015345   Durge M H;Khobragade N W (Math Dep MJP Educ Campus, Nagpur Univ, Nagpur-440 001) : An inverse unsteady-state problem of thermoelastic deformation of a finite length hollow cylinder in March-Zgrablich transform domain. Bull pure appl Sci-Sect E 2004, 23(2), 265-77.

An attempt has been made to solve two inverse problems of thermoelasticity. In both the problems an attempt has been made to determine the unknown temperature displacement and stress functions on upper plane surface of a thin finite length hollow cylinder occupying the space D: a ≤ r ≤ b, 0 ≤ z ≤ h by applying finite Marchi-Zgrablich transform and Laplace transform techniques. In the first problem the temperature {T(r,z,t)}_z=ξ = f(r,t) is a known function of r and t. The homogeneous boundary condition of the third kind is maintained on the curved surfaces while temperature is maintained at u(r,t) on the lower plane surface of the cylinder. In the second problem the heat flux {∂T(r,z,t)/∂z} = f(r,t) is a known function of r and t. The homogenous boundary condition of the third kind is maintained on the curved surfaces while heat flux is maintained at u(r, t) on the lower plane surface of the cylinder.

7 ref

015344   Dowaikh M A (Dep of Math, Appl Sci Fac, Umm AI-Qura University, Makkah, Saudi Arabia) : Boundary value problem of an infinite plate having a cruvilinear hole and flowing heat. Bull pure appl Sci-Sect E 2004, 23(2), 395-405.

The stress components σ_xx, σ_yy, σ_xy, when an initial heat is uniformly flowing in the perpendicular direction of an elastic plate having a curvilinear hole, are obtained. The method used is called complex variable method Cauchy method. Some applications are investigated. Many special and important cases are discussed and established from the work.

3 illus, 8 ref

015343   Dhanasekhran M;Sudha Balakrishnan S (Dep of Math, Thanthai Periyar Govt. Inst of Technol, Vellore, T.N, Email: dhanskar2000@yahoo.co.in) : Analysis of an M/G/1 retrial queue with unfilled requests repeated of multi-class customers. Bull pure appl Sci-Sect E 2004, 23(2), 305-13.

Analysis of a single server retrial queue of two classes of customers with feedback has been discussed. In case of blocking, the class-l customer leaves the system forever, whereas the class-II leaves the service area and enters the orbit and wait to be served later. After the service is completed the customers may comeback for service again. The analytical results for the queue length distribution as well as some performance measures of the system under steady state condition are obtained.

15 ref

015342   Das A;Dey A (NO, Indian Statistical Inst, New Delhi) : Designs for Diallel cross experiments with specific combining abilities. J Indian Soc Agric Statist 2004, 57(spl), 247-56.

For the data collected via a diallel cross experiment, a model that incorporates both general and specific combing ability effects has been postulated. Under such a model, conditions are derived for a block design to be orthogonal in the sense that contrasts among the general combining ability effects, after eliminating the block effects, are estimated free from the specific combining ability effects. Conditions are also derived for such a design to be universally optimal. Some remarks are made on the existence of universaly optimal designs.

8 ref

015341   Chaudhuri A (NO, Indian Statistical Inst, Kolkata) : Unbiased variance estimation on sub-sampling from a varying probability sample. J Indian Soc Agric Statist 2004, 57(spl), 129-33.

A simple procedure has been presented to estimate unbiasedly a survey population total and the variance of the estimator for the total based on an unequal probability sub-sample from an initially drawn sample by Rao et al. scheme from the population.

5 ref

015340   Chandran K P;Prajneshu (NO, Indian Agric Statist Res Inst, New Delhi) : Computation of growth rates in agriculture: Nonparametric regression approach. J Indian Soc Agric Statist 2004, 57(Spl), 382-92.

The usual parametric approach for growth rate analysis is to assume multiplicative error in the underlying nonlinear geometric model and then to fit the linearized model by "Method of least squares". The deficiencies of this approach are highlighted. It is argued that nonlinear estimation procedures should be employed for fitting the model and then only growth rates should be computed. However, unlike economic data, a peculiarity of data from agriculture is that response variable quite often moves in both upward and downward directions. Accordingly, postulation of a specific functional form for describing response variable is not justified. Fortunately, in such an eventuality, "Nonparametric regression methodology" may be employed which does not require any specification of functional form of the model. In this paper, it is advocated that nonparametric regression approach may be used in estimation of trend to compute growth rate against the usual parametric approach. As an illustration, total foodgrain production of India during the period 1987 to 2001 is considered and growth rate is computed.

