Separability of Hamilton-Jacobi and Klein-Gordon Equations in General Kerr-NUT-AdS Spacetimes

We demonstrate the separability of the Hamilton-Jacobi and scalar field equations in general higher dimensional Kerr-NUT-AdS spacetimes. No restriction on the parameters characterizing these metrics is imposed.Comment: 4 pages, no figure

Particle Motion and Scalar Field Propagation in Myers-Perry Black Hole Spacetimes in All Dimensions

We study separability of the Hamilton-Jacobi and massive Klein-Gordon equations in the general Myers-Perry black hole background in all dimensions. Complete separation of both equations is carried out in cases when there are two sets of equal black hole rotation parameters, which significantly enlarges the rotational symmetry group. We explicitly construct a nontrivial irreducible Killing tensor associated with the enlarged symmetry group which permits separation. We also derive first-order equations of motion for particles in these backgrounds and examine some of their properties.Comment: 16 pages, LaTeX2

Hidden Symmetry of Higher Dimensional Kerr-NUT-AdS Spacetimes

It is well known that 4-dimensional Kerr-NUT-AdS spacetime possesses the hidden symmetry associated with the Killing-Yano tensor. This tensor is "universal" in the sense that there exist coordinates where it does not depend on any of the free parameters of the metric. Recently the general higher dimensional Kerr-NUT-AdS solutions of the Einstein equations were obtained. We demonstrate that all these metrics with arbitrary rotation and NUT parameters admit a universal Killing-Yano tensor. We give an explicit presentation of the Killing-Yano and Killing tensors and briefly discuss their properties.Comment: 4 pages, some discussion and references are adde

Effect of Foliar Sprays of NAA, Triacontanol and Boron on Growth and Seed Quality in Bitter Gourd (Momordica charantia L.) Cv. Pusa Visesh

An investigation was undertaken to study the effect of foliar sprays of NAA, triacontanol and boron on vine growth, seed quality and storability in bitter gourd cv. Pusa Visesh. Results revealed that NAA at 50mg/l produced the longest vines (192.33 and 260.67cm), maximum leaf area (1.890 and 2.965cm2/vine), leaf area index (1.969 and 2.760) and leaf chlorophyll content (39.23 and 38.90 SPAD value) at 85 and 100 days after sowing (DAS), respectively. As for seed quality attributes, treatment with boron at 4mg/l recorded lowest seed moisture content and highest seed germination percentage (9.16% and 85.5%, respectively), followed by NAA at 50mg/l (9.21% and 85.25%, respectively) whereas, Control recorded highest seed moisture and lowest seed germination percentage (9.84% and 74.5%, respectively) recorded at the end of storage

The power output of local obscured and unobscured AGN: crossing the absorption barrier with Swift/BAT and IRAS

The Swift/BAT 9-month catalogue of active galactic nuclei (AGN) provides an unbiased census of local supermassive black hole accretion, and probes to all but the highest levels of absorption in AGN. We explore a method for characterising the bolometric output of both obscured and unobscured AGN by combining the hard X-ray data from Swift/BAT (14-195keV) with the reprocessed IR emission as seen with the IRAS all-sky surveys. This approach bypasses the complex modifications to the SED introduced by absorption in the optical, UV and 0.1-10 keV regimes and provides a long-term, average picture of the bolometric output of these sources. We broadly follow the approach of Pozzi et al. for calculating the bolometric luminosities by adding nuclear IR and hard X-ray luminosities, and consider different approaches for removing non-nuclear contamination in the large-aperture IRAS fluxes. Using mass estimates from the M_BH-L_bulge relation, we present the Eddington ratios \lambda_Edd and 2-10 keV bolometric corrections for a subsample of 63 AGN (35 obscured and 28 unobscured) from the Swift/BAT catalogue, and confirm previous indications of a low Eddington ratio distribution for both samples. Importantly, we find a tendency for low bolometric corrections (typically 10-30) for the obscured AGN in the sample (with a possible rise from ~15 for \lambda_Edd<0.03 to ~32 above this), providing a hitherto unseen window onto accretion processes in this class of AGN. This finding is of key importance in calculating the expected local black hole mass density from the X-ray background since it is composed of emission from a significant population of such obscured AGN. Analogous studies with high resolution IR data and a range of alternative models for the torus emission will form useful future extensions to this work. (Abridged)Comment: 19 pages, 16 figures, 2 tables. Accepted for publication in MNRA

