022055   Hila K (Mathematics Dep, Facultry of Natural Sciences, University of Gjirokastra, Gjirokastra, Albania, Email: kostag_hila@yahoo.com) : Some elements and green's relation H in le-Γ-semigroups. Far East J mathl Sci 2006, 21(2), 153-61.

Characterizations in le-Γ-semigroups has been given along with several properties that hold in every H-class of an le-Γ-semigroup satisfying Green's condition.

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022054   Gundogan H;Keciliouglu O (Mathematics Faculty of Arts and Sciences Dep, Kirikkale Univ, 71450, Yahsihan, Kirikkale, Turkey, Email: hagundogan@hotmail com) : Split quaternion lie group and A C<. Far East J mathl Sci 2006, 21(3), 285-92.

Set of split quaternions expressed in matrix form is considered and it has been shown that this forms a Lie group. Moreover, by showing S³₂ forms a Lie group, it is defined a C ^∞-action of this Lie group on split quaternion manifold. Some properties of this action are obtained and orbits are analyzed. By expanding this action to R⁴₂ it has been shown that the left translations are isometries.

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022053   Ganesan G;Latha D;RaghavendraRao C (Mathematics Dep, Jayaprakash Narayan College of Engineering, Mahabubnagar, Andhra Pradesh, Email: vidyadharshini@yahoo.co.in) : Knowledge acquisition using fuzzy rough bags. Int J mathl Sci 2006, 5(2), 265-77.

Several fuzzy systems work with max and min iperators for union (disjunction) and intersection (conjunction) respectively. But, in any fuzzy system based on learning process, max and min operators cannot be effective, as they don't alow acquisition. Describes a tool for fuzzy rough approximation using Lukasiewicz T and S norms.

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022052   Fitouhi A;Ben Hammouda M S;Binous W (De Mathematiques Dep, Faculte Des Sciences De Tunis, Campus Universitaire Del Menzah, Tunis, 1060, Tunisie, Email: ahmed fitouhi@fst rnu tn) : On a third singular differential operator and transmutation. Far East J mathl Sci 2006, 21(3), 303-29.

Authors are concerned with the operator, called generalized Airy operator, studied recently in great detail by Cholewinsky and Reneke. Completed the analysis presented by the previous authors and give special attention for some integral equations associated with this operator in establishing the correspondent transmutation theory in a suitable space. As application author introduced the generalized translation and the convolution product related to this operator.

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022051   Dubey R P;Singh N K (Engineering Mathematics Dep, Bhilai Institute of Technology, Bhilai House Durg-491 001) : Fixed point theorem for non-expansive type mappings in-quasi-uniform space. Math Educ 2006, 40(1), 36-9.

Fixed point theorem for non-expansive type mappings involving a very general contractive definition in quasi uniform space has been obtained.

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022050   Dorsett C (Mathematics Dep, Texas A & M Univ, Commerce, Texas-754 29 U.S.A.) : New characterizations of separation axioms. Bull Calcutta Mathl Soc 2007, 99(1), 37-44.

T_i spaces, i = 0,1,2; R_i spaces, i = 0,1; Urysohn spaces; weakly Urysohn spaces; regular, and normal spaces are further characterized investigated using mathematical induction, To-identification spaces, and related topologies.

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022049   Dolai P;Mandal B N (Mathematics Dep, Prasannaded Women's College, Jalpaigur-735 101) : Scattering of internal waves in a stratified fluid by the edge of an inertial surface. Bull Calcutta Mathl Soc 2007, 99(1), 5-20.

The problem of internal wave scattering by the edge of a semi-infinite inertial surface partly covering an exponentially stratified incompressible liquid of infinite depth is investigated in this paper. Assuming linear theory the problem is formulated in terms of a function related to the stream function describing the motion in the liquid. The related boundary value problem involves the Klein-Gordon equation which is a PDE of hyperbolic type. The BVP is solved with the aid of Wiener Hopf technique applied to a slightly more general problem and passing on to the limit in a manner so as to obtain the solution of the original problem. The scattered field is obtained in terms of integrals which are evaluated asymptotically in different regions for large distance from the edge. The asymptotic form of the wave field is plotted graphically for various cases to visualize the nature of the scattered wave field.

