009983   Ramachandran B (NO, , 29 Fourth Cross Street, Ramakrishna-Nagar, Chennai-600 028, Email: bramal933@yahoo.com) : Some pioneering results on infinite divisibility revisited. J Indian Statist Ass 2005, 43(1), 63-76.

Sections 1 and 2 of this semi-expository paper offer [alternative proofs for Thorin's closure (or "continuity") theorem on Generalized Gamma Convolutions (GGC's) and for an important segment of the proof of the GGC-ness of the log-normal laws have been offered. Section 3 offers a proof avoiding special functions theory for the complete monotonicity on (0, λ) of certain functions - a fact needed in Thorin's work above and later have been offered. Brief comments on some related results due to Thorin and Bondesson, a special case of which enables to establish have been offered, but again without making any appeal to special functions theory, the result established by Grosswald using such theory that the t-distributions are infinitely divisible.

11 ref

009982   Rakesh Kumar;Nagaich R K (Math Dep, Univ Coll of Engng Punjabi Univ, Patiala-147 002) : (NULL). Bull Calcutta Mathl Soc 2005, 97(4), 361-4.

The result of Yamaguchi (1976) has been generalised for a K-space with indefinite metric.

2 ref

009981   Rajneesh Kumar;Choudhary S (Math Dep, Kurukshetra Univ, Kurushetra-136 119, Email: rajneesh_kuk@rediffmail.com) : Stretch effect due to mechanical sources in a micropolar viscoelastic medium. Bull Allahabad Mathl Soc 2005, 20, 99-111.

The dynamic response of a homogeneous isotropic micropolar viscoelastic half-space with stretch subject to a set of normal point sources is investigated. The integral transforms have been inverted by using a numerical technique to obtain the normal displacement, normal force stress, tangential force stress, tangential couple stress and first moment in the physical domain for the two different sources. The result of these quantities for magnesium crystal like material are given and illustrated graphically.

4 illus, 13 ref

009980   Rajneesh Kumar;Ailawalia P (Math Dep, Kurukshetra Univ, Kurukshetra, Email: rajneesh_kuk@rediffmail.com) : Variations of moving load velocity at the boundary surface interface of two half spaces. Proc Natn Acad Sci India-Sect A 2005, 75(2), 111-20.

The steady state response of an orthotropic micropolar solid with an overlying elastic half-space subjected at the plane interface to a moving point load has been studied. The eigen-value approach using Fourier transforms has been employed and the transform has been inverted by using a numerical technique. The displacement and stress components in the physical domain are obtained numerically. The numerical results are illustrated graphically for a particular model.

6 illus, 28 ref

009979   Pranesh Kumar;Taneja I J (Math Dep Coll of Sci and Mgmt, Univ of Nth Br Columbia, Prince George BC V2N4Z9, Canada, Email: kumarp@unbc.ca) : Unified generalizations of relative Jensen-Shannon and arithmetic-geometric divergence measures, and their properties. Indian J Math mathl Sci 2005, 1(1), 51-71.

One parametric generalization of some non-symmetric divergence measures have been considered. The non-symmetric divergence measures are such as: Kullback-Leibler relative information, χ²-divergence, relative J-divergence, relative Jensen-Shannon divergence and relative arithmetic-geometric divergence. All the generalizations considered can be written as particular cases of the Csiszar f-divergence. By putting some conditions on the probability distributions, the aim has been to establish bounds on these divergence measures and their parametric generalizations in different situations.

30 ref

009978   Paul D R R;Rao K S (Fculty of Statist, S.T.B.C. Coll, Kurnool, Andhra Pradesh) : An order level inventory model for deteriorating items with inventory returns and special sales. Indian J Math mathl Sci 2005, 1(1), 35-43.

An order level inventory model is developed for deteriorating items with inventory returns and special sales. The problem of returning or of selling inventory that overflows the optimal stock is considered. A constant rate of deterioration is assumed. Two inventory mdodels viz., the infinite and finite horizon models are developed by assuming the lead time is zero and shortages are allowed. Numerical illustrations are provided to substantiate the results obtained in these models.

1 table, 6 ref

009977   Patil P N;Speckman P L (Sch of Math and Stattist, The Univ of Birmingham, Birmingham, B15 2TT, UK, Email: p.n.patil@for.mat.bham.ac.uk) : Constrained kernel regression. J Indian Statist Ass 2004, 42(1), 87-98.

