007078   Gulhane P A;Gudadhe A S (Maths Dep, Govt College of Engng, Amravati-444 604) : On structure formula for generalised LK transform. Bull pure appl Sci-Sect E 2006, 25(2), 277-80.

Deals with distributional generalized Laplace-Meijer (LK) transform of distributional function f in dual space of LK_a,b i.e. LK_a,b which is defined by LK{f(t,x)} = F(s,y) = <60> f(t,x), e^-at (xy)^1/2 K_{μ (xy) <62> for complex parameters s and y. The RHS has sense for f ε LKa,b and e^-at (xy)^1/2 Kμ (Xy) ε LKa,b. Mainly provides representation theorem for the defined generalized transform.}

5 ref

007077   Gopalan M A;Vidhyalakshmi S;Devibala S (Mathematics Dep, National College, Trichy, Tamil Nadu) : Integral solutions of ka(x<. Bull pure appl Sci-Sect E 2006, 25(2), 401-6.

Ternary quadatic homogeneous equation Ka(X² + y²) + bxy = 4Ka³z², (k, a, b ≠ 0) has been studied for its non-trivial integral solutions. A few special cases of the above equation are presented. Given a solution, a method of generation of solutions is exhibited.

10 ref

007076   Gopalan M A;Somnath M;Vanitha N (Mathematics Dep, National College, Trichy, Tamil Nadu) : Method of obtaining R₂ numbers. Bull pure appl Sci-Sect E 2006, 25(2), 371-4.

Elegant formulation to construct R₂ number and to generate a sequence of R₂ numbers, being given an R₂ numbers are presented.

3 ref

007075   Gopalan M A;Anbu Selvi R (NO, National College, Trichy, Tamil Nadu) : On the system of equations Xy = α<. Bull pure appl Sci-Sect E 2006, 25(2), 347-9.

Obtain patterns of non-zero distinct integer pairs (x,y) satisfying the double equations xy=α², 2(x+y)+xy=β² (β<153>α).

8 ref

007074   Gao Z;Ma Y (Coll of Sci, Xi'an Jiaotong Univ, , Xi'an, Peoples' Republic of China 710049, Email: dtgaozm@gmail.com) : Shape reconstruction of an inverse boundary value problem for the stationary heat conduction with a Robin condition. Indian J pure appl Math 2007, 38(2), 105-21.

Considers the inverse problem to determine the shape of an insulated inclusion within one heat conducting medium from a knowledge of the heat flux on the exterior boundary. The domain derivative of the operator mapping the interior Robin boundary onto the information of the heat flux on the exterior boundary is presented. This result can be used to derive some iterative regularization methods solving such ill-posed and nonlinear inverse problem. Numerical examples indicate the feasibility of our algorithm.

3 illus, 16 ref

007073   Fu X;Liu X (Mathematics Dep, East China Normal Univ, Shanghai-200 062, Peoples' Republic of China, Email: xifu@fa.uni-tuebingen.de) : Existence of solutions for neutral non-autonomousevolution equations with nonlocal conditions. Indian J pure appl Math 2006, 37(3), 179-92.

In this paper, by using Sadovskii fixed point theorem, authour study the existence of mild solutions and solutions of semilinear neutral functional differential evolution equations with nonlocal conditions. The results obtained are generalization and continuation of the recent results on this issue. In the end, two examples are given to row the applications of our results.

15 ref

007072   Felix Abramovich (Statistics and Operations Research Dep, Tel Aviv Univ, Tel Aviv 69978, Israe;, Email: felix@post.tau.ac.il) : Bayesia maximum a posteriori multipe testing procedure. Sankhya 2006, 68(Pt 3), 436-60.

Authors consider a Bayesian approach to multiple hypothesis testing. A hierarchical prior model is based on imposing a prior distribution π (k) on the number of hypotheses arising from alternatives (false nulls). Apply the maximum a posteriori (MAP) rule to find the most likely configuration of null and alternative hypotheses. The resulting MAP procedure and its closely related step-up and step-down versions compare ordered Bayes factors of individual hypotheses with a sequence of critical values depending on the prior. Discussed the relations between the proposed MAP procedure and the existing frequentist and Bayesian counterparts. A more detailed analysis is given for the normal data, where it was shown, in particular, that by choosing a specific π (k), the MAP procedure can mimic several known family wise error (FWE) and false discovery rate (FDR) controlling procedures. The performance of MAP procedures is illustrated on a simulated example.

