021575   Saadati R;Amini M (Math Dep, Islamic Azad Uaniversity, Ayatollah Amoli Branch, Iran) : D-boundedness and D-compactness in finite dimensional probabilistic normed spaces. Proc Indian Acad Sci-Mathl Sci 2005, 115(4), 483-92.

It has been proved that in a finite dimensional probabilistic normed space, every two probabilistic norms are equivalent and the notion of D compactness and D boundedness in probabilistic normed spaces have been studied.

10 ref

021574   Ryoo C S (Math Dep, Hannam Univ, Daejeon 306-791, Korea) : Twisted Bernoulli polynomials of higher order. Int J mathl Sci 2005, 4(2), 237-45.

Twisted Bernoulii polynomials B^(k)_n,w (x) of order k have been introduced. Finally, the distribution of the roots of the twisted Bernoulli polynomials B^(k)_n,w (x) of order k for values of the index n by using computer has been seen.

4 illus, 4 tables, 3 ref

021573   Roychoudhuri S K;Chattopadhyay(banerjee) M (Dep of Math, Burdwan Univ, Burdwan-713 104) : On dispersion relation of electro-magneto-visco-elastic plane waves. Proc Natn Acad Sci India-Sect A 2005, 75(4), 266-72.

A study is made of propagation of electro-magneto-visco-elastic plane waves in and electrically conducting infinite elastic solid permeated by a primary uniform magnetic field. A more general dispersion relation is deduced showing the effects of applied magnetic field and visco elastic parameters on the phase velocity of the waves. It is seen that if the primary magnetic field has both longitudinal and transverse components the displacement components u, v and the petrurbed magnetic field b2 are linked together. The coupled magneto-visco-elastic plane waves characterized by the dispersion equation are damped and dispersive.

13 ref

021572   Roy D (NO, Burdwan Univ, Burdwan) : Extension of the lack of memory property with characterization results. Calcutta Statist Ass Bull 2005, 56(Spl), 81-97.

In the reliability analysis the lack of memory property plays a pivotal role in conceptualizing some life distribution classes and in unique determination of the exponential distribution. On the other hand quite a few results like constancy of the coefficient of variation of the residual life, linearity of the mean residual life characterize the exponential distribution along with Lomax distribution. Question that arises is - can there by an extended version of the lack of memory property to tie together the exponential and the Lomax distributions through characterization. The paper presents an affirmatiave claim and extends the lack of memory property based on standarization technique. It also presents a stochastic version of this extended property with unique determination of the same life distributions. Attempts have also been made to define this extended lack of memory property in the bivariate set up and indicate the bivariate distributions that satisfy the same.

24 ref

021571   Rao G C;Sundarayya P (Math Dep, Andhra Univ, Visakhapatnam-530 003) : C-algebra as a poset. Int J mathl Sci 2005, 4(2), 225-36.

A partial ordering ≤ on a C-Algebra has been defined and * has been proved that the centre B (A) of a C-algebra A with T becomes a Boolean algebra under this partial ordering. A number necessary and sufficient conditions has been derived for a C-algebra <60> A, ∨, ∧ '<62> to become a Boolean algebra.

7 ref

021570   Ramji Lal;Shukla R P (Math Dep, Univ of Allahabad, Allahabad-211 002, Email: ramjilal@mri.ernet.in) : Transversals in non-discrete groups. Proc Indian Acad Sci-Mathl Sci 2005, 115(4), 429-35.

The concept of `topological right transversal' is introduced to study right transversals in topological groups. Given any right quasigroup S with a Tychonoff topology T, it is proved that there exists a Hausdorff topological group in which S can be embeded algebraically and topologically as a right transversal of a subgroup (not necessarily closed). It is also proved that if a topological right transversal (S, T_s, T^s, o) is such that T_s = T^s is a locally compact Hausdorff toplogy on S, then S can be embedded as a right transversal of a closed subgroup in a Hausdorff toplogical group which is universal in some sense.

12 ref

021569   Radul T;Repovs D (NO, , ) : On topological properties of the hartman-mycielski functor. Proc Indian Acad Sci-Mathl Sci 2005, 115(4), 477-82.

Some topological propertis of a normal functor H introduced earlier by Radul which is some functorial compactification of the Hartman-Mycielski construction HM have been investigated. It has been proved that the pair (H X, HMY) is homeomorphic to the pair (Q, σ) for each nondegenerated metrizable compactum X and each dense σ-compact subset Y.

