# Thin boundary layers of chiral smectics

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The collective dielectric relaxation processes of electroclinic liquid-crystal materials have been investigated in a thin (3.5 Î¼m) planar cell in the frequency range of 1 Hzâ€“10 MHz. Measurement of complex dielectric permittivity versus temperature has been taken on aligned samples...

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The authors obtain a holomorphic Lefschetz fixed point formula for certain non-compact ï¿½hyperbolicï¿½ Kï¿½hler manifolds (e.g. Kï¿½hler hyperbolic manifolds, bounded domains of holomorphy) by using the Bergman kernel. This result generalizes the early work of Donnelly and Fefferman.

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The article presents a mathematical analysis which studies specifically the case where the continuous complex Finsler metric given by Paul Finsler arises from the Carathï¿½odory pseudometric. In addition to the Finsler metric rigidity theorem, it considers the additional tool of bounded...

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The article offers information on a paper regarding the domains of holomorphy for irreducible unitary representations of simple Lie groups. It presents a unitary irreducible representation of pi and Hermitian belonging to a connected algebraic Lie group. Also presented is the theorem, notation,...

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We prove the holomorphy of a function that, at every point, preserves either angles or dilations with respect to a certain set.

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In the case of functions of one complex variable, Î© âŠ‚ C, it is well known [3] that we can arbitrarily choose a subset A âŠ‚ Î©, such that A does not have accumulation points in Î© and find a function f âˆˆ O(Î©) such that f as well as a finite number of its derivatives have...

- ORTHOGONALLY ADDITIVE AND ORTHOGONALLY MULTIPLICATIVE HOLOMORPHIC FUNCTIONS OF MATRICES. QINGYING BU; CHINGJOU LIAO; NGAI-CHING WONG // Annals of Functional Analysis;2014, Vol. 5 Issue 2, p80
Let H : Mm â†’ Mm be a holomorphic function of the algebra Mm of complex mÃ—m matrices. Suppose that H is orthogonally additive and orthogonally multiplicative on self-adjoint elements. We show that either the range of H consists of zero trace elements, or there is a scalar sequence...

- Normed Domains of Holomorphy. Krantz, Steven G. // International Journal of Mathematics & Mathematical Sciences;2010, p1
We treat the classical concept of domain of holomorphy in â„‚n when the holomorphic functions considered are restricted to lie in some Banach space. Positive and negative results are presented. A new view of the case n = 1 is considered.

- Superconducting transition width under magnetic field in MgB2 polycrystalline samples. Wang, C. C.; Zeng, R.; Xu, X.; Dou, S. X. // Journal of Applied Physics;Nov2010, Vol. 108 Issue 9, p093907
A systematic study on the superconducting transition width as a function of the applied magnetic field was performed in polycrystalline MgB2. A quantitative, yet universal relation between the two parameters was observed in all of the ceramics. It was found that the width decreases linearly with...