013580   Tomba I;Ashakiran Y (Mathematics Dep, Manipur Univ, Imphal) : Migration impact on population growth. Biosci Res Bull 2009, 25(2), 93-106.

Roy & Rao (1984) studied the programme impact on fertility by a method known as Standardization technique using the methods introduced by Rutherford and Cho (1973), Rutherford and Ogawa (1978), Das Gupta (1978), classifying the total change in fertility into components as non-programme effect, programme effect and interaction effect. In this paper an attempt has been made to study the impact of migration to population growth by classifying the total change in population growth into components as non-migration effect, migration-effect and inter-action effect. The impact has been analyzed giving the example with the population of Manipur by considering migrants, non-migrants etc.

3 tables, 8 ref

013579   Rosenthal J S (Statistics Dep, Toronto Univ, Toronto, Ontario, Canada M5S 3G3, Email: jeff@math.toronto.edu) : Optimising monte carlo search strategies for automated pattern detection. Far East J mathl Sci 2009, 32(3), 311-28.

Considers the relatively simple computer vision challenge of accurately detecting a "face" within a sea of pixels. Describes an interactive Java applet which accomplishes this task using a Monte Carlo search of the relevant configuration space. Discusses how to optimise various search parameters, both experimentally and by theoretical analysis.

4 illus, 7 ref

013578   Rongbo H;Yanhui L (Mathematics Dep, Guangdong Pharmaceutical Univ, Guangzhou 510006, P.R. China, Email: hrb@gdpu.edu.cn) : Fast implementation of ICA using discrete wavelet transformation. Far East J mathl Sci 2009, 32(3), 407-13.

A fast implementation of independent component analysis using discrete wavelet transformation (FICA) is presented in this paper. PICA is a hybrid architecture which is composed of two ICA processes which takes the high-frequency and low-frequency parts of the input signal decomposed via wavelet as its learning set respectively. The experimental result has shown that FICA successfully extract the independent components from the mixture and reduce a half extracting time cost.

4 illus, 6 ref

013577   Pashazadeh J (NO, Islamic Azad Univ, Branch Bonab, Iran, Email: jm_pashazadeh@yahoo.com) : Isomorphism theorem on algebras of triple semigroup of ternary functions over a set. Far East J mathl Sci 2009, 32(3), 423-30.

Defined algebras of triple semigroup and find an abstract characterization of triple semigroup of ternary functions over a set.

10 ref

013576   Nishimura H (Institute of Mathematics, Tsukuba Univ, Tsukuba, Ibaraki, 305-8571, Japan) : Synthetic vector analysis III from vector analysis to differential forms. Far East J mathl Sci 2009, 32(3), 335-46.

Simplify the discussion considerably in terms of differential forms, leading to the natural derivation of exterior differentiation in the usual form.

8 ref

013575   Matsugu Y;Yamada T (Mathematical Sciences Dep, Faculty of Science, Shinshu Univ, Matsumoto 390-8621, Japan, Email: matsugu@math.shinshu-u.ac.jp) : On stoll-shi's theorem concerning the fractional derivatives of holomorphic functions. Far East J mathl Sci 2009, 32(3), 359-86.

Author proves that the results of Stoll-Shi are still valid for these fractional derivatives R^s,t f and integrals R_s,tf.

6 ref

013574   Kondo M (School of Information Environment, Tokyo Denki Univ, Inzai, 270-1382, Japan, Email: kondo@sie.dendai.ac.jp) : Local commutative residuated lattices. Far East J mathl Sci 2009, 32(3), 347-57.

Authors proved general properties of local commutative residuated lattices, which are extended results, (1) For a commutative residuated lattice L, it is local if and only if ord(x) < ∞ or ord(x*) < ∞ for all x ∈ L. (2) If D is a perfect deductive system and D ⊆ F for a deductive system F, then F is also a perfect deductive system. (3) For a deductive system D, it is an ultra ds if and only if it is a maximal and perfect ds. As a consequence, the results hold at least for the local BL-algebras, local ML algebras, local MTL algebras, local MV algebras and so on.

5 ref

013573   Hiremath G R (Mathematics and Computer Science, North Carolina Pembroke, Pembroke, NC 28372, U.S.A.) : New conditions that make countably compact spaces compact. Far East J mathl Sci 2009, 32(3), 397-406.

