021525   Bandyopadhyay S;Bandyopapdhyay S (NO, Indian Statistical Inst, Kolkata) : Exact density of W classification statistic based on unmatched training sample from correlated populations. Calcutta Statist Ass Bull 2005, 56(Spl), 305-20.

A unit is to be classified into one of two correlated homoscedastic normal populations by W classification statistic. The two populations are like two different states of a disease. A sample unit can be observed in both the states (populations). The observations made on the same unit in the two populations are correlated. W is based on an unmatched training sample where N sample units are observed in both the populations and N_i - N units are observed in population i,i = 1, 2. The exact density of W in such set up is derived for unknown means and commmon dispersion matrix where the correlation linking the populations is known or unknown. Simulated density of W is plotted and probability of correct classification (PCC) is evaluated using simulation.

1 illus, 10 ref

021524   Bali R;Meena B L (Dep of Math, Univ of Raj, Jaipur-302 004) : Bianchi type v cosmological model with stiff fluid. Proc Natn Acad Sci India-Sect A 2005, 75(4), 273-7.

Stiff fluid Bianchi type V tilted cosmological model for perfect fluid distribution in General Relativity, has been investigated. The physical and geometrical aspects of the model are also discussed

35 ref

021523   Bali R;Meena B L (Dep of Math, Univ of Raj, Jaipur-302 004) : Bianchi type V cosmological model with Stiff fluid. Proc Natn Acad Sci India-Sect A 2005, 75(4), 273-7.

Stiff fluid Bianchi type V tilted cosmological model for perfect fluid distribution in General Relativity, has been investigated. The physical and geometrical aspects of the model are also discussed.

35 ref

021522   Arslan G;Ahsanullah M (Statist and Computer Sci Dep, Baskent Univ, 06530 Ankara, Turkey, Email: guvenca@baskent.edu.tr) : On chracteristic properties of the uniform distribution. Sankhya 2005, 67(4), 715-21.

Two characterizations of the uniform distribution using record values have been considered. The first chracterization is based on the relation X_U(m) - X_U(m-1) =^d X_L(m), m <62> 1, where X_U(m) and X_L(m) denote the m-the upper and lower record values, respectively. The second characterization involves the second record range.

14 ref

021521   Arnold B C (NO, Univ of Calif, Riverside, USA) : Procrustean strategies for incompatible conditional and marginal information. Calcutta Statist Ass Bull 2005, 56(Spl), 17-34.

Full or partial information about the marginals and conditionals of a bivariate distribution is likely to be incompatible. Additionally, information may come from heterogenous sources with limited agreement between sources. Some strategies for selecting a single "minimally incompatible" joint distribution are surveyed.

6 ref

021520   Anis M Z;Basu S K;Mitra M (NO, ISI, Kolkata) : Change point detection of failure rate functions. IAPQR Trans 2005, 30(1), 17-32.

Theory of change point analysis finds applications in diverse areas such as stock market analysis, industrial quality control and reliability studies. However, in the paper, which is largely expository in nature. Author has focused on inference problems concerning change points of hazard rate function in the context of reliability analysis. the typical models used by the different authors are critically examined. the models under parametric and non-parametric set ups as also complete and censored data are reviewed. the use of different statistical techniques such as weak converge theory, the theory of L-statistics, TTT transform methods, etc have been highlighted. the applicability of change point models in analyzing certain medical studies data is discussed. Possible directions of further research are indicated.

44 ref

021519   Angers J F;Kim P T (NO, Univ de Montreal, Canada) : Symmetry and Bayesian function estimation. Calcutta Statist Ass Bull 2005, 56(Spl), 57-80.

This paper develops Bayesian function estimationon compact Riemannian manifolds. The approach is to combine Bayesian methods along with aspects of spectral geometry associated with the Laplace-Beltrami operator on Riemannian manifolds. Although frequentist nonparametric function estimation in Euclidean space abound, to date, no attempt has been made with respect to Bayesian function estimation on a general Riemannian manifold. The Bayesian approach to function estimation is very natural for manifolds because one can elicit very specific prior information on the possible symmetries in question. One can then establish Bayes estimators that possess built in symmetries. A detailed analysis for the 2-sphere is provided.

