024696   Srivastava A;Khadke A;Gupta D (Sch of Stud in Math, Vikram Univ, Ujjain-456 010) : Construction of H-closed extensions using H-essential semilattice homomorphisms. Bull Calcutta Mathl Soc 2006, 98(1), 57-62.

A method to construct a compactification of a locally compact space which is a generalization of the method of constructing compactification by using a singular map was given by Caterino. Because of similar behaviour of H-closed spaces with compact spaces a method to construct an H-closed extension of a an LHC space in a natural way was obtained.

7 ref

024695   Srivastava A;Bhatia T (Sch of Stud in Math, Vikram Univ, Ujjain-456 010) : On pairwise R-compact bitopological spaces. Bull Calcutta Mathl Soc 2006, 98(2), 93-6.

The concept of R-compactness in Bitopological spaces has been intoroduced and various properties of these spaces have been studied.

6 ref

024694   Sinha S (Dep of Statist, Texas A & M Univerasity, USA) : Determining gene-environment interaction using projected score method. Calcutta Statist Ass Bull 2005, 57(225-226), 19-33.

A new method proposed for estimating multiplicative interactions between genetic and environmental factor on the risk of a disease using projected score approach. First the existing methods for determining gene-environment interactions through case-control study and case-only study design have been received. Then the proposed method based on projection theory has been discussed. An unbiased estimating equation for estimating the parameter of interest has been derived and then its asymptotic standard error. In addition, a score statistic is derived based on the derived estimating equation. The advantage of using the proposed method are : 1. Gain in efficiency of the parameter estimate and 2. Robustness to the other model parameters and gene-environment independence assumption. The proposed method is applied to a real case-control data on lung cancer. Compared the existing methods with the proposed method through a small simulation study which shows that the proposed method performs better than the existing methods in terms of efficiency in all situations irrespective of whether the genetic and/environmental factor are independent in the population.

4 tables, 13 ref

024693   Singh S B;Kasana H S (Math Dep, Punjabi Univ, Patiala-147 002) : Improved estimates for error in floating point representation analysis. Bull Calcutta Mathl Soc 2006, 98(2), 117-24.

There are two ways to translate a real number into its floating-point representation viz. rounding and chopping. Some sharper estimates for relative error in floating-point representation have been presented for both the cases. It has been shown that there is difference of one order of magnitude in finding the exact sum and difference of two numbers x and y using the existing methods in the literature and the method proposed by the authos. Thus whether one is interested in scientific computing, where rounding is usually preferred or in chopping, which is very useful in large industrial systems, these bounds may be useful in practical problems.

4 ref

024692   Shyam Lal;Srivastava A (Math Dep Fac of Sci, Univ of Allahabad, Allahabad-211 002) : Approximation of conjugate of Lip (ξ (t), p) function by almost triangular matrix summability method. Bull Calcutta Mathl Soc 2006, 98(1), 39-48.

Qureshi (1981) and Qureshi (1982) established two interesting results on the approximation of conjugate function f(x) of a function f∈ Lip α and Lip (α, p) classes by means of a conjugate series. A more general result than those of Qureshi (1981,1982) has been determined so that their results comes out as particular cases.

10 ref

024691   Shomberg J (Math Sci Dep, Univ of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201, USA, Email: shomberg@uwm.edu) : Holomorphic methods in PDE. Int J Math Analysis 2006, 1(2), 141-52.

A method for obtaining explicit harmonic solutions to some fully nonlinear elliptic PDE on R² has been introduced. The focus is on PDE that are expressed as a product of the determinant of the Hessian and a function of the squared norm of the gradient less some function f: det (D²u) Ψ <157> Du <157>²) = f(x,y). With an appropriate non-negative function Ψ and an appropriate non-positive radially symmetric function, R^<126>(s) = f(x,y) where s = √X² + y², it has been shown the existence of up to two distinct families of harmonic solutions to PDE of the following type: det (D²u) Ψ (<157>Du<157>²) = R^-(s). Applications to the Monge-Ampere equation and the prescribed Gauss curvature equation are also motivated.

2 illus, 8 ref

024690   Shatanawi W (Dep of Math, The Hashemite Univ, Zarqa, Jordan, Email: swasfi@hu.edu.jo) : A charaterization of λ (A*B)-nuclear maps where A and B are power sets of infinite types. Far East J mathl Sci 2005, 19(1), 47-55.

