Five Dimensional Cosmological Models in General Relativity

A Five dimensional Kaluza-Klein space-time is considered in the presence of a perfect fluid source with variable G and $\Lambda$. An expanding universe is found by using a relation between the metric potential and an equation of state. The gravitational constant is found to decrease with time as $G \sim t^{-(1-\omega)}$ whereas the variation for the cosmological constant follows as $\Lambda \sim t^{-2}$, $\Lambda \sim (\dot R/R)^2$ and $\Lambda \sim \ddot R/R$ where $\omega$ is the equation of state parameter and $R$ is the scale factor.Comment: 13 pages, 4 figures, accepted in Int. J. Theor. Phy

On the Generation of Positivstellensatz Witnesses in Degenerate Cases

One can reduce the problem of proving that a polynomial is nonnegative, or more generally of proving that a system of polynomial inequalities has no solutions, to finding polynomials that are sums of squares of polynomials and satisfy some linear equality (Positivstellensatz). This produces a witness for the desired property, from which it is reasonably easy to obtain a formal proof of the property suitable for a proof assistant such as Coq. The problem of finding a witness reduces to a feasibility problem in semidefinite programming, for which there exist numerical solvers. Unfortunately, this problem is in general not strictly feasible, meaning the solution can be a convex set with empty interior, in which case the numerical optimization method fails. Previously published methods thus assumed strict feasibility; we propose a workaround for this difficulty. We implemented our method and illustrate its use with examples, including extractions of proofs to Coq.Comment: To appear in ITP 201

The exposure of the hybrid detector of the Pierre Auger Observatory

The Pierre Auger Observatory is a detector for ultra-high energy cosmic rays. It consists of a surface array to measure secondary particles at ground level and a fluorescence detector to measure the development of air showers in the atmosphere above the array. The "hybrid" detection mode combines the information from the two subsystems. We describe the determination of the hybrid exposure for events observed by the fluorescence telescopes in coincidence with at least one water-Cherenkov detector of the surface array. A detailed knowledge of the time dependence of the detection operations is crucial for an accurate evaluation of the exposure. We discuss the relevance of monitoring data collected during operations, such as the status of the fluorescence detector, background light and atmospheric conditions, that are used in both simulation and reconstruction.Comment: Paper accepted by Astroparticle Physic

Observation of Orbitally Excited B_s Mesons

We report the first observation of two narrow resonances consistent with states of orbitally excited (L=1) B_s mesons using 1 fb^{-1} of ppbar collisions at sqrt{s} = 1.96 TeV collected with the CDF II detector at the Fermilab Tevatron. We use two-body decays into K^- and B^+ mesons reconstructed as B^+ \to J/\psi K^+, J/\psi \to \mu^+ \mu^- or B^+ \to \bar{D}^0 \pi^+, \bar{D}^0 \to K^+ \pi^-. We deduce the masses of the two states to be m(B_{s1}) = 5829.4 +- 0.7 MeV/c^2 and m(B_{s2}^*) = 5839.7 +- 0.7 MeV/c^2.Comment: Version accepted and published by Phys. Rev. Let

Development of new promising varieties of faba bean through traditional pedigree method for commercial cultivation in plain zone of India

A long term experiment was carried out in MAP Section, Department of Genetics & Plant Breeding,  CCS Haryana Agricultural University, Hisar from 2005-06 to 2018-19 on identification of elite genotypes from germplasm and their utilization in the development of high yielding variety through hybridization followed by traditional pedigree method to obtain desirable transgressive segregants in Faba bean. In the present investigation a number of germplasm lines were screened for seed yield and other related traits including national check Vikrant during 2005-06 under AICRN in augmented block design. As a result, ten elite genotypes identified i.e. EC117755, EC117799, EC248710, EC329675, HB123, HB180, HB430, HB204, HB 430, HB 502, HB 503 & one check variety, Vikrant. By using these elite genotypes, a number of F1 hybrids were made during 2005-06 and F2 to F6 generations were evaluated to identify the superior progenies during 2007-08 to 2011-12. After a long process of evaluation, rejection and selection, 20 superior transgressive segregant homozygous progenies were identified to make new entries. Later on, during 2012-2013, the superior entries (viz. HB12-1, HB12-5, HB12-8, HB12-9, HB12-11, HB12-12, HB12-13, HB12-14, HB12-15, HB12-26, HB12-28, HB12-29, HB12-30, HB12-31, HB12-34, HB12-36, HB12-37,HB12-38, HB12-39 and HB12-42) were evaluated at Hisar centre against Vikrant and found promising. Therefore, all these 20 genotypes were evaluated in SST during 2013-14, LST during 2014-15 and FYT during 2015-16. On the basis of above results, only five genotypes viz. HB12-8 (47.77q/ha), HB12-42 (47.70q/ha), HB12-15 (46.70q/ha), HB12-34 (46.14q/ha) and HB12-37 (45. 31q/ha) were found promising. These were further evaluated in multi-location trials at seven locations (i.e. Ambikpur, Delhi, Faizabad, Faridkot, Hisar, Ludhiana & Ranchi) for seed yield, quality and resistance against insect pest & disease in IVT and AVT during 2016-17 & 2017-18, respectively. Out of these, HB12-34 exhibited yield superiority over national checks,Vikrant and HFB-1 and free from insect pest and disease as well as low in vicine-covicine and high in protein content. Therefore, HB12-34 may be recommended for commercial cultivation in plain zone at national level