1 illus, 5 tables, 27 ref

007071   Dutta T K;Goswami N (Mathematics Dep, Gauhati Univ, Guwahati-781 014, Email: tkdutta2001@yahoo.co.in) : Compact approximation property in the tensor product of banach algebras. Bull pure appl Sci-Sect E 2006, 25(2), 331-40.

Let X₁ and X₂ be two Banach spaces and X₁ ⊗₁ X₂ be their projective tensor product. It is proved that the existence of compact approximation property in X₁ and X₂ ensures the existence of the same in X₁⊗₁X₂, and conversely. In addition, obtain analogous results regarding the metric compact approximation property in X₁ and X₂ and their projective tensor product.

11 ref

007070   Datta J;Bhattacharjee C;Bhattacahryya T K;De B R (Chemical Engineering Dep, Jadavpur University, Kolkata-700 032, Email: cbhattacharyya@chemical.jdvu.ac.in) : Mathematical analysis on certain physical properties applied on random coil model. Curr Sci 2007, 93(2), 231-3.

Random coil model is analysed to establish the mathematical support behind it. In this approach Stirling's approximation, weight factor and improper integral (gamma function) are analysed in detail. A correlation between the important modelling parameters like radius of gyration, root mean square separation, number of monomers and length of each monomer unit is established. Finally this model is validated by a standard object-oriented programming tool for a proªtein like serum albumin.

9 ref

007069   Cho Y J;Choi J;Jung M (Mathematics Education Dep, College of Education, Busan National University, Busan-609 735, Korea, Email: Choyj79@hanmail.net) : Note on an evaluation of ζ (p). Indian J pure appl Math 2006, 37(5), 259-63.

Since the time of Euler, many different evaluations of ζ (2p) have been presented. Stark also gave a recurrence formula for ζ (2p) by using Fejer's kernel. The purpose of this note is to show that the above mentioned recurrence formula of Stark can be obtained by making use of Lagrange's trigonometric identity simpler than Fejer's kernel. But his use of Fejer's kernel made it possible to connect ζ (2p+ 1) and I_2p := ƒ₀^π/2 θ^2p/sin² θdθ. Also reduce the known infinite series representation of I_2p to a finite series one.

7 ref

007068   Chitrakalarani T (KN Govt Arts College for Women, , Thanjavur-613 007, Email: chitricndran@yahoo.co.in) : Cumulative damage model and alertness of the worker. Bull pure appl Sci-Sect E 2006, 25(2), 447-50.

Mean time to reach the breakdown point or an uneconomic status of an organization is obtained by using the concept of alertness of the workers.

5 ref

007067   Cheng B;Shao J (Biostatistics Dep, Mailman School of Public Health Columbia Univ, 722 West 168th Street, Room 640, New York, NY 10032, USA, Email: bc2159@columbia.edu) : Testing treatment effects in two-way linear models: additive or full model. Sankhya 2006, 68(Pt 3), 392-408.

Under a two-way analysis of variance/covariance model, authors consider the problem of testing the main treatment effect (a fixed effect of primary interest) when the interaction between the treatment and the other factor (which is either fixed or random) is practically negligible but not exactly zero. Alªthough the theory for analysis of variance/covariance is well-developed (at least for the fixed effects models), practitioners are not clear on whether the test based on additive model (assuming no interaction) or the test based on full model (including interaction terms) should be adopted. The use of additive model is motivated by a possible gain in the power of the test. On the other hand, the use of full model addresses the concern of having an inflated size of the test when the interaction is not exactly zero. Under balanced fixed effects models, we show that the test based on additive model has correct size even if the additive model is wrong but its power may be very low in the presence of a small interaction effect; contrary to common beliefs, in many practical situations the gain in power by using the additive approach is not substantial even if the additive model is correct. Under unbalanced fixed effects models or balanced/unbalanced mixed effects models, the test based on additive model generally has an inflated size unless the additive model is correct.

1 illus, 14 ref

007066   Chen W;Xiong D;Ye Z (Mathematics Department of Nanchang Univ, , Nanchang 330 031, Peoples' Republic China, Email: chenwc@sjtu.edu.cn) : Information and dynamic coherent risk measures. Indian J pure appl Math 2007, 38(2), 79-96.