10 ref

021568   Prabhakar Rao R;Sutradhar B C (NO, Sri Sathya Sai Inst of Higher Learning, Vidyagiri, Prasanthinilayam-515 134) : Global test for the goodness of fit of generalized linear models : an estimating equation approach. Calcutta Statist Ass Bull 2005, 56(Spl), 251-81.

Generalized linear models are used to analyze a wide variety of discrete and continuous data with possible overdispersion under the assumption that the data follow an exponential family of distributions. The violation of this assumption may have adverse effects on the statistical inferences. The existing goodness of fit tests for checking this assumption are valid only for a standard exponential family of distributions with no overdispersion. A global goodness of fit test for the general exponential family of distributions which may or may not contian overdispersion has been developed. The proposed statistic has asymptotically standard Gaussian distribution which should be easy to implement.

9 ref

021567   Pommeret D (NO, Cent de Recherche en Economie et Statistique Ecole Nationale de la Sta, Rue Blaise Pascal, BP 37203, 35170 Bruz Cedex - France, Email: pommeret@ensai.fr) : Distance of a mixture from its parent distribution. Sankhya 2005, 67(4), 699-714.

Mixtures of distributions from a natural exponential family have been considered. Using an adequate basis of polynomials an expression of the difference between the mixed density and its parent is obtained. This technique is applied to evaluate the distance of the mixture from the parent distribution in L²-norm. Bounds are also derived in L¹-norm and for the difference between distribution functions. The results are illustrated by some examples through gamma, Poisson and normal mixtures. Finally, more general refined approximations of the mixture density are proposed and illustrated through a Poisson mixture model.

1 illus, 2 tables, 10 ref

021566   Pawar Y S;Patil M V (Math Dep, Shivaji Univ, Kolhapur-416 004) : Characterizations of a-disteributive lattice. Int J mathl Sci 2005, 4(2), 201-17.

A-distributive lattice and a-distributive semi lattice have been studied by Varlet. Additional characterizations of a-distributive lattice have been obtained by introducing the concept of a-ideal (a-semi ideal), prime a-ideal (prime a-semi ideal), maximal a-ideal (maximal prime a-ideal) and minimal prime a-ideal (minimal prime a-ideal) in bounded lattice L where a ∈ L and a ≠ 1.

4 ref

021565   Paraguas M D S;Kamil A A (Sch of Math Sci, Universiti Sains Malaysia, 11800 USM, Pulau Pinang, Malaysia, Email: msparaguas@yahoo.com) : Estimation of meat demand system in Malaysia: model selection between the Rotterdam model and the aids. Int J mathl Sci 2005, 4(2), 357-66.

Aggregated time series data for differentiated meat products namely, beef, pork, poultry and mutton were used to estimate and analyze Malysian market demand for meats. The study aimed to select the most appropriate demand model between the equally popular Rotterdam model and the first difference Linear Approximate Almost Ideal Demand System (LA/AIDS) model by using a non-nested test. Both models were accepted, but further diagnostic tests revealed that the first difference LA/AIDS represents more appropriately the Malaysian market demand for meat the the Rotterdam model. Also, the elasticities from the first difference LA/AIDS were found to be more reliabe than the Rotterdam model.

4 tables, 18 ref

021564   Padhye S (Sch of Stud in Math, Pt. Ravishankar Shukla Univ, Raipur-492 010, Email: sahadeo_mathrsu@yahoo.com ) : A signature scheme based on singular cubic curve. Int J mathl Sci 2005, 4(2), 261-6.

A fast RSA type public key cryptosystem based on singular cubic curve y²+axy=x³ mod Z_n was given by Koyama Kenji. A signature scheme based on said curve has been proposed. The signature scheme is two times faster than the standard RSA signature scheme for a K bit long message if [K/logn] is even.

8 ref

021563   Nie L;Yang M (Biostatistics Bioinformatics and Biomathematics Dep, Georgetown Univ, 4000 Reservoir Road, NW Washington, DC 20057, USA, Email: In54@georgetown.edu) : Strong consistency of MLE in nonlinear mixed-effects models with large cluster size. Sankhya 2005, 67(4), 736-63.

