021110   Shanmugam T N;Singaravelu A;Sivasubramanian S (Mathematics Dep, Anna Univ, Chennai-600 025, Email: shan@annauniv.edu ) : Linear operators associated with parabolic starlike functions. Int Rev pure appl Math 2006, 2(2), 225-32.

Objective of the present paper is to determine conditions on the parameters α₁,α₂, ... α_p, β₁,β₂, ... β_q so that I(f) will be in the class of parabolic starlike function S_p = {f ∈ A: Re[zf'/f] <62> |(zf'/f)-1|, z ∈ U}.

7 ref

021109   Shanmugam T N;Singaravelu A;Jeyaraman M P (Mathematics Dep, College of Engineering, Anna Univ, Chennai-600 025, Email: shan@annauniv.edu) : Differential sandwich theorems for certain analytic functions involvingg carlson-shaffer operator. Int Rev pure appl Math 2006, 2(2), 131-42.

Some applications of first order differential subordination and superordination to obtain sufficient conditions for a normalized function f to satisfy q₁(z) <62> (z/L(a,c)f(z))^μ <62> q₂(z) where, q₁ and q₂ are univalent in Δ: = {z:|z| <62> 1} have been given. Here, the symbol <60> stands for subordination.

9 ref

021108   Shanmugam T N;Jeyaraman M P;Singaravelu A (Mathematics Dep. College of Engineering, Anna Univ, Chennai-600 025, Email: shan@annauniv.edu) : Differential subordination and superordination for <128>-like functions. Int Rev pure appl Math 2006, 2(2), 143-150.

Authors give some applications of first order differential suboridnation and superordination to obtain sufficient conditions for the functions f to satisfy q₁(z) <60> zf'(z)/Φ(f(z)) <60> q₂(z). Here, the symbol '<60>' stands for subordiantion.

11 ref

021107   Shaheen A (Mathematics Dep, California State Univeristy, Los Angeles, 5151 State University Drive, Los Angeles, California 90032, Email: ashahee@calstatela.edu) : Trace formula for finite upper half planes. J Ramanujan Mathl Soc 2006, 21(4), 343-63.

Author proved a trace formula for finite upper half planes H_q. A brief outline is as follwos: Fix a subgroup Γ ⊂ GL (2, F_q). The adjacency operators Aα act on functions in L² (ΓH_q); thus it may consider A^{Γ _α} = Aα <157> L² (ΓHq). Also proved a trace formula which is an equallity between a weighted sum of the traces of the operators A^Γ_α and a sum over the conjugacy classes of Γ. The trace formula allows to compute the trace of A^Γ_α. Computed the trace formula for >q).

021106   Sawano Y;Tanaka H (Graduate School of Mathematical Sciences, Tokyo Univ, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan, Email: yosihiro@ms.u-tokyo.ac.jp) : Equivalent norms for the morrey space with non-doubling measures. Far East J mathl Sci 2006, 22(3), 387-404.

Under some growth condition Authors investigate the connection between RBMO and the Morrey spaces. Authors do not assume the doubling condition which has been a key property of harmonic analysis. Authors also obtain another type of equivalent norms.

11 ref

021105   Sanjeev Kumar;Sanjeet Kumar (Mathematics Dep, Institute of Basic Science, Dr. B.R.A. Univ, Khandari, Agra-282 002, Email: sanjeevibs@yahoo.co.in) : Numerical study of the axisymmetric blood flow in a constricted rigid tube. Int Rev pure appl Math 2006, 2(2), 99-109.

Model is to investigate the flow behavior of blood through a constricted rigicrrtrbe with an axi-symmetric stenosis. This work shows the combined role played by the geometry and the material non-linearity on the flow field. Thus, the present research is able to predict the main characteristics of the physiological flows and create some interest in biomedical applications. The governing equations are solved numerically using finite difference method, for viscosity fields, including separation and reattachment points, the distribution of pressure and wall shear stress and discussed in detail. The results of this model shows that the non-Newtonian character of blood is helpful in reducing the abnormal effect of the stenosis. The velocity profiles for various cases have been presented and compared with available Newtonian and non-Newtonian data in the literature.

5 illus, 14 ref

021104   Sanjari Farsipour N;Rasouli A (Statistics Dep, Shiraz University, Iran) : On the bayes estimation of the general half-normal distribution. Calcutta Statist Ass Bull 2006, 58(229-30), 37-51.