37 ref

021518   Ali M M;Nadarajah S (NO, Univ of Nebrasha, USA) : On the ratio of weibull random variables. IAPQR Trans 2005, 30(1), 43-52.

Distribution of the ratio X/Y is derived when X and Y are independent Weibull random variables. Extensive tabulations of the associated percentage points are also given.

1 illus, 14 ref

021517   Ahsanullah M (NO, Rider Univ, USA) : Weak records of geometric distribution. Calcutta Statist Ass Bull 2005, 56(Spl), 295-303.

Upper weak record values from sequence of independent identically distributed random variables are considered. Several distributional properties of the upper weak records from geometric distribution are presented. Based on these distributional properties some characterizations of the geometric distribution are given.

7 ref

021516   Ahmad M K;Salahuddin (Math Dep, Aligarh Muslim Univ, Aligarh-202 002, Email: ahmad_kalimuddin@yahoo.co.in) : On parametric generalized nonlinear implicit quasi-variational inclusions. Int J mathl Sci 2005, 4(2), 247-59.

The sensitivity analysis for generalized nonlinear implicit quasi-variational inclusions and generalized implicit proximal operator equations have been considered. The equivalence between the prarametric generalized nonlinear implicit quasivariational inclusions and parametric generalized implicit proximal operator equations by using the proximal operator technique without diffeaentiability of the given data have been established.

11 ref

021515   Aghalary R;Ali R M;Joshi S B;Ravichandran V (Math Dep, Univ of Urmia, Urmia, Iran, Email: raghalary@yahoo.com) : Inequalities for analytic functions defined by certain linear operators. Int J mathl Sci 2005, 4(2), 267-74.

Inequalities for analytic functions have been obtained in the open unit disk which are associated with the Dziok-Srivastava linear operator H^l,m_p and the multiplier transform I_p (n,λ).

17 ref

020542   Wu Z (Math and Statist Dep, Univ of Victoria, Victoria, B.C. Canada V8W 3P4, Email: ziliwu@email.com) : Characters of various convergent sequences. Far East J mathl Sci 2005, 19(2), 231-44.

For a sequence of complex-valued measurable functions the characters of almost uniform convergence, convergence in measure and convergence in L¹ from which Egoroffs Theorem, Riesz's Theorem and the Dominated Convergence Theorem follow respectively have been presented. Various sufficient conditions for exchanging the order of integration and limit for a convergent sequence in different senses have been sumamrised.

6 ref

020541   Vajjiravelu S;Sathya R;Iyengar N C S N (Sch of Computer Sci, Vellore Inst of Technol Deemed Univ, Vellore-632 014) : Key management associated with symmetric and asymmetric cryptography. Far East J mathl Sci 2005, 19(2), 133-43.

Cryptography is the art and science of encoding and decoding messages using mathematical algorithms that utilize a secret key. The concept has broadened to include managing messages that have some combination of privacy (by being unreadable to anyone but the sender and receiver); integrity (not modified while en route), and non repudiation (digitally signed in such a way that the originator cannot plausibly claim he or she did not originate it). Cryptographic keys are used to encrypt/decrypt data or to create/verify digital signatures. The secure distribution of these keys to the appropriate communicting parties is referred to as a key distribution or key establishment. The life cycle associated with the initialization, distribution, and cancellation of the keys is referred to as key management, with particular emphasis on key distribution.

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020540   Trell E (Primary Hlth Care Dep, Fac of Hlth Sci, SE-581 83 Linkoping, Sweden, Email: eritr@ihs.liu.se) : An excursion in and between curvature II. From classical lie algebra neighbourhood to QED and QCD of real elementary particles. Bull Calcutta Mathl Soc 2005, 97(6), 573-88.