Complete Integrability of Geodesic Motion in General Kerr-NUT-AdS Spacetimes

We explicitly exhibit n-1 constants of motion for geodesics in the general D-dimensional Kerr-NUT-AdS rotating black hole spacetime, arising from contractions of even powers of the 2-form obtained by contracting the geodesic velocity with the dual of the contraction of the velocity with the (D-2)-dimensional Killing-Yano tensor. These constants of motion are functionally independent of each other and of the D-n+1 constants of motion that arise from the metric and the D-n = [(D+1)/2] Killing vectors, making a total of D independent constants of motion in all dimensions D. The Poisson brackets of all pairs of these D constants are zero, so geodesic motion in these spacetimes is completely integrable.Comment: 4 pages. We have now found that the geodesic motion is not just integrable, but completely integrabl

Amplification of real-time high resolution melting analysis PCR method for polycystic kidney disease (PKD) gene mutations in autosomal dominant polycystic kidney disease patients

PKD1 and PKD2 are the two genes responsible for the development of autosomal dominant polycystic kidney disease (ADPKD). PKD1 gene mutations accounts for ≈85% of all ADPKD cases, while the remaining ≈15% of cases is caused by mutations in the PKD2 gene. Genotyping for PKD1 and PKD2 mutations was usually identified using conventional polymerase chain reaction (PCR) or PCR-single stranded conformation polymorphisms (SSCP) methods. In this study, we assessed the usefulness of eight common primers amplifying the respective genes in real-time high resolution melting analysis PCR (real-time HRMA PCR) in terms of time, cost and sensitivity with respect to PCR-SSCP method. We found that case sample can easily be differentiated from control sample by melting curve profile difference, although a primer was found to be less useful. We concluded that real-time HRMA PCR is a rapid and sensitive method to categorize samples based on the melting curve profiles with comparable sensitivity to conventional PCR-SSCP.Key words: Autosomal dominant polycystic kidney disease (ADPKD), real-time PCR, high resolution melting analysis, PKD1, PKD2

Genome-wide profiling of histone modifications (H3K9me2 and H4K12ac) and gene expression in rust (uromyces appendiculatus) inoculated common bean (Phaseolus vulgaris L)

Histone modifications such as methylation and acetylation play a significant role in controlling gene expression in unstressed and stressed plants. Genome-wide analysis of such stress-responsive modifications and genes in non-model crops is limited. We report the genome-wide profiling of histone methylation (H3K9me2) and acetylation (H4K12ac) in common bean (Phaseolus vulgaris L.) under rust (Uromyces appendiculatus) stress using two high-throughput approaches, chromatin immunoprecipitation sequencing (ChIP-Seq) and RNA sequencing (RNA-Seq). ChIP-Seq analysis revealed 1,235 and 556 histone methylation and acetylation responsive genes from common bean leaves treated with the rust pathogen at 0, 12 and 84 hour-after-inoculation (hai), while RNA-Seq analysis identified 145 and 1,763 genes differentially expressed between mock-inoculated and inoculated plants. The combined ChIP-Seq and RNA-Seq analyses identified some key defense responsive genes (calmodulin, cytochrome p450, chitinase, DNA Pol II, and LRR) and transcription factors (WRKY, bZIP, MYB, HSFB3, GRAS, NAC, and NMRA) in bean-rust interaction. Differential methylation and acetylation affected a large proportion of stress-responsive genes including resistant (R) proteins, detoxifying enzymes, and genes involved in ion flux and cell death. The genes identified were functionally classified using Gene Ontology (GO) and EuKaryotic Orthologous Groups (KOGs). The Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway analysis identified a putative pathway with ten key genes involved in plant-pathogen interactions. This first report of an integrated analysis of histone modifications and gene expression involved in the bean-rust interaction as reported here provides a comprehensive resource for other epigenomic regulation studies in non-model species under stress