It has been shown that if λ(A) and λ(B) are G_∞-spaces, then the sequence space of the form λ(A*B) is strong Kothe dual. Also, it has been proved that for nuclear G_∞-spaces λ(A), and λ(B), a bounded linear map T between Banach spaces E and F is λ(A*B)-nuclear if and only if it is pseudo-λ(A*B)-nuclear.

8 ref

024689   Sharma P R;Pareek D (Math Dep, Univ of Raj, Jaipur-302 004) : Unsteady flow and heat transfer through an elastico-viscous liquid along an infinite hot vertical porous moving plante with variable free stream and suction. Bull Calcutta Mathl Soc 2006, 98(2), 97-108.

Unsteady flow and heat transfer of an incompressible elastico-viscous liquid [Walters fluid (Model B')] along an infinite, hot, vertical, porous moving plate in the presence of oscillatory free stream and generalised variable suction through the plate are investigated. The governing equations of motion and energy are solved by successive perturbation technique. Skin-friction coefficient and rate of heat transfer in terms of Nusselts number at the plate are derived, their numerical discussion are given and their numerical values for various values of physical parameters are presented through tables. The velocity and temperature distributions are shown through graphs for various values of physical parameters. Skin-friction coefficient increases with the increase of frequency or the Eckert number, while it decreses with the increase of the Grashoff number, Prandtl number or phase angle when flow is along an externally cooled plate. Also, skin-friction coefficient increases due to increase in the Garashoff number, Prandtl number, the Eckert number, frequency, phase angle or non-Newtonian parameter, when flow is along an externally heated plate.

4 illus, 4 tables, 24 ref

024688   Sharma P R;Chawla S;Singh N K (Math Dep, Univ of Raj, Jaipur-302 004) : Heat transfer through MHD flow between a rotating disc and a stationary porous disc in the presence of heat source. Bull Calcutta Mathl Soc 2005, 97(5), 433-44.

Heat transfer through steady flow of a viscous incompressible electrically conducting fluid between a non-porous rotating disc and a stationary porous disc in the presence of heat source is investigated. The whole fluid flow region is divided into two regions, one is free fluid region and other is porous region. The fluid flow between the discs is governed by Navier-Stokes' equations incorporated with Maxwells equations and Darcy's law. The Hartmann number is playing an important role to increase the fluid temperature when the frictional heat is to be considered. The Eckert number is influenced in Nusselt number to increase or decrease the rate of heat transfer.

4 illus, 16 ref

024687   Sharma K K;Goel J (Dep of Statist, C.C.S. Univ, Meerut-250 005) : Further remark on sensitive character of sequential normal testing procedure. Int J agric statist Sci 2005, 1(1-2), 89-99.

Several studies deal with the non-robust character of various types of acceptance sampling plans. Many such studies also analyse the robust character of sequential testing procedures when the underlying failure time distribution has a monotone failure rate. A vast literature on the life testing plans in the Bayesian framework is also available where updating prior with experimental data has been the main concern. Highlighting the point that the basic normal lifetime distribution can be updated in respect of prior variations in its mean, the present study deals with the analysis of the sensitivity/robust character of sequential normal testing procedures when the mean of the basic normal distribution is considered as a random variable with posterior as its distribution. The robust character of the consistency of the random variable n, in view of prior variations, is also analysed.

3 illus, 1 table, 16 ref

024686   Sharma B;Ravindra Pratap L;Prahlad Kumar (P G Dep of Math, Patna Univ, Patna) : Queuing problem with balking and reneging for limited space. Math Educ 2005, 39(3), 186-9.

The steady state solutions of the queuing system with Poisson arrival, exponential waiting time and multiple server system with balking and reneging has been considered. It has been assumed that the customers arrive from a finite source and join the system with probability 1, when number of customers is less than or equal to the server and 1 -(n+1-s)/N when the number of customers is greater than the number of server. Joining customers wait a certain time for service to began. If it has not begin by that time, he leaves the queue. Service is done on first cum first served basis. Various queueing characteristics have been calculated.

1 ref

024685   Shanmugam T N;Sivasubramanian S (Math Dep, Coll of Engng Anna Univ, Chennai-600 025, Email: Shan@annauniv.edu) : Linear operators associated with k-uniformly convex and k-starlike functions. Bull Calcutta Mathl Soc 2006, 98(2), 153-60.