The search for conditions for the consistency of maximum likelihood estimators in nonliner mixed effects models is difficult due to the fact that, in general, the likelihood can only be expressed as an integral over the random effects. For repeated measurements or clustered data, focus is placed on asymptotic theory for the maximum likelihood estimator for the case where the cluster sizes go to infinity, which is a minimum assumption required to validate most of the available methods of inference in nonliner mixed-effects models. In particular, sufficient conditions have been established for the (strong) consistency of the maximum likelihood estimator of the fixed effects. The results extend the results of Jennrich (1969) and Wu (1981) for nonlinear fixed-effects models to nonlinear mixed-effects models.

2 tables, 26 ref

021562   Najafzadeh S;Kulkarni S R (Math Dep, Fergusson Coll, Pune-411 004, Email: Najafzadeh1234@yahoo.ie) : On application of generalized fractional derivative to univalent functions. Int J mathl Sci 2005, 4(2), 391-402.

Making use of fractional derivative and subordination a subclass of univalent functions with negative coefficients is introduced and some properties are proved e.g. coefficient bounds, Geometric property, inclusion property, extreme points, convex combination and integral representation.

8 ref

021561   Mukhopadhyay N (NO, Univ of Connecticut, U.S.A) : Estimating perception of distance : applied sequential methodologies in experimental psychology. Calcutta Statist Ass Bull 2005, 56(Spl), 35-55.

An eyewitness's description of a missing criminal, for example is very crucial for apprehending the individual. But, some accounts may be unreliable if it turned out that the witness was `far away' from a crime scene. Estimation of the perception of "distance" can be an important input in many situations including this one. A number of dessigned experiments were run, data collected, and analyzed in order to understand how individuals perceived "distance". These experiments and associated data analyses have some clear messages. When a subject was asked to guess the length of an object such as a straight line or a ruler, it was found time and again that one's answer routinely depended upon the presence or absence of landmarks or reference points and what one had thought that was being shown rather than what the true item really was. More investigations in experimental psychology are deemded essential in one's thorough understanding of human perception of "distance".

17 ref

021560   Mishra R K;Pandey H (Math Dep, Sant Longowal Inst of Engng & Technol, Longowal Punjab) : The possibility approach to solve multi objective minimum cost flow problems. Int J mathl Sci 2005, 4(2), 287-95.

Although there exist many optimization tools such as decomposition principle, goal programming, game theory and multi-objective programming almost all of these approaches can not meet the common features of the decision process of a multi-level decentralized organization. However, these approaches generally assume that the lower level decision is final and no further interaction is required. In this paper, the various available approaches to Multi-Objective MCF problem as suggested by S. Lee & H. Shish have been highlighted.

13 ref

021559   Martin E S (Statist Dep, Pontificia Universidad, Catolica de Chile, Casilla 306, Santiago 22, Chile, Email: esanmart@mat.puc.cl) : Ignorable common information, null sets and Basu's first theorem. Sankhya 2005, 67(4), 674-98.

Deals with the Intersection Property, or Basu's First Theorem, which is valid under a condition of no common information, also known as measurable separability. After formalizing this notion, it reviews the general properties and give operational chracterizations in two topical cases: the finite one and the multivariate normal one. It concludes discussing the relevence of these chracterisations for different fields as graphical models, zero entries in contingency tables, causal analysis and estimability in Markov processes.

4 illus, 52 ref

021558   Maity A;Sengupta D (NO, Texas A&M Univ, USA) : Perturbation technique for sample moment matching in kernel density estimation. Calcutta Statist Ass Bull 2005, 56(Spl), 161-88.

The fundamental idea of kernel smoothing technique can be recognized as one-parameter data perturbation with a smooth density. The usual kernel density estimates might not match arbitrary sample moments calculated from the unsmoothed data. A technique based on two-parameter data perturbation is developed for sample moment matching in kernel density estimation. It is known that the moments calculated from the resulting tuned kernel density estimate can be made arbitrarily close to the raw sample moments. Moreover, the pointwise rate of MISE of the resulting density estimates remains optimal. Relevant simulation studies are carried out to demonstrate the usefulness and other featurs of this technique.

5 tables, 16 ref

021557   Maes C;Redig F;Saada E (NO, Inst Voor Theoretische Fysica, K.U. Leuven, Celestijnenlaan 200D 3001 Leuven, Belgium, Email: Christian.Maes) : Abelian sandpile models in infinite volume. Sankhya 2005, 67(4), 634-61.