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022048   Dharmendra Kumar;Nabin Kumar (Physics Dep, K B Women's College, Madhepura-852 113) : On embedding property of Einstein spaces. Math Educ 2006, 40(1), 56-9.

Authors main aim here is to discuss some salient features of Einstein equations (1) in the context of its embedding to a pseudo-Euclidean space. It will be related to cosmological models of desitter, Einstein and Minkowski spaces.

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022047   Cheon E J (Mathematical Sciences Dep, Yamaguchi Univ, Yamaguchi-753 8512, Japan, Email: enju1000@naver com) : On generalized hamming weights of some linear codes. Far East J mathl Sci 2006, 21(3), 363-71.

Authors find the generalized Hamming weights of a linear code corresponding to the 0-cycle whose support is the union of two linear subspaces or its complement in P^k-1. It was also show that each of those codes satisfies the chain condition by constructing a sequence of subspaces in the projective space which determines the weight hierarchy of the code.

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022046   Chandra S;Sharma M (Mathematics Dep, S M Post-Graduate College, Chandausi-202 412) : On generalized norlund summability factors of orthogonal series. Math Educ 2006, 40(1), 47-55.

Two theorems on generalized Norlund summability factors of orthogonal series were proved which generalizes various known results.

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022045   Chahal J S (NO, Brigham Young University, USA, Email: jasbir@math.byu.edu) : Foundations of basic geometry. Resonance 2006, 11(7), 30-41.

The basic notions of length, area and volume were not alien to the prehistoric civilizations. The pyramids, palaces and great baths built more than 4000 years ago provide ample evidence. Begins investigation of geometry with a discussion of areas of simple geometric objects.

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022044   Chahal F S (NO, , ) : Solution of te cubic - a simple version of cardano's formula. Resonance 2007, 11(8), 53-61.

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022043   Caragiu M (Mathematics Dep, Ohio Northern University, Ada, OH 45810, U.S.A., Email: m-caragiul@onu.edu) : Codekets. Far East J mathl Sci 2006, 21(2), 133-41.

To every binary [n, k] code C we associate a quantum state <124>Ψ_C<209> ε N^⊗n, where H is the two-dimensional complex Hilbert space associated to the spin 1/2 particle. Author completely characterize the expectation values of the products of x-, y- or z-spins measured in the state <124>Ψ_C<209>, for each of the particles in a chosen subset. This establishes an interesting relationship with the dual code C^⊥. Also addressed the case of nonlinear codes, and derive both a bound satisfied by the expectations of spin products as well as a nice algebraic identity.

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022042   Bujurke N M;Shiralashetti S C;Salimath C S (Math Dep, Karnataka Univ, Dharwad-580 003) : Application of Single Term Haar Wavelet Series solution to non-linear stiff differential equation arising in physics. J appl mathl Analysis Applic 2006, 2(1), 51-69.

Presents Single Term Haar Wavelet Series (STHWS) approach to the solution of nonlinear stiff differential equations arising in Physics. The properties of single term Haar wavelet series are given. The method of implementation is discussed. Numerical solutions of some model equations are investigated for their stiffness and stability and numerical solutions are obtained to demonstrate the suitability and applicability of the method. The results in the form of block-pulse and discrete solutions are given, for nonlinear stiff systems. As compared with the TR BDF2 method of Shampine [12] and Gill's metheod. The STHWS turns out to be more effective in its ability to solve systems ranging from mildly to highly stiff equations. The method works even when higher order numerical methods for stiff systems fail to give solutions. The novel feature of the scheme is development of an algorithm exclusively for solving systems of non-linear algebraic equations resulting from STHWS. It reduces the computational effort enormously, at the same time, meeting accuracy requirements. We can see that the STHWS method takes substantially fewer steps and is about three times faster than Gill's method.

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022041   Biase D;Manca R (Department of Mathematics, Rhodes University, Grahamstown 6140, Sourth Africa, Email: v.murali@ru.ac.za) : Ordered partitions and finite fuzzy sets. Far East J mathl Sci 2006, 21(2), 121-32.

