013952   Bhowmik M;Pal M (Mathematics Dep, Vidyasagar Teachers Training College, Midnapore-721 101, Email: monoranjan_bhownuk@rediffmail.com) : Some results on intuitionistic fuzzy matrices and intuitionistic circulant fuzzy matrices and intuitionistic circulant fuzzy matrices. Int J mathl Sci 2008, 7(1-2), 81-96.

Introduced the maxmin and minmax compositions over the intuitionistic fuzzy matrices (IFM) and intuitionistic circulant fuzzy matrices (ICFM). Also show the conditions for convergence under maxmin and minmax compositions of the IFM and ICFM.

20 ref

013951   Benseridi H;Dilmi M (Mathematics Stif Dep, Faculty of Sciences, Ferhat Abbas Univ, 19000, Algeria, Email: m benseridi@yahoo.fr) : On the regularity for some boundary problems in spaces with weight. Int J mathl Sci 2008, 7(1-2), 141-53.

Introduced some boundary value problems of elasticity in plan domain with corners for a class of Sobolev spaces of double weight. We given generalization of some results of existence and unicity of the solution obteined by P. Grisvard [6] in classical spaces of nul weight, by D. Teniou [8] in Sobolev spaces of simple weight and by M. Dauge [4] for the system of Stokes.

1 illus, 11 ref

013950   Basu R;Sridharan R (NO, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400 005, Email: sraja@math.tifr.res.in) : On Forster's conjecture and related results. Punjab Univ Res J Sci 2007, 57, 13-66.

Gives self contained exposition of proofs of the Quillen-Suslin Theorem, a conjecture of Forster and some related work done by Indian Mathematicians in the field of Protective Modules and Complete Intersections.

48 ref

013949   Afrouzi G A;Sadeghi Z (Mathematics Dep, Faculty of Basic Sciences, Mazandaran Univ, Babolsar, Iran, Email: afrouzi@umz.ac.ir) : On stability properties of positive solutions for a boundary value problem. Int J mathl Sci 2008, 7(1-2), 63-7.

Stability of positive stationary solutions of the boundary value problem of the form {-Δu^{m(x) = λg(x)f((u(x)) in Ω {Bu(x) = 0 on ∂Ω Where Ω denotes a bounded region in Rn(n ≥ 1) with smooth boundary Bu(x) = αh(x)u + (1 - α) ∂u/∂n where α ∈ [0, 1], h : ∂Ω → R+ with h = 1 when α = 1, m > 1, ≥ λ > 0 is a real parameter, g is a weight function such that satisfies g(x) ∈ C(Ω) that either g(x) > 0 or g(x) < 0 for all x ∈ Ω. Here f: [0 + ∞) - (R+) is C1 function. If f(n)/u_m be strictly decreasing (increasing), it was establish that every positive stationary solution is stable.}

5 tables

013002   Zhou B;Ramane H S (Mathematics Dep, South China Normal Univ, Guangzhou 510631, People's Republic of China, Email: zhoubo@scnu.edu.cn) : On upper bounds for energy of bipartite graphs. Indian J pure appl Math 2008, 39(6), 483-90.

The energy E(G) of a graph G is the sum of the absolute values of its eigenvalues. In chemistry, the energy of a molecular graph is closely related to the total π-electron energy of the molecule represented by that graph. Provided upper bounds for the energy of bipartite graphs of a given bipartition and acyclic graphs. The graphs for which these bounds are attained are also characterized.

25 ref

013001   Zaidi S M A;Irfan M;Khan N M;Muhiuddin G (Mathematics Dep, Aligarh Muslim Univ, Aligarh-202 002, Email: zaidimath@rediffmail.com) : On G-sets. J Natn Acad Math India 2007, 21, 118-28.

Some basic properties of G-sets some properties of G-morphisms has been investigated.

3 ref

013000   Yang B (Mathematics Dep, Guangdong Education Institute, Guangzhou 510303, Peoples' Republic of China, Email: bcyang@pub.guangzhou.gd.cn) : On the norm of a linear operator and its applications. Indian J pure appl Math 2008, 39(3), 237-50.

