On the structure of generalized symmetric spaces of SLn𝔽q)

In this paper we extend previous results regarding SL₂(k) over any finite field k by investigating the structure of the symmetric spaces for the family of special linear groups SL_n(k) for any integer n>2. Specifically, we discuss the generalized and extended symmetric spaces of SL_n(k) for all conjugacy classes of involutions over a finite field of odd or even characteristic. We characterize the structure of these spaces and provide an explicit difference set in cases where the two spaces are not equal.     

The Smooth Representations of GL2(𝔒)

We give a classification of the smooth (complex) representations of GL₂(𝔬), where 𝔬 is the ring of integers in a non-Archimedean local field. The approach is based on Clifford theory of finite groups and a corresponding study of orbits and stabilizers. In terms of this classification, we identify the representations which are geometrically or infinitesimally induced, respectively.     

A New Characterization of PSL(p,q)

Abstract

Order components of a finite group are introduced in Chen [Chen, G. Y. (1996c) On Thompson's conjecture. J. Algebra 185:184–193]. It was proved that PSL(3, q), where q is an odd prime power, is uniquely determined by its order components [Iranmanesh, A., Alavi, S. H., Khosravi, B. (2002a). A characterization of PSL(3, q) where q is an odd prime power. J. Pure Appl. Algebra 170(2–3): 243–254]. Also in Iranmanesh et al. [Iranmanesh, A., Alavi, S. H., Khosravi, B. (2002b). A characterization of PSL(3, q) where q = 2 ⁿ . Acta Math. Sinica, English Ser. 18(3):463–472] and [Iranmanesh, A., Alavi, S. H. (2002). A characterization of simple groups PSL(5, q). Bull. Austral. Math. Soc. 65:211–222] it was proved that PSL(3, q) for q = 2 ⁿ and PSL(5, q) are uniquely determined by their order components. In this paper we prove that PSL(p, q) can be uniquely determined by its order components, where p is an odd prime number. A main consequence of our results is the validity of Thompson's conjecture for the groups under consideration.     

Fixed Point Theorems for (p,q)-Quasi-Contraction Mappings in Cone Metric Spaces

In this work, the authors introduce the concept of $(p,q)$-quasi-contraction mapping in a cone metric space. We prove the existence and uniqueness of a fixed point for a $(p,q)$-quasi-contraction mapping in a complete cone metric space. The results of this paper generalize and unify further fixed point theorems for quasi-contraction, convex contraction mappings and two-sided convex contraction of order $2$.     

On the 𝔉‐hypercentre of a finite group

The main objective of this paper is to study and describe the hypercentre of a finite group associated with saturated formations, in terms of some subgroup embedding properties related to permutability. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Discrete Series Characters for GL(n, q)

The discrete series characters of the finite general linear group GL(n, q) are expressed as uniquely defined integral linear combinations of characters induced from linear characters on certain subgroups Hd, n of GL(n, q). The coefficients in these linear combinations are determined (for all n, q) by a family of polynomials r(T) Z[T] indexed by the set of all partitions .     

Quasi-Deformations of 𝔰𝔩2(𝔽) Using Twisted Derivations

In this article we apply a method devised in Hartwig, Larsson, and Silvestrov (2006 Hartwig , J. T. , Larsson , D. , Silvestrov , S. D. ( 2006 ). Deformations of Lie algebras using σ-derivations . J. Algebra 295 : 314 – 361 .[Crossref], [Web of Science ®] , [Google Scholar]) and Larsson and Silvestrov (2005a Larsson , D. , Silvestrov , S. D. (2005a). Quasi-hom-Lie algebras, Central extensions and 2-cocycle-like identities. J. Algebra 288:321–344.[Crossref], [Web of Science ®] , [Google Scholar]) to the simple 3-dimensional Lie algebra 𝔰𝔩₂(𝔽). One of the main points of this deformation method is that the deformed algebra comes endowed with a canonical twisted Jacobi identity. We show in the present article that when our deformation scheme is applied to 𝔰𝔩₂(𝔽) we can, by choosing parameters suitably, deform 𝔰𝔩₂(𝔽) into the Heisenberg Lie algebra and some other 3-dimensional Lie algebras in addition to more exotic types of algebras, this being in stark contrast to the classical deformation schemes where 𝔰𝔩₂(𝔽) is rigid.     

