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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.

For, the authors have used the notion of conformal transformation and Douglas space.

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.

The authors introduced Douglas space of second kind and established conditions under which it can be transformed to a Douglas space of second kind.

The paper aims to consider non‐viscous, laminar mixed convection boundary‐layer flow over a horizontal moving porous flat plate, with chemical reaction.

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.

The investigated parameters are: buoyancy parameter, chemical reaction parameter, order of chemical reaction, Prandtl number and Schmidt number.

The partial differential equations are transformed to ordinary differential equations. The method of one parameter continuous group theory is used for this transformation.

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.

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.

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.

The results of this paper are new and interesting. Also, the Proposition 3.2 will be helpful in further study of this space.

In this paper, we consider the Heisenberg groups which play a crucial role in both geometry and theoretical physics.

In the first part, we retrieve the geometry of left-invariant Randers metrics on the Heisenberg group H_2n+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 H_2n+1 have constant negative scalar curvature.

In the second part, we present our main results. We show that the Heisenberg group H_2n+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.

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.

The purpose of this paper is to study the Bertotti–Kasner space-time and its geometric properties.

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.

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.

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 λW-tensor and discussed the canonical form of the Weyl tensor and the Petrov scalars. To the best of the literature survey, this idea is found to be modern. The results deliver new insight into the geometry of the nonstatic cylindrical vacuum solution of Einstein's field equations.

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  symmetric trans-Sasakian manifolds. Finally, they give a nontrivial example of three-dimensional proper trans-Sasakian manifold.

The authors have used the tensorial approach to achieve the goal.

A second-order parallel symmetric tensor on a three-dimensional trans-Sasakian manifold is a constant multiple of the associated Riemannian metric g.

The authors declare that the manuscript is original and it has not been submitted to any other journal for possible publication.

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.

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.

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 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.