In this paper, a characterization of the norm of a linear operator T : l^r → l^r(r > 1,r = p,q) is discussed, where T is represented by a generalized integral with certain kernel k_r(x, y). As its applications, a new bilinear operator inequality with the norm and the equivalent forms are obtained, and some new extended Hilbert's type inequalities with the best constant factors and the equivalent forms are established.

15 ref

012999   Yang A;Zhang Z;Ge W (Applied Mathematics Dep, Beijing Institute of Technology, Beijing, 100081, Pepole's Republic of China, Email: yangaij2004@163.com) : Existence of nonoscillatory solutions of second-order nonlinear neutral differential equations. Indian J pure appl Math 2008, 39(3), 227-35.

In this paper, the existence of nonoscillatory solutions of the second-order nonlinear neutral differential equations is studied. Some new sufficient conditions are given and four examples are constructed to show that the results here are almost sharp.

12 ref

012998   Wang Y (College of Mathematics, Jilin Normal Univ, Siping, Jilin 136000, Peoples' Republic of China, Email: ywang2004@mail.china.com) : Annihilator conditions with derivations in prime rings of characteristic 2. Indian J pure appl Math 2008, 39(6), 459-65.

Let R be a prime ring of characteristic 2 with d a nonzero derivation of R, L a noncentral Lie ideal of R, a ∈ R such that a[d(u), u]ⁿ is central, for all u & L, where n is a fixed positive integer. Then a = 0 unless R satisfies S₄, the standard identity in 4 variables.

15 ref

012997   Wang R N;Li Z Q;Ding X H (Mathematics Dep, Nanchang Univ, Nanchang 330031, Jiang Xi, People's Republic of China, Email: rnwang @ncu.edu.cn) : Nonlocal cauchy problems for semilinear evolution equations involving almost sectorial operators. Indian J pure appl Math 2008, 39(4), 333-46.

25 ref

012996   Wang M (School of Mathematics, Shandong Univ, Shandong, Peoples' Republic of China, Email: mqwang71@hotmail.com) : On the sum of a prime the square of a prime and the k-th power of a prime. Indian J pure appl Math 2008, 39(3), 151-71.

In this paper author proved that, when k is odd, with at most O(N^{1/2-2/5*4k-1*k+ε}) exceptions, all positive odd integers n ≤ N can be written as sums of a prime and a square of prime and a k-th power of prime; when k is even, with at most O(N^{1/2-2/5*4k-1xk+ε) exceptions, all positive odd integers n ≤ N with n = 0 or 1 (mod3), can be written as sums of a prime and a square of prime and a k-th power of prime.}

17 ref

012995   Verma V S (Mathematics and Statistics Dep, D.D.U. Gorakhpur Univ, Gorakhpur-273 009) : Mathematical study on mucus transport in the lung. J Natn Acad Math India 2007, 21, 107-17.

Two layer planar steady state mathematical model is proposed to study mucus transport in the respiratory tract due to airflow and formation of cilia porous bed in serous sublayer in contact with the epithelium. The effect of airflow is considered by prescribing air velocity at the mucus-air interface. It has been shown that mucus transport increases as the pressure drop or force due to gravity, air velocity and the slip parameter increase. It is also observed that mucus transport increases as the viscosity of mucus or serous layer fluid decreases.

4 illus, 12 ref

012994   Verma S R (Mathematics Dep, D.A.V.(P.G.) College, Kanpur, Uttar Pradesh) : Theoretical study of blood flow through an artery with mild stenosis under the influence of transverse magnetic field. J Natn Acad Math India 2007, 21, 39-48.

Axially symmetric, laminar steady flow of blood through an artery with mild stenosis under the influence of homogeneous transverse magnetic field. It is assumed that blood is Newtonian fluid, density and viscosity are constant. The analytical expressions for velocity profile, volumetric flow rate, pressure gradient and shear stress at the wall are obtained. The results are discussed graphically.

