010407   Sarkar S K (Statistics Dep, Fox School of Business and Management, Temple Univ, Philadelphia, PA 19122, USA, Email: sanat@temple.edu) : Rejoinder: on methods controlling the false discovery rate. Sankhya 2008, 70(pt 2), 183-5.

4 ref

010406   Sarkar S K (Statistics Dep, Fox School of Business and Management, Temple Univ, Philadelphia, PA 19122, USA, Email: sanat@templa.edu) : On methods controlling the false discovery rate. Sankhya 2008, 70(pt 2), 135-68.

Great upsurge in research has taken place during the last decade or so in the area of multiple testing due to its increased relevance in modern scientific investigations. A major portion of this research has been devoted to developing methods that control error rates more meaningful as well as powerful than traditional ones in the context of these investigations. The error rates measuring false discovery proportion, particulary the false discovery rate (FDR), and procedures controlling them have received the most attention. This article relates specifically to the FDR and is written with two basic objectives: (1) to put togethr some important development in theory and methodology of the FDR with finite number of hypotheses and report them with newer formulas, proofs and insights, and (2) to develop an error rate extending the FDR to one that directly incorporates dependence among the test statistics and methods that control.

1 illus, 50 ref

010405   Samman M (Mathematical Sciences Dep, King Fahd University of Petroleum & Minerals, Dhahran-31261, Saudi Arabia, Email: msamman@kfupm.edu.sa) : Clifford semigroups and seminear-rings of endomorphisms. Indian J pure appl Math 2008, 40(2), 131-45.

Structure of Clifford semigroups and seminear-rings ofendomorphisms of certain groups are connected. It is shown that, in some circumstances, if S is a Clifford semigroup, with underlying semilattice Λ, then the endomorphisms of S generate a Clifford semigroup E(S) whose underlying semilattice is the set of endomorphism of Λ.

11 ref

010404   Sahu R C;Mohapatra L K;Mohanty G (Mathematics Dep, K.S.E.B. College, Bhanjanagar-761 126, Email: rcsahu2@rediffmail.com) : Cosmological macro models in Einstein and Barber theories. J Indian Acad Math 2009, 31(1), 307-16.

An attempt has been made to investigate the problem of perfect fluid distribution satisfying the 'gamma law' of equation of state in the Bianchi type-1 space time in both the theories of gravitation proposed by Einstein [1] and Barber [2j. Some physical and geometrical properties of the solutions with singularity involved in the models are discussed.

25 ref

010403   Rong M A;Zhang J;Zhang Y (School of Science, The School of Electronic and Information Engineeirng, Xi's Jiaotong Un, Xi'an, Shaanxi 710049, People's Republic of China, Email: marong0109@163.com) : On the 2m-th power mean of Dirichlet L-functions with the weight of trigonometric sums. Proc Indian Acad Sci-Mathl Sci 2009, 119(4), 411-21.

Let p be a prime, x denote the Dirichlet character modulo p, f(x) = a₀ + a₁x + ... + a_kX^k is a k-degree polynomial with integral coefficients such that (p,a₀,a,v>1,..., a_k) = 1, for any integer m, the study the asymptotic property of Σ_x≠x0|Σ^{p- 1}_a=1 x(a)e (f(a)/p)|² |L(1,x)|^2m, where e(y) = e^2πiy. The main purpose is to use the analytic method to study the 2m-th power mean of Dirichlet L-functions with the weight of the general trigonometric sums and give an interesting asymptotic formula. This result is an extension of the previous results.

15 ref

010402   Romano J P;Shaikh A M;Wolf M (Statistics and Economics Dep, Stanford Univ, USA, Email: romano@stanford.edu) : Discussion: on methods controlling the false discovery rate. Sankhya 2008, 70(pt 2), 169-76.

7 ref

010401   Ponraj R (Mathematics Dep, Sri Paramakalyani College, Alwarkurichi-627 412, Email: ponrajmath@rediffmail.com) : Further results on (α₁, α₂,........, α_K), cordial labelling of graphs. J Indian Acad Math 2009, 31(1), 157-63.

