016922   Fonseca L G;Barbosa H J C (NO, , LNCC, Av. Getulio Vargas, 333 Quitandinha, Petropolis, RJ Brazil, CEP 25651 - 075, Email: goliatt@incc.br) : Similarity-based surrogate model for enhanced performance in genetic algorithms. Opsearch 2009, 46(1), 89-97.

In spite of their ability to deal with difficult optimization problems, genetic algorithms in general require a large number of evaluations in order to find an optimal or a satisfactory near-optimal solution. When expensive simulations are involved in the optimization process, using genetic algorithms as optimization tools can become unattractive. The use of surrogate models is an interesting alternative to overcome that drawback, either by replacing expensive evaluations or allowing for exploration of the search space. In this paper we introduce a surrogate model based on similarity measures into genetic algorithms in order to enhance the performance in optimization problems, under a fixed budget of simulations. Numerical experiments are conducted in order to assess the applicability and the performance in constrained and unconstrained optimization problems. The results show that the present framework arises as an attractive alternative to improve the final solutions with a fixed budget of expensive evaluations.

6 illus, 5 tables, 27 ref

016921   Ferrara M;Guerrini L (NO, Universita Mediterranea Di Reggio Calabria Facolta Di Giurisprudenza,, Via Dei Bianchi (Palazzo Zani) 2, 89100-Reggio Calabria, Italy, Email: massimiliano.ferrara@unric.it) : Environment and sustainable growth in a two-sector model with variable labor growth rate. Bull Calcutta Mathl Soc 2009, 101(6), 627-34.

Investigates a closed economy in which the production depends essentially on physical capital, natural capital and labor. Contrary to the standard literature, we assume that the labor growth rate is 11011 constant but variable over time. We show that the economy is sustainable in the long run if human activities have a net zero or positive effect the environment. Moreover, for any given tax rate (or MPC, i.e. marginal propensity to consume), we drive the set of sustainable MFCs (or tax rates).

9 ref

016920   Dixit S (Mathematics Dep, V.S.S.D. College, Kanpur, Uattar Pradesh) : Departure process of the GI/G/1 queue and its maclaurin series. Acta Cienc Indica-Math 2009, 35(2), 357-64.

Introduced the study the departure process of the GHG/1, we develop a simple recursive procedure to calculate the maclaurin series of its moments and covariances with respect to a parameter in the service time. Based on this recursive procedure the explicit formulas of the coefficient of these Maclaurin series can be obtained in terms of derivatives of the probability density function of the inter-arrival time evaluated at zero and the moments of the inter-arrival time and the service time. One important application of these Maclaurin series is that they can be used to obtain the entire response curves of the moments and variance of the departure process.

5 ref

016919   Dhar A K;Majumder D P (Mathematics Dep, Bengal Engineering and Science Univ, Shipur, P.O.B. Garden, Shibpur, Howrah-711 103, Email: asoke.dhar@rediffmail.com) : Nonlinear energy transfer within the peak of a narrow gravity wave spectrum in the presence of air flowing over water. Bull Calcutta Mathl Soc 2009, 101(6), 615-26.

An evolution equation for the surface gravity wave envelope in deep water in the presence of air flowing over water which is correct to third order in the wave steepness is derived, to discuss the resonant transfer of energy within the peak of a continuous narrow spectrum of water waves. For a symmetric normal spectrum the H-integrated energy transfer function dNλ/dτ gives very useful information. The curves for dNλ/dτ for diferent values of air flow velocity V show a strongly negative minima at the origin, with two positive maxima, symmetrically situated to either side. The one dimensional transfer function for the frequency spectrum has a pronounced minimum near the peak frequency, indicating the strong negative transfer there and two weaker maxima, one on each side. For a asymmetric spectra it can be seen that the μ-integrated transfer is markedly greater in the forward (low-frequency) face of the spectrum for different values of V. At the peak of the spectrum the transfer is still strongly negative.

3 illus, 8 ref

016918   Deep K;Bansal J C (Mahematics Dep, Indian Institute of Technology, Roorkee, Roorkee-247 667, Email: kusumfma@iitr.ernet.in) : Hybridization of particle swarm optimization with quadratic approximation. Opsearch 2009, 46(1), 3-24.

