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EQUATIONS SOLVABLE BY RADICALS IN A UNIQUELY DIVISIBLE GROUP
EQUATIONS SOLVABLE RADICALS UNIQUELY DIVISIBLE GROUP
2015/8/14
We study equations in groups G with unique m-th roots for each positive integer m. A word equation in two letters is an expression of the form w(X, A) = B, where w is a finite word in the alphabet {X,...
A NEW PARALLEL KERNEL-INDEPENDENT FAST MULTIPOLE METHOD
Fast multipole methods adaptive algorithms massively parallel computing boundary integral equations N-body problems viscous flows
2015/7/15
We present a new adaptive fast multipole algorithm and its parallel implementation. The algorithm is kernel-independent in the sense that the evaluation of pairwise interactions does not rely on any a...
Fast Algorithms for Boundary Integral Equations
Boundary integral equations Laplace equation Helmholtz equation fast algorithms fast multipole method hierarchical matrices wavelets multiscale methods multidirectional methods
2015/7/15
This article reviews several fast algorithms for boundary integral equations. After a brief introduction of the boundary integral equations for the Laplace and Helmholtz equations, we discuss in order...
A fast solver for the Stokes equations with distributed forces in complex geometries
Stokes equations Fast solvers Integral equations Double-layer potential Fast multipole methods Embedded domain methods Immersed interface methods Fictitious domain methods Cartesian grid methods Moving boundaries
2015/7/14
We present a new method for the solution of the Stokes equations. The main features of our method are: (1) it can be applied to arbitrary geometries in a black-box fashion; (2) it is second-order accu...
A kernel-independent adaptive fast multipole algorithm in two and three dimensions
Fast multipole methods Fast solvers Integral equations Single-layer potential Double-layer potential Particle methods N-body problems
2015/7/14
We present a new fast multipole method for particle simulations. The main feature of our algorithm is that it does not require the implementation of multipole expansions of the underlying kernel, and ...
关于Riemann积分理论的本质缺陷及以Lebesgue积分取代之的看法
Riemann积分 数学
2014/12/22
关于Riemann积分理论的本质缺陷及以Lebesgue积分取代之的看法。
On the prescribing σ2 curvature equation on S 4
σk curvature prescribing curvature fully nonlinear curvature equation
2014/4/3
Prescribing σk curvature equations are fully nonlinear generalizations of the prescribing Gaussian or scalar curvature equations. For a given a positive function K to be prescribed on the 4-dimensiona...
ABSENCE OF ANOMALOUS DISSIPATION OF ENERGY IN FORCED TWO DIMENSIONAL FLUID EQUATIONS
ABSENCE OF ANOMALOUS DISSIPATION OF ENERGY FORCED TWO DIMENSIONAL FLUID EQUATIONS
2014/4/3
Anomalous dissipation of energy in three dimensional turbulence is one of the basic statements of physical theory [55]. It has been veri ed experimentally to a large degree [75], but not mathematicall...
2n阶时滞微分方程周期解的存在性
2n阶边值问题 先验边界 周期解
2012/11/12
利用上下解方法研究2n阶时滞微分方程周期边值问题,建立了2n(n≥1)阶时滞微分方程周期边值问题解存在的充分条件。
发展了一种基于非结构网格的自适应方法,对高超声速无粘流场进行了数值模拟。根据流场参数的变化梯度确定加密边,由加密准则进行自适应网格剖分后得到分布合理的较密网格。通过预先生成的初始极密表面网格将边界的加密点投影到边界上,使得边界保持初始外形。通过求解三维Euler 方程,对三维双椭球高超声速绕流问题进行了数值模拟,计算结果和实验数据相吻合,表明了该文所建立方法的正确性和可靠性。
讨论了一类考虑竹笋影响竹子生长的非线性竹林发展系统，并利用特征线法和积分方程理论，证明了这个系统初边值问题古典解的存在唯一性.
关于一个非齐次核的Hilbert型积分不等式
权函数 Hilbert型积分不等式 等价式 逆式
2013/12/5
应用权函数的方法及实分析技巧,建立具有最佳常数因子的非齐次核为e－βxy(β>0)的Hilbert型积分不等式,并研究其等价式与相应逆式.
本文介绍了无穷级数与广义积分及其敛散性的判别方法,讨论了级数与广义积分的内在联系，给出了由此产生的一种无穷级数敛散性的判别法即柯西积分判别法，从而建立起了无穷积分与无穷级数敛散性之间的联系,为无穷级数敛散性的判别，提供了一个简便的方法.并在此基础上给出了通项为复合函数的级数敛散性的积分判别法.最后，给出了现行的数学分析、微积分与高等数学的教材中柯西积分判别法的一个新证明，获得了这个判别法的一个推广...
A Class of Special Solutions for the Ultradiscrete Painleve II Equation
ultradiscretization Painleve equation Airy equation q-difference equation
2011/10/9
Abstract: A class of special solutions are constructed in an intuitive way for the ultradiscrete analog of $q$-Painlev\'e II ($q$-PII) equation. The solutions are classified into four groups depending...