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Semi-derived Ringel-Hall algebras and Hall algebras of odd-periodic relative derived categories

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Science China mathematics 2024年第8期67卷 1735-1760页

作者： Ji Lin Liangang Peng department of mathematics and Statistics Fuyang Normal UniversityFuyang 236037China School of mathematics Sichuan UniversityChengdu 610064China

Let t be a positive integer and A be a hereditary abelian category satisfying some finiteness *** define the semi-derived Ringel-Hall algebra of A from the category C_(Z/t)(A)of Z/t-graded complexes and obtain a natural basis of the semi-derived Ringel-Hall ***,we describe the semiderived Ringel-Hall algebra by the generators and defining *** particular,if t is an odd integer,we show an embedding of the derived Hall algebra of the odd-periodic relative derived category in the extended semi-derived Ringel-Hall algebra.

关键词： hereditary abelian categories the categories of Z/t-graded complexes semi-derived Ringel-Hall algebras derived Hall algebras

Non-static plane symmetric perfect fluid solutions and Killing symmetries in f(R,T)gravity

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Communications in Theoretical Physics 2024年第2期76卷 145-150页

作者： Preeti Dalal Karanjeet Singh Sachin Kumar department of mathematics and Statistics Central University of PunjabBathinda151401PunjabIndia department of mathematics Jaypee University of Information TechnologySolan173234Himachal PradeshIndia

In this paper,the non-static solutions for perfect fluid distribution with plane symmetry in f(R,T)gravitational theory are ***,using the Lie symmetries,symmetry reductions are performed for considered vector fields to reduce the number of independent ***,corresponding to each reduction,exact solutions are *** vectors lead to different conserved ***,we figure out the Killing vector fields corresponding to all derived *** derived solutions are further studied and it is observed that all of the obtained spacetimes,at least admit to the minimal symmetry group which consists of δ_(y),δ_(z) and -zδ_(y)+yδ_(z).The obtained metrics,admit to 3,4,6,and 10,Killing vector *** of linear momentum in the direction of y and z,and angular momentum along the x axis is provided by all derived solutions.

关键词： Einstein field equations perfect fluid solutions f(R T)gravity killing symmetries

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 mathematics Nanchang UniversityNanchang330031China department of Physics and mathematics 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 mathematics 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=1Dskf(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

Results Involving Partial Differential Equations and Their Solution by Certain Integral Transform

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Computer Modeling in Engineering & Sciences 2024年第2期138卷 1593-1616页

作者： Rania Saadah Mohammed Amleh Ahmad Qazza Shrideh Al-Omari Ahmet Ocak Akdemir department of mathematics Faculty of ScienceZarqa UniversityZarqa13110Jordan department of mathematics Faculty of ScienceAl-Balqa Applied UniversityAmman11134Jordan department of mathematics Faculty of Science and LettersAgri Ibrahim莈鏴n UniversityAgri04100Turkey

In this study,we aimto investigate certain triple integral transformand its application to a class of partial *** discuss various properties of the new transformincluding inversion, linearity, existence, scaling andshifting, etc. Then,we derive several results enfolding partial derivatives and establish amulti-convolution ***, we apply the aforementioned transform to some classical functions and many types of partial differentialequations involving heat equations,wave equations, Laplace equations, and Poisson equations ***,wedraw some figures to illustrate 3-D contour plots for exact solutions of some selected examples involving differentvalues in their variables.

关键词： ARA transform double ARA transform triple ARA transform partial differential equations integral transform

Conservation laws,Lie symmetries,self adjointness,and soliton solutions for the Selkov–Schnakenberg system

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Communications in Theoretical Physics 2024年第2期76卷 29-44页

作者： Kashif Ali Aly R Seadawy Syed T R Rizvi Noor Aziz department of mathematics COMSATS University IslamabadLahore CampusPakistan mathematics department Faculty of ScienceTaibah UniversityAl-Madinah Al-Munawarah41411Saudi Arabia

In this article,we explore the famous Selkov–Schnakenberg(SS)system of coupled nonlinear partial differential equations(PDEs)for Lie symmetry analysis,self-adjointness,and conservation ***,miscellaneous soliton solutions like dark,bright,periodic,rational,Jacobian elliptic function,Weierstrass elliptic function,and hyperbolic solutions of the SS system will be achieved by a well-known technique called sub-ordinary differential *** these results are displayed graphically by 3D,2D,and contour plots.

关键词： Selkov-Schnakenberg system Lie symmetry analysis conservation laws adjointness integrability

Exact solutions for magnetohydrodynamic nanofluids flow and heat transfer over a permeable axisymmetric radially stretching/shrinking sheet

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Chinese Physics B 2024年第2期33卷 108-114页

作者： U.S.Mahabaleshwar G.P.Vanitha L.M.Pérez Emad H.Aly I.Pop department of Studies in mathematics Davangere UniversityShivagangothriDavangereIndia Departamento de F´ısica FACIUniversidad de Tarapac´aCasilla 7DAricaChile department of mathematics Faculty of EducationAin Shams UniversityRoxyCairoEgypt department of mathematics Babes-Bolyai University400084 Cluj-NapocaRomania

We report on the magnetohydrodynamic impact on the axisymmetric flow of Al_(2)O_(3)/Cu nanoparticles suspended in H_(2)O past a stretched/shrinked *** the use of partial differential equations and the corresponding thermophysical characteristics of nanoparticles,the physical flow process is *** resultant nonlinear system of partial differential equations is converted into a system of ordinary differential equations using the suitable similarity *** transformed differential equations are solved *** of the magnetic parameter,solid volume fraction and stretching/shrinking parameter on momentum and temperature distribution have been analyzed and interpreted *** skin friction and Nusselt number were also *** addition,existence of dual solution was deduced for the shrinking sheet and unique solution for the stretching ***,Al_(2)O_(3)/H_(2)O nanofluid flow has better thermal conductivity on comparing with Cu/H_(2)O ***,it was found that the first solutions of the stream are stable and physically realizable,whereas those of the second ones are unstable.

关键词： magnetohydrodynamic nanofluid stretching/shrinking sheet axisymmetric flow analytical solution suction/injection

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 department University of Wisconsin-MadisonMadisonWI 53706USA department of mathematics University of California-BerkeleyBerkeley CA 94720USA mathematics department 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 mathematics Al Zaytoonah University of JordanAmman11733Jordan Nonlinear Dynamics Research Center(NDRC) Ajman UniversityAjman 346United Arab Emirates department of mathematics Faculty of ScienceZarqa UniversityZarqa13110Jordan department of mathematics Prince Sattam Bin Abdulaziz UniversityAlkharj11942Saudi Arabia department of mathematics 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