Given the Generalized hypergeometric function _pF_q (α₁, α₂,..., α_p, β₁, β₂,..., β_q, Z), the operator I (α₁, α₂,..., α_p, β₁, β₂,..., β_q, Z) which is the Convolution of the function _pF_q (α₁, α₂,..., α_p, β₁, β₂,..., β_q, Z) with f(z) is analytic in the open unit disk has been studies. The objective was to find conditions on the parameters α₁, α₂,..., α_p, β₁, β₂,..., β_q for which the linear operator I(α₁, α₂,..., α_p, β₁, β₂,..., β_q, Z) were to be in various subclasses of starlike and convex functions. The results extend several earlier results.

21 ref

024684   Shafique M (Math Dep, Gomal Univ, D.I. Khan, Pakistan, Email: mshafique 6161@yahoo.com) : Numerical study of the three dimensional micropolar flow due to a stretching flat surface. Int J Math Analysis 2006, 1(2), 173-87.

Three dimensional, steady flow of a micropolar fluid, due to a stretching flat surface, is considered. The equeations of motion are reduced to a system of ordinary differential equations, which in turn are solved numerically using SOR method and Simpson's (1/3) rule, for three diferent combination of the three dimensionless parameters involved. The results are found for the values of θ in the range 0 ≤ θ ≥ 1.0, where θ = b/a, a and b are stretching rate in the x, y-directions respectively, and having dimension 1/time. Results are given both in tabular and graphical form. The accuracy of the results were checked by comparing them on different grid sizes and with the previous results where possible. The comparison is excellent.

4 illus, 8 tables, 16 ref

024683   Shafikov R;Verma K (Math Dep, Middlesex Coll Univ of Western Ontario, London, Ontario N6A 5B7, USA) : Boundary regularity of correspondences in C<. Proc Indian Acad Sci-Mathl Sci 2006, 116(1), 59-70.

Let M, M¹ be smooth, real analytic hypersurfaces of finite type in Cⁿ and ƒ⁹⁴ a holomorphic correspondence (not necessarily proper) that is defined on one side of M, extends continuously up to M and maps M to M'. It is shown that ƒ⁹⁴ must extend across M as a locally proper holomorphic correspondence. This is a version for correspondences of the Diederich-Pinchuk extension result for CR maps.

14 ref

024682   Sengupta T K;Talla S B;Pradhan S C (Dep of Aerospace Engng, Indian Inst of Technol, Kanpur-208 016, Email: tksen@iitk.ac.in) : Galerkin finite element methods for wave problems. Sadhana 2005, 30(5), 611-23.

Accuracy, stability and wave propagation properties of a few Galerkin methods. The basic Galerkin methods with piecewise linear basis functions (called G1 FEM here) and quadratic basis functions tcalled G2FEM) have been compared with the streamwise-upwind Petrov Galerkin(SUPG) method for their ability to solve wave problems. It is shown here that when the piecewise linear basis functions are replaced by quadratic polynomials, the stencils become much larger (involving five overlapping elements), with only a very small increase in spectral accuracy. It is also shown that all the three Galerkin methods have restricted ranges of wave numbers and circular frequencies over which the numerical dispersion relation matches with the physical dispersion relation - a central requirement for wave problems. The model one-dimensional convection equation is solved with a very fine uniform grid to show the above properties. With the help of discontinuous initial condition, also investigates the Gibbs' phenomenon for these methods.

5 illus, 8 ref

024681   Sen M K;Bhuniya A K (Math Dep, Univ of Calcutta, 35, Ballygunge Circular Road, Kolkata-700 019, Email: senmk@cal3.vsnl.net.in) : Completely k-regular semirings. Bull Calcutta Mathl Soc 2005, 97(5), 455-66.

An additive idempotent semiring S is k-regular if for all a in S there is x in S for which a + axa = axa and completely k-regular if moreover ax + ax²a = ax²a and xa + ax²a = ax²a. A completely k-regular and k-simple semiring is completely k-simple. It has been proved that a semiring S is completely k-regular if and only if it is a distributive lattice of completely k-simple semirings.

9 ref

024680   Sankaran P G;Nair M T (Dep of Statist, Cochin Univ of Sci and Technol, Cochin, Kerala) : On a finite mixture of pareto distributions. Calcutta Statist Ass Bull 2005, 57(225-226), 67-83.