The following results are established. (1) In the class of spaces with quasi strongly (α₁), the following hold: (a) Countable compactness implies compactness. (b) <67>₁ -compactness implies closed completeness. (c) Hereditary <67>₁ -compactness implies Borel completeness. (2) In the class of spaces with strongly (α₁), <67>₁ -compactness implies Borel completeness. (3) In the class of spaces with quasi (S₁) property, the following hold: (a) wΔ spaces are 6-refinable, regular spaces if and only if they have (C₂). (b) wΔ spaces are 6-refinable, regular spaces if they have semi-(C₂). (c) wM spaces are Hausdorff paracompact if and only if they have (C₂). (d) wM spaces are Hausdorff paracompact if they have semi- (C₂).

13 ref

013572   Guangshi X (Mathematics Dep, Nanjing Univ of Aeronautics and Astronautics, Nanjing 20016, P.R. China, Email: xgs01cn@yahoo.com.cn) : On strongly regular rings and SF-rings. Far East J mathl Sci 2009, 32(3), 387-96.

Some new properties of rings whose every maximal left (right) ideal is a quasi-ideal are given. Some characterizations of strongly regular rings are proved. A ring R is strongly regular if and only if (1) R is a left SF-ring whose every maximal left (right) ideal is a quasi-ideal if and only if (2) R is a left SF-ring whose every maximal essential left (right) ideal is a quasi-ideal and every idempotent is left semicentral if and only if (3) R is a left SF-ring whose every maximal essential left (right) ideal is a quasi-ideal and every complement right ideal is an ideal if and only if (4) R is a left SF-ring and r(a) is a quasi-ideal for any a ∈ {x | x^{2 = 0, x ∈ R}. In addition, we prove that if R is a left SF-ring whose every maximal essential left ideal is a quasi-ideal, then R is regular.}

16 ref

013571   Chen X R;Pan L J (Mathematics Dep, Jia Ying Univ, Meizhou Guangdong, 514015, P.R. China, Email: cxrgd@tom.com) : Existence of periodic solutions for third order differential equations with deviating argument. Far East J mathl Sci 2009, 32(3), 295-310.

By employing the coincidence degree theory of Mawhin, investigate the existence of periodic solutions for third order differential equations with deviating argument x'"(t) + ax"(t - tτ₂(t}) + bx'(t- τ ₁(t)) + cx(t) + f(t-x(t-τ(t)}) = p(t). Some new results on the existence of periodic solutions of the equations are obtained. Our theorems are related to not only a, b, c and f(t, x) but also the deviating arguments τ(t), τ₁ (t) and τ₂(t).

13 ref

013570   Chen X;Huang H;Wang Z (NO, National Univ of Defense Technology, Changsha, CO 410073, China, Email: cxhueann@63.com) : Success probability assessment based on information entropy. Def Sci J 2010, 60(3), 271-5.

The Bayesian method is superior to the classical statistical method on condition of small sample test. However, its evaluation results are not so good if subjective prior information is intervened. The success probability assessment about the success or failure tests of weapon products focussed in this paper, and a fusing evaluation method based on information entropy is proposed. Firstly, data from equivalent surrogate tests is converted into the prior information of an equivalent source by the information entropy theory. Secondly, the prior distribution of the success probability is identified via the Bootstrap method, and the posterior distribution is provided by the Bayesian method with the information of prototype tests in succession. Lastly, an example is given, and the results show that the proposed method is effective and valuable.

1 illus, 2 tables, 12 ref

013569   Ansari-Piri E;Zohri A (Mathmatics Faculty of Science, Guilan Univ, P.O. Box 1914, Rasht, Iran, Email: eansari@guilan.ac.ir) : Banach precompact elements of a complete metrizable topological algebra. Far East J mathl Sci 2009, 32(3), 329-33.

The compact operators play an important and fundamental role in general operator theory. In this note by generalizing the compactness criterion from normed algebras to general topological algebras, We study some properties of compact operators and precompact elements on Frechet algebras.

4 ref

013568   Ananda Kumar K;Punithavalli M (NO, Dr. S.N.S. Rajalakshmi College of Arts & Science, Ramakrishna College, Coimbatore, Tamil Nadu, Email: anandhsns@yahoo.co.in) : Minimal feature selection using statistical techniques. Adv Computnl Sci Tech 2010, 3(1), 33-8.

