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1 – 10 of 12Rishabh Ranjan, P.N. Pandey and Ajit Paul
In this paper, the authors prove that the Douglas space of second kind with a generalised form of special (α, β)-metric F, is conformally invariant.
Abstract
Purpose
In this paper, the authors prove that the Douglas space of second kind with a generalised form of special (α, β)-metric F, is conformally invariant.
Design/methodology/approach
For, the authors have used the notion of conformal transformation and Douglas space.
Findings
The authors found some results to show that the Douglas space of second kind with certain (α, β)-metrics such as Randers metric, first approximate Matsumoto metric along with some special (α, β)-metrics, is invariant under a conformal change.
Originality/value
The authors introduced Douglas space of second kind and established conditions under which it can be transformed to a Douglas space of second kind.
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M. Ferdows, Jashim Uddin, Mohammad Mehdi Rashidi and N. Rahimzadehc
The paper aims to consider non‐viscous, laminar mixed convection boundary‐layer flow over a horizontal moving porous flat plate, with chemical reaction.
Abstract
Purpose
The paper aims to consider non‐viscous, laminar mixed convection boundary‐layer flow over a horizontal moving porous flat plate, with chemical reaction.
Design/methodology/approach
The governing equations are expressed in non‐dimensional form and the series solutions of coupled system of equations are constructed for velocity, temperature and concentration functions using numerical method.
Findings
The investigated parameters are: buoyancy parameter, chemical reaction parameter, order of chemical reaction, Prandtl number and Schmidt number.
Originality/value
The partial differential equations are transformed to ordinary differential equations. The method of one parameter continuous group theory is used for this transformation.
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Cotton soliton is a newly introduced notion in the field of Riemannian manifolds. The object of this article is to study the properties of this soliton on certain contact metric…
Abstract
Purpose
Cotton soliton is a newly introduced notion in the field of Riemannian manifolds. The object of this article is to study the properties of this soliton on certain contact metric manifolds.
Design/methodology/approach
The authors consider the notion of Cotton soliton on almost Kenmotsu 3-manifolds. The authors use a local basis of the manifold that helps to study this notion in terms of partial differential equations.
Findings
First the authors consider that the potential vector field is pointwise collinear with the Reeb vector field and prove a non-existence of such Cotton soliton. Next the authors assume that the potential vector field is orthogonal to the Reeb vector field. It is proved that such a Cotton soliton on a non-Kenmotsu almost Kenmotsu 3-h-manifold such that the Reeb vector field is an eigen vector of the Ricci operator is steady and the manifold is locally isometric to.
Originality/value
The results of this paper are new and interesting. Also, the Proposition 3.2 will be helpful in further study of this space.
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Ghodratallah Fasihi-Ramandi and Shahroud Azami
In this paper, we consider the Heisenberg groups which play a crucial role in both geometry and theoretical physics.
Abstract
Purpose
In this paper, we consider the Heisenberg groups which play a crucial role in both geometry and theoretical physics.
Design/methodology/approach
In the first part, we retrieve the geometry of left-invariant Randers metrics on the Heisenberg group H2n+1, of dimension 2n + 1. Considering a left-invariant Randers metric, we give the Levi-Civita connection, curvature tensor, Ricci tensor and scalar curvature and show the Heisenberg groups H2n+1 have constant negative scalar curvature.
Findings
In the second part, we present our main results. We show that the Heisenberg group H2n+1 cannot admit Randers metric of Berwald and Ricci-quadratic Douglas types. Finally, the flag curvature of Z-Randers metrics in some special directions is obtained which shows that there exist flags of strictly negative and strictly positive curvatures.
Originality/value
In this work, we present complete Reimannian geometry of left invarint-metrics on Heisenberg groups. Also, some geometric properties of left-invarainat Randers metrics will be studied.
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H.M. Manjunatha, S.K. Narasimhamurthy and Zohreh Nekouee
The purpose of this paper is to study the Bertotti–Kasner space-time and its geometric properties.
