019337   Ameenal Bibi K;Selvakumar R (Mathematics Dep, Dhanabagiyam Krishnaswamy Mudaliar College(W), (Autonomous), Vellore-1 and Research Scholar at Vellore Institute of Technology, Vellore-600 014, Email: ameena_maths@rediffmail.com) : Domination partition in graphs. Bull pure appl Sci-Sect E 2008, 27(2), 349-55.

Let G=(V,E) be a simple, finite, undirected graph. A non-empty set DcV in G is a dominating set if every vertex in V-D is adjacent, to atleast one vertex in D. Let D be the minimum dominating set of G. If V-D contains a dominating set D' then D' is called an Inverse dominating set w.r. to D. The domination number is denoted by y(G) and it is the minimum cardinality of the minimal dominating set of G[3], The Inverse domination number is denoted by y'(G) and it is the minimum cardinality of the minimal inverse dominating set of G[4]. In this paper, we define, Domination partition set and Exact domination partition set. If the partition of the vertex xet V includes a dominating set and an inverse dominating set then V is called a Domination partition set. If the vertex set V is partitioned such that V is exactly equal to the union of a dominating set and an inverse dominating set then V is called an Exact domination partition set. The Domination partition number of a graph G is denoted by γ_p (G) and an Exact Domination partition number of a graph G is denoted by γ_Ep (G). Here, we establish some results concerning these parameters. AJso Nordhaus-Gaddum type results are obtained for these parameteis.

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019336   Alam A;Siddiqui M Y;Hakim M H (Moalijat Dep, Ajmal Khan Tibbiya College, Aligarh Muslim University, Aligarh-202 002, Email: draftab_alam@rediffmail.com) : Clinical efficacy of Withania coagulans Dunal and Trigonella foenum-graecum Linn. in Type 2 Diabetes mellitus. Indian J Tradl Knowledge 2009, 8(3), 405-9.

Type 2 Diabetes mellitus has become an epidemic. It is associated with several contributory factors including increased longevity, obesity, unsatisfactory diet, sedentary lifestyle and increasing urbanization. The medical and socioeconomic burden of the disease is caused by the associated complications, which impose enormous strains on healthcare system. Management includes not only diet and exercise but also anti-hyperglycaemic drugs. Several researches have been made to evaluate the hypoglycaemic effect of a lot of herbal drugs. In the trial, the combined effect of Withania coagulans Dunal and Trigonella foenum-graecum Linn. have been studied.

019335   Ahmad Ali S (Mathematics Dep, Amiruddaula Islamia Degree College, Lucknow-226 002, Email: ahmad67@rediffmail.com) : Leibnitz theorem for fractional derivative of generalized functions-II. Bull pure appl Math 2009, 3(1), 50-4.

Leibnitz theorem for the fractional derivative of the product of two generalized functions, earlier proved by the author, has further been generalized by differentiating (fractionally) the product with respect to a continuously differentiable increasing function.

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018302   Zuo K (Mathematics Dep, Hubei Normal Univ, Huangshi 435002, P.R. China, Email: xiangzuo28@yahoo.com) : Nonsingularity of difference and sum of two outer inverses of a given matrix. J Algebra Discrete Struct 2008, 6(2), 107-15.

Nonsingularity of the difference and sum of two outer inverses of a given matrix has been studie. By using the properties of the outer inverses of matrices and the millity of matrices, authors give some sufficient and necessary conditions on the nonsingularity of the difference and sum of two outer inverses of a given matrix. Some known results in the literature are generalized.

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018301   Yao Q (Applied Mathematics Dep, Nanjing Univ of Finance and Economics, Nanjing 210003, Peoples' Republic of China, Email: yaoqingliu2002@hotmail.com) : Existence and multiplicity of positive solutions to a semipositone (N,P) boundary valure problem. Indian J pure appl Math 2009, 40(1), 3-19.

