COMMON FIXED POINT THEOREM FOR WEAKLY COMPATIBLE MAPPINGS IN HILBERT SPACE

 In this paper we prove a common fixed point theorem for weakly compatible mappings satisfies certain  contractive condition in non- empty closed subset of a separable Hilbert Space. Our results generalize and extend the result Chauhan [7]

The STAR Photon Multiplicity Detector

Details concerning the design, fabrication and performance of STAR Photon Multiplicity Detector (PMD) are presented. The PMD will cover the forward region, within the pseudorapidity range 2.3--3.5, behind the forward time projection chamber. It will measure the spatial distribution of photons in order to study collective flow, fluctuation and chiral symmetry restoration.Comment: 15 pages, including 11 figures; to appear in a special NIM volume dedicated to the accelerator and detectors at RHI

Properties of heavy quarkonia and B_c mesons in the relativistic quark model

The mass spectra and electromagnetic decay rates of charmonium, bottomonium and B_c mesons are comprehensively investigated in the relativistic quark model. The presence of only heavy quarks allows the expansion in powers of their velocities. All relativistic corrections of order v^2/c^2, including retardation effects and one-loop radiative corrections, are systematically taken into account in the computations of the mass spectra. The obtained wave functions are used for the calculation of radiative magnetic dipole (M1) and electric dipole (E1) transitions. It is found that relativistic effects play a substantial role. Their account and the proper choice of the Lorentz structure of the quark-antiquark interaction in a meson is crucial for bringing theoretical predictions in accord with experimental data. A detailed comparison of the calculated decay rates and branching fractions with available experimental data for radiative decays of charmonium and bottomonium is presented. The possibilities to observe the currently missing spin-singlet S and P states as well as D states in bottomonium are discussed. The results for B_c masses and decays are compared with other quark model predictions.Comment: 31 pages, 2 figures, minor correction

Four Zero Texture Fermion Mass Matrices in SO(10) GUT

We attempt the integration of the phenomenologically successful four zero texture of fermion mass matrices with the renormalizable SO(10) GUT. The resulting scenario is found to be highly predictive. Firstly, we examine the phenomenological implications of a class of the lepton mass matrices with parallel texture structures and obtain interesting constraints on the parameters of the charged lepton and the neutrino mass matrices. We combine these phenomenological constraints with the constraints obtained from SO(10) GUT to reduce the number of the free parameters and to further constrain the allowed ranges of the free parameters. The solar/atmospheric mixing angles obtained in this analysis are in fairly good agreement with the data.Comment: 14 pages, 3 figures, 1 tabl

Follow-up plasma apolipoprotein E levels in the Australian Imaging, Biomarkers and Lifestyle Flagship Study of Ageing (AIBL) cohort

Introduction: Alzheimer's disease (AD) is a growing socioeconomic problem worldwide. Early diagnosis and prevention of this devastating disease have become a research priority. Consequently, the identification of clinically significant and sensitive blood biomarkers for its early detection is very important. Apolipoprotein E (APOE) is a well-known and established genetic risk factor for late-onset AD; however, the impact of the protein level on AD risk is unclear. We assessed the utility of plasma ApoE protein as a potential biomarker of AD in the large, well-characterised Australian Imaging, Biomarkers and Lifestyle Study of Ageing (AIBL) cohort. Methods: Total plasma ApoE levels were measured at 18-month follow-up using a commercial bead-based enzyme-linked immunosorbent assay: the Luminex xMAP human apolipoprotein kit. ApoE levels were then analysed between clinical classifications (healthy controls, mild cognitive impairment (MCI) and AD) and correlated with the data available from the AIBL cohort, including but not limited to APOE genotype and cerebral amyloid burden. Results: A significant decrease in ApoE levels was found in the AD group compared with the healthy controls. These results validate previously published ApoE protein levels at baseline obtained using different methodology. ApoE protein levels were also significantly affected, depending on APOE genotypes, with ε2/ε2 having the highest protein levels and ε4/ε4 having the lowest. Plasma ApoE levels were significantly negatively correlated with cerebral amyloid burden as measured by neuroimaging. Conclusions: ApoE is decreased in individuals with AD compared with healthy controls at 18-month follow-up, and this trend is consistent with our results published at baseline. The influence of APOE genotype and sex on the protein levels are also explored. It is clear that ApoE is a strong player in the aetiology of this disease at both the protein and genetic levels

Basic kinetic wealth-exchange models: common features and open problems

We review the basic kinetic wealth-exchange models of Angle [J. Angle, Social Forces 65 (1986) 293; J. Math. Sociol. 26 (2002) 217], Bennati [E. Bennati, Rivista Internazionale di Scienze Economiche e Commerciali 35 (1988) 735], Chakraborti and Chakrabarti [A. Chakraborti, B. K. Chakrabarti, Eur. Phys. J. B 17 (2000) 167], and of Dragulescu and Yakovenko [A. Dragulescu, V. M. Yakovenko, Eur. Phys. J. B 17 (2000) 723]. Analytical fitting forms for the equilibrium wealth distributions are proposed. The influence of heterogeneity is investigated, the appearance of the fat tail in the wealth distribution and the relaxation to equilibrium are discussed. A unified reformulation of the models considered is suggested.Comment: Updated version; 9 pages, 5 figures, 2 table

Pulsars as Fantastic Objects and Probes

Pulsars are fantastic objects, which show the extreme states of matters and plasma physics not understood yet. Pulsars can be used as probes for the detection of interstellar medium and even the gravitational waves. Here I review the basic facts of pulsars which should attract students to choose pulsar studies as their future projects.Comment: Invited Lecture on the "First Kodai-Trieste Workshop on Plasma Astrophysics", Kodaikanal Obs, India. Aug.27-Sept.7th, 2007. In: "Turbulence, Dynamos, Accretion Disks, Pulsars and Collective Plasma Processes". Get a copy from: http://www.springerlink.com/content/978-1-4020-8867-

Dynamical model and nonextensive statistical mechanics of a market index on large time windows

The shape and tails of partial distribution functions (PDF) for a financial signal, i.e. the S&P500 and the turbulent nature of the markets are linked through a model encompassing Tsallis nonextensive statistics and leading to evolution equations of the Langevin and Fokker-Planck type. A model originally proposed to describe the intermittent behavior of turbulent flows describes the behavior of normalized log-returns for such a financial market index, for small and large time windows, both for small and large log-returns. These turbulent market volatility (of normalized log-returns) distributions can be sufficiently well fitted with a $\chi^2$-distribution. The transition between the small time scale model of nonextensive, intermittent process and the large scale Gaussian extensive homogeneous fluctuation picture is found to be at $ca.$ a 200 day time lag. The intermittency exponent ($\kappa$) in the framework of the Kolmogorov log-normal model is found to be related to the scaling exponent of the PDF moments, -thereby giving weight to the model. The large value of $\kappa$ points to a large number of cascades in the turbulent process. The first Kramers-Moyal coefficient in the Fokker-Planck equation is almost equal to zero, indicating ''no restoring force''. A comparison is made between normalized log-returns and mere price increments.Comment: 40 pages, 14 figures; accepted for publication in Phys Rev