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。     

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.     

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.     

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.     

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.     

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．     

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 .     

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.     

零维代数簇的分解及其应用

本文利用Groebner基，给出了一种分解零维代数簇的方法，并且讨论了这种方法在理想的准素分解以及几何定理机器证明中的应用．     

一类对称函数的Schur凸性及其应用

给出一类对称函数 Schur凸性的推广 ,运用该结果并结合控制不等式理论建立若干对称函数不等式及 n维欧氏空间 En中的单形不等式 ,所得结果是以往某些结果的推广或补充 .     

倒向随机微分方程生成元的表示定理及其应用

本文建立了关于局部L2-有界的倒向随机微分方程生成元的表示定理,此定理推广了Co-quet等人的一个结果.应用该定理,本文给出了倒向随机微分方程的生成元是凹生成元的一个充分必要条件.     

Modular Representation Theory of Blocks with Trivial Intersection Defect Groups

We show that Uno's refinement of the projective conjecture of Dade holds for every block whose defect groups intersect trivially modulo the maximal normal p-subgroup. This corresponds to the block having p-local rank one as defined by Jianbei An and Eaton. An immediate consequence is that Dade's projective conjecture, Robinson's conjecture, Alperin's weight conjecture, the Isaacs–Navarro conjecture, the Alperin–McKay conjecture and Puig's nilpotent block conjecture hold for all trivial intersection blocks. Presented by A. Verschoren Mathematics Subject Classification (2000) Primary 20C20. Charles W. Eaton: Current address: School of Mathematics, University of Manchester, Sackville Street, PO Box 88, Manchester M60 1QC, U.K. e-mail: charles.eaton@manchester.ac.uk This research was supported in part by the Marsden Fund of New Zealand via grant #9144/3368248.     

一个积分不等式及其应用

给出了一个新的积分不等式及其应用.