Earlier Diophantine equation system and solutions were completely reproduced within the zero curvature Euclidean space of reconfirmed flat Universe. The continuation from the Straight to and within the Round endless form category exhaustively and exactly regenerates the elementary particle spectroscopy. When nanotechnology continues to reveal that elementary particles structurally appear and behave just as macroscopic matter down to the very level where they enter the observable physical reality this faithful real form representation and animation are most useful and valuable both per se and as manifested mathematics where visualized from embodies and performs the deeper formulas and logics beyond.

6 illus, 1 table, 60 ref

020539   Trell E (Hlth Sci Fac Linkoping Univ, Univ of Linkoping, SE-581 83 Linkoping, Sweden, Email: erit@ihs.liu.se) : An excursion in curvature I. Diophantine equations get real again in re-established flat euclidean space. Bull Calcutta Mathl Soc 2005, 97(6), 551-72.

The `hyperbolic jungle' is embedded in three-dimensional flat space, whose smallest constitutional bits are cubical. The genuine Euclidean canvas and its `cuBit' eigenvectors are retrieved both by historical source-searching and by self-generation, self-ordering and self-aggregation according to modern nanotechnology as well as `principle of duality' logics. This also provides the real parameterization, encapsulation and solution of the original Diophantine Equations and direct demonstration of Fermat's Last Theorem and Beal's conjecture and virtual quantum cavity incubation of the elementary particle spectroscopy.

5 illus, 66 ref

020538   Shuping G;Zhaolin J;Pengge Z (Gao Shuping and Zhang Pengge Math Dep, Xidian Univ, Xi'an, 710071, Shaanxi, China, Email: xdgaosp@263.net) : Algorithms of multi-objective transportation problems with uncertain coefficients. Far East J mathl Sci 2005, 19(2), 201-13.

Multi-objective transportation problems with uncertain coefficients have been discussed. The interval numbers and fuzzy numbers programmings of multi-objective transportation problem are proposed, respectivley. For the model of interval numbers prograamming an optimal satsifactory degree solution has been found by introducing the satisfactory degree function. The fuzzy programming with trapezoidal fuzzy number coefficients is reduced to multi-objective linear programming on the basis of a α-cut of the fuzzy numbers, that α level optimal solutions are obtained. Compared with existing methods. Finally numerical examples are illustrated the effectiveness and practicality of the proposed algorithms.

2 tables, 9 ref

020537   Sharma P R;Sharma S (Math Dep, Univ of Raj, Jaipur, Rajasthan) : Unsteady two-dimensional flow and heat transfer through an elastico-viscous liquid along an infinite hot vertical porous surface bounded by porous medium. Bull Calcutta Mathl Soc 2005, 97(6), 477-88.

Investigates unsteady two-dimensional flow and heat transfer through an incompressible elastico-viscous liquid [Walters fluid fluid (Model B')] along an infinite hot vertical porous surface bounded by porous medium with variable suction velocity and variable free stream. The governing equations of motion and energy are solved by the successive perturbation technique. The velocity and temperature distributions are derived, discussed numerically and shown through graphs. The expressions of skin-friction coefficient and Nusselt number at the surface are derived, discussed numerically and their numerical values for various values of physical parameters are presented.

4 illus, 1 table, 30 ref

020536   Saraf R;Navalagi G (Math Dep, Govt K.N.G. Coll, DAMOH-470 661) : Weak and strong forms of α-irresoluteness in fuzzy topological spaces. Int Rev pure appl Math 2005, 1(2), 213-22.

Three new classes of functions using fuzzy gα-closed sets called ap-F α-irresolute functions, ap-F α-closed functions and contra fuzzy α-irresolute functions have been introduced and studied. The connections between these functions and other existing fuzzy topological functions are studied. Also, the characterizations of fuzzy α- T_1/2-spaces have been obtained via these defined functions.

13 ref

020535   Samanta H K (Math Dep, Univ of Burdwan, Burdwan-713 104) : On intersection of multifunctions in locally convex linear topological space. Bull Calcutta Mathl Soc 2005, 97(6), 543-50.

A suficient condition under which the intersection of two polarly upper semi-continuous multifunctions is still polarly upper semi-continuous in locally convex linear topological space has been obtained. Moreover the concept of intersection of multification is applied to the optimization problems of both equality and inequality type of constraints.

