scholarly journals A Characterization of GRW Spacetimes

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2209
Author(s):  
Ibrahim Al-Dayel ◽  
Sharief Deshmukh ◽  
Mohd. Danish Siddiqi
Keyword(s):  
Vector Field ◽  
Potential Function ◽  
Laplace Operator ◽  
Einstein Manifold ◽  
Lorentzian Manifold ◽  
De Rham ◽  
Associated Function ◽  
Simply Connected ◽  
The Way

We show presence a special torse-forming vector field (a particular form of torse-forming of a vector field) on generalized Robertson–Walker (GRW) spacetime, which is an eigenvector of the de Rham–Laplace operator. This paves the way to showing that the presence of a time-like special torse-forming vector field ξ with potential function ρ on a Lorentzian manifold (M,g), dimM>5, which is an eigenvector of the de Rham Laplace operator, gives a characterization of a GRW-spacetime. We show that if, in addition, the function ξ(ρ) is nowhere zero, then the fibers of the GRW-spacetime are compact. Finally, we show that on a simply connected Lorentzian manifold (M,g) that admits a time-like special torse-forming vector field ξ, there is a function f called the associated function of ξ. It is shown that if a connected Lorentzian manifold (M,g), dimM>4, admits a time-like special torse-forming vector field ξ with associated function f nowhere zero and satisfies the Fischer–Marsden equation, then (M,g) is a quasi-Einstein manifold.

Concircularity on GRW-space-times and conformally flat spaces

2021 ◽  
pp. 2150132
Author(s):  
Sharief Deshmukh ◽  
Ibrahim Al-Dayel
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Potential Function ◽  
Lorentzian Manifold ◽  
Momentum Tensor ◽  
Conformally Flat ◽  
Smooth Functions ◽  
Necessary And Sufficient ◽  
Flat Riemannian Manifold

There are two smooth functions [Formula: see text] and [Formula: see text] associated to a nontrivial concircular vector field [Formula: see text] on a connected Riemannian manifold [Formula: see text], called potential function and connecting function. In this paper, we show that presence of a timelike nontrivial concircular vector field influences the geometry of generalized Robertson–Walker space-times. We use a timelike concircular vector field [Formula: see text] on an [Formula: see text] -dimensional connected conformally flat Lorentzian manifold, [Formula: see text], to find a characterization of generalized Robertson–Walker space-time with  fibers Einstein manifolds. It is interesting to note that for [Formula: see text] the concircular vector field annihilates energy-momentum tensor and also that in this case the potential function [Formula: see text] is harmonic. In the second part of this paper, we show that presence of a nontrivial concircular vector field [Formula: see text] with connecting function [Formula: see text] on a complete and connected [Formula: see text] -dimensional conformally flat Riemannian manifold [Formula: see text], [Formula: see text], with Ricci curvature [Formula: see text] non-negative, satisfying [Formula: see text], is necessary and sufficient for [Formula: see text] to be isometric to either a sphere [Formula: see text] or to the Euclidean space [Formula: see text], where [Formula: see text] is the scalar curvature.

scholarly journals On an Anti-Torqued Vector Field on Riemannian Manifolds

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2201
Author(s):  
Sharief Deshmukh ◽  
Ibrahim Al-Dayel ◽  
Devaraja Mallesha Naik
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Riemannian Manifolds ◽  
Vector Fields ◽  
Compact Riemannian Manifold ◽  
Killing Vector ◽  
Dual Vector ◽  
Definition Of ◽  
Simply Connected

A torqued vector field ξ is a torse-forming vector field on a Riemannian manifold that is orthogonal to the dual vector field of the 1-form in the definition of torse-forming vector field. In this paper, we introduce an anti-torqued vector field which is opposite to torqued vector field in the sense it is parallel to the dual vector field to the 1-form in the definition of torse-forming vector fields. It is interesting to note that anti-torqued vector fields do not reduce to concircular vector fields nor to Killing vector fields and thus, give a unique class among the classes of special vector fields on Riemannian manifolds. These vector fields do not exist on compact and simply connected Riemannian manifolds. We use anti-torqued vector fields to find two characterizations of Euclidean spaces. Furthermore, a characterization of an Einstein manifold is obtained using the combination of a torqued vector field and Fischer–Marsden equation. We also find a condition under which the scalar curvature of a compact Riemannian manifold admitting an anti-torqued vector field is strictly negative.