Since its introduction by Bak, Tang and Wiessenfeld, the abelian sandpile dynamics has been studied extensively in finite volume. There are many problems posed by the existence of a sandpile dynamics in an infinite volume S: its invariant distribution should be the thermodynamic limit (does the latter exist?) of the invariant measure for the finite vlume dynamics; the extension of the sand grains addition operator to infinite volume is related to the boundary effects of the dynamics in finite volume; finally, the crucial difficulty of the definition of a Markov process in infinite volume is that, dueto sand avalanches, the interaction is long range, so that the use of the Hille-Yosida theorem is possible. The needed results in finite volume are recalled and then how to deal with infinite volume when S = Z, S = T is an infinite tree, S = Z^d large, and when the dynamcis is dissipative (i.e. sand grains may disappear at each toppling are explained.

3 illus, 21 ref

021556   Ma Q (NO, Coll of Math and Inf Sci Northwest Norm university, Lanzhou, Gansu-730 070, China) : Global attractors of the suspension bridge equations with linear memory. Int J mathl Sci 2005, 4(2), 367-77.

The model with linear memory arise in the case of a generalized Kirchhoot viscoelastic bar, where a bending-moment relation with memory is considered. After defining a new variable the existence of the global attractors for the model (1.1) with non-smooth semi-linear term u⁺ and linear memory using the new semigroup approach have been discussed.

10 ref

021555   Larsen M D (NO, Iowa St Univ, USA) : Latent class analysis of 1997 NSF survey data on science PhDs. Calcutta Statist Ass Bull 2005, 56(Spl), 189-208.

The field of Information Technology (IT) has provided extraordinary job growth in the United States over the last two decades; however, women and some minority groups are severely under represented in IT occupations, especially in management positions. These groups also on average receive lower salaries than their counterparts. The U.S. National Science Foundation's SESTAT database is created from biennial nationally representative surveys of U.S. scientists and engineers. SESTAT provides detailed information, such as employment history, educational background, and demorgaphic characteristics. These data are analyzed here using latent class analysis, which is an exploratory technique that can be used to cluster cases based on categorical variables. The data are from the 1997 Survey of Doctoral Recipients. The subset of respondents received Ph.D.'s between 1990 and 1996 in either than physical or biological sciences or in engineering and work at higher educational institutions. There are a few significant differences between men and women in desired work activities, job search resources, and adequacy of doctoral training. There are many large, significant differnces in limitations when searching for a job, work activities, and family and career status. Latent class analysis helped identify important subgroups of females and males based on clustering simultaneously on several categorical variables.

7 ref

021554   Lahiri I;Dutta S K (Dep of Math, Univ of Kalyani, Kalyani-741 235, Email: ilahiri@vsnl.com) : Relative valiron defects of metromorphic functions. Proc Natn Acad Sci India-Sect A 2005, 75(4), 255-65.

Compares the relative Valiron defect with the relative Nevanlinna defect of a meromorphic function

5 ref

021553   Kramer W (NO, Universitat Dortmund, Dortmund, Germany) : On the ordering of probability forecasts. Sankhya 2005, 67(4), 662-9.

Explores the relationship between various orderings among the probability forecasts that have been suggested in the literature. It is shown that well calibrated forecasters are in general not comparable according to the domination ordering suggested by Vardeman and Meeden (1983) and that the domination ordering in conjunction with semicalibration implies the rest.

021552   Joseph K T (Sch of Math, Tata Inst of Fundamental Res, Homi Bhabha Road, Mumbai-400 005, Email: ktj@math.tifr.res.in) : Large time behaviour of solutions of a system of generalized burgers equation. Proc Indian Acad Sci-Mathl Sci 2005, 115(4), 509-17.

The asymptotic behaviour of solutions of a system of N partial differentiala equations has been studied. When N = 1 the equation reduces to the Burgers equation and was studied by Hopf. Both the inviscid and viscous case have been considered and a new feature in the asymptotic behaviour has been shown.

10 ref

021551   Jain J L;Meitei A J (Fac Math Sci, Univ of Delhi, Delhi-7) : Equivalence of different expressions on transient solutions of M/M/1 Queueing system. Int J mathl Sci 2005, 4(2), 309-21.

