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, J. Number Theory , 166 ( 2016 ), 41 – 46 . 10.1016/j.jnt.2016.02.020 [6] SHIU , P. , The denominators of harmonic numbers , arXiv:1607.02863v1 . [7] Wu , B. L. and Chen , Y. G. , On certain properties of harmonic numbers , J. Number

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thus contributes to the growing body of studies that have found parallels and common denominators between substance addiction and behavioral addictions ( Hasin et al., 2013 ; Petry, 2016 ). Thus, overall, this study helps to fill a gap in the

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Abstract  

Previous research has shown that Web link based metrics can correlate with traditional research assessment at the university level. In this study, we test whether the same is true for the computer science departments in the UK. The relevant Web Impact Factors (WIFs) were calculated from the link data collected both from AltaVista and the special academic crawler of the University of Wolverhampton. The numbers of staff members and Web pages in each computer science department were used as denominators for the WIFs calculation. The number of inlinks to the computer science departments correlated significantly with their research productivities, and WIFs with numbers of staff members as denominators correlated significantly with their Research Assessment Exercise (RAE) ratings. The number of staff members was confirmed to be a better indicator of departmental size than the number of Web pages within the department's domain.

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Abstract  

Let fodd(z):= ∑ k=1ζ(2k + 1)z2k be the power series with the values of the Riemann ζ function at odd integers as coefficients. This function can be analytically continued to a meromorphic function over C. We prove that 1 and the values of fodd at rational points with relatively prime denominators are linearly independent over ―Q. Some arithmetical properties of the sequence {ζ(2k+1)} k=1 are deduced.

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Periodica Mathematica Hungarica
Authors: Pakwan Riyapan, Vichian Laohakosol and Tuangrat Chaichana

Summary  

Two types of explicit continued fractions are presented. The continued fractions of the first type include those discovered by Shallit in 1979 and 1982, which were later generalized by Pethő. They are further extended here using Peth\H o's method. The continued fractions of the second type include those whose partial denominators form an arithmetic progression as expounded by Lehmer in 1973. We give here another derivation based on a modification of Komatsu's method and derive its generalization. Similar results are also established for continued fractions in the field of formal series over a finite base field.

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Abstract  

The present paper establishes a complete result on approximation by rational functions with prescribed numerator degree in L pspaces for 1 < p < ∞ and proves that if f(x)∈L p [-1,1] changes sign exactly l times in (-1,1), then there exists r(x)∈R n l such that

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\left\| {f(x) - r(x)} \right\|_{L^p } \leqq C_{p,l,b} \omega (f,n^{ - 1} )_{L^p } ,$$ \end{document}
where R n l indicates all rational functions whose denominators consist of polynomials of degree n and numerators polynomials of degree l, and C p , l,b is a positive constant depending only on p, l and b which relates to the distance among the sign change points of f(x) and will be given in 3.

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Various aspects of the Mediterranean diet were analyzed in a series of studies conducted in Northern Italy on over 20,000 cases of several major cancers and 18,000 controls. For most digestive tract cancers, the risk decreased with increasing vegetable and fruit consumption, with relative risks between 0.3 and 0.7 for the highest level of intake, and the population attributable risks for low intake of vegetables and fruit ranged between 15 and 40%. Less strong inverse relations were observed for other (epithelial) cancers, too. A number of micronutrients contained in vegetables and fruit showed an inverse relation with cancer risk. In particular, flavones, flavonols and resveratrol were inversely related to breast cancer risk. Olive oil, which is the main common denominator of the Mediterranean diet, has also been inversely related to cancers of the colorectum and breast, and mainly of the upper digestive and respiratory tract.

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Abstract  

Data were compiled and linearly correlated on the growth in the gross domestic product (GDP) with the academic chemical engineering literature over a recent 26-year period for five different English-speaking countries, namely, the United States, Canada, Great Britain, India and Australia. The publication figures were also scaled to the total number of chemical engineering schools in the country; furthermore, all of these data were normalized from zero to unity, using the figures for the most recent year (1996) as the denominators, and then correlated against each other in linear fashion. Resulting confidence levels were in excess of 99% for each of the individual five countries, as well as for the entire set of normalized data for all of the countries.

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