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 $k=3$

Detection of Salmonella in Poultry Using Conventional Culture Methods and Polymerase Chain Reaction Technique

A study was carried out to evaluate three culture media and PCR for the detection of Salmonella spp. to improve Salmonella monitoring program. A total of 109 samples were collected from two farms. Sixty four samples were collected from farm A. These included 16 cloacal swabs collected from broilers before slaughtering, 18 intestinal swabs and 20 caecal swabs collected from broilers after evisceration, and 10 cloacal swabs collected from village chickens. Forty five samples were collected from farm B, which included 15 cloacal swabs from each of village chickens, turkeys, and guinea fowls. Samples were pre-enriched in BPW and investigated by plating them on XLT4 agar after enrichment in selenite cystine broth, BPLS agar after enrichment in Rappaport-Vasilliadis broth, and DIASALM directly after pre-enric hment in BPW. Suspected positive colonies were confirmed biochemically and serologically. DIASALM and BPLS agar were comparatively evaluated against XLT4 agar as the "gold standard" using Kappa statistic to determine the level of agreement between them. A total of 27 (24.77%) Salmonella were detected from the 109 samples. Isolation rates for XLT4, DIASALM, and BPLS were 20.20% (22 out of 109), 17.43% (19 out of 109), and 13.8% (15 out of 109), respectively. The sensitivity and agreement (Kappa statistic) with the "gold standard" for each evaluated detection method were: 70.4% and 0.69 (substantial) for DIASALM and 55.56% and 0.58 (mode rate) for BPLS. For the detection of Salmonella spp. by PCR, bacterial chromosomal DNA was extracted by boiling. Amplicons (429 bp) and (284 bp) derived from primers to the genomic random fragment (primers ST11 and ST15) and invA genes (primers 139 and 141) respectively, were confirmed as Salmonella specific on ethidium bromide-stained agarose gels. Using PCR assay Salmonella was detected 24% (13 out of 54) and 13% (7 out of 54) in broilers in farm A using primers ST11-ST15 and 139-141, respectively. Poultry species in farm B were negative for Salmonella by PCR. A specific primer was used for the detection of Salmonella enteritidis. None of Salmonella detected was Salmonella enteritidis. This study concluded that XLT4 agar is the most sensitive medium and is very specific for the isolation of Salmonella from chicken feces. DIASALM is a good medium for the isolation of Salmonella. The inability of PCR to successfully detect Salmonella specific products from all the samples that were positive for isolation is not clear. However, this would be partly explained by the presence of inhibitor factors in the DNA preparations. In addition, the primer set ST11-ST15 used in this study has not before been tested on cloacal swabs and fecal samples from poultry. Perhaps, with improved DNA extraction method may overcome the inhibitory problem and also low yield of DNA. PCR should be used together with cultivation for the detection of Salmonella especially when the serovar is to be determined

The normal ranges of cardiovascular parameters measured using the ultrasonic cardiac output monitor

The ultrasonic cardiac output monitor (USCOM) is a noninvasive transcutaneous continuous wave Doppler method for assessing hemodynamics. There are no published reference ranges for normal values in adults (aged 18– 60 years) for this device. This study aimed to (1) measure cardiovascular indices using USCOM in healthy adults aged 18–60 years; (2) combine these data with those for healthy children (aged 0–12), adolescents (aged 12–18), and the elderly (aged over 60) from our previously published studies in order to present normal ranges for all ages, and (3) establish normal ranges of USCOM-derived variables according to both weight and age. This was a population- based cross-sectional observational study of healthy Chinese subjects aged 0.5–89 years in Hong Kong. USCOM scans were performed on all subjects, to produce measurements including stroke volume, cardiac output, and systemic vascular resistance. Data from previously published studies (children, adolescents, and the elderly) were included. Normal ranges were defined as lying between the 2.5th and 97.5th percentiles. A total of 2218 subjects were studied (mean age = 16.4, range = 0.5–89; 52% male). From previous studies, 1197 children (aged 0–12, 55% male), 590 adolescents (aged 12–18, 49% male), and 77 elderly (aged 60–89, 55% male) were included. New data were collected from 354 adults aged 18–60 (47% male). Normal ranges are presented according to age and weight. We present comprehensive normal ranges for hemodynamic parameters obtained with USCOM in healthy subjects of all ages from infancy to the elderly