There is a one-to-one correspondence between ordered partitions and kernels of fuzzy subsets under a natural equivalence relation on them, on any n-set X_n. Author discuss some aspects of this correspondence with respect to counting and their implications to generating functions f(x)=e^tx/(2-e^x) for some integral values of t.

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022040   Bandyopadhyay C;Modak S (Mathematics Dep, Burdwan Univ, Burdwan-713 104) : New topology via-operator. Proc Natn Acad Sci India-Sect A 2006, 76(Pt 4), 317-20.

A new topology with the help of Ψ- operator has been introduced and compared with other topologies.

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022039   Bali R;Singh K N;Jain S (Mathematics Dep, Rajasthan Univ, Jaipur-302 004) : Bianchi type I non-static magnetized barotropic perfect fluid cosmological model in general relativity. Proc Natn Acad Sci India-Sect A 2006, 76(Pt 4), 339-44.

Bianchi type I non-static barotropic perfect fluid cosmological model in presence of magnetic field, is investigated. The magnetic field is due to an electric current produced along ;x-axis. To get a determinate model, Authors used a supplementary condition B₄₄/B+C₄₄/C=0 where B and C are metric potentials. The behaviour of the model in presence of magnetic field is investigated. The physical and geometrical aspects of the model are also discussed.

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022038   Balajti Z;Dudas I (Descriptive Geometry Dep, University of Miskolc, ) : Mathematical model for analying of helicoid surfaces having the same axis. Int J mathl Sci 2006, 5(2), 279-91.

Developed a summarized general kinematic model for examination of mating of cylindrical helicoid surfaces and their tools, furthermore conical helicoid surfaces and their tools on the base of Dudas type general mathematical mode, which is suitable to deal with examination at the same time, when there axis are the same. The aim of the paper to show a new model which is suitable for neglecting the errors of the other. All of these can be done in one mathematical model. This model supporses the existence of a new CNC machine tool, which is suitable for production of proper production in case of changing axis distance as well.

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022037   Arunkumar A;Chockalingam S;Kannan K;Shenbaga Vinayaga Moorthi N;Rudramoorthy R (Production Engineering Dep, PSG College of Technology, Coimbatore, Email: kkannan@mail.psgtech.ac.in) : Simulation of flow distribution in a shell and tube heat exchanger a CFD based approach. Int J mathl Sci 2006, 5(2), 249-64.

Non-uniform flow distribution from header to the branch pipes in a flow system will lead to 25% decrease in effectiveness of a cross flow heat exchanger [4]. Both analytical and experimental approach reported so far is applicable to a limited number of engineering applications. This simulation study is an attempt to illustrate how Computational Fluid Dynamics (CFD) software can be an effective tool for filling up the requirement. The predicted results are compared with the available experimental data to validate the CFD procedure. The effect of various parameters on flow distribution in a flow system is also investigated. The present approach can be adopted for any flow system including Shell and tube heat exchangers.

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022036   Aramaki J (NO, Tokyo Denki University, Hatoyama-machi, Saitama 350-0394, Japan, Email: aramaki@r.dendai.ac.jp) : Upper critical field and location of surgface nucleation for the Ginzburg-Langau system in non-constant applied field. Far East J mathl Sci 2006, 23(1), 89-125.

Considered the Ginzburg-Landau system in the theory of ssuperconductivity. In the case where an applied magnetic field is non-constant also obtained the asymptotics of the upper critical field with lower order term and examine the location of surface nucleation. The asymptotics of the upper critical field is closely related to that of the lowest eigenvalue of the corresponding Schrodinge operator. Asymptotics also obtained.

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022035   Alexiou D;Alwadi Y (NO, West Macedonia Univ, Greece) : Blowing-up along exceptional curve. Far East J mathl Sci 2006, 21(3), 251-7.

Let X be a 3-dimensional complex manifold, and C ⊆ X be an exceptional curve. Consider the blowing-up of X along C, namely, μ₁: X₁→X and exceptional divisor E₁ = μ₁^-1(C). It was proved that C₁ ⊆ X₁ is also an exceptional curve.

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022034   Aldihan N (Mathematics Dep, Girls College of Education, P O Box 61410 Riyadh, Saudi Arabia, Email: n_aldihan@hotmail com) : Partial sum of certain meromorphic functions. Far East J mathl Sci 2006, 21(3), 341-54.