Existence of multiple positive solutions is considered for a nonlinear (n,p) boundary value problem where the nonlinear term has a lower bound of function type. By investigating Green function a suitable cone is constructed. By applying fixed point theorem on cone the existence of m positive solutions is established where m is an arbitrary positive integer.

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018300   Wang X;Xia J;Cao G (College of Mathematics and Information Science of GuangZhou Univ, GuangZhou Univ City, GuangZhou 510006, Peoples' Republi of China, Email: wangxiaofeng514@hotmail.com) : Trace class toeplitz operators on dirichlet space with unbounded symbols. Indian J pure appl Math 2009, 40(1), 21-8.

Trace class Toeplitz operators Tϕ on Dirichlet space D with symbol function ϕ that is unbounded on neighborhood of unit circle are conducted.

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018299   Tiwari C M (Post-Graduate Dep, Studies in Mathematics, Feroze Gandhi College, Rae Bareli) : Neutrix product of two distributions using fractional differentiation. J Indian Acad Math 2008, 30(1), 13-22.

Defines the product of two distributions proved the Leibniz rule for fractional derivative on the neutrix limit. Also obtaines an expression for the product of an arbitrary distribution with dirac-delta function on neutrix limit and discuss few particular cases.

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018298   Singh R;Andure N W (NO, Amravati Univ, Amravati) : Bayes estimators for the parameters of poisson type - exponential class model using non-informative priors. IAPQR Trans 2008, 33(2), 121-8.

Deals with the estimation of parameters of Poisson type exponential class model for software evaluation. Estimators of the number of failures and failure rate have been proposed under squared error loss function using non-informative priors. These estimators have been compared with corresponding maximum likelihood estimators using Monte Carlo simulation.

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018297   Singh K N;Singh P K (Mathematics Dep, S.G.P.G. College, Dobhi, Jaunpur-222 149) : On almost Euler summability of a fourier series. J Indian Acad Math 2008, 30(1), 63-9.

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018296   Shuliang H (Mathematics Dep, Chuzhou Univ, Chuzhou Anhui, 239012, P.R. China, Email: shulianghuang@sina.com) : On commutativity of σ-prime rings. J Algebra Discrete Struct 2008, 6(2), 89-93.

Let R be a 2-torsion free σ-prime ring with involution σ, I a nonzero σ-ideal and d a nonzero derivation commuting with σ. In the paper it is proved that if either d(x) o d(y) = 0 or d(x) o d(y) = x o y for all x, y E I, then R is a commutative ring.

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018295   Shrivastava S S (Mathematics Dep, Government P.G. College, Shahdol, Madhya Pradesh) : Generalized hypergeometric functions, Hermite polynomials and time dependent Schrodinger equation. J Indian Acad Math 2008, 30(1), 189-98.

Obtains two series solutions of a special one dimensional time dependent Schrodinger equation involvinmg Hermite polynomials, generalized hypergeometric functions and Fox's H-function.

018294   Sanyal D C;Karak A K (Mathematics Dep, Kalyani Univ, Kalyani-741 235, Email: des_klyuniv@yahoo.com) : Pulsatile flow of blood through a rough thin-walled elasti tube. J Indian Acad Math 2008, 30(1), 93-104.

Pulsatile flow of blood containing particles through a rough thin-walled elastic tube is studied. The interaction of the solid and fluid particles is considered by taking into account that the internal forces and the drag forces produced by the liquid on the solid particles and the interactions of solid-solid are negligible. The phase velocity ratio and the reduction of amplitude are found out as a function of the frequency parameter.

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018293   Sana P;Ghosh A K (Mathematics Dep, Jadavpur Univ, Kolkata-700 032, Email: akg10143@yahoo.co.in) : On the flow of a viscoelastic oldroyd-B fluid induced by an oscillating plate. J Indian Acad Math 2008, 30(1), 257-77.