Cancer Classification based on microarray gene expression is an important problem. In this work, we use a ANOVA based feature selection method we choose some important genes form thousands of genes, after that, we classify the microarray data sets with a fuzzy neural network (FNN) that we proposed earlier. This FNN combines important features of initial fuzzy model self-organization, parameter optimization and rule-base simplification. We applied this FNN to well-known gene expression data sets i.e., the Lymphoma data set with 3 sub-types. The result in the lymphoma data set show that the FNN can obtain 100% accuracy with a much smaller number of genes in comparison with previously published Our simple yet very effective method involves two steps. In the first step, choose some important genes using an Analysis of Variance (ANOVA) ranking scheme. In the second step, test the classification capability of all simple combinations of those important genes using a good classifier. The approach obtained very high accuracy with only two genes.

1 illus, 2 tables, 22 ref

013567   Al-Hawari M (Mathematics Dep, Jadara Univ, Irbid, Jordan, Email: analysi2003@yahoo.com) : On some nymerical radius inequalities and bounds for the zeros of polynomials. Far East J mathl Sci 2009, 32(3), 415-22.

It is shown that, if A ∈ M_n, then (||A²||1/2)/√2 ≤ w(A) ≤ √√1/2 (||A²|| + ||A²||), and also that, if A and 5 are in M_n, then 2||AB|| ≤ || A* A + BB*|| ≤ 1/2[||A||² + || B ||² + √ (||A||² - || B||²)² + 4|| AB ||²], where w(.) and || . || are the numerical radius and the usual operator norm, respectively. We apply the numerical radius inequality to derive new bounds for the zeros of these polynomials.

13 ref

012447   Akre R S (NO, , 1/5 New Subhedar Lay out, Nagpur-440 024) : Impact of socio-economic status upon attitude towards mathematics. Indian J Psychometry Educ 2008, 39(1), 78-80.

As the twenty first century draws near, the dependency on the technology becomes invariable. UNESCO (1976) reprotedthat literacy is an essential instrument for all the social changes. In India high percentage of illiteracy is a very serious matter. The illiteracy increases due to the 40 percent drop-out rates at the secondary school. The fear in the mathematics subject is one of the reasons of the drop-out from the school. Mathematics plays an important role in the development of the individual as well as nation. Mathematics is the compulsory subject up to the secondary school level. Attitude is one of the Psychological factors to determine the patterns of life as well as the success and happiness. There are some factors and situations to create an attitude to a particular subject. Therefore, the present study reflects on the impact of socio-economic Status upon attitude towards Mathematics. Study may be helpful to achieve "education to all 6-14 years group children ". Study may be helpful to minimise high percentage of illiteracy and to suggest ways in the success of achievement in Mathematics.

1 table, 6 ref

011427   Yang P;Zengji Du;Weigao Ge (Mathematics Dep, Shijazhuang Mechanical Engineering College, Shijiazhuang, Hebei Province 05003, People;s Republic of China, Email: duzengji@163.com) : Solvability of boundary value problem at resonance for third-order functional differential equations. Proc Indian Acad Sci-Mathl Sci 2008, 118(2), 307-18.

Devoted to the study of boundary value problem of third-order functional differential equations. Obtains some existence results for the problem at resonance under the condition that the nonlinear terms is bounded or generally unbounded. In this paper we mainly use the topological degree theory.

17 ref

011426   Valero O (Departamento de Ciencias Mathematicas e Informatica, Universidad de las Islas Baleares, Edificio Anselm Turmeda, 07122, Palma de Mallorca, Baleares, Spain, Email: o.valero@uib.es) : Closed graph and open mapping theorems for normed cones. Proc Indian Acad Sci-Mathl Sci 2008, 118(2), 245-54.

Quasi-normed cone is a pair (X, p) such that X is a (not necessarily cancellative) cone and q is a quasi-norm on X. The aim of this paper is to prove a closed graph and an open mapping type theorem for quasi-normed cones. This is done with the help of appropriate notions of completeness, continuity and openness that arise in a natural way from the setting of bitopological spaces.

32 ref

011425   Shi G;Zhang J (Mathematics Dep, Tianjin Univ, Tianjin 300072, People's Rapublic of China, Email: glshi@tju.edu.cn ) : Positive solutions for higher order singular p-Laplacian boundary value problems. Proc Indian Acad Sci-Mathl Sci 2008, 118(2), 295-305.

Investigates 2m-th (m ≥ 2) order singular p-Laplacian boundary value problems, and obtains the necessary and sufficient conditions for existence of positive solutions for sublinear 2m-th order singular p-Laplacian BVPs on closed interval.

15 ref

011424   Sarkar R P (Stat-Math Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata-700 108, Email: rudra@isical.ac.in) : Abel transform on PSL (2, R) and some of its applications. Proc Indian Acad Sci-Mathl Sci 2008, 118(2), 255-72.