Different transient solutions of the M/M/1 Queueing model have been studied by different authors. An attempt has been made to derive the different solution on the transient probability distribution of the number of units in a M/M/1 Queueing System using one as base formula. While doing so all the necessary identities, which are used in connecting these different expressions have been derived.

22 ref

021550   Jaggi C K;Kausar A;Goel S K (Opl Res Dep Fac of Math Sci, Univ of Delhi, Delhi-110 007) : Impact of media insertions on production-inventory system of deteriorating items. Int J mathl Sci 2005, 4(2), 379-90.

2 illus, 3 tables, 11 ref

021549   Jaggi C K;Goel S K (Opl Res Dep Fac of Math Sci, Univ of Delhi, Delhi-110 007) : Economic ordering policies of deteriorating items with trade-credit under inflationary conditions. Int J mathl Sci 2005, 4(2), 275-86.

The paper presents the economic order policies of the deteriorating items under inflationary conditions when the supplier offers credit policy of type "d/D₁ Net D" using a discounted cash flow (DCF) approach. A comprehensive sensitivity analysis has also been done.

17 ref

021548   Jacroux M (Math Sci Dep, Washington St Univ, Pullman, WA 99164, USA, Email: jacroux@wsu.edu) : Determination and construction of optimally sequenced fractional factorial block designs. Sankhya 2005, 67(4), 764-84.

Jacroux (2006) sugested an optimality criterion for sequencing two-level 2^m-k fractional factorial designs that are blocked in 2^p blocks size 2^m-k-p. This criterion essentially was to sequence blocks so that main effects become estimable as early and as efficiently as possible in the sequencing process. Using computer search methods, Jacroux (2006) also obtains optimal sequencing plants for most of the designs published in Sun, Wu and Chen (1997). The criterion for optimal sequencing of individual blocked 2^m-k designs is extended to that of selecting an optimal design and sequencing plan over all available designs for given values of m, k, and p. A systematic means for identifying and constructing designs which are either optimal or close to being optimal under the criterion suggested is also developed.

4 tables, 20 ref

021547   Ispir N;Yuksel I (Math Dep, Gazi Univ Sci & Arts Fac, 06500 Teknikokullar, Ankara, Turkey, Email: nispir@gazi.edu.tr) : Rate of convergence by certain Bezier type operators for bounded variation functions. Int J mathl Sci 2005, 4(2), 329-39.

The rate of approximation by Bezier variant of a new sequence of linear positive operators for functions of bounded variation has been investigated. Results of Gupta have been extended and generalised.

8 ref

021546   Hognas G;Mukherjea A (Math Dep, Abo Akademi Univ, 20500, Abo, Finland, Email: ghognas@abo.fi) : Products of I.I.D. random nonnegative matrices : their skeletons and convergence in distribution. Sankhya 2005, 67(4), 615-33.

Under mild conditions, it is shown that if X1, X2,...is a sequence of d by random nonnegative i.i.d. matrices, then the convergence in distribution of products X1X2...Xn essentially depends on the skeletons of X1. (Two d by d nonnegative matrices have the same skeleton if their positive entries appear on identical positions.

14 ref

021545   Ghosh H;Das A;Midha C K (NO, Indian Agric Statist Res Inst, Library Avenue, New Delhi-110 012, Email: him_adri@iasri.res.in) : Optimal designs for estimation of ratio of variance components in diallel crosses. Sankhya 2005, 67(4), 785-94.

The results on optimal designs for diallel crosses are presently available for the standard fixed effects linear model. In some cases, however, parental lines may be randomly selected from the population of lines resulting in a random effects model. Ghosh and Das (2003) discussed A-optimal designs in this context for estimation of hertiability. An unbiased estimator of the ratio of the vriance components which has a one-to-one relation with heritability has been proposed. An expression of the variance of this unbiased estimator of the ratio variance components is obtained. Through minimization of the variance optimal designs and certain connections with the optimization problem under the fixed effects model are shown.

12 ref

021544   Ghaffari A (Math Dep, Semman university, Seman, Iran, Email: ghaffari1380@yahoo.com) : Topologically left invariant means of semigroup algebras. Proc Indian Acad Sci-Mathl Sci 2005, 115(4), 453-9.

Let M (S) be the Banach algebra of all bounded regular borer measures on a locally compact Hausdorft semitopological semigroup S with variation norm and convolution as multiplication. Necessary and sufficient conditions for M (S) to have a topologically left invariant mean have been obtained.