Let S = { α₁, α₂, ......, α_k} be a finite set of distinct integers and f be a function from the vertex set V(G) of a graph G to S. For each edge uv of G assign the label f(u)f{v), f is called (α₁, α₂, ...., α_k) - cordial labeling if | v_f (α_i) - v_f (α_j)| ≤ 1, i ≠j, i,j ∈ {1,2,...., k} and | e_f (α_iα_j) - e_f (α_rα_s)| ≤ 1, i,j,r,s ∈ {1,2,..., k) where v_f (x) and e_f (x) denote respectively the number of vertices and edges labelled with the integer x. A graph that admits a (α₁, α₂, ...., α_k) - cordial labeling is called the (α₁, α₂, ...., α_k) - cordial graph. Investigates (α₁, α₂) - cordial behavior of some standard graphs.

5 ref

010400   Patel J;Patel P A (NO, Sardar Patel Univ, Vallabh Vidyanagar) : Monte carlo comparison of some estimators of a finite population total under the midzuno-sen sampling scheme. J Indian Statist Ass 2008, 46(2), 141-53.

Considerable attention has been given to the estimation of the population total under the Midzuno-Sen sampling scheme (Prabhu-Ajgaonkar (1967), (1969), (1970) and Rao (1967)). Three unbiased estimators are available in the literature. Analytically, no estimator is found to be better than the rest. In this article, using small and large natural populations, an empirical comparison of these estimators has been made. It is found that, for most of the populations, when the relationship between y and x is well represented by a straight line passing through origin, ratio estimator performs very well.

3 tables, 12 ref

010399   Pan R K;Sinha S (NO, Institute of Mathematical Sciences, C.I.T. Campus, Chennai-600 113, Email: rajkp@imsc.res.in) : Modular networks with hierarchical organization: the dynamical implications of complex structure. Pramana J Phys 2008, 71(2), 331-40.

Several networks occurring in real life have modular structures that are arranged in a hierarchical fashion. Proposed a model for such networks, using a stochastic generation method. Using this model show that, the scaling relation between the clustering and degree of the nodes is not a necessary property of hierarchical modular networks, as had previously been suggested on the basis of a deter-ministically constructed model. We also look at dynamics on such networks, in particular, the stability of equilibria of network dynamics and of synchronized activity in the network. For both of these, we find that, increasing modularity or the number of hierarchical levels tends to increase the probability of instability. As both hierarchy and modularity are seen in natural systems, which necessarily have to be robust against environmental fluctuations, we conclude that additional constraints are necessary for the emergence of hierarchical structure, similar to the occurrence of modularity through multi-constraint optimization as shown by us previously.

6 illus, 27 ref

010398   Naik S (Mathematics Dep, Indian Institute of Technology, IIT-Guwahati, Guwahati-781 039, Email: spn20@yahoo.com) : Generalized cesaro operators on mixed norm spaces. J Indian Acad Math 2009, 31(1), 295-306.

The boundedness of generalized Cesaro operators P^b,c for Re b ≥ Rec > 0 on mixed norm space H_{p, q} (φ), 0 < p, q ≤ ∞ is proved. In particular b = 1 + α and c = 1, P^b,c becomes the α-Cesaro operator C^α, Re α ≤ 0 and further for α = 0 it becomes classical Cesaro operator. Thus our results extend the results of Shi and Ren.

15 ref

010397   Nageswara Rao V (Statistics Dep, Univ Arts & Science College, Warangal-506 001) : PTS estimation of scale parameter of a two - parameter exponential distribution. J Indian Acad Math 2009, 31(1), 185-8.

An estimator of the scale parameter of a two - parameter exponential distribution is constructed after incorporating a preliminary test of significance regarding equality of scale parameters of two populations. Expressions for its bias and Mean Squared Error(MSE) are derived and made recommendations regarding its suitability over the Minimum Variance Unbiased Estimator(UMVUE).

2 ref

010396   Nagarajarao I H;Ushakanthi A V S (Mathematics Dep, Gayatri College for P.G. Courses, Visakhapatnam 45, Email: ihnrao@rediffmail.com) : On a refined fractional programming problem. J Indian Acad Math 2009, 31(1), 213-19.