Finite mixtures of probability distributions arise as models of income and wealth in many practical problems. The present paper, we study the properties of finite mixture of Pareto distributions in the context of income analysis have been studied. Estimation of the parameters of the finite mixture of Pareto distributions has been developed using different methods for complete as well as censored samples. A simulation study and a data analysis are carried out to assess the performance of the estimators.

4 tables, 14 ref

024679   Sahoo L N;Senapati S C (Dep of Statist, Utkal Univ, Bhubaneswar-751 004) : A class of estimators using auxiliary information in stratified sampling. Int J agric statist Sci 2005, 1(1-2), 81-7.

Presents a general class of estimator for a finite population total availing information on two auxiliary variables. The discussion is motivated on the assumption that the stratum level totals of one auxiliary variable are known whereas for the other only overall total is known.

2 tables, 3 ref

024678   Sahoo L N;Dalabehera M (Dep of Statist, Utkal Univ, Bhubaneswar-751 004) : Unbiased estimators using harmonic mean of the auxiliary variable. Int J agric statist Sci 2005, 1(1-2), 11-6.

For the purpose of estimating population mean, we develop Hartley-Ross (1954)-type unbiased estimators using harmonic mean of the auxiliary variable in the context of ratio and product methods of estimation. Performance of the suggested estimators compared to the traditional ones have also been examined.

2 tables, 13 ref

024677   Roy K;Prasad R (Dharmapur, , Keshonarayanpur-848 504) : On characterisation of Finsler metrics. Math Educ 2005, 39(3), 182-5.

Irrvestigates the significant geometric properties of Randers metrics and its applications in general Theory of Relativity. M. Matsumoto showed that if a Randers metric of Lindsberg type have constant curvature, then it is Minkowskian. All locally projectively flat Randers metric with constant flag curvature and its impact on Minkowskian space has been classified.

6 ref

024676   Roy A;Khattree R (Dep of Mgmt Sci and Statist, The Univ of Texas at San Antonio, USA) : Classification based on multivariate repeated measures with time effect on mean vector and an AR (1) correlation structure on the repeated measures. Calcutta Statist Ass Bull 2005, 57(225-226), 49-65.

In repeated measures studies how observations change over time is often of prime-interest. Modelling this time effect in the context of discrimination, is the objective of the article. The problem of classification with multiple q-variate observations with time effect on each individual has been studied. The covariance matrices as well as mean vectors are modelled respectively to accommodate the correlation between the successive repeated measures and to describe the time effects. Computation schemes for maximum likelihood estimation of required population paramters are provided.

12 ref

024675   Ray A K (Dep of Math (Retd.), Jadavpur Univ, Kolkata-700 032) : Condition that a second degree equation in two variables represents a pair of real lines. Math Educ 2005, 39(3), 161-5.

It is known that the condition that a second degree equation in two variables represents a pair of lines in a plane. But then the two lines may be real or complex. The paper finds the condition such that the given equation represents two real lines. This is not to be found in any treatise.

2 illus, 3 ref

024674   Ravindra G V (Math Dep, Washington Univ, St. Louis, MO 63130, USA, Email: ravindra@math.wustl.edu) : Zero cycles on certain surfaces in arbitrary characteristic. Proc Indian Acad Sci-Mathl Sci 2006, 116(1), 37-50.

Let k be a field of arbitrary characteristic. Let S be a singular surface defined over k with multiple rational curve singularities and suppose that the Chow group of zero cycles of its normalisation S^- is finite dimensional. Numerical conditions under which the Chow group of zero cycles of S is finite dimensional have been given.

4 tables, 14 ref

024673   Rasoul Dadashzadeh;Nimse S B (The Fac Member of Islamic, Azad Univ of Bonab, Iran, Email: r-dadashazadh@yahoo.com) : Multiobjective optimization with linguistic variables. Int J Math Analysis 2006, 1(2), 241-8.

Fuzzy mathematical programming problems in which the functional relationship between the decision variables and the objective function is not completely known have been interpreted. The knowledge-base consists of a block of fuzzy if-then rules, where the antecedent part of the rules contains some linguistic values of the decision variablees and the consequence part is a crisp value of the objective functions. Use of simplified fuzzy reasoning method to determine the crisp functional relationship between the objective function and the decision variables has been suggested and the resulting (usually nonlinear) programming problem to find a fair optimal solution to the original fuzzy problem has been solved.