Unsteady motion generated in a semi-infinite expanse of an incompressible viscoelastic Oldroyd-B fluid due to oscillations of an infinite flat plate in its own plane bounding the fluid starting impulsively from rest is investigated. The inquiries are made about the complete solutions for the velocity field and the shear stress on the wall. The Steady-state velocity distribution and the structure of the associated boundary layer determined. Asymptotic solutions for the velocity fieid at small and large values of time are obtained. The results are analyzed quantitatively and the effects of the fluid-elasticity and the frequency of oscillations of the plate on them are discussed. It is found that the thinning and the thickening effects of the elasticity of the fluid on the ultimate boundary layer depend on the frequency of the oscillations of the plate. Many known results are recovered as special cases of the present analysis.

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018292   Saluja G S (Mathematics & I.T. Dep, Govt. College of Science, Raipur, Email: saluja_1963@rediffmail.com) : On common fixed point of two asymptotically quasi-non-expansive mappings with errors in Banach space. J Indian Acad Math 2008, 30(1), 123-35.

Studies strong convergence of common fixed points of two asymptotically quasi-nonexpansive mappings and prove that if K is a nonempty closed convex subset of a real Banach space E and let S, T : K → K be two asymptotically quasi-nonexpansive mappings with sequences {u_n}, {u_n} ⊂ [0, ∞). It is proved that {x_n}^∞_{n = 1} converges strongly to some common fixed point of S and T. Result are significant generalization of corresponding results of Ghosh and Debnath [3], Petryshyn and williamson [6] and Qihou [7,8].

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018291   Sakalkar A;Thakar S (Mathematics Dep, North Maharashtra Univ, Jalgaon-425 001) : Generation of first integrals of equations of motion. J Indian Acad Math 2008, 30(1), 205-19.

Hamilton's equations of motion for non conservative dynamical system are derived in the set of new canonical variables. Energy like functions are constructed in these new canonical variables. Mass and potential functions are chosen in such a way that these energy like functions become invariant surfaces of the given dynamical system represented in the set of new canonical variables. The invariant surfaces expressed in terms of the original set of canonical variables are the first integrals of the equations representing the given dynamical system. These first integrals are obtained by the inversion of the canonical transformation.

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018290   Sahu S K;Kalam A;Sahoo C K (P.G. Dep of Statistics, Sambalpur Univ, Sambalpur-768 019) : Inventory model with the demand rate dependent on stock and constant deterioration. J Indian Acad Math 2008, 30(1), 221-8.

The demand rate is dependent on-hand Inventory level and the items have constant rate of deterioration with complete or partial backlogging and without backlogging. A suitable sensitive analysis the optimum lot-size and order level were obtained. Results are demonstrated for an instance of the model.

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018289   Rathod V P;Ahmed H (Studies and Dep, Research Mathematics, Gulbarga Univ, Gulbarga-585 106, Email: rathod_vijaykumar@rediffmail.com) : Pulsatile inclined two layered flow under periodic body acceleration. J Indian Acad Math 2008, 30(1), 137-51.

Interesting mathematical mode! has been formulated to study the pulsatile inclined two-layer blood flow under periodic body acceleration. The effect of periodic body acceleration on the blood flowing through a uniform inclined cylindrical tube has been analyzed. Blood is considered as a couple stress fluid, analytic expressions for axial velocity, core region, peripheral layer and flow rate have been obtained by applying finite Hankel and Laplace transform technique. The velocity variation for different parameters have been discussed and presented in the form of graphs. The result has been compared with existing theoretical models and is found in good agreement with the other results.

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018288   Ramaraj T;Komahan G (Mathematics Dep, A.V.V.M. Sri Pushpam College, Poondi-613 503) : Lung cancer and tumor detection using directional edge filtering techniques. J Indian Acad Math 2008, 30(1), 303-10.

