复合矩阵与伴随矩阵的关系及应用

本文给出了复合矩阵与伴随矩阵的一个关系式及其应用,并指出文［１］中给出的关系是错误的     

半单重特征值的条件数

此处θ(x_1,y_1)表示分别由x_1与y_1所张成的两个1维子空间之间的夹角.Wilkinson指出,s_1~(-1)的大小反映了λ_1对于A的元素的变化的敏感性程度,因此s_1~(-1)被叫做单特征值λ_1的条件数. 现设λ_1是A的半单m_1重特征值(即λ_1的初等因子均为线性),?_1与?_1分别     

一个不等式的进一步推广和加强

利用幂级数展式和凸函数的性质把关于一个不等式的推广和强化的两个最新结果推广到更加一般的情形p(p -1 ) d ap- 1pn+1-ap- 1pm <∑nk=m1a1pk相似文献   

一类组合不等式的简证与推广

利用概率方法给出了形如sum from k=1 to n(1/k)>π/4(sum from k=1 to n((-1)k-1Cnk)1/(k～1/2))与sum from k=1 to n(1/k)<2～(1/2)(sum from k=1 to n((-1)k-1Cnk)1/k2)1/2的组合不等式.     

Fibonacci和Lucas序列的混合卷积公式

通过Fibonacci序列和Lucas序列的生成函数,利用导函数的性质,得到了Fibonacci序列和Lucas序列构成的混合卷积∑a1+a2+…+ak+b1+b2+…+b1+c1+c2+…+cm=na1Fa1+1…akFak+1.Fb1…Fb1.Lc1+1…Lcm+1的计算公式.     

Extensions of the Kantorovich Inequality and the Bauer-Fike Inequality

This paper proves a Kantorovich-type inequality on the matrix of the type $\frac{1}{2}(Q^H_1 AQ_1 Q^H_1A^{-1} Q_1+Q^H_1A^{-1}Q_1Q^H_1AQ_1)$, where $A$ is an $n\times n$ positive definite Hermitian matrix and $Q_1$ is an $n\times m$ matrix with rank $(Q_1)=m$. The result is applied to get an extension of the Bauer-Fike inequality on condition numbers of similarities that block diagonalized matrices.     