14 ref

024672   Rajneesh Kumar;Leena Rani (Math Dep, Kurukshetra Univ, Kurukshetra-136 119) : Effects of mechanical and thermal sources in orthorhombic thermoelastic material. Bull Calcutta Mathl Soc 2006, 98(1), 13-24.

A dynamical two-dimensional problem of thermoelasticity has been considered to investigate the disturbance due to mechanical (horizontal or vertical) and thermal source in a homogeneous, thermally condcting orthorhomic material. Laplace and Fourier transforms are applied to basic equations to form a vector matrix differential equation, which is then solved by eigenvalue approach. The displacements, stresses and temperature distribution so obtained in the physical domain are computed numerically and illustrated graphically. The numerical results of these quantities for zinc crystal-like material are illustrated to show the comparison of the results. For the theories of coupled thermoelasticity (CT) and uncoupled thermoelasticity (UCT) for insulated boundary and temperature gradient boundary.

4 illus, 11 ref

024671   Rajesh kumar (Maths Dep, Govt. Polytechnic, Gulzarbagh, Patna-800 007) : On lattice theoretic characerisation of maximal α-recursive sets. Math Educ 2005, 39(3), 193-5.

A necessary and sufficient condition is obtained for the existence of maximal α-recursive enumerable sets. G. Kreisel derived some results related to generalisations of recursion theory. A Lattice theoretic approach developed in view of specific properties of maximal sets in terms of quotient Lattice Σ(α).

6 ref

024670   Rahaman F;Mandal S;Kalam M (Math Dep, Jadavpur Univ, Kolkata-700 032, Email: farook_rahaman@yahoo.com) : Higher dimensional Reissner-Nordstrom black hole and test particles. Bull Calcutta Mathl Soc 2006, 98(1), 7-12.

A detailed analysis of the motion of the test particles have been done around Reissner-Nordstrom black hole in higher dimension. The study of the trajectories of the test particle has done by using the Hamilton-Jacobi formalism. Test particles with various masses and electric charges have been considered and its behavior both in static equilibrium and non equilibrium cases have been examined.

12 ref

024669   Pradhan B (SQC & OR Div, Indian Statistical Inst, Kolkata) : An application of multivariate statistical technique for cost effective decision making-a case study. Calcutta Statist Ass Bull 2005, 57(225-226), 109-19.

Focuses on the application of multivariate statistical techniques for making a cost effective decision in an industrial set up. The objective of the study was to take a decision with respect to several parameters whether a particular product can be sent to the customer or not. The techniques like MANOVA, discriminant and classification function analysis have been used to fulfil the objectives. An optimum classification rule has been established for making the decision. A cost benefit analysis has also been done after implementing the proposed optimum decision-making rule.

3 tables, 7 ref

024668   Pillai R N;Saji Kumar V R (NO, Valiyavilakom, Thiruvananthapuram, Kerala) : Geometric infinite divisibility and the waiting time paradox. Calcutta Statist Ass Bull 2005, 57(225-226), 129-36.

It is shown that the waiting time W in a stationary renewal process generated by X has the form W = X + V, with Y non-negative independent of X if and only if X is a geometrically infinitely divisible random variable. This is an improvement over Van Harn and Steutel (1995) where the converse is left unproved.

4 ref

024667   Peng Y (Math Dep, Shaoyang Univesity, Shaoyang, Hunan 422000, P.R. China, Email: pengyh2004@sina.com) : Global stability for nonlinear delay differential equations. Far East J mathl Sci 2006, 20(2), 179-88.

A sufficient condition is established for the global asymptotic stability of the nonlinear delay differential equation x'(t) + a(t)x(t-τ) = b(t)f(x(t-σ)), t ≥ 0, which generalizes and improves some existing results in the literature.

9 ref

024666   Pawar Y S;Patil M V (Math Dep, Shivaji Univ, Kolhapur-416 004) : α<. Bull Calcutta Mathl Soc 2006, 98(2), 161-8.

A theory of α^a-ideals in a-distributive lattices is developed by illustrating examples. Several characterizations of α^a-ideals in a-distributive lattices are obtained. Necessary and sufficient conditions for a-distributive lattices to be a-quasi-complemented are proved.