In this article-Authors consider Bayes estimation of the general half ªnormal distribution. The general half-normal distribution is defined in Pewsey (2002). The parameters estimation on the basis of symmetric Squared-error and asymmetric LINEX loss function under conjugate priors have been obtained. The admissibility of estimators with respect to risk efficiency of them are studied.

8 tables, 6 ref

021103   Saluja A S;Yuel A K;Rajput A (Mathematics Dep, J.H. Govt. P.G. College, Betul-460 001) : A common fixed point theorem for a family of R-weak commuting mappings in 2-menger spaces. Math Educ 2006, 40(2), 129-36.

Author obtain a common fixed point theorem for a family of R-weak commuting mappings on 2-Menger space.

6 ref

021102   Saji Kumar V R;Pillai R N (NO, Kerala Univ Library, Univ of Kerala, Kerala) : Single server queue with batch arrivals and α - poisson distribution. Calcutta Statist Ass Bull 2006, 58(229-30), 93-103.

Authors consider a single server non-Markovian queueing system with α-Poisson arrivals and server vacations. When α = 1, it reduces to the usual M^X <157> G <157> 1 model with batch arrivals.

21 ref

021101   Saini R K;Manish Kumar;Chauhan S (Mathematics Dep, D.A.V. College, Muzaffar Nagar, U.P.) : Fixed point theorems on fuzzy 2-metric space. Reflection Des Ra 2006, 1(2), 121-34.

Purpose of this paper is to introduce the concept of fuzzy 2- metric space following the definition of fuzzy metric space given by George and Veeramani in the development of fuzzy mathematics and to prove some fixed point theorems in this space.

7 ref

021100   Sahu M K (NO, Government Post Graduate College, Gadarwara-487 551) : Some fixed point theorems on compact space. Int Rev pure appl Math 2006, 2(2), 151-4.

Some fixed point theorems has been established for a self mapping satisfying a new contractive type condition in a compact space.

6 ref

021099   Saha M (Mathematics Dep, Raniganj Girl's College, Raniganj-713 347, Email: mantusaha@yahoo.com) : On some random fixed points of mappings over a Banach space with a probability measure. Proc Natn Acad Sci India-Sect A 2006, 76(Pt 3), 219-24.

Some random fixed point theorems have been proved in a separable Banach space equipped with a complete probability measure. The class of operators dealt with here includes some known deterministic operators as available in current literature of fixed point theory.

6 ref

021098   Ramachandra Prasad V;Bhaskar Reddy N; Muthucumaraswamy R (Mathematics Dep, Sri Venkateswara Univ, Tirupati-517 502) : Finite difference analysis of radiation effects on MHD free convection flow with mass transfer past a semi-infinite vertical plate in the presence of heat source/sink. Int Rev pure appl Math 2006, 2(2), 111-30.

Effects of radiation on hydromagnetic unsteady free convection boundary layer flow of an incompressible Newtonian, electrically conducting fluid past a semi-infinite vertical plate on taking into account the effects of mass transfer and heat generation/absorption has been analyzed. By means of an implicit finite difference method the boundary layer equations are transformed into linear algebraic system and then solved numerically by an implicit finite difference method. Representative velocity, temperature, and species concentration are shown graphically. Also the local and average skin-friction, Nusselt number and Sherwood numbers are presented graphically. The effects of radiation parameter, magnetic parameter, heat generation/absorption parameter, buoyancy ratio and Schmidt number on the numerical solutions are presented and discussed.

15 illus, 30 ref

021097   Pinheiro A;Sen P K;Pinheiro H P (Statistics Dep, UNICAMP, Brazil) : Parametric modelling of genomic sequences distance. Calcutta Statist Ass Bull 2006, 58(229-30), 1-14.

Genomic data models relate to a large number of positions exhibiting categorical responses, and larger part of that provides no statistical information. For this reason, a reduction in complexity attained by focusing on the functional part of sequences (genes) is helpful for an appraisal of the statistical inter site dependence. The problem of homogeneity among groups of genomic sequences incorporating the available (heuristic) evidence of diversity in categorical data models is considered here. The proposed fully operational parametric statistical model is fortified with flexibility to withstand use in several organisms and adaptability to inter site dependence. Properties of the proposed inference proceªdures are studied and an illustrative real data example is thoroughly explored.

2 tables, 20 ref

021096   Paranjpe S A;Gore A P (Statistics Dep, Univ of Pune, Pune) : Inference on ratio of two medians. Calcutta Statist Ass Bull 2006, 58(229-30), 134-41.

