014952   Chaurasia V B L;Jain M (Mathematics Dep, Univ of Rajasthan, Jaipur-302 004) : Generalized fractional calculus of the H<. Acta Cienc Indica-Math 2007, 33(4), 1653-66.

The paper is devoted to study the generalized fractional calculus of arbitrary complex order for the H^- -function defined by Inayat Hussain. The classical fractional integrals and derivatives of Riemann-Liouville type are treated. The present paper is intended to generalize the paper. The considered generalized fractional integration and differentiation operators contain the Gauss Hypergeometric function as a kernel and generalize classical Riemann-Liouville, Erdelyi-Kober types ones. It is proved that the generalized fractional integrals and derivatives of H^- -function turn also out H^- -functions but of greater order. Especially, the obtained results define more precise and general ones than known.

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014951   Chauhan J S;Yadav B S (Mathematics Dep, Agra Coll, Agra (U.P.)) : MHD efect on visco elastic fluid through a long uniform tube. Acta Cienc Indica-Math 2007, 33(4), 1507-12.

Unsteady flow of dusty visco elastic fluid through a long uniform tube, whose cross section is curvilinear quadrilateral bounded by the arcs and radii of two concentric circles under the influence of time varying pressure gradient has been considered. Expressions for the velocities of liquid and dust particles are obtained by using operational methods. Some particular cases for different pressure gradient have also been discussed.

10 ref

014950   Chatterjee K;Yu C W;Srinivasan S;Poggie J (Electrical Engineering Dep, The Cooper Union for the Advancement of Science and Art Room 459, 51 Astor Place New York, NY 10003-7185, USA, Email: chatte@cooper.edu) : New floating random walk methodology for neumann and mixed boundary condition problems without reflections at boundaries: validation with laplace's equation in one dimension. Far East J mathl Sci 2007, 26(3), 705-13.

A new floating random walk methodology for Neumann and mixed boundary condition problems is proposed in this paper. Traditional floating random walk algorithms for Neumann and mixed boundary condition problems have involved "reflecting boundaries" resulting in relatively large computational times. This paper proposes the elimination of the use of reflecting boundaries through the use of novel Green's functions mimicking the boundary conditions of the problem of interest. The methodology has been validated by a solution of the ***

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014949   Caso L;Transirico M (Pipartimento di Matematica e Informatica, Universita di Salerno, Via Ponte Don Melillo I-84084, Fisciano (SA), Italy, Email: lorcaso@unisa.it) : Dirichlet problem for elliptic equations in weighted sobolev spaces. J Analysis Applic 2007, 5(3), 167-83.

Some existence and uniqueness results for the Dirichlet problem for elliptic equations with singular coefficients in weighted Sobolev spaces are proved.

19 ref

014948   Borkar M S;Hajare M H (Mathematics Dep, Mahatma Jyotic phule Educational Campus, Amravati Road, Rashtrasant Tukdoji Maharaj Nagar Univ, Nagpur-444 033, Email: mukund@rediffmail.com) : Spherically symmetric spacetime through its characteristic vectors. Vidarbha J Sci 2008, 3(1), 40-6.

Spherically symmetric space time have been studied through its analytical invariant by assuming the various forms of characteristic vectors and discussed its properties. It is seen that the space time is conformally flat for the vectors (α₁,β₂), (α₁ β₃), (α₂, β₄), (α₃, β₄) and non conformally flat occurs only at (α₂,β₃).

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014947   Bhoosnurmath S S;Dyavanal R S (Mathematics Dep, Karnatak Univ, Dharwad-58003, Email: ssbmath@yahoo.com) : Fixed points and normality criteria. Int J mathl Sci 2007, 6(2), 149-61.

To prove some sufficient condition for a family of meromorphic functions to be normal in a domain, Nevanlinna theory combined with some well-known results about normal families is used.