Series of directional edge enhancement and edge extraction methods that can be accurately detect the shape of the Cancer and early stages of tumores A two-step registration, corresponding to global and local matching, is applied for current and prior images assisted by their corresponding edge images. The subtraction images were then processed by a rule-based CAD system. The majority of lung cancer in temporal subtraction images were lit-up. The percentile method is used to set a global threshold for each film. This method of template matching for detecting early stage tumors gives substantially better detectfon results. A large number of digitized mammogram images were used for evaluation of this method. The result obtained by applying these techniques to a set of test images are described further.

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018287   Rafiuddin;Ramana Murthy M V;Thiagarajan S; Chenna Krishna Reddy M (Humanities & Sciences Dep, C.V.R. College of Engg., Vastu Nagar, Mangalpally (Y.), Ibrahimpatan, (M.), P R., District-501 510) : MHD unsteady memory convective flow through porous medium. J Indian Acad Math 2008, 30(1), 293-302.

Free convective unsteady flow through porous medium of variable permeability bounded by an infinite vertical porous plate with constant heat flux under the influence of transverse uniform magnetic field has been investigated in the study. The permeability of porous medium fluctuates with time about the constant mean. Approximate solutions for velocity, temperature and skin friction are obtained. The effects of various parameters on velocity, skin friction amplitude and phase are shown graphically. Fluctuating parts of velocity 'M_r' and 'M_i' are found and discussed.

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018286   Qiu Y (Mathematics Dep, China Univ of Mining and Technology, Xuzhou 221008, Email: property111@yahoo.com.cn) : Derivations of group algebras over fields. J Algebra Discrete Struct 2008, 6(2), 75-82.

Let F be an algebraic closed field of characteristic zero, K a finite group and FK the group algebra of K over F. All derivations of FK are characterized.

018285   Pon Sundar (Mathematics Dep, Kandasamy Kandar's College, P. Velur Post-638 182, Email: pskkctnad@yahoo.com) : Oscillatory behaviour of higher order neutral nonlinear forced difference equations with oscillating coefficients. J Indian Acad Math 2008, 30(1), 111-21.

Oscillation criteria are given for higher order neutral nonlinear forced difference equations with oscillating coefficients of the form Δ^m [x(n) + p(n) x (τ (n))] + Σ^r_i=1 q_i (n) f_i(x(σ_i(n))) = e(n).

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018284   Palaniappan N;Shanmugasundaran A (Mathematics Dep, Alagappa Univ, Karaikudi, Email: palaniappan1950@yahoo.com) : Fuzzy number groupoid, semi fuzzy number group and fuzzy number monoid. J Indian Acad Math 2008, 30(1), 105-9.

Introduces the definition of fuzzy number groupoid, semi fuzzy number group and fuzzy number monoid. Also discusses some important theorems.

018283   Palani Chetty G (Mathematics Dep, I.R.T. Polytechnic College, Krishnagiri-365 108) : On some what fuzzy faintly precontinuous functions. J Indian Acad Math 2008, 30(1), 179-88.

Concept of some what fuzzy faintly precontinuous functions, some what fuzzy faintly preopen functions, weakly some what fuzzy faintly preopen functions are introduced. Some characterizations and interesting properties of these functions are discussed.

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018282   Nashine H P (Mathematics Dep, Raipur Institute of Technology, Chhatauna Mandir Hasaud, Raipur-492 101, Email: hemantnashine@rediffmail.com) : Results on coincidence and fixed points for nonconvex set in q-normed space. J Indian Acad Math 2008, 30(1), 33-42.

Uses the concept of q-normed space given by Kothe and the concept of non-convexity due to Dotson in order to apply them to find coincidence and fixed point results to a class of relatively non-expansive mappings for the families of four self mappings. As a consequence, our results generalize the results of Jungck.

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018281   Nadarajah S;Mitov G K;Mitov K V (NO, Manchester Univ, Manchester, U K, Email: mbbsn2@manchester.ac.uk) : Non-parametric estimate for PR (X<Y). IAPQR Trans 2008, 33(2), 109-20.