4 illus, 23 ref

012993   Vasuki K R (Mathematics Dep, Acharya Institute of Technology, Soldevanahalli, Chikkabanavara (Post), Hesaragatta Road, Bangalore-560 090, Email: vasuki_kr@rediffmail.com) : On some of Ramanujan'S P-Q modular equations. J Indian Mathl Soc 2006, 73(3-4), 131-43.

In this paper, author gave new proofs of five P-Q modular equations of Ramanujan found in the unorganized pages of second notebook. Previously, these identities were proved by Berndt by using the theory of modular forms. We also obtain two new identities of the same nature.

6 ref

012992   Upadhyay S K;Yadav R N (Mathematics and Statistics Dep, D.D.U. Gorakhpur Univ, Gorakhpur-273 009) : Generalized Hankel convolution on Banach space valued gevery ultradistribution. J Natn Acad Math India 2007, 21, 65-78.

Characterization of generalized Hankel convolution on Banach-spaced-valued Gevery type ultradistribution of type (H^μA))' and (Q^μ_ω (A))' are investigated by using the theory of Hankel transformation.

12 ref

012991   Udaya Chandrika K;Ebenesar Anna Bagyam J (Mathematics Dep, Avinashilingam Univ of Women, Coimbatore-641 043) : Two phase retrial queue with impatient customers and orbital search. Res Highlight 2008, 18(3), 152-7.

2 illus, 2 tables, 3 ref

012990   Tiwari B (Mathematics Dep, B.R.D.P.G. College, Deoria-274 001, Email: banktesh76@yahoo.com) : On finsler spaces satisfying quasi-T'-condition. J Natn Acad Math India 2007, 21, 95-103.

Quasi-T'-condition in Finsler spaces has been introduced; which is weaker to semi-T'-condition, T'-condition and T-condition in Finsler spaces; and to study some special Finsler spaces satisfying Quasi-T'-condition.

10 ref

012989   Tariqul Hasan M;Sutradhar B C;Sneddon G (Mathematics and Statistics Dep, New Brunswick Univ, Fredericton, NB E32B 5A3, Canada, Email: thasan@unb.ca) : On correlation models for longitudinal failure time data. Sankhya 2007, 69(Pt3), 548-80.

When repeated failure times are collected from a large number of independent individuals, interest is focused primarily on the efficient estimation of the effects of the associated covariates on the failure times. The construction of the efficient estimating equations requires the modelling of the true correlation structure of the repeated failure times. There exists several bivariate correlation structures, such as the Clayton model, Kendall's rank and the so-called grade models, for the repeated failure times. These existing correlation structures are, however, limited to the equi-correlation case only. In this paper, as an alternative to the existing bivariate correlation structures, we introduce a class of observation-driven multivariate correlation structures appropriate for non-stationary failure times, which also accommodate the equi-correlation model as a special case. The proposed correlation structure for failure times is exploited to obtain the correlation structure of the cumulative hazard variates in order to construct the true correlation based estimating equations for the hazard ratio parameters. The efficiency loss due to any model mis-specification is examined through a simulation study. A numerical example is considered to illustrate the estimation methodology.

18 ref

012988   Sutradhar B C;Farrell P J (Mathematics and Statistics Dep, Memorial Univ of Newfoundland, St. John's, NL A1C 5S7, Canada, Email: bsutradh@math.mun.ca) : On optimal lag 1 dependence estimation for dynamic binary models with application to asthma data. Sankhya 2007, 69(Pt3), 448-67.

In some longitudinal studies for binary data, the expectation of the binary response variable of an individual at a given point of time may depend on the covariate history up to the time. In the same token, the variance at a given point of time and the correlation of the two responses at two given time points may also depend on the history of the time dependent covariates of the individual. In this paper, we exploit a dynamic logistic model to analyse such history based binary data. A moment based generalized quasi-likelihood (GQL) approach is considered for optimal estimation for the effects of the covariates as well as dynamic dependence. The estimation approach is applied to re-analyse a longitudinal binary data on asthma status.