Investigate the use of Abel transform on PSL₂ (R) as a tool beyond K-biinvariant setup, discuss its properties and show some applications.

26 ref

011423   Miao Y U (College of Mathematics and Information Science, Henan Normal Univ, 453 007 Henan, China, Email: yumiao728@yahoo.co.cn) : Central limit theorem and almost sure central limit theorem for the product of some partial sums. Proc Indian Acad Sci-Mathl Sci 2008, 118(2), 289-94.

Central limit theorem and almost sure central limit theorem for products of some partial sums of independent identically distributed random variables.

10 ref

011422   Mehta V B;Subramanian S (School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400 005, Email: vikram@math.tifr.res.in) : Some remarks on the local fundamental group scheme. Proc Indian Acad Sci-Mathl Sci 2008, 118(2), 207-11.

Introduced the local fundamental group scheme and study its properties under base change of the base field.

6 ref

011421   Khashyarmanesh K;Khosh-Ahang F (Mathematics Dep, Ferdowsi Univ of Mashhad, Centre of Excellence in Analysis on Algebrai, P.O. Box 1159-91775, Email: khashyar@ipm.ir ) : On the finiteness properties of matlis duals of local cohomology modules. Proc Indian Acad Sci-Mathl Sci 2008, 118(2), 197-206.

Let R be a complete semi-local ring with respect to the topology defined by its Jacobson radical, a an ideal of R, and M a finitely generated R-module. Let DR(-) := Hom_R (-, E), where E is the injective hull of the direct sum of all simple R -modules. If n is a positive integer such that Ext^{j_R (R/a, DR (Ht_a (M))) is finitely generated for all > n and all j ≥ 0, then we show that Hom_R(R/a, D_R(Hn_a(M))) is also finitely generated. Specially, the set of prime ideals in Coass_R(Hn_a(M)) which contains a is finite. Next, assume that (R, m) is a complete local ring. We study the finiteness properties of D_R(Hr_a (R)) where r is the least integer i such that Hi_a(R) is not Artinian.}

31 ref

011420   Kalelkar T (Stat-Math Unit, Indian Statistical Institute, Bangalore-560 009, Email: tejas@isibang.ac.in) : Euler characteristic and quadrilaterals of normal surfaces. Proc Indian Acad Sci-Mathl Sci 2008, 118(2), 227-23.

Let M be a compact 3-manifold with a triangulation τ. Authour give an inequality relating the Euler characteristic of a surface F normally embedded in M with the number of normal quadrilaterals in F. This gives a relation between a topological invariant of the surface and a quantity derived from its combinatorial description. Secondly, we obtain an inequality relating the number of normal triangles and normal quadrilaterals of F, that depends on the maximum number of tetrahedrons that share a vertex in τ.

1 illus, 11 ref

011419   Hertweck M (NO, Universitat Stuttgart, Fachbereich Mathematik, IGT, Pfaffenwaldring 57, 70550 Stuttgart, Germany, Email: hertweck@mathematik.uni-stuttgart.de) : Zassenhaus conjecture for A₆. Proc Indian Acad Sci-Mathl Sci 2008, 118(2), 189-95.

For the alternating group A₆ of degree 6, Zassenhaus' conjecture about rational conjugacy of torsion units in integral group rings is confirmed.

2 tables, 22 ref

011418   Gronb Ek N (Mathematical Sciences Dep, Universitetsparken 5, DK-2100 Copenhagen, Denmark, Email: gronbaek@math.ku.dk) : Push-outs of derivations. Proc Indian Acad Sci-Mathl Sci 2008, 118(2), 225-43.

Let 21 be a Banach algebra and let X be a Banach 2l-bimodule. In studying H^{1 (21, X) it is often useful to extend a given derivation D: 21 → X to a Banach algebra B containing 21 as an ideal, thereby exploiting (or establishing) hereditary properties. This is usually done using (bounded/unbounded) approximate identities to obtain the extension as a limit of operators b → D(ba) - b.D(a), a ∈ 21 in an appropriate operator topology, the main point in the proof being to show that the limit map is in fact a derivation. In this paper we make clear which part of this approach is analytic and which algebraic by presenting an algebraic scheme that gives derivations in all situations at the cost of enlarging the module. We use our construction to give improvements and shorter proofs of some results from the literature and to give a necessary and sufficient condition that biprojectivity and biflatness is inherited to ideals.}

10 ref

011417   Garg D;Singh J;Kumar K (Mathematics Dep, Geeta Institute for Management and Technology, Kurukshetra-136 118, Email: kuldeepnitk@yahoo.com) : Performance analysis of a cattle feed plant. Icfai Univ J Sci Technol 2009, 5(2), 83-94.

