Multipliers for p-Bessel sequences in Banach spaces

Multipliers have been recently introduced as operators for Bessel sequences and frames in Hilbert spaces. These operators are defined by a fixed multiplication pattern (the symbol) which is inserted between the analysis and synthesis operators. In this paper, we will generalize the concept of Bessel multipliers for p-Bessel and p-Riesz sequences in Banach spaces. It will be shown that bounded symbols lead to bounded operators. Symbols converging to zero induce compact operators. Furthermore, we will give sufficient conditions for multipliers to be nuclear operators. Finally, we will show the continuous dependency of the multipliers on their parameters.Comment: 17 page

Discrete coherent states for higher Landau levels

We consider the quantum dynamics of a charged particle evolving under the action of a constant homogeneous magnetic field, with emphasis on the discrete subgroups of the Heisenberg group (in the Euclidean case) and of the SL(2, R) group (in the Hyperbolic case). We investigate completeness properties of discrete coherent states associated with higher order Euclidean and hyperbolic Landau levels, partially extending classic results of Perelomov and of Bargmann, Butera, Girardello and Klauder. In the Euclidean case, our results follow from identifying the completeness problem with known results from the theory of Gabor frames. The results for the hyperbolic setting follow by using a combination of methods from coherent states, time-scale analysis and the theory of Fuchsian groups and their associated automorphic forms.Comment: Revised for Annals of Physic

Yukawa Coupling Unification in Supersymmetric Models

We present an updated assessment of the viability of t-b-tau Yukawa coupling unification in supersymmetric models. For the superpotential Higgs mass parameter mu>0, we find unification to less than 1% is possible, but only for GUT scale scalar mass parameter m_{16}~8-20 TeV, and small values of gaugino mass m_{1/2}<400 GeV. Such models require that a GUT scale mass splitting exists amongst Higgs scalars with m_{H_u}^2<m_{H_d}^2. Viable solutions lead to a radiatively generated inverted scalar mass hierarchy, with third generation and Higgs scalars being lighter than other sfermions. These models have very heavy sfermions, so that unwanted flavor changing and CP violating SUSY processes are suppressed, but may suffer from some fine-tuning requirements. While the generated spectra satisfy b->s gamma and (g-2)_mu constraints, there exists tension with the dark matter relic density unless m_{16}<3 TeV. These models offer prospects for a SUSY discovery at the Fermilab Tevatron collider via the search for chargino_1 neutralino_2 -> 3 leptons events, or via gluino pair production. If mu<0, Yukawa coupling unification to less than 5% can occur for m_{16} and m_{1/2}>1-2 TeV. Consistency of negative mu Yukawa unified models with b->s gamma, (g-2)_mu, and relic density all imply very large values of m_{1/2} typically greater than about 2.5 TeV, in which case direct detection of sparticles may be a challenge even at the LHC.Comment: 38 pages, 15 figures. Fig.15 changed, some references were added. A copy of the paper with better resolution figures can be found at http://www.hep.fsu.edu/~balazs/Physics/Papers/2003

Systems biology of energetic and atomic costs in the yeast transcriptome, proteome, and metabolome

Proteins vary in their cost to the cell and natural selection may favour the use of proteins that are cheaper to produce. We develop a novel approach to estimate the amino acid biosynthetic cost based on genome-scale metabolic models, and directly investigate the effects of biosynthetic cost on transcriptomic, proteomic and metabolomic data in _Saccharomyces cerevisiae_. We find that our systems approach to formulating biosynthetic cost produces a novel measure that explains similar levels of variation in gene expression compared with previously reported cost measures. Regardless of the measure used, the cost of amino acid synthesis is weakly associated with transcript and protein levels, independent of codon usage bias. In contrast, energetic costs explain a large proportion of variation in levels of free amino acids. In the economy of the yeast cell, there appears to be no single currency to compute the cost of amino acid synthesis, and thus a systems approach is necessary to uncover the full effects of amino acid biosynthetic cost in complex biological systems that vary with cellular and environmental conditions

Feline primary erythrocytosis: a multicentre case series of 18 cats

A retrospective multicentre case series of feline primary erythrocytosis (PE) was evaluated. The aim was to gain better understanding of disease presentation and progression to guide management and prognostication. Case records were assessed for evidence of increased packed cell volume (PCV; >48%), sufficient investigation to rule out relative and secondary erythrocytosis, and follow-up data for at least 12 months or until death. Eighteen cats were included in the case series. No significant trends in signalment were noted. Seizures and mentation changes were the most common presenting signs (both n = 10). Median PCV was 70% (median total protein concentration of 76 g/l) with no other consistent haematological changes. Sixteen cats survived to discharge. Phlebotomy was performed initially in 15/16 surviving animals and performed after discharge in 10/16. Hydroxyurea was the most common adjunctive therapy, used in 10/16 cats. Of the 16 patients surviving to discharge, 14 patients were still alive at the conclusion of the study (survival time >17 months post-discharge), with the two non-survivors having lived for 5 years or more after diagnosis. PCV, when stabilised, did not correlate with resolution of clinical signs

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

Robust Constraints on Dark Matter Annihilation into Gamma Rays and Charged Particles

Using gamma-ray data from observations of the Milky Way, Andromeda (M31), and the cosmic background, we calculate conservative upper limits on the dark matter self-annihilation cross section to a number of final states, over a wide range of dark matter masses. We first constrain annihilation to a pair of monoenergetic gamma rays, and show that in general our results are unchanged for a broader annihilation spectrum, if at least a few gamma rays are produced with energies within a factor of a few from the dark matter mass. We then place constraints on the self-annihilation cross section to an electron-positron pair, using gamma rays produced via internal bremsstrahlung radiative corrections. We also place constraints on annihilation into the other charged leptons. We make conservative assumptions about the astrophysical inputs, and demonstrate how our derived bounds would be strengthened if stronger assumptions about these inputs are adopted.Comment: 7 pages, 5 figures. Talk given at DSU 09, Melbourne, Australia, June 200