5 tables, 9 ref

012987   Surya Narain;Sinha N (Mathematics Dep, Harish Chandra Post Graduate College, Varanasi, Uttar Pradesh) : Magneto-elastic radial vibration of an aeolotropic cylindrical shell of visco-elastic material. J Natn Acad Math India 2007, 21, 49-64.

Magneto-elastic radial vibration of aeolotropic cylindrical shell of visco-elastic material. The density of the material of the shell has been taken in the form ρ = ρ₀ rⁿ, where ρ₀ is constant and n is any integer. Frequency equations in several cases are derived.

3 illus, 3 tables, 8 ref

012986   Sunder V S (NO, Institute of Mathematical Sciences, Chennai-600 113, Email: sunder@imsc.res.in) : Riesz representation theorem. Indian J pure appl Math 2008, 39(6), 467-81.

The goal of this note is to provide a self-contained proof of the celebrated Riesz Representation theorem. The proof relies on the Hahn-Banach theorem and the fact that compact metric spaces are quotients of the Cantor set.

7 ref

012985   Sri Padmavati B (Mathematics & Statistics Dep, Hyderabad Univ, Hyderabad-500 046) : Divergence-free vector fields. Indian J pure appl Math 2008, 39(4), 317-21.

8 ref

012984   Sinha S;Mukherjee B;Ghosh M (Statistics Dep, Texas A&M Univ, College Station, TX 77843, USA, Email: sinha@stat.tamu.edu) : Modelling association among bivariate exposures in matched case-control studies. Sankhya 2007, 69(Pt3), 379-404.

Considers the problem of modelling association between two exposure variables in a matched case-control study, where both the exposures may be partially missing. The exposure variables could all be categorical or continuous or could be a mixed set of some categorical and some continuous variables. Association models for the missing exposure variables using the completely observed covariates and disease status are proposed for each of the three scenarios. The models account for varying stratum heterogeneity in different matched sets. Three real data examples accompany the proposed models. The examples as well as a small scale simulation study indicate that in presence of missingness and association, modelling the association between the exposures rather than ignoring it, often leads to better estimates of the relative risk parameters with smaller standard errors. Estimation of the model parameters is carried out in a Bayesian framework and the estimates are compared with classical conditional logistic regression estimates.

5 tables, 33 ref

012983   Singh M M;Kashyap A K (Mathematics Dep, Chatrapati Shivaji Institute of Technology, Chhattisgarh, Durg-491 001, Email: madanmohansingh@rediffmail.com) : Note on quasi-regularity in near-rings. J Natn Acad Math India 2007, 21, 104-6.

Purpose is to generalize the concept of quasi-regularity in near-rings with unit element [1] to near rings without unit element.

1 table, 3 ref

012982   Singh K K (Mathematics Dep, North-Eastern Hill Univ, Shillong-793 022) : Propagation of a magnetogasdynamic cylindrical shock wave in a self-gravitating, radiative and rotating gas with variable density. J Natn Acad Math India 2007, 21, 129-45.

Similarity solutions are obtained for one-dimensional adiabatic flow behind a magnetogasdynamic cylindrical shock wave propagating in a rotating gas in presence of an azimuthal magnetic field taking the self-gravitation and radiation heat-flux into account. The density and the magnetic field in the medium ahead of the shock are assumed to be varying and obeying power laws. In order to obtain the similarity solutions the angular velocity of the ambient medium is assumed to be decreasing as the distance from the axis increases. Effects of variation of radiation and gravitational parameters, on the flow field behind the shock, are obtained.

4 illus, 1 table, 15 ref

012981   Singh H K;Singh T B (Mathematics Dep, Delhi Univ, Delhi-110 007, Email: tej_b_singh@yahoo.co.in) : Fixed point free involutions on cohomology projective spaces. Indian J pure appl Math 2008, 39(3), 285-91.