2 illus, 1 table, 11 ref

015339   Chakrabarty D (Dep of Statist, Handique Girls Coll, Guwahati-781 001) : A theoretical definition of probability based on common sense. Bull pure appl Sci-Sect E 2004, 23(2), 343-9.

A theoretical definition of probability, that has been thought of as a basis of searching for method/methods of determining the exact value of the probability of an event, has been derived logically starting from the common sense (or common meaning) of the two terms viz. "chance" and "probability". Also, the basic properties of probability that are theorems derived from its classical approach and which are the axioms of its axiomatic definition have been derived from the theoretical definition introduced.

20 ref

015338   Arya A S;Arya P (NO, Indian Agric Statist Res Inst, New Delhi) : Circulant designs: Critical review and new insights. J Indian Soc Agric Statist 2004, 57(spl), 289-308.

A detailed and critical review of cyclic and circulant designs with their application aspect and speciality has been presented. New results on the construction, analysis and related problems of circulant designs have been included to make the presentation more comprehensive and meaningful for users in applied fields like Agricultural and Biological sciences.

^iia1 table, 127 ref

015337   Akhtar P M;Sarma K L A P (Dep of Statist, Sri Krishnadevara Univ, Anatapur-515 003) : Optimization of Casp-Cusum schemes based on truncated gamma distribution. Bull pure appl Sci-Sect E 2004, 23(2), 215-23.

Weibull and Gamma distributions are applicable in all the three phases of the Lifetime distribution of any unit. Results relating to CASP-CUSUM schemes based on Weibull distribution have been discussed earlie. CASP-CUSUM schemes based on the continuous variable where the variable under consideration follows a two parametric truncated Gamma distribution. The two parametric Gamma distribution plays a vital role in Statistical Quality Control, particularly in estimating reliability by considering its failure distribution. By suitably changing the parameters of the distribution one can apply in all the three phases of lifetime distribution of product namely (i) Debugging phase (ii) Random Failure Phase, and (iii) Wearout Phase respectively. Optimum CASP-CUSUM schemes are suggested based on numerical results obtained.

11 tables, 4 ref

015336   Agarwal S C;Mittal S K;Sachin Kumar (NO, M.M. (P.G.) Coll, Modinagar-201 204) : Operational behaviour of a parallel redundant complex system with two types of failures with environmental effect under preemptive resume repair discipline. Bull pure appl Sci-Sect E 2004, 23(2), 253-63.

A complex system consisting of two s-independent repairable subsystems A & B in series (1-out-of-2:F.) Subsystem A consists of two identical unit arranged in parallel redundancy (l-out-of 2: G). Subsystem B consists of only one unit with two types of failure viz. partial & catastrophic. Partial failure in B reduces the efficiency 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 arbitrary distribution under preemptive resume repair discipline. Laplace transform of various state probabilities have been evaluated along with steady state behaviour of the complex system. Numerical examples have been added to highlight the important result.

3 illus, 6 ref

014245   Xu H K (NO, Sch of Math Sci Univ of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban 4000, South Africa, Email: xuhk@ukzn.ac.za) : Asymptotic and weakly asymptotic contractions. Indian J pure appl Math 2005, 36(3), 145-50.

Asymptotic contractions have been recently introduced by Kirk, it has been proved by an ultraproduct technique that an asymptotic contraction on a complete metric space has a unique fixed point provided the mapping has a bounded orbit. A simple and elementary proof is given in this note. Moreover, weakly asymptotic contractions are introduced and it is proved that a weakly asymptotic contraction on a complete metric space has a unique fixed point should the mapping has a bounded orbit.

12 ref

014244   Weidong W;Gangsong L (Dep of Math, Shanghai Univ, Shanghai 200436, Peoples' Republic of China, Email: wangwd722@eyou.com) : Lp-dual mixed quermassintegrals. Indian J pure appl Math 2005, 36(4), 177-88.

Associated with the notions of L_P-harmonic radial combination and dual quermassimegrals, is given the "dual" of L_P -mixed quermassintegrals - the notion of L_P -dual mixed quermassimegrals, the L_P -dual mixed volume is its special case. Further an integral representation and inequalities for L_P-dual mixed quermassintegrals have been proved.

8 ref

014243   Tutuncu D K (Dep of Math, Univ of Hacettepe, 06532 Beytepe, Ankara, Turkey, Email: keskin@hacettepe.edu.tr ) : On coclosed submodules. Indian J pure appl Math 2005, 36(3), 135-44.