Particle swarm optimization (PSO) has been extensively used in recent years for the optimization of nonlinear optimization problems. Two of the most popular variants of PSO are PSO-W (PSO with inertia weight) and PSO-C (PSO with constriction factor). Efforts have also been made to hybridize PSO with other methodologies to improve its performance. In this paper we present the hybridization of PSO with quadratic approximation operator (QA). The hybridization is performed by splitting the whole swarm into two subswarms in such a way that the PSO operators are applied on one subswarm, whereas the QA operator is applied on the other subswarm, ensuring that both subswarms are updated using the global best particle of the entire swarm. Based on this concept, two algorithms, namely qPSO-W and qPSO-C have been developed and their performance is evaluated with respect to PSO-W and PSO-C on the basis of 15 benchmark test problems and 3 real life problems taken from literature. The numerical and graphical results are a proof that the hybridized approach is a definite improvement in terms of efficiency, reliability and robustness.

4 illus, 4 tables, 41 ref

016917   Chauhan T S;Indiwar Singh Chauhan;Singh R K (Mathematics Dep, Bareilly College, Bareilly, Uttar Pradesh) : Kaehlerian conharmonic curvature tensor. Acta Cienc Indica-Math 2009, 35(2), 339-41.

Defined and studied Kaehlerian Conharmonic Curvature Tensor. In the end, an important theorem on the Kaehlerian Conharmonic Curvature Tensor has been investigated.

7 ref

016916   Bondar K L;Borkar V C;Patil S T (P.G. Dep of Mathematics, N.E.S. Science College, Nanded-431 605) : Comparison results for difference φ-laplacian boundary value problems. Vidarbha J Sci 2010, 5(2), 10-14.

Studies the Comparison results, lower and upper solutions to nonlinear difference φ-Laplacian boundary value problems.

11 ref

016915   Bhaskara Rama Sarma B;Pattabhiramacharyulu N C;Lalitha S V N L (Faculty of Mathematics, Narayana Educational Institutions, Hyderabad, Andhra Pradesh) : Recursive procedure for two-species competing eco-system with decay & replenishment for one species. Acta Cienc Indica-Math 2009, 35(2), 487-96.

Four stage recursive procedure is adopted to give an approximate solution to the mathematical model equations of a two-species competitive eco-system incorporating decay and replenishment for one of the species. Numerical examples are provided to explain trajectories of the solutions. The conclusions are recorded from the graphs.

12 illus, 7 ref

016914   Baskar Babujee J;Senbagamalar J (Mathematics Dep, Anna Univ Chennai, Chennai-600 025) : Wiener index for special trees isomorphic to hydrocarbons. Acta Cienc Indica-Math 2009, 35(2), 575-8.

Wiener index W(G) is a topological index that relates molecular structure and physical and chemical properties of certain hydrocarbon compounds. The wiener number or wiener index W(G) is defined as the half of the sum of the distances between every pair of vertices of G. In this paper we obtain W(G) for certain class of trees like y-tree, Hoffman tree P₅ Θ K₁ and (1, 4)-bi-regular caterpillar isomorphic to some organic compounds.

2 illus, 5 ref

016913   Arockiarani I;Mohana K (Mathematics Dep, Nirmala College for Women, Coimbatore-641 018) : πg-closed sets and π-normal spaces in bitopological settings. Acta Cienc Indica-Math 2009, 35(2), 457-65.

Introduced πg-closed sets in bitopological space and obtain some of their properties. Further we study π-normal spaces and their characterizations in bitopological settings.

16 ref

016912   Amur K S;Naik K S (Mathematics Dep, Karnatak Univ, Dharwad-580 003) : Canonical asymptotic vector fields on the hyper-helicoid. Bull Calcutta Mathl Soc 2009, 101(6), 591-602.

The existence of a parametric hyper-helicoid M²ⁿ(n ≥ 1) in R²ⁿ⁺¹ with Weierstrass representation was established by Amur and Venkataraman in (Amur and Venkataraman, 1991). It was shown amongst other things that M²ⁿ admits an involutive asymptotic distribution Δε of dimension n and hence is foliated. In this paper it is shown that M²ⁿ admits another distinct asymptotic involutive distribution Δ_η and therefore, M²ⁿ is doubly foliated. The two distributions are used in singling out a set of canonical vectorfields which have properties quite similar to those possessed by asymptotic directions on a minimal sxirface in R³ in relation to the principal directions.

016911   Akbar Ansari M (Mathematics Dep, Ranchi Univ, Ranchi, Jharkhand-834 008) : Note on hadamard matrices. Acta Cienc Indica-Math 2009, 35(2), 381-4.

Discussed two methods of construction of Hadamard matrices from known Hadamard matrices. While the first of these is a direct generalization Sylvester construction of Hadamard matrices, the second one is similar to the Williamson's construction of hadamard matrices.

8 ref

016910   Agney Kumar;Singh K K (Mathematics Dep, Mangalayatan Univ, Aligarh, Uttar Pradesh) : Effect of MHD on unsteady flow of visco-elastic oldroyd fluid through a rectangular channel. Acta Cienc Indica-Math 2009, 35(2), 385-92.