Let X be a finitistic space with the mod 2 cohomology ring isomorphic to that of CPⁿ, n odd. In this paper, we determine the mod 2 cohomology ring of the orbit space of a fixed point free involution on X. This gives a classification of cohomology type of spaces with the fundamental group Z2 and the covering space a complex projective space. Moreover, shown that there exists no equivariant map S^m → X for m > 2 relative to the antipodal action on S^m.

9 ref

012980   Singh Chandel R C;Chauhan S S (Mathematics Dep, Dayanand Vedic Post Graduate College, Orai-285 001) : Applications of multiple hypergeometric function of Srivastava-Daoust and generalized polynomials of Srivastava in two boundary value problems. J Natn Acad Math India 2007, 21, 19-38.

Multiple hypergeometric function of Srivastava and Daoust ([5, 6, 7]; also see [8]) and generalized polynomials of Srivastava [9] in two boundary value problems. Evaluated an integral involving the product of the general class of polynomials of and multiple hypergeometric function to solve a problem on heat conduction in a finite bar and to establish an expansion formula involving product of the above general class of polynomials and the multiple hypergeometric function. Some special cases are also discussed. another problem on electrostatic potential in spherical region.

13 ref

012979   Singh A K;Gupta U C (Mathematics Dep, H.N.B. Garhwal Univ, Campus Badshahithaul, Tehri Garhwal-249 199) : On sasakian concircular recurrent spaces of second order. J Indian Mathl Soc 2006, 73(3-4), 221-6.

8 ref

012978   Shukla N V C (Mathematics & Astronomy Dep, Lucknow Univ, Lucknow-226 007) : Cartesian product of r almost product manifolds. J Natn Acad Math India 2007, 21, 88-94.

Cartesian product of two manifolds has been studied by Pandey [1] and others. In this paper, r manifolds admitting almost product structure have been taken, and their Cartesian product has been studied.

4 ref

012977   Shirali S A (NO, Rishi Valley School, Rishi Valley-517 352, Email: shirali@gmail.com) : Algebraic methods in plane geometry, 2.cubic curves. Resonance 2008, 13(11), 1027-40.

Explored some connections between plane geometry and the algebra of conies. Now bring cubic curves into the picture. Offer another algebraic proof of Pascal's theorem, and show how a group operation may be defined on the points of a cubic curve. We also show how these ideas help in finding taxicab numbers of the kind made famous by the "1729" incident featuring Hardy and Ramanujan.

10 illus, 4 ref

012976   Shah S;Das T K (Mathematics Dep, Faculty of Science, The M.S. Univ of Baroda, Vadodara-390 002, Email: skshah2002@yahoo.co.in) : On absolutes of nearly hausdorff spaces. J Indian Mathl Soc 2006, 73(3-4), 213-19.

Constructed here the covariant function r from the category ℵδ(Π) of nearly Hausdorff spaces with property n and density preserving epimor- phisms to the category ℵ_c(k) of compact nearly Hausdorff spaces and continuous maps. Studied absolutes for nearly Hausdorff spaces and construct the covariant functor E from the category ε_d of nearly Hausdorff spaces and density preserving epimorphisms to the category ε_c of extrem-ally disconnected Hausdorff spaces and continuous maps. Finally, Obtained commutativity of the functors E and r.

17 ref

012975   Sankaran P G;Antony A A (Statistics Dep, Cochin Univ of Science and Technology, Cochin-782 022, Email: sankaranpg@yahoo.com) : Bivariate competing risks models under random left truncation and right censoring. Sankhya 2007, 69(Pt3), 425-47.

In survival or reliability studies, it is common to have truncated data due to the limited time span of the study or dropouts of the subjects for various reasons. The estimation of survivor function under left truncation was first discussed by Kaplan and Meier by extending the well known product-limit estimator of the survivor function. The focus of this paper is on the nonparametric estimation of the survivor function and the cause-specific sub-distribution functions in bivariate competing risks set up, when the observations are subject to random left truncation and right censoring. Various asymptotic properties of the estimators are discussed. A simulation study discussing the empirical behaviour of the estimator is carried out. We illustrate the procedure by a data set.

