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arXiv 2023年

作者： Li, Yangcheng Zhang, Yong School of Mathematics and Statistics Changsha University of Science and Technology Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha410114 China

Many authors studied the problem that rational triangle pairs (triangle-parallelogram pairs) with the same area and the same perimeter. They investigated this problem by solving the rational solutions of the corresponding Diophantine equations. In this paper, we give a unified description of this problem by using the affine transformation in a rectangular coordinate system. According to the fact that two triangles with the same area and the same perimeter determine an affine transformation, this problem can be reduced to solving a specific Diophantine system. Moreover, we will give some rational solutions to this Diophantine *** Codes 11D72, 51M25, 51N10, 11G05 Copyright © 2023, The Authors. All rights reserved.

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Artificial neural networking (ANN) analysis for heat and entropy generation in flow of non-Newtonian fluid between two rotating disks

Artificial neural networking (ANN) analysis for heat and ent...

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作者： Zhao, Tie-Hong Khan, M. Ijaz Chu, Yu-Ming Department of Mathematics Hangzhou Normal University Hangzhou311121 China Department of Mathematics and Statistics Riphah International University I-14 Islamabad44000 Pakistan Department of Mathematics Huzhou University Huzhou313000 China Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science and Technology Changsha410114 China

Mixed convection is a mechanism of heat transport in a thermodynamic system in which the motion of fluid particles is produced by gravity as well as external forces like fans, pumps, or any other devices. Such type of heat transport has a fruitful application in daily life due to reliable maintenance. In this regard, numerous researchers and analyst have focused on the importance of mixed convective flow to explore its different aspects, and frequent research articles are published in this area. In this work, mixed convective entropy optimized nanomaterial magnetohydrodynamics (MHD) flow of Ree-Eyring fluid is discussed between two rotating disks. The effects of porosity and velocity slip are considered. Both the disks are rotating with different angular frequency and stretching rates. modeling is performed for the energy equation subject to heat generation/absorption, dissipation, radiative heat flux, and Joule heating. Four types of irreversibilities are discussed, and total entropy rate is calculated. The obtained results are compared with past studies and found good agreement with them. The physical curiosity like skin friction and Sherwood and Nusselt numbers are numerically calculated. Series solutions are computed via homotopy method. Our obtained outcomes show that the velocity and temperature fields show contrast behavior against larger magnetic parameter. It is also noticed that the entropy rate and Bejan number have opposite behaviors against higher values of Weissenberg number. The entropy rate increases for higher Weissenberg number while Bejan number decays. © 2021 John Wiley & Sons, Ltd.

关键词： Activation energy

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Accurate adaptive deep learning method for solving elliptic problems

arXiv

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arXiv 2024年

作者： Ying, Jinyong Xie, Yaqi Li, Jiao Wang, Hongqiao School of Mathematics and Statistics HNP-LAMA Central South University Hunan Changsha410083 China School of Mathematics and Statistics Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science and Technology Hunan Changsha410114 China

Deep learning method is of great importance in solving partial differential equations. In this paper, inspired by the failure-informed idea proposed by Gao ***. (SIAM Journal on Scientific Computing 45(4)(2023)) and as an improvement, a new accurate adaptive deep learning method is proposed for solving elliptic problems, including the interface problems and the convection-dominated problems. Based on the failure probability framework, the piecewise uniform distribution is used to approximate the optimal proposal distribution and an kernel-based method is proposed for efficient sampling. Together with the improved Levenberg-Marquardt optimization method, the proposed adaptive deep learning method shows great potential in improving solution accuracy. Numerical tests on the elliptic problems without interface conditions, on the elliptic interface problem, and on the convection-dominated problems demonstrate the effectiveness of the proposed method, as it reduces the relative errors by a factor varying from 102 to 104 for different cases. Copyright © 2024, The Authors. All rights reserved.