Authors start from proposing the axiomatic definition of a F_T-coherent risk measure in terms of its negative, a F_T-coherent risk adjusted value φT : L∞(F) → L∞(F_T), where F_T F_T ⊆ F is aU the market information available to an agent at the stopping time T and F is all the information at the terminal time T. Then we show that a F_T-coherent risk adjusted value satisfying the Fatou property can be represented by a L^l-norm closed F_T-convex set of probability measures P_T. Under discrete time setting, call a collection of F_k-coherent risk measures, k = 0, 1,..., T, a dynamic coherent risk measure. Show that a dynamic coherent risk adjusted value φ =^{^} {φ_o, φ_l,...,φ_T = id} satisfies the Fatou property, the relevant condition and the time consistent property, if and only if all the φ_k'S are defined directly by a weak-m-stable set of probability measures P; moreover, if the section rPT at any a stopping time T is defined too by the weak-m-stable set p, then P is a m-stable set. Finally we extend our results to a dynamic coherent risk measure defined on financial positions with cash-flows.

19 ref

007065   Chandrasekhara Rao K;Chinnadurai V;Singaravel T M (Srinivasa Ramanujan Centre, SASTRA Deemed Univ, Kumbakonam-612 001) : Some sequence spaces defined by moduli. Bull pure appl Sci-Sect E 2006, 25(2), 355-60.

Deals with rate entire and analytic sequence-space.

3 ref

007064   Chandrasekhara Ra K;Subramanian N;Guru Moorthy N (Mathematics Dep, Srinivasa Ramanujan Centre, SASTRA, Deemed Univ, Thanjavur-613 402, Email: nsmaths@yahoo.com) : Double integrated rate space ξξ lπ. Bull pure appl Sci-Sect E 2006, 25(2), 385-99.

Deals with first part is the BK-AK property of the double integrated rate space ξξlπ importance of δ^k in this content is printed out. Authors investigate a determing set for double integrated rate space ξξ lπ. The set of all infinite matrices tranforming ξξ lπ into the BK-AK space Y is denoted by (ξξ lπ :Y).

4 ref

007063   Chakrabarty D (ep of Statistics, Handique girls' College, Guwahati-781 001) : (NULL). Bull pure appl Sci-Sect E 2006, 25(2), 471-81.

Concept of probability definable space has been introduced and the existing concept viz. the concept of sample space has been termed, for convenience, as outcome space in the current study. Applying this definition, the probability mass functions of binomial distribution and multinomial distribution have been obtained on the basis of cointossing experiment and multifaced body-throwing experiment respectively.

17 ref

007062   Causeur D (Laboratoire de Mathematiques Appliquees Agrocamplus Rennes, , 65 Rue De Saint-Brieuc - CS 84215 35042 Rennes Cedex, France, Email: david.causeur@agrocampus-rennes.fr ) : MIVQUE and maximum likelihood estimation for multivariate linear models with incomplete observations. Sankhya 2006, 68(Pt 3), 409-35.

Problem of estimating the parameters of multivariate linear models in the context of an arbitrary pattern of missing data is addressed in the present paper. While this problem is frequently handled by EM strategies, Author propose a Gauss-Markov approach based on an initial linearization of the covariance of the model. A complete class of quadratic estimators is first exhibited in order to derive locally Minimum Variance Quadratic Unbiased Estimators (MIVQUE) of the variance parameter. Apart from the interest in locally MIVQUE itself, this approach gives more insight into maximum likelihood estimation. Indeed, an iterated version of MIVQUE is proposed as an alªternative to EM to calculate the maximum likelihood estimators. Finally, MIVQUE and maximum likelihood estimation are compared by simulations.

2 illus, 3 tables, 23 ref

007061   Borthakur P J;Hazarika G C (Mathematics Dep, Duliajan College, Duliajan, Assam) : Effects of variable viscosity and thermal conductivity on flow and heat transfer of a stretching surface in a rotating micropolar fluid with suction and blowing. Bull pure appl Sci-Sect E 2006, 25(2), 361-70.

Numerical investigation has been carried out to determine the heat transfer occurring in the boundary layer on a two-dimensional stretching surface in a rotaing micropolar fluid subject to suction and blowing considering the sheet with prescribed wall temperature. The fluid viscosity and thermal conductivity are assumed to vary with temperature. The solutions to the governing set of non-linear differntial equations are obtained by using shooting method. The solutions depend on the parameters L. which is the ratio of rotation rate to the stretching rate and suction or blowing A. The effects of different parameters such as Prandtl number Pr, Eckert number Ec, Viscosity parameter θ_k thermal conductivity parameter θand micro-rotation parameter G on velocity, temperature and micro-rotation distribution are discussed. It is observed that viscosity and thermal conductivity with variable property is prominent.

1 illus, 4 tables, 9 ref

007060   Bhatra Charyulu N C (Informatics Dep, O.U. College for Women, Koti, Hyderabad-500 195) : Methods for the construction of weighing designs. Bull pure appl Sci-Sect E 2006, 25(2), 433-7.

