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Ramanujan's cubic transformation and generalized modular equation

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Science China Mathematics 2015年第11期58卷 2387-2404页

作者： WANG MiaoKun chu yuming SONG YingQing College of Mathematics and Econometrics Hunan University School of Mathematics and Computation Science Hunan City University

We study the quotient of hypergeometric functions in the theory of Ramanujan＇s generalized modular equation for a ∈ （0, 1/2], and find an infinite product for- mula for μ1/3（r） by use of the properties of μ＊a（r） and Ramanujan＇s cubic transformation. Besides, a new cubic transformation formula of hypergeometric function is given, which complements the Ramanujan＇s cubic transformation.

关键词： Gaussian hypergeometric function Ramanujan's cubic transformation generalized modular equa-tion infinite product modular function

Inequalities for the Gaussian hypergeometric function

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Science China Mathematics 2014年第11期57卷 2369-2380页

作者： SONG YingQing ZHOU PeiGui chu yuming School of Mathematics and Computation Science Hunan City University College of Science and Art Zhejiang Sci-Tech University

we study the monotonicity of certain combinations of the Gaussian hypergeometric functions F(-1/2,1/2;1;1- xc) and F(-1/2- δ,1/2 + δ;1;1- xd) on(0,1) for given 0 < c 5d/6 < ∞ andδ∈(-1/2,1/2),and find the largest ... 详细信息

关键词： Gaussian hypergeometric function monotonicity inequality

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

MONOTONICITY,CONVEXITY AND INEQUALITIES INVOLVING THE GENERALIZED ELLIPTIC INTEGRALS

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Acta Mathematica Scientia 2019年第5期39卷 1440-1450页

作者： Miaokun WANG Wen ZHANG yuming chu Department of Mathematics Huzhou University Huzhou 313000 China Friedman Brain Institute Icahn School of Medicine at Mount Sinai New York NY 10029 USA College of Science Hunan City University Yiyang 313000 China

We establish the monotonicity and convexity properties for several special functions involving the generalized elliptic integrals, and present some new analytic inequalities.

关键词： Gaussian hypergeometric function generalized elliptic integrals convexity inequality

ON THE BOUNDS OF THE PERIMETER OF AN ELLIPSE

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Acta Mathematica Scientia 2022年第2期42卷 491-501页

作者： Tiehong ZHAO Miaokun WANG yuming chu Department of Mathematics Hangzhou Normal UniversityHangzhou 311121China Department of Mathematics Huzhou UniversityHuzhou 313000China

In this paper,we present new bounds for the perimeter of an ellipse in terms of harmonic,geometric,arithmetic and quadratic means;these new bounds represent improvements upon some previously known results.

关键词： Gaussian hypergeometric function complete elliptic integral ellipse perimeter

Solution of an open problem for Schur convexity or concavity of the Gini mean values

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Science China Mathematics 2009年第8期52卷 2099-2106页

作者： chu yuming XIA WeiFeng Department of Mathematics Huzhou Teachers CollegeHuzhou 313000China School of Teacher Education Huzhou Teachers CollegeHuzhou 313000China

The Schur convexity or concavity problem of the Gini mean values S(a, b; x, y) with respect to (x, y) ∈ (0, ∞) × (0, ∞) for fixed (a, b) ∈ ? × ? is still open. In this paper, we prove that S(a, b; x, y) is Schur convex with respect to (x, y) ∈ (0, ∞) × (0, ∞) if and only if (a, b) ∈ {(a, b): a ? 0, b ? 0, a + b ? 1}, and Schur concave with respect to (x, y) ∈ (0, ∞) × (0, ∞) if and only if (a, b) ∈ {(a, b): b ? 0, b ? a, a + b ? 1} ∩ {(a, b): a ? 0, a ? b, a + b ? 1}.

关键词： Gini mean values Schur convex Schur concave 26D15 26D99 26B25

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Computer Methodologies for the Comparison of Some Efficient Derivative FreeSimultaneous Iterative Methods for Finding Roots of Non-Linear Equations

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Computers, Materials & Continua 2021年第1期66卷 275-290页

作者： yuming chu Naila Rafiq Mudassir Shams Saima Akram Nazir Ahmad Mir Humaira Kalsoom Department of Mathematics Huzhou UniversityHuzhou313000China Department of Mathematics National University of Modern LanguagesIslamabadPakistan Department of Mathematics and Statistics Riphah International University I-14Islamabad44000Pakistan Center for Advanced Studies in Pure and Applied Mathematics Bahauddin Zakariya University MultanPakistan School of Mathematical Sciences Zhejiang UniversityHanghou310027China