Problem of interest is confidence interval for ratio of two locaªtion parameters. The classical Fieller's theorem yields such a confidence interval for ratio of normal means. Resulting CI may sometimes be inadmissible. Also a median may be more appropriate location parameter if the parent distribution is skew. Sampling distribution of ratio of two medians as an alter-native to Fieller's theorem has been explored. Probability density function has been obtained for this statistic in case of Weibull parent populations. Use of this result to obtain confidence intervals becomes intractable for moderate sample sizes. A simulation based approach is therefore proposed. Results are applied to a study of two skin care products, based on dermatological assessment. Lastly also explored the possibility of using the 'proportional hazards' approach for this purpose.

2 ref

021095   Pande M K;Surinder Kumar (Statistics Dep, Kumaun University, Nainital-263 002) : Estimation of population mean using supplementary information. Proc Natn Acad Sci India-Sect A 2006, 76(Pt 3), 243-6.

For estimating the population mean of a variable of interest class of ratio-product type estimators are investigated by performing efficiency comparisons. Situations are identified under which proposed estimators are better than sample mean and the customary ratio and product estimators. Comparisons are computer-aided empirical studies with Monte-Carlo simulation from hypothetical bivariate normal population. Some artificial populations are also considered which are suitable for positive and negative correlation situations.

5 tables, 1 ref

021094   Panchal M K;Singh M P;Chandramouli A B (NO, C.C.S. University, Meerut, U.P.) : Axially symmetric fluid flow through porous medium. Reflection Des Ra 2006, 1(2), 153-8.

Equation of motion of Stream function, Velocity potential, Complex potential, Velocity and Pressure have been investigated. This also represents an analytical study of the steady incompressible flow-past an impervious sphere embedded in a porous medium of constant porosity.

10 ref

021093   Ould Haye M;Saleh A K M E (Carleton Univ, , Canada) : Quasi-empirical bayes methods of estimation in arma (p,q) models with vague prior informat on MA (q)<. Calcutta Statist Ass Bull 2006, 58(229-30), 53-75.

Paper investigates the asymptotic properties of various esªtimators of autocorrelations in an ARMA(p, q) model when vague non-sampling information on the moving average part is available. In particular, authors discuss the usual MLE (called unrestricted estimator), restricted MLE (based on vague information), preliminary test estimator, shrinkage estimator and the positive rule estimator of the autocorrelations. It is shown that near the prior information on the MA-parameters, the restricted, preliminary test and shrinkage estimators of the autoregressive parameters perform better than the unrestricted estimator, while their superiority changes as MA-parameters divert from the prior informations. The analysis is based on the asymptotic properties of the estimators under contiguous alternatives.

11 ref

021092   Noot R (NO, I.R.M.A., Universite Louis Pasteur and CNRS, 7 rue Rene Descartes, 670, , Email: rutger.noot@math.u-strasbg.fr) : Lifting systems of Galois representations associated to abelian varieties. J Ramanujan Mathl Soc 2006, 21(4), 299-342.

It is shown that a Galois representation associated to an abelian variety admits a weak geometric lift to a group with simply connected derived group. In certain cases, such a weak geometric lift is itself associated to an abelian variety. This means that the conjecture of Fontaine and Mazur is confirmed for these representations. In other cases, one may find a lift which can not be found back in the etale cohomology of any abelian variety. The, Fontaine-Mazur conjecture remains open for these repreªsentations. Nevertheless, certain consequences of the conjecture can be established.

30 ref

021091   Navaneetha Kumar V;Janaki Ramudu P;Sivasakthi Balan K (Management Studies Dep, Adhiyamaan College of Engineering, Hosur, Tamilnadu) : Dynamic inventory model- a physical model. Int Rev pure appl Math 2006, 2(2), 155-8.

Authors obtained a new simulation analogous inventory model for finding buffer stock level, reorder level and order quantity with respect to variable production speed through electrical circuit system by equating inventory system parameter with electrical circuit system parameter.

5 ref

021090   Nadarajah S;Golam Kibria B M (Statistics Dep, Univ of Nebraska, Lincoln, USA) : On the exact distribution for the product and ratio of normal and t random variables. Calcutta Statist Ass Bull 2006, 58(229-30), 77-92.