Shakespeare Afoot

2018 ◽  
Author(s):  
John Kerrigan
Keyword(s):  
Early Modern ◽  
Richard Iii ◽  
Midsummer Night's Dream ◽  
As You Like It ◽  
A Midsummer Night's Dream ◽  
History Of ◽  
The Way

That Shakespeare adds a limp to the received characterization of Richard III is only the most conspicuous instance of his interest in how actors walked, ran, danced, and wandered. His attention to actors’ footwork, as an originating condition of performance, can be traced from Richard III through A Midsummer Night’s Dream and As You Like It into Macbeth, which is preoccupied with the topic and activity all the way to the protagonist’s melancholy conclusion that ‘Life’s but a walking shadow, a poor player | That struts and frets his hour upon the stage’. Drawing on classical and early modern accounts of how people walk and should walk, on ideas about time and prosody, and the experience of disability, this chapter cites episodes in the history of performance to show how actors, including Alleyn, Garrick, and Olivier, have worked with the opportunities to dramatize footwork that are provided by Shakespeare’s plays.

scholarly journals Compact Differences of Composition Operators on Bergman Spaces Induced by Doubling Weights

2021 ◽  
Author(s):  
Bin Liu ◽  
Jouni Rättyä ◽  
Fanglei Wu
Keyword(s):  
Bergman Space ◽  
Open Problem ◽  
Lebesgue Space ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Carleson Measures ◽  
Doubling Weights ◽  
The Way

AbstractBounded and compact differences of two composition operators acting from the weighted Bergman space $$A^p_\omega $$ A ω p to the Lebesgue space $$L^q_\nu $$ L ν q , where $$0<q<p<\infty $$ 0 < q < p < ∞ and $$\omega $$ ω belongs to the class "Equation missing" of radial weights satisfying two-sided doubling conditions, are characterized. On the way to the proofs a new description of q-Carleson measures for $$A^p_\omega $$ A ω p , with $$p>q$$ p > q and "Equation missing", involving pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of q-Carleson measures for the classical weighted Bergman space $$A^p_\alpha $$ A α p with $$-1<\alpha <\infty $$ - 1 < α < ∞ to the setting of doubling weights. The case "Equation missing" is also briefly discussed and an open problem concerning this case is posed.

CHARACTERIZATION OF SUPER QUASI-EINSTEIN MANIFOLD

2014 ◽  
Vol 60 (1) ◽  
pp. 99-108
Author(s):  
K. Halder ◽  
B. Pal ◽  
A. Bhattacharyya ◽  
T. De
Keyword(s):  
Einstein Manifold ◽  
Odd Dimensions

Abstract In this paper we give characterizations of super quasi-Einstein manifold, mixed super quasi-Einstein manifold and mixed generalized quasi-Einstein manifold for both even and odd dimensions.

scholarly journals cis-Tetrachlorido-bis(indazole)osmium(iv) and its osmium(iii) analogues: paving the way towards the cis-isomer of the ruthenium anticancer drugs KP1019 and/or NKP1339

2017 ◽  
Vol 46 (35) ◽  
pp. 11925-11941 ◽  
Author(s):  
Gabriel E. Büchel ◽  
Susanne Kossatz ◽  
Ahmad Sadique ◽  
Peter Rapta ◽  
Michal Zalibera ◽  
...  
Keyword(s):  
Anticancer Drugs ◽  
Synthesis And Characterization ◽  
Cis Isomer ◽  
The Way

The synthesis and characterization of cis-[OsIVCl4(κN2-1H-indazole)2] and its 1e-reduced analog are reported.

scholarly journals Point configurations, phylogenetic trees, and dissimilarity vectors