A cattle feed plant consisting of various units, such as elevator, grinder, hopper, mixer, winch, palletiser, and screw conveyor. These units have been arranged in a series. Failure and repair rates of each machine are assumed to be constant. The mathematical model of a cattle feed plant has been developed using a birth-death Markov Process. The differential equations have been solved for the steady-state. The system performance has been studied for various availability levels for different combinations of failures and repair rates of the subsystems.

7 illus, 7 tables, 10 ref

011416   Franz U;Skalski A (Departement Mathematiques de Besancon Universite de Franche-Comte 16, , route de Gray, 25 030 Besancon cedex, France, Email: uwe.franz@univ.fcomte.fr) : Approximation of quantum Levy processes by quantum random walks. Proc Indian Acad Sci-Mathl Sci 2008, 118(2), 281-8.

Every quantum Levy process with a bounded stochastic generator is shown to arise as a strong limit of a family of suitably scaled quantum random walks.

23 ref

011415   Baek H K (Mathematics Dep, Kyungpook National Univ, 702-701, South Korea, Email: hkbaek@knu.ac.kr) : Regularities of multifractal measures. Proc Indian Acad Sci-Mathl Sci 2008, 118(2), 273-9.

First, authour prove the decomposition theorem for the regularities of multifractal Hausdorff measure and packing measure in M^{d. This decomposition theorem enables us to split a set into regular and irregular parts, so that we can analyze each separately, and recombine them without affecting density properties. Next, we give some properties related to multifractal Hausdorff and packing densities. Finally, extend the density theorem in [6] to any measurable set.}

10 ref

011414   Arnab R;Singh S;Serumaga-Zake P A E (NO, Botswana Univ, Botswana, Email: arnabr@mopipi.ub.bw) : Alternative estimators for multi-character surveys. J Indian Soc Agric Statist 2009, 63(2), 133-7.

The problems of estimating the population total in multi-character surveys in varying probability sampling schemes when the measure of size is not well-related to the study variables, have been considered by Rao (1966), Scott and Smith (1969) and Amab (2001). In the present note, their results are extended for a wider class of superpopulation models and sampling designs.

13 ref

011413   Adsul B;Subrahmanyam K V (NO, Chennai Mathematical Institute, Plot H1, SIPCOT IT Park, Padur P.O., Siruseri-603 103, Email: abharat@cmi.ac.in) : Geometric approach to the kronecker problem I: the two row case. Proc Indian Acad Sci-Mathl Sci 2008, 118(2), 213-26.

Given two irreducible representations μ, v of the symmetric group S_d, the Kronecker problem is to find an explicit rule, giving the multiplicity of an irreducible representation, A, of S_d, in the tensor product of μ and v. We propose a geometric approach to investigate this problem. We demonstrate its effectiveness by obtaining explicit formulas for the tensor product multiplicities, when the irreducible representations are parameterized by partitions with at most two rows.

15 ref

011412   Adhikari S D;Balasubramanian R;Pappalardi F; Rath P (NO, Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad-211 019) : Some zero-sum constants with weights. Proc Indian Acad Sci-Mathl Sci 2008, 118(2), 183-8.

For an abelian group G, the Davenport constant D(G) is defined to be the smallest natural number k such that any sequence of k elements in G has a nonempty subsequence whose sum is zero (the identity element). Motivated by some recent developments around the notion of Davenport constant with weights, we study them in some basic cases. We also define a new combinatorial invariant related to (Z/nZ)^{d, more in the spirit of some constants considered by Harborth and others and obtain its exact value in the case of (Z/nZ)2 where n is an odd integer.}

15 ref

010426   Zhou S (School of Mathematics and Physics, , Mengxi Road 2, Zhenjiang, Jiangsu-212 003, People's Republic of China, Email: zsz_cumt@163.com) : Some results of fractional K-factors. Indian J pure appl Math 2008, 40(2), 113-21.

Let G be a graph, and k a positive integer. In this paper, we present some sufficient conditions for the existence of a fractional k-factor in a simple graph depending on δ(G) and the neighborhood of independent sets. Furthermore, it is showed that the results are best possible in some sense.