In this article,we construct the most powerful family of simultaneous iterative method with global convergence behavior among all the existing methods in literature for finding all roots of non-linear *** analysis proved that the order of convergence of the family of derivative free simultaneous iterative method is *** main aim is to check out the most regularly used simultaneous iterative methods for finding all roots of non-linear equations by studying their dynamical planes,numerical experiments and CPU *** planes of iterative methods are drawn by using MATLAB for the comparison of global convergence properties of simultaneous iterative *** behavior of the higher order simultaneous iterative methods are also illustrated by residual graph obtained from some numerical test *** test examples,dynamical behavior and computational efficiency are provided to present the performance and dominant efficiency of the newly constructed derivative free family of simultaneous iterative method over existing higher order simultaneous methods in literature.

关键词： Non-linear equation iterative method simultaneous method basins of attractions computational efficiency

SHARP BOUNDS FOR TOADER-TYPE MEANS IN TERMS OF TWO-PARAMETER MEANS

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Acta Mathematica Scientia 2021年第3期41卷 719-728页

作者： Yueying YANG Weimao QIAN Hongwei ZHANG yuming chu School of Mechanical and Electrical Engineering Huzhou Vocational&Technical CollegeHuzhou 313000China School of Continuing Education Huzhou Vocational&Technical CollegeHuzhou 313000China School of Mathematics and Statistics Changsha University of Science&TechnologyChangsha 410014China Department of Mathematics Huzhou UniversityHuzhou 313000China

In the article,we prove that the double inequalities Gp[λ1a+(1-λ1)b,λ1 b+(1-λ1)a]A1-p(a,b)0 with a≠b if and only ifλ1≤1/2-(1-(2/π)2/p)1/2/2,μ1≥1/2-(2p)1/2/(4 p),λ2≤1/2+(2(3/(2 s)(E(21/2/2)/π)1/s)-1)1/2/2 andμ2≥1/2+s1/2/(4 s)ifλ1,μ1∈(0,1/2),λ2,μ2∈(1/2,1),p≥1 and s≥1/2,where G(a,b)=(ab)1/2,A(a,b)=(a+b)/2,T(a,b)=∫0π/2(a2 cos2 t+b2 sin2)1/2 tdt/π,Q(a,b)=((a2+b2)/2)1/2,C(a,b)=(a2+b2)/(a+b)and E(r)=∫0π/2(1-r^(2) sin^(2))1/2 tdt.

关键词： Geometric mean arithmetic mean Toader mean ontraharmonic mean complete elliptic integral

Entropy generation approach with heat and mass transfer in magnetohydrodynamic stagnation point flow of a tangent hyperbolic nanofluid

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Applied Mathematics and Mechanics(English Edition) 2021年第8期42卷 1205-1218页

作者： Tiehong ZHAO M.R.KHAN yuming chu A.ISSAKHOV R.ALI S.KHAN Department of Mathematics Hangzhou Normal UniversityHangzhou 311121China LSEC and ICMSEC Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 1001900China School of Mathematical Science University of Chinese Academy of SciencesBeijing 1001900China Department of Mathematics Huzhou UniversityHangzhou 313000Zhejiang ProvinceChina Department of Mathematical and Computer Modeling Al-Farabi Kazakh National UniversityAlmaty 050040Kazakhstan Department of Mathematical and Computer Modeling Kazakh British-Technical UniversityAlmaty 050000Kazakhstan School of Mathematics and Statistics Central South UniversityChangsha 410083China

This work examines the entropy generation with heat and mass transfer in magnetohydrodynamic(MHD)stagnation point flow across a stretchable *** heat transport process is investigated with respect to the viscous dissipation and thermal radiation,whereas the mass transport is observed under the influence of a chemical *** irreversibe factor is measured through the application of the second law of *** established non-linear partial differential equations(PDEs)have been replaced by acceptable ordinary differential equations(ODEs),which are solved numerically via the bvp4 c method(built-in package in MATLAB).The numerical analysis of the resulting ODEs is carried out on the different flow parameters,and their effects on the rate of heat transport,friction drag,concentration,and the entropy generation are *** is determined that the concentration estimation and the Sherwood number reduce and enhance for higher values of the chemical reaction parameter and the Schmidt number,although the rate of heat transport is increased for the Eckert number and heat generation/absorption parameter,*** entropy generation augments with boosting values of the Brinkman number,and decays with escalating values of both the radiation parameter and the Weissenberg number.

关键词： tangent hyperbolic fluid magnetohydrodynamic(MHD) viscous dissipation stagnation point flow heat generation/absorption thermal radiation