15 ref

021543   Garge S M (Sch of Math, Tata Inst of Fundamental Res, Colaba, Mumbai-400 005, Email: shripad@math.tifr.res.in) : On the orders of finite semisimple groups. Proc Indian Acad Sci-Mathl Sci 2005, 115(4), 411-27.

The aim of this paper is to investigate the order coincidences among the finite semisimple groups and to give a reasoning of such order coincidences through the transitive actions of compact Lie groups. In is a theorem of Artin ad Tits that a finite simple group is determined by its order, with the exception of the groups (A₃(2), A₂(4) and (B_n(q), C_n (q)) for n ≥ 3, q odd. The situation for finite semisimple groups of Lie type has investigated. It turns out that the order of the finite group H (F_q) for a split semisimple algebraic group H defined over F_q, does not determine the group H up to isomorphism, but it determines the field F_q under some mild conditions. Then puts a group structure on the pairs (H_{1, H2) of split semisimple groups defined over a fixed field Fq such that the orders of the finite groups H1 (Fq) and H2 (Fq) are the same and the groupsa Hi have no common simple direct factors. An explicit set of generators for this abelian, torsion-free group. Finally shows that the order coincidences for some of these generators can be understood by the inclusions of transitive actions of compact Lie groups.}

14 ref

021542   Gandhi B K;Sreedevi K (NO, JNT Univ, Kukatpally, Hyderabad) : Beta-multiplicative functions. Int J mathl Sci 2005, 4(2), 297-308.

Beta-multiplicative functions have been defined. β-multiplicative function is the generalization of multiplicative and completely multiplicative functions. It has been shown that if ƒ is β-multiplicative, then f(1) = 1; if ƒ is β-multiplicative and if ƒ(n) ≠ 0 then ƒ(1) ≠ 0, so the inverse of ƒ, ƒ^-1 exists; if ƒ is β-multiplicative function, then ƒ^-1 is also a β-multiplicative function. i.e. ƒ^-1 (m n) = ƒ^-1 (m) ƒ^-1 (n) for all (m, n) ε β; if ƒ and g are β-multiplicative functions, then their Dirchlet product ƒ^* g is also a β-multiplicative function. i.e. (ƒ^* g) (m n) = (ƒ^* g) (m) (ƒ^* g) (n) for all (m,n) ε β; if ƒ and g are β-multiplicative functions, then their Unitary product f x g is also a β-multiplicative function. i.e. (ƒ x g) (m n) = (ƒ x g) (m) (ƒ x g) (n). Several more properties of β-multiplicative functions have also been shown.

5 ref

021541   Findley D F (NO, , ) : Convergence of a Robbins-Monro algorithm for recursive estimation with non-monotone weights for a function with a restricted domain and multiple zeros. Calcutta Statist Ass Bull 2005, 56(Spl), 1-15.

Convergence properties are established for the output of a deterministic Robbins-Monro recursion whose function can have singularities and multiple zeros. The analysis is built largely on slight adaptations of some lemmas and proofs of Fradkov published only in an untranslated Russian monograph (Derevitzkii and Fradkov, 1981). A gap in Fradkov's proof of the final lemma is fixed but only for the scalar case. The results can be applied to results of Cantor (2001) to establish the convergence of two well-known time series model recursive estimation schemes in the case of an incorrect moving average model. For such models, it is known that maximum likelihood estimates can converge w.p.1 to a set of values rather than to a single value. When the limit set is finite, the results show that, on a given realization of the time series, the (recursive) estimates will converge to single value. This is the first result establishing that estimates of a moving average coefficient do not oscillate forever among different limit set values when there are more than one.

4 ref

021540   Erkus E;Duman O (Math Dep Fac of Sci and Arts, Canakkale Onsekiz Mart Univ, Terzioglu Kampusu 17020, Canakkale, Turkey) : A-statistical extension of the Korovkin type approximation theorem. Proc Indian Acad Sci-Mathl Sci 2005, 115(4), 499-508.

Using the concept of A-statistical convergence which is a regular (non-matrix) summability method a general Korovkin type approximation Theorem which concerns the problem of approximating a function ƒ by means of a sequence {L_nƒ} of positive linear operators has been obtained.