014946   Bhaumik R N;Chaudhuri D R (Mathematics Dep, Tripura University, Suryamaninagar, Tripura-799 130, Email: bhaumik-r-n@yahoo.co.in) : Pre z-super continuous functions. Int J mathl Sci 2007, 6(2), 163-70.

In 2002, Kohli and Kumar (3) introduced a new strong form of continuity called Z-super continuous functions. The aim of this paper is to generalize this concept of z-super continuous function. The concept of pre Z-super continuous functions are introduced and some of their basic properties are studied.

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014945   Bhaumik R N;Chaudhuri D R (Mathematics Dep, Tripura Univ, Suryamaninagar, Tripura-799 130) : Lightly pre normal spaces. Acta Cienc Indica-Math 2007, 33(4), 1359-64.

The concepts of lightly normal spaces and p-normal spaces are weaker form of normality. A topological space is called lightly normal [11] if for each pair of disjoint a closed set A and a zero set B, there exists disjoint open sets U and V such that A ⊂ U and B ⊂ V. A topological space is called p-normal space [10,11] if for each pair of disjoint closed sets A and B, there exists disjoint preopen sets U and V such that A ⊂ U and B ⊂ V. In this paper, new concept, called lightly pre-normal space, which is a generalization of both the above concepts. A topological space is called lightly pre normal if for each pair of disjoint a closed set A and a zero set B, there exists disjoint preopen sets U and V such that A ⊂ U and B ⊂ V. Clearly every p-normal and lightly normal spaces are lightly pre normal. These spaces are characterized with the help of preclosure and gp-open sets and are preserved under continuous, preopen, pre gp-closed surjective functions and M-preclosed continuous surjective functions. Some other properties of these and their relation to other concepts of normality are also studied.

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014944   Besigye-Bafaki G;Luboobi L S (Mathematics Dep, Makerere University, P.O. Box 7062, Kampala, Uganda) : Transmission of schistosomiasis and its dynamics in the human - snail hosts. Int J Math Analysis 2006, 3(1), 1-18.

Modes of transmission of schistosomiasis are considered. The transmission model is developed with an aim of establishing possible endemic equilibria within the community. Analysis of the model reveals that if the recovery rate β of human infectives and the death rate of snails β are increased, and if at the same time the contact rate k of the human hosts with infested water is reduced, the disease gets eradicated from the community. Otherwise, the disease becomes endemic within the community which is a very much undesirable condition for the human population because of the debilitating nature of schistosomiasis. It is found out that this endemic state becomes stable if both the recovery rate β of human infectives and the death rate of snails are reduced. It can be made unstable by deworming the human infectives and killing snails by use of molluscicides. Educating the community about the modes of transmission of the disease helps in reducing the contact rate with infested waters and hence disease prevention.

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014943   Basu M;Sinha S (Mathematics Dep, Kalyani Univ, Kalyani, West Bengal, Pin-741 235, Email: manjusri_basu@yahoo.com) : Ordering policy for deteriorating items with two component demand and price breaks allowing shortages. Opsearch 2007, 44(1), 51-72.

Deals with an EOQ model of an inventory problem with a two-component demand rate: (i) For a certain period the demand rate is quadratic depending on stock, (ii) For the rest of the cycle the demand rate is constant. Price breaks are also taken into account. Effects of deterioration are considered. Considers an EOQ model with a two-component demand rate, deterioration of items and price breaks. Shortages are allowed. The effectiveness of this model is illustrated with a numerical example and sensitivity analysis has been performed.

4 tables, 22 ref

014942   Basavanagoud B;Tallur S S (Mathematics Dep, Karnatak Univ, Dharwad-580 003) : Further results on degree splitting graph of a graph. Acta Cienc Indica-Math 2007, 33(4), 1403-14.

In this paper, author presented some properties of degree splitting graphs. Characterize those graphs whose degree splitting graphs are connected and unicyclic. Found connectivity, edge-connectivity and establish necessary and sufficient condition for degree splitting graphs to be eulerian and investigate hamiltonian property. Further was found girth" and determine those graphs whose degree splitting graphs are k-trees, and determine covering invariants (i.e., α₀, β₀, α₁, β₁,γ₁, n₀) for these graphs and find the chromatic number for degree splitting graphs.

