Proof of a determinant evaluation conjectured by Bombieri, Hunt and van der Poorten

A determinant evaluation is proven, a special case of which establishes a conjecture of Bombieri, Hunt, and van der Poorten (Experimental Math\. {\bf 4} (1995), 87--96) that arose in the study of Thue's method of approximating algebraic numbers.Comment: AMSTe

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

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

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.

Super congruences and Euler numbers

Let $p>3$ be a prime. We prove that $$\sum_{k=0}^{p-1}\binom{2k}{k}/2^k=(-1)^{(p-1)/2}-p^2E_{p-3} (mod p^3),$$ $$\sum_{k=1}^{(p-1)/2}\binom{2k}{k}/k=(-1)^{(p+1)/2}8/3*pE_{p-3} (mod p^2),$$ $$\sum_{k=0}^{(p-1)/2}\binom{2k}{k}^2/16^k=(-1)^{(p-1)/2}+p^2E_{p-3} (mod p^3)$$, where E_0,E_1,E_2,... are Euler numbers. Our new approach is of combinatorial nature. We also formulate many conjectures concerning super congruences and relate most of them to Euler numbers or Bernoulli numbers. Motivated by our investigation of super congruences, we also raise a conjecture on 7 new series for $\pi^2$, $\pi^{-2}$ and the constant $K:=\sum_{k>0}(k/3)/k^2$ (with (-) the Jacobi symbol), two of which are $$\sum_{k=1}^\infty(10k-3)8^k/(k^3\binom{2k}{k}^2\binom{3k}{k})=\pi^2/2$$ and $$\sum_{k>0}(15k-4)(-27)^{k-1}/(k^3\binom{2k}{k}^2\binom{3k}k)=K.$

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

Continued fractions and irrationality exponents for modified engel and pierce series

An Engel series is a sum of reciprocals of a non-decreasing sequence (xn) of positive integers, which is such that each term is divisible by the previous one, and a Pierce series is an alternating sum of the reciprocals of a sequence with the same property. Given an arbitrary rational number, we show that there is a family of Engel series which when added to it produces a transcendental number ? whose continued fraction expansion is determined explicitly by the corresponding sequence (xn), where the latter is generated by a certain nonlinear recurrence of second order. We also present an analogous result for a rational number with a Pierce series added to or subtracted from it. In both situations (a rational number combined with either an Engel or a Pierce series), the irrationality exponent is bounded below by (3 + ?5)/2, and we further identify infinite families of transcendental numbers ? whose irrationality exponent can be computed precisely. In addition, we construct the continued fraction expansion for an arbitrary rational number added to an Engel series with the stronger property that x2j divides xj+1 for all j