An elementary proof of the irrationality of Tschakaloff series

We present a new proof of the irrationality of values of the series $T_q(z)=\sum_{n=0}^\infty z^nq^{-n(n-1)/2}$ in both qualitative and quantitative forms. The proof is based on a hypergeometric construction of rational approximations to $T_q(z)$.Comment: 5 pages, AMSTe

ZnO薄膜を用いた光導波路型波長変換デバイスの設計と作製に関する研究

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The sixth Painleve transcendent and uniformization of algebraic curves

We exhibit a remarkable connection between sixth equation of Painleve list and infinite families of explicitly uniformizable algebraic curves. Fuchsian equations, congruences for group transformations, differential calculus of functions and differentials on corresponding Riemann surfaces, Abelian integrals, analytic connections (generalizations of Chazy's equations), and other attributes of uniformization can be obtained for these curves. As byproducts of the theory, we establish relations between Picard-Hitchin's curves, hyperelliptic curves, punctured tori, Heun's equations, and the famous differential equation which Apery used to prove the irrationality of Riemann's zeta(3).Comment: Final version. Numerous improvements; English, 49 pages, 1 table, no figures, LaTe

On Local Behavior of Holomorphic Functions Along Complex Submanifolds of C^N

In this paper we establish some general results on local behavior of holomorphic functions along complex submanifolds of \Co^{N}. As a corollary, we present multi-dimensional generalizations of an important result of Coman and Poletsky on Bernstein type inequalities on transcendental curves in \Co^{2}.Comment: minor changes in the formulation and the proof of Lemma 8.

The Ks-band Tully-Fisher Relation - A Determination of the Hubble Parameter from 218 ScI Galaxies and 16 Galaxy Clusters

The value of the Hubble Parameter (H0) is determined using the morphologically type dependent Ks-band Tully-Fisher Relation (K-TFR). The slope and zero point are determined using 36 calibrator galaxies with ScI morphology. Calibration distances are adopted from direct Cepheid distances, and group or companion distances derived with the Surface Brightness Fluctuation Method or Type Ia Supernova. Distances are determined to 16 galaxy clusters and 218 ScI galaxies with minimum distances of 40.0 Mpc. From the 16 galaxy clusters a weighted mean Hubble Parameter of H0=84.2 +/-6 km s-1 Mpc-1 is found. From the 218 ScI galaxies a Hubble Parameter of H0=83.4 +/-8 km s-1 Mpc-1 is found. When the zero point of the K-TFR is corrected to account for recent results that find a Large Magellanic Cloud distance modulus of 18.39 +/-0.05 a Hubble Parameter of 88.0 +/-6 km s-1 Mpc-1 is found. A comparison with the results of the Hubble Key Project (Freedman et al 2001) is made and discrepancies between the K-TFR distances and the HKP I-TFR distances are discussed. Implications for Lamda-CDM cosmology are considered with H0=84 km s-1 Mpc-1. (Abridged)Comment: 37 pages including 12 tables and 7 figures. Final version accepted for publication in the Journal of Astrophysics & Astronom

Hepatitis C Virus Induces the Cannabinoid Receptor 1

BACKGROUND: Activation of hepatic CB(1) receptors (CB(1)) is associated with steatosis and fibrosis in experimental forms of liver disease. However, CB(1) expression has not been assessed in patients with chronic hepatitis C (CHC), a disease associated with insulin resistance, steatosis and metabolic disturbance. We aimed to determine the importance and explore the associations of CB(1) expression in CHC. METHODS: CB(1) receptor mRNA was measured by real time quantitative PCR on extracted liver tissue from 88 patients with CHC (genotypes 1 and 3), 12 controls and 10 patients with chronic hepatitis B (CHB). The Huh7/JFH1 Hepatitis C virus (HCV) cell culture model was used to validate results. PRINCIPAL FINDINGS: CB(1) was expressed in all patients with CHC and levels were 6-fold higher than in controls (P<0.001). CB(1) expression increased with fibrosis stage, with cirrhotics having up to a 2 fold up-regulation compared to those with low fibrosis stage (p<0.05). Even in mild CHC with no steatosis (F0-1), CB(1) levels remained substantially greater than in controls (p<0.001) and in those with mild CHB (F0-1; p<0.001). Huh7 cells infected with JFH-1 HCV showed an 8-fold upregulation of CB(1), and CB(1) expression directly correlated with the percentage of cells infected over time, suggesting that CB(1) is an HCV inducible gene. While HCV structural proteins appear essential for CB(1) induction, there was no core genotype specific difference in CB(1) expression. CB(1) significantly increased with steatosis grade, primarily driven by patients with genotype 3 CHC. In genotype 3 patients, CB(1) correlated with SREBP-1c and its downstream target FASN (SREBP-1c; R=0.37, FASN; R=0.39, p<0.05 for both). CONCLUSIONS/SIGNIFICANCE: CB(1) is up-regulated in CHC and is associated with increased steatosis in genotype 3. It is induced by the hepatitis C virus

Obstructive Sleep Apnea Is Associated with Liver Damage and Atherosclerosis in Patients with Non-Alcoholic Fatty Liver Disease

We assessed whether obstructive sleep apnea (OSA) and nocturnal hypoxemia are associated with severity of liver fibrosis and carotid atherosclerosis in patients with biopsy-proven NAFLD and low prevalence of morbid obesity. Secondary aim was to explore the association of OSA and hypoxemia with NASH and severity of liver pathological changes