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Unsteady MHD Casson Nanofluid Flow Past an Exponentially Accelerated Vertical Plate:An Analytical Strategy

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Computer Modeling in Engineering & Sciences 2024年第7期140卷 431-460页

作者： T.Aghalya R.Tamizharasi department of mathematics School of Advanced SciencesVellore Institute of TechnologyVelloreTamilnadu632014India

In this study,the characteristics of heat transfer on an unsteady magnetohydrodynamic(MHD)Casson nanofluid over an exponentially accelerated vertical porous plate with rotating effects were *** flow was driven by the combined effects of the magnetic field,heat radiation,heat source/sink and chemical *** oxide(CuO)and titanium oxide(TiO2)are acknowledged as nanoparticle *** nondimensional governing equations were subjected to the Laplace transformation technique to derive closed-form *** representations are provided to analyze how changes in physical parameters,such as the magnetic field,heat radiation,heat source/sink and chemical reaction,affect the velocity,temperature and concentration *** computed values of skin friction,heat and mass transfer rates at the surface were tabulated for various sets of input *** is perceived that there is a drop in temperature due to the rise in the heat source/sink and the Prandtl *** should be noted that a boost in the thermal radiation parameter prompts an increase in *** increase in the Prandtl number,heat source/sink parameter,time and a decrease in the thermal radiation parameter result in an increase in theNusselt *** computed values of the skin friction,heat andmass transfer rates at the surface were tabulated for various values of the flow *** present results were compared with those of previously published studies andwere found to be in excellent *** research has practical applications in areas such as drug delivery,thermal medicine and cancer treatment.

关键词： Thermal radiation radiative flux nanofluid copper oxide titanium oxide accelerated plate

Big Theta Equals Small Theta Generically

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Acta Mathematica Sinica,English Series 2024年第3期40卷 717-730页

作者： Rui CHEN Jia Liang ZOU institute for advanced study in Mathmatics Zhejiang UniversityHangzhou 310058P.R.China department of mathematics University of Michigan530 Church StAnn ArborMI 48109USA

In this paper we consider the theta correspondence over a non-Archimedean local *** the homological method and the theory of derivatives,we show that under a mild condition the bigtheta lift is irreducible.

关键词： Theta correspondence derivatives

Deformation of Rigid Conjugate Self-dual Galois Representations

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1599-1644页

作者： Yi Feng LIU Yi Chao TIAN Liang XIAO Wei ZHANG Xin Wen ZHU institute for advanced study in mathematics Zhejiang UniversityHangzhou 310058P.R.China Morningside Center of mathematics AMSSChinese Academy of SciencesBeijing 100190P.R.China New Cornerstone Lab Beijing International Center for Mathematical ResearchPeking Ui Beijing 100871P.R.China department of mathematics Massachusetts Institute of TechnologyCambridge MA 02139United States department of mathematics Stanford UniversityStanfordCA 94305United States

In this article,we study deformations of conjugate self-dual Galois *** study is ***,we prove an R=T type theorem for a conjugate self-dual Galois representation with coefficients in a finite field,satisfying a certain property called ***,we study the rigidity property for the family of residue Galois representations attached to a symmetric power of an elliptic curve,as well as to a regular algebraic conjugate self-dual cuspidal representation.

关键词： Galois deformation rigid conjugate self-dual Galois representations

Impact of vaccination on the dynamics of COVID-19:A mathematical study using fractional derivatives

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International Journal of Biomathematics 2024年第2期17卷 201-232页

作者： Shraddha Ramdas Bandekar Mini Ghosh C.Rajivganthi Division of mathematics School of Advanced Sciences Vellore Institute of TechnologyChennaiIndia

Arrival of a new disease marks a yearlong destruction of human lives and economy in general,and if the disease turns out to be a pandemic the loss is ***-19 is one such pandemic that has claimed millions of lives till *** is a suffering throughout the world due to various factors associated with the pandemic,be it loss of livelihoods because of sudden shutdown of companies and lockdown,or loss of lives due to lack of medical aid and inadequate vaccination *** this study,we develop a six-compartmental epidemiological model incorporating *** motivation behind the study is to analyze the significance of higher vaccination efficacy and higher rate of population getting vaccinated in controlling the rise in infectives and thereby the untimely demise of various *** work begins with an ordinary differential equation model followed by stability analysis of the same,after which a fractional-order derivative model of the same is formulated and the existence of uniformly stable solution for the system is *** addition to this,we present the stability of the equilibria in general for the fractional model *** sensitivity analysis of the basic reproduction number along with its correlation with various parameters is *** addition to this,sensitivity of certain state variables in the fractional model with respect to *** orders as well with respect to different infection rate is exhibited in this *** related to lockdown and usage of face shields are incorporated in the entire study,and importance of these is highlighted in the study as *** major takeaway from the study is that mere vaccination will not sufice in eradication of the *** vaccine efficacy plays a major role along with other intervention included in the *** numerical simulations are carried out in MATLAB software using ode45 and fdel2.