Using Al-Oboudi differential operator, Authors study a class of meromorphic functions of negative and positive coefficients. A necessary and sufficient condition for functions to belong to these classes are obtained. Further, coefficients, extremal functions and partial sums an studied.

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022033   Akhilesh Kumar;Singh D N (Mathematics Dep, Dwarka Nath College, Masaurhi-804 452) : Unification of certain generalized polynomials of N-variables. Math Educ 2006, 40(1), 60-7.

Object of the present paper is to derive a generalized polynomial system T_n {(x_m), y} with the help of a generating relation involving the Lauricella function in the notation of Burchnall and Chaundy .

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022032   Ahmad M S (NO, , PO, Cheawra-811 304 Mohalla-Chotipokher Dist - Sheikhpura) : Probability measure and its impact on Von-Neumann algebra. Math Educ 2006, 40(1), 71-5.

For semi finite or finite Von-Neumann algebras, laws of large numbers have been investigated in non-commutative probability theory. Main aim here is to discuss the notion of convergence in measure for Kolmogorv's law of large numbers. The role of random variable in probability theory is similar to an element of Von-Neumann algebra where as the probability measure is counter part of a faithful state in Von-Neumann algebra. Established here some reformulated structure of a faithful state in Von-Neumann algebra. also established some reformulated structure of strong law of large numbers in non commutative context.

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022031   Aggarwala B D (Mathematics and Statistics Dep, University of Calgary, Calgary, Alberta, T2N 1N4, Canada, Email: aggarwal@math.ucalgary.ca) : On estimating HIV prevalence in India. Far East J mathl Sci 2006, 21(2), 197-210.

Mathematical model has been presented based on the Expectation Maximization (EM) algorithm, to estimate HIV prevalence in a society and apply this model to the case of India. Taking the worst case scenario, and assuming that there were 200,000 AIDS patients in India at the end of 2004, and that the ARV's have had no impact at all. Demonstrated that the HIV prevalence in India, at the end of 2004 was, most probably, below 2.5 million.

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022030   Acikgoz A;Yuksel S (Mathematics Dept, Faculty of Arts and Sciences, Selcuk University, 42031 Campus, Konya, Turkey, Email: syuksel@selcuk.edu.tr) : On δ-I-regular sets and two decompositions of R-I-continuity. Far East J mathl Sci 2006, 23(1), 53-64.

Notion of δ-I-regular sets is introduced and some of its properties are investigated. It is shown that it is weaker than the notion of R-I-open sets. Two decompositions of R-I-open sets are obtained.

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022029   Achari J;Pande N A (Mathematics, Statistics and Computer Science Dep, N E S Science College, Nanded-431 605, Email: jachari@vayumail com) : Fixed point theorems for a family of selfmaps on groups. Math Educ 2006, 40(1), 1-6.

Family of selfmaps {f_i: G → G i ∈ I) on a group (G, *), given by f_i (g) = g', for each g∈ G, is under consideration. Authors obtain fixed point theorems for these maps. It is interesting to see that many standard results from the Group Theory can be reformulated in terms of fixed points of these maps, as has been exemplified by few ones in concluding part of the paper.

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022028   Abe Y (University of Toyama, , Toyama 930-85555, Japan, Email: abe@sci.u-toyama.ac.jp) : Quasi-abelian functions and varieties in the sense of severi, I. limits of abelian varieties. Far East J mathl Sci 2006, 23(1), 17-28.

Author call meromorphic functions which admit an algebraic addition theorem quasi-abelian functions in the sense of Severi, and the corresponding group variety a quasi-abelian variety in the sense of Severi. Moduli space of quasi-abelian varieties was constructed in the sense of Severi.

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021132   Yadav R K;Purohit S D (Mathematics and Statistics Dep, J.N. Vyas Univesity, Jodhpur-342 005, Email: rkmdyadav@yahoo.co.in) : On q-Laplace transforms in certain q-hypergeometric polynomials. Proc Natn Acad Sci India-Sect A 2006, 76(Pt 3), 235-42.

