Rotating dust solutions of Einstein's equations with 3-dimensional symmetry groups; Part 1: Two Killing fields spanned on u^{\alpha} and w^{\alpha }

For a rotating dust with a 3-dimensional symmetry group all possible metric forms can be classified and, within each class, explicitly written out. This is made possible by the formalism of Pleba\'nski based on the Darboux theorem. In the resulting coordinates, the Killing vector fields (if any exist) assume a special form. Each Killing vector field may be either spanned on the fields of velocity and rotation or linearly independent of them. By considering all such cases one arrives at the classification. With respect to the structures of the groups, this is just the Bianchi classification, but with all possible orientations of the orbits taken into account. In this paper, which is part 1 of a 3-part series, all solutions are considered for which two Killing fields are spanned on velocity and rotation. The solutions of Lanczos and G\"{o}del are identified as special cases, and their new invariant definitions are provided. In addition, a new invariant definition is given of the Ozsvath class III solution.Comment: 23 pages, LaTe

A Non - Singular Cosmological Model with Shear and Rotation

We have investigated a non-static and rotating model of the universe with an imperfect fluid distribution. It is found that the model is free from singularity and represents an ever expanding universe with shear and rotation vanishing for large value of time.Comment: 10 pages, late

Molecular Clock on a Neutral Network

The number of fixed mutations accumulated in an evolving population often displays a variance that is significantly larger than the mean (the overdispersed molecular clock). By examining a generic evolutionary process on a neutral network of high-fitness genotypes, we establish a formalism for computing all cumulants of the full probability distribution of accumulated mutations in terms of graph properties of the neutral network, and use the formalism to prove overdispersion of the molecular clock. We further show that significant overdispersion arises naturally in evolution when the neutral network is highly sparse, exhibits large global fluctuations in neutrality, and small local fluctuations in neutrality. The results are also relevant for elucidating the topological structure of a neutral network from empirical measurements of the substitution process.Comment: 10 page

Crystal structure of a mixed solvated form of amoxapine acetate

The mixed solvated salt 4-(2-chloro­dibenzo[b,f][1,4]oxazepin-11-yl)piperazin-1-ium acetate-acetic acid-cyclo­hexane (2/2/1), C17H17ClN3O+·C2H3O2-·C2H4O2·0.5C6H12, crystallizes with one mol­ecule of protonated amoxapine (AXPN), an acetate anion and a mol­ecule of acetic acid together with half a mol­ecule of cyclo­hexane. In the centrosymmetric crystal, both enanti­omers of the protonated AXPN mol­ecule stack alternatively along [001]. Acetate anions connect the AXPN cations through N-H...O hydrogen bonding in the [010] direction, creating a sheet lying parallel to (100). The acetic acid mol­ecules are linked to the acetate anions via O-H...O hydrogen bonds within the sheets. Within the sheets there are also a number of C-H...O hydrogen bonds present. The cyclo­hexane solvent mol­ecules occupy the space between the sheets

Multilingual Android based application for Meteorological Units Conversions and Calculation of empirical relationship.

Meteorological data can be expressed in several units. Various climatological and physical parameters are used for calculating evapotranpiration, irrigation demand, soil moisture etc. from meteorological data. Some of these data are directly measured in weather stations. Other parameters are related to commonly measured data on field and can be derived with the help of a direct or empirical relationship. Many a times on field and on time calculation or conversion are required. Android is a mobile based, free of cost operating system; used by majority of the mobile manufactures and equally appreciated and used by handheld users. Person working on field collects data and an android mobile based multilingual converter and calculator can assist in solving major issues pertaining to on field and on time conversions and calculation in regional language. DOI: 10.17762/ijritcc2321-8169.15011

Rotating dust solutions of Einstein's equations with 3-dimensional symmetry groups, Part 3: All Killing fields linearly independent of u^{\alpha} and w^{\alpha}

This is the third and last part of a series of 3 papers. Using the same method and the same coordinates as in parts 1 and 2, rotating dust solutions of Einstein's equations are investigated that possess 3-dimensional symmetry groups, under the assumption that each of the Killing vectors is linearly independent of velocity $u^{\alpha}$ and rotation $w^{\alpha}$ at every point of the spacetime region under consideration. The Killing fields are found and the Killing equations are solved for the components of the metric tensor in every case that arises. No progress was made with the Einstein equations in any of the cases, and no previously known solutions were identified. A brief overview of literature on solutions with rotating sources is given.Comment: One missing piece, signaled after eq. (10.7), is added after (10.21). List of corrections: In (3.7) wrong subscript in vorticity; In (3.10) wrong subscript in last term of g_{23}; In (4.23) wrong formulae for g_{12} and g_{22}; In (7.17) missing factor in velocity; In (7.18) one wrong factor in g_{22}; In (10.9) factor in vorticity; In (10.15) - (10.20) y_0 = 0; In (10.20) wrong second term in y. The rewriting typos did not influence result

Relation Between Einstein And Quantum Field Equations

We show that there exists a choice of scalar field modes, such that the evolution of the quantum field in the zero-mass and large-mass limits is consistent with the Einstein equations for the background geometry. This choice of modes is also consistent with zero production of these particles and thus corresponds to a preferred vacuum state preserved by the evolution. In the zero-mass limit, we find that the quantum field equation implies the Einstein equation for the scale factor of a radiation-dominated universe; in the large-mass case, it implies the corresponding Einstein equation for a matter-dominated universe. Conversely, if the classical radiation-dominated or matter-dominated Einstein equations hold, there is no production of scalar particles in the zero and large mass limits, respectively. The suppression of particle production in the large mass limit is over and above the expected suppression at large mass. Our results hold for a certain class of conformally ultrastatic background geometries and therefore generalize previous results by one of us for spatially flat Robertson-Walker background geometries. In these geometries, we find that the temporal part of the graviton equations reduces to the temporal equation for a massless minimally coupled scalar field, and therefore the results for massless particle production hold also for gravitons. Within the class of modes we study, we also find that the requirement of zero production of massless scalar particles is not consistent with a non-zero cosmological constant. Possible implications are discussed.Comment: Latex, 24 pages. Minor changes in text from original versio

Measurement of cervical length using transvaginal sonography for prediction of preterm labour

Background: Preterm labour and delivery cause major health burden to the society due to high perinatal morbidities and mortality and long-term health implications and also affects maternal. An effective and objective way for predicting preterm delivery is measurement of cervical length by transvaginal sonography as it allows better quality and accurate visualization of uterine cervix. Cervical length (<25 mm) is good and accurate cervical biometry for prediction of preterm birth. The objective of this study was to measure cervical length by transvaginal sonography for predicting preterm labour and fetal outcome.Methods: This prospective observational study was conducted in department of obstetrics and gynaecology, at SVPIMSR hospital, Ahmedabad from July 2018 to December 2019 in 150 antenatal women to assess cervical changes (cervical length, dilatation of internal OS, funnelling etc.) between 16 to 24 weeks of gestation and these cases followed till delivery and results were analysed.Results:150 antenatal women who fulfilled the selection criteria were studied using transvaginal ultrasound between 16-24 weeks of gestation, out of them 36 (24%) women delivered preterm babies. The sensitivity, specificity, positive predictive value (PPV) and negative predictive value (NPV) recorded in this study were 80.5%, 94.73%, 82.85% and 93.91% respectively.Conclusion: Transvaginal sonography is the most useful and better, safe, accurate, most effective, less expensive, objective and acceptable technique for assessing cervical length in all antenatal women and predicting the preterm labour when assessed between 16 -24 weeks of gestational age