14 ref

010425   Yue Xi;Yuansheng Y;Liping W (School of Information Technolog, Wuyi University, Jiangmen-529 020, Peoples' Republic of China) : Super vertex-magic total labelings of flower snark and related graph. Indian J pure appl Math 2008, 40(2), 123-9.

Graph G is called super vertex-magic total labelings if there exists a bijection f from V(G)UE(G) to {1,2,...,<124>V(G)<124> + <124>E(G)<124>} such that f(v) + Σf(vu) = C where the sume is over all vertices u adjacent to v and f(V(G)) = {1,2,...,<124>V(G)<124>}, f(E(G)) = <124>V(G)<124> + 1, <124>V(G)<124> + 2,..., <124>V(G)<124> + <124>E(G)<124>}. For odd n ≥ 5, the flower snark F_n = (V,E) is a simple undirected cubic graph with 4n vertices, where V = {b_i : 0 ≤ i ≤ n - 1} U {c_i : 0 ≤ i ≤ 2n - 1} U {a_i : 0 ≤ i ≤ n - 1} and E = {b_ib_{i+1) mod 2n} : 0 ≤i≤ n-1}. U {c_ic_{i+1) mod 2n} : 0 ≤i≤2n-1} U {a_ib_i,a_ic_i,a_ic_n+i : 0≤i≤n-1}. For n=3 or even n≥4, F_n is called the related graph of flower snark. In this paper Authors show that flower snark and related graph are super vertex-magic.

2 illus, 12 ref

010424   Yousefi B;Soltani R (Mathematics Dep, Payame-Noor Univ, Shiraz Moallem Square, South Imam Street, P.O. Box 71345-1774, Shiraz, Iran, Email: bahmann@spnu.ac.ir) : Hypercyclicity of the adjoint of weighted composition operators. Proc Indian Acad Sci-Mathl Sci 2009, 119(4), 513-19.

Investigates the hypercyclicity of the adjoint of weighted composition operator in special function spaces.

9 ref

010423   Yang B;Liu X (School of Mathematics and Computer Science, Fujian Normal Univ, Fuzhou 350108, People's Republic of China, Email: bgyang@163.com) : Hypersurfaces satisfying L_rx = R_x in sphere S<. Proc Indian Acad Sci-Mathl Sci 2009, 119(4), 487-99.

Using the method of moving frames, we consider hypersurfaces in Euclidean sphere Sⁿ⁺¹ or hyperbolic space Hⁿ⁺¹ whose position vector x satisfies L_rx = Rx, where L_r is the linearized operator of the (r + l)-th mean curvature of the hypersurfaces for a fixed r = 0, ..., n - 1, R ∈ R^(n+2)x(n+2). If the -t mean curvature H_r is constant, we prove that the only hypersurfaces satisfying that condition are r-minimal (H_r+1 = 0) or isoparametric. In particular, we locally classify such hypersurfaces which are not r-minimal.

12 ref

010422   Wu Y;Ghosal S (Biological Statistics and Computational Biology Dep, Cornell Univ, USA, Email: yw392@cornell.edu) : Posterior consistency for some semi-parametric problems. Sankhya 2008, 70(pt 2), 267-313.

The Bayesian approach to analyzing semi-jparametric models/are gaining popularity in practice. For the Cox proportional hazard model, it has been shown recently that the posterior is consistent and leads to asymptotically accurate confidence intervals under a Levy process prior on the cumulative hazard rate. The explicit expression of the posterior distribution together with independent increment structure of Levy process play a key role in the development. However, except for one-dimensional linear regression with an unknown error distribution and binary response regression with unknown link function, even consistency of Bayesian procedures has not been studied for a general prior distribution. Considered consistency of Bayesian inference for several semi-parametric models including multiple linear regression with an unknown error distribution, exponential frailty model, generalized linear model with unknown link function, Cox proportional hazard model where the baseline hazard function is unknown, accelerated failure time models and partial linear regression model. Gave sufficient conditions under which the posterior distribution of the parametric part is consistent in the Euclidean distance while the non-parametric part is consistent with respect to some topology such as the weak topology. Results are obtained by verifying the conditions of an appropriate modification of a celebrated result of Schwartz. Our general consistency result applies also to the case of independent, non-identically distributed observations. Application of the theorem requires showing the existence of exponentially consistent tests for the complements of the neighborhoods of the "true" value of the parameter and the prior positivity of a Kullback-Leibler type of neighborhood of the true distribution of the observations. Constructed the required tests and give sufficient conditions for positivity of prior probabilities of Kullback-Leibler neighborhoods in all the examples considered.