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014941   Ballico E (Mathematics Dep, University of Trento, 38050 P0v0 (TN), Italy, Email: ballico@science.unitn.it) : Coherent systems on smoothe elliptic curves over a finite field. Int J Math Analysis 2006, 2(1-3), 31-42.

Let X be an elliptic curve defined over Fq. Here we study the existence of geometrically polystable vector bundles E defined over Fq and with further geometric properties and the existence of α-stable coherent systems (E, V) of type (n, d, k), k ε {n - 1, n, n + 1}, defined over Fp.

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014940   Ansari M S (Applied Science and Hsumanities Section, University Polytechnic, Aligarh Muslim University, Aligarh-202 002, Email: ahmad_kalimuddin@yahoo.co.in) : Convergence of certain cosing sums in the metric space L. Indian J Math mathl Sci 2007, 6(2), 245-51.

Generalization of the theorem of Babu Ram [6] and Mcrsuq [5) by introducing the notion 6-quasi-convex sequences.

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014939   Amigo J M (Centro de Investigacion Operativa, Universidad Miguel Hernandez, Avda de la Universidad s/n. 03202 Elche, Spain) : Accelerated collatz dynamic. Int J Math Analysis 2006, 2(1-3), 1-18.

Collatz sequence (n₀, n₁,.), defined as n_k+1 = 3n_k +1 or n_k/2 if n_k is odd or even, respectively, is analized as the orbit of n₀ under certain discrete dynamic U defined on the odd integers. In particular, the basin of attraction of the (unique) fixed point 1 is characterized. The Collatz conjecture (i.e. n_k = 1 for some k depending on n₀ or, equivalently, the basin of attraction of 1 in the dynamic U is the whole set of odd numbers) leads then to an equivalent conjecture concerning the representation of odd numbers as sums of positive powers of 2 and negative powers of 3. Relations to exponential Diophantine equations are also discussed.

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014938   Alheety M I;Gore S D (Statistics Dep, Faculty of Science, Pune University, Pune) : New types of shrinkage estimator. Far East J mathl Sci 2007, 26(3), 685-96.

Class of biased estimators, defined by the so-called shrinkage estimator (Mayer and Willke [9]), is very popular in research. In this paper, authors introduce some other types of the shrinkage estimator by replacing the least squares estimator (OLS) by Liu estimator (LE) and by Ridge estimator (RR). Auhtors investigate the properties of these estimators and authors find that these estimators have smaller variance than shrinkage OLS estimator, Liu estimator, and Ridge estimator. Authors also introduce a new type of shrinkage parameter and find that it is better than other types of shrinkage parameter. This is observed from the results of simulations. Finally, author compare these new types of shrinkage estimator with shrinkage OLS, LE and RR estimators in terms of mean squared error.

1 table, 14 ref

014937   Al-Shaqsi K;Darus M (School of Mathematical Sciences, Faculty of Science and Technology, Kebangsaan Malaysia Univ, Bangi 43600 Selengor D. Ehsan, Malaysia, Email: ommath@hotmail.com) : On certain class of analytic functions with negative coefficients for operators on hilbert space. Far East J mathl Sci 2007, 26(3), 737-47.

Authors introduce a class Mⁿλ(a, b, α, β, γ; A), defined by a generalised Ruscheweyh derivative operator introduced by authors in [1]. Further, authors defined this class using the notion of operator on Hilbert space. Some properties related to the aforementioned class are obtained.

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014936   Agrawal N;Jain R C (Research Scholar, Rajiv Gandhi Proudyogiki Vishwavidyalaya, , Bhopal (M.P.)) : Decision making under uncertainty for sustainable environment. Acta Cienc Indica-Math 2007, 33(4), 1351-8.