The Refined Fractional Programming Problem (RFPP) with Objective function of the following form : f(x) = (ax + p) + (cx + q)/(ex + r)^{m; Ax ≥ b; x ≥ 0, m being a positive integer, has been solved by reducing it to a Fractional Programming Problem (FPP). Further, under extra conditions, it is shown that the solution of the RFPP can be obtained through an associated LPP.}

2 ref

010395   Mishra A (NO, Patna Univ, Patna) : On a quasi-logarithmic series distribution. J Indian Statist Ass 2008, 46(2), 127-39.

A quasi logarithmic series distribution (QLSD) in which the probability of an event is linearly dependent on the number of successes has been obtained as a limiting case of a zero-truncated quasi negative binomial distribution. The mean and the first inverse moment of the distribution have been obtained. The estimation of parameters has been discussed and the distribution has been fitted to some observed data-sets to test its goodness of fit.

17 ref

010394   Meshram D K;Khobragade N W (Mathematics Dep, MJP Educational Campus, RTM Nagpur Univ, Nagpur-440 033, Email: khobragadenw@rediffmail.com) : Numerical study of stress functions in a thin annular disc due to partially distributed heat supply. J Indian Acad Math 2009, 31(1), 233-40.

An attempt is made to determine the unknown temperature, displacement and stress functions, due to partially distributed heat supply -Q₀ f(r, t)/λ at z=0 in a thin annular disc occupying the space a ≤ r ≤ b, -h ≤ z ≤ h by applying Marchi-Zgrablich transform and Laplace transform techniques.

6 ref

010393   Majumdar A;Yau D (Mathematics Dep, Indian Institute of Science, Bangalore-560 012, Email: anita@math.iisc.ernet.in) : Cohomology with coefficients for operadic coalgebras. Proc Indian Acad Sci-Mathl Sci 2009, 119(4), 431-52.

Corepresentations of a coalgebra over a quadratic operad are defined, and various characterizations of them are given. Cohomology of such an operadic coalgebra with coefficients in a corepresentation is then studied.

21 ref

010392   Lv X;Tang X (Mathematics Dep, Huzhou Teachers College, Huzhou, Zhejiang 313000, China, Email: lvxf@hutc.zj.cn) : Weighted composition operators between different bergman spaces of bounded symmetric domains. Proc Indian Acad Sci-Mathl Sci 2009, 119(4), 521-9.

Consider the boundedness and compactness of the weighted composition operators between different Bergman spaces of bounded symmetric domains in terms of the Carleson measure. As an application, we study the multipliers between different Bergman spaces.

12 ref

010391   Linga Raju T;Nagavalli M (Engineering Mathematics Dep, Univ College of Engineering, Andhra Univ, Visakhapatnam-530 003, Email: tlraju45@yahoo.com) : Hall effect on HMF of an ionized gas between parallel plates in a slip flow regime. J Indian Acad Math 2009, 31(1), 135-42.

An attempt has been made to study the effect of Hall currents on hydromagnetic flow (HMF) of an ionized gas between two parallel plates in a slip flow regime for both the cases: one for non-conducting and the other for conducting plates. It is assumed that the magnetic Reynolds number is small. The exact solutions of the resulting governing equations are obtained for the primary and secondary velocity distributions, and their corresponding mean velocities have also been obtained. Effects of the Hall parameter a, velocity slip parameter β, Hartmann number H_a and the ionization parameters (that is, the ratio of the electron pressure to the total pressure) on the velocity field are discussed numerically and are also shown graphically.

8 illus, 11 ref

010390   Ledoan A;Zaharescu A (Mathematics Dep, Rochester Univ, Hylan Building, Rochester, New York 14627-0138, USA, Email: ledoan@math.rochester.edu) : Real moments of the restrictive factor. Proc Indian Acad Sci-Mathl Sci 2009, 119(4), 559-66.

Let λ be a real number such that 0 <A < 1. We establish asymptotic formulas for the weightedreal moments ∑_n≤x R^λ(n)(1-n/x), where R(n) = Π^k_v=1 p^αv-1_v is the Atanassov strong restrictive factor function and n = Π^k_v=1 p^{αV is the prime factorization of n.}

010389   Lakshmi S;Venkatesh A (Mathematics Dep, Kunthavai Nachiyar Govt. Arts College for Women, Thanjavur, Email: laktnj@rediff.com) : Stochastic model for the secretion of dopamine due to stress leading to schizophrenia. J Indian Acad Math 2009, 31(1), 77-83.

