DEEPAK KUMAR
Articles written in Proceedings – Mathematical Sciences
Volume 109 Issue 4 November 1999 pp 441-452
Stokes drag on axially symmetric bodies: a new approach
Sunil Datta Deepak Kumar Srivastava
In this paper a new approach to evaluate the drag force in a simple way on a restricted axially symmetric body placed in a uniform stream (i) parallel to its axis, (ii) transverse to its axis, is advanced when the flow is governed by the Stokes equations. The method exploits the well-known integral for evaluating the drag on a sphere. The method not only provides the value of the drag on prolate and oblate spheroids and a deformed sphere in axial flow which already exists in literature but also new results for a cycloidal body, an egg shaped body and a deformed sphere in transverse flow. The salient results are exhibited graphically. The limitations imposed on the analysis because of the lack of fore and aft symmetry in the case of an eggshaped body is also indicated. It is also seen that the analysis can be extended to calculate the couple on a body rotating about its axis of symmetry.
Volume 110 Issue 1 February 2000 pp 117-120
Slow rotation of a sphere with source at its centre in a viscous fluid
Sunil Datta Deepak Kumar Srivastava
In this note, the problem of a sphere carrying a fluid source at its centre and rotating with slow uniform angular velocity about a diameter is studied. The analysis reveals that only the azimuthal component of velocity exists and is seen that the effect of the source is to decrease it. Also, the couple on the sphere is found to decrease on account of the source.
Volume 112 Issue 2 May 2002 pp 289-297
Some intersections and identifications in integral group rings
Let
Volume 118 Issue 4 November 2008 pp 537-546
Some Augmentation Quotients of Integral Group Rings
Deepak Kumar Gumber Ram Karan Indu Pal
Let 𝐺 be a group and 𝐻 be a subgroup of 𝐺. A complete description of $\Delta(G)\Delta^n(H)/\Delta^{n+1}(H)$ is given, and as a consequence the structures of $\Delta(G)/\Delta(H)$ and $\Delta^2(G)/\Delta^2(H)$ are determined. Also, the structure of $\Delta^n(G)/\Delta^n(H)$ for all $n\geq 1$ is determined when 𝐺 is a free group.
Volume 129 Issue 3 June 2019 Article ID 0037 Research Article
$C^{\ast}$-algebra-valued partial metric space and fixed point theorems
SUMIT CHANDOK DEEPAK KUMAR CHOONKIL PARK
In this paper, we introduce the notion of $C^{\ast}$-algebra-valued partial metric space which is more general than partial metric space. Some fixed point results using C-class functions on such spaces are obtained. Moreover, some illustrated examples are also provided.
Volume 131, 2021
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