Let R be a ring and let M be a right R-module. M is called a T-module if M/A ≅ M/B, where A is a coclosed submodule of M and B is any submodule of M, implies that B is a coclosed submodule of M. In this note author introduce T-modules to characterize when any finite direct sum of lifting/discrete modules is discrete. Moreover, It was proved that any amply supplemented module is discrete if and only if it is a ⊕-supplemented T-module. Let M = M₁⊕...⊕M_n be an amply supplemented module. It has been proved that M is a T-module if and only if every M_i is a T-module and M₁, M_n are relatively projective.

8 ref

014242   Sundar P;Graef J R (Dep of Math, Kandaswami Kandar Coll, Paramathi Velur-638 182) : Positive solutions of an odd order neutral nonlinear delay difference equation. Indian J Math 2005, 47(1), 33-50.

Author has considered the nonlinear neutral difference equation Δ^m [y(n)-p(n) y (n-k)+q(n) Π<124> y (n-σ_i) <124>^α1 sgn y (n-σ_i]=0, (e) where m ≥ 1 is odd, k <62> 0 and σ₁ ≥ are integers, p (n) ≥ 0, q (n) ≥ 0, α_i <62> 0, for i= 1, 2,,l and Σ¹_i=1 α₁=1. A comparison theorem is proved and as a consequence, some new oscillation criteria for (e) are derived.

21 ref

014241   Srivastava R C (Dep Math and Statist, D.D.U. Gorakhpur Univ, Gorakhpur, Email: ramesh_maths_ddu@indiatimes.com) : Interaction of reflected shock waves in a cubical cavity. Natn Acad Sci Lett 2005, 28(1-2), 13-20.

The three dimensional shock wave interaction with plane walls in a cubical cavity is investigated numerically. The shock waves are generated by the explosion of a centered gas volume of high pressure in cubical or spherical shape, symmetrically positioned around the midpoint of the cube. The shock capturing technique is used to follow the propagation of strong planear spherical shock waves. The shock waves are reflected specularly at the rigid walls and interact with the shocks moving towards the edges and corners of the cube. Especially focussing effects are investigated after long calculation times. The conservation of energy in the cube is analysed pointwise. The symmetry preserving character of the difference scheme is analysed for long computational times. The numerical model is based on the strong conservative form the the three-dimensional time-dependent system of the Eulerian equaitons.

7 illus, 24 ref

014240   Singh S L;Ashish Kumar;Hashim A M (Dep of Math, Gurukula Kangri Univ, Hardwar, Email: vedicmri@sancharnet. in) : Fixed points of contractive maps. Indian J Math 2005, 47(1), 51-8.

In metric fixed-point theory, fixed-point theorems for contractive maps require the continuity of maps and compactness of the space. The purpose of the paper is to obtain fixed-point theorems for maps satisfying contractive type maps on (not necessarily complete) metric spaces, wherein, besides other relaxations, the continuity of maps is replaced by reciprocal continuity. A pair of reciprocally continuous maps may be discontinuous on a metric space. The remarkable aspect of such fixed-point theorems is that the maps may be discontinuous at their common fixed point.

22 ref

014239   Singh S L (NO, , 21, Govind Nagar, Rishikesh-249 201, Email: vedicmri@sancharnet.in) : Remarks on Sarkhel's comparison of Banach and Kannan contraction. Natn Acad Sci Lett 2005, 28(3-4), 117-18.

Show that Sarkhel's conclusion is true only if the Banach contraction constant is less than 1/3.

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014238   Singh P;Gill A N (Dep of Math, Guru Nanak Dev Univ, Amritsar) : Multiple three-decision procedure: exponential case. Panjab Univ Res J Sci 2004, 54, 27-36.

Let an observation from population or system π_i follow exponential distribution with probability density function (pdf), f(x|μ_i, ϑ_i) = (1/ϑ_i)exp[-(x - μ_i)/ϑ_i]I_[<109>i,∞](x) where μ_i (-∞ <60> μ_i <60> ∞ is the location parameter, ϑ_i(ϑ_i <62> 0) is the scale parameter and I_A(X) is the indicator function of event A, i= 0,1,...,k. The population π_i(π₀) is called the treatment (control) population, i= 1,...,k. In this paper, a multiple three-decision procedure, based on equal sample sizes say n from the treatment populations and a sample of size n₀ (possibly different from n) from the control population, for two-sided comparisons of treatments better than the control (μ_i-μ₀ <62> 0) and the treatments worse than the control (μ_i-μ₀ <60> 0) on the lines of Bohrer (1979), Boher et al. (1981) and Liu (1997), is proposed such that for a given a α (0 <60> α <60> 01) the probability of no misclassification is at least 1-α irrespective of the configuration of μ = (μ₀, μ₁,..., μ₁). The constants necessary for the implementation of the proposed procedure have been provided. The scale version of the proposed procedure has also been discussed with application to normal probability distribution models.

