics Division of Science and TechnologyUniversity of EducationLahore 54770Pakistan Department of mathematics The Islamia University of BahawalpurBahawalpur 63100Pakistan

This paper examines the transport analysis,including both heat transfer and mass transfer,in hybrid nanofluid flow containing gyrotactic microorganisms towards a curved oscillatory *** influence of magnetic fields is also inspected in terms of their physical *** depict the phenomena of transport,modified versions of both Fick's and Fourier's laws are ***,the characteristics of both heterogeneous and homogeneous chemical reactions are also *** a curvilinear coordinate system,the flow problem is formulated as partial differential equations(PDEs)for momentum,concentration,microorganism field,and *** analytical solution to the obtained flow equations is achieved utilizing the homotopy analysis method(HAM).The effects of significant flow parameters on the pressure and microorganism fields,velocity,oscillation velocity,concentration,and temperature distributions are shown via ***,the variations in skin friction,mass transfer rate,heat transfer rate,and local motile number due to different involved parameters are presented in tables and are analyzed in *** results indicate that the curves of velocity and temperature fields are enhanced as the values of the solid volume fraction variables *** is also verified that the concentration rate field decreases as the values of the homogeneous reaction strength parameter and the radius of curvature parameter increase,and it increases with the Schmidt number and the heterogeneous reaction strength *** outcomes show a favorable response of the motile number to advanced values of the Peclet number,the Schmidt number,the microorganism difference parameter,and the bio-convective Lewis number.

关键词： hybrid nanofuid oscillating curved stretchable sheet gyrotactic microorganism Cattaneo-Christov heat and mass flux chemical reaction analytical solution

A thermoelastic model with two relaxations for the vibration of a microbeam resting on elastic foundations

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Applied mathematics and Mechanics(English Edition) 2025年第4期46卷 711-722页

作者： Z.S.HAFED A.M.ZENKOUR Department of mathematics Faculty of ScienceKing Khalid UniversityAbha21589Saudi Arabia Department of mathematics Faculty of ScienceKing Abdulaziz UniversityJeddah21589Saudi Arabia Department of mathematics Faculty of ScienceKafrelsheikh UniversityKafrelsheikh33516Egypt

The Euler-Bernoulli(E-B)beam theory is combined with Green-Lindsay's(G-L)generalized thermoelasticity theory to analyze the vibration of *** frequency control equation,based on the two-parameter Winkler-Pasternak elastic foundation for simply-supported microbeams,is *** study investigates the effects of the side-to-thickness ratio and relaxation time parameters on the vibrational natural frequency of thermoelastic microbeam *** frequencies derived from the present model are compared with those from Lord and Shulman's(L-S)*** fourthorder solutions for natural vibration frequencies are graphically displayed for ***,attention should be paid to the use of effective foundations to prevent microbeam damage caused by contraction and expansion problems caused by high temperatures.

关键词： Green-Lindsay's(G-L)model thermoelastic vibration Euler-Bernoulli(E-B)theory elastic foundation

Stabilities of delay stochastic McKean-Vlasov equations in the G-framework

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science China(Information sciences) 2025年第1期68卷 255-277页

作者： Haiyan YUAN Quanxin ZHU Department of mathematics Heilongjiang Institute of Technology Key Laboratory of Computing and Stochastic mathematics (Ministry of education) School of Mathematics and Statistics Hunan Normal University

This article focuses on a type of stochastic Mc Kean-Vlasov equation in the G-framework(G-SMVE) and addresses the stability issue for delay stochastic Mc Kean-Vlasov equations in the G-framework(G-SMVDEs). Distribution dependence and uncertainty prevent us from directly applying the stochastic analysis method for stochastic Mc Kean-Vlasov equations(SMVEs)to G-SMVEs directly. To overcome this difficulty, we introduce definitions, including the derivative of a function with a law under the G-expectation and the Lions derivatives. Then we construct a new G-It? formula for G-SMVEs according to the G-It? formula for stochastic differential equations in the G-framework(G-SDEs) and the It? formula for SMVEs. Using the new G-It? formula and the Lyapunov functional method, we investigate the moment exponential stability and almost sure asymptotic stability of G-SMVDEs. To overcome the difficulty in obtaining the distribution dependence of the exact solution to the G-SMVDE, we introduce the empirical measure and the corresponding interacting particle system, and then prove the stability equivalence between the underlying G-SMVDE and the corresponding interacting particle system. Two examples are used to confirm our theoretical results.