Formulation of Weighing problem has initially originated in a study by Yates in which it was shown that if several light objects are weighed in groups rather than individually, and the weights of the individual objects are estimates by the method of least squares, then the precision of the estimates of the weights of the objects increases quite considerably. Hotelling showed that the variance of the estimate of the weights of individual objects is half of the obtainable from the Yates scheme for seven objects. Various methods for the construction of weighing designs are found in the literature. Some methods for the construction of weighing designs using suitable balanced ternary designs have been presented and the various optimality criteria of the weighting designs are found in the literature. Some methods for the construction of weighing designs using suitable balanced ternary designs have been presented and the various optimality criteria of the weighing designs are derived.

5 tables, 8 ref

007059   Bai Z;Ma M;Ge W (Institute of Mathematics, Shandong Univ Science and Technology, Qingdao-266 510, People's Republic of China, Email: zhanbingbai@163.com) : Existence and multiplicity of positive solutions for a class of four-point boundary value problems. Indian J pure appl Math 2006, 37(4), 237-45.

Authors are concerned with the second-order four-point boundary-value problem x"(t) + h(t)f(t,x(t),x'(t)) = 0,0 <60> t <60> 1, x(0) = ax(ξ),x(1) = bx(<104>), where 0 <60> ξ <60> <104> <60> 1,0 ≤ a <60> 1/(1-ξ),0 ≤ b <60> 1/<104> and aξ (1 - b) + (1 - a)(1 - bη) <62> 0; h : [0,1] → [0, ∞), f : [0,1] x [0, ∞) x (-∞, +∞) → [0, ∞) are nonnegative continuous functions. Sufficient conditions are obtained that guarantee the existence of triple positive solutions by a simple application of a new fixed-point theorem due to Avery and Peterson.

16 ref

007058   Ansari A H;Gupta U S (MCA Dep, Siliguri Institute of Technology, Siliguri-734 225) : Forced axi-symmetric response of polar orthotropic tapered circular plates resulting of elastic foundation. Indian J pure appl Math 2006, 37(4), 209-221.

Forced axi-symmetric response of polar orthotropic circular plates of linearly varying thickness resting on elastic foundation has been suited on the basis of classical plate theory. An approximate solution of the problem has been obtained by Ritz Method, which employs functions based upon the static deflection of polar orthotropic circular plates. The effect of elastic foundation together with orthotropy on deflection function and bending moments have been studied for various values of taper parameter, rigidity ratio, foundation parameter, flexibility parameter under different types of loading. A comparison of results with those available in literature shows an excellent agreement.

20 illus, 2 tables, 25 ref

007057   Amirov R K;Cakmak Y;Gulyaz S (Mathematics Dep, Faculty of Art and Science, Cumhuriyet Univ, 58140, Sivas-Turkey, Email: emirov@cumhuriyet.edu.tr) : Boundary value problem for second-order differential equations with Coulomb singularity on a finite interval. Indian J pure appl Math 2006, 37(3), 125-40.

Boundary value problem for second-order differential equations with Coulomb singularity on a finite interval has been studied. Asymptotic formulae for the eigenvalues and eigenfunctions have been obtained. Moreover Weyl function for the problem under consideration has been defined and uniqueness theorem for solution of inverse problem according to this function has been proved.

9 ref

007056   Akbulut A;Bairamov E (Mathematics Dep, Gazi University, Kyrpehir Faculty of Arts and Science, Kyrpehir, Turkey, Email: aakbulut@gazi.edu.tr) : Discrete spectrum of a general quadratic pencil of schrodinger equations. Indian J pure appl Math 2006, 37(5), 307-15.

In this paper, using the boundary properties of the analytic functions.we investigate the structure of the discrete spectrum of the boundary value problem -y" + [V (x) + 2λU (x) - λ²]y + F = 0, x ε R₊ = [0, ∞) ay'(0) + βy(0) = 0, where U, V and F are complex valued functions and α, β ε C with <157>α<157> + <157>β<157> ≠0.

14 ref

007055   Agarwal S C;Mittal S K;Sachin Kumar (NO, M.M. (P.G.) Colll, Modinagar-201 204) : Operational behavior of a parallel redundant complex system with two types of failures with environmental effect under preemptive-Repeat repair discipline. Bull pure appl Sci-Sect E 2006, 25(2), 265-75.