Paper considers the exact distributions of the product <157> xy <157> and the ratio <157> X/Y <157> when X and Y are normal and Student's t random variables distributed independently of each other. Apart from its intrinsic interest possible applications of these results include Bayesian wavelet shrinkage, project density derivations, calculations in the theoretical analysis of project indices and computation of certain moments. Several R programs are given for computing the associated pdfs, cdfs, percentile points and the random numbers. The use of the R programs is illustrated by tabulating the associated percentage points.

2 illus, 2 tables, 26 ref

021089   Muthucumaraswamy R;Chandrakala P;Antony Raj S (Information Technology Dep, Sri Venkateshwara College of Engineering, Sriperumbudur-602 105, Email: msamy@svce.ac.in) : Thermal radiation effects on moving vertical plate with chemical reaction. Int Rev pure appl Math 2006, 2(2), 203-11.

Analysis is performed to study the effects of thermal radiation on unsteady free convective flow over a moving vertical plate with mass transfer in the presence of homogenous first order chemical reaction. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The temperature and concentration level near the plate are raised linearly with time. The dimensionless governing equations are solved using the Laplace transform technique. The velocity and skin-friction are studied for different parameters like the radiation parameter, chemical reaction parameter, Schmidt number, thermal Grashof number, mass Grashof number and time. It is observed that the velocity increases with decreasing radiation parameter or chemical reaction parameter.

1 table, 9 ref

021088   Muktibodh A;Sheikh U;Juneja D;Barhate R; Miglani Y (NO, Mohota Science College, Umred Road, Nagpur-440 009) : Sequences of pyramidal numbers. Scienta Magna 2007, 3(1), 39-45.

Shyam Sunder Gupta has defined Smarandache consecutive and reversed Smarandache sequences of Triangular numbers. Delfim F.M.Torres and Viorica Teca have further investigated these sequences and defined mirror and symmetric Smarandache sequences of Triangular numbers making use of Maple system. One of the authors A.S.Muktibodh working on the same lines has defined and investigated consecutive, reversed, mirror and symmetric Smarandache sequences of pentagonal numbers of dimension 2 using the Maple system. Authors have, defined and investigated the s-consecutive, s-reversed, s-mirror and s-symmetric sequences of Pyramidal numbers (Triangular numbers of dimension 3.) using Maple 6.

4 ref

021087   Muktibodh A S (NO, Mohota Science College, Umred Road, Nagpur-440 009) : Smarandache mukti-squares. Scienta Magna 2007, 3(1), 102-7.

Smarandache quasigroups which are Smarandache non-associative structures have been introduced. A quasigroup is a groupoid whose composition table is a Latin square. There are squares in the Latin squares which seem to be of importance to study the structure of Latin Squares. Considered the particular type of squares properly contained in the Latin squares which themselves contain a Latin square. Such Latin squares are termed as Smarandache Mukti-Squares or SMS. Extension of some SMS to Latin squares is also considered.

6 ref

021086   Mittal S K;Deepankar Sharma;Neelam Sharma (Mathematics Dep, M.M. (P.G.) College, Delhi-Meerut Road, Modinagar, U.P) : Profit estimation for a standby redundant complex system under pre-emptive repeat repair. Reflection Des Ra 2006, 1(2), 159-74.

Mixed redundant complex system for availability and profit estimation under some specified assumptions have been considered. This complex system involves standby and parallel redundancies to improve its performance. Laplace transform and supplementary variable techniques have been used to formulate and solve the mathematical model. Laplace transforms of various state probabilities have been obtained. Transition-state diagram is shown in fig. Steady-state (or ergodic) behavior and some particular cases are also given. Availability and profit function for the complex system are evaluated. One numerical example with graphical illustration has also been given to show the changes in the values of availability and profit function.

5 illus, 7 ref

021085   Melli J (Mathematics Dep, Faculty of Sciences, Damascus Univ, Damascus, Syria) : About interpolation theorem for pair of space (Lρ, L∞). Far East J mathl Sci 2006, 22(3), 405-15.

Banach space Z has the interpolation property with respect to the pair (X, Y) if each T, which is a bounded linear operator from X to X and from Y to Y, can be extended to a bounded linear operator from Z to Z. If X = L^p, Y = L^∞, then we give a necessary and sufficient condition for a Banach function space Z on (0, l), 0 <60> l ≤ + ∞ to have this property. The condition is that g <60> f^p and f ∈ Z should imply g ∈ Z, here g <60> f^p means that g*^p <60> f*^p in the Hardy-Littewood-polya sense, while h* denotes the decreasing rearrangement of the function |h|. If the norms ||T||_X, ||T||_y are given, then we can estimate ||T||_z, however, there is a gap between the necessary and sufficient conditions consisting of an unknown factor not exceeding λ_p, λ_q ≤ 2^1/q, 1/p + 1/q = 1.