There is an extensive literature on probability-based models of risk in decision-making, the literature on dealing with environmental uncertainty and in particular, with what will be termed 'hard uncertainty' in decision-making is rather limited. The purpose of this paper is therefore to review some of the major issues raised and to develop a suitable decision-making framework, which can provide the basis for the interpretation and analysis of the model of decision making under uncertainty. This paper demonstrates that the application of the Fuzzy set theory and Shackle model are useful tools in terms of explaining the way decisions are made in the face of uncertainty and could be fruitfully applied to other case studies involving environmental decisions, as well as other nonªenvironmental decisions conditioned by hard uncertainty.

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014935   Agarwal S;Garg M (Mathematics Dep, C.C.S. Univ, Meerut (U.P.)) : On ψ-closed sets in bitopological spaces. Acta Cienc Indica-Math 2007, 33(4), 1605-14.

In this paper author introduced ψ-closed wets in bitopological spaces. Properties of these sets are investigated and then new class of bitopological spaces called (i, j)-ST^g_1/2, (i, j)-S^gT_1/2, (i, j)-ST^*_1/2 and (i, j)-S^*T_1/2 spaces have been introduced. Further ψ-continuous map, ψ-irresolute map, pre semi closed, pre semi generalized closed and pre ψ-closed maps have been studied in bitopological spaces.

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014934   Aage C T;Salunke J N (School of Mathematical Science, North Maharashtra Univ, Jalgaon-425 001, Email: caage17@gamil.com) : Some fixed point theorems in compact metric spaces. Vidarbha J Sci 2008, 3(1), 16-21.

Presents some fixed point theorems in compact metric spaces. These are proved by using elementary theory of calculus. Further unique- ness of fixed point deduced by using definition of a metric.

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014004   Yadav R N;Rajput S S;Choudhary S;Bhardwaj R (Resource Development Center, Regional Res Lab, Bhopal) : Some fixed point theorems for rational inquality in 2-metric spaces. Acta Cienc Indica-Math 2007, 33(3), 709-14.

Unique fixed-point theorems, through new symmetric rational expression have been established.

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014003   Yadav R N;Rajput S S;Choudhary S;Bhardwaj R (Mathematics Dep, TRUBA College of Engineering & information Technology, Bhopal, M.P) : Fixed point & common fixed point theorems for non contraction type mapping on-2-Banach space. Acta Cienc Indica-Math 2007, 33(3), 737-44.

Some fixed point and common Fixed point theorems using two Banach Space have been proved.

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014002   Yadav D K (Applied Mathematics Dep, HMR Institute of Technology & Management, (Guru Govind Singh Indraprastha Univ), Hamidpur, Delhi-36) : Review of the defination of subject and of the theorem: the empty set is a subset of every set. Acta Cienc Indica-Math 2007, 33(3), 755-9.

Redefined the "subset" in the Set Theory after discussing the classical definition of the subset and the theorem: "the empty set is a subset of every set."

36 ref

014001   Verma S;Permar K (NO, Electronics & Telecommunication, NIT, Raipur-429 010) : Parallel boolean minimizer using gray code: paraboomig. Acta Cienc Indica-Math 2007, 33(3), 959-72.

Novel method of Boolean function minimization is proposed in the present paper. Unit distance and reflection properties of Gray code are used to generate all possible prime implicants of the given Boolean function. The proposed method is developed from scratch and the rules to generate Pls are also developed. The proposed method is shown to be readily adaptable to develop a parallel algorithm for faster minimization of Boolean functions exploiting the reflection property of Gray code. An algorithm is developed to generate all possible prime implicants of the given set of minterms (the on-set) on parallel basis and the subsequent solution of covering problem. The parallel algorithm is simulated for a star topology of multiprocessors using single program multiple data (SPMD) paradigm. The proposed parallel algorithm is implemented on an example. It is shown that parallel generation of all possible implicants by the proposed method gives considerable time saving for Boolean functions, especially those having large number of variables. It is shown that using load balancing the time saving can be further increased.