10 tables, 7 ref

014237   Singh K D;Gorla M G;Hans Raj (Dep of Math, ICDEOL Himachal Pradesh Univ, Summer-Hill, Shimla) : A periodic solution of oscillatory couette flow through porous medium in rotating system. Indian J pure appl Math 2005, 36(3), 151-9.

Exact solution of oscillatory Ekman boundary layer flow through a porous medium bounded by two horizontal flat plates is obtained. One of the plates is at rest ana the other oscillating in its own plane. The entire system rotates about an axis normal to the plates. The effects of conolis force and the permeability of the porous medium on the flow field are studied. It is found during, mathematical Analysis that even in the special case of resonance (w = 2Ω) the solution obtained by Mazumder is incorrect as contended by Ganapathy.

1 illus, 1 table, 23 ref

014236   Shankar P N (Computnl and Theoretical Fluid Dynamics Div, Natn Aerospace Laboratories, Bangalore-560 017, Email: pn_shankar55@rediffmail.com) : A new separation of variables method for complex geometries. Curr Sci 2005, 88(2), 266-9.

A procedure has recently been discovered by which the classical separation of variables method can be extended to solve linear boundary value problems for complex geometries. In brief, the procedure consists of embedding the given complex geometry in a larger domain on which complete sets of eigenfunctions exist The latter are then used to represent the field in the given complex geometry. Since the eigenfunctions are not in general orthogonal on the given boundary, the unknown coefficients are evaluated by a least squares procedure. The details in a specific example, that of two-dimensional heat conduction in a solid of complex shape, are given so that the method can be easily understood and applied. In this case the field satisfies Laplace's equation with given data on the boundary. Since the method is simple and easy to apply, it provides an efficient, extremely accurate and elegant alternative to brute force computation. It is hoped that the method will be taught to college and university students who should have no difficulty in grasping it.

3 illus, 1 table, 3 ref

014235   Sajid M;Kapoor G P (Dep of Math, Indian Inst of Technol, Kanpur-208 216, Email: msajid@iitk.ac.in) : Dynamics of non-critically finite odd transcendental meromorphic function λ sinh z/x<. Indian J pure appl Math 2005, 36(4), 203-21.

The dynamical behaviour of non-critically finite odd transcendental meromorphic function ψ_λ(z)= λ sinh z/z² is described. Bifurcation in the dynamics of ψ_λ(x) is shown to occur at λ = λ* (= 2.69528), where λ* = x³/sinh x and x is the unique positive real solution of the equation tanh x=x/3. The images of the Julia sets of ψ_λ (z) are computer generated by using the characterization of its Julia set as the closure of the set of points with orbits escaping to infinity under iterations.

5 illus, 1 table, 21 ref

014234   Rajneesh Kumar;Leena Rani (Math Dep, Kurukshetra Univ, Kurukshetra-136 119, Email: rajneesh_kuk@ rediffmail.com ) : Mechanical and thermal sources in generalized thermoelastic half-space with voids. Indian J pure appl Math 2005, 36(3), 113-33.

The dynamic response of a homogeneous, isotropic, generalized thermoelaslic half-space with voids subjected to time harmonic normal force and thermal source is investigated by applying the Fourier transform. The displacements, stresses, temperature distribution and change in volume fraction field so obtained in the physical domain are computed numerically and illustrated graphically. The numerical results of these quantities for magnesium crystal-like material are illustrated to depict the effect of various sources in the Lord-Shulman (L-S)] theory and Green-Lindsay (G-L) theory for an insulated boundary and temperature gradient boundary. Some particular cases have been deduced.

12 illus, 25 ref

014233   Manish Kumar;Rani M (Dep of Computer Applic, Shri Ramswaroop Coll of Engg. and Mgmt U.P. Tech Univ, Tiwariganj, Faizabad Road Lucknow-226 018, Email: mani_kr_2000@yahoo.com) : An experiment with summability methods in the dyanamics of the logistic model. Indian J Math 2005, 47(1), 77-89.

The main purpose of the paper is to introduce Norlund summability methods in the dynamics of the logistic function. The experimental analysis shows some striking features in this new kind of dynamics.