31 ref

010421   Withers C S (Applied Mathematics Group, Industrial Research Limited, Lower Hutt, New Zealand, Email: C.Withers@irl.cri.nz) : Analysis bias reduction for k-sample functionals. Sankhya 2008, 70(pt 2), 186-222.

Analytic methods have been for nonparametric bias reduction that remove the need for computationally intensive methods like the bootstrap and the jack-knife. Calls an estimate pth order if its bias has magnitude n^-p₀ as n₀ → ∞, where n₀ is the sample size (or the minimum sample size if the estimate is a function of more than one sample). Most estimates are only first order and require O(N) calculations, where N is the total sample size. The usual bootstrap and jackknife estimates are second order but they are computationally intensive, requiring O(N²) calculations for one sample. By contrast Jaeckel's infinitesimal jackknife is an analytic second order one sample estimate requiring only O(N) calculations. When pth order bootstrap and jackknife estimates are available, they require O(N^p) calculations, and so become even more computationally intensive if one chooses p > 2. For general p it provide analytic pth order nonparametric estimates that require only O(N) calculations. Our estimates are given in terms of the von Mises derivatives of the functional being estimated, evaluated at the empirical distribution. For products of moments an unbiased estimate exists: our form for this "polykay" is much simpler than the usual form in terms of power sums.

19 ref

010420   Vijayasankar N;Elangovan R;Sathyamoorthi R; Sureshkumar R (Statistics Dep, Annamalai Univ, Annamalai Nagar-608 002) : Estimation of expected time to recruitment with wastage threshold as truncated distribution. J Indian Acad Math 2009, 31(1), 259-68.

One of the important aspects of study in manpower planning is the study of wastage. Wastage in the depletion of manpower from an organization. It is mainly due to the policy decisions regarding wages, perquisities and targets. Recruitment is not advisable frequently since it is not cost effective. Hence wastage on successive occasions are allowed to cumulate till the cumulative damage crosses a threshold level, at which the organization faces a breakdown due to want of manpower. Many authors have estimated the expected to recruitment or the break down point of the organization from the view point of the manpower loss. In doing so the shock models and cumulative damage process as discussed by Esary prochan and Marshall (1973) has been used. It is quite common to observe that the recruitment policies are also quite similar to that or the recording mechanism in inventory management. (S,s) policies are quite common. Based on his concept, thee threshold is taken to be only above 's' and not above 'S'. This implies that if the cumulative total manpower wastage if only is above 's', recruitment can be made and also it cannot be allowed to go beyond 'S'. Subject to this condition using the concept of truncated distributions, the expected time to recruitment used its variance are derived in this paper. In doing so, is assumed that the threshold level which indicates me time to recruitment is a random variable following Erlang2 distribution and truncated both at lefts and right. Numerical illustrations are also provided using simulated data.

4 illus, 2 ref

010419   Tailor M R (Mathematics Dep, The Patidar Girls Science College, Bardoli-394 602) : Laminar flow in porous media with triangular duct. J Indian Acad Math 2009, 31(1), 49-58.

The fully developed laminar flow of a viscous incompressible liquid in along porous triangular duct has (Δ BCD ) Fig. [2.1] been investigared. The generalised momentum equation which governs the flow has been solved by finite element method. The analytical and numerical results are given.

2 tables, 8 ref

010418   Sundar P;Murugesan A (Mathematics Dep, Kandaswami Kandar's College, Veluur (Namakkal)-638 182, Email: ponsuanda_kkc@yahoo.co.in) : Oscillation of neutral delay difference equations with variable coefficients. J Indian Acad Math 2009, 31(1), 221-31.

Considers the neutral delay difference equations of the form Δ[x(n) - p(n)x(n - τ)] + q(n)x(n - σ) = 0, where τ and σ are nonegative integers. A sharp oscillation criteria is obtained for this equation which improves previously known results. The relevance of the result obtained is illustrated with an example.

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010417   Subramanian N;Murugesan C (Mathematics Dep, Sastra Univ, Tanjore-613 402, Email: nsmaths@yahoo.com) : Difference Orlicz space of entire sequences. J Indian Acad Math 2009, 31(1), 269-76.

This paper is devoted to a study of the general properties of the Orlicz difference sequence space, Γ_M (Δ).

13 ref

010416   Srivastava A K (Chandra Kuti, Cooks Compound, Ghasiyari Mandi, Lucknow-226 001) : Fifth and sixth order mock theta functions represented AS ₃φ₂. J Indian Acad Math 2009, 31(1), 119-33.