8 illus, 1 tables, 21 ref

014000   Veluchamy T;Girja G (Mathematics Dep, Govt. Arts College, Coimbatopre, Tamilnadu) : An Algebra on the discrete number system-A. Acta Cienc Indica-Math 2007, 33(3), 795-800.

Usual number system plays a major role in Mathematics. But many more number systems may be developed like Quaternion. An attempt is made to enhance the algebraic richness of the discrete number system, the set of integers modulo 7, Z₇ and it's algebraic extension A₇. The introduction briefs a historic note on the earlier discrete function theories and the next sections explain the algebraic fundamentals that can be established on this new number system.

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013999   Varadarajan G;Prabhakaran A R;Srinivasa Rao (Mathematics Dep, Srinivas Ramanujan Center, SASTRU Univ, Kumbakonam-612 001) : Integral solutions of ax<. Acta Cienc Indica-Math 2007, 33(3), 815-18.

Ternary quadratic homogeneous Diophantine equation ax² + b y²= cz² where a, b and c are perfect numbers; or, a, b and c are in geometric progression, are studied in this note and the solutions classified.

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013998   Tribedi U N;Jalan R B (Mathematics Dep, Bela Coll, Darbhanga, I.N.M.U, Kameshwar Nagar, Darbhanga) : Characterisation of levy-measures and integration. Acta Cienc Indica-Math 2007, 33(3), 1069-72.

Main aim here is to reformulate the properties of Levy-measures on a complete separable vector metric space. Levy-measures have full characterisation in terms of measures and integration. Theory on Hilbert as developed by S.T. Troyanski and M.I. Kedac. The main purpose here is to derive some applications for sums of conditionally convert series.

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013997   Tomba I;Ruhinikumar I (Mathematics Dep, Manipur Univ, Canchipur, Imphal-795 003) : Criss-cross epidemic model for silent infectious diseases : threshold condition. Acta Cienc Indica-Math 2007, 33(3), 1213-18.

Considering the (SIS) epidemic model where the contraction does not confer immunity and an individual removed for treatment become susceptible again after recovery, the threshold condition for a non zero steady state infected population is <62> 1 [3]. In this paper, we consider that an SI (Susceptible-Infective) epidemic model assuming that the infected individuals in a particular class, motivated by self consciousness, awareness and self controlling devises check themselves for further spreading the disease to others, then the modified threshold condition for a non zero steady state infected population is K₀ = K∞ = 2ξ, and the condition, necessary for an true epidemic to occur is c²pp'<62>γyy'.'

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013996   Thiagarajan K;Pushpalatha L;Lakshmi Pandian V (Mathematics Dep, Mysore Univ, Manasagangaothri, Mysore, Karnatka) : Special study in (2,3)- distance coloring and (2,3)-distance graphs. Acta Cienc Indica-Math 2007, 33(3), 933-6.

Defined (2, 3) - Distance Graph and (2, 3) -Distance Coloring for the connected graph G. Got some beautiful graphs under (2, 3) -- Distance graph scheme for paths and cycles. Also we observed new results under (2, 3) - Distance coloring scheme for paths and cycles.

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013995   Thiagarajan K;Pushpalatha L;Jeyabharathi S (Mathematics Dep, Mysore Univ, Manasagangothri, Mysore, Karnataka) : Graph color coding for number system. Acta Cienc Indica-Math 2007, 33(3), 929-32.

New type of coding system using colored graphs has been introduced. The notion of fundamental theorem of arithmetic serves as an important tool to develop the concept of graph coding in a new direction.

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013994   Thiagarajan K;Jaya Bharathi S;Pushpalatha L (NO, Mysore Univ, Mysore, Karnataka) : Comprative power of graph splicing langauges on self cross-over graph system. Acta Cienc Indica-Math 2007, 33(3), 973-80.