关键词： Numerical methods

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Iteration problem for several chaos in non-autonomous discrete system

arXiv

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arXiv 2024年

作者： Zeng, Hongbo Huang, Chuangxia Liu, Bingwen School of Mathematics and Statistics Changsha University of Science and Technology Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Hunan Changsha410114 China College of Data Science Jiaxing University Zhejiang Jiaxing314001 China

In this paper we investigate the iteration problem for several chaos in non-autonomous discrete system (X, f1,∞). Firstly, we prove that the Li-Yorke chaos of a non-autonomous discrete dynamical system is preserved under iterations when f1,∞ converges to f, which weakens the condition in the literature that f1,∞ uniformly converges to f . Besides, we prove that both DC2’ and Kato’s chaos of a non-autonomous discrete dynamical system are iteration invariants. Additionally, we give a sufficient condition for non-autonomous discrete dynamical system to be Li-Yorke chaos. Finally, we give an example to show that the DC3 of a non-autonomous discrete dynamical system is not inherited under iterations, which partly answers an open question proposed by Wu and Zhu(Chaos in a class of non-autonomous discrete systems, ***. 2013,26:431-436). Copyright © 2024, The Authors. All rights reserved.

关键词： Dynamical systems

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Global Dynamics of Delay Differential Equations with Non-Monotone Bistable Nonlinearities and Time-Varying Delays

SSRN

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SSRN 2024年

作者： Huang, Chuangxia Ding, Xiaodan Yu, Jianshe College of Science Hunan University of Science and Engineering Hunan Yongzhou425199 China School of Mathematics and Statistics Changsha University of Science and Technology Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Hunan Changsha410114 China Guangzhou Center for Applied Mathematics Guangzhou University Guangzhou510006 China

In this paper, we consider a class of non-autonomous delay differential equations incorporating non-monotone bistable nonlinearities and multiple time-varying delays, where the zero equilibrium point may coexist with at most two positive equilibrium points. We aim to provide a fairly complete description of the global dynamics, including global asymptotic stability, semi-stability, bi-stability, and basins of attraction. Characterizing the attractiveness of a positive equilibrium point is a very signiﬁcant challenge even in the case of the non-linear initial values crossing this equilibrium point. Here, we combine the differential inequality technique, the ﬂuctuation lemma and the domain decomposition strategy to overcome the difﬁculties. The obtained results improve and generalize some existing ones. © 2024, The Authors. All rights reserved.

关键词： Asymptotic stability

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modeling and numerical analysis of nanoliquid (titanium oxide, graphene oxide) flow viscous fluid with second order velocity slip and entropy generation

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Chinese Journal of Chemical engineering 2021年第3期34卷 17-25页

作者： M.Ijaz Khan Seifedine Kadry Yuming Chu M.Waqas Department of Mathematics Riphah International UniversityFaisalabad CampusFaisalabad 38000Pakistan Department of Mathematics and Computer Science Beirut Arab UniversityBeirutLebanon Department of Mathematics Huzhou UniversityHuzhou 313000China Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science&TechnologyChangsha 410114China NUTECH School of Applied Sciences and Humanities National University of TechnologyIslamabad 44000Pakistan

The prime objective of the present communication is to examine the entropy-optimized second order velocity slip Darcy–Forchheimer hybrid nanofluid flow of viscous material between two rotating *** conducting flow is considered and saturated through Darcy–Forchheimer *** the disks are rotating with different angular frequencies and stretches with different *** graphene oxide and titanium dioxide are considered for hybrid nanoparticles and water as a continuous phase *** heating,heat generation/absorption and viscous dissipation effects are incorporated in the mathematical modeling of energy ***,binary chemical reaction with activation energy is *** total entropy rate is calculated in the presence of heat transfer irreversibility,fluid friction irreversibility,Joule heating irreversibility,porosity irreversibility and chemical reaction irreversibility through thermodynamics second *** nonlinear governing equations are first converted into ordinary differential equations through implementation of appropriate similarity transformations and then numerical solutions are calculated through Built-in-Shooting *** of sundry flow variables on the entropy generation rate,velocity,concentration,Bejan number,temperature are discussed graphically for both graphene oxide and titanium dioxide hybrid *** engineering interest like skin friction coefficient and Nusselt number are computed numerically and presented through *** is noticed from the obtained results that entropy generation rate and Bejan number have similar effects versus diffusion *** entropy generation rate is more against the higher Brinkman number.