Master fonnula for the q-Laplace transfonns of the pralized basic hypergeometric functions has been derived. The q-Laplace transfonns of several well-known q-polynomials (including the bibasic polynomials) have also been derived. Interestingly the q-images of certain q-hypergeometric polynomials have been established either in terms of a known q-polynomial or in terms of the basic Kampe de Feriet function. Some special cases have been deduced as the applications of the main results.

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021131   Vyawahare A W (Mathematics Dep, M.M. College of Science, Nagpur-440 009, Email: vanant_ngp@sancharnet.in) : A new function on divisibility. Math Educ 2006, 40(2), 122-8.

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021130   Vivek Kumar;Pal R;Pundir S K (NO, S.D. (P.G.) College, Muzaffarnagar-251 001) : Thermal instability of couple-stress fluid in the presence of variable gravity field and rotation. Reflection Des Ra 2006, 1(2), 175-88.

Problem of thermal instability of a couple-stress fluid is considered in the presence of variable gravity field and rotation. It is found that in the absence rotation, PES is valid. In the absence of rotation, couple-stress fluid has a stabilizing effect on the system when the density increases upward. The effect of concentration on the system is also considered as a particular case.

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021129   Vinod Kumar;Singh T P;Rajender Kumar (Mathematics Dep, S.B.M.N. Engng College, Asthal Bohar, Rohtak, Haryana) : Steady-state behaviour of queue model comprised of two sub-systems with biserial channels linked with a common channel. Reflection Des Ra 2006, 1(2), 135-52.

Studies the Steady-State behaviour of a typical network queues in which a common service channel is linked in series with each of two systems containing two sub-biserial service channels. The arrivals and service pattern in the system both follow Poisson-stream. The various queue characterstics like Mean Queue Size, Variance of the queue length, Average Waiting Time have been obtained explicitly by applying Generating function techniqe (g.f.t) and Laws flcalculus. The model is very useful in decision making process in the industries, in administrative setup, in the Banking service system, Production concerns, networking and many business service system etc.

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021128   Vasumathi A;Dhanavanthan P;Srividya R (Mathematics Dep, Pondicherry Univ, Puducherry, Email: vaa72@yahoo.co.in) : Application of optimization techniques in lamination industry- a case study. Int Rev pure appl Math 2006, 2(2), 177-202.

Authors collected information from the lamination company, which manufactures lamination products with different sizes and specifications. The authors applied linear programming technique in five different cases which is suitable for lamination industry. The researchers discussed in this article, to get maximum profit by manufacturing how many units in each products. Also they suggested that the company has to laminate only Maxi size to get maximum profit.

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021127   Tokdar S T (Department of Statistics, Purdue Univ, 150 N Univ St W Lafayette, In 47906, USA, Email: stoker@stat.purdue.edu) : Posterior consistency of dirichlet location-scale mixture of normals in dednsity estimation and regression. Sankhya 2006, 68(Pt 1), 90-110.

Sufficient conditions were provided under which a Dirichlet location-scale mixture of normal prior achieves weak and strong posterior consistency at a true density. Conditions involve both the prior and the true density from which observations are obtained. They consider it to be a significant improvement over the existing results since conditions cover the case of fat tailed densities like the Cauchy, with a standard choice for the base measure of the Dirichlet process. This provides a wider choice for using these popular mixture priors for nonparametric density estimation and semi parametric regression problems.

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021126   Tehri R;Saha L M (Mathematics Dep, Zakir Hussain College, University of Delhi, Delhi-110 002) : Controlling chaotic oscillations in a buckled elastic beam by periodic parametric perturbation. Math Educ 2006, 40(2), 81-7.

Vibrational Chaotic and irregular motion have been investigated in the Buckled elastic beam. Synchronization and controlling of such chaotic motion by varying the cubic parameter periodically as well as adding a phase shift periodic motion have been adopted. Numerical calculations and graphics results justify such investigation.

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021125   Tehranchi A;Kulkarni S R;Mostahsan T (Mathematics Dep, Islamic Azad Univ, South Tehran branch, Tehran, Iran, Email: tehranchiab@yahoo.co.uk) : Differential subordination defined by multiplier transformation and differential operator. J Analysis Computn 2006, 2(2), 201-12.