Stochastic model to access dimensions of reactions to human stress is presented and Atypical Antipsychotic Drugs(APDs), Dopamine D₂ antogonist properties are described. The results are consistent that the idea that the problem of human stress to a significant extent. The study was to examine the effect of stress on medial prefrontal cortex and on Nucleus Accumbens, Dopamine release using atypical APDs. The application of compound-Renewal damage model is taken up to estimate the expected time to reach breakdown point and its variance.

1 illus, 14 ref

010388   Koul H L;Aggarwal D (NO, Michigan State Univ, USA) : Minimum empirical distance goodness-of-fit tests for current status data. J Indian Statist Ass 2008, 46(2), 79-125.

Deals with the problem of fitting a parametric model to the distribution function of the event occurrence time with current status data. The proposed goodness-of-fit test is based on minimum empirical distance statistic used to fit a regression model. Asymptotic normality of minimum empirical distance test statistic and estimator under the model being fitted in a general regression set up is established. These results are then used to fit a parametric model to the distribution of the event occurrence time based on current status data. A simulation study is included to exhibit the finite sample level and power behavior, and to make a comparison of the proposed test with the one sample Cramer-von Mises test based on nonparametric maximum likelihood estimator of the distribution function of the event occurrence time.

9 tables, 15 ref

010387   Kosan M T (Mathematics Dep, Gebze Institute of Technology, Cayirova Campus, 41400 Gebze-Kocaeli, Turkey, Email: mtkosan@gyte.edu.tr) : On artinian generalized local cohomology modules. Proc Indian Acad Sci-Mathl Sci 2009, 119(4), 453-8.

Let R be a commutative Noetherian ring with non-zero identity and a be a maximal ideal of R. An R-module M is called minimax if there is a finitely generated submodule N of M such that M/N is Artinian. Over a Gorenstein local ring R of finite Krull dimension, we proved that the Socle of Hⁿ_a(R) is a minimax R-module for each n ≥ 0.

9 ref

010386   Khan A;Patni P (Mathematics and Statistics Dep, Jai Narain Vyas Univ, Jodhpur, Email: draiyubkhan@gmail.com) : Gravitational instability of an interstellar medium in a horizontal magnetic field. J Indian Acad Math 2009, 31(1), 173-84.

Studied the effects of Hall currents on magnetogravitational stability of interstellar medium. The streaming motion is also assumed to be horizontal. MHD linearized equations and applying normal mode technique, the dispersion relation has been derived and solved numerically. It is found that the rotation and magnetic field have stabilizing effect while Hall current has destabilizing effect on the growth rate of unstable configuration.

3 illus, 9 ref

010385   Kataria H R (Mathematics Dep, Faculty of Science, M.S. Univ of Baroda, Vadodara-390 002) : Fourier sine series solution representing the common pressure gradient for one dimensional flow through the stratum containing oil, water and gas. J Indian Acad Math 2009, 31(1), 203-12.

Represents the simultaneous flow of three immiscible fluids namely oil, water and gas. Each fuel satisfies Darcy's law and equation of continuity. The system of governing equation for each fluid has been derived. Further these three systems of equations are combined to get a single second order linear partial differential equation which governs flow of fluids in porous media. Authors have obtained fourier sine series solution under the assumption that the pressure gradient can be expressed as a sum of steady state pressure and the transient pressure.

1 illus, 5 ref

010384   Kannan S S;Pattanayak S K (NO, Chennai Mathematical Institute, Plot H1, SIPCOT IT Park, Padur Post Office, Siruseri-603 103, Email: kannan@cmi.ac.in) : Torus quotients of homogeneous spaces - minimal dimensional schubert varieties admitting semi-stable points. Proc Indian Acad Sci-Mathl Sci 2009, 119(4), 469-85.

In this paper, for any simple, simply connected algebraic group G of type B, C or D and for any maximal parabolic subgroup P of G, we describe all minimal dimensional Schubert varieties in G/P admitting semistable points for the action of a maximal torus T with respect to an ample line bundle on G/P. We also describe, for any semi-simple simply connected algebraic group G and for any Borel subgroup B of G, all Coxeter elements τ for which the Schubert variety X (τ) admits a semistable point for the action of the torus T with respect to a non-trivial line bundle on G/B.

