Theoretical analysis on convergence behavior of rank filters

This paper systematically studies the convergence behavior of rank filters. The problem of convergence behavior of rank filters has been solved completely for bounded sequences. Moreover, some properties of its limiting sequences and recurrent sequences are obtained.     

我国普通高等教育发展水平的全局主成分分析

本文根据 1995年、1997年和 1999年共同构成的关于我国普通高等教育发展水平的时序立体数据表 ,通过全局主成分分析得到公共主成分子空间L(F1,F2 ,… ,Fm) ,并在该子空间对我国高等教育发展背景和现状进行统计分析 ,给出了排名和变化趋势。     

Abel范畴中态射乘积诱导的短正合列及其应用

本文给出了Ａｂｅｌ范畴中态射乘积αβγ诱导的短正合列的立体交换图。其中共有７个３×３平面，３０条线。每一条线（两端的零对象省略）都是一个短正合列．这些短正合列用到ｐ－除环上的矩阵，可以导出一系列矩阵秩的恒等式，它不仅推广了域上矩阵秩的结果，还能得到一些新的关系式．     

Cleft extensions of a family of braided Hopf algebras

We introduce a family of braided Hopf algebras that (in characteristic zero) generalizes the rank 1 Hopf algebras introduced by Krop and Radford and we study its cleft extensions.     

On a family of 2-automatic sequences generating algebraic continued fractions in characteristic 2

We present family of automatic sequences that define algebraic continued fractions in characteristic 2. This family is constructed from ultimately period words and contains the period-doubling sequence.     

关于三幂等矩阵的秩特征的研究

本文对已有的关于三幂等矩阵秩的等式作了进一步研究，指出其中有些可以作为判定三幂等矩阵的充要条件，即三幂等矩阵的秩特征等式，本文还证明了有无穷多种三幂等矩阵的秩特征等式形式．     

上三角矩阵代数上的可加保极小秩映射

The additive mappings that preserve the minimal rank on the algebra of all n × n upper triangular matrices over a field of characteristic 0 are characterized.     

关于格的卡氏积的特征多项式和几何性

利用格L_i(i=1,2)的性质研究了它们的卡氏积L=L_1×L_2的性质,得到了L的秩函数、Mbius函数和特征多项式,并且由L_i的几何性证明了L的几何性.     

关于具有限秩的可解群

关于具有限秩的可解群本文得到了它的正规列的交换商因子的一种排序,推出了这类群的所有拟循环了群构成它的一个特征子群,了秩ｎ的可解群的Ｈｉｒｓｃｈ不变量≤ｎ,并由此界定了秩ｎ的无挠可解群的导出长度。     

Rank theorems of operators between Banach spaces

Let E and F be Banach spaces, and B(E,F) all of bounded linear operators on E into F. Let T0∈B(E,F) with an outer inverse T#0∈B(F,E). Then a characteristic condition of S=(I+T#0(T-T0))-1T#0 with T∈B(E,F) and ‖T#0(T-T0)‖<1, being a generalized inverse of T, is presented, and hence, a rank theorem of operators on E into F is established (which generalizes the rank theorem of matrices to Banach spaces). Consequently, an improved finite rank theorem and a new rank theorem are deduced. These results will be very useful to nonlinear functional analysis.     

Investigations of c-differential uniformity of permutations with Carlitz rank 3

The c-differential uniformity is recently proposed to reflect resistance against some variants of differential attack. Finding functions with low c-differential uniformity is attracting attention from many researchers. For even characteristic, it is known that permutations of low Carlitz rank have good cryptographic parameters, for example, low differential uniformity, high nonlinearity, etc. In this paper we show that permutations with low Carlitz rank have low c-differential uniformity. We also investigate c-differential uniformity of permutations with Carlitz rank 3 in detail.     

秩为1矩阵的性质及应用

给出了秩1矩阵的结构,讨论了这类矩阵在矩阵运算、对角化、标准型等方面的性质,推广和改进了文[1]的一些相关结果,并指出了它的若干应用,重点讨论了一类矩阵,得到了有关结论和方法.     

On the Generation of Some Embeddable GF(2) Geometries

The generating rank is determined for several GF(2)-embeddable geometries and it is demonstrated that their generating and embedding ranks are equal. Specifically, we prove that each of the two generalized hexagons of order (2, 2) has generating rank 14, that the central involution geometry of the Hall-Janko sporadic group has generating rank 28, and that the dual polar space DU(6,2) has generating rank 22. We also include a survey of all instances in which either the generating or embedding rank of an embeddable GF(2) geometry is known.     

Asymptotic Bound on the Characteristic Function of Signed Linear Serial Rank Statistics

This work establishes an asymptotic bound on the characteristic function of signed linear serial rank statistics. The result is obtained under rather general conditions including the important case of van der Waerden scores. It generalizes the result of Seoh (1983, Ph.D. Thesis, Department of Mathematics, Indiana University) and constitutes an essential step to the elaboration of Berry-Esséen's bounds and the establishment of Edgeworth expansions. These statistics constitute a natural tool for testing the hypothesis of white noise with a symmetrical (unspecified) distribution in comparison to other alternative hypothesis of serial dependence.     

Method of elementary transformation to compute Moore-Penrose inverse

Method of elementary transformation to compute Moore-Penrose inverse is given by applying the rank equalities of matrix. The inheritable properties of Moore-Penrose inverse on rank are also discussed.     

Bounded rank of C-algebras

We introduce a concept of the bounded rank (with respect to a positive constant) for unital C^*-algebras as a modification of the usual real rank and present a series of conditions insuring that bounded and real ranks coincide. These observations are then used to prove that for a given n and K>0 there exists a separable unital C^*-algebra Z_n^K such that every other separable unital C^*-algebra of bounded rank with respect to K at most n is a quotient of Z_n^K.     

半群O_n(k)的秩

设O_n是有限链[n]上的保序变换半群.对任意1≤k≤n-1,研究半群O_n(k)={α∈O_n:(x∈[n]x≤k→xα≤k}的秩和幂等元秩,证明了半群O_n(k)的秩为2n-3.进一步,得到了半群O_n(k)(2≤k≤n-1)的幂等元秩为n和半群O_n(1)的幂等元秩为n-1.     

Kapranov rank vs. tropical rank

We show that determining Kapranov rank of tropical matrices is not only NP-hard over any infinite field, but if solving Diophantine equations over the rational numbers is undecidable, then determining Kapranov rank over the rational numbers is also undecidable. We prove that Kapranov rank of tropical matrices is not bounded in terms of tropical rank, answering a question of Develin, Santos, and Sturmfels.

     

Some theoretical limitations of second-order algorithms for smooth constrained optimization

In second-order algorithms, we investigate the relevance of the constant rank of the full set of active constraints in ensuring global convergence to a second-order stationary point under a constraint qualification. We show that second-order stationarity is not expected in the non-constant rank case if the growth of so-called tangent AKKT2 sequences is not controlled. Since no algorithm controls their growth, we argue that there is a theoretical limitation of algorithms in finding second-order stationary points without constant rank assumptions.