Generalized Convexity and Inequalities

Let R+ = (0,infinity) and let M be the family of all mean values of two numbers in R+ (some examples are the arithmetic, geometric, and harmonic means). Given m1, m2 in M, we say that a function f : R+ to R+ is (m1,m2)-convex if f(m1(x,y)) < or = m2(f(x),f(y)) for all x, y in R+ . The usual convexity is the special case when both mean values are arithmetic means. We study the dependence of (m1,m2)-convexity on m1 and m2 and give sufficient conditions for (m1,m2)-convexity of functions defined by Maclaurin series. The criteria involve the Maclaurin coefficients. Our results yield a class of new inequalities for several special functions such as the Gaussian hypergeometric function and a generalized Bessel function.Comment: 17 page

Tietze Extension Theorem for Ordered Fuzzy Gδ-extremally Disconnected Spaces

In this paper, a new class of fuzzy topological spaces called ordered fuzzy G -extremally disconnected spaces is introduced. Tietze extension theorem for ordered fuzzy Gδ-extremally disconnected spaces has been discussed as in [10] besides proving several other propositions and lemmas

Seed coat mediated resistance against Aspergillus flavus infection in peanut

Toxic metabolites known as aflatoxins are produced via certain species of the Aspergillus genus, specifically A. flavus, A. parasiticus, A. nomius, and A. tamarie. Although various pre- and post-harvest strategies have been employed, aflatoxin contamination remains a major problem within peanut crop, especially in subtropical environments. Aflatoxins are the most well-known and researched mycotoxins produced within the Aspergillus genus (namely Aspergillus flavus) and are classified as group 1 carcinogens. Their effects and etiology have been extensively researched and aflatoxins are commonly linked to growth defects and liver diseases in humans and livestock. Despite the known importance of seed coats in plant defense against pathogens, peanut seed coat mediated defenses against Aspergillus flavus resistance, have not received considerable attention. The peanut seed coat (testa) is primarily composed of a complex cell wall matrix consisting of cellulose, lignin, hemicellulose, phenolic compounds, and structural proteins. Due to cell wall desiccation during seed coat maturation, postharvest A. flavus infection occurs without the pathogen encountering any active genetic resistance from the live cell(s) and the testa acts as a physical and biochemical barrier only against infection. The structure of peanut seed coat cell walls and the presence of polyphenolic compounds have been reported to inhibit the growth of A. flavus and aflatoxin contamination; however, there is no comprehensive information available on peanut seed coat mediated resistance. We have recently reviewed various plant breeding, genomic, and molecular mechanisms, and management practices for reducing A. flavus infection and aflatoxin contamination. Further, we have also proved that seed coat acts as a physical and biochemical barrier against A. flavus infection. The current review focuses specifically on the peanut seed coat cell wall-mediated disease resistance, which will enable researchers to understand the mechanism and design efficient strategies for seed coat cell wall-mediated resistance against A. flavus infection and aflatoxin contamination

Hawking Radiation from AdS Black Holes

We investigate Hawking radiation from black holes in (d+1)-dimensional anti-de Sitter space. We focus on s-waves, make use of the geometrical optics approximation, and follow three approaches to analyze the radiation. First, we compute a Bogoliubov transformation between Kruskal and asymptotic coordinates and compare the different vacua. Second, following a method due to Kraus, Parikh, and Wilczek, we view Hawking radiation as a tunneling process across the horizon and compute the tunneling probablility. This approach uses an anti-de Sitter version of a metric originally introduced by Painleve for Schwarzschild black holes. From the tunneling probability one also finds a leading correction to the semi-classical emission rate arising from the backreaction to the background geometry. Finally, we consider a spherically symmetric collapse geometry and the Bogoliubov transformation between the initial vacuum state and the vacuum of an asymptotic observer.Comment: 13 pages, latex2e, v2: some clarifications and references adde

De Sitter and Schwarzschild-De Sitter According to Schwarzschild and De Sitter

When de Sitter first introduced his celebrated spacetime, he claimed, following Schwarzschild, that its spatial sections have the topology of the real projective space RP^3 (that is, the topology of the group manifold SO(3)) rather than, as is almost universally assumed today, that of the sphere S^3. (In modern language, Schwarzschild was disturbed by the non-local correlations enforced by S^3 geometry.) Thus, what we today call "de Sitter space" would not have been accepted as such by de Sitter. There is no real basis within classical cosmology for preferring S^3 to RP^3, but the general feeling appears to be that the distinction is in any case of little importance. We wish to argue that, in the light of current concerns about the nature of de Sitter space, this is a mistake. In particular, we argue that the difference between "dS(S^3)" and "dS(RP^3)" may be very important in attacking the problem of understanding horizon entropies. In the approach to de Sitter entropy via Schwarzschild-de Sitter spacetime, we find that the apparently trivial difference between RP^3 and S^3 actually leads to very different perspectives on this major question of quantum cosmology.Comment: 26 pages, 8 figures, typos fixed, references added, equation numbers finally fixed, JHEP versio