Aim of this paper is to investigate the flow of visco-elastic Oldroyd fluid with transient pressure gradient through a rectangular channel in the presence of magnetic field. Here we considered the first and second order Oldroyd fluid and investigate the same problem in this new visco-elastic model. The numerical expressions of the velocity profiles have been given for both first and second order fluids.

7 ref

016909   Agney Kumar (Mathematics Dep, Mangalayatan Univ, Beswan, Aligarh-202 145) : Numerical analysis of unsteady flow of visco-elastic first order oldroyd fluid through porous media in a rectangular channel. Acta Cienc Indica-Math 2009, 35(2), 599-604.

Aim of present paper is to investigate the flow of visco-elastic Oldroyd fluid through porous media in a rectangular channel under time varying body force. The numerical expression of the velocity profiles of a fluid element of the problem has been given. The result of visco-elastic Maxwell fluid, Rivlin-Ericksen liquid and purely viscous fluid have been also determined.

8 ref

016908   Agney Kumar (Mathematics Dep, Mangalayatan Univ, Baswan, Aligarh-20215) : Casson fluid flow with homogeneous porous medium. Acta Cienc Indica-Math 2009, 35(2), 551-8.

Model of Casson fluid flow in a tube filled with a homogeneous porous medium is investigated by using suitable numerical technique. The initial motivation for studying this problem is to understand the blood flow in an artery under pathological situations when the fatty plaques of the cholesterol and artery clogging blood clots are generated in the lumen of the coronary artery. Here we study the nature of frictional resistance which will fall upto a certain level of permeability and then after it will become steady.

6 illus, 8 ref

016907   Agney Kumar (Mahematics Dep, Mangalayatan Univ, Aligarh, Uttar Pradesh) : Numerical analysis of unsteady flow of viscoelastic first order oldroyd fluid through porous media. Acta Cienc Indica-Math 2009, 35(2), 547-50.

Investigated the flow of visco-elastic Oldroyd fluid through porous media in a rectangular channel with transient pressure gradient. Numerical expression of the velocity profiles has been given. The result of visco-elastic Maxwell fluid and purely viscous fluid have been determined.

7 ref

016906   Agney Kumar (Mathematics Dep, Mangalayatan Univ, Aligarh, Utar Pradesh) : Numerical study of flow of dusty incompressible visco-elastic second order oldroyd fluid through rectangular channel. Acta Cienc Indica-Math 2009, 35(2), 399-404.

Aims of the paper is to investigate the unsteady flow of dusty incompressible visco-elastic second order Oldroyd fluid with transient pressure gradient through a rectangular channel. The exact solutions for the liquid velocity and particle velocity have been obtained.

9 ref

016905   Agney Kumar (Mathematics Dep, Mangalayatan Univ, Aligarh, Uttar Pradesh) : Numerical analysis of flow of dusty visco-elastic first order oldroyd fluid through a rectangular channel. Acta Cienc Indica-Math 2009, 35(2), 393-7.

Aim of this paper is to investigate the unsteady flow of dusty incompressible visco-elastic first order Oldroyd fluid with transient pressure gradient through a rectangular channel. The exact solutions for the liquid velocity and particle velocity have been obtained.

10 ref

015708   Zhour Z A (Mathematics Dep, Faculty of Science and Information Technology, Zarqa Private University (ZPU), P.O. Box 2000, Zarqa 1311, Jordan, Email: Zeyad 1968@yahoo.com) : Numrical solutions of the general matrix convolution equations based on the iterative methods and box convolution product. Far East J mathl Sci 2009, 32(2), 199-215.

Considered box convolution product and give an application to find the approximate solutions of the general coupled matrix convolution equations by using iterative methods. Furthermore, we prove that these solutions consistently converge to the exact solutions for any initial value.

14 ref

015707   Yingxin Guo;Wang J (Mathematics Dep, Qufu Normal University, Qufu 273165, Shandong, P.R.China, Email: yxguo312@163.com) : Necessary and sufficient condition of Lf-netted spaces in terms of ω-structure. Far East J mathl Sci 2009, 32(2), 181-4.

Necessary and sufficent of LF_netted spaces in terms of g-functions have been established.

3 ref

015706   Yang X L;Tang J S (NO, College of Mechanics and Aerospace, Human University, Changsha, Hunan-110 082, China, Email: yangxianlin88@126.com) : Exact solutions to the generalized lienard equation and its applications. Pramana J Phys 2008, 71(6), 1231-45.