6 ref

024665   Patil K B;Deore R P (NO, Jai-Hind Coll Dhule, Dhule-424 002) : Some results on semirings and semimodules. Bull Calcutta Mathl Soc 2006, 98(1), 49-56.

Ring of differences of any cancellative semiring R and module of differences of any cancellative semimodule M have been defined and some results on ideals in ring of differences R^e have been proved. A very important lemma in the theory of semirings, called Nakayama lemma over a cancellative and commutative semiring R analogous to rings has been estabilished. The notion of exact sequences of R-semimodules and R-homomorphisms and it is proved, if the sequence of R-semimodules and R-homomorphisms is exact, the sequence of R-semimodules and R-homomorphisms is exact, then the sequence of modules of differences and homorphisms over a ring of differences is exact and the converse, for semisubtractive and zerosumfree semimodules.

6 ref

024664   Park J S;Kwun Y C (Math Educ Dep, Chinju Natn Univ of Educ, Jinju, 660-756, Korea, Email: parkjs@cue.ac.kr) : Controllability of the nonlinear neutral fuzzy integro differential equation on E<. Far East J mathl Sci 2005, 19(1), 11-24.

Controllability for the nonlinear neutral fuzzy integro-differential equations on Eⁿ_N has been studied by using the concept of fuzzy numbers of dimension whose values are normal, convex, upper semicontinuous and compactly supporated surface in Rⁿ, where Eⁿ_N is the set of all fuzzy numbers in Rⁿ with edges having bases parallel to axes X₁, X₂..., X_n.

11 ref

024663   Pardeep Kumar;Rohan Lal (Dep of Math, ICDEOL Himachal Pradesh Univ, Summer-Hill, Shimla-171 005) : Immiscible, viscoelastic (Walters B) liquid-liquid displacement in permeable media. Math Educ 2005, 39(2), 79-86.

Slow, immiscible, viscoelastic (Walters B') liquid-liquid displacements in a permeable medium is considered. The necessary and sufficient criteria for stability are that the displacing fluid is denser, less mobile, the ratio of medium permeability to viscoelasticity of the displacing fluid is greater than the ratio of medium permeability to the viscoelasticity of the displaced fluid and product of medium porosity and (ν₂'α₂/k₂' + ν₁'α₁/k₁') less than unity. The instability criteria and critical wave length are found to be the same as those for ordinary viscous liquid-liquid displacements in permeable media.

7 ref

024662   Pandya M;Bhatt S P (Dep of Statist, Bhavnaear Univ, Bhavnagar-364 002) : Bayes estimation of change point in censored inverse Weibull distribution. Int J agric statist Sci 2005, 1(1-2), 17-26.

Deals with Bayes procedures for obtaining Bayes estimators of continuous type Change Point for censored Inverse Weibull samples, both when a poor and a more detailed prior information is introduced into the inferential procedure. Also, we have obtained the Bayes estimators of τ under the asymmetric loss function. The effect of correct and wrong prior information on the Bayes estimators is also studied.

4 tables, 14 ref

024661   Pandya M (Dep of Statist, Bhavnagar Univ, Bhavnagar-364 002) : Bayes estimation about change point model: AR(1) with mixed errors. Int J agric statist Sci 2005, 1(1-2), 41-9.

Let AR (1) model be x_i = β_i x_i-1 + ε_i where ε_i are assumed to have a mixture distribution, mixture of degenerated at zero and exponential distribution with mixing proportion p₁ but later it was found . that there was a change in the system at sorne point of time m and it is reflected in the sequence after x_m by change in proportion p₂ and P₂ The Bayes estimators of p₂, p₂ and m under linex and general entropy loss functions are derived.

3 tables, 6 ref

024660   Palaniappan Y (Dep of Math, Arignar Anna Govt Arts Coll, Musiri-621 201) : On the structure of an R-semigroup. Math Educ 2005, 39(3), 168-74.

An R-semigroup R has been defined and it is seen that it is the direct product of a rectangular band B and a semigroup with identity S. It also seen that R is a semi-inflation of its subsemigroups. It is proved that R ≅ B x S is a fine band B of sub R-semigroups. It is found that there exists a decomposition of an R-semigroup R = B x S and that each decomposed pan bRb, b ∈ Bis the intersection of two deflatable semigroups of R in which one is a left ideal of R and the other is a right ideal of R.

