Free analysis and planar algebras

We study 2-cabled analogs of Voiculescu's trace and free Gibbs states on Jones planar algebras. These states are traces on a tower of graded algebras associated to a Jones planar algebra. Among our results is that, with a suitable definition, finiteness of free Fisher information for planar algebra traces implies that the associated tower of von Neumann algebras consists of factors, and that the standard invariant of the associated inclusion is exactly the original planar algebra. We also give conditions that imply that the associated von Neumann algebras are non-$\Gamma$ non-$L^2$ rigid factors

Structural and magnetic properties of transition metal substituted ZnO

Structural and magnetic properties have been studied for polycrystalline Zn_{1-x}TM_xO, where TM (transition metal ions) = Mn, Fe, and Co. No bulk ferromagnetism was observed for single-phase materials, contrary to the existing theories. Single-phase samples demonstrate paramagnetic Curie-Weiss behavior with antiferromagnetic interactions, similar to other diluted magnetic semiconductors. Non-optimal synthesis conditions lead to formation of second phases that are responsible for spin-glass behavior (ZnMnO_3 impurity for Zn_{1-x}Mn_xO (S. Kolesnik et al., J. Supercond.: Incorp. Novel Magn. 15, 251 (2002)) or high-temperature ferromagnetic ordering (Co metal for Zn_{1-x}Co_xO with the Curie temperature T_C > 800 K or (Zn,Fe)_3O_4 for Zn_{1-x}Fe_xO with T_C = 440 K).Comment: RevTeX, 6 pages, 7 figures, To be published in J. Appl. Phy

Star product formula of theta functions

As a noncommutative generalization of the addition formula of theta functions, we construct a class of theta functions which are closed with respect to the Moyal star product of a fixed noncommutative parameter. These theta functions can be regarded as bases of the space of holomorphic homomorphisms between holomorphic line bundles over noncommutative complex tori.Comment: 12 page

Electro-optical properties of an orthoconic liquid crystal mixture (W-182) and its molecular dynamics

We observed that the perfect dark state problem could be solved by using orthoconic antiferroelectric liquid crystal (OAFLC) instead of normal AFLC by comparing the properties of isocontrast and dispersion chromaticity of W-182 OAFLC and normal AFLC CS-4001. We electro-optically observed that several subphases such as SmCγ*, SmC*β, SmC*α and antiferroelectric SmI*A phases exist in W-182 OAFLC. We dielectrically observed in 4 μm thin cell that during heating, several new phases appeared. In the high temperature antiferroelectric region, a higher order than SmC* phase could be detected dielectrically, in the temperature range of 91–98 °C, behaving similar to SmCγ* and also, another phase below SmC* region could be dielectrically detected in the temperature range of 103–1100 °C, behaving similar to SmCα*, and an antiferroelectric, similar to SmIA* phase, was observed in the lower temperature region of the antiferroelectric phase; those are definitely arising due to surface force and interfacial charges interactions. We observed both PH and PL relaxation modes in both cells, although they differed in their strength and relaxation frequency. We studied extensively our observations of PH and PL modes in the antiferroelectric region, a Goldstone mode in the ferroelectric region and a soft mode in the ferroelectric region and SmA* phases

Null Branes in Curved Backgrounds

We consider null bosonic p-branes in curved space-times. Some exact solutions of the classical equations of motion and of the constraints for the null membrane in general stationary, axially symmetrical, four dimensional, gravity background are found.Comment: 19 pages, LaTeX, no figures. Extended version. To appear in Phys. Rev.

h-deformation of GL(1|1)

h-deformation of (graded) Hopf algebra of functions on supergroup GL(1|1) is introduced via a contration of GL_q (1|1). The deformation parameter h is odd (grassmann). Related differential calculus on h-superplane is presented.Comment: latex file, 8 pages, minor change