关键词： Darcy-Forchheimer porous medium Titanium dioxide and graphene oxide nanoparticles Second order velocity slip Convective boundary condition Activation energy Heat generation/absorption

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O(t^(-β))-SYNCHRONIZATION AND ASYMPTOTIC SYNCHRONIZATION OF DELAYED FRACTIONAL ORDER NEURAL NETWORKS

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Acta Mathematica Scientia 2022年第4期42卷 1273-1292页

作者： Anbalagan PRATAP Ramachandran RAJA Jinde CAO Chuangxia HUANG Jehad ALZABUT Ovidiu BAGDASAR Department of Mathematics Alagappa UniversityKaraikudi 630004India Ramanujan Centre for Higher Mathematics Alagappa UniversityKaraikudi 630004India School of Mathematics Southeast UniversityNanjing 211189China Yonsei Frontier Lab Yonsei UniversitySeoul03722South Korea Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science and TechnologyChangsha410114China Department of Mathematics and General Sciences Prince Sultan UniversityRiyadh 12435Saudi Arabia Department of Electronics Computing and MathematicsUniversity of DerbyUnited Kingdom

This article explores the O(t^(-β))synchronization and asymptotic synchronization for fractional order BAM neural networks(FBAMNNs)with discrete delays,distributed delays and non-identical *** designing a state feedback control law and a new kind of fractional order Lyapunov functional,a new set of algebraic sufficient conditions are derived to guarantee the O(t^(-β))Synchronization and asymptotic synchronization of the considered FBAMNNs model;this can easily be evaluated without using a MATLAB LMI control ***,two numerical examples,along with the simulation results,illustrate the correctness and viability of the exhibited synchronization results.

关键词： O(t^(-β))-synchronization asymptotic synchronization BAM neural networks fractional order state feedback control law

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Exit identities for diusion processes observed at Poisson arrival times

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Frontiers of Mathematics in China 2020年第3期15卷 507-528页

作者： Yingqiu LI Ye CHEN Shilin WANG Zhaohui PENG School of Mathematics and Statistics Changsha University of Science and TechnologyChangsha 410004China College of Mathematics and Physics Hunan University of Arts and ScienceChangde 415000China Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science and TechnologyChangsha 410004China

For diffusion processes,we extend various two-sided exit identities to the situation when the process is only observed at arrival times of an independent Poisson *** results are expressed in terms of solutions to the ... 详细信息

关键词： Time-homogeneous diffusion process exit problem Poisson arrival time Brownian motion

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Identification of natural allelic variation in TTL1 controlling thermotolerance and grain size by a rice super pan-genome∞

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Journal of Integrative Plant Biology 2023年第12期65卷 2541-2551页

作者： Yarong Lin Yiwang Zhu Yuchao Cui Hongge Qian Qiaoling Yuan Rui Chen Yan Lin Jianmin Chen Xishi Zhou Chuanlin Shi Huiying He Taijiao Hu Chenbo Gu Xiaoman Yu Xiying Zhu Yuexing Wang Qian Qian Cuijun Zhang Feng Wang Lianguang Shang Institute of Biotechnology Fujian Academy of Agricultural Sciences/Fujian Provincial Key Laboratory of Genetic Engineering for AgricultureFuzhou 350003China Shenzhen Branch Guangdong Laboratory of Lingnan Modern AgricultureGenome Analysis Laboratory of the Ministry of Agriculture and Rural AffairsAgricultural Genomics Institute at ShenzhenChinese Academy of Agricultural SciencesShenzhen 518124China Xiamen Key Laboratory for Plant Genetics School of Life SciencesXiamen UniversityXiamen 361102China College of Bioscience and Biotechnology Hunan Agricultural UniversityChangsha 410128China State Key Laboratory of Rice Biology China National Rice Research InstituteHangzhou 311401China Yazhouwan National Laboratory Sanya City 572024China