From ten to four and back again: how to generalize the geometry

We discuss the four-dimensional N=1 effective approach in the study of warped type II flux compactifications with SU(3)x SU(3)-structure to AdS_4 or flat Minkowski space-time. The non-trivial warping makes it natural to use a supergravity formulation invariant under local complexified Weyl transformations. We obtain the classical superpotential from a standard argument involving domain walls and generalized calibrations and show how the resulting F-flatness and D-flatness equations exactly reproduce the full ten-dimensional supersymmetry equations. Furthermore, we consider the effect of non-perturbative corrections to this superpotential arising from gaugino condensation or Euclidean D-brane instantons. For the latter we derive the supersymmetry conditions in N=1 flux vacua in full generality. We find that the non-perturbative corrections induce a quantum deformation of the internal generalized geometry. Smeared instantons allow to understand KKLT-like AdS vacua from a ten-dimensional point of view. On the other hand, non-smeared instantons in IIB warped Calabi-Yau compactifications 'destabilize' the Calabi-Yau complex structure into a genuine generalized complex one. This deformation gives a geometrical explanation of the non-trivial superpotential for mobile D3-branes induced by the non-perturbative corrections.Comment: LaTeX, 47 pages, v2, references, hyperref added, v3, correcting small inaccuracies in eqs. (2.6a) and (5.16

The Taming of Closed Time-like Curves

We consider a $R^{1,d}/Z_2$ orbifold, where $Z_2$ acts by time and space reversal, also known as the embedding space of the elliptic de Sitter space. The background has two potentially dangerous problems: time-nonorientability and the existence of closed time-like curves. We first show that closed causal curves disappear after a proper definition of the time function. We then consider the one-loop vacuum expectation value of the stress tensor. A naive QFT analysis yields a divergent result. We then analyze the stress tensor in bosonic string theory, and find the same result as if the target space would be just the Minkowski space $R^{1,d}$, suggesting a zero result for the superstring. This leads us to propose a proper reformulation of QFT, and recalculate the stress tensor. We find almost the same result as in Minkowski space, except for a potential divergence at the initial time slice of the orbifold, analogous to a spacelike Big Bang singularity. Finally, we argue that it is possible to define local S-matrices, even if the spacetime is globally time-nonorientable.Comment: 37 pages, LaTeX2e, uses amssymb, amsmath and epsf macros, 8 eps and 3 ps figures; (v2): Two additional comments + one reference added; (v3): corrections in discussion of CTCs + some clarification

U(N) Instantons on N=1/2 superspace -- exact solution & geometry of moduli space

We construct the exact solution of one (anti)instanton in N=1/2 super Yang-Mills theory defined on non(anti)commutative superspace. We first identify N = 1/2 superconformal invariance as maximal spacetime symmetry. For gauge group U(2), SU(2) part of the solution is given by the standard (anti)instanton, but U(1) field strength also turns out nonzero. The solution is SO(4) rotationally symmetric. For gauge group U(N), in contrast to the U(2) case, we show that the entire U(N) part of the solution is deformed by non(anti)commutativity and fermion zero-modes. The solution is no longer rotationally symmetric; it is polarized into an axially symmetric configuration because of the underlying non(anti)commutativity. We compute the `information metric' of one (anti) instanton. We find that moduli space geometry is deformed from hyperbolic space (Euclidean anti-de Sitter space) in a way anticipated from reduced spacetime symmetry. Remarkably, the volume measure of the moduli space turns out to be independent of the non(anti)commutativity. Implications to D-branes in Ramond- Ramond flux background and Maldacena's gauge-gravity correspondence are discussed.Comment: 39 pages, 3 figures, JHEP style; v2. typos corrected + a paragraph adde

A role for XRCC2 gene polymorphisms in breast cancer risk and survival

Background The XRCC2 gene is a key mediator in the homologous recombination repair of DNA double strand breaks. It is hypothesised that inherited variants in the XRCC2 gene might also affect susceptibility to, and survival from, breast cancer. Methods The study genotyped 12 XRCC2 tagging single nucleotide polymorphisms (SNPs) in 1131 breast cancer cases and 1148 controls from the Sheffield Breast Cancer Study (SBCS), and examined their associations with breast cancer risk and survival by estimating ORs and HRs, and their corresponding 95% CIs. Positive findings were further investigated in 860 cases and 869 controls from the Utah Breast Cancer Study (UBCS) and jointly analysed together with available published data for breast cancer risk. The survival findings were further confirmed in studies (8074 cases) from the Breast Cancer Association Consortium (BCAC). Results The most significant association with breast cancer risk in the SBCS dataset was the XRCC2 rs3218408 SNP (recessive model p=2.3×10−4, minor allele frequency (MAF)=0.23). This SNP yielded an ORrec of 1.64 (95% CI 1.25 to 2.16) in a two-site analysis of SBCS and UBCS, and a meta-ORrec of 1.33 (95% CI 1.12 to 1.57) when all published data were included. This SNP may mark a rare risk haplotype carried by two in 1000 of the control population. Furthermore, the XRCC2 coding R188H SNP (rs3218536, MAF=0.08) was significantly associated with poor survival, with an increased per-allele HR of 1.58 (95% CI 1.01 to 2.49) in a multivariate analysis. This effect was still evident in a pooled meta-analysis of 8781 breast cancer patients from the BCAC (HR 1.19, 95% CI 1.05 to 1.36; p=0.01). Conclusions These findings suggest that XRCC2 SNPs may influence breast cancer risk and survival

Black Hole Thermodynamics and Statistical Mechanics

We have known for more than thirty years that black holes behave as thermodynamic systems, radiating as black bodies with characteristic temperatures and entropies. This behavior is not only interesting in its own right; it could also, through a statistical mechanical description, cast light on some of the deep problems of quantizing gravity. In these lectures, I review what we currently know about black hole thermodynamics and statistical mechanics, suggest a rather speculative "universal" characterization of the underlying states, and describe some key open questions.Comment: 35 pages, Springer macros; for the Proceedings of the 4th Aegean Summer School on Black Hole