17 ref

021539   Dubickas A (Math and Informatics Dep, Vilnius Univ, Naugarduko 24, Vilnius LT-03225, Lithuania, Email: arturas.dubickas@maf.vu.lt) : There are infinitely many limit points of the fractional parts of powers. Proc Indian Acad Sci-Mathl Sci 2005, 115(4), 391-7.

Suppose that α <62> 1 is an algebraic number and ξ <62> 0 is a real number. It has been proved that the sequence of fractional parts (ξαⁿ), n = 1,2,3,..., has infinitely many limit points except when α is a PV-number and ξ ∈ Q(α). For ξ = 1 and α being a rational non-integer number, this result was proved by Vijayaraghavan.

19 ref

021538   Daoud A S (Dep of mathematics Fac of Sci, Univ of Zagazig, Zagazig, Egypt, Email: asdaoud27@yahoo.com) : The variances in a single-mode squeezed vacuum state. Indian J Phys 2006, 80(3), 301-6.

In Calculates the variances in single-mode pure and mixed-squeezed vacuum states. Direct relationships between the variances and the mean number of photons, present in the coherent state of the mode, are obtained. The results assure that the squeezed states have less uncertainty in one quadrature than the coherent state. Some interesting properties of the squeezed states are followed as consequences of introducing the P-representation to describe the state of the mode.

^ssc22 ref

021537   Cui Y;Hudzik H;Petrot N;Suanta S; Szymaszkiewicz A (Math Dep, Harbin Univ of Sci and Technol, Harbin 150 080, People's Republic of China) : Basic topological and geometric properties of cesaro-orlicz spaces. Proc Indian Acad Sci-Mathl Sci 2005, 115(4), 461-76.

Necessary and sufficient conditions under which the Cesaro-Orlicz dequence space ces_φ is nontrivial are presented. It is proved that for the Luxemburg norm, Cesaro-Orlicz spaces ces _φ have the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuous elements in ces_φ can be defined in two ways. Finally, criteria for strict monotonicity, uniform monotonicity and rotundity (+strict convexity) of the spaces ces_φ are given.

22 ref

021536   Chaudhuri A (NO, Indian Statistical Inst, Kolkata-700 108) : Estimation in multi-stage sampling with partially missing first stage units. Calcutta Statist Ass Bull 2005, 56(Spl), 113-24.

It is a practical problem to suitably estimate a finite population total providing an estimate of its measure of error when a sample is taken in multi stages but some of the chosen first-stage units cannot be covered. Presuming the misses to occur at random, certain estimators of total along with estimators of their measures of error are derived covering varying probability sampling.

7 ref

021535   Chatterjee K;Fang K T (NO, Visva-Bharati Univ, Visva Bharati P.O., Santiniketan-731 235) : Mixed level dispersion experiments. Calcutta Statist Ass Bull 2005, 56(Spl), 99-111.

Rosenbaum (1996) and Hedayat and Stufken (1999) considered the construction of compound orthgonal arrays for the two-level factors which are useful in the study of dispersion experiments, pioneered by Taguchi (1986). This paper provides a general method of constructing such arrays and their applications to obtain several asymmetric compound orthogonal arrays for mixed level dispersion experiments. Such arrays are also found to be universally optimal even if the model includes some more parameters.

9 ref

021534   Chandra N K;Roy D (NO, Kalyani Univ, Kalyani-741 235) : Classification of distributions based on reversed hazard rate. Calcutta Statist Ass Bull 2005, 56(Spl), 231-49.

Growing importance of reversed hazard rate (RHR) and inactivity time, as measaures of the life distributions, can be noticed from the recent literature on survival and reliabiity analysis. Keeping in mind this special role of RHR and the mean inactivity time, an attempt to define different classes of distribution has been made and study their implicative relationships studied. A probability bound has also been proposed for the increasing RHR class of distributions.

17 ref

021533   Bose M;Shah K R (NO, Indian Statistical Inst, Kolkata-700 108) : Estimation of residual effects in repeated measurements designs. Calcutta Statist Ass Bull 2005, 56(Spl), 125-43.

Under the standard model and using an approximate design theory approach, necessary and sufficient conditions for a repeated measurements design to be universally optimal for residual effects have been given. In exact design theory, it is shown that symmetric optimal designs can be derived from a single linear equation. Examples of optimal designs, which can be obtained from these conditions, are given. Many of the existing optimal designs, together with new ones, can be obtained by this method. Bounds are given for computing the efficiencies of designs for estimating residual effects.