8 ref

020534   Salvi R (Math Dep, Politecnico di Milano, P.zza L. da Vinci 32,20133 Milan, Italy) : Existence and uniqueness results for non-newtonian fluids of the oldroyd type. Int Rev pure appl Math 2005, 1(2), 165-212.

A full system of equations modelling the motion of a fluid/solid physical system has been developed. If the solid is a viscohyperelastic material.A differential model (Oldroyd type model) for viscoelastic fluids is obtained. The unique solvability of the system of equations is established locally in time and globally in time with so called smallness restrictions. Moreover, existence of a weak solution is treated.

15 ref

020533   Ryoo C S;Jang L C;Kim T;Rim S H (Math Dep, Hannam Univ, Daejeon-306 791, Korea) : Restudying q-bernoulli polynomials with mathematica. Int Rev pure appl Math 2005, 1(2), 143-53.

Some formulae of q-Bernoulli polynomials using generating function have been given and the behaviour of the real roots of the q-Bernoulli polynomials βn,q (x) have been discussed for values of the index n by using computer.

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020532   Ram Nivas;Verma G (Math and Astr Dep, Univ of Lucknow U.P., Lucknow, Email: mivas@sify.com) : HSU - structure in the cotangent bundle. Bull Calcutta Mathl Soc 2005, 97(6), 503-10.

Tangent and cotangent bundle of a diffferentiable manifold have been studied by Yano, Ishihara (1973), Yano and Patterson (1967) and others. The Hsu-structure in contangent bundle have been studied. Some interesting results have been proved.

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020531   Rajagopal R;Magesh N;Selvaraj C (Appl Math Dep, Debub Univ, Post Box No. 05, Awassa, Ethiopia, Email: rajamrajagopal@yahoo.co.in) : On a subclass of close-to-convex function of order α. Int Rev pure appl Math 2005, 1(2), 223-8.

A subclass of close-to-convex function is defined and its properties like co-efficient estimates, distortion theorems, radius of convexity and other properties are studied.

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020530   Natarajan P N (NO, , Old No. 2/3, New No. 3/3, Second Main Road, R.A. Puram, Chennai-600 028, Email: pinnangudinatarajan@hotmail.com) : On translativity of weighted means in non-Archimedean fields. Indian J Math 2005, 47(2-3), 123-30.

If K denotes a complete, non-trivially valued, non-archimedean field sequences and infinte matrices have entries in K. A few theorems on the translativity of the weighted means or (N^-, pn) methods in K have been proved.

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020529   Nashine H K (Math Dep, Raipur Inst of Technol, Mandir Hasaud, Chhatauna, Raipur-492 101, Email: hemantnashine@rediffmail.com) : Existence of best approximant for generalized I-nonexpansive maps in non-convex set. Indian J Math 2005, 47(2-3), 279-88.

Some results on existence of best approximant in terms of a common fixed point for generalized I-nonexpansive mappings without using the starshapedness condition of domain and affineness condition of mappings in a Banach space are established. The work generalizes the recent result of Shahzad and the result of Mukherjee and Som. A property known as property (Γ) is defined to restore the affineness nature of mappings.

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020528   Narasimhamurthy S K;Bagewadi C S (PG Stud in Math Dep, Kuvempu Univ, Jnana Sahyadri, Shankaraghatta-577 451, Shimoga, Email: nmurthysk@rediffmail.com) : Submanifolds of H-conformally flat Finsler space. Bull Calcutta Mathl Soc 2005, 97(6), 523-30.

Let F^m be a submanifold of a Finsler space Fⁿ. It has been proved that an umbilical submanifold of constant curvature of an H-conformally flat Finsler space is an umbilical submanifold of type k and its converse part. It has been shown that a totally umbilical Finsler submanifold of type k of an affinely connected H-conformally flat recurrent Finsler space, whose recurrent vector is normal to the submanifold is of minimal variety if and only if it is Minkowskian.