Interpolation

021084   Maran A K (C & CM Div, Central Food Technological Research Institute (CFTRI-CSIR), Mysore-570 020, Email: klmaran@yahoo.com) : General formulae for any regular polygon. Math Educ 2006, 40(2), 95-8.

6 illus

021083   Macci C;Petrella L (Dipartimento Di Matematica, Univ Di Roma "Tor Vergata", Via Della Ricerca Scientifica I-00133 Rome, Italy, Email: macci@mat.uniroma2.it) : Mixtures of conjugate prior distributions and large deviations for level crossing probabilities. Sankhya 2006, 68(Pt 1), 61-89.

Authors presented asymptotic estimates of level crossing probabilities from a Bayesian point of view, based on large deviations. For the Bayesian analysis a finite mixture of conjugate prior distributions to model the uncertainty on the unknown parameters of the two classes of stochastic processes considered: the Brownian motion and the compound Poisson proªcess with upward jumps and negative drift. The estimates of level crossing probabilities are derived as a consequence of large deviation principles for posterior distributions.

21 ref

021082   Li L (Mathematics Dep, University of Puerto Rico, Rio Piedras, PR 00931-335, USA, Email: llangquing@yahoo.com) : Reduction to dimension two of local spectrum for simple AH algebras. J Ramanujan Mathl Soc 2006, 21(4), 365-90.

It is proved that an inductive limit of matrix algebras over spaces with uniformly bounded dimension can be written as an inductive limit of certain very special subhomogeneous algebras - namely, direct sum of dimension drop interval algebras and matrix algebras over two dimensional spaces with torsion H² groups.

34 ref

021081   Lee J J (Mathematics Dep, Queen's University, Kingston, Ontario, K7L 3N6, Canada, Email: jjlee@mast.queensu.ca) : Corrigendum to "Ranks of Elliptic curves". J Ramanujan Mathl Soc 2006, 21(4), 297-8.

Theorem 4.20 of [4] is incorrect as it stands. This was pointed out by several people. For example, the curve y² + y = x³ + x² - 142x + 182 satisfies the condition in Theorem 4.20 of [4], but it has rank 5.

4 ref

021080   Kulli V R;Soner N D (Mathematics Dep, Gulbarga Univ, Gulbarga-585 106) : Connected total domination number of a graph. J Analysis Computn 2006, 2(2), 183-9.

Set of vertices D in G is a total dominating set if every vertex in V is dominated by at least one vertex in D If the induced subgraph (D) is connected, then 0 is called a connected total dominating set. The connected total domination number γ_Ct (G) of G is the minimum number of vertices in a connected total dominating set of. In this paper, author initiated the study of this new parameter and present some bounds and some exact values for γ_ct (G). Also Nordhaus-Gaddum type results are obtained.

4 ref

021079   Kuldip Singh;Sarva Jit Singh;Vinay Kumar (Mathematics Dep, Guru Jambheshwar University, Hisar-125 001) : Displacement and strain fields due to axially symmetric sources in an elastic half-space in welded contact with another elastic half-space. Proc Natn Acad Sci India-Sect A 2006, 76(Pt 3), 209-18.

Closed form analytical expressions for the displacement and strain components due to five axially symmetric sources, namely, a vertical force, a vertical dipole, a centre of dilatation, a tensile dislocation on a horizontal fault and a compensated linear vector dipole (CLVD) in an elastic half-space in welded contact with another elastic half-space are obtained. The effect of rigidity contrast of the two half-spaces is investigated numerically. The elastic field due to these axially symmetric point sources in two welded half-spaces is compared with the corresponding field in a half-space and in a homogeneous unbounded medium.

4 illus, 2 tables, 17 ref

021078   Krishnamoorthy S (NO, Govt. College (Autonomous), Kumbakonam-612 001) : On G.C.D. and L.C.M. matrices. Math Educ 2006, 40(2), 88-94.

