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By gluing together the sides of eight copies of an all-right angled hyperbolic 6-dimensional polytope, two orientable hyperbolic 6-manifolds with Euler characteristic −1 are constructed. They ar...
We prove that every subgroup of p-power index in a right-angled Artin group is conjugacy p-separable. In particular, every right-angled Artin group is conjugacy p-separable. A consequence of this resu...
An example of non-homeomorphic conjugate varieties      example  non-homeomorphic conjugate varieties        font style='font-size:12px;'> 2010/12/13
We give examples of smooth quasi-projective varieties over complex numbers, in the context of connected Shimura varieties, which are not homeomor-phic to a conjugate of itself by an automorphism of th...
Rigidity of Frameworks Supported on Surfaces      bar-joint framework  framework on a surface  rigid framework       font style='font-size:12px;'> 2010/12/9
A theorem of Laman gives a combinatorial character-isation of the graphs that admit a realisation as a minimally rigid generic bar-joint framework in R2. A more general theory is devel-oped for framew...
This work deals with function theory on quantum complex hyperbolic spaces. The prin-cipal notions are expounded. We obtain explicit formulas for invariant integrals on ‘finite’ functions on a quantum...
Tropicalization is a procedure for associating a polyhedral complex to a subva-riety of an algebraic torus. We study the question on which graphs arise from tropicalizing algebraic curves. By using Ba...
We establish a symmetrization procedure in a context of general orthogonal expansions associated with a second order differential operator L, a ‘Laplacian’. Combined with a unified conjugacy scheme fu...
We define a transformation on harmonic maps N : M ! S2 from a Riemann surface M into the 2–sphere which depends on a parameter μ 2 C, the so–called μ–Darboux transformation.
We consider new implicit-explicit (IMEX) Runge-Kutta methods for hyperbolic systems of conservation laws with stiff relaxation terms. The explicit part is treated by a strong-stability-preserving (SSP...
非齐次超双曲型方程的特征问题     超双曲型方程  特征问题  基本解    存在性       font style='font-size:12px;'> 2009/11/11
证明了一类非齐次超双曲型方程特征问题解的存在性及唯一性。
关于一阶双曲型方程差分解的外推及其稳定性     差分解  双曲型方程  一阶       font style='font-size:12px;'> 2009/10/26
0)初边值问题的差分格式,并给出了相应的关于时间变量t的外推算法,但未涉及这些算法的稳定性问题。本文首先对各差分格式的稳定性予以讨论,导出其稳定性条件,然后提出一类改进的差分格式,它们比[1]~[3]中的算法有较高的精度或较好的稳定性。
A new finite volume scheme, based on first order monotone scheme and limited linear reconstruction, is constructed for scalar hyperbolic conservation laws in two dimension,the scheme satisfies the max...
求解守恒型双曲方程组的TVD-FCT格式及其应用     TVD-FCT格式  双曲方程组  守恒型       font style='font-size:12px;'> 2009/10/23
本文研究如下守恒型双曲方程组的物理解的计算: αU/αt+αf(U)/αx=0,(x,t)∈R×R~+,(1.1) U(x,0)=U_0(x),U(x,t)∈R~m.问题(1.1)在流体力学领域中经常遇到,它描述了一维可压流的非定常流动.解决好(1.1)的求解问题,具有重要的意义. 求解(1.1)的数值方法很多.这些数值方法有的精度低,对激波有抹平现象,有的精度高,但在激波附近出现伪振荡,甚至出...
双曲型守恒律方程的小波解法     小波解法  守恒律方程  双曲型       font style='font-size:12px;'> 2009/10/23
本文基于Hamilton-Jacobi方程的小波Galerkin近似和微分算子的小波表示,讨论一维双曲型守恒律方程初值问题的Daubechies小波解.由于小波在空间和时间上的局部性,本方法适用于处理具有奇异解的问题,可以有效的防止数值振荡.数值试验的结果表明,本方法是可行的.
本文将四阶CWENO(中心加权基本无振荡)格式、LevelSet方法以及四阶NCE—RK(自然连续外推的Runge—Kutta)方法结合起来,追踪了一维双曲守恒律方程的激波解.利用NSFD(非标准有限差分)格式来扩展CWENO重构的范围同时提高格式的精度.上述方法也能成功追踪二维双曲守恒律方程的激波解.还将本方法与标准的激波捕捉方法相比较,由此可知基于LevelSet方法的格式的有效性和逐点收敛性...

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