Consider a regression function whose general functional form is unknown but it is known to pass through the origin. Nonparametric estimators such as the Nadaraya-Watson type kernel method can provide a `reasonable' estimator of a regression function as a whole, however they do not satisfy such a constraint at the origin. Further, if the origin is at the boundary of the design density, then many kernel estimators not only fail to satisfy the constraint but also have higher order bias at the origin than in the interior. There are methods to improve the bias at the boundary by way of using special boundary kernels, but these estimators do not satisfy constraints. A method based on a semiparametric approach to modify the usual kernel estimator so as to satisfy such a constraint without losing the structure and appealing statistical properties of the kernel estimator in the interior has been proposed.

2 illus, 13 ref

009976   Patel N W;Patel M N (Stattist Dep, St. Xavier's Coll, Navrangpura, Ahmedabad-380 009) : A problem in discreted life testing with progressive changing failure rate. J Indian Statist Ass 2005, 43(1), 51-62.

In life testing experiments, a situation may arise when the items are put on test at different times and at one particular instant; one knows only the time of failure or the time since it is on test if it has not failed up to that instant. Such problems are considered by Bartholomew (1957) and Srivastava (1967) for the exponential distribution. Here authors have considered the Geometric distribution, discrete life time model, with two stage progressive censoring with changing failure rate when items of an equipment are installed on different trials and some of the items are still working while the rest have failed. The of maximum likelihood method has been used to estimate the parameters in case of both the stages of censoring. Bias of the estimates is also discussed. A numerical example is given to exemplify the estimation procedure.

2 tables, 5 ref

009975   Pasalic E;Johansson T;Maitra S;Sarkar P (Inf Technol Dep, Lund Univ, P.O. Box 118, 221 00 Lund, Sweden, Email: enes@it.lth.se) : New constructions of resilient and correlation immune boolean functions achieving the upper bound of nonlinearity. J Indian Statist Ass 2004, 42(2), 287-307.

Weight divisibility results on resilient and correlation immune Boolean functions have received a lot of attention. These results provide a nontrivial upper bound on nonlinearity of resilient and correlation immune (CI) Boolean functions of certain order. An open problem in the design of resilient Boolean functions is to provide funcstions which attain the upper bound on nonlinearity. A classical search technique to construct 7-variable, 2-resilient Boolean function swith nonlinearity 56 has been used. Combinatiorial techniques are applied to reduce this search space. This solves the maximum nonlinearity issue for 7-variable functions with any order of resiliency. A construction method which is similar to Tarannivov's construction, but much simpler to understand has been presented. Using the 7-variable function as the initial one an infinite sequence of Boolean functions on n = 7+3i variables (i≥0) with order of resiliency m = 2+2i, algebraic degree 4+i and nonlinearity 2^n-1 - 2^m-1 has been constructed. These functions resiliency, stream ciphers.

21 ref

009974   Pardeep Kumar;Sharma P (Math Dep, ICDEOL Himachal Pradesh Univ, Shimla) : Thermal instability of couple-stress fluid permeated wtih suspended particles in hydromagnetics in porous medium. Proc Natn Acad Sci India-Sect A 2005, 75(2), 141-5.

The effect of suspended particles on the thermal instability of couple-stress viscoelastic fluid in hydromagnetics in porous medium is considered. The medium permeability and suspended particles hasten the onset of convection whereas the magnetic field and couple-stress postpone the onset of convection, for the case of stationary convection. The principle of exchange of stabilities is found to hold good for couple-stress fluid permeated with suspended particles in the absence of magnetic field. The magnetic field introduces oscillatory modes in the system which were non-existent in its absence.

4 illus, 7 ref

009973   Okafor F C (NO, Univ of Nigeria, Nsukka, Nigeria) : Sub-sampling the non-respondents in two-stage sampling over two successive occasions. J Indian Statist Ass 2005, 43(1), 33-49.

Several studies carried out in sampling with partial replacement of units assumed total response from the sample units. The present study looks at the situation where some sample units do not supply the necessary information. The estimates of the population total and change in the population total from one occeasion to the next have been adjusted for unit non-response using Hansen and Hurwitz (1946) technique. It has been shown empirically that the estimator, T, obtained from partial matchin gat the first and second stages of sampling is more efficient than the estimator, T_o, obtained when there is no partial matching of units. The proposed estimators have been applied to the estimation of total hectares of land planted in 1999/2000 planting season and change in the land planted between 1998/1999 and 1999/2000 planting seasons in Botswana.

