Mathematical modeling of thrombus growth in microvessels

JPRM-Vol. 1 (2008), Issue 1, pp. 195 – 205 Open Access Full-Text PDF
A. G. Alenitsyn, A. S. Kondratyev, I. Mikhailova, I. Siddique
Abstract: Richardson’s phenomenological mathematical model of the thrombi growth in microvessels is extended to describe more realistic features of the phenomenon. Main directions of the generalization of Richardson’s model are: 1) the dependence of platelet activation time on the distance from the injured vessel wall; 2) the nonhomogeneity of the platelet distribution in blood flow in the vicinity of the vessel wall. The generalization of the model corresponds to the main experimental results concerning thrombi formation obtained in recent years. The extended model permits to achieve a numerical agreement between model and experimental data.
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Exact solutions for some unsteady flows of generalized second grade fluids in cylindrical domains

JPRM-Vol. 1 (2008), Issue 1, pp. 171 – 180 Open Access Full-Text PDF
Amir Mahmood, Constantin Fetecau, Imran Siddique
Abstract: The velocity field and the adequate shear stress, corresponding to the unsteady flow of generalized second grade fluids due to a constantly accelerating circular cylinder, are determined by means of the Hankel and Laplace transforms. The solutions that have been obtained satisfy all imposed initial and boundary conditions and for \(β → 1\) reduce to the similar solutions for the second grade fluids performing the same motion.
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A greedy approach for computing longest common subsequences

JPRM-Vol. 1 (2008), Issue 1, pp. 165 – 170 Open Access Full-Text PDF
Afroza Begum
Abstract: This paper presents an algorithm for computing Longest Common Subsequences for two sequences. Given two strings \(X\) and \(Y\) of length \(m\) and \(n\), we present a greedy algorithm, which requires \(O(n log s)\) preprocessing time, where s is distinct symbols appearing in string \(Y\) and \(O(m)\) time to determines Longest Common Subsequences.
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On the partition dimension of some wheel related graphs

JPRM-Vol. 1 (2008), Issue 1, pp. 154 – 164 Open Access Full-Text PDF
Imran Javaid, Sara Shoukat
Abstract: Let G be a connected graph. For a vertex \(v ∈ V (G)\) and an ordered \(k-\)partition \(Π = {S_1, S_2, …, S_k}\) of \(V (G)\), the representation of \(v\) with respect to \(Π\) is the \(k-\)vector r \((v|Π) = (d(v, S_1), d(v, S_2), …, d(v, S_k))\) where \(d(v, S_i) = min_{w∈S_i} d(v, w)(1 ≤ i ≤ k)\). The k-partition \(Π\) is said to be resolving if the k-vectors \(r(v|Π), v ∈ V (G)\), are distinct. The minimum \(k\) for which there is a resolving \(k\)-partition of \(V (G)\) is called the partition dimension of \(G\), denoted by \(pd(G)\). In this paper, we give upper bounds for the cardinality of vertices in some wheel related graphs namely gear graph, helm, sunflower and friendship graph with given partition dimension \(k\).
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Contractible fibers of polynomial functions

JPRM-Vol. 1 (2008), Issue 1, pp. 148 – 153 Open Access Full-Text PDF
Zahid Raza
Abstract: In this short note, we investigate the topology of complex polynomials \(f(x, y)\) in two variables. The description of the topology of the corresponding level curves \(C_t : f(x, y) = t\) is directly related to the vanishing of the leading coefficients cj (t) of the discriminant of the polynomial \(f(x, y) − t\), regarded as polynomials in \(t\).
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\(G_p\)-Finiteness of tensor product

JPRM-Vol. 1 (2008), Issue 1, pp. 143 – 147 Open Access Full-Text PDF
M.S. Balasubramani, K. T. Ravindran
Abstract: In this paper we introduce \(G_P\) finiteness of a Von-Neumann algebra and we define a G-dimension function. Then we prove a result on tensor product of fixed point algebra under group of automorphisms and finally verify a result under which the tensor product is \(G_P\) finite.
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Common fixed point theorems for two mappings in \(D^∗\)-metric spaces

JPRM-Vol. 1 (2008), Issue 1, pp. 132 – 142 Open Access Full-Text PDF
Shaban Sedghi, Nabi Shobe, Shahram Sedghi
Abstract: In this paper, we give some new definitions of \(D^∗\)-metric spaces and we prove a common fixed point theorem for two mappings under the condition of weakly compatible mappings in complete \(D^∗\)-metric spaces. We get some improved versions of several fixed point theorems in complete \(D^∗)-metric spaces.
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On random covering of a circle

JPRM-Vol. 1 (2008), Issue 1, pp. 127 – 131 Open Access Full-Text PDF
Muhammad Naeem
Abstract: Let \(X_{j}\), \(j = 1, 2, …, n\) be the independent and identically distributed random vectors which take the values on the unit circumference. Let \(S_{n}\) be the area of the convex polygon having \(X_{j}\) as vertices. The paper by Nagaev and Goldfield (1989) has proved the asymptotic normality of random variableSn. Our main aim is to show that the random variableSn can be represented as a sum of functions of uniform spacings. This allows us to apply known results related to uniform spacings for the analysis of \(S_n\).
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On the gracefulness of the digraphs \(n − C_{m}\) for \(m\) odd

JPRM-Vol. 1 (2008), Issue 1, pp. 118 – 126 Open Access Full-Text PDF
Zhao Lingqi, Jirimutu, Xirong Xu, Wang Lei
Abstract: A digraph D(V, E) is said to be graceful if there exists an injection \(f : V (G) → {0, 1, · · · , |E|}\) such that the induced function \(f’:E(G) → {1, 2, · · · , |E|}\) which is defined by \(f'(u, v) = [f(v)−f(u)] (mod |E|+1)\) for every directed edge \((u, v)\) is a bijection. Here, \(f\) is called a graceful labeling (graceful numbering) of \(D(V, E)\), while \(f’\) is called the induced edge’s graceful labeling of D. In this paper we discuss the gracefulness of the digraph \(n − C_{m}\) and prove that \(n − C_{m}\) is a graceful digraph for \(m = 5, 7, 9, 11, 13\) and even n.
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