Carathéodory - Fejér Problem for Pairs of Meromorphic Functions

We continue our study of families of pairs of matrix-valued meromorphic functions P(ρ,P) depending on two parameters p and P introduced in [2]. These include as special cases the projective Schur, Nevanlinna and Carathéodory classes. A two sided Carathéodory Fejér interpolation problem is defined and solved in P(ρ,P), using the fundamental matrix inequality method. A corresponding Schur algorithm is studied. Finally we also consider the case of functions (as opposed to pairs).     

发展型Navier-Stokes方程基于压力稳定化方法的谱逼近格式

本文采用压力稳定化方法近似模拟不可压缩条件,进而构造了发展型非周期NavierStokes方程的全离散Legendre谱逼近计算格式,严格分析了格式的广义稳定性与收敛性．本文建立的逼近结果也适用其它非周期问题．     

Sasaki空间型M-2n+1(c)中的极小积分子流形

本文重新给出了Ｓａｓａｋｉ空间型中极小积分子流形的关于Ｒｉｃｉ曲率的内蕴刚性定理,它改进了［２］及［３］中的有关定理,而且取消了［３］中关于维数的限制．对３维极小积分子流形,又给出了一个关于数量曲率的内蕴刚性定理．     

Legendre transform of the noninteracting kinetic energy: Especially from March–Murray perturbation theory based on plane waves

The Legendre transform of the noninteracting kinetic energy is derived from the March–Murray perturbation theory based on plane waves. Further useful relations are summarized, and it is shown that insight can be gained from simple model systems where nonperturbative equations can be derived. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 138–142, 2001     

高阶奇异积分的小波逼近及数值计算

该文所讨论的是在Ｈａｄａｍａｒｄ主值意义下，高阶奇异积分（犛犳）（狋）＝∫ 犳（狓）（狓－狋）狀＋１ｄ狓，　　狀≥１的小波逼近及数值计算．特别是当小波函数未知时，借助于方程（３．１），对高阶奇异积分作数值计算，建立了收敛性定理．     

On the derivative of the associated Legendre function of the first kind of integer degree with respect to its order (with applications to the construction of the associated Legendre function of the second kind of integer degree and order)

The derivative of the associated Legendre function of the first kind of integer degree with respect to its order, , is studied. After deriving and investigating general formulas for μ arbitrary complex, a detailed discussion of , where m is a non-negative integer, is carried out. The results are applied to obtain several explicit expressions for the associated Legendre function of the second kind of integer degree and order, . In particular, we arrive at formulas which generalize to the case of (0 ≤ m ≤ n) the well-known Christoffel’s representation of the Legendre function of the second kind, Q _n (z). The derivatives and , all with m > n, are also evaluated.     

Meson contributions in the Nambu-Jona-Lasinio model

We discuss the problem of calculating corrections to the mean-field approximation in the Nambu-Jona-Lasinio model. To calculate such corrections, we propose using the method of the Legendre transformation with respect to a bilocal source, which allows taking symmetry constraints related to the chiral Ward identity into account effectively. Using the proposed method, we determine the corrections to the quark propagator and the two-particle quark function. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 159, No. 1, pp. 81–95, April, 2009.     

Legendre polynomial solutions of high-order linear Fredholm integro-differential equations

In this study, a Legendre collocation matrix method is presented to solve high-order Linear Fredholm integro-differential equations under the mixed conditions in terms of Legendre polynomials. The proposed method converts the equation and conditions to matrix equations, by means of collocation points on the interval [−1, 1], which corresponding to systems of linear algebraic equations with Legendre coefficients. Thus, by solving the matrix equation, Legendre coefficients and polynomial approach are obtained. Also examples that illustrate the pertinent features of the method are presented and by using the error analysis, the results are discussed.