对称凸集上初等对称函数为Schur-凹的充要条件

设x,y∈Rⁿ,x被y所控制记作x(?)y。又w∈Rⁿ,令S_k(x)为第k个初等对称函数。Q_m,n为前n个自然数取m个的严格增序列的集合。对于β∈Q_m,n写w_β=(W_{^β(1),…,WB(m)}∈R^m。本文主要证明了下面的结论:(1)S_k(x)在(?)_w上是Schur-凹的充要条件是(2)S_k(x)≥0,(?)x∈(?)_w的充要条件是S_k(w)≥0且S_k(x)在(?)_w上是Schur-凹的(3)S_k(x)≥0,(?)x∈(?)的充要条件是     

一个特殊的二项系数

利用发生函数和矩阵方法,研究了一个特殊的二项式系数[n λ n-k]和它所构成的矩阵.得到以[n λ n-k]为矩阵元素的Pascal型矩阵的指数分解和乘积分解公式.同时,考察了与二项式型多项式相伴的函数矩阵Pn,λ[x]及其性质.     

具有二项式型多项式下三角矩阵的性质

n 1阶下三角方阵Ln[x]定义为:(Ln[x])ij=(?)i-j(x)l(i,j)(如果i≥j),否则为0,且满足条件l(i,k)l(k,j)=l(i,j)(k-j i-j)和 ,即二项式型多项式函数矩阵.n 1阶方阵Ln定义为:当i≥j时,(Ln)ij=l(i,j),否则为0.本文研究了比Pascal函数矩阵及Lah矩阵更广泛的一类矩阵Ln[x]与Ln,得到了更一般的结果和一些组合恒等式.     

拟线性抛物方程组第一边界问题的有限差分法 ——Ⅲ.稳定性

讨论如下拟线性抛物组第一边值问题的显式、弱隐式和强隐式差分解u_t=(-1)^M+1A(x,t,u,…,u_x^M-1)u_x^2M+f(x,t,u,…,u_x^2M-1(x,t)∈Q_T={O<x<l,0<t≤T.}，u_x^k(0，t)=u_x^k(l，t)=0 (k=0，1，…，M -1)，0<t≤T，u(x，0)=φ(x)，0≤x≤l，其中u，φ和f是m维向量值函数，A是m×m正定矩阵，u_t=∂u/∂t，u_x^k=∂^ku/∂x^k.在以下意义下证明了该问题的一般有限差分格式的稳定性：即离散向量解在W₂^(2M，M)(Q_T)中的离散范数是连续地依赖于初始数据的H^M离散范数，以及矩阵A与自由项f的相应的离散范数.     

三角域上Bernstein多项式的Lipschitz常数

设T是平面上以T₁,T₂,T₃为顶点的三角形,f(p)为定义在T上的函数,称Bⁿ(f,P):=(?)f(i/n,j/n,k/n)B_i,j,kⁿ(P),为f的n次Bernstein多项式,这儿B_i,j,kⁿ(P):(n!)/(i!j!k!)uⁱv^jω^k是Bernstein基函数,(u,v,w)是P关于T的重心坐标。 B.M.Brown等人对单变量的Bernstein多项式证明了如果f∈Lip_Aλ,0<λ≤1,则对所有的n,都有B^α(f,x)∈Lip_Aλ。本文的目的是对定义在三角域T:{(x,y):x≥0,y≥0,x+y≤1}上的Bernstein多项式证明了类似的结果: 设f(P)∈Lip_Aλ,0<λ≤1,则对所有的n,Bⁿ(f,P)∈Lip_(2^1/2λA)λ,并且,在一定意义上,常数2^1/2λA是最好的。 上述结果对于任意的锐角或直角三角形T,也是成立的。 最后还指出,当T可为钝角三角形时,则不存在同一常数C,使对所有的n和任意三角形T,有Bⁿ(f,P)∈Lip_cλ。     

两类下三角形Pascal矩阵的相似性

本文研究了Pascal矩阵与位移Pascal矩阵之间的关系.利用组合恒等式与矩阵分解的方法,得到了Pascal矩阵以及位移Pascal矩阵与若当标准型之间的过渡矩阵.同时也得到了这两类矩阵在域Zp上的最小多项式.     