Some new exact solutions of the generalized Lienard equation are obtained, and the solutions of the equation are applied to solve nonlinear wave equations with nonlinear terms of any order directly. The generalized one-dimensional Klein-Gordon equation, the generalized Ablowitz (A) equation and the generalized Gerdjikov-Ivanov (GI) equaªtion are investigated and abundant new exact travelling wave solutions are obtained that, include solitary wave solutions and triangular periodic wave solutions.

16 ref

015705   Wang W (Mathematics Dep, Yuanpei College, Shaoxing University, Zhejiang Shaoxing, 312 000, P.R. China) : Well-posedness and regularity of an M<. Sankhya 2008, 70(Pt 1), 69-83.

In this paper, the solution of a M^{x /G/l queueing system with vacation times is investigated. By using the method of functional analysis, especially, the linear operator theory and the Co semigroup theory on Banach space, we prove the well-posedness of the system, and show the existence of positive solution.}

23 ref

015704   Uddin N (Statistics and Actuarial Science Dep, University of Central Florida, Orlando, FL 32816, USA, Email: muddin@mail.ucf.edu) : MV-optimal designs for three treatments when observations are correlated. Sankhya 2008, 70(Pt 1), 113-20.

The MV-optimality problem of block designs for three treatments in b = 3n± 1 blocks each of size three under the assumption that blocks behave independently but there is correlation among the observations within the same block according to first order autoregressive process.

11 ref

015703   Sutradhar B C;Prabhakar Rao R;Pandit V N (Mathematics and Statistics Dep, Memorial University of Newfoundland St. John's, NL, Canada A1C 5S7, , Email: bsutradh@math.mum.ca) : Generalized method of moments versus generalized quasilikelihood inferences in Binary panel data models. Sankhya 2008, 70(Pt 1), 34-62.

Generalized method of moments (GMM) estimation approach has a long history in the econometrics literature. Since the seminal paper of Hansen (1982, Econometrica), this GMM approach has been widely used mainly by econometricians to obtain consistent and efficient estimates for regression parameters in the class of linear dynamic dependence models. To reflect its importance on both theoretical and applied econometrics, the Journal of Business and Economic Statistics (JBES) has recently launched an interesting special issue (JBES, 2002, Vol. 20, No.4) on this GMM estimation approach. In this paper, we propose a generalized quasilikelihood (GQL) approach, which, as compared to the GMM approach, appears to produce more efficient estimates for the regression and the dynamic dependence parameters in the non-linear regression set up. We examine this superior efficiency performance of the GQL approach in the context of binary panel data analysis, through both asymptotic and simulation studies. The GMM and GQL estimation approaches are illustrated by re-analyzing the Survey of Labour and Income Dynamics (SLID) data from Statistics Canada.

9 tables, 21 ref

015702   Sutradhar B C (Mathematics and Statistics Dep, Memorial University, St. John's NL, Canada A1C 5S7, Email: bsutradh@math.mun.ca) : Inferences in familial poisson mixed models for survey data. Sankhya 2008, 70(Pt 1), 18-33.

Consistent and efficient estimation of the parameters of the generalized linear mixed models (GLMMs) have proven to be difficult in the infinite population set up. This estimation issue becomes more complex in the finite population set up where the estimation is done based on a sample of small number of clusters chosen from a finite population with large number of unbalanced clusters. This paper examines the role of the sampling designs on the estimation of the parameters of the GLMM based super-population for clustered count data.

3 tables, 13 ref

015701   Sreedhar Babu M;Bhaskar Redy N;Subba Reddy M V (Mathematics Dep, S. V. University, Tirupati-517 502, Email: drmvsubbreddy@yahoo.co.in) : Effect of variable viscosity on the peristaltic motion of a jeffrey fluid in a symmertic channel. Ultra Scient phys Sci 2009, 21(2), 395-402.

The peristaltic motion of an incompressible Jeffrey fluid with variable viscosity in a two-dimensional symmetric channel under the long wavelength and low Reynolds number assumptions is investigated. Analytical solutions are obtained for axial velocity and axial pressure gradient. The effects of viscosity parameter α, material parameter λ1 and amplitude ratio Φ on the pumping characteristics and the friction force are studied through graphs in detail.

9 illus, 10 ref

015700   Sivasubramanian M (Mathematics Dep, Dr. Mahalingam College of Engineering and Technology, Pollachi-642 003, Email: profpk49@yahoo.com) : Phenomenon in geometric analysis. Indian J Sci Technol 2009, 2(4), 23-4.