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021124   Szeto G;Xue L (Mathematics Dep, Bradley Univ, Peoria, Illinois 61625, U. S. A., Email: szeto@bradley.edu) : Galois and automorphism groups of a semiconnected galois extension. Far East J mathl Sci 2006, 22(3), 417-28.

Let B be a Galois extension with Galois group G possessing finitely many central idempotents. Then the Galois groups which are isomorphic with G are computed, and a relation between Aut_BG(B) and G is also obtained.

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021123   Swaminathan A (Mathematics Dep, Indian Institute of Technology Roorkee, Roorkee-247 667, Email: mathswami@yahoo.com) : Hypergeometric transforms of certain class of analytic functions. Int Rev pure appl Math 2006, 2(2), 91-8.

Author aims at finding certain conditions on a, b and c such that hypergeometric transform zF(a, b;c; z) * f(z) satisfies certain inclusion properties to be in certain subclasses of analytic functions. Here F(a,b;c;z) is the well known Gaussian hypergeometric function and f (z) is in certain class of analytic functions with * denoting the Hadamard product type convolution.

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021122   Suyalatu;Shuyan Qi (College of Mathematics Science, Inner Mongolia Normal Univ, Huhhot 010022, P. R. China, Email: suyila@imnu.edu.cn) : On some generalization of ϕ-uniform convexity and dual concepts. Far East J mathl Sci 2006, 22(3), 345-67.

Notions like k-uniform convexity and k-uniform smoothness are introduced in locally convex spaces. It is shown that k-uniformly convex locally convex spaces (respectively, k-uniformly smooth locally convex spaces) are generalizations of both k-uniformly convex Banach spaces and uniformly convex locally convex spaces (respectively, k-uniformly smooth Banach spaces and uniformly convex locally smooth spaces). It is proved that k-uniformly convex locally convex spaces include (k + 1) -uniformly convex locally convex spaces (respectively, k-uniformly smooth locally convex spaces include (k + 1) -uniformly smooth locally convex spaces). However, the converse inclusions are not necessarily true. Also, some necessary and sufficient conditions of k-uniformly convex locally convex spaces (respectively, k-uniformly smooth locally convex spaces) are obtained.

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021121   Sunil kumar (NO, , C/o Dr. Janeshwar Singh, No.-6, Tata College Colony, Chaibasa-833 202) : A generalization of multi-functions of KY fan's best approximation theorem. Math Educ 2006, 40(2), 115-17.

Author prove a theorem of Ky Fan type best approximation for set valued mappings in an approximately convex subset of a locally convex space.

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021120   Sun S (159 MM BLDG, Department of Mathematics and Statistics, Wright State University, Dayton, OH 45435, USA, Email: shuxia.sun@wright.edu) : Bootstrapping the sample quantile of a weakly dependent sequence. Sankhya 2006, 68(Pt 1), 130-66.

Authors investigated consistency properties of block bootstrap apªproximations for sample quantiles of weakly dependent data. Under mild weak dependence conditions and mild smoothness conditions on the onedimensional marginal distribution function, it was shown that the moving block bootstrap method provides a valid approximation to the distribution of normalized sample quantile in the almost sure sense. Strong consistency of the block bootstrap estimator of the asymptotic variance of the sample quantile is also established under similar conditions. For the proof, Authors develop some exponential inequalities for block bootstrap moments and also develop some almost sure bounds on the oscillations of the empirical distribution function of strongly mixing random variables, which may be of some independent interest.

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021119   Srinivas V;Umameshwar Rao R (Mathematics Dep, Sreenidhi Institute of Science & Technology, Ghatkesar-501 301) : A common fixed point theorem for four selfmaps. Math Educ 2006, 40(2), 99-104.

Author Generalize a fixed point theorem of B. Fisher [1]. Brian Fisher [1] has proved the following fixed point theorem.

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021118   Srinivas K V R (Mathematics Dep, G.V.P. College of Engineering, Visakhapatnam-41, Email: srinivas_kandarpa06) : Certain properties, examples of peo-semi groups and le-semi groups. Int Rev pure appl Math 2006, 2(2), 85-90.