4 tables, 26 ref

012974   Sakalkar A;Thakar S (Mathematics Dep, North Maharashtra Univ, Jalgaon-425 001) : Application of canonical transformation to generate invariants of non-conservative system. Indian J pure appl Math 2008, 39(4), 353-68.

In this paper, a method based upon Hamilton's integral variational principle is developed to determine invariants for non-conservative dynamical system d/dt (∂L/∂q) - ∂L/∂q = N(t,q^T,q^T) denoted by (L,N) using Hamiltonian approach. In the Hamiltonian form the system is denoted by (H,N) where N = N(t,q^T, q^T (t,q^T,p^T)).. A family of canonical transformations is generated that preserves the form of Hamilton's equations of motion for some Hamiltonian like function. These functions consist of the Hamiltonian function K in the transformed coordinates and an additional function R dependent on the non-conservative force N. In the new co-ordinates the non-conservative system can be completely described by (K + R,N). Noether's theorem is applied to the transformed system to determine invariant of the system in the original variables. The method is illustrated for few examples.

15 ref

012973   Ranganathan S;Senthilvelan T;Sriram G (Mechanical Engineering Dep, Sri Chandrasekharendra Saraswathi Vishwa Maha Vidyalaya, Enathur, Kanchipuram-631 561) : Mathematical modeling of process parameters on hard turning of AISI 316 SS by WC insert. J scient ind Res 2009, 68(7), 592-6.

Presents a newly developed mathematical modeling for process parameters on hard turning of AISI 316 stainless steel by tungsten carbide inserts (WC). Regression analysis and ANOVA theory was used to predict surface roughness (Ra) and tool wear (V_B). WC tool inserts performed machining of AISI 316 SS to study main and interaction effects of process parameters [cutting speed (V_s), feed rate (fs) and depth of cut (a_p)]. Adequacies of developed model were verified by calculation of correlation coefficient (r). These models can be effectively used to predict Ra of work piece and V_B of WC insert.

012972   Pathak R S;Pandey C P (Mathematics Dep, Banaras Hindu Univ, Varanasi-221 005) : Wavelet transform in a generalized Sobolev space. J Indian Mathl Soc 2006, 73(3-4), 235-47.

The continuous wavelet transform is studied on the generalized Sobolev space B^ω_{p, k}. Boundedness results in this Sobolev space are obtained. Local generalized Sobolev space is defined and some of its important properties are discussed. Wavelet transform with compactly supported wavelet is also studied.

7 ref

012971   Pathak A K (Mathematics Dep, Govt. Motilal Vigyan Mahavidyalaya, Bhopal) : Birkhoff interpolation problem on the unit circle in the complex plane. J Indian Mathl Soc 2006, 73(3-4), 227-33.

Considered the regularity of certain Birkhoff interpolation on perturbed roots of unity. In particular, the regularity of Birkhoff interpolation for the case (0, m) on the zeros of (z²ⁿ + 1)(z- 1)(z-ς) where ς³ = 1 and ς²ⁿ ≠ 1 has been studied.

14 ref

012970   Pant R P (Mathematics Dep, Kumaon Univ, D.S.B. Campus, Nainital-263 002) : Fixed point theorems and divisibility of polynomials. J Indian Mathl Soc 2006, 73(3-4), 121-30.

The aim of the paper is to study the dynamics and fixed points of a class of functions induced by integers and then apply the fixed point theorem to obtain general tests of divisibility of numbers. In the second part, we generalize the theorems on divisibility to obtain conditions of divisibility of polynomials by cubic polynomials. We not only obtain generalizations of the well-known remainder theorem and the factor theorem of algebra but also compute explicit value of the quotient. The results are computationally explicit and can be easily implemented on digital computers.

4 ref

012969   Nordman D J;Lahiri S N;Fridley B L (Statistics Dep, Iowa State Univ, Ames, IA 50010, USA, Email: dnordman@iastate.edu) : Optimal block size for variance estimation by a spatial block bootstrap method. Sankhya 2007, 69(Pt3), 468-93.