11 ref

014232   Magill K D (NO, , Mathematics Building, Room 244, Suny At Buffalo Buffalo, NY 14260-2900 USA, Email: kdmagill@acsu.buffalo.edu) : Characterizations of some rings within the class of nonassociative euclidean nearrings. Indian J Math 2005, 47(1), 91-7.

Author determined up to isomorphism, all those nonassociative Euclidean nearrings Nⁿ with additive group Rⁿ, the n-dimensional Euclidean group where Nⁿ contains n linearly independent elements, some of which are left identities, and the remainder of which are left annihilators. Showed that, in fact, these are all associative rings. Determine the ideals and quotient ring of these rings and investigated the multiplicative semigroups of these rings.

8 ref

014231   Ma R (Dep of Math, Northwest Norm Univ, Lanzhou-730 070, P.R. China) : Multiplicity result for an m-point boundary value problem at resonance. Indian J Math 2005, 47(1), 15-31.

Deals with second order m-point value problem u" (t)= ƒ (t,u(y)), t ∈ (0,1) u' (0)=0, u(1)=Σ^m-1_i=1 a_iu (ξ_i), where ƒ: [0,1]x R →R is continuous, a_i, and ξ_i ∈ [0, ∞) are given constants such that Σ^m-1_i=1 a_i=1, and 0= ξ₁ <60> ξ₂ <60>...<60> ξ_m-1 <60> ξ_m =1. Author has developed the methods of lower and upper solutions by the existence of connected sets of solutions to parameterized families of equations. As applications of these methods, Authors get several multiplicity results for the problems under consideration.

15 ref

014230   Khurana S S (Dep of Math, Univ of Iowa, Iowa City, Iowa 52242, U.S.A.) : Measures with τ-smooth marginals. Indian J pure appl Math 2005, 36(4), 169-75.

An example is given of two τ-smooth positive measures μ₁, μ₂ on completely regular Hausdorff spaces X₁, X₂, and a net [ν_α] of τ-smooth positive measures on X₁ x X₂ such that the marginals of {ν_α} converge to μ₁, μ₂ but {ν_α} converges to a non-τ-smooth measure. It is proved that if μ₁ is tight then ν_α converges to a τ-smooth measure. As a consequence, a Strassen type theorem is proved for τ-smooth measures.

10 ref

014229   HE L;FU S;Yan X (NO, Coll of Math and Inf Hebei Norm Univ, Shijiazhuang, Hebei, 050U16, Peoples' Republic of China, Email: Iianfa88heinfo.net) : Some dynamical properties of the minimal continuous semi-flows. Indian J pure appl Math 2005, 36(4), 189-201.

The topologgical dynamical properties of minimal continuous semi-flows on a compact metric space have been studied. Firstly a minimal continuous semi-flow with minimal sets of its time-one map have been conducted. Secondly, by using the connection. It has been proved that the minimal continuous semi-flow is a minimal continuous now if its time-one map is open, and for any minimal continuous semi-flow, there is an invariant residual set such that the restriction to the set is a minimal continuous flow. Finally, it has been shown that any noninvertible, minimal continuous semi-flow is a factor of a minimal continuous flow, and there is no noninvertible, minimal continuous semi-flow on a two-dimensional compact manifold.

1 illus, 7 ref

014228   Gupta T;Ballal S;Bharaadwaj N;Kandaswamy (NO, Meenakshi Ammal Dent Coll and Hosp, Chennai) : Vital Statistics. J Conserv Dent 2005, 8(2), 12-14.

Emphasizes the importance of statistics in collection, presentation, analysis and interpretation of comparative data, as any research outcome depends to a large extent on the analysis of the comparative values obtained. Outlines the steps involved in a statistical study, namely-selection of sample size, selection of type of test to be employed and analysis of results in a simplified manner.

8 ref

014227   Gupta N;Saha L M (Dep of Math, Univ of Delhi, Delhi-110 007) : Regularity and chaos in stellar variability. Natn Acad Sci Lett 2005, 28(3-4), 109-15.

A set of equations for coupled oscillator, with nonlinear and non-adiabatic terms describing the model for stellar variability, has been written. Their evolutionary behaviour show period doubling as well as chaotic phenomena when parameters are varied. Such chaotic behaviour may be suppressed by using certain periodic parametric variation. Numerical results show interesting features.

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014226   Calvo D (Dipartimento di Matematica, Universita di Torino, Via Carlo Alberto 10, 10123 Torino, Italy, Email: calvo@dm.unito.it) : Cauchy problem in inhomogeneous gevrey classes for operator with constant coefficients. Indian J Math 2005, 47(1), 59-76.