Let S = {x₁, x₂, x₃ ....x_n} be a set of distinct positive integers. Then n x n matrix (S) = (s_ij) where (s_ij = (x_i,x_j),the greatest common divisior of x_i and x_j is called the greatest common divisior (G.C.D) matrix on S and it is denoted by (S)_n. The nxn matrix [S] = [s_ij], where s_ij = [x_i x_j], the least common multiple of x_i and x_j is called the least common multiple (L C. M) matrix on S and it is denoted by [S]_n. The set S is factor closed if it contains every divisior of each of its elements. It S is factor - closed, we calculate the inverses of the G. C. D. and L. C. M. matrices on S and show that [S] (S)^-1 an integral matrix]. Authors newly define L.C.M. and G.C.D. matrices, for sets and also for union of two sets. Their relationship is also discussed.

021077   Keshwar R;Yadav P;Singh S P (Mathematics Dep, R.L.S.Y. College, Aurangabad) : Fuzzy integrals in fuzzy sets. Math Educ 2006, 40(2), 119-21.

Author define fuzzy integral in fuzzy sets of a positive measurable function with respect to fuzzy measure and obtained some, results.

5 ref

021076   Jha K K;Jha H (Mathematics Dep, C.M. Science College, Darbhanga-846 004) : Quotient ring of rings. Math Educ 2006, 40(2), 147-50.

Aim of this research paper is to give extensions of rings to rings of quotients. Most of the Mathematicians have imposed enough conditions so as to make the given ring is a vanishing singular ideal. In this present paper, Authors collect these results and present in a gener-alized form as far as possible.

5 ref

021075   Jeong N G;Park S E W (Mathematics Dep, Seonam Univ, Namwon 590-170, South Korea) : Full sign pattern matrices that allow idempotency with rank ϕ. Far East J mathl Sci 2006, 22(3), 321-32.

Matrix entries are from the set {+, -}. A full sign pattern A is said to allow idempotency if there is an idempotent matrix B whose entries have signs indicated by A. Investigates full sign patterns which allow idempotency. And some interesting constructions of idempotent matrices with rank k.

7 ref

021074   Husain S;Firdoshkhan M;Salahuddin (Applied Mathematics Dep, Z.H.C. Engg. & Tech., Aligarh Muslim Univ, Aligarh-202 002) : Generalized nonlinear implicit quasi-variational inclusions. Int Rev pure appl Math 2006, 2(2), 213-23.

Authors introduce and study a new class of generalized nonlinear implicit quasi-variational inclusions. An iterative algorithm for finding the approximate solutions of this problem is considered. Some convergence results for this iterative algorithm are derived.

17 ref

021073   Hashemi M (Mathematics Dep, Faculty of Science, Guilan Univ, P. O. Box 451 Rasht, Iran, Email: m_hashemi@guilan.ac.ir) : Some remarks on the n-permutational property. Far East J mathl Sci 2006, 22(3), 381-6.

Classification methods of n-permutational property are defined for the group, G on the lower central series and elements. Studied the relationship between them and the direct product in these properties.

8 ref

021072   Hasan A;Khan R A;Mohd A (Mechanical Engng Dep, Inderprastha Engng Coll, Ghaziabad-201 010, Email: alihasan786@rediffmail.com) : Identification of multiple jointed kinematic chains. J Analysis Computn 2006, 2(2), 175-82.

New method to determine a set of identification number for a given multiple jointed kinematic chain has been presented. The method is based on the graph theoretic approach and extended adjacency [W]matrix. The [W]matrix has been defined and developed leading to a mathematical equation and an identification set which is an invariant of a given mechanism kinematic chain. Two structural invariants ,sum of absolute eigen values [w∑] and maximum absolute eigen value [Wmax] have been derived for detection of isomorphism and identification of distinct mechanism derived from a given mechanism kinematic chain.

2 illus, 7 ref

021071   Hari Kishan;Gupta S;Anshoo Singh (Mathematics Dep, D.N. (P.G.) College, CCS University, Meerut, Uttar Pradesh) : Optimality conditions for linear fractional bilevel programs of bounded decision variables. Reflection Des Ra 2006, 1(2), 97-106.

Optimal conditions of the linear fractional bilevel programming problems of bounded decision variables have been developed based on duality theory. For the case of non-negativity of the variables, the results of Neelam Malhotra & S. R. Arora (1999) and that of Herminia 1. Calvete & Carmen Gale (2005) have heen critically discussed.

9 ref

021070   Gyan Prakash;Sharma A;Verma M P;Sodha M S (DST Project, Institute of Advanced Studies in Education, Lucknow University, Lucknow-226 007) : On self focusing of donut laser mode in plasmas. Proc Natn Acad Sci India-Sect A 2006, 76(Pt 3), 257-63.

