A note on idempotents in finite AW*-factors

We prove that the value of the quasi-trace on an idempotent element in an AW*-factor of type is the same as the dimension of its left (or right) support.

     

A description of Hilbert -modules in which all closed submodules are orthogonally closed

Let , be -algebras and a full Hilbert --bimodule such that every closed right submodule is orthogonally closed, i.e., . Then there are families of Hilbert spaces , such that and are isomorphic to -direct sums , resp. , and is isomorphic to the outer direct sum .

     

欧拉游历间K1—变换下的算法复杂性

本文主要讨论了欧拉图方面的国际权威ＨｅｒｂｅｒｔＦｌｅｉｃｈｎｅｒ教授所著书［１］中的一个问题；对欧拉图Ｇ的任意两个欧拉游历要经过多少Ｋ－变换或Ｋ＾＊－变换才能从一个游历得到另一个游历？我们得到的结论是：对欧拉图Ｇ中的任两个欧拉游历Ｔ、Ｔ＇最多经过‖Ｅ（Ｇ）‖－‖Ｖ（Ｇ）‖－变换可以使Ｔ变换成Ｔ＇。且此结果不能再改进。进一步我们分别对Ｋ－变换和Ｋ＆－变换的算法复杂性进行了讨论。     

P－正则半群的双序集

本文刻划了双序集Ｅ为某Ｐ－正则半群的幂等元双序集的充要条件．所得定理不仅推广了Ｄ．Ｅａｓｄｏｗｎ关于带的双序集的结论，而且导出了正则＊－半群的幂等元双序集的一个刻划．进而还对Ｐ－正则半群的若干特殊情形及向非正则半群的推广进行了讨论．     

TEM01模式激光对两能级原子的作用力研究

推导了两能级原子在稳态和小速度一阶微扰近似下的受力矢量方程，并分析表明ＴＥＭ０１模光场以原子的作用力中存在旋涡力，对在大正失谐δ〉〉Ω０〉〉Г和ｚ〈〈ｚ０＝ｋｗ＾２／λ条件下的ＴＥＭ０１模行波和驻波场中原子的受力进行了分析，对行波场，自发辐射对原子运动的影响很大，但在ｒ〈〈λ区域内原子受到横向囚禁力；对驻波场，自发辐射的影响可以忽略，考虑在ｚ方向波长范围内原子的平均受力得到的结论为：在横向，除了有     

Homomorphisms between Poisson JC*-Algebras

It is shown that every almost linear mapping of a unital Poisson JC*-algebra to a unital Poisson JC*-algebra is a Poisson JC*-algebra homomorphism when h(2 ⁿ uy) = h(2 ⁿ u) h(y), h(3 ⁿ u y) = h(3 ⁿ u) h(y) or h(q ⁿ u y) = h(q ⁿ u) h(y) for all , all unitary elements and n = 0, 1, 2, · · · , and that every almost linear almost multiplicative mapping is a Poisson JC*-algebra homomorphism when h(2x) = 2h(x), h(3x) = 3h(x) or h(qx) = qh(x) for all . Here the numbers 2, 3, q depend on the functional equations given in the almost linear mappings or in the almost linear almost multiplicative mappings.Moreover, we prove the Cauchy–Rassias stability of Poisson JC*-algebra homomorphisms in Poisson JC*-algebras.*This work was supported by grant No. R05-2003-000-10006-0 from the Basic Research Program of the Korea Science & Engineering Foundation.     

Bioorganometallic chemistry: biocatalytic oxidation reactions with biomimetic NAD/NADH co-factors and [Cp*Rh(bpy)H] for selective organic synthesis

The biocatalytic, regioselective hydroxylation of 2-hydroxybiphenyl to the corresponding catechol was accomplished utilizing the monooxygenase 2-hydroxybiphenyl 3-monooxygenase (HbpA). The necessary natural 1,4-dihydronicotinamde adenine dinucleotide (NADH) co-factor for this biocatalytic process was replaced by a biomimetic co-factor, N-benzyl-1,4-dihydronicotinamide, 1b. The interaction between the flavin (FAD) containing HbpA enzyme and the corresponding biomimetic NADH compound, N-benzyl-1,4-dihdronicotinamide, 1b, for hydride transfer, was shown to readily occur. The in situ recycling of the reduced NADH biomimic 1b from 1a was accomplished with [Cp*Rh(bpy)H](Cl); however, productive coupling of this regeneration reaction to the enzymatic hydroxylation reaction was not totally successful, due to a deactivation process concerning the HbpA enzyme peripheral groups; i.e., -SH or -NH₂ possibly reacting with the precatalyst, [Cp*Rh(bpy)(H₂O)](Cl)₂, and thus inhibiting the co-factor regeneration process. The deactivation mechanism was studied, and a promising strategy of derivatizing these peripheral -SH or -NH₂ groups with a polymer containing epoxide was successful in circumventing the undesired interaction between HbpA and the precatalyst. This latter strategy allowed tandem co-factor regeneration using 1a or 2a, [Cp*Rh(bpy)(H₂O)](Cl)₂, and formate ion, in conjunction with the polymer bound, FAD containing HbpA enzyme to provide the catechol product.     

When Is a Sum of Partial Reflections Equal to a Scalar Operator?

We describe the set of values of the parameter for which there exists a Hilbert space H and n partial reflections A ₁,...,A _n (self-adjoint operators such that A _k ³ =A_k or, which is the same, self-adjoint operators whose spectra belong to the set {-1,0,1}) whose sum is equal to the scalar operator I _H .     

Fourier Invariant Partially Approximating Subalgebras of the Irrational Rotation C*-Algebra

For a dense G-set of parameters, the irrational rotation algebrais shown to contain infinitely many C*-subalgebras satisfyingthe following properties. Each subalgebra is isomorphic to adirect sum of two matrix algebras of the same (perfect square)dimension; the Fourier transform maps each summand onto theother; the corresponding unit projection is approximately central;the compressions of the canonical generators of the irrationalrotation algebra are approximately contained in the subalgebra.2000 Mathematics Subject Classification 46L80, 46L40, 46L35.