Poe-semi group is an ordered semi group having greatest element 'e'. In this paper it is obtained that "If 'f' is an idempotent element in a poe-semi group 'S' then ef and fe are idempotents and also ef ≥ f, fe>f''. A necessary and sufficient condition for an element in poe-semi group to be intra regular is also obtained. It is observed in le-semi group that" If e ≥ ef and e ≥ fe for all idempotents e, f in 'S'", then the restriction of the partial order to E(S) is the usual order on E(S). Finally it is observed that in an le-semi group if (a]_L = (f]_L for some idempotent T then ea is an idempotent and (a]_L = (ea]_L.

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021117   Singh T P;Vij I;Mittal S K;Gupta D (NO, D.A.V. College, Sadhaura, Yamuna Nagar, Haryana) : Minimizing rental cost under specified rental policy in two stage flow shop, the processing time associated with probabilities including job-block criteria. Reflection Des Ra 2006, 1(2), 107-20.

Deals with two machine general flow shop problem in which the processing time of the jobs is associated with probabilities, follow some restrictive renting policy including equivalent job-block criteria. The object of the study is to find an algorithm to minimize the rental cost of the machines under specified renting policy. The numerical example is given to demonstrate the algorithm.

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021116   Singh S P (Mathematics Dep, T.D.P.G. College, Jaunpur-222 022) : Note on mock θ-functions of order three and continued fractions. Proc Natn Acad Sci India-Sect A 2006, 76(Pt 3), 205-7.

Making use of Fine's definitions of the mock θ-functions of order three, observes continued fraction representations for the same.

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021115   Singh S;Jha G S (Mathematics Dep (Retd.), D.S. College, Katihar) : Lagrange's equation NX<. Math Educ 2006, 40(2), 144-6.

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021114   Shrivastava P;Patel N;Parihar C L (NO, , ) : Relation among lucas, fibonacci, pell and pell-lucas numbers in subscripts form. Int Rev pure appl Math 2006, 2(2), 233-41.

Authors have derived some identities of Fibonacci and Lucas numbers with the subscript as Pell and Pell Lucas numbers and some identities of Pell and Pell-Lucas numbers with their subscript as Fibonacci and Lucas numbers, ie. numbers having form like F_Pn, F_Qn, L_Pn, L_Qn, P_Fn, P_Pn, Q_Qn, Q_Ln, using their form.

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021113   Shobha B (Mathematics and Statistics Dep, Univ of Hyderabad, Hyderabad) : Precision diagnostics in regression modelling. Calcutta Statist Ass Bull 2006, 58(229-30), 105-14.

Authors consider a linear regression model with intraclass correlation structure and study the behaviour of the precision diagnostic statistic COVRATIO as a function of the intraclass correlation coefficient ρ. Interestingly, it turns out that for the model with intercept, COVRATIO is a monotonically decreasing function of ρ. Thus if the model errors have larger correlation, then it is more stable with regard to deletion of observations. Also considered the ratio of traces TRATIO of the least squares estimator of the parameter vector under data reduction and without data reduction. This ratio is also decreasing in p implying that loss of precision when model errors have the same high correlation is smaller when an observation is deleted. Lastly, author determined the linear parametric function (LPF) whose BLUE is affected the most by data reduction.

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021112   Sharma S (Mathematics Dep, Bhilai Institute of Technology, Durg-491 001) : Non-linear oscillation of inter-connected satellites system under the combined influence of the solar radiation pressure and dissipative force of general nature at ω = 1. Math Educ 2006, 40(2), 105-14.

Study of non-linear effects due to the combined influence of the solar radiation pressure and some perturbing forces of general nature on the motion and stability of two satellites connected by a light, flexible and inextensible string in the central gravitational field of the Earth in an elliptical orbit of the centre of mass of the system in the neighbourhood of the main resonance ω = 1. The effect of the Earth shadow has been taken into consideration on the system.

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021111   Sharma K P (Mathematics Dep, Jawaharlal Nehru Rajkiya Mahavidyalaya, Port Blair-744 104) : On chain conditions and its impact on associative rings. Math Educ 2006, 40(2), 137-40.

Main purpose in this paper is to investigate stability condition for positive integers on associative rings- (1) Authors main aim here is to modify the results derived on Kurosh's Construction of the lower radical in the class of associative rings and its termination for positive integers (2).

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