Presents a complex system consisting of two s-independent repairable system A&B in series (1-out-of-2: F). Subsystem A consists of two iddentical units arranged in parallel redundancy (1-out-of-2: G). Subsystem B consists of only one unit with two types of failure viz. partial and catastrophic. Partial failure in B reduces the eficiency of the system whereas catastrophic failure breaks down the system completely. The whole system may also fail due to environmental failure. The failure time for the system follows exponential distribution whereas repair time assumes arbitray distribution under preemptive- repeat repair discipline. Laplace transform of various stage probabilities have been evaluated along with steady state behavior of the comples system. Numerical examples have been added to highlight the important results.

1 illus, 5 ref

005938   Saralees Nadarajah;Gupta A K (School of Mathematics, Manchester Univ, U. K.) : Exponentiated gamma distribution with application to drought data. Calcutta Statist Ass Bull 2007, 59(233-4), 29-54.

Gamma distributions are some of the most popular models for hydrological processes. In this paper, a very flexible family which contains the gamma distribution as a particular case is introduced. This distribution generalizes the standard gamma distribution in the same way the exponentiated exponential distribution (Gupta et al., 1998; Roy, 1998) generalizes the standard exponential distribution. We refer to this new distribution as the exponentiated gamma distribution. A comprehensive treatment of the mathematical properties is provided by deriving expressions for various particular cases and bounds, analytical shapes of the corresponding probability density function and the hazard rate function, moment generating function, the nth moment, skewness, kurtosis, mean deviation, Shannon entropy, and the asymptotic distribution of the extreme order statistics. Estimation procedure by the method of maximum likelihood and an expression for the Fisher information matrix are also provided. Finally, an application to drought data from the State of Nebraska is illustrated.

4 illus, 3 tables, 28 ref

005937   Sankaran P G;Gleeja V L;Jacob T M (Statistics Dep, Cochin Univ Science and Technology, India) : Nonparametric estimation of reversed hazard rate. Calcutta Statist Ass Bull 2007, 59(233-4), 55-68.

As hazard function, the role of reversed hazard rate function is well known in reliability analysis. This function is useful in the analysis of left censored lifetime data as well as in the study of parallel systems. In this paper, Author discuss nonparametric estimation of reversed hazard rate function for the complete sample as well as for the right-censored observations. Properties of estimators are investigated. Performance of the estimators is studied using a simulated data. Author illustrate the procedures with real data sets.

5 tables, 16 ref

005936   Rajneesh Kumar;Hundal B S (Mathematics Dep, Kurukshetra Univ, Kurukshetra, Haryana, Email: hundal_bs@yahoo.co.in) : Surface wave propagation in a fluid-saturated incompressible porous medium. Sadhana 2007, 32(3), 155-66.

A study of surface wave propagation in a fluid-saturated incompressible porous half-space lying under a uniform layer of liquid is presented. The dispersion relation connecting the phase velocity with wave number is derived. The variation of phase velocity and attenuation coefficients with wave number is presented graphically and discussed. As a particular case, the propagation of Rayleigh type surface waves at the free surface of an incompressible porous half-space is also deduced and discussed.

3 illus, 29 ref

005935   Rahman M M;Dharmadhikari A D (Statistics Dep, Rajshahi Univ, Bangladesh) : Step-stress accelerated life testing for pareto distribution with type I censoring. Calcutta Statist Ass Bull 2007, 59(233-4), 69-86.

This paper presents step-stress accelerated life test for the Pareto distribution with type I censoring. It is assumed that Pareto scale parameter depends on the stress variable and the shape parameter remains constant. It is also assumed that failures occur according to a cumulative exposure model(CEM) by Nelson (1990). On the basis of this model author describe maximum likelihood estimation procedure and expression of the Fisher information matrix has been derived in closed form. A simulation study has been done to obtain the maximum likelihood estimates(MLE), Fisher information matrix and hence the variance-covariance matrix of the parameters. For selected values of the design parameters the optimum low stress as well as the stress change time are obtained which minimize the asymptotic variance of the MLE of a stated percentile.

4 tables, 13 ref

005934   Mukhopadhyay S;Khuri A I (Biostatistics Dep, Medical College of Georgia, U.S.A.) : Bias in multivariate generalized linear models. Calcutta Statist Ass Bull 2007, 59(233-4), 87-105.

In this article, an expression is derived for the bias associated with maximum likelihood estimates of the parameters in a multivartate generalized linear model (MGLM). This expression represents an extension of the bias formula in the case of a univariate generalized linear model. One important objective of the proposed extension is to obtain an expression for the mean squared error of prediction matrix, which can be used as a criterion for comparing response surface designs for a MGLM. An application of the bias formula is presented in the special case of the bivariate binary distribution. A numerical example is given to illustrate this particular application.