Unimodular bimode gravity and the coherent scalar-graviton field as galaxy dark matter

The explicit violation of the general gauge invariance/relativity is adopted as the origin of dark matter and dark energy of the gravitational nature. The violation of the local scale invariance alone, with the residual unimodular one, is considered. Besides the four-volume preserving deformation mode -- the transverse-tensor graviton -- the metric comprises a compression mode -- the scalar graviton, or the systolon. A unimodular invariant and general covariant metric theory of the bimode/scalar-tensor gravity is consistently worked out. To reduce the primordial ambiguity of the theory a dynamical global symmetry is imposed, with its subsequent spontaneous breaking revealed. The static spherically symmetric case in the empty, but possibly for the origin, space is studied. A three-parameter solution describing a new static space structure -- the dark lacuna -- is constructed. It enjoys the property of gravitational confinement, with the logarithmic potential of gravitational attraction at the periphery, and results in the asymptotically flat rotation curves. Comprising a super-massive dark fracture (a scalar-modified black hole) at the origin surrounded by a cored dark halo, the dark lacunas are proposed as a prototype model of galaxies, implying an ultimate account for the distributed non-gravitational matter and a putative asphericity or rotation.Comment: 38 pages, 10 figures; exposition improved, remarks added, accepted for publicatio

Genetics of grain yield and its components in wheat under heat stress

Heat stress is a matter of a great concern for the wheat crop. Heat stress usually either hastens crop development or shortens the grain filling duration, which severely reduces grain yield. Being a complex trait, understanding the genetics and gene interactions of stress tolerance are the two primary requirements for improving yield levels. Genetic analysis through generation mean analysis helps to find out the nature of gene actions involved in a concerned trait by providing an estimate of main gene effects (additive and dominance) along with their digenic interactions (additive × additive, additive × dominance, and dominance × dominance). In the present investigation, we elucidated the inheritance pattern of different yield contributing traits under heat stress using different cross combinations which could be helpful for selecting a suitable breeding strategy. Thus six generations of five crosses were sown normal (non-stress, TS) and late (heat stress, LS) in a randomized block design with three replications during two crop seasons. The model was not adequate for late sown conditions indicating the expression of epistatic genes under stress conditions. The traits i.e. Days to heading (DH), Days to anthesis (DA), Days to maturity (DM), Grain filling duration (GFD), Grain yield (GY), Thousand grain weight (TGW), Grain weight per spike (GWS) and Heat susceptibility index (HSI) under heat stress conditions were found under the control of additive gene action with dominance × dominance interaction, additive gene action with additive × dominance epistatic effect, dominance gene action with additive × additive interaction effect, additive and dominance gene action with dominance × dominance interaction effect, additive gene action with additive × dominance epistatic effect, additive gene action with additive × additive interaction effect and dominance gene action with additive × additive interaction effect, respectively

Evaluation of sesamum gum as an excipient in matrix tablets

In developing countries modern medicines are often beyond the affordability of the majority of the population. This is due to the reliance on expensive imported raw materials despite the abundance of natural resources which could provide an equivalent or even an improved function. The aim of this study was to investigate the potential of sesamum gum (SG) extracted from the leaves of Sesamum radiatum (readily cultivated in sub-Saharan Africa) as a matrix former. Directly compressed matrix tablets were prepared from the extract and compared with similar matrices of HPMC (K4M) using theophylline as a model water soluble drug. The compaction, swelling, erosion and drug release from the matrices were studied in deionized water, 0.1 N HCl (pH 1.2) and phosphate buffer (pH 6.8) using USP apparatus II. The data from the swelling, erosion and drug release studies were also fitted into the respective mathematical models. Results showed that the matrices underwent a combination of swelling and erosion, with the swelling action being controlled by the rate of hydration in the medium. SG also controlled the release of theophylline similar to the HPMC and therefore may have use as an alternative excipient in regions where Sesamum radiatum can be easily cultivated

Potential Genetic Overlap Between Insomnia and Sleep Symptoms in Major Depressive Disorder: A Polygenic Risk Score Analysis

Background: The prevalence of insomnia and hypersomnia in depressed individuals is substantially higher than that found in the general population. Unfortunately, these concurrent sleep problems can have profound effects on the disease course. Although the full biology of sleep remains to be elucidated, a recent genome-wide association (GWAS) of insomnia, and other sleep traits in over 1 million individuals was recently published and provides many promising hits for genetics of insomnia in a population-based sample. Methods: Using data from the largest available GWAS of insomnia and other sleep traits, we sought to test if sleep variable PRS scores derived from population-based studies predicted sleep variables in samples of depressed cases [Psychiatric Genomics Consortium - Major Depressive Disorder subjects (PGC MDD)]. A leave-one-out analysis was performed to determine the effects that each individual study had on our results. Results: The only significant finding was for insomnia, where p-value threshold, p = 0.05 was associated with insomnia in our PGC MDD sample (R2 = 1.75−3, p = 0.006). Conclusion: Our results reveal that <1% of variance is explained by the variants that cover the two significant p-value thresholds, which is in line with the fact that depression and insomnia are both polygenic disorders. To the best of our knowledge, this is the first study to investigate genetic overlap between the general population and a depression sample for insomnia, which has important treatment implications, such as leading to novel drug targets in future research efforts