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020527   Mittal M L;Uaday Singh;Mishra V N;Priti S; Mittal S S (Math Dep, IIT Roorkee, Roorkee-247 667, Email: mymitfma@iitr.ernet.in) : Approximation of functions (signals) belonging to lip (ξ(t), p)-class by means of conjugate fourier series using linear operators. Indian J Math 2005, 47(2-3), 217-29.

Mittal and Rhoades have initiated the studies of error estimates E_n (ƒ) through Trigonometric Fourier Approximations (t.f.a) for the situations in which the summability matrix T does not have monotone rows. Degree of approximation of function ƒ, conjugate of a periodic function ƒ, belonging to Lip (ξ (t), p) -class by matrix (without monotone rows) operators on a conjugate series of Fourier series associated with ƒ, The theorem generalizes the results of Lal and Nigam and Qureshi.

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020526   Lokhandwala K;Shah Y K;Shah N H (Statist Dep, Guj Univ, Ahmedabad-380 009, Email: nita_sha_h@rediffmail.com) : Determination of the EOQ under permissible delay in payments allowing partial payment when quantity received is uncertain. Punjab Univ Res J Sci 2005, 55, 43-9.

Inventory problem when delay in payments is permissible and yield is random. In practice, the supplier offers some credit period for settlement of accounts which is advantageous for the retailer in the sense that he can sell the product during that time and can earn some interest on the sales revenue during the permissible period of delay. In this problem facility of a part payment is introduced. The effect of part payment on the optimal solution is studied. The working of the model is illustrated with the numerical example.

8 tables, 9 ref

020525   Lin C S (Math Dep, Bishop's Univ, Lennoxville, Quebec, Canada, J1M 1Z7, Email: plin@ubishops.ca) : On strictly convex space, inner product space and their characterizations. Far East J mathl Sci 2005, 19(2), 121-32.

An inner product space has been characteised in terms of a strictly convex space, and the space having the Property C. A general condition is given which characterizes inner product spaces among normed linear spaces; and it has been shown in particular that many classical conditions are its special cases.

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020524   Lahiri B K;Tiwari K S (B-1/146 Kalyani West Bengal-741 235, , , Email: bklahiri@hotpop.com) : Periodic points of a set-valued mapping. Indian J Math 2005, 47(2-3), 249-57.

Two periodic (possibly fixed) point theorems have been proved for set-valued mappings in a metric space using the Hsausdorff metric.

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020523   Kasuga T;Sakai R (Math Dep, Kumamoto Natn Coll of Technol, Nishigohshi-machi, Kikuchi-gun, Kumamoto 861-1102, Japan, Email: qq6k6yv9@sage.ocn.ne.jp) : Conditions for uniform or mean convergence of higher order Hermite Fejer interpolation polynomials with generalized Freud-type weights. Far East J mathl Sci 2005, 19(2), 145-99.

For the Freud-type weight W²_rQ(x) = <157> x <157>^2r exp(-2Q(x)) the orthonormal polynomials {P_n(W²_rQ; x)}^∞_n=0, have been considered and then the higher order Hermite-Fejer interpolation polynomial based at the zeros {X_kn}ⁿ_k=1 of P_n(W²_rQ; x) was constructed. Certain conditions for L_p-convergence 1 <60> p ≤ <133, of the higher order Hermite-Fejer interpolation polynomials have been given. They are extension of Lubinsky-Matjila Theorem for the Lagrrange interpolation polynomials. The corresponding results for the Laguerre-type weights on R⁺ = [0, ∞) were considered.

9 ref

020522   Jarvis A F;Larcombe P J;French D R (NO, , , Email: A.F.Jarvis@sheffield.ac.uk) : On small prime divisibility of the Catalan-Larcombe-French sequence. Indian J Math 2005, 47(2-3), 159-81.

Some divisibility properties of the general term of the Catalan-Larcombe-French sequence by small primes have been presented, recovering its known 2-adic valuation. New explicit results for divisibility by 3, 5, 7 and 11 are also developed, and the work generalised. Numberical computations lead to some other divisibility criteria and a number theoretic link with the Franel number.