9 ref

010383   Kannan R;Ganesan A;Sathiyamoorthi R; Malarvizhi G (Statistics Dep, Annamalai Univ, Annamalai Nagar-608 002, Email: statkannan@yahoo.co.in) : Stochastic model for time to cross antigenic diversity threshold of HIV transmission under alertness. J Indian Acad Math 2009, 31(1), 85-98.

The paper focuses on the study of a stochastic model for predicting the time to cross antigenic diversity threshold of HIV transmission under alertness. As the immune capacities of an individual vary and also have its own resistance, the antigenic diversity threshold is different for different persons. The concept of preventive strategies is gaining the greater importance now a day in view of both prevention and delay in the process of seroconversion. The effectiveness of such preventive strategy is investigated using a stochastic model by appropriate conceptualization of the problem. In this paper it is assume that threshold distribution is Gamma which doesn't satisfy the LMP property. In doing so the concept of antigenic diversity threshold has discussed by Stilianakis et al., (1994) and shock model approach by Esary et al., (1973) is used. The mean time to cross antigenic diversity threshold and its variance are derived and numerical illustration is provided using simulation.

6 illus, 5 ref

010382   Jayakumar K;Jilesh V (Statistics Dep, Calicut Univ, Kerala-673 625, Email: jkumar19@rediffmail.com) : Skew symmetric distribution. Sci Soc 2008, 6(2), 135-43.

Skew generalized forms of symmetric distributions have find applications in finance, engineering, chemical physics, civil engineering, geographical information systems, grain size distribution, stock returns and exchange rate changes, business firm growth, human heredity, information theory, pattern recognition, image and signal processing. This paper is a review of different methods of generating skew distributions from symmetric ones. Special attention is given to skew normal and asymmetric Laplace distributions.

42 ref

010381   Jain K (Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore-560 064, Email: hain@jncasr.ac.in) : Adaptation dynamics of the quasispecies model. Pramana J Phys 2008, 71(2), 275-82.

Study is the adaptation dynamics of an initially nialadapted population evolving via the elementary processes of mutation and selection. The evolution occurs on rugged fitness landscapes which are defined on the multi-dimensional genotypic space and have many local peaks separated by low fitness valleys. Mainly focus on the Eigen's model that describes the deterministic dynamics of an infinite number of self-replicating molecules. In the stationary state, for small mutation rates such a population forms a quasispecies which consists of the fittest genotype and its closely related mutants. The quasispecies dynamics on rugged fitness landscape follow a punctuated (or step-like) pattern in which a population jumps from a low fitness peak to a higher one, stays there for a considerable time before shifting the peak again and eventually reaches the global maximum of the fitness landscape. We calculate exactly several prpperties of this dynamical process within a simplified version of the quasispecies model.

2 illus, 12 ref

010380   Huang Z;Zhang R (Statistics and Actuarial Science Dep, East China Normal University, Shanghai-200 241, Peoples' Republic of China) : Nonparametric inference for single-index function in varying-coefficient single-index model. Indian J pure appl Math 2008, 40(2), 87-111.

Varying coefficient single-index model (VCSIM) with back-fitting algorithms is very important in statistical modeling, but the inferences for single-index function on the model have not been very well developed. There are also few tools available to answer such a frequently asked question, such as whether the relationship between Y and X is nonlinear. In order to address this issue, we extent the generalized likelihood ratio (GLR) tests to the model, using the estimates obtained by the local linear method, backfitting technique. We demonstrate that under the null hypotheses the proposed GLR statistics follow asymptotically rescaled chi-squared distribution, with the scale constants and the degree of freedom being independent of the nuisance parameters, which is called the Wilks phenomenon. Both simulated and real data examples are used to illustrate our proposed methodology.

4 illus, 1 table, 17 ref

010379   Govindarajan A;Ramamurthy V (Mathematics Dep, SRM Univ, Kattankulathur-603 203) : MHD 3 dimensional dusty flow past a porous plate. J Indian Acad Math 2009, 31(1), 143-56.