6 tables, 10 ref

009972   Nikov V;Nikova S;Preneel B (Math and Computing Sci Dep, Eindhoven Univ of Technol, P.O. Box 513, 5600 MB, Eindhoven, the etherlands, Email: v.nikov@tue.n1) : On metering schemes. J Indian Statist Ass 2004, 42(2), 261-86.

In order to decide on advertisement fees for web servers, Naor and Pinkas introduced (threshold) metering schemes secure against coalitions of corrupt servers and clients. Several researchers have generalized the idea of Naor and Pinkas. First metering scheme with pricing and dynamic multi- thresh-old metering schemes have been propsed; later the solution has been extended to allow general access structures and an approach based on linear algebra has been introduced. But all previous papers consider the following scenario - a general (or threshold) access structure for the clients and a threshold access structure fot the servers. The model has been generalized allowing a general access structure for the servers, moreover it has been strengthened by limiting the possibility of corrupt servers to help each other. A more efficient protocol satisfying the requirements of the new model is described. Naor and Pinkas show that one should be able to verify the shares received from clients also, i.e., one needs to verify the shares received from clients. Most metering schemes do not offer this feature. But Ogata and Kurosawa pointed out a minor flaw in the extension protocol by Naor and Pinkas providing detection of such illegal behavior and propose a correction. So the used linear algbra approach has been extended in order to build robust unconditionally secure general metering schemes....

6 illus, 15 ref

009971   Nazrul Islam Khan M (Appl Sci Dep, Azad Inst of Engng and Technol, Natkur, Post-Chandrawal, Bangla Bazar Road, Lucknow-226 002, Email: nazrul73@rediffmail.com) : On generalised Ricci-recurrent Lorentzian Para-Sasakian manifold. Proc Natn Acad Sci India-Sect A 2005, 75(2), 147-8.

Deals with a generalised Ricci-Recurrent Lorentzian Para-Sasakian manifold and also when it admits cyclic Ricci-tensor.

6 ref

009970   Natarajan R;Chandrasekhar P;Yadavalli V S S; Malada A (Math Dep, Presidency Coll, Chennai-600 005) : A study a two unit parallel system with Erlangian repair time. Bull Allahabad Mathl Soc 2005, 20, 25-33.

A two unit parallel suystem, wherein the failure rate of a unit is constant and the repair time distribution is a two stage Erlang distribution. Measures of system performance such as reliability, system availability and steady state availability are derived. Also a consistent asymptotically normal (CAN) estimator, a 100 (1-α)% asymptotic confidence interval for the steady state availability of the system and a maximum likelihood estimator (MLE) of the system reliability are obtained.

7 ref

009969   Nanda A K;Sengupta D (Math Dep, Indian Inst of Technol, Kharagpur-721 302, Email: asok@maths.iitkgp.ernet.in) : Discrete life distributions with decreasing reversed hazard. Sankhya 2005, 67(Pt 1), 106-25.

The class of discrete distributions for which the distribution function is a log-concave sequence has been considered. It is shown that such distributions arise from a wide variety of circumstances in Reliability, and that these have a decreasing reversed hazard rate. After examining the closures of the class under certain key operations, sharp upper and lower bounds on the reliability function of the member distributiosn are given. Some useful inequalities for maintained systems are provided. Some results for the related class of discrete concave distributions are also given.

13 ref

009968   Nam K B;Choi S H;Chakrabarti M (Math Dep, Univ of Wisconsin-Whitewater, Whitewater, WI 53190, USA, Email: namk@uww.edu) : Lie algebra without ad-diagonal. J Computnl Math optimiz 2005, 1(3), 141-9.

Generalized W-type Lie algebra W (m,m] is introduced using exponential functions. Also generalized S-type Lie algebras S(m,m] over F is introduced. It has been shown that the Lie algenras W(m,m] and S(m,m] have no ad-diagonal with respect to any basis of them.

9 ref

009967   Nabar S P;Deshmukh S C (Stattist Dep, Univ of Mumbai, Mumbai-400 098) : Two-piece logistic distribution. J Indian Statist Ass 2004, 42(1), 79-85.

