iosr-Jm   Volume-4 ~ Issue-5

Abstract: Calcium dynamics in oocytes plays an important role in oocyte maturation. The calcium concentration is regulated at high levels in oocytes through various mechanisms in order to meet the requiremnts of oocyte maturation. The understanding of these mechanisms are crucial in understanding the processes of reproduction. In this paper an attempt has been made to develop a finite element model of calcium dynamics in oocyte. The model incorporates the parameters like diffusion coefficient, leak from Endoplasmic Reticulum(ER), and buffers namely 1,2-bis(o-aminophenoxy)ethane-N,N,N',N'-tetraacetic acid(BAPTA) and ethylene glycol-bis(2-aminoethylether)-N,N,N',N'-tetraacetic acid(EGTA). The proposed model is solved numerically using appropriate initial and boundary conditions. A program has been developed in MATLAB 7.11 for the entire problem and simulated on a 32-bit machine to compute the numerical results. The effect of BAPTA, EGTA and Leak from ER is studied in the neighbourhood of L-type calcium channel on calcium distribution in oocyte.
Keywords: Finite Element Method, EGTA, BAPTA, ER Leak, Reaction Diffusion Equation

[1] Z. Machaty, J. J. Ramsoondar, A. J. Bonk, K. R. Bondioli and R. Prather, Capacitative Calcium Entry Mechanism in Porcine
Oocytes, Biology of Reproduction 66(3) (2002) 667-674
[2] M. S. Jafri, S. Vajda, P. Pasik and B. Gillo, A membrane model for Cytosolic calcium oscillations. A study using Xenopus oocytes,
Biophysical Journal 63 (1992) 235-246.
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implications for synaptic plasticity, Biochimica et Biophysica Acta 1600 (2002) 12-18.
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(1992) 283-294.
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Abstract:We generalize fifth order mock theta functions of Ramanujan and eighth order mock theta functions of Gordon and McIntosh. We show they are 𝐹𝑞 -functions and give their alternative definition. We give expansion formula and give relationship among these functions. 2000 Mathematics Subject Classification.33D15
Keywords: Bilateral series, mock theta functions.

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Abstract:If M is a differtiable manifold of dimension n,then its cotangent bundle 𝑇∗(M) is a differtiable manifold of dimension 2n[1].In the present paper, complete and horizontal lifts of (1,1) tensor fields of M ,which are tensor fields of same type in 𝑇∗(M) , are studied. The Nijenhuis tensor of complete lift and Integrability of the Hsu-structure in𝑇∗(M) are also studied.

Keywords: Cotangent Bundle,Hsu-structure,differentiable manifold , Complete and horizontal lifts, Integrability.

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cotangent bundle.VSRD Technical and Non-Technical International Journal ,2(4) ,pp.213-218
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jointly with 11th International Conference of Tensor Society), University of Tokyo, Japan Sept. 5-10, 2011, pp. 39 – 42.

Abstract: Cascade reliability model is a special type of Stress- Strength model. The n- Cascade system is a hierarchical standby redundancy system, where the standby component taking the place of failed component with decreased value of stress and independently distributed strength. In assessing system reliability it is first necessary to define and categorize different modes of system failures. The individual distributions that are combined to form the mixture distribution are called mixer components. In this paper it has been discussed that the reliability of n- cascade system when strength follows mixed exponential distribution and stress follows exponential distribution.

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Electron Reliability, Pergamon Press, OXFORD, Vol.33, No.4, pp: 477-479.
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Abstract:Traffic flow micro simulations are popular for the planning of transport problems due to their temporal and spatial resolution. Cellular automata (CA) model are mathematical idealizations of physical systems in which space and time are discrete, and physical quantities take on a finite set of discrete values .In this paper , we are exploring the usefulness of CA to traffic flow modeling. A CA model is applied to a single-lane highway with a ring topology. Also two-lane traffic flow with lane changing is discussed. Simulations results show the ability of this modeling paradigm to capture the most important features of the traffic flow phenomena.

Keywords: Cellular Automata, Lane Changing, Micro Simulation, Traffic Flow.

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Version1.0, Los Alamos National Laboratory.
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the American Control Conference. Vol.3, pp. 2041-2045.
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Transportation Research Part C: Emerging Technologies 10, 275-301.
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Schreckenberg models", Physical Review E, vol. 63, no. 5, Article ID 056117, 5 pages.
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Abstract:Transportation problem is a special type of linear programming problem. This paper introduce a new approach to transportation problem namely, Revised Distribution method (RDI), for solving a wide range of such problems. The new method is based on allocating units to the cells in the transportation matrix starting with minimum demand or supply to the cell with minimum cost in the transportation matrix and then try to find an optimum solution to the given transportation problem. The proposed method is a systematic procedure, easy to apply and can be utilized for all types of Transportation problem with maximize or minimize objective functions. At the end, this method is illustrated with some numerical example..

Keywords: Transportation problem, Linear programming Problem, MODI method

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[3] Hamdy A. Taha, Operations Research, an introduction, 8th Ed. (2007).
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Abstract:In this paper the terms completely prime ideal, prime ideal, m-system. globally idempotent , semi simple elements of a ternary semigroup are Introduced. It is proved that an ideal A of a ternary semigroup T is completely prime if and only if T\A is either sub semigroup of T or empty. It is proved that if T is a globally idempotent ternary semigroup then every maximal ideal of T is a prime ideal of T. In this paper the terms completely semiprime ideal, semiprime ideal, n-system, d-system and i-system are introduced. It is proved that the non-empty intersection of any family of a completely prime ideal and prime ideal of a ternary semigroup T is a completely semiprime ideal of T. It is also proved that an ideal A of a ternary semigroup T is completely semiprime if and only if T\A is a d-system of T or empty..

Keywords: Ideal completely prime ideal, prime ideal, m-system, n-system, d-system, i-system, globally idempotent, semisimple elements, completely semiprime ideal, semi prime ideal, irreducible ideal, strongly irreducible ideal, radical, complete radical of ternary semigroup.

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