关键词： delay stochastic McKean-Vlasov equations Wasserstein distance G-Brownian motion Lions derivative stability

Unsupervised multiplex graph diffusion networks with multi-level canonical correlation analysis for multiplex graph representation learning

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science China(Information sciences) 2025年第3期68卷 66-79页

作者： Sichao FU Qinmu PENG Yange HE Baokun DU Bin ZOU Xiao-Yuan JING Xinge YOU School of Electronic Information and Communications Huazhong University of Science and Technology Platform Operation and Marketing Center JD Retail faculty of mathematics and Statistics Hubei Key Laboratory of Applied Mathematics Hubei University School of Computer science Wuhan University

In recent years, unsupervised multiplex graph representation learning(UMGRL) has received increasing research interest, which aims to learn discriminative node features from the multiplex graphs supervised by data without the guidance of labels. Although these designed UMGRL methods have obtained great success in various graph-related tasks, most existing UMGRL models still have the following issues: highly depending on complex self-supervised strategies(i.e., data augmentation,pretext tasks, and negative pairs sampling), restricted receptive fields, and only aggregating low-frequency information between nodes. In this paper, we propose a simple unsupervised multiplex graph diffusion network(UMGDN) with the aid of multi-level canonical correlation analysis to solve the above issues. Specifically, we first decouple the feature transform and propagation processes of the graph convolution layer to further improve the generalization of the learnable parameters. And then, we propose adaptive diffusion propagation to capture long-range dependency relationships between nodes, not the local neighborhood interactions. Finally, a multi-level canonical correlation analysis loss on both the feature transform and propagation processes is proposed to maximize the correlation of the same node features from multiple graphs for guiding model optimization. Compared to the existing UMGRL models, our proposed UMGDN does not need to introduce any data augmentation, negative pairs sampling techniques, complex pretext tasks, and also adaptively aggregates the optimal frequency information between nodes to generate more robust node embeddings. Extensive experiments on four popular datasets and two graph-related tasks demonstrate the effectiveness of the proposed method.

关键词： unsupervised multiplex graph representation learning graph neural networks node classification node clustering

Neural network analysis for prediction of heat transfer of aqueous hybrid nanofluid flow in a variable porous space with varying film thickness over a stretched surface

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Chinese Physics B 2025年第2期34卷 316-326页

作者： Abeer S Alnahdi Taza Gul Department of mathematics and Statistics Faculty of ScienceImam Mohammad Ibn Saud Islamic University(IMSIU)RiyadhSaudi Arabia mathematics Department City University of Science and Information TechnologyPeshawar25000Pakistan DoST-Directorate General of science and Technology Khyber Pakhtunkhwa Peshawar25000Pakistan

The high thermal conductivity of the nanoparticles in hybrid nanofluids results in enhanced thermal conductivity associated with their base *** heat transfer is a result of this high thermal conductivity,which has significant applications in heat exchangers and engineering *** optimize heat transfer,a liquid film of Cu and TiO_(2)hybrid nanofluid behind a stretching sheet in a variable porous medium is being considered due to its *** nature of the fluid is considered time-dependent and the thickness of the liquid film is measured variable adjustable with the variable porous space and favorable for the uniform flow of the liquid *** solution of the problem is acquired using the homotopy analysis method HAM,and the artificial neural network ANN is applied to obtain detailed information in the form of error estimation and validations using the fitting curve *** data is utilized to train the ANN in this study,which uses Cu and TiO_(2)hybrid nanofluids in a variable porous space for unsteady thin film flow,and it is used to train the *** results indicate that Cu and TiO_(2)play a greater role in boosting the rate.

关键词： thin film of Cu and TiO_(2)hybrid nanofluids variable porous space unsteady stretching sheet viscous dissipation heat transfer optimization artificial neural network

An infrastructure software perspective toward computation offloading between executable specifications and foundation models

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science China(Information sciences) 2025年第4期68卷 380-382页

作者： Dezhi RAN Mengzhou WU Yuan CAO Assaf MARRON David HAREL Tao XIE Key Laboratory of High Confidence Software Technologies (PKU) Ministry of Education School of Computer SciencePeking University School of Electronics Engineering and Computer science Peking University Department of Computer science and Applied mathematics Weizmann Institute of Science

Foundation models(FMs) [1] have revolutionized software development and become the core components of large software systems. This paradigm shift, however, demands fundamental re-imagining of software engineering theories and methodologies [2]. Instead of replacing existing software modules implemented by symbolic logic, incorporating FMs' capabilities to build software systems requires entirely new modules that leverage the unique capabilities of ***, while FMs excel at handling uncertainty, recognizing patterns, and processing unstructured data, we need new engineering theories that support the paradigm shift from explicitly programming and maintaining user-defined symbolic logic to creating rich, expressive requirements that FMs can accurately perceive and implement.

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Practical approach for detecting k-nonseparability of multipartite quantum states

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science China(Physics,Mechanics & Astronomy) 2025年第1期68卷 28-44页

作者： Jie Guo Jinchuan Hou Xiaofei Qi Kan He College of mathematics Taiyuan University of TechnologyTaiyuan 030006China School of mathematics and Statistics Shanxi UniversityTaiyuan 030006China Key Laboratory of Complex Systems and Data science of Ministry of education Shanxi UniversityTaiyuan 030006China

The instantaneous detection of entanglement in quantum states poses a significant challenge in the fields of quantum computation and quantum information,and there are no practical methods or tools to complete this task satisfactorily so *** propose a sufficient and necessary criterion of k-nonseparability for any n-partite finite or infinite dimensional systems,2≤k≤*** criterion serves as the foundation for a practical scheme designed to detect entanglement and k-nonseparability across multipar-tite finite-dimensional *** exemplify the application of our scheme,we have developed a software tool that facilitates swift and precise identification of entanglement,k-nonseparability,and genuine entanglement within n-qubit systems,specifically tailored for systems with 2≤n≤4.

关键词： multipartite systems entanglement states entanglement witnesses k-nonseparability