Deals with the Cauchy problem in the spaces of inhomogeneous Gevrey functions, that extend the standard Gevrey classes by means of the Fourier transform and are based on a given weight function. The well posedness is proved for a class of weakly hyperbolic operators with constant coefficients, characterized by some weighted Levi-type conditions on the lower order terms.

16 ref

014225   Baruah N D;Bora J (Dep of Math Sci, Tezpur Univ, Napaam-784 028, Email: nayan@tezu.ernet.in) : New of Ramanujan's modular equations of degree 9. Indian J Math 2005, 47(1), 99-102.

Authors find new proofs of some of Ramanujan's modular equations of composite degree 9 by using his theta-function identities.

13 ref

014224   Acharya M;Sinha D (Dep of Appl Math, Delhi Coll of Engng, Bawana Road, Delhi-110 042, Email: mukti1948@yahoo.com) : Characterizations of line sigraphs. Natn Acad Sci Lett 2005, 28(1-2), 31-4.

Given a signed graph (or, in short, sigraph) S = (V, E; σ) on the graph G = (V, E), its line sigraph L(S) is a sigraph defined on the line graph L(G) of G by defining an edge ef in it negative if and only if both e and ƒ are adjacent negative edges in S. In this communication, authors has defined a given sigraph S to be a line sigraph if there exists a sigraph H such that L(H) ≅ S (read as "L(H) is isomorphic to S"). Structural characterizations of line sigraphs, extending the well- known characterization of line graphs due to L.W. Beineke.

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013204   Zhao F Z;Wang T (Appl Math Dep, Dalian Univ of Technol, Dalian-116 024, China) : Some new Rogers-Ramanujan type identities. Bull Allahabad Mathl Soc 2004, 19, 1-8.

By using a transformation formula of basic hypergeometric functions and other result, some new Rogers-Ramanujan type identities have been obtained.

9 ref

013203   Yousefi B;Rezaei H (Dep STOPWORD Math, Coll of Sci, Shiraz University, Shiraz 71454, Iran, Email: byousefi@hafez.shirazu.ac.ir) : Some necessary and sufficient conditions for Hypercyclicity Criterion. Proc Indian Acad Sci-Mathl Sci 2005, 115(2), 209-16.

Necessary and sufficient conditions for an operator on a separable Hilbert space to satisfy the hypercyclicity criterion have been given.

23 ref

013202   Yang Q (Dep STOPWORD Math, Wuhan Univ, 430072 Hubei, China, Email: yangqi99@public.wh.hb.cn) : L<. Proc Indian Acad Sci-Mathl Sci 2005, 115(2), 191-200.

Given a Calderon-Zygmund (C-Z for short) operator T, which satisfies Hormander condition, it has been proved that: if T maps all the characteristic atoms to WL, then T is continuous from L^p to L^p(1 <60> p <60> ∞). So the study of strong continuity on arbitrary function in L^p has been changed into the study of weak continuity on characteristic functions.

12 ref

013201   Subramaniam R (NO, PSG Coll of Arts & Sci, Coimbatore-641 014) : Minimum sample size required for estimating the progeny population of mean and variance. Sugar Tech 2005, 7(2-3), 96-100.

Minimum sample size is defined as the minimum number of individuals necessary to estimate with reasonable precision, mean and variance of seedlings and theirclones of inter-varietal progeny population in sugarcane (Sach sp) through simulation technique.

^ssc8 tables, 7 ref

013200   Singh B;Sharma R K;Singh M (Sch STOPWORD Stud STOPWORD Math, Vikram Univ, Ujjain-456 010) : Common fixed points for weakly compatible maps in uniform spaces. Bull Allahabad Mathl Soc 2004, 19, 27-34.

Some common fixed point theorems for weakly compatible, not necessarily continuous maps which generalize several known corresponding results in uniform spaces have been proved.

14 ref

013199   Shonhiwa T (Math Dep, Swaziland Univ, P.O. Bag 4, Kwaluseni, Swaziland M201, Email: temba@maths.uz.ac.zw) : A note on a class of binomial sums. Bull Allahabad Mathl Soc 2004, 19, 19-26.

Particular case of Binomial sums of the form S_f (n,k) = Σⁿ_i=0 f (i,k) (n/i) has been considered. The generating function for S_f (n,k) has been obtained and for a specific f(n, k) a relationship between S_f(n, k) and A_k (j) = Σ^j_d=k (-1)^{j-d(j/d)[d/k] has been established. The motivation for studying such sums comes from the many identities that arise for particular cases of the function f(n,k), with a reference to Gould and Menon.}

4 ref

013198   Sharma M D (Dep STOPWORD Math, Kurukshetra Univ, Kurukshetra-136 119, Email: mohan_here@rediffmail.com) : Polarisations of quasi-waves in a general anisotropic porous solid saturated with viscous fluid. J Earth Syst Sci 2005, 114(4), 411-19.