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020521   Hashemi M;Doostie H (Math Dep Fac of Sci, Guilan Univ, P.O.Box 451 Rasht, Iran, Email: m_hashemi@guilan.ac.ir) : On the n-permutational property in semigroups and categories. Far East J mathl Sci 2005, 19(2), 223-9.

Following the study of Longobardi in 1988 on the n-permutational propeprty of the groups and its generalization to the semigroups in 1997. Some properties of n-permutational semigroups have been investigated and this notion to the categories has been generalized.

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020520   Gould H W (Math Dep, West Virginia Univ, Morgantown, WV 265-06-6310, Email: gould@math.wvu.edu) : Classes of iterated binomial transforms. Indian J Math 2005, 47(2-3), 183-203.

Several classes of binomial transforms and their iterations have been defined and explored.

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020519   Gavruta P;Jung S M;Lee K S (Math Dep, Tech Univ of Timisoara, 1900-Timisoara, Romania, Email: pgavruta@email.ro) : Remarks on the pexider equations modulo a subgroup. Far East J mathl Sci 2005, 19(2), 215-22.

Let X and Y be topological vector spaces and K be a countable, discrete subgroup of Y. Assume that functions f, g. h : X → Y satisfy f (x + y) - g(x) - h(y) ∈ K resp. 2f(x + y/2) - g(x) - h(y) ∈ K. Some conditions are established under which there exists an additive function deviating from f, g and h within K.

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020518   Franjic I;Pecaric J;Vukelic A (Fac of Fd Technol and Biotechnol Math Dep, Univ of Zagreb, Pierottijeva 6, 10000 Zagreb, Croatia, Email: ifranjic@pbf.hr) : General Euler-Simpson formulae. Indian J Math 2005, 47(2-3), 139-57.

General Simpson formulae, have been considered, using some Euler-type identities. A number of inequalities, for funcitons whose derivatives are either functions of bounded variation or Lipschitzian functions or R-integrable functions, are proved.

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020517   EKici E (Math Dep, Canakkale Onsekiz Mart Univ, Terzioglu Campus, 17020 Canakkale/Turkey, Email: eekici@comu.edu.tr ) : On gamma-us spaces. Indian J Math 2005, 47(2-3), 131-8.

Gamma-US topological spaces have been introduced and studied. Also, γ-convergency, sequentially γ-compact sets, sequentially γ-continuous functions, sequentially nearly γ-continuous functions, sequentially γ-compact preserving functions and sequentially sub-γ continuous functions have been introduced.

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020516   Doostie H;Maghasedi M (NO, , ) : On the fibonacci length of symmetric groups. Int Rev pure appl Math 2005, 1(2), 155-63.

Calculating and deriving the properties of the Fibonacci length of finite groups have been done since 1990, where the Fibonacci length of the finite group G =<60>a₁,...,a_n<62> is defined to be the least integer l such that for the Fibonacci sequence of the elements of the group G, all of the equalities a_l+k = a_k, k = 1,..., n hold. One of the questions posed in 2002 was the deriving relationships between the lengths of a group and a subgroup of it. This problem has been investigated for the symmetric groups, alternating groups and 2-Sylow subgroups by giving suitable generating sets for them. This adds to the small classes of finite groups for them the Finonacci length have been calculated.

2 tables, 11 ref

020515   Dixit K K;Pathak A L (Math Dep, Janta Coll, Bakewar, Etawah, Uttar Pradesh) : On a new class of close-to convex functions with positive coefficients. Bull Calcutta Mathl Soc 2005, 97(6), 531-42.

A systematic investigation of a new class of close-to convex functions, which is defined in terms of fractional derivative, has been presented. Apart from various coefficient bounds and a number of characterization and disstortion theorems, many useful properties of functions are obtained.

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020514   Deka R K;Mazumdar M K;Soundalgekar V M (Math Dep, Gauhati Univ, Guwahati-781 014, Email: rkdgu@yahoo.com) : Effect of frequency on the transient for stokes's oscillating plate-an exact solution in known functions. Indian J Math 2005, 47(2-3), 205-16.

