CertainC*-algebras with real rank zero and their corona and multiplier algebras: II

We first determine the homotopy classes of nontrivial projections in a purely infinite simpleC*-algebraA, in the associated multiplier algebraM(A) and the corona algebraM A/A in terms ofK _*(A). Then we describe the generalized Fredholm indices as the group of homotopy classes of non-trivial projections ofA; consequently, we determine theK _*-groups of all hereditaryC*-subalgebras of certain corona algebras. Secondly, we consider a group structure of *-isomorphism classes of hereditaryC*-subalgebras of purely infinite simpleC*-algebras. In addition, we prove that ifA is aC*-algebra of real rank zero, then each unitary ofA, in caseA it unital, each unitary ofM(A) and ofM(A)/A, in caseA is nonunital but -unital, can be factored into a product of a unitary homotopic to the identity and a unitary matrix whose entries are all partial isometries (with respect to a decomposition of the identity).Partially supported by a grant from the National Science Foundation.     

K-theory for finite covariant systems

LetA be a real or complex Banach algebra and assume that is an action of a finite groupG onA by means of continuous automorphisms. To such a finite covariant system (A, G, ), we associate an Abelian groupK(A, G, ). We obtain some classical exact sequences for an algebraA and a closed invariant idealI. We also compute the group in a few important special cases. Doing so, we relate our new invariant to the classicalK ₀ andK ₁ of a Banach algebra and to theK-theory of ₂-graded Banach algebras. Finally, we obtain a result that gives a close relationship of our groupK(A, G, ) with theK-theory of the crossed productA G. In particular, we prove a six-term exact sequence involving our groupK(A, G, ) and theK-groups ofA G. In this way, we hope to contribute to the well-known problem of finding theK-theory of the crossed productA G in the case of an action of a finite group.     

Anodic behavior of nickel-based alloys in the electrolytic production of NF3

The Ni-based alloys, such as Ni-Co, Ni-Mn, Ni-Ag, Ni-Cu, Ni-Al and Ni-Si, prepared by hot isostatic pressing (HIP) at 1000 °C under 2 × 10⁸ Pa for 2 h were employed as the anodes for electrolytic production of NF₃. The current efficiencies for NF₃ formation were 42-38, 52-40, 52-47, 63-62, 50 and 41% for Ni-Co, Ni-Mn, Ni-Ag, Ni-Cu, Ni-Al and Ni-Si alloys, respectively. The current efficiencies only on Ni-Cu alloys with Cu concentrations lower than 10 mol% were almost the same as those on Ni sheet and HIPed Ni anodes, whereas those on the other alloys used in this study were smaller compared with those on both Ni anodes. On the other hand, the current losses caused by anodic dissolution of Ni-Co, Ni-Mn, Ni-Ag, Ni-Cu, Ni-Al and Ni-Si alloy electrodes were 7.95-4.42, 6.40-7.02, 5.60-6.30, 3.34-6.33, 5.10 and 0.18%, respectively. The anode consumptions of Ni-5 mol% Cu and Ni-5 mol% Si alloys were almost the same or smaller compared with those of Ni sheet and HIPed Ni electrodes, though those of other alloys used were large compared with those of both Ni anodes. Consequently, addition of Cu to the nickel matrix is available for a cheaper cost of anode with keeping a same current efficiency as that on the Ni anode and addition of Si to the nickel matrix is effective for decreasing anode consumption largely. A Ni sheet electrode containing a trace of impurities, such as Co, Mn, Ag and Al, is also favorable as the anode for electrolytic production of NF₃.     

Accuracy and CPU time of JE-TLM,PLRC-TLM and CRC-TLM methods for plasma medium

The current density (JE), the piecewise linear recursive convolution (PLRC) and the constant convolution recursive (CRC) techniques are developed and integrated into the transmission line matrix (TLM) algorithm. A comparison of these three schemes according to the criteria of accuracy and CPU time is presented. Numerical experiments show that JE provides the most accurate solution and requires the least CPU time; PLRC is nearly as accurate but consumes more CPU time than CRC.     

On the simplicity of some kac-moody groups

Recently, Marcuson extended the classical construction of Tits systems in Steinberg groups to include the Kac-Moody Steinberg groups associated with the infinite dimensional versions of the great Lie algebras. If these Lie algebras and their Kac-Moody groups are viewed as limits of their finite dimensional counterparts, more direct methods may be employed. In fact, the Kac-Moody Chevalley groups of these Lie algebras are seen to be simple.     

Sobolev spaces on Lie groups: Embedding theorems and algebra properties

Let G be a noncompact connected Lie group, denote with ρ a right Haar measure and choose a family of linearly independent left-invariant vector fields X on G satisfying Hörmander's condition. Let χ be a positive character of G and consider the measure ${\mu }_{\chi }$ whose density with respect to ρ is χ. In this paper, we introduce Sobolev spaces $L_{\alpha }^p({\mu }_{\chi })$ adapted to X and ${\mu }_{\chi }$ ($1<p<\infty$, $\alpha \ge 0$) and study embedding theorems and algebra properties of these spaces. As an application, we prove local well-posedness and regularity results of solutions of some nonlinear heat and Schrödinger equations on the group.     

Spin-polarized current and tunnel magnetoresistance in heterogeneous single-barrier magnetic tunnel junctions

Current in heterogeneous tunnel junctions is studied in the framework of the parabolic conduction-band model. The developed model of the electron tunneling takes explicitly into account the difference of effective masses between ferromagnetic and insulating layers and between conduction subbands. Calculations for Fe/MgO/Fe-like structures have shown the essential impact of effective mass differences in regions (constituents) of the structure on the tunnel magnetoresistance of the junction.