It has been established that it is impossible to deduce Euclid V from Euclid I, II, III, and IV. The investigations devoted to the parallel postulate gave rise to a number of equivalent propositions to this problem. Also, while attempting to prove this statement as a special theorem Gauss, Bolyai and Lobachevsky independently found a consistent model of first non-Euclidean geometry namely hyperbolic geometry. Gauss's student Riemann developed another branch of non-Euclidean geometry which is known as Riemannian geometry. The formulae of Lobachevskyian geometry widely used tot sty the properties of atomic objects in quantum physics. Einstein's general theory of relativity is nothing but beautiful application of Riemannian geometry. Einstein derived these field equations by analyzing geometry of space-time. Author re-visited the parallel postulate and by protecting himself under Saccheri's umbrella found a consistent geometric result which challenged the previous contributions in this field.

2 illus, 6 ref

015699   Shunmugapriya S;Lakshmi S (Mathematics Dep, A.A.M. Engineering College, Kovilvenni, Tamil Nudu) : Weibull model in the MPFC to regulate HPA activity of stress experience. Bio Sci Res Bull 2009, 25(1), 41-9.

The hypothalamic pituitary adrenal axis (HPA) habituates or gradually decreases its activity with repeated exposure to the same stressor. During habituation the HPA axis likely requires input form Cortical and limbic regions involved in the processing of cognitive information that is important in coping to stress. Brain regions such as the medial prefrontal cortex (MPFC) are recognized as important in mediating these processes. The MPFC modulates stress related behavior and it regulates acute and repeated stress-induced HPA responses. CRH-l receptors which integrated neuro endocrine behavioral and au tonomic responses to stress are localized in the MPFC but have not been specifically examined with respect to HPA regulation. CRH receptor activity in the MPFC contributes to stressªinduced regulation of HPA activity and anxiety-related behavior and that CRH release in MPFC may differentially regulate HP A responses in acutely compared to repeatedly stressed. We use a Weibull model of graphical approaches used extensively in determining a mixture of two Weibull distribution is suited to a given set of failure data and the results connected with the medical report.

1 illus, 10 ref

015698   Senthil Kumar p;Lakshmi S (NO, Kunthavai Nachiar Govt. Arts College for Women, Thanjavur, Tamil Nadu) : Stochastic model for resilience analysis due to smoking and cortisol. Bio Sci Res Bull 2009, 25(1), 1-7.

The purpose of study was smoking is associated acutely with elevated cortisol levels. However, the results of comparisons of cortisol levels in smokers and nonsmokers have been inconsistent and the significance of cortisol re~ponses in smoking cessation is unclear. Smoking cessation was accompanied by an abrupt decrease in salivary cortisol and this was sustained over the abstinence period cortisol. There was marginal association between the decrease in cortisol and smoking relapse rates. This paper introduces a simple node failure model based on user lifetimes and studies the resilience of k regular peer to peer networks in which nodes stay online for random periods of time. The cumulative distribution function of residuals for Pareto lifetimes with [3] F(x) = 1- [1+x/β)-a, a > 1 is given by F_R(X) = 1- (1+x/β]^1-a.

2 illus, 10 ref

015697   Sapna (Mathematics Dep, H.B. Technological Institute, Kanpur-208 002, Email: sapna1980jan@rediffmail.com) : Analysis of non-newtonian fluid flow in a stenosed artery. Ultra Scient phys Sci 2009, 21(2), 307-14.

The numerical illustration presented at the end of the paper provides the results for the resistance to flow, apparent viscosity and the wall shear stress through their graphical representations. It has been shown that the resistance to flow, apparent viscosity and wall shear stress increases with the size of the stenosis but these increases is comparatively small due to non-Newtonian behavior of the blood indicating the usefulness of its rheological character in the functioning of the diseased arterial circulation. Few comparisons with the existing results have been made in order to validate the applicability of the present model.

9 illus, 22 ref

015696   Ramesh Kumar A;Lakshmi S (Mathematics Dep, K.N. Govt Arts College for Women, Thanjavur, Tamil Nadu, ) : EN model for 5-HT_2c agonist mCPP on blood pressure and heart rate. Bio Sci Res Bull 2009, 25(1), 9-16.

In the present study the role of central 5- HT_2c receptors in the control of blood pressure and heart rate in non-stressed and stressed, adult, male, wistar rats are discussed. Third ventricle injections of the 5- HT_2c agonist mCPP elicited a significant increase in blood pressure in non-stressed animals. The exponential normal regression model provides a flexible parametric approach to constructing growth charts or centile curves. We develop diagnostics for this model, with a special emphasis towards assessing the impact of individual cases all estimated centile curves.

2 illus, 10 ref

015695   Rajesh V;Sridevi C;Varma S V K (Mathematics Dep, Narayana Engineering College, Nellore-524 004, Email: v.rajesh30@gmail.com) : Chemical reaction effects on transient MHD free convection and mass transfer flow of dissipative fluid with heat generation and thermal diffusion past an infinite vertical plate. Ultra Scient phys Sci 2009, 21(2), 285-94.