Proposes a non-parametric estimate of R = Pr (X< Y) based on a simple property of the uniform distribution. Illustrates the use of the estimate with bootstrap confidence intervals for four commonly known distributions (normal, exponential, gamma and beta).

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018280   Mujumdar N S;Sharma K C (Engineering Sciences Dep, Bharati Vidyapeeth Univ College of Engineering, Dhankawadi, Pune-411 043, Email: mujum66@yahoo.com) : Analytical solution for a fully developed polymeric fluid flow using ECTN model in a cylindrical pipe. J Indian Acad Math 2008, 30(1), 153-77.

Flow analysis of polymeric fluids having the characteristics of semi-dilute and concentrated solutions of hydrophilic polymers consisting of Hydrogen-bounding capacity such as polyacrylamide (PAm), poly acrylic acid (PAA), poly vinyl alcohol (PVA) etc. have been discussed. Analytical expressions are derived for velocity vector, the stress components and viscosity function in a fully developed cylindrical pipe flow using energetically crosslinked transient network (ECTN) model.

1 illus, 1 table, 6 ref

018279   Loonker D;Banerji P K (Mathematics Dep, Faculty of Science, J.N.V. Univ, Jodhpur-342 005, Email: deshnap@yahoo.com) : Mehler-Fock transform of tempered distribution. J Indian Acad Math 2008, 30(1), 229-36.

Distribution spaces (or the generalized functions) have been, during the past, worked upon on many integral transforms. Tempered distribution is one of the classes of distribution spaces. In this paper, we obtain results for the tempered distribution for the Mehler-Fock transformations.

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018278   Kushwaha R P (Mathematics Dep, Government College of Science, Madhya Pradesh) : Fractional integration and integral representations of multivariable H-function. J Indian Acad Math 2008, 30(1), 199-204.

The aim of this paper is to establish fractional integration and integral representation for multivariable H-function. Some interesting special cases of main results have also been discussed.

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018277   Kore B G (Statistics Dep, Balwant College, Vita-415 311) : New approach to solve unbalanced transportation problem. J Indian Acad Math 2008, 30(1), 43-54.

Proves a new theorem on existence of a feasible solution to the Unbalanced Transportation Problem (UTP). Proposes two new methods to obtain an Initial Basic Feasible Solution (IBFS) of the UTP without balancing it. By this new approach, achieves the goal with less number of computations and iterations. Further, we illustrate a new approach by suitable example.

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018276   Koh S H;Jeon H S;Kim Y G (Mathematics Dep, Institute of Pure and Applied Mathematics, Chonbuk National Univ, Jeonju, Jeonbuk 561-756, Republic of Korea, Email: yanggon@chonbuk.ac.kr) : Simple modules over certain lie algebras. J Algebra Discrete Struct 2008, 6(2), 83-7.

Let F be an algebraically closed field of characteristic p ≥ 7. Let L be any classical type over F. Authors find out simple L ⊗_F F ((X))-modules.

018275   Jain S;Mukesh Kumar (Mathematics Dep, Government College, Ajmer-305 001, Email: drjainsanjay1@rediffmail.com) : Inventory model with power demand pattern, Weibull distribution deterioration and shortages. J Indian Acad Math 2008, 30(1), 55-61.

An attempt has been made for obtaining a deterministic inventory model for power demand pattern incorporating two-parameter Weibull distribution deterioration and shortages.

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018274   Guo W;Wang Y;Shi L (Mathematics Dep, Xuzhou Normal Univ, Xuzhou 221116, P.R. China, Email: wbguo@xznu.edu.cn) : Nearly s-normal subgroups of a finite group. J Algebra Discrete Struct 2008, 6(2), 95-106.

Subgroup H of a group G is said to be nearly s-normal in G if there exists a normal subgroup N such that H N is a normal subgroup of G and H ∩ N ≤ H_sG, where H_sG is the largest s-permutable subgroup of G contained in H. Obtained some results on nearly s-normal subgroups and supersoluble groups are hence characterized by this kind of subgroups.

