幂等算子线性组合的幂等性

设P与Q是Hilbert空间中的两个不同的幂等算子.本文主要刻画了幂等算子P与Q的线性组合仍是幂等算子的充要条件,从而推广了Baksalary与Baksalary (2000)的结论.值得指出的是,我们通过严密的推理发现,其定理的条件P_1P_2≠P_2P_1是非必要的.     

The existence spectrum of golf designs

In this note, a golf design of order 41 is constructed. Combined Colbourn and Nonay's result, the existence spectrum of golf design of order υ is the set {υ: υ≡1 (mod 2), υ ≥ 3, υ ≠ 5}. © 2005 Wiley Periodicals, Inc. J Combin Designs 15: 84–89, 2007     

An eigenvector existence theorem in idempotent analysis

In this paper, we prove an eigenvector existence theorem for linear operators on abstract idempotent spaces in the framework of the algebraic approach. Earlier, an algebraic version of a similar statement was known only for operators in free finite-dimensional semimodules. The corresponding result for compact operators in semimodules of real continuous functions is known in the case of topological semimodules.     

广义n幂等与超广义n幂等算子

For an integer n≥2,we say that an operator A is an n-idempotent ifA~n=A;A is a generalized n-idempotent if A~n=A~*;A is a hyper-generalized n-iclempotent if A~n=A~ .The set of all n-idempotents,all generalized n-idempotentsand all hyper-generalized n-idempotents are denoted by I_n(H),GI_n(H)andHGI_n(H),respectively.In this note,we obtain a chain of proper inclusionsGI_n(H)HGI_n(H)I_(n 2)(H).     

自由Abel群上超群结构的分类

本文在研究一个生成元的Abel群的基础上,建立了两个生成元的Abel群到实数加群的同态方法,并对自由Abel群上的超群结构进行了分析与研究,给出了正规超群的分类,进而推进一个重要结论:自由Abel群构于实数加群及其子群.     

Almost all minimal idempotent varieties are congruence modular

We show that, up to term equivalence, the only minimal idempotent varieties that are not congruence modular are the variety of sets and the variety of semilattices. From this it follows that a minimal idempotent variety that is not congruence distributive is term equivalent to the variety of sets, the variety of semilattices, or a variety of affine modules over a simple ring. Received March 29, 1999; accepted in final form February 8, 2000.     

Exchange rings with stable range one

We characterize exchange rings having stable range one. An exchange ring R has stable range one if and only if for any regular a ∈ R, there exist an e ∈ E(R) and a u ∈ U(R) such that a = e + u and aR ⋂ eR = 0 if and only if for any regular a ∈ R, there exist e ∈ r.ann(a ⁺) and u ∈ U(R) such that a = e + u if and only if for any a, b ∈ R, R/aR ≅ R/bR ⇒ aR ≅ bR.     

Fault tolerant forwarding and optical indexes: A design theory approach

We study the problem of designing fault tolerant routings in both complete and complete bipartite optical networks. We show that this problem has strong connections to various fundamental problems in design theory. Using a design theory approach, we find optimal f‐fault tolerant arc‐forwarding indexes for all complete networks and all complete balanced bipartite networks. Similarly, we find almost exact values for f‐fault tolerant optical indexes for these networks. © 2005 Wiley Periodicals, Inc. J Combin Designs     

The Idempotent Manifold in a Clifford Algebra

The idempotent sets in sufficiently sophisticated algebras form manifolds and Hausdorff spaces. In this paper it is shown how the idempotents in a real Clifford algebra Cl_p,q can be calculated by nilpotents and reflections. Minimal sets of nilpotents are given and generating relations are defined. It is shown that the manifold thus constructed is complete. Every idempotent in the manifold can be calculated in the way proposed here, namely by a nilpotent multinomial form.     

On the lattice of matric-extensible radicals. II

Summary We continue our study of the lattice of matric-extensible radicals of associative rings. We find some atoms generated by simple rings of the lattices of all matric-extensible radicals, matric-extensible supernilpotent radicals and matric-extensible special radicals. We consider *-rings, which were previously defined by the second author, and consider when they generate atoms of these lattices.