The effects of chemical reaction on transient MHD free convection mass transfer flow of dissipative fluid past an infinite vertical porous isothemal plate in the presence of heat generation, thermal diffusion and viscous on is studied numerically. The Problem is governed by a coupled nonlinear of partial differential equations. This system is solved numerically by applying explicit finite difference method. The effect of chemical reaction parameter (K) in the presence of Heat generation parameter (H) and Soret number (So) is examined on Velocity, Temperature and Concentration. The numerical values of skin friction, the rate of heat transfer and the rate of mass transfer are entered tables. It is found that chemical reaction parameter K decreases velocity and concentration in the presence or no presence of Heat source parameter Hand Sorel number So. Further, it has no effect on temperature.

9 illus, 3 tables, 18 ref

015694   Patil P B (NO, College of Rural Home Science, University of Agricultural Sciences, Dharwad, Karnataka) : Identification and development of instructional strategies to accelerate mathematics learning among slow learners. Asian J Home Sci 2009, 3(2), 108-110.

The study was carried out with the objectives to identify, develop instructional strategies, see the impact of strategies developed and promote the best instructional strategy to teach the slow learners. The study was undertaken in one Government and one private school of Dharwad taluk which were within 10km radius from Dharwad city. First standard students were selected to teach maths subject. Questionnaire was developed to carry out the pre test. Instructional strategies i.e. materials, picture book, peer tutoring and individualized instruction were developed and their impact was seen by conducting the post test. The results revealed significant difference between pre-test and post-test scores of control and experimental group students taught using different strategies. The different strategies i.e. materials, picture book, peer tutoring and individualized instruction were significantly effective in improving the ability of learning mathematics of slow learners. Students of the experimental groups performed significantly better than the students from the control group after the intervention programme.

3 tables, 4 ref

015693   Mollin R A (Mathematics and Statisties Dep, University of Calgary, Calgary, Alberta, Canada, T2N 1N4, Email: ramollin@math.ucalgary.ca) : Characterization of D = p<. Far East J mathl Sci 2009, 32(2), 285-94.

Settled the open problem of characterizing those nonsquare integers D > 1 which are a sum of two relatively prime squares when x^{2 - Dy2 = -1 has no solution in integers x,y.}

5 ref

015692   Ludkovsky S V (Applied Mathematics Dep, Moscow State Technical University MIREA, av. Vernadsky 78, Moscow 119454, Russia, Email: sludkowski@mail.ru) : Infinite dimensional unitary representations of dense subgroups of exotic groups. Far East J mathl Sci 2009, 32(2), 169-80.

Commutative infinite dimensional topological Lie groups has been discussed. On them quasi-invariant Gaussian measures are considered. For such groups with the help of measures strongly continuous unitary representations and among them topologically irreducible are investigated.

24 ref

015691   Lakshmi S;Venkatesh A (Kunthavai Nachiyar Govt. Arts College for Women, , Thanjavur, Tamil Nadu, Email: lakshmi291082@yahoo.co.in) : Cumulative damage threshold crossing model for the effect of stress on dopamine levels in the cortical areas. Bio Sci Res Bull 2009, 25(1), 29-34.

The theoretical study for the effect of stress on Dopamine (DA) levels in tIle hippocampal network in comparison to the prefrontal cortex (PFC) is investigated. Using a cumulative damage threshold crossing model, the reliability function of dopamine have been obtained during the stress produced by the administration of psycho stimulant drug cocaine in the perirhinal cortex (pRC), entorhinal cortex (EC) and prefrontal cortex (PFC). The result shows that the increased levels of dopamine in the PFC compared with PRC and EC.

1 illus, 3 ref

015690   Lakshmi S;Punithavathi R (Kunthavai Nachiar Govt. Arts College for Women, , Thanjavur, Tamil Nadu) : Mathematical model for size distribution of histamine release from mast cells. Bio Sci Res Bull 2009, 25(1), 35-40.

Mast cells are known to accumulate at sites of inflammation and upon activation to release their granule content, eg., histamine, cytokines and proteases. The secretory leukocyte protease inhibitor (SLPI) is produced in the respiratory mucous and plays a role in regulating the activity of the proteases. The size distribution is fitted with histamine release from HMC-l cells. The size distribution is utilised for each inflammatory action, and proved that histamine is large.

11 ref

015689   Kalimuthu S (NO, , SF 211, Kanjampatti P.O., Pollachi-642 003, Email: postulate.kalimuthu0@gmail.com) : Parallel postulate - return of the roaring lion. Indian J Sci Technol 2009, 2(4), 16-22.