Two-pice logistic distribution has been considered and the problem of finding the fisher information matrix and variance covariance matrix have been considered.

3 ref

009966   Muthucumaraswamy R;Kulandaivel T (Inf Technol Dep, Sri Venkateswara Coll of Engng, Sriperumbudur-602 105) : MHD effects on impulsively started infinite vertical isothermal plate with variable mass diffusion. Bull Allahabad Mathl Soc 2005, 20, 67-78.

Theoretical solution for hydromagnetic flow past an impulsicrly started infinite vertical isothermal plate with variable mass diffusion is obtained. The dimensionless governing equations are solved using the Laplace transform technique. The plate temperature is raised to T_w' and the concentration level near the plate is raised linearly with time. The solutions for the velocity and skin-friction are obtained for different Hartmann number and multiple buoyancy effects aiding and opposing. It is observed that the velocity decreases in the presence of magnetic field, as compared to its absence.

3 illus, 1 table, 5 ref

009965   Muralidharan K;Lathika P (Stattist Dep, Bhavnagar Univ, Bhavnagar-364 002, Email: lmv murali@yahoo.com) : A note on fisher information matrix of weibull distribution. J Indian Statist Ass 2004, 42(1), 75-8.

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009964   Mukhopadhyay S (Cryptology Res Grp Appl Stattist Unit, Indian Statistical Inst, 203, B.T. Road, Kolkata, Email: Sourav_t@isical.ac.in) : Time / memory trade-off : a survey. J Indian Statist Ass 2004, 42(2), 231-60.

Time/memory trade-off appears in many searching task such as the knapsaack-like problem, discrete logarithm problem and inverting a one-way function. This technique is used in cryptanalysis of block and stream cipher. A survey of time/memory trade-off emphasiziang specifically on inverting one-way functions has been presented.

3 illus, 1 table, 41 ref

009963   Mohanta S K;Baisnab A P (NO, Haldia Government Coll, Purba Midnapur-721 657) : A class of Ciric operators and their fixed points. Bull Allahabad Mathl Soc 2005, 20, 79-88.

Some results on fixed points have been proved for a class of Ciric operators so widened to include a number of well-known operators as available in recent fixed point theory.

8 ref

009962   Modi H B;Ranabhatt G A (Math Dep, Bhavnagar Univ, Bhavnagar-364 002, Email: hbm_bhav_uni@yahoo.com) : Generalized altrnating series. Bull Allahabad Mathl Soc 2005, 20, 89-98.

It is known that the alternating series: Σ^∞_K=1 1/2k(2k-1) = 1-1/2 + 1/3 - 1/4 +... sums to ln (log) 2. This result has been generalized and the sum of the altermating series: Σ^∞_K=1 1/rk(rk-1) = Σ^∞_K=1 {(1/rk-1 - 1/rk)}, for r a positive rational number, r <62> 1 has been found.

3 ref

009961   Matveeva I I (NO, Sobolev Inst of Math, Novosibirsk 630 090 Russia, Email: matveeva@math.nsc.ru) : On a class of boundary value problems for systems of Sobolev type. J Analysis Applic 2005, 3(2), 129-50.

A class of initial-boundary value problems for systems of Sobolev type is considered. Unique solvability in special weighted Sobolev spaces has been proved. It has been shown that quantity of solvability conditions can be decreased.

9 ref

009960   Maitra S (Appl Stattist unit, Indian Statitistics Unit, 203, B.T. Road, Calcutta 700 108, Email: subho@isical.ac.in) : Autocorrelation values of highly nonlinear balanced boolean functions on even number of variables. J Indian Statist Ass 2004, 42(2), 219-29.

Highly nonlinear balanced Boolean functions with very good autocorrelation property have wide applications as cryptographic components. A well known construction of balanced Boolean functions by modifying Maiorana- Mc Farland type bent functions in analysed here. It is known that these functions are of very high nonlinearity and good algebraic degree. It has been shown that the functions of this class possess very good autocorrelation property too.

7 ref

009959   Lee K S;Jung S M (Math Educ Dep, Korea Natn Univ of Educ, Choong-Book, Cheong-Won, 363-791 Korea, Email: kslee@knue.ac.kr) : Calculation of chromatic polynomials by use of the broken-circuit modules. J Computnl Math optimiz 2005, 1(3), 131-9.