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018273   Gireesha B J;Bagewadi C S;Prasannakumara B C (Mathematics & Computer Science Dep, Kuvempu Univ, Jnana Sahyadri-577 451, Email: icon2004im@rediffmail.com) : Flow of unsteady dusty fluid under varying linear pressure gradient. J Indian Acad Math 2008, 30(1), 83-91.

Geometry of laminar flow of an unsteady viscous liquid with uniform distribution of dust particles between two infinite stationary parallel plates under the influence of pressure gradient varying linearly with time has been investigated using differential geometry techniques. Initially the fluid and dust particles are at rest. The analytical expressions for velocities of fluid and dust particles are obtained by using Laplace transform methods. The changes in the velocity profiles at different times are shown graphically.

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018272   Ghute V B;Shirke D T (NO, K.B.P. Mahavidyalaya, Pandharpur, Solapur, Email: vbghute_stats@rediffmail.com) : Synthetic T<. IAPQR Trans 2008, 33(2), 95-107.

Studies have shown that the sysnthetic 7² control chart detects process shifts faster than the Hotelling's T² chart. Extends these studies to process that are monitored with variable sample sizes. Simulation results show that the synthetic T² VSS chart is quicker than the synthetic T² and the Hotelling's T² charts in detecting almost all shifts in the process mean vector.

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018271   Ganesan V;Sundar Rajan B (NO, Periyar E.V.R. College, Tiruchirapalli, Email: vgstat@yahoo.co.in) : Bulk arrival queue with breakdown analysis. IAPQR Trans 2008, 33(2), 129-44.

Single server Markovian queue in which the units arrive in batches of variable size is considered. The units are served one by one in order of their batch arrival and the service times are distributed exponentially. The service may subject to random breakdowns and the failed channel waits before its repairs could be started. The delay times, due to repair, are distributed according to Gamma distribution. The expressions for the steady-state probabilities and expected number of units in the system have been derived. The numerical values are computed and their corresponding curves are exhibited.

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018270   Dorsett C (Mathematics Dep, Texas A & M Univ-Commerce, Commerce, Texas 75429-3011 USA) : New characterizations of normal and strong normal spaces. J Indian Acad Math 2008, 30(1), 279-91.

Completely normal is strengthened to strongly normal, and each of normal, completely normal, and strongly normal are further investigated and characterized.

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018269   Ding A;Li S (School of Mathematics and Computing Science, Hunan Univ of Science and Technology, Xiangtan, P.R. China, Email: axding@126.com) : Regular *-congruences on quasi regular *-semigroups. J Algebra Discrete Struct 2008, 6(2), 63-73.

Unary semigroup (5,*) is said to be a quasi regular *-semigroup if it satisfies the identities x'" = x', (xy)* = y'x* and x'x"x' = x'. It is clear that regular *-semigroups are quasi regular *-semigroups. In this paper, the concept of projection kernel normal system of (S, *) is introduced and in particular, the projection kernel of a unary congruence on a quasi regular *-semigroup (S, *) is considered. It is shown that if a family of subsets of S forms a projection kernel normal system, then it is a projection kernel of some regular *-congruence on (5,*) and each regular *-congruence on a quasi regular *-semigroup can be uniquely determined by its projection kernel. Our results generalize the corresponding results on regular *-semigroups obtained by Imaoka [5].

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018268   Darafsheh M R;Iranmanesh A;Moosavi S A (School of Mathematics, College of Science, Tehran Univ, Tehran, Iran, Email: darafsheh@ut.ac.ir) : 2-Frobenius Q-groups. Indian J pure appl Math 2009, 40(1), 29-34.

Finite group G whose all irreducible characters are rational is called a Q-group. In this note some results concerning the structure of a 2-Frobenius Q-group are obtained.

