The <Emphasis Type="Italic">N</Emphasis> = 1 Triplet Vertex Operator Superalgebras

We introduce a newfamily of C ₂-cofinite N = 1 vertex operator superalgebras , m ≥ 1, which are natural super analogs of the triplet vertex algebra family , p ≥ 2, important in logarithmic conformal field theory. We classify irreducible -modules and discuss logarithmic modules. We also compute bosonic and fermionic formulas of irreducible characters. Finally, we contemplate possible connections between the category of -modules and the category of modules for the quantum group , , by focusing primarily on properties of characters and the Zhu’s algebra . This paper is a continuation of our paper Adv. Math. 217, no.6, 2664–2699 (2008). The second author was partially supported by NSF grant DMS-0802962.     

Generalized tensor ABCD law for an elliptical Gaussian beam passing through an astigmatic optical system in turbulent atmosphere

The propagation of an elliptical Gaussian beam (EGB) through an astigmatic ABCD optical system in a turbulent atmosphere is investigated. An analytical formula for the average intensity of an EGB and a generalized tensor ABCD law for the generalized complex curvature tensor are derived. As an application example, we derived an analytical formula for the average intensity of an elliptical flat-topped beam propagating through an astigmatic ABCD optical system in a turbulent atmosphere. As a numerical example, the focusing properties of an EGB focused by a thin lens in a turbulent atmosphere are studied. It is found that the focused beam at the focal plane becomes a circular Gaussian beam when the atmospheric turbulence is strong enough, and the beam width of the circular Gaussian beam is determined by atmospheric turbulence strength, focal length of the thin lens, and wavelength of the initial beam but is independent of the initial beam widths (i.e., initial intensity distribution).     

Light propagation in highly birefringent photonic liquid crystal fibers

Photonic liquid crystal fibers have already been demonstrated as a promising perspective for creation of new classes of dynamically tunable optical fiber devices. By combining different geometries of photonic crystal fibers with a variety of different liquid crystals it is possible to obtain a new generation of fibers with dynamically tunable properties, e.g., transmission spectra, attenuation or dispersion. In this paper, tunable birefringence in a commercially available highly birefringent Blazephotonics PM-1550-01 photonic crystal fiber selectively filled with a low birefringence liquid crystal has been experimentally demonstrated. Theses experimental results have been compared with simulations based on the multipole method.     

Vibrational spectra of two BEDT-TTF-based organic conductors: charge order

Infrared and Raman investigations of two phases of bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF) based organic conductors with the same CF₃CF₂SO₃⁻ anion: β′-(BEDT-TTF)₂CF₃CF₂SO₃ and δ′-(BEDT-TTF)₂CF₃CF₂SO₃, are shortly reviewed and compared with the most typical infrared properties of the family of (BEDT-TTF)₂RR′SO₃ organic conductors, where R = SF₅, CF₃, and R′ are CH₂, CF₂, CHF, CHFCF₂, and CH₂CF₂. The role of the molecular structur and spatial organization of the counterions is discussed. Presented at 2-nd International Conference on Functional Materials and Devices, ICFMD 2008, June 16–19, 2008, Kuala Lumpur, Malaysia     

Picosecond laser ablation of nano-sized WTi thin film

Interaction of an Nd:YAG laser, operating at 532 nm wavelength and pulse duration of 40 ps, with tungsten-titanium (WTi) thin film (thickness, 190 nm) deposited on single silicon (100) substrate was studied. Laser fluences of 10.5 and 13.4 J/cm² were found to be sufficient for modification of the WTi/silicon target system. The energy absorbed from the Nd:YAG laser beam is partially converted to thermal energy, which generates a series of effects, such as melting, vaporization of the molten material, shock waves, etc. The following WTi/silicon surface morphological changes were observed: (i) ablation of the thin film during the first laser pulse. The boundary of damage area was relatively sharp after action of one pulse whereas it was quite diffuse after irradiation with more than 10 pulses; (ii) appearance of some nano-structures (e.g., nano-ripples) in the irradiated region; (iii) appearance of the micro-cracking. The process of the laser interaction with WTi/silicon target was accompanied by formation of plasma.     

Set-valued dynamic systems and random iterations of set-valued weaker contractions in uniform spaces

Set-valued weaker contractions in uniform, locally convex and metric spaces are defined and dynamic systems of such weaker contractions are studied. Conditions guaranteeing the convergence of generalized sequences of random iterations and iterations and the existence and uniqueness of endpoints of set-valued weaker contractions are established. Our definitions and results are new for set-valued maps in uniform, locally convex and metric spaces and even for single-valued maps.     

Additive results for the generalized Drazin inverse in a Banach algebra

In this paper we investigate additive properties of the generalized Drazin inverse in a Banach algebra. We find some new conditions under which the generalized Drazin inverse of the sum a + b could be explicitly expressed in terms of a, a^d, b, b^d. Also, some recent results of Castro and Koliha [New additive results for the g-Drazin inverse, Proc. Roy. Soc. Edinburgh Sect. A 134 (2004) 1085-1097] are extended.     

The Matsumoto-Yor property and the structure of the Wishart distribution

This paper establishes a link between a generalized matrix Matsumoto-Yor (MY) property and the Wishart distribution. This link highlights certain conditional independence properties within blocks of the Wishart and leads to a new characterization of the Wishart distribution similar to the one recently obtained by Geiger and Heckerman but involving independences for only three pairs of block partitionings of the random matrix.In the process, we obtain two other main results. The first one is an extension of the MY independence property to random matrices of different dimensions. The second result is its converse. It extends previous characterizations of the matrix generalized inverse Gaussian and Wishart seen as a couple of distributions.We present two proofs for the generalized MY property. The first proof relies on a new version of Herz's identity for Bessel functions of matrix arguments. The second proof uses a representation of the MY property through the structure of the Wishart.     

CRYRING at the LSR at FLAIR

FLAIR will be the next-generation facility for physics with low-energy antiprotons, providing antiprotons at energies from tens of MeV down to rest. It will also offer unique possibilities for physics with highly charged ions at very low energies. The FLAIR facility will have two deceleration rings, the LSR which will decelerate antiprotons to 300 keV and the USR which will bring them down further to 20 keV. The LSR will consist of the present CRYRING at the Manne Siegbahn Laboratory. During the next few years, CRYRING will be modified with respect to injection and extraction, to allow injection of 30 MeV antiprotons and to provide it with both fast (single-turn) and slow (resonant) extraction at a variable energy. We here describe plans and preparations for the transfer of CRYRING to FLAIR, giving, in particular, an overview of new components for injection and extraction.     

Long alternating paths in bicolored point sets

Given n red and n blue points in convex position in the plane, we show that there exists a noncrossing alternating path of length . We disprove a conjecture of Erd?s by constructing an example without any such path of length greater than .