Several properties of the chromatic polynomials have been proved by use of the graphic arrangements. It is known that one can induce the graphic arrangement from a given graph, and the chromatic polynomial of a graph is the chanracteristic polynomial of the graphic arrangement. The broken-circuit basis has been used to calculate the minimum and maximum possible values of the coefficients of the chromatic polynomials.

5 ref

009958   Lahiri J;Pramanik S;Layk G C;Chakraborty A K; Mazumdar H P (NO, , M.R.B. Vidyamandir, Madhyamgram, 24-Parganas (N), W.B) : Hydromagnetic flow over a heated stretching surface with temperature-dependent viscosity. Bull Calcutta Mathl Soc 2005, 97(3), 207-16.

The effects of a transverse magnetic field on the steady incompressible fluid flow past a heated stretching sheet are investigated. Fluid viscosity is being assumed to vary with temperature. With appropriate similarity transformations, the momentum equations for fluid flow and the equation for energy are reduced to a set of ordinary differential equations, which are then solved mumerically by shooting method. The results are presented graphically and analysed.

6 illus, 1 table, 10 ref

009957   Lahiri B K;Banerjee D (Math Dep, Visva-Bharati Univ, Santiniketan-731 235, Email: indrajit@cal2.vsnl.net.in ) : Relative order of meromorphic functions. Proc Natn Acad Sci India-Sect A 2005, 75(2), 129-35.

In the paper authors has improved some theorems proved earlier and establish the consistency of the definition of relative order of meromrophic functions when the related functions are entire.

5 ref

009956   Lahiri B K;Banerjee D (NO, , B-1/146 Kalyani, West Bengal-741 235) : A note on relative order of entire functions. Bull Calcutta Mathl Soc 2005, 97(3), 201-6.

Regular growth and regular relative growth (with respect to an entire function) of entire functions have been considered and it has been shown that under certain condition they are equal. Also considering the concept of relative exponent of convergence introduced it has been shown that the relative exponent of convergence may exceed the relative order, a major departure from classical result. Further, an analogue of Borel's first theorem connecting relative order and relative canonical product has been presented.

5 ref

009955   Kwasniewski A K (NO, Inst of Computer Sci Bialystok Univ, PL-15-887 Bialystok, UL. Sosnowa 64, Poland, Email: kwandr@uwb.edu.pl) : Extended finite operator calculus - an example of algebraization of analysis. Bull Allahabad Mathl Soc 2005, 20, 1-24.

"A calculus of sequences" started in 1993 by Ward constitutes the general scheme for extensions of classical operator calculus of Rota-Mullin considered by many afterwards and after Ward. Because of the notation the Ward's calculus of sequences will be called in its afterwards elaborated form - a ψ-calculus. The ψ-calculus in parts appears to be almost automatic, natural extension of classical operator of Rota-Mullin or equivalently - of umbral calculus of Roman and Rota.

33 ref

009954   Kotwal K S;Shinde R L (Stattist Dep Sch of Math Sci, North Maharashtra Univ, Jalgaon-425 001, Email: kirtee_kamalja@yahoo.com) : Markov binomial and trinomial distributions. J Indian Statist Ass 2005, 43(1), 15-31.

For the sequence of Markov Bernoulli trials, the Markov Binomial distribution is derived by using renewal theory approach. The probability generating function of Markov Trinomial distribution is obtained in the case of {0, 1,2}-valued time homogeneous Markov chain {X_n, n ≥ 0}. Distributions of some related random variables are also investigated. Numerical aresults on probability distributions are presented based on computer programming.

3 tables, 5 ref

009953   Kon M A;Raphael L A;Williams D A (Math Dep, Boston Univ, Boston, MA, 02215, USA, Email: mkon@math.bu.edu) : Extending Girosi's approximation estimates for functions in Sobolev spaces via statistical learning theory. J Analysis Applic 2005, 3(2), 67-90.

An extension of Girosi's approximation error bound using the notion VC dimnsion in statistical learning theory is derived for kernel spaces, and in particular, L^p Sobpolev spaces L^p_s (R^d), 1 ≤ p <60> λ, s <62>). Applications include non-assymptotic, uniform error bound approximations of f ε L^p_s (R^d) by finite linear combinations of weighted Gaussians with different centers and variances for 1 ≤ p <60> ∞, and by Haar scaling functions when p=2.