The self-focusing/defocusing of a laser beam in the TEM^*₀₁ ~I (donut) mode in a non-absorbing plasma has been investigated taking into account one the ponderomotive and the other relativistic nonlinearities. It is seen that the beam power-beam width plane can be divided in three regions, characterized by steady divergence, oscillatory divergence and self focusing. The dependence of beam width on distance of propagation has also been illustrated for typical points in the three regions of the beam power-beam width plane. The results have been compared with those corresponding to beams of the same power with Gaussian radial distribution of irradiance.

4 illus, 17 ref

021069   Gupta R;Satish Kumar;Agrawal D C (Statistics Dep, C.C.S. University, Meerut) : Two unit parallel system with inspection, repair and post repair. Reflection Des Ra 2006, 1(2), 189-200.

Presents the analysis of a two identical unit parallel system mode/ with two types of repair-I and II. Whenever a unit fails, it requires inspection to decide whether the failed unit needs type-I repair or type-II repair. On completion of the repair the unit is finally checked and re-repaired if required. This final checking of the unit is named as post repair. A single server is always available with the system who inspects and repairs (including post-repair) of a failed unit. The failure and repair time distributions of a unit are assumed to be independent and uncorrelated random variables. The distribution of time to failure of a unit is taken to be exponential while the distributions of inspection time, type-I and type-II repair times and post repair lime are taken to he general having different c.d.f.'s. The post-repaired unit always works as good us new. Using regenerative point technique, various important measures of system effectiveness are obtained.

3 illus, 7 ref

021068   Gireesha B J;Bagewadi C S;Prasannakumara B C (P.G. Studies and Research in Mathematics and Computer Sci, Kuvempu Univ, Shankaraghatta-577 451) : Flow of unsteady dusty fluid under varying periodic pressure gradient. J Analysis Computn 2006, 2(2), 167-73.

Laminar flow of an unsteady viscous fluid with uniform distribution of dust particles between two infinite parallel plates is studied. The flow is due to the movement of upper plate with constant speed U in tangential direction and under the influence of periodic pressure gradient. The flow analysis is carried out using differential geometry technique and analytical solutions for velocities of fluid and dust particles are obtained and graphs of velocity profiles are drawn.

3 illus, 12 ref

021067   Ghosh H;Sunilkumar G;Prajneshu (NO, Indian Agric Statistics Res Inst, New Delhi) : Self exciting threshold autoregressive models for describing cyclical data. Calcutta Statist Ass Bull 2006, 58(229-30), 115-32.

Authors thoroughly study a very important family of nonlinear time-series models, viz. Self exciting threshold autoregressive (SETAR) types of models. A heartening feature of this family is that it is capable of describing cyclical data. As an illustration, SETAR models are then applied to country's lac exªport data during the period 1900-2000, obtained from Annual reports of Shellac Export Promotion Council, Kolkata. It is shown that fitted model, based on minimum Akaike information criterion (AIC), exhibits a threshold behaviour. Finally, attempts are made to obtain optimal predictor for out-of-sample data based on fitted SETAR model, which is found to be quite satisfactory.

4 illus, 5 tables, 11 ref

021066   Ghosh H;Iquebal M A;Prajneshu (Indian Agricultural Statistics Research Institute, , Library Avenue, Pusa, New Delhi-110 012, Email: hghosh@gmail.com) : On mixture nonlinear time-series modelling and forecasting for ARCH effects. Sankhya 2006, 68(Pt 1), 111-29.

In the class of Nonlinear time-series models, Gaussian mixture transition distribution (GMTD) and Mixture autoregressive (MAR) models may be employed to describe those data sets that depict sudden bursts, outliers and flat stretches at irregular time-epochs. In order to capture volatility explicitly, recently a new family, viz. MAR-Autoregressive conditional heteroscedastic (MAR-ARCH) has been introduced in the literature. In this paper, these three families are studied by considering weekly wholesale onion price data during April, 1998 to March, 2002. Presence of ARCH in detrended and deseasonalised series is tested by Naive-Lagrange multiplier (Naive-LM) test. Estimation of parameters is done using Expectation-Maximization (EM) algorithm and best model from each family is selected on basis of Bayesian information criterion (BIC). The salient feature of work done is that, for selected models, formulae for carrying out out-of-sample forecasting up to three-steps ahead have been obtained theoretically, perhaps for the first time, by recursive use of conditional expectation and conditional variance. In respect of out-of-sample data, results derived enable us to compute best predictor, prediction error variance, and predictive density. It is concluded that a two-component MAR-ARCH provides best description of the data for modelling as well as forecasting purposes.