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018267   Chena Ram (Mathematics and Statistics Dep, Faculty of Science, Jai Narain Vyas Univ, New Campus, Jodhpur-342 005, Email: chenaramchoudhary@rediffmail.com) : On solutions of fractional differential equations. J Indian Acad Math 2008, 30(1), 237-48.

Nishimoto's fractional calculus, usually called N-fractional calculus, concepts are employed to obtain the solution of certain specific second order linear differential equation, which is supported by a suitable example. Justification of the analysis, provided, enhance the apparent importance.

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018266   Borkar M S (P.G. Dep of Mathematics, R.T.M., Nagpur Univ, University Campus, Amravati Road, Nagpur-440 033) : Analytical invariants of spherically symmetric space time. J Indian Acad Math 2008, 30(1), 1-12.

Considering the pairs (α_i, β_i) of orthogonal unit vectors α_i (space like) and β_i, (time like) of the form : α_i = (α₁, 0, 0, α₄), β_i = (β_i, 0, 0, 0), β_i = (0, 0, 0, β₄), and α_i = (α₁, 0, 0, 0), α_i = (0, 0, 0, α₄), β_i, = (β₁, 0, 0, β₄), the analytical invariants ρa = 1, ... 5, σ, σ, K, K of spherically symmetric space time are investigated and deduced that σ₁ = iσ₃, - σ₁ = iσ₃, K₁ = iK₃, - K₁ = iK₃ showing that σ₁, - σ₁, K₁ - K₁ are the rotations of σ₃, σ₃, K₃, K₃ through 90° in positive (anticlockwise) direction.

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018265   Biswas D (Mathematics Dep, Indian Institute of Technology Kharagpur, Kharagpur-721 302, Email: d_priya05@yahoo.co.in) : Quaternionic analysis. J Indian Acad Math 2008, 30(1), 247-56.

Advent of a class of quantities, consisting of quadruples of reals, usually called the quaternions, had undoubtedly initiated a new trend of concept in modern mathematics. The versatility of complex analysis has clearly indicated the presence of a function theory of quaternion variables. It is attempted to present an overview of quaternionic analysis. In the endeavour, preliminaries about quaternions, function theory of quaternion variables, Cauchy's theorem and the proof of Cauchy's Integral formula, are presented. Finally, applications of both quaternions and quaternionic analysis, are included in brief.

018264   Bhimani G C;Aora S H;Patel M N (NO, Saurashtra Univ, Rajkot, Email: gcbhimani@yahoo.co.in) : Estimation under progressive type-II censoring for legth biased exponential distribution. IAPQR Trans 2008, 33(2), 83-94.

Estimation related to parameters of the length biased exponential distribution has been discussed, based on progressively Type II censored samples. Maximum likelihood estimators as well as approximate Bayes estimators ofthe parameters are developed. A simulation study is considered for different patterns of censoring.

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018263   Behere G;Khot P G (Statistics Dep, Institute of Science, Nagpur) : Unexpected encounter in duality. J Indian Acad Math 2008, 30(1), 23-31.

Constructes L. P. P. by considering symmetric matrix. The terms of this matrix are obtained from a progressive series. This L. P. P. is such that its dual has exactly same coefficients as its primal i.e. [A], [b] and [c] are exactly same in primal and dual L. P. P. Many such L. P. Ps. are constructed and solved with the help of Tora package and the results so obtained are generalised and stated in the form of theorem.

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018262   Baues H J;Mikhailov R (Max-Planck-Institut fur Mathematik, Vivatsgasse 7, 53111, Bonn, Germany, Email: baues@mpim-bann.mpg.de) : Homotopy types of reduced 2-nilpotent simplicial groups. Indian J pure appl Math 2009, 40(1), 35-80.