33 ref

009952   Koenker R (Economics Dep, Univ of Illinois at Urbana-Champaign, Champaign, IL 61820, USA, Email: rkoenker@uiuc.edu) : Inequality constrained quantile regression. Sankhya 2005, 67(Pt 2), 418-40.

An algorithm for computing parametric linear quantile regression estimates subject to linear inequality constraints is described. The algorithm is a variant of the interior point algorithm described in Koenker and Portnoy (1997) for unconstrained quantile regression and is consequently quite efficient even for large problems, particularly when the inherent sparsity of the resulting linear algebra is exploited. Applications to qualitatively constrained nonparametric regression are described in the penultimate sections. Implementations of the algorithm are available in MATLAB and R.

3 illus, 33 ref

009951   Khan R A (Math Dep, Cleveland St Univ, Cleveland, OH 44115, U.S.A) : A remark on an interesting inequality. Bull Allahabad Mathl Soc 2005, 20, 47-9.

An inequality given by mitrinovic in his book "Analytic Inequalities" is generalized for certain functions whose log transformations are convex.

2 ref

009950   Jutla C S (IBM T. J. Watson Res Cent, , Yorktown Heights, NY 10598, U.S.A) : Building more secure PRFs from PRPs. J Indian Statist Ass 2004, 42(2), 179-87.

Given two independent random permutations P1, and P2 from n bits to n bits and f a fixed 2-to-1 function on n bits, it has been shown that F = P2 o f o P1 is a function, such that it cannot be distinguished from a random function in less that 2^(2/3-c)n queries, where c <62> 0 is any constant.

6 ref

009949   Jureckova J (Statist Dep, Charles Univ in Prague, Sokolovska 83, CZ-186 75 Prauge 8, Czech Republic, Email: jurecko@karlin.mff.cuni.cz) : Two-step regression quantiles. Sankhya 2005, 67(Pt 2), 227-52.

A new version of the regression α-quantile has been proposed in the linear regression model, ordering the residuals with respect to an initial R-estimate of the slope parameter. In this way a consistent estimator of (β₀ + F^-1(α), β₁,..., β_p), asymptotically equivalent to the regression α-quantile of Koenker and Bassett has been obtained. The result is extended to the extreme regression quantiles. Similarly a version of the autoregression quantile in the linear AR(p) model has been constructed. An estimate of the extreme error in the linear regression and autoregression models, using the initial R-estimate of the slope has been proposed. A simulation experiment illustrates a very small difference between the original regression quantiles and their new versions, and a very good approximation of the extreme errors.

4 illus, 3 tables, 27 ref

009948   Jain S;Mangal A (Math Dep, Government Coll, Ajmer-305 001) : Modified fourier elimination technique for fractional programming problem. Acharya Nagarjuna Int J Math Inf Technol 2004, 1(2), 121-31.

A new method has been developed for solving a Fractional Programming Problem (FPP) by adopting Modified Fourier elimination technique of inequalities. The method is quite useful because the calculations involved are simple and takes least time. The method has been illustrated by a numerical example.

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009947   Jain N K;Rakesh Kumar (Statist and Opl Res Dep, Kurukshetra Univ, Kurukshetra-136 119) : M/G/1 queue with catastrophes. Indian J Math mathl Sci 2005, 1(1), 45-50.

An M/G/1 queuing system with catastrophes has been studied. The steady state solution of the model has been derived by using Supplementary Variable technique. Also the Laplace Stieltjes Transform of the virtual waiting time of the queuing model under consideration has been obtained.

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009946   Jaggi C K;Aggarwal K K;Goel S K (Opl Res Dep Fac of Math Sci, Univ of Delhi, Delhi-110 007, Email: ckjaggi@or.du.ac.in ) : A marketing-oriented inventory model for stock-dependent demand rate under permissible delay in payments. Indian J Math mathl Sci 2005, 1(1), 9-21.

A deterministic inventory model for instantaneous stock dependent demand rate with permissible delay in payments has been investigated. The demand rate also depends on marketing parameters viz., price of product and number of insertions in the media. The otpimal number of insertions and optimal cycle length is derived jointly by maximizing the net profit per unit time. The numerical solution of the model is obtained and the sensitivity of the parameters involved in the model is also examined.