22 ref

021532   Bhosle U N (NO, Tata Inst of Fundamental Res, Homi Bhabha Road, Mumbai-400 005, Email: sa@math.tifr.res.in) : Vector bundles with a fixed determinant on an irreducibe nodal curve. Proc Indian Acad Sci-Mathl Sci 2005, 115(4), 445-51.

Let M be the moduli space of generalized parabolic bundles (GPBs) of rank r and degree d on a smooth curve X. Let M_L- be the closure of its subset consisting of GPBs with fixed determinant L^-. A moduli functor for which M_L- is the coarse moduli schemi has been defineds. Using the correspondence between GPBs on x and torsion-free sheaves on a nodal curve Y of which X is a desingularization, shows that M_L-can be regarded as the compactified moduli schemi of vector bundles on Y with fixed determinant. A natural scheme structure is obtained on the closure of the subset consisting of torsion-free sheaves with a fixed determinant in the moduli space of torsion-free sheaves on Y. The relation to Seshadri-Nagaraj conjecture is studied.

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021531   Bhatt S J;Dedania H V (Math Dep, Sardar Patel Univ, Vallabh Vidyanagar-388 120, Email: subhashbhaib@yahoo.co.in) : Note on generalized characters. Proc Indian Acad Sci-Mathl Sci 2005, 115(4), 437-44.

For a compactly generated LCA group G, it is shown that the set H(G) of all generalized characters on G equipped with the compact-open topology is a LCA group and H(G) + G^{^} (the dual group of G) if and only if G is compact. Both results fail for arbitrary LCA groups. Further, if G is second countable, then the Gel' fand space of the commutative convolution algebra C_c (G) equipped with the inductive limit topology is topologically homeomorphic to H (G).

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021530   Bhatnagar S (Math Dep, Panjab Univ, Chandigarh-160 014, Email: bhsavita@pu.ac.in) : Algebra of absolutely continuous functions and its multipliers. Proc Indian Acad Sci-Mathl Sci 2005, 115(4), 383-9.

The algebra AC_p of absolutely continuous functions ƒ on [0,1] satisfying ƒ (O) = O, ƒ^e ∈ L^{pp have been studied.}

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021529   Batir N (Math Dep Fac of Arts and Sci, Yuzuncu Yil Univ, 65080 Van, Turkey, Email: Necdet_batir@hotmail.com) : On the series ∑<. Proc Indian Acad Sci-Mathl Sci 2005, 115(4), 371-81.

The series ∑^∞_k=1 (3k/k)^-1 k^-n x^k has been inverstigated. Obtaining some integral representations of them the sum of them has been evaluated explicity for n = 0, 1, 2.

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021528   Basaak G K;Dasgupta A (Math Dep, Univ of Baristol, University Walk, bsristol, BS8 1TW, UK) : Functional central limit theorem for a class of urn models. Proc Indian Acad Sci-Mathl Sci 2005, 115(4), 493-8.

An independent increments Gaussian process associated to a class of multicolor urn models has constructed. The construction uses random variables from the urn model which are different from the random variables for which central limit theorems are available in the two color case.

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021527   Banerjee K (NO, St. Xavier's Coll, Kolkata) : Detailed classification problem. Calcutta Statist Ass Bull 2005, 56(Spl), 283-94.

The classification problem is concerned with allocation of new observations on several variables to two or more distinct categories known to exist a priori, on the basis of some pre-solved cases. Most of the existing solutions to the problem lack detailed inference with respect to the outcomes of the concerned random experiment. An alternatiave procedure is therefore suggested from frequentist viewpoint, involving relative credentials placed on the different candidate groups in terms of betting odds. The underlying theory was introduced in Chatterjee and Chattopadhyay (1993), the present study being an application twoards the classification problem. Performance of the proposed rule has been studied for some real-life examples through discriminant analysis.

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021526   Bandyopadhyay S;Das P;Mandal N K (NO, Mahendra Res Cent, Kolkata) : Generalisation of Latin Square type association scheme and related factorial designs. Calcutta Statist Ass Bull 2005, 56(Spl), 145-59.

Latin Square type association scheme has been generalized and on the basis of this association scheme, a class of designs having orthogonal factorial structure and partial balance has been introduced. Some of its combinatorial properties have also been studied.

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