Classified the homotopy types of reduced 2-nilpotent simplicial groups in terms of the homology and boundary invariants b, β. This contains as special cases results of J.H.C. Whitehead on 1-connected 4-dimensional complexes and of Quillen on reduced 2-nilpotent rational simplicial groups. Moreover it yields for 1-nilpotent (or abelian) simplicial groups a classification due to Dold-Kan. Describes a new natural structure of the integral homology of any simply connected space. Classify the homotopy types of connective spectra in the category of 2-nilpotent simplicial groups. Moreover we compute homotopy groups of spheres in the category of m-nilpotent groups for m = 2, 3 and partially for m = 4,5.

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018261   Barad H C;Patel D M (Mathematics Dep, Sir P.T. Sarvajanik College of Science, Surat-395 001) : Numerical solution of saturation problem arising in fluid-flow through porous media. J Indian Acad Math 2008, 30(1), 71-82.

Numerical methods are developed for solving problem in applied mathematics, physics, engineering. These methods are efficient to produce sufficiently approximate solution of partial differential equations which arise in practice. Of these methods implicit finite difference method is the most popular. Crank-Nicolson two-level implicit finite difference scheme for solving saturation problem arising in fluid-flow through Porous media. The one dimensional saturation equation is solved using a second level implicit relation and is known as Crank-Nicolson formula. Also its computational result as well as graphical representation are given.

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017317   Ojha A K;Mallick D (Mathematics Det, , Bhubaneswr-751 014, Orissa) : Existence of absolute stability of normal neural networks using hermitian and skew hermitian weight matrices. J Computnl Math optimiz 2008, 4(3), 171-83.

Dynamics of the neural networks essentially depends on the connectivity properties of the system. The convergent dynamªics of a class of neural networks with normal connection matrices has been studied by using Lyapunov function and spectral analysis of connection matrices. The absolute stability of networks has been verified by considering all the real part of the eigenvalues which are negative. The result have been generalized on the symmetric neural network to a larger class of asymmetric networks. Considered a different class of Hermitian and skew Hermitian weight matric. It has been train the network algorithm to form normal maªtrices. awe studied that normal neural network has interesting structural feat s in their weight matrices and also proved the necªessary and sufficient condition of the stability of normal neural netªworks. These results have wide application in neural optimization and classification problem.

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017316   Kang J H (Mathematics Dep, Andrews University, Berrien Springs MI 49104, U.S.A., Email: kang@andrews.edu) : Cooperative biological model with combined self-limitation and cooperation terms. J Computnl Math optimiz 2008, 4(2), 113-26.

Non-existence and existence of the positive solution for the generalized cooperation biological model for two species of animals Δu + u(a+g(u,v)) = 0 in Ω Δv + v(d+h(u,v)) = 0 in Ω u = v = 0 on δΩ were investigated. The techniques used in this paper, are elliptic theory, upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties for the solution of logistic equations.

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017315   Ferrentino R (Economic Sciences and Statistics Dep, University of Salerno, Fisciano (Sa), Italy, Email: rferrentino@unisa.it) : On the function of seal. J Computnl Math optimiz 2008, 4(3), 157-67.

Object of study is the analysis, in a particªular case, of the function of Seal used in the problem of the determiªnation of the non ruin function in finite times.

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017314   Ferrentino R (Economic Sciences and Statistics Dep, University Salerno Fisciano (Sa) Italy, , Email: rferrentino@unisa.it) : Application of the mixture of exponentials to the risk theory. J Computnl Math optimiz 2008, 4(3), 145-56.

Problem of the solution of the equation of Dickson is formalized and solved with the Laplace trasform into the case in which the distribution function of sums at the risk is a mixture of two exponentials.

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017313   Ferrentino R (Economic Sciences and Statistics Dep, University of Salerno, Fisciano (Sa) Italy, Email: referrentino@unisa.it) : Some relations among minty variational inequalities of differential type and increasing along rays functions. J Computnl Math optimiz 2008, 4(2), 93-112.

Investigates the link between a Minty variational inequality and the notion of increasing along rays function. It is shown that vector increasing along rays functions can be characterized in term of existence of a soultion of a generalized Minty variational inequality.

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