Freund[4] introduced the graph Splicing Scheme for the DNA molecules. Dassow and Mintrana [3] studies the Hyperedge replacement graph and examine the notation of self Cross-over system. K.G Subramanian et al. [13] examines the relationships between graph splicing Languages of Freund and Hyperedge replacement graph Languages. LGSCOG (Line graphs of Self-Cross over Graphs) for the self Cross-over systems has been proposed and get homomorphism properties between Line Graphs in graph splicing languages. Proved the relations between the Graphs when the numbers of splicing language have the same number of molecules.

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013993   Swatmaram;Phaneendra T (Mathematics Dep, Chaitanya Bharathi Institute of Technology, Chaitanya Bharathi P.O., Gandipet, Hyderabad-500 075) : Common fixed point of weakly compatible self-maps using asymptotic regularity. Acta Cienc Indica-Math 2007, 33(3), 1243-7.

With the notion of asymptotic regularity, a result of Ciric and hence of Sharma and Yuel to three weakly compatible self-maps has been extended.

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013992   Suresh K K;Jayalakshmi S (Statistics Dep, Bharathiar Univ, Coimbatore-641 046) : Designing of tightened normal tightened scheme under minium angle method. Acta Cienc Indica-Math 2007, 33(3), 1073-82.

New procedure for designing Tightened-Normal-Tightened^ Sampling scheme involving Minimum Angle Method has been presented. Procedure and necessary tables are provided for the selection of sampling scheme through minimum angle criteria involving producer and consumer quality levels.

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013991   Subramanyam D;Veera Raghava Reddy G;Prabhakar Reddy N;Varma S V K (Mechanical Engineering Dep, S.V.U.C.E, Tripati-517 502) : MDH flow through a circular cylinder bounded by a permeable bed. Acta Cienc Indica-Math 2007, 33(3), 989-98.

Unsteady laminar viscous conducting fluid through a circular cylinder bounded by permeable bed under the influence of exponentially decreasing pressure gradient has been studied. A uniform constant magnetic field is applied in azimuthal direction (i.e. in the direction of θ). The expressions for velocity and mass flux are obtained and discussed graphically.

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013990   Srivastava S (Mathematics Dep, Harish Post Graduate College, Varanasi, Uttar Pradesh) : Identification proximity. Acta Cienc Indica-Math 2007, 33(3), 1101-7.

Some results on identification proximity have been proved and two sufficient conditions for an onto proximal continuous map to be a p identification map has been obtained. A characterization for a p-identification map to be a p-open map has also been proved. An analogue of first isomorphism theorem in the context of proximity spaces has been dealt with.

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013989   Srinivasan A;Sudha K (Bishop Heber College, , Tiruchirappalli-17) : Mean and variance of the time to recruitment in a four graded manpower system for an univariate (max) policy of recruitment. Acta Cienc Indica-Math 2007, 33(3), 1167-73.

In any organization, successive exit of personnel leads of wastage in the form of man hours. The breakdown of the organization is triggered whenever the cumulative loss of manpower exceeds a particular level called threshold, beyond which the organization cannot sustain due to loss of protectivity. In this paper, an organization having four grades, with independent thresholds is considered and the mean and variance of the time to recruitment in this organization are obtained using the shock model and cumulative damage process of reliability theory. The analytical results are numerically illustrated by assuming specific distributions.

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013988   Srinivasan A;Buvaneswari B (Mathematics P.G. and Research Dep, Bishop Heber College (Autonomous), Tiruchirappalli-620 017) : Cost analysis on an univariate policy of recruitment in a single graded manpower system having a random threshold for exits. Acta Cienc Indica-Math 2007, 33(3), 1155-60.

Univariate policy of recruitment based on shock model approach for a single graded marketing organization which is subjected to exit of personal due to its various policy decisions, is considered. An explicit expression for the long-run average cost per unit time is derived when the threshold for exit is a continuous random variable. The results are numerically illustrated by assuming specific distribution.

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013987   Srinivas G;Sivaiah S;Prasada Rao D R V (NO, , G.R.I.E.T., Hyderabad, Andhra pardesh) : Magnetohydrodynamic convective flow and heat transfer of a viscous heat generating fluid through a rectangular duct. Acta Cienc Indica-Math 2007, 33(3), 847-56.