关键词： Caputo fractional derivative basic reproduction number stability analysis sensitivityanalysis vaccination

Stability of the Phase Separation State for Compressible Navier-Stokes/Allen-Cahn System

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 45-74页

作者： Ya-zhou Chen Hakho Hong Xiao-ding Shi department of mathematics College of Mathematics and PhysicsBeijing University of Chemical TechnologyBeijing100029China institute of mathematics State Academy of SciencesPyongyangKorea

This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/AllenCahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global solutions and the stability of the phase separation state are proved under the small initial perturbations. Moreover, the optimal time decay rates are obtained for higher-order spatial derivatives of density,velocity and phase. Our results imply that if the immiscible two-phase flow is initially located near the phase separation state, then under small perturbation conditions, the solution exists globally and decays algebraically to the complete separation state of the two-phase flow, that is, there will be no interface fracture, vacuum, shock wave, mass concentration at any time, and the interface thickness tends to zero as the time t → +∞.

关键词： Navier-Stokes/Allen-Cahn system existence uniqueness large time behavior decay rate

Influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel

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Applied mathematics and Mechanics(English Edition) 2024年第3期45卷 563-580页

作者： N.HUMNEKAR D.SRINIVASACHARYA department of mathematics National Institute of TechnologyWarangal 506004TelanganaIndia

The influence of variable viscosity and double diffusion on the convective stability of a nanofluid flow in an inclined porous channel is *** DarcyBrinkman model is used to characterize the fluid flow dynamics in porous *** analytical solutions are obtained for the unidirectional and completely developed *** on a normal mode analysis,the generalized eigenvalue problem under a perturbed state is *** eigenvalue problem is then solved by the spectral ***,the critical Rayleigh number with the corresponding wavenumber is evaluated at the assigned values of the other flow-governing *** results show that increasing the Darcy number,the Lewis number,the Dufour parameter,or the Soret parameter increases the stability of the system,whereas increasing the inclination angle of the channel destabilizes the ***,the flow is the most unstable when the channel is vertically oriented.

关键词： nanofluid inclined channel variable viscosity linear stability double dif-fusion porous medium

Special Unipotent Representations of Simple Linear Lie Groups of Type A

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Acta Mathematica Sinica,English Series 2024年第3期40卷 707-716页

作者： Dan BARBASCH Jia Jun MA Bin Yong SUN Chen Bo ZHU department of mathematics Cornell UniversityIthacaNY 14853USA School of Mathematical Sciences Xiamen UniversityXiamen 361005P.R.China department of mathematics Xiamen University Malaysia CampusSepangSelangor Darul Ehsan43900Malaysia institute for advanced study in mathematics&New Cornerstone Science Laboratory Zhejiang UniversityHangzhou 310058P.R.China department of mathematics National University of Singapore10 Lower Kent Ridge RoadSingapore 119076

Let G be a special linear group over the real,the complex or the quaternion,or a special unitary *** this note,we determine all special unipotent representations of G in the sense of Arthur and Barbasch-Vogan,and show... 详细信息

关键词： Special unipotent representations unitary representations coherent continuation Weyl group representations

Flag Varieties of Type B/C and Twisted Yangian

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Algebra Colloquium 2024年第1期31卷 129-148页

作者： Zhijie Dong Haitao Ma institute for advanced study in mathematics of HIT Harbin institute of Technology Harbin 150001China College of Mathematical Science Harbin Engineering University Harbin 150001China

We study the convolution algebra H_(*)^(G×C^(*))(Z)of G×C^(*)-equivariant homology group on the Steinberg variety of type B/C and define an algebra Y that maps to H_(*)^(G×C^(*))(Z).We also study the G-equivariant ... 详细信息

关键词： Yangian fag variety convolution algebra

Mirror symmetry for special nilpotent orbit closures In Memory of Professor Gang Xiao

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Science China mathematics 2024年

作者： Baohua Fu Yongbin Ruan Yaoxiong Wen AMSS HLM and MCM Chinese Academy of Sciences Korea institute for advanced study institute for advanced study in mathematics Zhejiang University School of Mathematical Sciences University of Chinese Academy of Sciences

Motivated by geometric Langlands, we initiate a program to study the mirror symmetry between nilpotent orbit closures of a semisimple Lie algebra and those of its Langlands dual. The most interesting case is Bn via Cn. Classically, there is a famous Springer duality between special orbits. Therefore, it is natural to speculate that the mirror symmetry we seek may coincide with Springer duality in the context of special ***, such a naive statement fails. To remedy the situation, we propose a conjecture which asserts the mirror symmetry for certain parabolic/induced covers of special orbits. Then, we prove the conjecture for Richardson orbits and obtain certain partial results in general. In the process, we reveal some very interesting and yet subtle structures of these finite covers, which are related to Lusztig’s canonical quotients of special nilpotent orbits. For example, there is a mysterious asymmetry in the footprint or range of degrees of these finite covers. Finally, we provide two examples to show that the mirror symmetry fails outside the footprint.

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