2 tables, 11 ref

005933   Jayakumar K;Mundassery D A (Statistics Dep, Calcut Univ, Kerala, India) : On moran's bivariate gamma and bivariate negative binomial distribution. Calcutta Statist Ass Bull 2007, 59(233-4), 15-27.

Characterizations of Moran's bivariate gamma distribution and bivariate negative binomial distribution are obtained. Autoregressive models with Moran's bivariate gamma distribution as marginals are devel-oped.

8 ref

005932   Chen W C;Maiti T (Iowa State, Ames Univ, U. S. A) : Analysis of cDNA microarray experiment with external controls: a mixed model approach. Calcutta Statist Ass Bull 2007, 59(233-4), 116-35.

The aim of this article is to obtain the calibration curves by external controls in the c.DNA microarray data set. Anonlinear mixed model is found to be suitable for this purpose. The fitted calibration curves could be used to predict the concentrations of the relative expressions by the inverse functions of the fitted curves. After giving some background introduction for a cDNA microarray experiment with external controls, the article focuses on two parts. First, checked the source of experiment variation by using linear model on the slide, dye, and pin effects, and determine the quality of the data set by using quasi-likelihood method for the model with random effect for pins. Second proposed a non-linear model based on a four-parameter logistic function, with two possible random effects structures on pins and base on the concentrations. The inverse function of the fitted model is then used to predict the concentrations from the expression intensities of the external controls.

10 ref

005931   Bandyopadhyay S (NO, Mahendra Research Services, Kolkata) : On construction on pencilwise orthogonal and balanced designs. Calcutta Statist Ass Bull 2007, 59(233-4), 107-15.

In this paper some constructions of the Pencilwise Orthogonal and Balanced Designs of Das (2001), mainly based on difference and composition methods, are given.

10 ref

005930   Asha G;John Rejeesh C (Statistics Dep, Cochin Univ Science and Technology, India) : Models characterized by the reversed lack of memory property. Calcutta Statist Ass Bull 2007, 59(233-4), 1-14.

Block et.al (1998) studied the properties of the reversed hazard rate (rhr) and characterized a class of distributions having constant rhr in its interval of support. In this paper author study another equivalent characterization of this class along with its bivariate extensions.

16 ref

004931   Zhang B G;Lian F Y (Mathematics Dep, China Ocean Univ, Qingdao-266 071, Peoples' Republic of China) : Oscillation criteria for certain difference equations with continuous vairables. Indian J pure appl Math 2006, 37(6), 325-41.

Concernes with the delay difference equation x(t) - x(t-τ) + Σ^m_i=1 pi(t)x(t - σ_i) =0, t ≥ 0, where 0 <60> τ<60>σ₁... <60> σ_m, pi ∈ C(R,R⁺, lim inf pi(t) = pi^- ≥ 0, i = 1,2,...,m. Establishes some new sufficient conditions for the oscillation of all solutions of the above equation in the case when that the corresponding "limiting" equation x(t) - x(t - r) + Σ^m_i=1 pi^- x(t-σ_i) = 0, t ≥ 0 admits non-oscillatory solutions and improve the previous corresponding results about the above equation.

10 ref

004930   Yan L;Yoshida N (Mathematics Dep, Dong Hua Univ, Shanghai-200 051, Peoples' Republic of China) : Oscillations of characteristic initial value problems for hyperbolic equations with delays. Indian J pure appl Math 2006, 37(6), 357-67.

Characteristic initial value problems for hyperbolic equations with delays are considered, and sufficient conditions for every solution to be oscillatory are derived. Approach is to reduce the characteristic initial value problems to one-dimensional oscillation problems for functional differential equations.

17 ref

004929   Udai Chandrika K (Avinashilingam Deemed University, , Coimbatore) : Transient analysis of a system with queue dependent servers. Opsearch 2006, 43(2), 178-189.

The analysis of an infinite capacity Markovian queueing model with number of heterogeneous channels depending on system size. The model consists of one regular channel and a maximum of c additional channels. By defining generating function and using the properties of Bessel functions, the transient probabilities and hence the steady state results are derived.

2 illus, 5 ref

004928   Stevic S (NO, Mathematical Institute of the Serbian Academy of Science, Knez Mihailova 35/1, 11000 Beograd, Serbia, Email: sstevic@ptt.yu) : Boundedness and compactness of an integral operator in a weighted space on the polydisc. Indian J pure appl Math 2006, 37(6), 343-55.