Continuously increasing global temperatures present great challenges to food *** size,one of the critical components determining grain yield in rice(Oryza sativa L.),is a prime target for genetic ***,there is an immediate need for genetic improvement in rice to maintain grain yield under heat ***,quantitative trait loci(QTLs)endowing heat stress tolerance and grain size in rice are extremely ***,we identified a novel negative regulator with pleiotropic effects,Thermo‐Tolerance and grain Length 1(TTL1),from the super pan‐genomic and transcriptomic ***‐of‐function mutations in TTL1 enhanced heat tolerance,and caused an increase in grain size by coordinating cell expansion and ***1 was shown to function as a transcriptional regulator and localized to the nucleus and cell ***,haplotype analysis showed that hapL and hapS of TTL1 were obviously correlated with variations of thermotolerance and grain size in a core collection of *** evolution analysis of available rice germplasms suggested that TTL1 was selected during domestication of the indica and japonica rice subspecies,but still had much breeding potential for increasing grain length and *** findings provide insights into TTL1 as a novel potential target for the development of high‐yield and thermotolerant rice varieties.

关键词： domestication grain size heat tolerance pan‐genome natural variation

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Koningipyridines A and B,two nitrogen-containing polyketides from the fungus Trichoderma koningiopsis SC-5

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Natural Products and Bioprospecting 2024年第1期14卷 120-132页

作者： Weiwei Peng Qi Huang Xin Ke Wenxuan Wang Yan Chen Zihuan Sang Chen Chen Siyu Qin Yuting Zheng Haibo Tan Zhenxing Zou Xiangya School of Pharmaceutical Sciences Hunan Key Laboratory of Diagnostic and Therapeutic Drug Research for Chronic DiseasesCentral South UniversityChangsha410013People's Republic of China National Engineering Research Center of Navel Orange Gannan Normal UniversityGanzhou341000People's Republic of China Key Laboratory of National Forestry and Grassland Administration on Plant Conservation and Utilization in Southern China State Key Laboratory of Plant Diversity and Specialty CropsKey Laboratory of South China Agricultural Plant Molecular Analysis and Genetic ImprovementGuangdong Provincial Key Laboratory of Applied BotanySouth China Botanical GardenChinese Academy of SciencesGuangzhou510650People's Republic of China Department of Pharmacy Xiangya HospitalCentral South UniversityChangsha410013People's Republic of China

Two novel koninginin derivatives,koningipyridines A and B(1 and 2),along with four known compounds(3-6)were isolated from the EtOAc extract of the endophytic fungus Trichoderma koningiopsis *** them,koningipyridine A featured an unprecedented pentacyclic ketal skeleton with the formation of a fascinating 6/6/5/6/5 fused ring system and shared a characteristic pyridine core,which represents the first example of nitrogen-containing koninginin-type natural ***,koningipyridine B was the first member in the koninginin family sharing a unique 6/6/5 dihydropyridine skeleton,and it was suggested to be the critical biosynthetic precursor of koningipyridine *** structures of 1 and 2 were elucidated by the interpretation of 1D and 2D NMR spectroscopy,HRESIMS data,as well as theoretical calculations of 13C NMR and electronic circular dichroism(ECD).Moreover,all isolates were screened for antimicrobial activities against Staphylococcus aureus,MRSA,and Escherichia coli as well as the cytotoxic effects against three cancer cell lines(A549,Hela,and HepG2).

关键词： Trichoderma koningiopsis Endophytic fungi Secondary metabolites Koningipyridine Cytotoxic activity

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