THE GENERALIZED RIEMANN-HILBERT BOUNDARY VALUE PROBLEM FOR A SYSTEM OF SECOND ORDER QUASI-LINEAR ELLIPTIC EQUATIONS

In this paper, we consider the generalized Riemann-Hilberij problem for second order quasi-linear elliptic complex equation \[\begin{array}{l} \frac{{{\partial ^2}w}}{{\partial {{\bar z}^2}}} + {q_1}(z,w,\frac{{\partial w}}{{\partial \bar z}},\frac{{\partial w}}{{\partial z}})\frac{{{\partial ^2}w}}{{\partial {z^2}}} + {q_2}(z,w,\frac{{\partial w}}{{\partial \bar z}},\frac{{\partial w}}{{\partial z}})\frac{{{\partial ^2}\bar w}}{{\partial z\partial \bar z}}\{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} + {q_3}(z,w,\frac{{\partial w}}{{\partial \bar z}},\frac{{\partial w}}{{\partial z}})\frac{{{\partial ^2}w}}{{\partial z\partial \bar z}} + {q_4}(z,w,\frac{{\partial w}}{{\partial \bar z}},\frac{{\partial w}}{{\partial z}})\frac{{{\partial ^2}\bar w}}{{\partial z\partial \bar z}}{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} (1)\{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} + \gamma (z,w,\frac{{\partial w}}{{\partial \bar z}},\frac{{\partial w}}{{\partial z}}),z \in G \end{array}\] satifying the boundary condition \[{\mathop{\rm Re}\nolimits} \left[ {{{\bar \lambda }_1}(z)\frac{{\partial w}}{{\partial \bar z}}} \right] = {\gamma _1}(z),{\mathop{\rm Re}\nolimits} \left[ {{{\bar \lambda }_2}(z)\frac{{\partial w}}{{\partial \bar z}}} \right] = {\gamma _2}(z),z \in \gamma {\kern 1pt} {\kern 1pt} {\kern 1pt} (2)\] Many authors (see that papers 1, 4-6) have studied the Diriohlet problem and Riemann-Hilbert problem for linear elliptic complex equation. In our papers 2, 3 we also considered the generalized Riemann-Hilbert problem of the general second order linear elliptic complex equation. We obtained the existence theorem, the explicit form of generalized solution and the sufficient and necessary conditions for the solvability of the above mentioned boundary value problem. Based on these results and applying the property of the introduced integral operators and Schauder's fixed-point principle, it can be proved that the analogous deductions in 3 also hold for the generalized Riemann-Hilber problem (1), (2) of the quasi-linear complex equation, i, e., we have the following theorem: Theorem, If the coefficients of second order quasi-linear elliptic complex equation (1) satifies some conditions then i) When index \({n_1} \ge 0,{n_2} \ge 0\), the boundary value problem (1), (2) is always solvable and the solution depends on 2 \(2({n_1} + {n_2} + 1)\) arbitrary real constants. ii) When index \({n_1} \ge 0,{n_2} < 0{\kern 1pt} {\kern 1pt} {\kern 1pt} (or{\kern 1pt} {\kern 1pt} {\kern 1pt} {n_1} < 0,{n_2} \ge 0{\kern 1pt} )\), the sufficient and necessary condition for the solvability of the above mentioned boundary value problem (1),(2) consists of \( - 2{n_2} - 1{\kern 1pt} {\kern 1pt} {\kern 1pt} ( - 2n, - 1)\) real equalities, if and only if the equalities are satisfied, the boundary value problem is solvable and the solution depends on \(2{n_1} + 1{\kern 1pt} {\kern 1pt} (2{n_2} + 1)\) arbitrary real constants. iii)When index \({n_1} < 0,{n_2} < 0\), the sufficient and necessary condition for the solvability of the above mentioned boundary value problem (1) , (2) consists of \( - 2({n_1} + {n_2} + 1)\) real equalities, if and only if the equalitieis are satisfied, the boundary-value problem is solvable. Finally, in the similar way, we may farther extend the result to the case of the nonlinear uniform elliptic complex equation.     

p—级数与几个广义积分

本文给出了ｐ—级数与广义积分∫１０ｌｎｋ－１ｘ１－ｘｄｘ，∫１０ｌｎｋ－１ｘ１＋ｘｄｘ，∫１０ｌｎｋ－１ｘ１－ｘ２ｄｘ，∫１０ｌｎｋ－１ｘ１＋ｘ２ｄｘ之间的关系．并通过一些ｐ—级数的求和，给出了上述广义积分中某些积分的积分值．     

Regularity for weakly (K1, K2)-quasiregular mappings

In this paper, we first give the definition of weakly (K1, K2)-quasiregular mappings, and then by using the Hodge decomposition and the weakly reverse Holder inequality, we obtain their regularity property: For any ql that satisfies 0 < K1n(n+4)/22n+1 × 100n2[23n/2(25n + 1)](n - q1) < 1, there exists p1 = p1(n, q1, K1, K2) > n, such that any (K1, K2)-quasiregular mapping f ∈W(loc)(1,q1)(Ω,Rn) is in fact in W(loc)(1,p1)(Ω,Rn). That is, f is (K1, K2)-quasiregular in the usual sense.     

关于Hardy不等式的加强改进

对 Hardy不等式 ,建立如下结构的加强不等式 :∑∞n=11n∑nk=1akp 1 ,an≥ 0 (n∈ N) ,0 <∑∞n=1apn<∞ ,Cp=1 -(1 -p- 1) p- 1,p≥ 2 ;1 -p- 1,1 相似文献   

FLAT TIME-LIKE SUBMANIFOLDS IN ANTI-DE SITTER SPACE H_1~(2n-1) (-1)

By using dressing actions of the G(n1,n-1)1,1-system, the authors study geometric transformations for flat time-like n-submanifolds with flat, non-degenerate normal bundle in anti-de Sitter space H1(2n-1)(-1), where G(n-1,n-1)1,1 = O(2n - 2, 2)/O(n - 1,1)×O(n-1, 1).     