Studies operators of the form T₉(f) (z) = ƒ^z1₀ .... ƒ^zn₀ f(ζ₁, ..., ζ_n)g(<122>₁, ....ζ_n) ∏ⁿ_j=1 dζ_j where g is a fixed holomorphic function on the unit polydisc Uⁿ, on the space Sα→ (Uⁿ) defined by Sα→(Uⁿ) = { f ∈ H (Uⁿ) <157> sup_z∈Uⁿ <157>f(z) <157> ∏ⁿ_j=1 (1-<157>z_j<157>)α^j <60> ∞}, where α= (α₁, ......,α_n), α_j <62> 0, j = 1, ..., n. It is shown that the operator T_g is bounded on Sα→(Uⁿ) if and only if sup_z∈Uⁿ ∏ⁿ_j = 1 (1 - <157>z_j<157>)<157>g(z) <157> <60> ∞, and compact if and only if lim_z→∂Uⁿ ∏ⁿ_j=1 (1 - <157>z_j<157>)<157>g(z) <157> = 0. Also, we give a necessary and sufficient condition for a holomorphic function on the polydisc to be a p-Bloch function, when p ∈[1,2).

18 ref

004927   Mahapatra N K;Maiti M (Dep of Mathematics, Panskura Banamali College, Panskura R.S-721 152, Purba Medinipur, W.B., Email: nirmal_hridoy@yahoo.co.in) : (NULL). Opsearch 2006, 43(2), 117-131.

A multi-item, multi-objective inventory model of deteriorating items with stock and time dependent demands is formulated in fuzzy-stochastic environment with finite time horizon. In this model, it is assumed that setup cost of the items varies directly with the maximum inventory. Also, unit purchase cost is a random parameter represented by Normal distribution and the deterioration rate is imprecise in nature and defined by a trapezodial fuzzy number. The model is reduced to an equivalent deterministic model using chance constrained and graded mean integration representation techniques. Single objective E- and V-models are solved using generalized reduced gradient (GRG) technique and multi-objective E_V model is solved by Augmented Fuzzy Max-Min Approach. the models are illustrated numerically.

3 tables, 24 ref

004926   Kuyucu F (Mathematics Dep, Cukurova Univ, 01330, Adana, Turkey) : Remainders and products of compactifications. Indian J pure appl Math 2006, 37(6), 321-4.

In [1] a product operation of compactifications is defined. Investigates the relations among products of some compactifications of X, compactifications generated by some subsets of C<42>(X) and some remainders of X.

6 ref

004925   Kapoor R;Arora S R (Dep of Mathematics, , University of Delhi, Email: reena_3105@rediffmail.com) : Linearization of a 0-1 quadratic fractional programming problem. Opsearch 2006, 43(2), 190-207.

The considered problem is the reduction of 0-1 Quadratic Fractional Programming Problem (0-1 QF) to 0-1 Linear Mixed Programming problem (0-1 MLP). The method used to solve the linearized problem is based upon the branch and bound method. Numerical problems are solved with the help of the software `Lindo'.

7 ref

004924   Guo W;Shum K P;Skiba A (Mathematics Dep, Xuzhou Normal Univ, Xuzhou-221 116, People's Republic of China, Email: wbguo@pub.xz.jsinfo.net) : On primitive subgroups of finite groups. Indian J pure appl Math 2006, 37(6), 369-76.

Subgroup H of a group G is called primitive if it is a proper subgroup in the intersection of all subgroups of G containing H as its proper subgroup. In 1971, Johnson proved that a finite group G is supersoluble if every primitive subgroup of G has a prime-power index in G. It is known that the converse of this result is generally not true. Investigates the structure of finite groups satisfying the Johnson's property. In particular, by extending the main result of Johnson, we prove that a finite group G is supersoluble if every primitive subgroup of G has a nilpotent Hall supplement in G. Thus, the result of Johnson is strengthened.

8 ref

004923   Gopalan M N;Kumar U A;Subramanya J M (NO, SDM Institute of Management Development, Mysore) : (NULL). Opsearch 2006, 43(2), 208-222.

The stochastic analysis of a two-stage production system with two production machines in parallel in the first stage and subject to inspection. The time taken to process a job on a machine and the time taken for inspection of the finished job are random governed by probability distributions which are quite general. Semi-finished jobs processed by the machines in the first-stage are transferred to the machine in the second stage for further processing. Machine in the second stage processes two type of products based on the semi-finished products transferred from the machines in the first stage. Inspection is carried out of the items processed by machines in the second stage and only good items are accepted, while others are scrapped. The analysis is carried out by employing the state-space method and the regeneration-point technique. Several measures of system performance, transient in nature, are evaluated. A cost analysis is also carried out by using some of the measures of system performance obtained.

