The irrationality of a number theoretical series

Denote by $\sigma_k(n)$ the sum of the $k$-th powers of the divisors of $n$, and let $S_k=\sum_{n\geq 1}\frac{\sigma_k(n)}{n!}$. We prove that Schinzel's conjecture H implies that $S_k$ is irrational, and give an unconditional proof for the case $k=3$

Quantum transport of slow charge carriers in quasicrystals and correlated systems

We show that the semi-classical model of conduction breaks down if the mean free path of charge carriers is smaller than a typical extension of their wavefunction. This situation is realized for sufficiently slow charge carriers and leads to a transition from a metallic like to an insulating like regime when scattering by defects increases. This explains the unconventional conduction properties of quasicrystals and related alloys. The conduction properties of some heavy fermions or polaronic systems, where charge carriers are also slow, present a deep analogy.Comment: 4 page

Point sets that minimize (≤k)(\le k)-edges, 3-decomposable drawings, and the rectilinear crossing number of K30K_{30}

There are two properties shared by all known crossing-minimizing geometric drawings of $K_n$, for $n$ a multiple of 3. First, the underlying $n$-point set of these drawings has exactly $3\binom{k+2}{2}$ $(\le k)$-edges, for all $0\le k < n/3$. Second, all such drawings have the $n$ points divided into three groups of equal size; this last property is captured under the concept of 3-decomposability. In this paper we show that these properties are tightly related: every $n$-point set with exactly $3\binom{k+2}{2}$ $(\le k)$-edges for all $0\le k < n/3$, is 3-decomposable. As an application, we prove that the rectilinear crossing number of $K_{30}$ is 9726.Comment: 14 page

Short-term reliability of inflammatory mediators and response to exercise in the heat.

Prospective application of serum cytokines, lipopolysaccharide (LPS), and heat shock proteins (eHSPs) requires reliable measurement of these biomarkers that can signify exercise-induced heat stress in hot conditions. To accomplish this, both short-term (7 day) reliability (at rest, n = 12) and the acute responsiveness of each biomarker to exercise in the heat (pre and post 60-min cycling, 34.5°C and 70% RH, n = 20) were evaluated. Serum was analysed for the concentration of C-reactive protein (CRP), interleukin-6 (IL-6), heat shock protein 72 (eHSP72), immunoglobulin M (IgM) and LPS. Test–retest reliability was determined as the coefficient of variation (CV). Biomarkers with the least short-term within-participant variation were IL-6 (19%, ±20%; CV, ±95% confidence limits (CL)) and LPS (23%, ±13%). Greater variability was observed for IgM, eHSP72 and CRP (CV range 28–38%). IL-6 exhibited the largest increase in response to acute exercise (95%, ±11%, P = < 0.001) and although CRP had a modest CV (12%, ±7%), it increased substantially post-exercise (P = 0.02, ES; 0.78). In contrast, eHSP72 and LPS exhibited trivial changes post-exercise. It appears variation of common inflammatory markers after exercise in the heat is not always discernible from short-term (weekly) variation

Evidence for a Young Stellar Population in NGC 5018

Two absorption line indices, Ca II and Hdelta/FeI4045, measured from high resolution spectra are used with evolutionary synthesis models to verify the presence of a young stellar population in NGC 5018. The derived age of this population is about ~2.8 Gyr with a metallicity roughly solar and it completely dominates the integrated light of the galaxy near 4000 A.Comment: 13 pages, 7 figures (figs 3-7 are color figures), to be published in the May 2000 issue of the Astrophysical Journa

Primary Phagocytosis of Neurons by Inflamed Microglia: Potential Roles in Neurodegeneration

Microglial phagocytosis of dead or dying neurons can be beneficial by preventing the release of damaging and/or pro-inflammatory intracellular components. However, there is now evidence that under certain conditions, such as inflammation, microglia can also phagocytose viable neurons, thus executing their death. Such phagocytic cell death may result from exposure of phosphatidylserine (PS) or other eat-me signals on otherwise viable neurons as a result of physiological activation or sub-toxic insult, and neuronal phagocytosis by activated microglia. In this review, we discuss the mechanisms of phagocytic cell death and its potential roles in Alzheimer’s Disease, Parkinson’s Disease, and Frontotemporal Dementia