Abstract
Purpose
The purpose of this paper is to study the Bertotti–Kasner space-time and its geometric properties.
Design/methodology/approach
This paper is based on the features of λ-tensor and the technique of six-dimensional formalism introduced by Pirani and followed by W. Borgiel, Z. Ahsan et al. and H.M. Manjunatha et al. This technique helps to describe both the geometric properties and the nature of the gravitational field of the space-times in the Segre characteristic.
Findings
The Gaussian curvature quantities specify the curvature of Bertotti–Kasner space-time. They are expressed in terms of invariants of the curvature tensor. The Petrov canonical form and the Weyl invariants have also been obtained.
Originality/value
The findings are revealed to be both physically and geometrically interesting for the description of the gravitational field of the cylindrical universe of Bertotti–Kasner type as far as the literature is concerned. Given the technique of six-dimensional formalism, the authors have defined the Weyl conformal
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Sudhakar Kumar Chaubey and Uday Chand De
The authors set the goal to find the solution of the Eisenhart problem within the framework of three-dimensional trans-Sasakian manifolds. Also, they prove some results of the…
Abstract
Purpose
The authors set the goal to find the solution of the Eisenhart problem within the framework of three-dimensional trans-Sasakian manifolds. Also, they prove some results of the Ricci solitons, η-Ricci solitons and three-dimensional weakly
Design/methodology/approach
The authors have used the tensorial approach to achieve the goal.
Findings
A second-order parallel symmetric tensor on a three-dimensional trans-Sasakian manifold is a constant multiple of the associated Riemannian metric g.
Originality/value
The authors declare that the manuscript is original and it has not been submitted to any other journal for possible publication.
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Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community…
Abstract
Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.
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An extension of the Schwarz‐Christoffel transformation is described to formally map polygons which contain curved boundaries. The curved boundaries are divided into small ‘curved…
Abstract
An extension of the Schwarz‐Christoffel transformation is described to formally map polygons which contain curved boundaries. The curved boundaries are divided into small ‘curved elements’ and each element is approximated by a second degree polynomial (higher degree polynomials can also be used). The iterative algorithm of evaluating the unknown constants of the basic S‐C transformation described in a companion paper is applied to the extended S‐C transformation to compute its unknown constants, including the coefficients of the polynomials. Excellent results are achieved as far as accuracy and convergence are concerned. Examples including a practical application, are provided. The mapping of curved polygons is important because they provide a better model of a physical device.
M.A. Chaudhry and R. Schinzinger
Introduction of curved boundaries in polygonally shaped integrated circuit planar resistors causes a crease in maximum electric field intensities and current densities present in…
Abstract
Introduction of curved boundaries in polygonally shaped integrated circuit planar resistors causes a crease in maximum electric field intensities and current densities present in them, and consequently decreases the likelihood of their failure. The presence of curved boundaries can also decrease the area occupied by the resistor. Therefore, polygonal resistors with curved boundaries can be highly desirable in integrated circuits. Resistances of conductors with curved boundaries are readily computed using conformal mapping, particularly the numerically, extended Schwarz‐Christoffel transformation developed by the authors. The resulting algorithm is applicable to polygonal resistors of arbitrary shape and is easily programmable. Several examples are presented. Rapid convergence and accurate results are obtained.
The problem of determining the shape of a polygonal integrated circuit planar resistor to a desired value of resistance has applications in the IC fabrication technology. The…
Abstract
The problem of determining the shape of a polygonal integrated circuit planar resistor to a desired value of resistance has applications in the IC fabrication technology. The resistor design problem can be simplified for modular applications and fabrication by changing only one parameter of the polygon, e.g., length of a slit, to achieve the desired value of resistance. This paper describes a method of numerical conformal mapping to compute the length of the slit to obtain the desired value of resistance when the shape of the polygon is given. The extended Schwarz‐Christoffel transformation developed by the author and others is used when polygons with curved segments are encountered. The resulting algorithm is easily programmable and accurate. Rapid convergence is achieved. Examples are given and other applications of the method are presented.