7 ref

024659   Narayan A;Shrivastava S (Math Dep, Bhilai Inst of Technol, Durg-491 001) : Effects of solar radiation pressure and magnetic field of the earth on stability of cable-connectecd satellites system in equatorial orbit. Bull Calcutta Mathl Soc 2005, 97(5), 417-32.

Effects of the solar radiation pressure and magnetic field due to the Earth on the stability of two satellites connected by a light flexible and inextensible cable moving in equatorial orbit, has been studied. The equations of motion of the system have been deduced with respect to the centre of mass of the system, which is assumed to move along Keplerian elliptical orbit (in particular circular). The effects of the Earth shadow have been taken into consideration in analysis. It has been established that the particular solutions of the nonlinear, non-homogeneous and non-autonomous differential equations of relative motion, remain stable, provided the parameter due to the solar radiation pressure and the Earth magnetic field lie within a certain limit.

5 illus, 2 tables, 15 ref

024658   Narang M S;Sud U C;Gupta A K (Indian, Agric Statist Res Inst, Library Avenue, New Delhi-110 012) : Estimation of seemingly unrelated regression in random coefficient model with unequal numbers of observations. Int J agric statist Sci 2005, 1(1-2), 101-5.

Estimator is developed for seemingly unrelated two-equation model in which the regression coefficients are random and the numbers of observations are unequal and the order of observations can not be disturbed as in time-series data. The results given by Sharma (1993) are the particular cases of the situation discussed.

3 ref

024657   Narang M S;Sud U C;Gupta A K (NO, Indian Agric Statist Res Inst, Library Avenue, New Delhi-110 012) : Estimation of finite population regression coefficient in repeat survey. Int J agric statist Sci 2005, 1(1-2), 1-9.

Two different estimators of finite population regression coefficient for the current occasion which make use of information on both the occasions have been developed. One is based on different type estimator for the finite population regression coefficient for the matched portion of the sample. The other is based on the maximum likelihood estimator for the corresponding portion, of the sample. Both the estimators are more precise than the ordinary estimator (which makes no use of the available previous occasion information) in most situations.

9 ref

024656   Nam K B;Kwon M (Math Dep, Univ of Wisconsin-Whitewater, Whitewater, WI 53190 USA, Email: namk@uww.edu) : Notes on W-type non-associative algebras I. J appl Algebra Discrete Structs 2005, 3(3), 131-8.

The non-associative algebra change the notation to (N_n,m,s) was defined in an earlier paper titled "Lie admissible non-association algebras." A generalized non-associative algebra (N_n,m,s) which is simple has been defined. The non-associative algebra automorphism group Aut_men (N_0,s,0) of the non-associative algebra N_0,s,0 is found in paper titled "On some non-associative algebras using additive groups". Non-associative algebra automorphism group Aut_non(N_0,0,s) of the non-associative algebra N_0,0,s has been found in this paper.

6 ref

024655   Nam H S (Dep of Math Educ, Coll of Educ, Sungkyunkwan University, Seoul-110-745, Korea, Email: heedol@skku.edu) : Remarks on the relation between the equation of a line in C and the linear transformation. Math Educ 2005, 39(2), 68-72.

The equation of a line in the complex plane has been considered. From the generalized form of the equation, the linear transformations have been introduced and it has been shown that every invertible linear transform maps a line to a line. A definition of an ellipse has been given and the formula for the major diameter has been derived. The equation of a tangent line of an ellipse has been derived.

2 ref

024654   Nam H S (Math Educ Dep, Coll of Educ, Sungkyunkwan University, Seoul-110-745, Email: heedol@skku.edu) : Lagrange's multiplier rule in the complex plane. Math Educ 2005, 39(3), 127-30.

The formula for the Lagrange's multiplier rule in the complex plane has been derived. Instead of rewriting the problem in terms of real variables, one can solve the problem directly using complex differentiation. As an application, for given ellipse, major and minor axes and diameters have been computed.

1 ref

024653   Najafzadeh S;Kulkarni S R (Math Dep, Fergusson Coll, Pune-411 004, Email: najafzadeh1234@yahoo.ie) : An integral operator and its application on multivalent functions defined by hypergeometric and exponential functions. Far East J mathl Sci 2006, 20(2), 121-33.

