Flow of an Oldroyd-B fluid over an infinite plate subject to a time-dependent shear stress

JPRM-Vol. 1 (2011), Issue 1, pp. 52 – 62 Open Access Full-Text PDF
Nazish Shahid, Mehwish Rana, M. A. Imran
Abstract: The velocity field and the shear stress corresponding to the unsteady flow of an Oldroyd-B fluid due to an infinite flat plate, subject to a time-dependent shear stress, are established in integral form using the Fourier cosine transform. Similar solutions for Maxwell, Second grade and Newtonian fluids are recovered as limiting cases of general solutions. These solutions satisfy both the governing equations and all imposed initial and boundary conditions. Finally, a comparison between the four models as well as the influence of the pertinent parameters on the fluid motion is underlined by graphical illustrations.
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Shape preserving constrained data visualization using rational functions

JPRM-Vol. 1 (2011), Issue 1, pp. 35 – 51 Open Access Full-Text PDF
Tahira S. Shaikh, Muhammad Sarfraz, Malik Zawwar Hussain
Abstract: This work has been contributed on the visualization of curves and surfaces for constrained data. A rational cubic function, with free shape parameters in its description, has been introduced and used. This function has been constrained to visualize the preservation of shape of the data by imposing constraints on free parameters. The rational cubic curve case has also been extended to a rational bi-cubic partially blended surface to visualize the shape preserving surface to constrained data.
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On existence of canonical number system in certain classes of pure algebraic number fields

JPRM-Vol. 1 (2011), Issue 1, pp. 19 – 24 Open Access Full-Text PDF
Abdul Hameed, Toru Nakahara, Syed Muhammad Husnine, Shahzad Ahmad
Abstract: Canonical Number System can be considered as natural generalization of radix representation of rational integers to algebraic integers. We determine the existence of Canonical Number System in two classes of pure algebraic number fields of degree \(2^n\) and \(n\).
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Outputs in random \(f\)-ary recursive circuits

JPRM-Vol. 1 (2011), Issue 1, pp. 09 – 18 Open Access Full-Text PDF
Mehri Javanian, Mohammad Q. Vahidi-Asl
Abstract: This paper extends the study of outputs for random recursive binary circuits in Tsukiji and Mahmoud (Algorithmica 31(2001), 403). We show via martingales that a suitably normalized version of the number of outputs in random f-ary recursive circuits converges in distribution to a normal random variate.
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The domination cover pebbling number of the square of a path

JPRM-Vol. 1 (2011), Issue 1, pp. 01 – 08 Open Access Full-Text PDF
A. Lourdusamy, T. Mathivanan
Abstract: Given a configuration of pebbles on the vertices of a connected graph \(G\), a pebbling move (or pebbling step) is defined as the removal of two pebbles from a vertex and placing one pebble on an adjacent vertex. The domination cover pebbling number, \(ψ(G)\), of a graph \(G\) is the minimum number of pebbles that have to be placed on \(V (G)\) such that after a sequence of pebbling moves, the set of vertices with pebbles forms a dominating set of \(G\), regardless of the initial configuration. In this paper, we determine the domination cover pebbling number for the square of a path.
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