Steady flow and heat transfer of a viscous heat generating electrically conducting fluid through a rectangular vertical duct under a transverse magnetic field have been analysed. The dissipative terms are taken into account in the energy equation. The equations for the velocity and induced magnetic field are suitably coupled. The walls of the duct normal to the direction of the applied magnetic field are thermally insulated and those parallel to the field are maintained at constant temperature. The Galerkin finite element method with eight nodded serendipity elements is used to obtain the velocity, the temperature, the induced magnetic field, the shear stresses, the Nusselt number. Their behavior is discussed for variations in the governing parameters.

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013986   Srinivas G;Sivaiah S;Prasada Rao D R V (NO, G.R.I.E.T., Hyderabad (A.P.), India) : Finite element analysis of MHD free convective flow through a porous medium in a vertical channel. Acta Cienc Indica-Math 2007, 33(3), 677-85.

Fully developed free convective flow of an electrically conducting viscous incompressible fluid through a saturated porous medium in a vertical channel using Brinkman's model taking into account the viscous has been analysed. A uniform magnetic field of strength H_ο is applied normal to the boundary. The non-linear equations governing the flow and heat transfer have been analysed by using the finite element method. The velocity, temperature and Nusselt number are evaluated to the second order and their behaviour is discussed for variations in the governing parameters. Observed that the dissipation reduces velocity and suction Reynolds number enhances u.

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013985   Sivaiah S;Srinivas G;Prasad Rao D R V (NO, , T.R.R. Engineering College, Hyderabad) : Heat and mass transfer in a viscous heat generating fluid through a porous medium in a circular duct. Acta Cienc Indica-Math 2007, 33(3), 889-99.

Free convective heat and mass transfer flow of an incompressible viscous fluid through a heat generated saturated porous medium enclosed in a circular duct using Brinkman model have been investigated. The lower half portion of the duct is insulated while the tipper half is maintained at constant temperature and concentration. The Galerkin finite element method with six nodded triangular elements is adopted to obtain the iterative solutions for the stream function, temperature and concentration by the coupled non linear equations. The flow being symmetric, the expressions for velocity, temperature and concentration are obtained in typical quadrant of circular duct. Their behavior is discussed for variation in governing parameters Ra, D^-1, N, Sc and α. The local rate of heat transfer and mass transfer are also investigated computationally.

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013984   Singh T P;Vij I;Mittal S K (Maths Dep, D.A.V. College, Sadhaura, Haryana) : Optimal rental cost in restrictive 3-stage scheduling including job block concept. Acta Cienc Indica-Math 2007, 33(3), 761-7.

Deals nx3 flow-shop problem in which the processing time of jobs associated with probabilities, follow some restrictive rental policy. The concept of equivalent job for a job-block is being included in the study. The object of the paper is to find optimal sequence of jobs which minimizes the total rental cost of the machines. An algorithm has been obtained by using heuristic approach. The algorithm is made clear through numerical illustration.

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013983   Singh R;Singh B K;Rajan S (Maths Dep, Magadh Univ, Bodh Gaya (Bihar)) : Note on the formulation of the <. Acta Cienc Indica-Math 2007, 33(3), 999-1006.

H₂ optimal control models, the control design as a problem of minimizing the H₂ norm on the closed-loop transfer function while utilizing a state or measurement feedback controller. The H₂ optimal control problem is a deterministic setting of the linear quadratic Gaussian (LQG) control problem. LQG control theory is a powerful design tool which involves a linear model of a plant in a state-space description. Here we assumes properties for disturbances and measurement noise and translates the design specifications into a quadratic performance criterion consisting of state variables and control signal inputs and the objective is to minimize the performance criterion while at the same time, guaranteeing closed-loop stability. This involves the task of solving for the optimal compensator parameters, while are contained in the output feedback gain matrix.

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