Generic Existence and Approximation of Fixed Points for Nonexpansive Set-valued Maps

We study nonexpansive set-valued maps in Banach and metric spaces. We are concerned, in particular, with the generic existence and approximation of fixed points, as well as with the structure of fixed point sets.      

On complements of 𝔉-residuals of finite groups

A formation 𝔉 of finite groups has the generalized Wielandt property for residuals, or 𝔉 is a GWP-formation, if the 𝔉-residual of a group generated by two 𝔉-subnormal subgroups is the subgroup generated by their 𝔉-residuals. The main aim of the paper is to determine some su?cient conditions for a finite group to split over its 𝔉-residual.     

Generalized quadrangles admitting PSL(2,q) × PSL(2,q)

In this paper, we classify the generalized quadrangles of order (s,t), s ≠ 1 ≠ t, which admit the natural action of PSL(2,s) × PSL(2,s) on a subGQ of order (s,1). This generalizes a recent result of J. De Kaey and H. Van Maldeghem 3 , by whom the classification was obtained for the case s = t. © 2005 Wiley Periodicals, Inc. J Combin Designs.     

一类随机减算子随机不动点存在唯一性定理及应用

该文在没有任何连续性和紧性条件下, 得到了一类随机减算子随机不动点存在唯一性定理, 并由此给出了应用到随机积分方程的两个例子.     

On Some Geometric Representations of GL N (𝔬)

We study a family of complex representations of the group GL _n (𝔬), where 𝔬 is the ring of integers of a non-archimedean local field F. These representations occur in the restriction of the Grassmann representation of GL _n (F) to its maximal compact subgroup GL _n (𝔬). We compute explicitly the transition matrix between a geometric basis of the Hecke algebra associated with the representation and an algebraic basis that consists of its minimal idempotents. The transition matrix involves combinatorial invariants of lattices of submodules of finite 𝔬-modules. The idempotents are p-adic analogs of the multivariable Jacobi polynomials.     

3‐Spontaneous Emission Error Designs from PSL(2, q) or PGL(2, q)

Quantum jump codes are quantum codes that correct errors caused by quantum jumps. A spontaneous emission error design (SEED) was introduced by Beth et al. in 2003 to construct quantum jump codes. In this paper, we study the existence of 3‐SEEDs from PSL(2, q) or PGL(2, q). By doing this, a large number of 3‐ SEEDs are derived for prime powers q and all .     

Foxby equivalences associated to Gorenstein categories 𝒢(𝒳,𝒴,𝒵)

In this paper, we establish some new Foxby equivalences between some Gorenstein subcategories in the Auslander class 𝒜_C(R) and that in the Bass class ?_C(S) in a general setting. Our results provide a unification and generalization of some known results and generate some new Foxby equivalences of categories.     

Degree distribution of the greatest common divisor of polynomials over 𝔽q

We study the degree distribution of the greatest common divisor of two or more random polynomials over a finite field ??_q. We provide estimates for several parameters like number of distinct common irreducible factors, number of irreducible factors counting repetitions, and total degree of the gcd of two or more polynomials. We show that the limiting distribution of a random variable counting the total degree of the gcd is geometric and that the distributions of random variables counting the number of common factors (with and without repetitions) are very close to Poisson distributions when q is large. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006     

增算子不动点的迭代求法及其应用

设E是Banach空间 ,本文在空间C[I,E]中得到了若干新的增算子不动点的存在性定理及其不动点的迭代求法 .作为应用 ,我们研究了Banach空间上非线性积分方程最大解和最小解及其单调迭代方法