Positivity of energy for asymptotically locally AdS spacetimes

We derive necessary conditions for the spinorial Witten-Nester energy to be well-defined for asymptotically locally AdS spacetimes. We find that the conformal boundary should admit a spinor satisfying certain differential conditions and in odd dimensions the boundary metric should be conformally Einstein. We show that these conditions are satisfied by asymptotically AdS spacetimes. The gravitational energy (obtained using the holographic stress energy tensor) and the spinorial energy are equal in even dimensions and differ by a bounded quantity related to the conformal anomaly in odd dimensions.Comment: 36 pages, 1 figure; minor corrections, JHEP versio

Some extremal functions in Fourier analysis, III

We obtain the best approximation in $L^1(\R)$, by entire functions of exponential type, for a class of even functions that includes $e^{-\lambda|x|}$, where $\lambda >0$, $\log |x|$ and $|x|^{\alpha}$, where $-1 < \alpha < 1$. We also give periodic versions of these results where the approximating functions are trigonometric polynomials of bounded degree.Comment: 26 pages. Submitte

Conserved Charges in Even Dimensional Asymptotically locally Anti-de Sitter Space-times

Based on the recent paper hep-th/0503045, we derive a formula of calculating conserved charges in even dimensional asymptotically {\it locally} anti-de Sitter space-times by using the definition of Wald and Zoupas. This formula generalizes the one proposed by Ashtekar {\it et al}. Using the new formula we compute the masses of Taub-Bolt-AdS space-times by treating Taub-Nut-AdS space-times as the reference solution. Our result agrees with those resulting from "background subtraction" method or "boundary counterterm" method. We also calculate the conserved charges of Kerr-Taub-Nut-AdS solutions in four dimensions and higher dimensional Kerr-AdS solutions with Nut charges. The mass of (un)wrapped brane solutions in any dimension is given.Comment: Latex, 28 pages, v2: minor changes, to appear in JHE

Quantum corrections to the mass of the supersymmetric vortex

We calculate quantum corrections to the mass of the vortex in N=2 supersymmetric abelian Higgs model in (2+1) dimensions. We put the system in a box and apply the zeta function regularization. The boundary conditions inevitably violate a part of the supersymmetries. Remaining supersymmetry is however enough to ensure isospectrality of relevant operators in bosonic and fermionic sectors. A non-zero correction to the mass of the vortex comes from finite renormalization of couplings.Comment: Latex, 18 pp; v2 reference added; v3 minor change

Holographic Description of Gravitational Anomalies

The holographic duality can be extended to include quantum theories with broken coordinate invariance leading to the appearance of the gravitational anomalies. On the gravity side one adds the gravitational Chern-Simons term to the bulk action which gauge invariance is only up to the boundary terms. We analyze in detail how the gravitational anomalies originate from the modified Einstein equations in the bulk. As a side observation we find that the gravitational Chern-Simons functional has interesting conformal properties. It is invariant under conformal transformations. Moreover, its metric variation produces conformal tensor which is a generalization of the Cotton tensor to dimension $d+1=4k-1, k\in Z$. We calculate the modification of the holographic stress-energy tensor that is due to the Chern-Simons term and use the bulk Einstein equations to find its divergence and thus reproduce the gravitational anomaly. Explicit calculation of the anomaly is carried out in dimensions $d=2$ and $d=6$. The result of the holographic calculation is compared with that of the descent method and agreement is found. The gravitational Chern-Simons term originates by Kaluza-Klein mechanism from a one-loop modification of M-theory action. This modification is discussed in the context of the gravitational anomaly in six-dimensional $(2,0)$ theory. The agreement with earlier conjectured anomaly is found.Comment: 24 pages, Latex; presentation re-structured, new references adde

Ancient Gondwana break-up explains the distribution of the mycoheterotrophic family Corsiaceae (Liliales)

Plant science