4 illus, 3 tables, 23 ref

009945   Huskova M (Statist Dep, Charles Univ of Prague, Sokolovska 83, CZ-186 75 Praha 8, Email: marie.huskova@karlin.mff.cuni.cz) : Bootstrap in detection of changes in linear regression. Sankhya 2005, 67(Pt 2), 200-26.

Applications of bootstrap with and without replacement in change point analysis in linear regression models are discussed. Particularly, bootstrap based approximations for critical values for two classes of M-type test procedures are treated. As a particular case L₁ procedures and regression quantile procedures have been obtained. Their asymptotic performance is investigated and finite sample properties are checked in a simulation study.

8 illus, 5 tables, 19 ref

009944   Huang M N L;Chen R B;Chen Y Y (Appl Math Dep, Natn Sun Yat-Sen Univ, Kaohsiung, Taiwan, 804, R.O.C., Email: lomn@math.nsysu.edu.tw) : C-optimal designs for weighted polynomial models. Sankhya 2005, 67(Pt 1), 90-105.

c-optimal design problems for weighted polynomial models are discussed. Vectors c, where c-optimal designs are supported by some extreme points of a certain equioscillating function, are characterized, and this equioscillating function is a linear combination of the regression functions. These results are then applied to the no-intercept model in which the optimal designs for estimating certain individual parameters can be found. Examples of applications of the above results in finding locally c-optimal designs for some nonlinear models are discussed. Finally the results are extended to a more general linear model.

4 tables, 14 ref

009943   Greenshtein E (Stattist Dep, Haifa Univ, Haifa 31905, Israel, Email: egreensh@stat.purdue.edu) : Prediction, model selection and random dimension penalties. Sankhya 2005, 67(Pt 1), 46-73.

For Z¹,..., Zⁿ be i.i.d. vectors, each consisting of a response and a few explanatory variables, suupose one has K collections of predictors, i.e., collections of functions of the explanatory variables, that predict the response variable. Given the "empirically best" predictor within each of the collections, a criterion to select a predictor from those K candidates based on minimax regret has been suggested also it has been shown how to find an asymptotically optimal selection procedure under this criterion. Then it has been shown how the conventional setting of moodel selection is related to the above. Conventionally, the term `model' refers to a collection of distributions, while its analog in the setting is a collection of predictors. The assumptions about the possible distributios of Z<sup>i</sup> (the model) are non-parametric, while the collections of the predictors are assumed to be `conveniently' parametrized.

1 illus, 19 ref

009942   Ghosh S R;Dasgupta H (NO, , A-9/83, Kalyani-741 235 Nadia, West Bengal, Email: hiranmaydg@yahoo.com) : Classification of points of continuities and discontinuities of a mapping in topological spaces. Bull Calcutta Mathl Soc 2005, 97(4), 283-96.

A distinction between a point of continuity in global sense and a point of continuity in local sense has been pointed out in general topological spaces after classifying points of continuities and discontinuities and also their interrelationships. In particular, a sufficient condition has been found for a bijective open map on a Hausdorff space to be continuous. Furthermore, behaviour of discontinuous functions which closely resemble with continuous functions somewhere are scrutinzied and discussed when the range space is compact and Hausdorff.

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009941   Gasmi A;Soltani F (Math Dep Fac of Sci of Tunis, Univ of EL-Manar Tunis, 2092 Tunis Tunisia, Email: Abdessalem. Gasmi@fst.rnu.tn) : Fock spaces for the Bessel-struve kernel. J Analysis Applic 2005, 3(2), 91-106.

A class of spaces of entire functions associated to the Bessel-struve operator has been studied. Some results regarding the toeplitz operators and the Weyl relations on these spaces have been arrived at.

11 ref

009940   Ganesan G;Rao C R (Math Dep, Jayaprakash Narayan Coll of Engng, Mahabubnagar, Andhra Pradesh, Email: elgee110201@yahoo.com) : Rough fuzzy groups. Indian J Math mathl Sci 2005, 1(1), 1-8.