Wave propagation is studied in a general anisotropic poroelastic solid saturated with a viscous fluid flowing through its pores of anisotropic permeability. The extended version of Biot's theory is used to derive a system of modified Christoffel equations for the propagation of plane harmonic waves in such media. The non-trivial solution of this system is ensured by a biquadratic equation whose roots represent the complex velocities of four attenuating quasi-waves in the medium. These complex velocities define phase velocity and attenuation of each quasi-wave propagating along a given phase direction in three-dimensional space. The solution itself defines the polarisations of the quasi-waves along with phase shift. The variations of polarisations of quasi-waves with their phase direction, are computed for a realistic numerical model.

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013197   Sharma M D (Dep STOPWORD Math, Kurukshetra Univ, India-136 119, Email: mohan_here@rediffmail.com) : Acceleration of near-field scattering from an inhomogeneous spherical shell. J Earth Syst Sci 2005, 114(4), 401-10.

Three dimensional scattering of near-field, from a point source, is studied for acceleration in the time domain. The perturbation method is applied to define the acceleration for the first order scattering from a weak inhomogeneity in a homogeneous surrounding. A body force, arising from the interaction between the primary waves and the inhomogeneity, acts as the source generating the scattered motion. The acceleration of scattered waves is related to the velocity and density fluctuations of the inhomogeneity. No restrictions are placed on the inhomogeneity size or locations of the source and receiver. Decoupling of scattered motion enables the identification of different phases. Integral expressions are derived for the scattering acceleration due to the incidence of near-field wave (from an impulsive point force) at a radially inhomogeneous volume element. These integrals are solved further for scattering from an inhomogeneous spherical shell. The accelerations for back scattering are obtained as a special case. These accelerations are simple analytically solvable expressions in closed form. Only spherical asymmetry of P wave velocity inhomogeneity can affect the scattered S acceleration. Scattered P acceleration is affected by the gradient of 5 wave velocity inhomogeneity. The back scattering of near-field from a spherical shell, is independent of radial inhomogeneity of P wave velocity. Inhomogeneity with smoothly perturbed S wave velocity does not back-scatter any acceleration. Accelerations are computed numerically for scattering from a part of inhomogeneous spherical shell. Hypothetical models are considered to study the effects of the distances of spherical shell from source, receiver, its thickness and its position relative to the direction of impulsive force.

5 illus, 11 ref

013196   Shankar P N;Kidambi R (Computnl STOPWORD Theoretical Fluid Dynamics Div, Natn Aerospace Laboratories, Bangalore 560 017, Email: pn_snankar55@rediffmail.com) : Contact angle in inviscid fluid mechanics. Proc Indian Acad Sci-Mathl Sci 2005, 115(2), 227-40.

It has been shown that in general, the specification of a contact angle condition at the contact line in inviscid fluid motions is incompatible with the classical field equations and boundary conditions generally applicable to them. The limited conditions under which such a specification is permissible are derived; however, these include cases where the static meniscus is not flat. In view of this situation, the status of the many 'solutions' in the literature which prescribe a contact angle in potential flows comes into question. It has been suggested that these solutions which attempt to incorporate a phenomenological, but incompatible, condition are in some, imprecise sense 'weak-type solutions'; they satisfy or are likely to satisfy, at least in the limit, the governing equations and boundary conditions everywhere except in the neighbourhood of the contact line.

2 illus, 19 ref

013195   Rajneesh Kumar;Ailawalia P (Dep STOPWORD Math, Kurukshetra Univ, Kurukshetra, Haryana, Email: rajneesh_kuk@rediffmail.com) : Interactions of moving load velocity at fluid/micropolar viscoelastic solid interface. Bull Allahabad Mathl Soc 2004, 19, 35-48.

Steady state response of a micropolar viscoelastic solid with an overlaying infinite non-viscous fluid 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, microrotation and stress components are obtained in the transformed domain. The results for micropolar viscoelastic solid and micropolar elastic solid are compared. Variations of moving load velocity on normal displacement, force stress and couple stress have been shown numerically for a particular model.

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013194   Parihar C L;Bansal P (NO, Indian Acad of Math, Indore, M.P.) : Fractional calculus. Bull Allahabad Mathl Soc 2004, 19, 99-108.