Block selection problem for a block bootstrap variance estimator applied to spatial data on a regular grid has been consiclued. Precise. formulae for the optimal block sizes that minimize the mean squared error of the bootstrap variance estimator has been developed. Then described and practical methods for estimating these spatial block sizes, and prove the consistency of a block selection method by Hall, Horowitz and Jing (1995), originally introduced for time series. The spatial block bootstrap method is illustrated through data examples, and its performance is investigated through several simula-tion studies.

3 tables, 29 ref

012968   Narain D;Tripathi A R (Mathematics and Statistics Dep, D.D.U. Gorakhpur Univ, Gorakhpur-273 009) : Analytic vector field admitting semi-symmetric metric connection on almost Hermite manifold. J Natn Acad Math India 2007, 21, 7-18.

Properties of Riemannian manifold admitting semi-symmetric metric connection were studied by many author [1], [2], [3] and [4]. Obtained conditions that if a vector field V is contravariant almost analytic with respect to Levi-civita connection then it is also contravariant almost analytic with respect to semi-symmetric metric connection. Further, we have obtained some results on curvature tensor and specific curvature tensor, assuming V is affine Killing Vector.

7 ref

012967   Ma B;Gao C (Mathematics Dep, Northwest Normal Univ, Lanzhou 730070, People's Republic of China, Email: mary@nwnu.edu.cn) : Sign-changing solutions of nonlinear boundary value problems of difference equations. Indian J pure appl Math 2008, 39(4), 323-32.

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012966   Liu H;Wang T (Applied Mathematics Dep, Dalian Univ of Technology, Dalian-116 024, Email: hmliu99@yahoo.com.cn) : Some new Rogers-Ramanujan type identities. J Indian Mathl Soc 2006, 73(3-4), 145-51.

The main object of the paper is to further generalize an identity, which was obtained by I. Gessel and D. Stanton and extended subsequently by F.Z. Zhao and T.M. Wang. Besides, some new Rogers-Ramanujan type identities are established.

11 ref

012965   Lin H;Song P X K;Zhou Q M (Faculty of Mathematics, Sichuan Univ, Chengdu, Sichuan, 61004, Peoples Republic of China, Email: hzlin@scu.edu.cn) : Varying-coefficient marginal models and applications in longitudinal data analysis. Sankhya 2007, 69(Pt3), 581-614.

Class of nonparametric marginal models in which the regression coefficients are assumed to be time-varying smooth functions Such models are appealing in longitudinal data analysis to characterize considered.time-dependent effects of covariates on the expected value of the response variable. A local quasi-likelihood method is employed to estimate the coefficient functions, based on the nonparametric technique of local polynomial kernel regression. We establish the asymptotic distribution theory for the estimators considered. We conduct Monte Carlo simulation studies to compare two types of kernel-based GEE methods with global and local variance structures, respectively. We illustrate the proposed models via three real-world data sets from a clinical trial of multiple sclerosis, a quality of life study in chemotherapeutic treatments on breast cancer, and a genomic fine-scale mapping association study on chromosomal region 5q31 for Crohn's disease.

4 illus, 2 tables, 30 ref

012964   Lianggui F (Mathematics and Systems Science Dep, National Univ of Defense Technology, Changsha 410073, Peoples' Republic of China, Email: fenglg2002@sina.com) : Simultaneously reducing two quaternionic matrices and its applications. Indian J pure appl Math 2008, 39(6), 509-22.

Given two m x n quaternionic matrices A and B, we prove that A and B can be equivalent to complex matrices simultaneously. As applications, author converted some quaternionic matrix equations into the equivalent complex counterparts, thereby obtained an approach of determining the consistency and finding the general solutions of them without any additional assumption.

21 ref

012963   Karan Singh R;Subodh Chandra (Statistics Dep, Lucknow Univ, Lucknow-226 007) : Estimator of population ratio under observational errors. J Natn Acad Math India 2007, 21, 79-87.

Effects of observational errors on an estimator obtained as population ratio estimators are examined. A comparative study is made among the proposed the ration estimator in presence of observational errors. Information is accumulating about the nature and magnitude of error of observation in ratio estimates and skill provides estimates of simple response variance and its ratio to the total response variance.