低于临界阶的Riesz球形平均的一类极大函数

设S_R^δ(f)(x)为f(x)的k维Fourier级数的δ阶Riesz球形平均,{R_j}₁^∞为Hadamard缺项序列。本文建立了关于极大算子的两个不等式:和此处0a/2。作为推论,得到:L²(Q_k)中函数的Fourier级数球形部份和的缺项序列a. e. 收敛。     

半质环交换性的一点注记

Let R be a semi-prime ring, C be the center of R. Let F_i (x, y) (i = 1, 2) be a product of the m times x's and n times y's.In this paper following theorem is proved: (I ) implies (Ⅱ), where( Ⅰ )If f₁(x,y) -f₂(x,y) ∈C for every x,y in R, then R is commutative;(Ⅱ)If f₁ (x,y) + f₂(x, y) ∈C for every x,y in R, then R is commutative.Thus very short proves of some theorems of references[5], [8], [9] are be given.     

有相间质量交换的悬浮体两相流基本方程

本文针对悬浮体两相流,经过分柝推导,将Ishii用对无限多个间断求和表示的、一般形式的相间动量交换率M_k和能量交换率E_k简化为有简明物理意义的几项之和。结果表明:(1)各相动量方程中与压强梯度有关的项是(—α_k▽p),它可由基本守恒原理导出,不必引入“压力分担假设”;(2)相间阻力作用点的平均速度是相界面移动的平均速度,它近似等于离散相的平均速度,因此阻力做功项分别是f_dc·和f_cd·,而不能用流体平均速度;(3)类似地,相变带给各相的动量分别是和,不能用;(4)由于相变过程伴随着显热与潜热之间的转换,因此相间传热Q_dc与Q_cd的代数和不等于零,代表显热与潜热总和的Q_ic和Q_id,它们的和(Q_ic+Q_id)等于零。     

Pascal三角形与Pascal矩阵

Pascal三角形中隐含着二项系数的许多相关性质 .本文从线性代数的观点研究了 Pascal矩阵的性质及其应用 ,并将这种矩阵推广到了更一般的形式     

Pascal k-elminated functional matrix and eulerian numbers

In this paper we shall first introduce the Pascal k-eliminated functional matrices P_n,k [x y z] and CP_n,k [x y z]. Then, using these matrices we obtain several important combinatorial identities. Finally, using the matrix inversion of P_n,k [x y z] and CP_n,k [x y z], we derive an interesting formula for Eulerian numbers [7]     

Pascal算子矩阵在组合恒等式中的应用

定义了四种Pascal算子矩阵,给出了它们的代数性质及它们之间的关系,并且利用二项式型多项式序列、算子及哑运算得到许多组合恒等式.     

Pascal算子矩阵在组合恒等式中的应用(英文)

定义了四种Pascal算子矩阵,给出了它们的代数性质及它们之间的关系,并且利用二项式型多项式序列、算子及哑运算得到许多组合恒等式.     

Jordan canonical form of Pascal-type matrices via sequences of binomial type

In this paper, we study the Jordan canonical form of the generalized Pascal functional matrix associated with a sequence of binomial type, and demonstrate that the transition matrix between the generalized Pascal functional matrix and its Jordan canonical form is the iteration matrix associated with the binomial sequence. In addition, some combinatorial identities are derived from the corresponding matrix factorization.     

Reflecting the pascal matrix about its main antidiagonal

Let B denote either of two varieties of order n Pascal matrix, i.e., one whose entries are the binomial coefficients. Let B_R denote the reflection of B about its main antidiagonal. The matrix B is always invertible modulo n; our main result asserts that B^-1 ≡ B^R mod n if and only if n is prime. In the course of motivating this result we encounter and highlight some of the difficulties with the matrix exponential under modular arithmetic. We then use our main result to extend the "Fibonacci diagonal" property of Pascal matrices.     

Reflecting the pascal matrix about its main antidiagonal

Let B denote either of two varieties of order n Pascal matrix, i.e., one whose entries are the binomial coefficients. Let B_R denote the reflection of B about its main antidiagonal. The matrix B is always invertible modulo n; our main result asserts that B^-1 ≡ B^R mod n if and only if n is prime. In the course of motivating this result we encounter and highlight some of the difficulties with the matrix exponential under modular arithmetic. We then use our main result to extend the "Fibonacci diagonal" property of Pascal matrices.     

Some combinatorial identities via Fibonacci numbers

The Pascal matrix and the Stirling matrices of the first kind and the second kind obtained from the Fibonacci matrix are studied, respectively. Also, we obtain combinatorial identities from the matrix representation of the Pascal matrix, the Stirling matrices of the first kind and the second kind and the Fibonacci matrix.     

Pascal k-elminated functional matrix and eulerian numbers

In this paper we shall first introduce the Pascal k-eliminated functional matrices P_n,k[xyz] and CP_n,k[xyz]. Then, using these matrices we obtain several important combinatorial identities. Finally, using the matrix inversion of P_n,k[xyz] and CP_n,k[xyz], we derive an interesting formula for Eulerian numbers [7]