2 illus, 13 ref

021065   Ganesan K (Mathematics Dep, S.R.M. Univ, Kattankulathur, Chennai-603 203, Email: gansan_k@yahoo.com) : On arithmetic operations of symmetric trapezoidal fuzzy numbers. Int Rev pure appl Math 2006, 2(2), 163-75.

By introducing a new set of arithmetic operations on symmetric trapezoidal fuzzy numbers and a simple ranking for the comparison of symmetric, trapezoidal fuzzy numbers, Authors propose a theory for the study of arithmetic operations on symmetric trapezoidal fuzzy numbers.

12 ref

021064   Ganatsiou C;Perakis K (Civil Engineering Dep, Section of Mathematics and Statistics School of, Thessaly Univ, Pedion Areos 38334 Volos, Greece) : On the approximation theory to the nearest integer continued fraction expansions. Far East J mathl Sci 2006, 22(3), 291-304.

By using the theory of stochastic dependence with complete connections author studied the problem of approximation of a nonzero irrational number y ∈ [-1/2, 1/2] by the n-th convergent of the nearest integer continued fraction expansion. In particular, obtained some important applications of the strong law of large numbers for the associated Markov chain of the corresponding random system with complete connections which lead to the calculation of the entropy by using the well-known Kolmogorov-Sinai's theorem.

18 ref

021063   Diaz-Garcia J A;Caro-Lopera F J (Statistics and Computation Dep, Universidad Autonoma Agraria, Antonio Narro 25315 Buenavista, Saltillo Coahuila, Mexico, Email: jadiaz@uaaan.mx) : Alternative approach for deriving the laplace-beltrami operator for the zonal polynomials of positive semidefinite and definite matrix argument. Far East J mathl Sci 2006, 22(3), 273-90.

By using the linear structure theory of Magnus [Linear Structures, Charles Griffin and Company Ltd., London, 1988], this work proposes an alternative way to James [Ann. Math. Statist. 39 (1968), 1711-1718] for obtaining the Laplace-Beltrami operator, which has the zonal polynomials of positive definite matrix argument as eigenfunctions. In particular, an explicit expression for the matrix G(v(X)), which appears in the metric (ds)² = dv'(X)G(v(X))dv(X), is obtained; also, the invariance of (ds)² under congruence transformations is proved. Explicit forms for (ds)² and G(v(X)) are also derived under the spectral decomposition X = HYH'. In a new approach, a differential metric depending on the Moore-Penrose inverse is proposed for the space of in x in positive semidefinite matrices. As in the definite case, the Laplace-Beltrami operator for the zonal polynomials of positive semidefinite matrix argument is derived. In a parallel way the invariance of (ds)² is established and explicit expressions for the metric and the matrix G(.) are obtained in terms of X and its spectral decomposition.

16 ref

021062   De-Shan Sun;Xing-Xingh HE;Cheng Jia (Institute of Mathematics, Liaoning Normal Univ, Liaoning, Dalian 116029, P. R. China, Email: sdeshan@163.com) : Face recognition by linear programming multi-class support vector machines. Far East J mathl Sci 2006, 22(3), 369-79.

One-class support vector machine (1-SVM) based on linear programming is extended to multi-class classification. In addition, a new face recognition model is proposed by using kernel principal component analysis (KPCA) and multi-class support vector machines. The method first extracts features of the face image by KPCA, and then trains the multi-class support vector machines by using the extracted features. Finally, face recognition is performed using multi-class support vector machine. The results of simulation experiments at ORL face image database show that the proposed method obtains good recognition precision and decreases recognition time.

18 ref

021061   Dasgupta R (Statistics and Mathematics Unit, Indian Statistical institute, Kolkata) : Modeling of material wastage by ornstein-uhlenbeck process. Calcutta Statist Ass Bull 2006, 58(229-30), 15-35.

Consider the problem of modeling the proportion wastage arising out of trimming the edges of paper and metal sheets to give these a regular shape. It is observed that curved edges in such cases may follow the sample path of a Ornstein - Uhlenbeck process. The production characteristic can then be expressed in terms of the parameters of the process which are estimable from the observed shape of the edge. Sample edge trajectories of two production processes are analysed and the production efficiency is interpreted in terms of proportion wastage.

6 illus, 12 ref