An exact solution to the transient for Stokes's oscillating plate is derived in terms of time t ant the frequency ω, when the plate oscillating as sin (ωt) or {-cos(ωt)}. It is observed that the maximum of the transient solution shifts towards the oscillating plante as ω increases and this is more in the case of { - cos (ωt) as compared to the case of sin (ωt)}. However, the transient solution which is the difference between the steady-state and starting profile decreases as ω increases showing the existence of steady-state solution. In general, in the presence of frequency the oscillation does not require longer time for transition to decay.

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020513   De U C;Kim Y H;Shaikh A A (Math Dep, Univ of Kalyani, Kalyani-741 235, Email: ucde@klyuniv.ernet.in) : Contact metric manifolds with ξ belonging to the (k, μ)-nullity distribution. Indian J Math 2005, 47(2-3), 295-304.

A study of contact metric manifolds with characteristic vector field ξ belonging to the (k, μ)-nullity satisfying R(X, ζ). C = 0, where R (X, Y) is considered as a derivation of the tensor algebra at each point of the manifold for tangent vectors X, Y and C is the Weyl conformal curvature tensor of type (1,3) has been presented.

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020512   Datta S K (Math Dep, Krishnath Coll, Berhampore, Murshidabad-742 101) : On the growth of composition of entire and meromorphic functions. Indian J Math 2005, 47(2-3), 231-48.

Growth properties of composite entire and meromorphic functions have been studied improving earlier results.

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020511   Bhargava S;Adiga C;Anitha N (Stud in Math Dep, Univ of Mysore, Manasa Gangotri, Mysore-570 006) : On a class of n-parity partitions. Indian J Math 2005, 47(2-3), 289-93.

The notion of N-parity partitions has been introduced and the generating function for a certain class of such partitons has been obtained. Thus it will be possible to relate such partitions to certain compositions.

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020510   Banik S;Kanoria M (Appl Math Dep, Univ of Calcutta, 92 A.P.C. Road, Kolkata-700 009, Email: k_mri@yahoo.com) : Stress distribution in an infinite isotropic plate containing a hole under bending moment. Bull Calcutta Mathl Soc 2005, 97(6), 517-22.

The paper deals with the stress distribution in an infinite isotropic plate containing a hole made up of two equal circular arcs under constant bending moment perpendicular to the neutral axis. The solution has been obtained in an integral form with the use of bipolar co-ordinates. The numerical estimates of the circumferential stress have been obtained for a variety of configuration of the hole and depicted graphically.

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020509   Bandyopadhyay N;Roychoudhuri S K (Math Dep, Burdwan Univ, Golapbag, Burdwan, W.B.) : Thermo-elastic wave propagation without energy dissipation in an elastic half-space. Bull Calcutta Mathl Soc 2005, 97(6), 489-502.

Generalized dynamical theory of thermo-elasticity without energy dissipation (Type II) proposed by Green and Naghdi (GN) (1993) is used to study one dimensional thermo-elastic wave propagation in an elastic half space with plane boundary subjected to a (i) step-input of stress and zero temperature (ii) zero stress and step-input of temperature (iii) zero stress and suddenly applied temperature. The exact discontinuities of the fields at the wave fronts are studied analyzed in detail. The displacement is found to be continuous at both the wave fronts while temperature and stress suffer finite jump at these locations in cases (i) and (ii). In case (iii), displacement suffer finite discontinuity at the two wave fronts while temperature and stress suffer delta function singularity at both the elastic and thermal wave fronts. The results derived are compared with earlier results. In the temperature-rate dependent theory of thermo-elasticity (Green and Lindsay (GL) 1972), though the displacement and temperature are both continuous at both the wave fronts, in the GN theory of thermoelasticity, the temperature and stress suffer finite jumps at these locations in case (i). In case (iii), using GN theory, displacement is discontinuous at the two wave fronts while temperature and stress suffer delta function singularity at these locations. But in the temperature-rate dependent theory (GL theory), it is observed that displacement, temperature and stress-all exhibit delta function singularity at these locations. The thermo elastic theory without energy dissipation brings into light some results not encountered in the previous results obtained by using temperature rate dependent theory of GL. In case (ii), the temperature and stress suffer finite jumps at the two wave fronts in GN theory while the displacement is observed to be continuous at these locations.