Origin of "Fractional Calculus" and its historical development contributed by different mathematicians from mid-nineteenth century to last decades of nineteenth century has been discussed. Although fractional calculus is a generalization of calculus and its mathematical history is equally long. A long standing controversy is also - discussed with modern definition of fractional calculus in twentieth century. Attention has been focused over that definition of fractional calculus, which was proposed by great mathematician Katsuyuki Nishimoto during twentieth century. This may be considerd survey of fractional calculus, which is a part of mathematics, dealing with generalization of derivatives to derivatives of arbitrary order not necessarily an integer. It concerns with study of differentiation and integration to non-integer (fractional) order. With the aid of theory of fractional calculus one can introduce an operator D^v, where v could be rational or irrational, positive or negative, real or complex.

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013193   Mirmostafaee A K (Dep STOPWORD Math, Damghan Univ of Sci, P.O. 36715/364, Damghan, Iran, Email: kmirmostafaee@dubs.ac.ir) : Convex renorming and fragmentability. Proc Indian Acad Sci-Mathl Sci 2005, 115(2), 201-7.

Using the game approach to fragmentability, new and simpler proofs of the following known results: (a)if the Banach space admits an equivalent Kadec norm, then its weak topology is fragmented by a metric which is stronger than the norm topology. (b) if the Banach space admits an equivalent rotund norm, then its weak topology is fragmented by a metric. (c) if the Banach space is weakly locally uniformly rotund, then its weak topology is fragmented by a metric which is stronger than the norm topology are given.

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013192   Mathur P (Dep STOPWORD mathematics, Dav Coll, Kanpur) : (0,1,3)*-Interpolation on the projected zeros of an ultraspherical polynomial on the unit circle. Bull Allahabad Mathl Soc 2004, 19, 49-72.

Authors has extended the study of Siquing Xie's (0, 1, 3)*-interpolation by taking a set of nodes obtained by projecting the zeros of (1-x²)P_n^(λ) (x), where P_n^(λ) (x) is the n^th ultraspherical polynomial with -1/2 <60> λ ≤ 1/2, on the unit circle.

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013191   Lanzhe L (Coll STOPWORD Math STOPWORD Computer, Changsha Univ of Sci and Technol, Changsha 410077, People's Republic of China, Email: lanzheliu@263.net) : Some BMO estimates for vector-valued multilinear singular integral operators. Proc Indian Acad Sci-Mathl Sci 2005, 115(2), 167-90.

Some BMO end-point estimates for some vector-valued multilinear operators related to certain singular integral operators have been proved.

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013190   Kausz I (NWF I - Mathematik, Universitat Regensburg, 93040 Regensburg, Germany) : Twisted vector bundles on pointed nodal curves. Proc Indian Acad Sci-Mathl Sci 2005, 115(2), 147-65.

Motivated by the quest for a good compactification of the moduli space of G-bundles on a nodal curve establishes a striking relationship between Abramovich's and Vistoli's twisted bundles and Gieseker vector bundles.

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013189   Kamra M (Math Dep, Post Grad Regional Cent, Rewari-123 401) : An analogue of plancherel theorem and translation invariant operators on L<. Bull Allahabad Mathl Soc 2004, 19, 9-17.

For a compact abelian group G and a Hilbert space H, it L² (G, H) denote H-valued square integrable functions. An analogue of Plancherel theorem for L² (G, H)is proved. Using this result a characterization of translation invariant operators on L² (G, H) has been given.

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013188   Jensen A;Krishna M (Dep STOPWORD Math Sci STOPWORD MaPhySto, Aalborg Univ, Fr. Bajers Vej 7G, DK-9220 Aalborg <166>, Denmark, Email: krishna@imsc.res.in) : New criteria to identify spectrum. Proc Indian Acad Sci-Mathl Sci 2005, 115(2), 217-226.

Some new criteria for identifying the components of a probability measure, in its Lebesgue decornposition have been given. This enables one to give new criteria to identify spectral types of self-adjoint operators on Hilbert spaces, especially those of interest.

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013187   Dey A;Parthasarathi R (Inst STOPWORD Math Sci, CIT Campus, Taramani, Chennai-600 113, Email: arijit@imsc.res.in) : On harder-Narasimhan reductions for Higgs principal bundles. Proc Indian Acad Sci-Mathl Sci 2005, 115(2), 127-46.

The existence and uniqueness of H-N reduction for the Higgs principal bundles over nonsingular projective variety is shown. The notion of H-N reduction for (T, G)-bundles and ramified G-bundles over a smooth curve have been extended.

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