逆差商的一个紧凑行列式表示

本文给出了逆差商的一个紧凑行列式表示,从该表示式易知,一个函数在某ｎ＋１个点的ｎ阶逆差商与这些点的排序有关,但与前ｎ－１个点的局部换序无关．此外,还从另一角度定义倒差商,得出了倒差商与逆差商之间的关系以及倒差商的整体换序无关性．     

垂直密度表示及其应用

该文论述了Vertical Density Representation (VDR)的历史发展, 现状及其在随机数生成, 多元密度构造等领域的应用及在非正态多元统计分析的潜在应用.     

Representation of Continuous Functions and Its Applications

In this work, we introduce a Representation of continuous real-valued functions defined over a real Hilbert space. As a consequence, we can introduce a Sandwich Theorem for semi-continuous functions, a Separation Theorem for closed sets and a representation Theorem of lower semi-continuous functions.     

结构矩阵的三角表示及其应用

利用位移铁和交换Hessenberg矩阵代数给出结构矩阵的三角表示,并讨论在Toeplitz矩阵和Toeplitz Hankel矩阵方面的应用。     

范畴的K—根与Jacobson结构定理

本文得到三方面结果：（1）定义加法范畴的K－根，给出它的模刻划式。（2）给出J－根的内部刻划。（3）给出J－半单范畴结构中由本原范畴组成的完全同态象类的具体形式和范畴为J－半单范畴的充要条件。     

稀疏表示及其在人脸识别中的应用

稀疏表示是近年来新兴的一种数据表示方法,是对人类大脑皮层编码机制的模拟。稀疏表示以其良好的鲁棒性、抗干扰能力、可解释性和判别性等优势,广泛应用于模式识别领域。基于稀疏表示的分类器在人脸识别领域取得了令人惊喜的成就,它将训练样本看成字典,寻求测试样本在字典下的最稀疏的表示,即用尽可能少的训练样本的线性组合来重构测试样本。但是经典的基于稀疏表示的分类器没有考虑训练样本的类别信息,以致被选中的训练样本来自许多类,不利于分类,因此基于组稀疏的分类器被提出。组稀疏方法考虑了训练样本的类别相似性,其目的是用尽可能少类别的训练样本来表示测试样本,然而这类方法的缺点是同类的训练样本或者同时被选中或者同时被丢弃。在实际中,人脸受到光照、表情、姿势甚至遮挡等因素的影响,样本之间关系比较复杂,因此最后介绍局部加权组结构稀疏表示方法。该方法尽量用来自于与测试样本相似的类的训练样本和来自测试样本邻域的训练样本来表示测试样本,以减轻不相关类的干扰,并使得表示更稀疏和更具判别性。     

Schubert修正的紧凑形式

在本文中我们推导出了Schubert修正的紧凑形式,该紧凑形式保留了Schubert修正的稀疏传递性,还可使我们利用有记忆算法有效的求解一定的非线性方程组。     

Modular Sesquilinear Forms and Generalized Stinespring Representation

We consider completely positive maps defined on locally C*-algebra and taking values in the space of sesquilinear forms on Hilbert C*-module M. We construct the Stinespring type representation for this type of maps and show that any two minimal Stinespring representations are unitarily equivalent.     

A Level Set Representation Method for N-Dimensional Convex Shape and Applications

In this work,we present a new method for convex shape representation,which is regardless of the dimension of the concerned objects,using level-set approaches.To the best of our knowledge,the proposed prior is the first one which can work for high dimensional objects.Convexity prior is very useful for object completion in computer vision.It is a very challenging task to represent high dimensional convex objects.In this paper,we first prove that the convexity of the considered object is equivalent to the convexity of the associated signed distance function.Then,the second order condition of convex functions is used to characterize the shape convexity equivalently.We apply this new method to two applications:object segmentation with convexity prior and convex hull problem(especially with outliers).For both applications,the involved problems can be written as a general optimization problem with three constraints.An algorithm based on the alternating direction method of multipliers is presented for the optimization problem.Numerical experiments are conducted to verify the effectiveness of the proposed representation method and algorithm.     

Elementary Theories for Rogers Semilattices

It is proved that for every level of the arithmetic hierarchy, there exist infinitely many families of sets with pairwise non-elementarily equivalent Rogers semilattices.Supported by INTAS grant No. 00-499.__________Translated from Algebra i Logika, Vol. 44, No. 3, pp. 261–268, May–June, 2005.     

Matrix Representation of Recursive Sequences of Order $3$ and Its Applications

Here presented is a matrix representation of recursive number sequences of order $3$ defined by $a_n=pa_{n-1}+qa_{n-2}+ra_{n-3}$ with arbitrary initial conditions $a_0,$ $a_1=0$, and $a_2$ and their special cases of Padovan number sequence and Perrin number sequence with initial conditions $a_0=a_1=0$ and $a_2=1$ and $a_0=3$, $a_1=0$, and $a_2=2$, respectively. The matrix representation is used to construct many well known and new identities of recursive number sequences as well as Pavodan and Perrin sequences.     

随机变量和的模函数分布及其应用

介绍了一个在计算机科学、信息科学等学科中具有广泛应用的随机变量和的模函数,计算了其分布,并提供了该函数在图像信息安全领域的一个应用例子,验证了理论结果.     

Esakia Style Duality for Implicative Semilattices

We develop a new duality for implicative semilattices, generalizing Esakia duality for Heyting algebras. Our duality is a restricted version of generalized Priestley duality for distributive semilattices, and provides an improvement of Vrancken-Mawet and Celani dualities. We also show that Heyting algebra homomorphisms can be characterized by means of special partial functions between Esakia spaces. On the one hand, this yields a new duality for Heyting algebras, which is an alternative to Esakia duality. On the other hand, it provides a natural generalization of Köhler’s partial functions between finite posets to the infinite case.     

Phantom Maps and Purity in Modular Representation Theory, II

In the second part of this paper, we use the theory described in the first part to construct an example of a counterintuitive phenomenon. We show how to produce examples of filtered systems in the stable module category stmod(kG) which do not lift to filtered systems in the module category mod(kG). Our main tool is the Extended Milnor Sequence, a five-term exact sequence which specializes to the classical Milnor sequence under certain countability conditions.     

模糊数的一种新运算方法及其若干应用

首先给出了模糊数的一种新的函数表示定理;基于该表示定理 ,提出了模糊数的一种新运算方法并将其直接应用到模糊数理论中若干问题的讨论,包括:模糊数的差问题,绝对值问题以及模糊数的确界问题 .     

范德蒙行列式的新证明及其应用

首先给出范德蒙行列式的一个新的证明,与以前的证明相比,本文给出的证明更具有通用性．其次介绍范德蒙行列式在n阶行列式计算和在向量组线性相关性证明中的两个应用．     

Galois Theory of Thick Subcategories in Modular Representation Theory

D. J. Benson, J. F. Carlson, and J. Rickard [1997, Fund. Math.153, 59–80] classified the tensor-closed thick subcategories of finite-dimensional representations of finite groups over algebraically closed fields. In this paper, we remove the algebraically closed hypothesis by applying some Galois theory. Our methods apply more generally to finite-dimensional cocommutative Hopf algebras over a field. Thus they allow us to drop the algebraically closed hypothesis in the classification of thick subcategories of modules over finite-dimensional sub-Hopf algebras of the Steenrod algebra as well.