In any fuzzy system, the fuzzy numbers are used for fuzzification and defuzzification. In parallel, rough fuzzy sets are used to approximate the given fuzzy set with reference to the given crisp knowledge. By using cosets of a subgroup H of a finite Group (G,^*), G can be partitioned. In particular, when the subgroup is normal, the quotient group can be defined. For any fuzzy subset M of G, with respect to the partition obtained by the cosets of any normal subgroup N of G, the rough fuzzy approximations are obtaiend. By using onto isomorphism s from the classes thus obtained to Z_{0 where O (G/N) represents the number of classes, the fuzzy ordered pairs are obtained. Using them, a group is constructed, which is called a rough fuzzy group (G,^*,M,Nσ).}

9 ref

009939   Furno M (NO, , Via Orazio 27D, 80122 Napoli, Italy, Email: furnoma@tin.it) : The Glejser test and the medaian regression. Sankhya 2005, 67(Pt 2), 335-58.

The Glejser test is affected by a non-vanishing estimation effect in the presence of skewness. It has been shown that such effect occurs with contaminated errors as well, and that skewness correction is inappropriate when there is contamination. The use of residuals estimated with conditional median regression (least absolute deviations or LAD), and it has been discussed why LAD is effective against both skewness and contamination. The effectivenes of LAD is confirmed by simulations. Wtih contaminated errors, both standard and skewness corrected Glejser tests perform poorly when based on least squares residuals. However, they perform very well when implemented using LAD residuals. The latter turns out to be a good alternative to bootstrap methods, which is generally used to solve the discrepancy between asymptotic and finite sample behaviour of a test.

3 tables, 11 ref

009938   Filiol E (Army Signals Acad Virol and Cryptology Lab, , B.P. 18, 35998 Rennes, France, Email: eric.filiol@esat.terre.defense.gouv.fr) : Repetition codes cryptanalysis of block ciphers. J Indian Statist Ass 2004, 42(2), 159-78.

A new theoretical model of block cipher cryptanalysis based on the use of a well-known error correcting code: the repetition codes has been presented. First it has been demonstrated how to describe a block cipher with such a code before explaining how to design a new ciphertext only cryptanalysis of these cryptosystems on the assumption that plaintext belongs to a particular class. It has than been shown how known plaintext linear cryptanalysis can be generalized by a more general repetition approach. Two cryptanalysis algorithms are presented. The first one uses a single repetition code while the second one uses concatenated codes whose outer and inner codes are repetition codes. The two algorithms have been compared and it has been proved that thre first one is more efficient than the second one. Open problems and technical parameters are finally given as well as improvements on Matsui's DES cryptanalysis.

2 illus, 1 table, 12 ref

009937   Esposti M D;Farinelli C;Tolomelli A (Math Dep, Universita di Bologna, Piazza di Porta S. Donato 5 1-40127 Bologna Italy, Email: desposti@dm.inibo.it) : Compression estimates for a class of dictionary based compressors. J Computnl Math optimiz 2005, 1(3), 177-98.

A parsing algorithm for estimating the information content of symbolic strings generated by various dynamical systems and biological data have been considered. It has been shown how a suitable coding of the dictionary is sufficient to turn it into optimal compressor.

13 illus, 18 ref

009936   De U C;De B K;Saha D (Math Dep, Univ of Kalyani, Kalyani- 741 235) : On a type of Kaehler space. Bull Calcutta Mathl Soc 2005, 97(4), 319-24.

Generalized projective 2-recurrent Kaehler Spaces have been studied.

6 ref

009935   De Blasi F S;Pianigiani G (Centro Vito Volterra Dipartimento Di Matematica, Universita Di Roma "Tor Vergata" Via Della Ricerca Scientifica, 1-00133 Roma-Italy) : Pseudo-barycenters and approximations of multifunctions in metric spaces. Bull Calcutta Mathl Soc 2005, 97(4), 325-38.

For a class of Pompeiu-Hausdorff upper semicontinuous multifunctions, with values in a convex metric space, continuous ε-approximations are constructed. The approach is based on the notion of pseucdo barycenter and on partition of unity techniques.

16 ref

009934   Dabrowska D M (Biostatistics Dep, Univ of Calif, Los Angeles, CA 90095-1772, USA, Email: dorota@brahms.ph.ucla.edu) : Quantile regression in transformation models. Sankhya 2005, 67(Pt 2), 153-86.

Conditional quantiles provide a natural tool for reporting results from regression analysis based on semiparametric transformation models. Estimation and construction of confidence sets in the presence of censoring have been considered.

3 illus, 1 table, 19 ref