2021 ◽  
Vol 118 (12) ◽  
pp. e2021244118
Author(s):  
Alessio Caminata ◽  
Noah Giansiracusa ◽  
Han-Bom Moon ◽  
Luca Schaffler
Keyword(s):  
Phylogenetic Trees ◽  
Geometric Interpretation ◽  
Explicit Characterization ◽  
Point Configurations ◽  
Definition Of ◽  
Tropical Basis ◽  
The Way

In 2004, Pachter and Speyer introduced the higher dissimilarity maps for phylogenetic trees and asked two important questions about their relation to the tropical Grassmannian. Multiple authors, using independent methods, answered affirmatively the first of these questions, showing that dissimilarity vectors lie on the tropical Grassmannian, but the second question, whether the set of dissimilarity vectors forms a tropical subvariety, remained opened. We resolve this question by showing that the tropical balancing condition fails. However, by replacing the definition of the dissimilarity map with a weighted variant, we show that weighted dissimilarity vectors form a tropical subvariety of the tropical Grassmannian in exactly the way that Pachter and Speyer envisioned. Moreover, we provide a geometric interpretation in terms of configurations of points on rational normal curves and construct a finite tropical basis that yields an explicit characterization of weighted dissimilarity vectors.

scholarly journals Possible Worlds in Translation: Coleman Barks’s Rendition of a Story from Rumi’s Masnavi

2021 ◽  
Vol 44 (3) ◽  
Author(s):  
Vahid Medhat ◽  
Hossein Pirnajmuddin ◽  
Pyeaam Abbasi
Keyword(s):  
Internal Structure ◽  
English Translation ◽  
Possible Worlds ◽  
Translation Studies ◽  
Original Text ◽  
Main Character ◽  
Source Text ◽  
Narrative Worlds ◽  
The Way

This article applies the theory of possible worlds to the field of translation studies by examining the narrative worlds of original and translated texts. Specifically, Marie-Laure Ryan’s characterization of possible worlds provides an account of the internal structure of the textual universe and the progression of the plot. Based on this account, one of the stories from Rumi’s Masnavi is compared to Coleman Barks’s English translation. The possible worlds of the characters and the unfolding of the plots in both texts are examined to assess the degree of compatibility between the textual universes of the original and the translated texts and how significant this might be. It also examines how readers reconstruct the narrative worlds projected by the two texts. The analysis reveals some inconsistencies in the way the textual universes of the original and translated texts are furnished and in the way readers reconstruct the narrative worlds of the two texts. The inability of translation to fully render the main character results in some loss in terms of the pungency and pithiness of the original text. It is also shown that the source text presents a richer domain of the virtual in comparison, suggesting a higher degree of tellability in the textual universe of the Masnavi’s narrative.

scholarly journals Novel Mega Best-Seller Karya Luluk HF Mariposa dalam Kajian Resepsi Sastra

2021 ◽  
Vol 19 (2) ◽  
pp. 152
Author(s):  
Tania Intan ◽  
Muhamad Adji
Keyword(s):  
Aggressive Behavior ◽  
Research Data ◽  
The Novel ◽  
Research Results ◽  
Female Protagonist ◽  
Data Source ◽  
The Difference ◽  
Horizon Of Expectations ◽  
The Way

This study discusses the reception of readers of the mega best-seller novel entitled Mariposa by Luluk HF. The purpose of this study is to (1) describe the reader's responses, (2) describe the horizon of readers' expectations, and (3) describe the factors that cause differences in responses and the horizon of expectations of readers of Mariposa's novel. The method applied is descriptive qualitative. This study uses a reception aesthetic approach that seeks to find consistent reception patterns as a reflection of the way the reader responds to the text. The research data consisted of texts containing the responses of twenty respondents from the data source in the form of the Goodreads reader site. The research results obtained are as follows. First, not all readers respond positively to the intrinsic elements of the novel, especially the characterization of the female protagonist who is considered to show aggressive behavior with a love motive. Second, most of the horizons of readers' expectations do not match the reality in Mariposa. Readings are generally motivated by curiosity because of the hyperbolic labeling of the novel, recommendations from friends, and the discourse of filming the novel. Third, the factors that cause the difference or suitability of the horizon of readers' expectations for the Mariposa novel are knowledge of literature, knowledge of life, and experience of reading literary works.

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