Generalized GM (1, 1) model and its application in forecasting of fuel production

Grey theory is one approach that can be used to construct a model with limited samples to provide better forecasting advantage for short-term problems. Generally, the GM (1, 1) and Discrete GM (1, 1) models are two typical grey forecasting models in grey theory. However, there are two shortcomings in the above grey models respectively, i.e., the homogeneous-exponent simulative deviation in GM (1, 1) model, and the unequal conversion between the original and white equations in DGM (1, 1) model. In this paper, we firstly propose a novel Generalized GM (1, 1) model termed GGM (1, 1) model, based on GM (1, 1) and DGM (1, 1) models, to overcome the above shortcomings. Then, we detailedly study four important properties in this new grey model. Four estimative approaches of stepwise ratio in GGM (1, 1) model context is also covered. In the end, we simulate and forecast the fuel production in China during the period 2003–2010 using three GM (1, 1) models. The empirical results show that GGM (1, 1) model has higher simulative and predictive accuracy than GM (1, 1) and DGM (1, 1) models. This work contributes significantly to improve grey forecasting theory and proposes a optimized GM (1, 1) model.     

Partial Decidable Presentations in Hyperarithmetic

Siberian Mathematical Journal - We study the problem of the existence of decidable and positive $$\Pi_1^1$$ - and $$\Sigma_1^1$$ -numberings of the families of $$\Pi_1^1$$ - and $$\Sigma_1^1$$...     

Pm‖Cmax问题的算法AKK的一个改进的最坏情况性能比

本文考虑的是平行机排序问题Pm‖Cmax.对此问题Knuth和Kleitman给出了一个近似算法AKK,Graham证明了此算法的最坏情况性能比不大于1＋1-1/m/1＋｜k/m｜,而且当k≡0（modm）时这个界是紧的.在本文中我们给出了此算法的一个改进的最坏情况性能比： 1＋max{1-1/m/1＋k1＋1/m,1-1/m-k2/1＋k1},其中k1和k2为非负整数且k1m＋k2=k.本文证明了当k2≠0时,它好于Graham的结果,同时我们给出了两个实例说明这个界是紧的.     

四元数矩阵积的特征值与奇异值的不等式

运用优化不等式理论和四元数体上的几何理论 ,得到了四元数矩阵积的特征值与奇异值的几个不等式 .     

On 𝔬𝔰𝔭(1 | 2)-Relative Cohomology on S 1|1

We compute the second 𝔬𝔰𝔭(1 | 2) ?relative cohomology space of 𝒦(1) with coefficients in the module of λ-densities 𝔉_λ on S ^1|1. This result allows us to compute the second 𝔬𝔰𝔭(1 | 2) ?relative cohomology space of 𝒦(1) with coefficients in the Poisson superalgebra 𝒮𝒫. We explicitly give 2-cocycles spanning these cohomology spaces.     

SYMMETRIC AND ASYMMETRIC DIOPHANTINE APPROXIMATION

§1. Introduction Let ξbe an irrational number with simple continued fraction expansion ξ= [a0;a1,···,ai,···]and pi be its ith convergent. In [1], the present author considered the well-known inequality q     

A generalization of Ryser's theorem on term rank

In his work on classes of (0, 1)-matrices with given row and column sum vectors, Herbert Ryser proved that the maximum term rank possible in a normalized class, ρ, can be realized by a matrix having ρ (independent) 1's in positions (1, ρ), (2, ρ − 1), … , (ρ, 1). We study the positions occupied by sets of t ρ independent 1's.     

復式乘積和球面乘積的關係

<正> 1.設X為一拓撲空間,以a_i表示X的n_i次同偷羣∏_(ni)(X)的一個元素.在球面乘積S~(n1)×…×S~(nr)中,最高次元的腔胞記為e~(n1+…+nr).在S~(n1)×…×S~(nr)中除去e~(n1+…+nr)而得一空間Y.設S~(nl)為nl次元球,為了印刷方便起見,把S~(nl)記作S(nl).在S(ni)中取一參考點x_i~o.設i_1相似文献   

Limit cycles of a lienard cubic system with quadratic friction function

We consider a Lienard cubic system with quadratic friction function and suggest a method for constructing such systems with the following distributions of limit cycles around the singular points: ((2, 0), 0), ((0, 2), 0), ((1, 1), 1), ((1, 1), 0), ((1, 0), 1), ((0, 1), 1), ((0, 0), 2), ((0, 1), 2), and ((1, 0), 2).