This paper analyses the effects of magnetic field and dust parameters on the three dimensional flow of an incompressible viscous dusty fluid past a porous plate under the following conditions: (1) The dusty fluid is electrically conducting (2) The free stream velocity is uniform (3) The plate is subjected to a periodic suction velocity distribution (4) The plate temperature is constant (5) A magnetic field of uniform strength is applied in the direction normal to the plate. The problem is solved by using perturbation method. Solutions are obtained for the velocity field, temperature (both fluid and dust) and skin friction. The effects of Hartmann number (M), suction parameter (a) and dust parameters f and Λ on the velocity field and skin friction are discussed with the help of graph and tables. The velocity profiles of both the fluid and dust increase with an increase of either suction parameter (or) Hartmann number (M).

3 illus, 1 table, 11 ref

010378   Duraphe S;Mishra A;Shrivastava K (Mathematics Dep, M.V.M. College, Bhopal, Email: duraphe_sus65@rediffmail.com) : Results on chain preserving maps. J Indian Acad Math 2009, 31(1), 99-105.

In this paper the concepts of chain preserving maps, strongly chain preserving maps and g-continuous maps in metric spaces are introduced. It is shown that a strongly chain preserving map lies between contraction and continuous map. Many properties of chain preserving maps and strongly chain preserving maps are proved.

6 ref

010377   Devi H;Mohamed Tajik M (Mathematics Dep, Kongunadu Arts & Science College, Coimbatore 29) : Decomposition of g α g homeomorphsms on topological spaces. J Indian Acad Math 2009, 31(1), 15-21.

Two new classes of generalized homocomorphisms are introduced and shown that one of those classes has a group structure. Moreover, some properties of those two homomorphisms are obtained.

8 ref

010376   Denis R Y;Singh S N (Mathematics & Statistics Dep, Gorakhpur Univ, Gorakhpur-273 009, Email: ddry@sancharnet.in) : On certain modular identities and evaluation of theta functions with application. J Indian Acad Math 2009, 31(1), 277-87.

By making use of certain modular equations of Ramanujan authors attempt to establish certain modular identities which will be helpful in evaluating certain theta functions. Authors shall also discuss some of their applications.

4 ref

010375   Chaudhari O K;Khot P G;Deshmukh K C (G.H.R. College of Engineeirng, RTM Nagpur Univ, Nagpur, Email: onkarkc_24@rediffmail.com) : Mathematical model of transportation problem (MMTP) in fuzzy environment (FMMTO). J Indian Acad Math 2009, 31(1), 59-64.

A transportation problem has been considered in fuzzy environment in supply and demand constraints to minimize the total cost of transportation. Flexible values of supply and demands are considered as fuzzy in nature and fuzzy set theory has been used to convert the fuzzy model into crisp one for the optimization relative to the degree of association between supply and demand determinants. Corresponding operator has been used to assign the fuzzy membership function corresponding to fuzzy sets for fuzzy objectives.

2 illus, 10 ref

010374   Casnati G;Notari R (Dipartimento di Matematics, Politecnico di Torino, c.so. Duca degli Abruzzi 24, 10129 Torino, Italy, Email: casnati@calvino.polito.it) : Poincare series of a local gorenstein ring of multiplicity up to 10 is rational. Proc Indian Acad Sci-Mathl Sci 2009, 119(4), 459-68.

Let R be a local, Gorenstein ring with algebraically closed residue field k of characteristic 0 and let P_R(z) := ∑^∞_p=0 dim_k(Tor^R_p(k, k))z^p be its Poincare series. We compute P_R when R belongs to aparticular class defined in the Introduction, proving its rationality. As a by-product we prove the rationality of P_R for all local, Gorenstein rings of multiplicity at most 10.

19 ref

010373   Bose D;Madan S;Mohanty P;Shrivastava S (Mathematics and Statistics Dep, Indian Institute of Technology, Kanpur-208 016) : Relations between bilinear multipilers on R<. Proc Indian Acad Sci-Mathl Sci 2009, 119(4), 501-12.

Proves the bilinear analogue of de Leeuw's result for periodic bilinear multipliers and some Jodeit type extension results for bilinear multipliers.

15 ref

010372   Biswas D (Mathematics Dep, Indian Institute of Technology, Kharagpur-721 302, Email: d_priya05@yahoo.co.in) : Cayley transform and the unit cycle in the parabolic case. J Indian Acad Math 2009, 31(1), 37-48.

