2,061 research outputs found
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 and rotation 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
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