半平面中有限阶解析函数的因子分解

与经典有限阶整函数的Hadamard因子分解定理和半平面中属于Hardy空间的解析函数的内外函数的因子分解类似,对右半平面中有限阶ρ解析函数f,可以分解为三个解析函数G,eQ和eg的乘积GeQeg,其中G是一个加权Blaschke乘积,Q是一个次数不超过ρ的多项式以及eg是一个加权外函数,log|G|,ReQ和Reg-log|f|在右半平面的边界恒为零．     

The Riemann Problem and Matrix-Valued Potentials with a Convergent Baker-Akhiezer Function

We obtain a simple sufficient condition for the solvability of the Riemann factorization problem for matrix-valued functions on a circle. This condition is based on the symmetry principle. As an application, we consider nonlinear evolution equations that can be obtained by a unitary reduction from the zero-curvature equations connecting a linear function of the spectral parameter z and a polynomial of z. We consider solutions obtained by dressing the zero solution with a function holomorphic at infinity. We show that all such solutions are meromorphic functions on ℂ _xt ² without singularities on ℝ _xt ² . This class of solutions contains all generic finite-gap solutions and many rapidly decreasing solutions but is not exhausted by them. Any solution of this class, regarded as a function of x for almost every fixed t ∈ ℂ, is a potential with a convergent Baker-Akhiezer function for the corresponding matrix-valued differential operator of the first order.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 3, pp. 453–471, September, 2005.     

关于隐式LU分解算法分解算法求矩阵主子阵逆的注记（英）

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关于K-分块循环矩阵及其对角化问题的讨论

给出了K-分块循环矩阵的概念,并探讨了K-分块循环矩阵的相似类及其对角化问题.     

A globally well-posed finite element algorithm for aerodynamics applications

A finite element CFD algorithm is developed for Euler and Navier-Stokes aerodynamic applications. For the linear basis, the resultant approximation is at least second-order-accurate in time and space for synergistic use of three procedures: (1) a Taylor weak statement, which provides for derivation of companion conservation law systems with embedded dispersion-error control mechanisms; (2) a stiffly stable second-order-accurate implicit Rosenbrock-Runge-Kutta temporal algorithm; and (3) a matrix tensor product factorization that permits efficient numerical linear algebra handling of the terminal large-matrix statement. Thorough analyses are presented regarding well-posed boundary conditions for inviscid and viscous flow specifications. Numerical solutions are generated and compared for critical evaluation of quasi-one- and two-dimensional Euler and Navier-Stokes benchmark test problems. Of critical importance, essentially non-oscillatory solutions are uniformly attained for a range of supercritical flow situations with shocks.     

本质正规算子的模C_2近似酉等价

本文刻划了本质正规算子模的近似酉等价，并且改进了Ｃａｒｒｙ和Ｐｉｎｃｕｓ在［１］中的一些结果。     

Weak Factorization Systems and Topological Functors

Weak factorization systems, important in homotopy theory, are related to injective objects in comma-categories. Our main result is that full functors and topological functors form a weak factorization system in the category of small categories, and that this is not cofibrantly generated. We also present a weak factorization system on the category of posets which is not cofibrantly generated. No such weak factorization systems were known until recently. This answers an open problem posed by M. Hovey.     

An ILU smoother for the incompressible Navier-Stokes equations in general co-ordinates

The solution of the incompressible Navier-Stokes equations in general two- and three-dimensional domains using a multigrid method is considered. Because a great variety of boundary-fitted grids may occur, robustness is at a premium. Therefore a new ILU smoother called CILU (collective ILU) is described, based on r-transformations. In CILU the matrix that is factorized is block-structured, with blocks corresponding to the set of physical variables. A multigrid algorithm using CILU as smoother is investigated. The performance of the algorithm in two and three dimensions is assessed by numerical experments. The results show that CILU is a good smoother for the incompressible Navier-Stokes equations discretized on general non-orthogonal curvilinear grids.     

Forced flexural-and-torsional vibrations of a cantilever beam of constant cross section

The paper addresses the forced flexural-and-torsional vibrations of a cantilever beam of constant cross section. The relevant boundary-value problem is solved. The system of two partial differential equations of the fourth order that describes these vibrations is analyzed in a vector-function space and is subjected to an equivalent transformation to obtain one vector equation of the fourth order with two matrices as coefficients. One is an idempotent matrix; the other is a diagonal matrix. This makes it much easier to construct a Cauchy vector function as an analytic function of these matrices __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 8, pp. 102–114, August 2007.     

Semiovals contained in the union of three concurrent lines

Semiovals which are contained in the union of three concurrent lines are studied. The notion of a strong semioval is introduced, and a complete classification of these objects in PG(2,p) and PG(2,p²), p an odd prime, is given. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 491–501, 2007