Classification of General Sequences by Frame-Related Operators

This note is a survey and collection of results, as well as presenting some original research. For Bessel sequences and frames, the analysis, synthesis and frame operators as well as the Gram matrix are well-known, bounded operators. We investigate these operators for arbitrary sequences, which in general lead to possibly unbounded operators. We characterize various classes of sequences in terms of these operators and vice-versa. Finally, we classify these sequences by operators applied on orthonormal bases

Epoch Dependent Dark Energy

We present a model in which the equation of state parameter w approaches -1 near a particular value of z, and has significant negative values in a restricted range of z. For example, one can have w ~ -1 near z = 1, and w > -0.2 from z = 0 to z = 0.3, and for z > 9. The ingredients of the model are neutral fermions (which may be neutrinos, neutralinos, etc) which are very weakly coupled to a light scalar field. This model emphasises the importance of the proposed studies of the properties of dark energy into the region z > 1.Comment: 7pp., 2 figs. Invited talk at the 5th Int'l. Wkshp. on the Dark Side of the Universe, 1-5 June 2009 Melbourne, DSU09; to appear in the proceeding

Quantum Mechanics of Damped Systems II. Damping and Parabolic Potential Barrier

We investigate the resonant states for the parabolic potential barrier known also as inverted or reversed oscillator. They correspond to the poles of meromorphic continuation of the resolvent operator to the complex energy plane. As a byproduct we establish an interesting relation between parabolic cylinder functions (representing energy eigenfunctions of our system) and a class of Gel'fand distributions used in our recent paper.Comment: 14 page

Large Extra Dimensions at Linear Colliders

In this talk, I first present the motivation for theories wherein extra spacetime dimensions can be compactified to have large magnitudes. In particular, I discuss the Arkani-Hamed, Dimopoulos, Dvali (ADD) scenario. I present the constraints that have been derived on these models from current experiments and the expectations from future colliders. I concentrate particularly on the possibilities of probing these extra dimensions at future linear colliders.Comment: Talk given at the Third International Workshop on Electron-Electron Interactions at TeV Energies (e- e- 99), Santa Cruz, California, 10-12 Dec 1999. 7 pages, LaTeX, style files attache