The object of this paper is to show the intimate relationship of certain mock theta functions and q-hypergeometric series. Several very interesting and simple transformations connecting such functions with q-series have been investigated.

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010415   Sreehari M (NO, , 6-B, Vrundavan Park, New Sama Road, Vadodara-390 008, Email: msreehari03@yahoo.co.uk) : On a class of discrete distributions analogous to burr family. J Indian Statist Ass 2008, 46(2), 163-81.

Using a difference equation analogous to the differential equation governing the Burr family of continuous distributions we derive six families of discrete distributions. It is shown that one of the families contains all unbounded discrete distributions and also the "discretized" versions of nonegative continuous distributions. Several special cases are investigated resulting in a few interesting new distributions. Some characterization results also are obtained and use of a characterization result in model selection is illustrated.

010414   Sitrarasu M R;Deena Merit C K (Mathematics Dep, Kongunadu Arts and Science College, Coimbatore-641 029, Email: sitrarasu23@yahoo.com) : The M<. J Indian Acad Math 2009, 31(1), 241-58.

In real life situations, the dependence of arrival to service and the control of arrivals are inevitable. Owing to the importance, we consider the M^{[X]/Ma,b/1/N/FIFO interdependent queueing model with controllable arrival rates. The steady state probabilities and other performance measures are derived using the system of steady state equations. The numerical analysis and the graphs help us to control the queue length with the suitable selection of parameters.}

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010413   Singh S P (Mathematics Dep, T.D.P.G. College, Jaunpur-222 002) : On evaluation of Ramanujan's theta for a particular value of q. J Indian Acad Math 2009, 31(1), 189-201.

In this paper, making use of a modular equation of degree three, we have evaluated certain Ramanujan's theta functions for q = e^-π.

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010412   Singh M R;Shambhu Singh L (Mathematics Dep, Manipur Univ, Canchlpur, Imphal-795 003, Email: mranjitmu@rediffmail.com) : Fixed point theorem via biased maps. J Indian Acad Math 2009, 31(1), 65-75.

Study the inter-relationship between the compatible pair of type (C) and the various types of biased maps.. Further the results of Pathak et al [7] and Murthy et al [6] are generalized. Illustrated examples are also given.

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010411   Singh M M;Dwivedi V (NO, Chhatrapati Shivaji Institute of Technology, Kolihapuri, Shivaji Nagar, P.O. Pisegaon, Durg, Chhattisgarh-491 001) : Some contributions to relativistic mechanics. J Indian Acad Math 2009, 31(1), 1-13.

Inspite of being one of the most elegant human discovery, the theory of relativity still continues to be a subject of varied interpretations. Many paradoxes exist or are so pointed out mostly due to confused approach. There is nothing inherently disturbing. This has been the stand in the paper which consists of determination of simultaneity without light signals and derivations of Lorentz transformations without using the constancy of velocity of light.

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010410   Sharma M;Bhatnagar S (NO, S.K. Univ, Jammu, Jammu & Kashmir) : General class of estimators for estimation of population mean through auxiliary information. J Indian Statist Ass 2008, 46(2), 155-61.

A general class of product type estimators for the estimation of population mean has been worked out. Its large sample properties are compared with the conventional product estimator as well as the estimators proposed by Robson (1957), Singh (1989), Dubey (1993) and Sharma (2007). The proposed estimator shows an improvement over these estimators according to the mean squared error criterion.

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010409   Sen P K (Biostatistics and Statistics & Operations Research Dep, The Univ of North Carolina At Chapel Hill, USA, Email: pksen@bios.unc.edu) : Discussion: on methods controlling the false discovery Rate. Sankhya 2008, 70(pt 2), 177-82.

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010408   Saxena R K;Ram J;Suthar D L (Mathematics and Statistics Dep, Jai Narain Vyas Univ, Jodhpur, Email: ram.saxena@yahoo.com) : Fractional calculus of generalized Mittag-Leffler function. J Indian Acad Math 2009, 31(1), 165-72.

The paper is devoted to the development of fractional calculus of generalized Mittag-Leffler function studied by Kilbas et al. Relations of this generalized Mittag-Leffler function with Riemann-Liouville fractional calculus operators are derived. The results obtained unify and extend the results given by Saxena and Saigo [10], Kilbas and Saigo [2], and Saxena, Kalla & Kiryakova [9] for the multiindex Mittag-Leffler functions studied by Kiryakova.

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