12 ref

012962   Karan R;Indu (Mathematics Dep, Kurukshetra Univ, Kurukshetra-136 119, Email: ramkaran_math@rediffmail.com) : On the lie augmentation quotients of integral group rings. Indian J pure appl Math 2008, 39(3), 273-84.

Let G be a group. A complete description of the abelian group LQ₂(G) is given and the structure of LQ₃(G) is also determined when lower central factors of G are free abelian. As a consequence the structures of Δⁿ(G)/Δ⁽ⁿ⁾(G) and Δⁿ(G)/Δ⁽ⁿ⁺¹⁾(G) are determined for smaller values of n.

10 ref

012961   Horova I;Pospisil Z;Zelinka J (Mathematics and Statistics Dep, Faculty of Science, Masaryk Univ, Kotlarska, CZ 611 37 Brno, Czech Republic, Email: horova@math.muni.cz) : Semiparametric estimation of hazard function for cancer patients. Sankhya 2007, 69(Pt3), 494-513.

Survival of cancer pa-tients has been student. First, a parametric form of hazard function is proposed. This model results from a recent model of cancer cells population dynamics given in the paper Kozusko and Bajzer (Mathematical Biosciences, 2003) and depends on several parameters. The method of estimating such parameters is described as well. On the other hand, the nonparametric methods seem to be appropriate for survival data. Among them, the methods of kernel estimation of hazard functions are very effective ones. But there is a serious difficulty with them, namely the choice of a smoothing parameter. We propose an alternative method for the bandwidth selection based on the aforementioned parametric method. The theory developed is applied to four data sets.

5 illus, 5 tables, 32 ref

012960   Hartl M (NO, , LAMAV and FR CNRS 2956, ISTV2, Universite de Valenciennes et du Hainaut-Cambresis, Le Mont Houy, 59313 Valenciennes Cede, Email: Manfred.Hartl@univ-valenciennes.fr) : Relative second fox and third dimension subgroup of arbitrary groups. Indian J pure appl Math 2008, 39(5), 435-51.

Let I_R(G) denote the augmentation ideal of the group algebra R(G) of a group G with coefficients in a commutative ring R. We give a complete description of the third relative dimension subgroup G ∩ (1 + I_R(K)I_R(G) + I³_R(G)) and the second relative Fox subgroup G ∩ (1 + I_R(K)I_R(H) + I²_R(G)I_R(H)) for any subgroups K and H of G.

20 ref

012959   Grace S R;Agarwal R P;Aktas M F (Engineering Mathematics Dep, Faculty of Engineering, Cairo Univ, Orman, Giza 12221, Egypt, Email: srgrace@eng.cu.edu.eg) : On the oscillation of third order functional differential equations. Indian J pure appl Math 2008, 39(6), 491-507.

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012958   Giri R D;Bahatkar P B (NO, , 128-A, Aakar Nagar, Katol Road, Nagpur-440 013) : Three theorems on commutativity of s-unital rings. J Indian Mathl Soc 2006, 73(3-4), 249-56.

Three commutativity theorems are proved for one sided s-unital rings using three different commutator identities involving polynomials of the type f (X) ∈ X²I(X) with f(1) = ± 1 where I is the ring of integers. We also give counterexamples to show the essentiality of the conditions taken in the hypotheses.

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012957   Fernandez L M;Hans-Uber M B (Geometry and Topology Dep, Faculty of Mathematics Univ of Sevilla, Apartado de Correos 1160, 41080-Sevilla, Spain, Email: lmfer@us.es) : Induced structures on slant submanifolds of metric F-manifolds. Indian J pure appl Math 2008, 39(5), 411-22.

Study was carried nut to obtain an induced structure on a slant submanifold of a metric f-manifold. Moreover, author give conditions for any isometric immersion between two metric/-manifolds to be slant and proved a characterization theorem when the submanifold has the smallest possible dimension to be proper slant.

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