2 illus, 6 ref

003979   Walker S G (Institute of Mathematics, Statistics and Actuarial Science, Kent Univ, Canterbury, CT2 7NZ, UK, Email: s.g.walker@kent.ac.uk) : Bayesian inference via a minimization rule. Sankhya 2006, 68(Pt2), 542-53.

Author consider the Bayesian posterior distribution as the solution to a minimization rule, first observed by Zellner (1988). The expression to be minimized is a mixture of two pieces, one piece involving the prior distribution, which is minimized by the prior, and the other piece involves the data, which is minimized by the measure putting all the mass on the maximum likelihood estimator. From this perspective of the posterior distribution, Bayesian model selection and the search for an objective prior distribution, can be viewed in a way which is different from usual Bayesian approaches.

7 ref

003978   Umamaheshwar Rao R;Srinivas V;Rangamma M (Mathematics Dep, Sreenidhi Institute of Science and Technology, Ghatkesar, R.R. Dist-501 301) : Common fixed point theorem of compatible mappings of type (A) using reciprocally continuous mappings. Bull pure appl Sci-Sect E 2006, 25(1), 225-30.

Aim of this paper is to prove a common fixed point theorem which generalizes the result of S.LSingh and S.P.Singh |3] by weaker conditions such as reeiprocally continuous, compatible mappings of type (A) and associated sequence.

3 ref

003977   Thilagavathi K;Vivin J V (Mathematics Dep, Kongunadu Arts and Science College, Coimbatore-641 029, Email: ktmaths@yahoo.com) : N - leaf and star n - leaf. Bull pure appl Sci-Sect E 2006, 25(1), 209-13.

Author define the new concept of n - leaf n(L), star n- leaf and we prove some preliminary theorems. Discuss the properties relating the line and total graphs of n - leaf and star n- leaf. A relationship between the covering and colouring of the total graph of star n - leaf is derived.

3 illus, 6 ref

003976   Thilagavathi K;Vernold J V (Mathematics Dep, Kongunadu Arts and Science College, Coimbatore-641 029) : Arena graph. Bull pure appl Sci-Sect E 2006, 25(1), 165-70.

Author introduce the new concept (m, n) -arena. The order of a (m, n) - arena is denoted by f(m, n). In this paper author prove some results and show that the hajos union of the largest complete sub graph K_n-1 (Clique) and the shortest cycle (girth) in a (n-1, n) - arena is Hamiltonian and Eulerian depending on n.

5 ref

003975   Suvarna K;Bharathi D (Mathematics Dep, Sri Krishnadevaraya Univ, Ananatapur-515 003) : Some theorems on primitive accessible rings. Bull pure appl Sci-Sect E 2006, 25(1), 105-7.

Author show that a left primitive accessible ring is either associative or simple with right identity element.

2 ref

003974   Sundaram M;Ponraj R;Somasundaram S (Mathematics Dep, Sri Paramakalyani College, Alwarkurichi-627 412) : Total product cordial labeling of graphs. Bull pure appl Sci-Sect E 2006, 25(1), 199-203.

Simple graph G=(V. E) has a labeling f defined on V ∪ E, such that each vertex has 0 or 1 as its label and the label of any edge xy is f(x) f(y). f is called a total product cordial labeling of G if <124> f(0) - f(l) <124> ≤1 where f(i) denotes the sum of the number of vertices and the number of edges labelled with i(i=0.1). Author investigate the total product cordial behaviour of a few standard graphs.

5 ref

003973   Subba Rao S (Statistics Dep, Texas A&M Univ, College Station, Texas, TX-77843, USA, Email: suhasini@stat.tamu.edu) : Uniform convergence of an arch (∞)estimator. Sankhya 2006, 68(Pt4), 600-20.

Parameter estimation for a class of ARCH(∞) models, which do not necessarily have a parametric form has been cosidered. The estimation is based on a normalized least squares approach, where the normalization is the weighted sum of past observations. The number of parameters estimated depends on the sample size and increases as the sample size grows. Using maximal inequalities for martingales and mixingales we derive a uniform rate of convergence for the parameter estimator. We show that the rate of convergence depends both on the number of parameters estimated and the rate that the ARCH(∞) parameters tend to zero.

17 ref

003972   Smarandache F (Mathematics Dep, New Mexico Univ, Gallup, NM-87301, USA) : Triple inequality with series and improper integrals. Bull pure appl Sci-Sect E 2006, 25(1), 215-17.

As a consequence of the Integral Test author find a triple inequality which bounds up and down both a series with respect to (ts corresponding improper integral, and reciprocally an improper integral with respect to its corresponding series.

1 ref