7 illus, 17 ref

020508   Baljeet Singh;Jagdish Singh;Ajay Kumar (NO, Govt Coll, Sector 11, Chandigarh-160 011, Email: baljeet@networkindia.net ) : Propagation of thermoelastic waves at a solid-solid interface in presence of cracks. Indian J Math 2005, 47(2-3), 259-78.

The reflection and refraction of plane thermal wave at an interface between a generalized thermoelastic solid half-space and a generalized thermoelastic solid half-space in presence of saturated cracks is studied. The boundary conditions at the interface are solved to obtain six nonhomogeneous equations involving reflection and refraction coefficients. These six equations are solved numerically for a particular model. The reflection and refraction coefficients are plotted against angle of incidence of obliquely incident thermal wave. Various reflected and refracted waves are found affected by the presence of saturated cracks.

7 illus, 30 ref

020507   Bahuguna D;Shukla R K (Math Dep, Indian Inst of Technol, Kanpur-208 016, Email: d_bahuguna@yahoo.com) : Application of Rothe's method to delay differential equations. Bull Calcutta Mathl Soc 2005, 97(6), 511-16.

Semilinear delay differential equation which appears in the study of migration problems in population dynamics have been considered. Rothe's method has been applied to study the time discretization and convergence of the sequence of the approximate solution. The initial boundary value problem has been rewritten as an abstract evolution equation in a Banach space that can be analyzed for the existence and uniqueness of a solution.

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019561   Yadav S P (Math and Computer Applics Dep, Model Sci Coll A.P.B. Univ, Rewa (M.P.), Email: yadavsp@sancharnet.in) : On some asymptotic orders of Jacobi polynomials. J Indian Acad Math 2005, 27(1), 33-8.

Jacobi polynomials are the most general polynomials defined on the interval [-1, 1]. Its particular cases are Trigonometric, Legendre, Ultrasperical, and Laplace polynomials which are versatile tools in many applications. Some asymptotic values of these have been given through Jacobi polynomials in the interval of [-1, 1].

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019560   Wu W (Math Dep, East China Norm Univ, Shanghai-200 062, P.R. China, Email: wwu@math.ecnu.edu.cn) : Non-commutative metrics on matrix state spaces. J Ramanujan Mathl Soc 2005, 20(3), 215-54.

The theory of quantization to introduce matrix versions of metric on the state space of a C^* -algebra and Lipschitz seminorm on the algebra has been used. It has been shown that a lower semicontinuous matrix Lipschitz seminorm is determined by its associated matrix metrics on the matrix state spaces. A matrix metric comes from a lower semicontinuous matrix Lip-norm if and only if it is convex, midpoint balanced, and midpoint concave. The operator space of Lipschitz functions with a matrix norm coming from a closed matrix Lip-norm is the operator space dual of an operator space. These resuts generalize results of Rieffel to the quantized situation.

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019559   Vijayasankar N;Elangovan R;Sathiyamoorthy R (Statist Dep, Annamalai Univ, Annamalai Nagar-608 002) : Estimation of expected time to recruitment usign shock model approach. Bull pure appl Sci-Sect E 2005, 24(1), 195-205.

In studies relating to manpower planning, wastage is an important aspect. Wastage of manpower in any organization would adversely affect the normal routine of the organization. The alternative is to go for recruitments to make up the loss of manpower. Frequent recruitments are also not advised in view of the cost involved. Hence the management would try to carry out the normal activities with the existing available manpower. Policy decisions relating to wages, perquisties, incentives and also targets would result in loss of manpower, since the packages may not be satisfactory. The wastage on successive occasion is linear and cumulative. As and when the cumulative loss of manpower crosses a level called threshold, the organization cannot postpone recruitment. The expected time to recruitment and its variance are derived using the Shock Model and Cumulative Damage process approach.

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