By using hypergeometric and exponential functions a p-valent function of the form f(z) = mz^p + ∑^2p_k=p+1 t_k-p-1z^k-p-1 - (e^z + ₂F₁ (a, b; c; z)) that satisfies the condition Re {z(Q^α_βf(z))' + ηz²(Q^α_{βf(z))"/ηz(Q^αβ< D>f(z))' + (1 - η)(Q^αβf(z))} <62>γ is defined. Then sharp coefficient inequalities, quasi-Hadamard product and distortion bounds are found.}

12 ref

024652   Nadarajah S;Ahsanullah M (Dep of Statist, Univ of Nebraska, Lincoln, U.S.A.) : On the beta record values. Calcutta Statist Ass Bull 2005, 57(225-226), 85-94.

Explicit algebraic expressions are derived for computing the means, variances and the covariances of the record values from a beta distribution. The derivation uses a representation theorem due to Bairamov and Ahsanullah (2000) and a series expansion for the inverse function of the standard beta cdf. The results generalize those presented in Nadarajah and Ahsanullah (2004) for the arc-sine distribution.

13 ref

024651   Murugusundaramoorthy G;Rosy T (Dep of Math, Vellore Inst of Technol, Deemed University, Vellore-632 014, Email: gmsmoorthy@yahoo.com) : Fractional calculus and their applications to certain subclass of α uniformly starlike functions. Far East J mathl Sci 2005, 19(1), 57-70.

A new class S(λ, α) of starlike functions is introduced. A subclass TS(λ, α) of S (λ, α)with negative coefficients is also considerd. Coefficient estimates, and closure theorems are obtained. Further partial sum ƒ_n(z) and ƒ(z) in these classes are considered and sharp lower bounds for the ratios of real part of ƒ(z) to ƒ_n(z) and ƒ'(z) to ƒ'_n(z) are determined.

11 ref

024650   Mittal S K;Gupta S;Mittal C (Dep of Math, M.M.(P.G.) Coll, Modinagar, Uttar Pradesh) : Analytic behaviour of a parallel redundant complex system under pre-emptive repeat repair policy. Int J agric statist Sci 2005, 1(1-2), 65-79.

Reliability of a parallel redundant complex system consisting of two classes suffer two types of failure, viz., hardware and enviormental while the system has three modes, i.e., normal, degraded and failed. The repair is carried out instantaneously under general time distribution. Pre-emptive repeat repair policy is adopted for the system. Laplace transform (LT) and supplementary variable techniques have been utilised to obtain the probabilities of the system being in various states. The ergodic behaviour of the system and some more reliability parameters have also been evaluated.

4 illus, 1 table, 2 ref

024649   Misra B L;Saxena R B;Rai A L (Dep of System Sci and Statist, Rani Durgawati Vishwavidyalaya, Jabalpur, Madhya Pradesh) : Piece-wise regression for equally spaced data. J agric Issues 2004, 9(1-2), 63-9.

Present study attempts to show the relationship of response variable to the predictor variable (equally spaced time series), the use of piece -wise regression is more efficient than fitting an orthogonal polynomial regression. The procedure is illustrated through real life data.

1 ref

024648   Mishra B K (NO, Math Grp Birla Inst of Technol & Sci, Pilani-333031, Email: bimal@bits-pilani.ac.in) : Newtonian model for blood flow through an arterial stenosis - an in-vitro treatment. Math Educ 2005, 39(3), 151-60.

The resistance to flow-across atherosclerosis situated on uniform or non-uniform cross-section of artery has been analyzed. Assuming the blood as Newtonian, incompressible and homogeneous fluid, a generalized expression for resistance to flow has been derived for arthrosclerosis. To confirm the validity of the result of theoretical model an in-vitro expenmental analysis has been made.

2 illus, 4 tables 8 ref

024647   Merouani A;Serrar T;Sedik Djabi (NO, Universit of Setif, Algeria, Email: badri_merouani@yahoo.fr) : A monotony method in quasistatic processes for viscoplastic materials with ε a nonlinear function. Far East J mathl Sci 2006, 20(2), 151-62.

A quasistatic problem for semi-linear rate-type viscoplastic models with internal state variables are studied. The existence and uniqueness of the solution are proved by using monotony arguments followed by a Cauchy-Lipschitz technique.

5 ref