Without assuming the fifth Euclidean postulate, the author established the following theorems: 1.There exists a spherical quadrilateral whose interior angle sum is equal to 360 degrees. 2 .The sum of the interior angles of a triangle is a straight angle.

2 illus, 22 ref

015688   Ghosh S;Pal R (California University, , Riverside, CA 92521-0138, USA, Email: subir.ghosh@ucr.edu) : Model identification and discrimination of simple linear regression. Sankhya 2008, 70(Pt 1), 121-32.

The paper considers the issue of designing an experiment to determine which of two competing simple regression models, the linear model MI and the quadratic model MII, better describes the data by first identifying both models and then discriminating between them. The discrimination between models is considered by comparing both fitted observations and predicted observations. Two criterion functions I and J are proposed. The criterion function I is completely new. We observe that the celebrated Kiefer-Wolfowitz design (Kiefer and Wolfowitz (1959)) does not perform very well under the proposed new criterion function I. It is shown that the criterion function J is in fact the criterion function for the Kiefer- Wolfowitz design and therefore it performs the best under J. We also demonstrate that the Biswas-Chaudhuri sequential designs (Biswas and Chaudhuri (2002)) at various stages are in fact designs within a class Dl considered in this paper. We are therefore able to evaluate the performance of Biswas-Chaudhuri designs with respect to the I criterion function. We have considered another class of designs D₂ and obtained the best design within this class with respect to the J criterion function.

13 ref

015687   Ghosh J K;Bogdan M;Samanta T (NO, Statistics Dep, West Lafayette, IN 47907, USA, Email: jayanta@isical.ac.in ) : Applied statistics and the Indianness of Indian data. Sankhya 2008, 70(Pt 1), 1-17.

Author an overview of current and possible future directions of Applied Statistics and explore choice of topics (e.g., Bioinformatics), paradigms and methodology. We also provide a tentative assessment of special problems arising in analysis of Indian data. Some priorities and need for special care in applied work are suggested, specially in the Indian context.

65 ref

015686   Eshan A A;Al solamy F R (Mathematics Dep, Taif University, P.O. Box 20314, Makkah 21599, Saudi Arabia, Email: ameeraeshan@hotmail.com) : General submanifolds of a kaehler manifold-II. Far East J mathl Sci 2009, 32(2), 185-98.

Studied most general class of submanifolds of a Kaehler manifold initiated in [4], which includes all existing classes of submanifolds (complex submanifolds, totally real sub manifolds, CR-submanifolds, slant submanifolds). Such a sub manifold M of a Kaehler manifold M has naturally defined operators Φ, F, ψ and G. We study the geometry of a general submanifold with parallel F and obtain a condition under which a general submanifold is a complex sub manifold.

7 ref

015685   Bhattacharya S (Bayesian and Interdisciplinary Research Unit, Indian Statistical Institute, 203, B.T. Road Kolkata-700 108, Email: sourabh@isical.ac.in) : Gibbs sampling based Bayesian analysis of mixtures with unknown number of components. Sankhya 2008, 70(Pt 1), 133-55.

For mixture models' with unknown number of components, Bayesian approaches, as considered by Escobar and West (1995) and Richardson and Green (1997), are reconciled here through a simple Gibbs sampling approach. Specifically, we consider exactly the same direct set up as used by Richardson and Green (1997), but put Dirichlet process prior on the mixture components; the latter has also been used by Escobar and West (1995) albeit in a different set up. The reconciliation we propose here yields a simple Gibbs sampling scheme for learning about all the "unknowns, including the unknown number of components. Thus, we completely avoid complicated reversible jump Markov chain Monte Carlo (RJMCMC) methods, yet tackle variable dimensionality simply and efficiently. Moreover, we demonstrate, using both simulated and real data sets, and pseudo-Bayes factors, that our proposed model outperforms that of Escobar and West (1995), while enjoying, at the same time, computational superiority over the methods proposed by Richardson and Green (1997) and Escobar and West (1995). We also discuss issues related to clustering and argue that in principle, our approach is capable of learning about the number of clusters in the sample as well as in the population, while the approach of Escobar and West (1995) is suitable for learning about the number of clusters in tile sample only.

3 illus, 20 ref

015684   Beran J;Schutzner M (Mathematics and Statistics Dep, University of Konstanz, Germany, Email: jan.beran@uni-konstanz.de) : Effect of long memory in volatility on location estimation. Sankhya 2008, 70(Pt 1), 84-112.

Consider the question in how far long memory in volatility affects the asymptotic distribution of location estimators. Specifically, consider M-estimation for models with finite moments. Under symmetry assumptions, the asymptotic distribution turns out to be the same as under independence, even if a nonlinear estimator is used. However, for nonlinear estimators, deviations from these assumptions can imply a slower rate of convergence and hence asymptotic efficiency zero compared to the sample mean. This means that for long-memory volatility models, estimators that are robust with respect to bias, turn out to be extremely sensitive with respect to the variance. Simulations and data examples illustrate the results by comparing the asymptotic behaviour of the sample mean, the median and a Huber estimator with an intermediate tuning parameter.

5 illus, 69 ref

015683   Beatrice B;Russo F (SAGL Via Maggio 9, Lugano, Switzerland, , , Email: biago@exmachina.ch) : Package for decomposing B<. Far East J mathl Sci 2009, 32(2), 217-29.

Deals with the package OSB 1.0, which allows us to optimize some algorithmic criteria, involved in the study of the tents and, more generally, in that of the B^{1 -groups.}

7 ref

015682   Aramaki J;Nurmuhammad A;Tomioka S (Mathematical Sciences Dep, Faculty of Science and Engineering, Tokyo Denki University, Hatoyama-Machi Saitama 350-0394, Japan, Email: Aramaki@r.dendai.ac.jp) : Semi-linear elliptic problem with the de gennes boundary condition associated with superconductivity. Far East J mathl Sci 2009, 32(2), 153-67.

Show that the results of Lu and Pan [9] also hold for more general semi-linear elliptic equations. This problem is associated with the Ginzburg-Landau system of superconductivity. Under the de Gennes boundary condition, we show that the results hold in a domain in R^{n, where n may be general. Of course, the results are an extension of [9].}

11 ref

015681   Ali G (United states Environmental Protection Agency office of Water, Office, , 1200 Pennsylvania Avenue, NW, Washington D.C. USA, Email: ali.ghulam@epa.gov) : Expected utility in econometric random Utility models. Sankhya 2008, 70(Pt 1), 63-8.

Misspecification of expected utility for random utility models could result in an undervaluation of environmental amenities. The expression for the expected value of visiting sites for econometrically estimating welfare losses of recreational amenities, presented by some authors, appears to be incorrect. In this article, we present a direct and correct derivation and approximation of the expected utility for the random utility models.

15 ref

015680   Aggarwal B D;Smith R J (Mathematics and Statistics Dep, University of Calgary, Calgary, Alberta, Canada) : Do frequent doses of HAART block the HIV blips. Far East J mathl Sci 2009, 32(2), 231-51.

Presented model consisting of six differential equations to show that sufficiently farge doses of HAART tend to suppress the HIV blips that may otherwise occur because of change in the infection coefficient of the virus. We also show that large doses of HAART will eradicate the reservoir of latently infected CD4+ T cells in a patient.

8 illus, 15 ref

015679   Afrouzi G A;Vahidi J;Alizadeh M (Mathematics Dep, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran, Email: afrouzi@umz.ac.ir) : Existence of positive weak solutions for a class of semipositonep-laplacian systems involving the weight functions. Far East J mathl Sci 2009, 32(2), 253-9.

10 ref

015678   Afrouzi G A;Graily E (Mathematics Dep, Faculty of Basic Sciences, Mazandaran University, Babolsar, Iran, Email: afrouzi@umz.ac.ir) : Existence non-negative solutions for a class of semipositione problems. Far East J mathl Sci 2009, 32(2), 261-5.

It is shown that every continuous image of a compact Hausdorff a -scattered space X (i.e., every subset A of X with <157> A <157> ≥ a has an isolated point relative to A and a is the least regular cardinal with this property) is b -scattered for some b ≤ a. Consequently, if X is a compact Hausdorff a -scattered, where a ≥ c and c is the cardinality of continuum, then a = 0 the first infinite cardinal and X is scattered. Surprisingly, it follows that in any compact Hausdorff space X, every non-empty subset has an isolated point if and only if every uncountable subset of X has an isolated point.

6 ref

015677   Adesanya S O;Ayeni R O (Mathematical Sciences Dep, Redeemer's University, Redemption City, Nigeria, Email: adesanyaolumide@yahoo.com) : Anatomically based model of visco-elastic blood flow in a stenosed artery: effect of hematocrit variations on the flow property. Far East J mathl Sci 2009, 32(2), 275-83.

Authors model the stenosed arterial blood flow considering the effects of viscosity, wall deformation and fluid-structure interaction. The visco-elastic blood behaviour was described using Eying-Powel model. Our result shows a significant difference when compared with the Newtonian model in literature;-welsubmit that the non-Newtonian blood property cannot be neglected.

3 illus, 1 table, 7 ref