Authors have introduced the notion of Cayley transform and the unit cycle for the parabolic case. One of the main purposes for introducing Cayley transform is to simplify certain calculations in the upper half plane. Also proved some properties relating to the parabolic Cayley transform.

4 illus, 18 ref

010371   Bhattacharya A (Abhishek Bhattacharya, Statistical Science Dep, Duke Univ, Box 90251, Durham, NC 27708, Email: abhishek.bhattacharya@duke.edu) : Statistical analysis on manifold: a nonparametric approach for inference on shape spaces. Sankhya 2008, 70(pt 2), 223-66.

Concerns nonparametric statistics on manifolds with special emphasis on landmark based shape spaces in which a k-ad, i.e., a set of k points or landmarks on an object or a scene, is observed in 2D or 3D, for purposes of identification, discrimination, or diagnostics. Two different notions of shape are considered: reflection shape invariant under all translations, scaling and orthogonal transformations, and affine shape invariant under all affine transformations. A computation of the extrinsic mean reflection shape, which has remained unresolved in earlier works, is given in arbitrary dimensions, enabling one to extend nonparametric inference on Kendall type shape manifolds from 2D to higher dimensions. For both reflection and affine shapes, two sample test statistics are constructed based on appropriate choice of or-thonormal frames on the tangent bundle and computations of differentials of projection maps with respect to them at the sample extrinsic mean. The samples in consideration can be either independent or be the outcome of a matched pair experiment. Examples are included to illustrate the theory.

3 illus, 36 ref

010370   Bhadauria B S;Sherani M A (Mathematics and Statistics Dep, Faculty of Science, Jai Narain Vyas Univ, Jodhpur-342 001, Email: drbsbhadauria@yahoo.com) : Effect of gravity modulation on the onset of Darcy convection in a rotating porous medium. J Indian Acad Math 2009, 31(1), 107-18.

The paper is devoted to the study of linear thermal instability problem in a fluid-saturated porous medium under the influence of rotation with gravity modulation. The study is done using extended Darcy model. Gravitational field is considered to be having two parts: a constant part, and a time-dependent periodic part, which can be obtained by shaking the fluid. Perturbation procedure based on the small amplitude of imposed gravity modulation, which was proposed by Venezian [42], is used to study the combined effect of rotation, permeability and gravity modulation on the stability in a fluid-saturated-porous medium. The correction of critical Darcy Rayleigh number is calculated as function of frequency of modulation, Darcy Taylor number and Vadasz number. It is found that rotation advances the onset of thermal instability in the fluid-saturated-porous medium.

44 ref

010369   Berend D;Dubickas A (Mathematics and Computer Science Dep, Ben-Gurion Univ, Beer Sheva 84105, Israel, Email: berend@math.bgu.ac.il) : Good points for diophantine approximation. Proc Indian Acad Sci-Mathl Sci 2009, 119(4), 423-9.

Given a sequence (x_n)^∞_n=1 of real numbers in the interval [0, 1) and a sequence (δ_n)^∞_n=1 of positive numbers tending to zero, considers the size of the set of numbers in [0, 1] which can be 'well approximated' by terms of the first sequence, namely, those y ∈ [0, 1] for which the inequality |y - X_n| < δ_n holds for infinitely many positive integers n. We show that the set of 'well approximable' points by a sequence (x_n)^∞_n=1, which is dense in [0, l],is 'quite large' no matter how fast the sequence (δ_n)^∞_n=1 converges to zero. On the other hand, for any sequence of positive numbers (δ_n)^∞_n1 tending to zero, there is a well distributed sequence (x_n)^∞;_n=1 in the interval [0, 1] such that the set of 'well approximable' points y is 'quite small'.

11 ref

010368   Badshah V H;Meena G (NO, Vikram Univ, Ujjain 45610) : Common fixed point for compatible mappings on 2-metric space. J Indian Acad Math 2009, 31(1), 23-30.

Aims of the of the paper is to obtain a common fixed point theorem by using reciprocal continuity with the concept of asymptotic regularity for compatible mappings.

5 ref

010367   Athreya K B (Mathematics and Statistics Dep, Iowa State Univ, USA, Email: kba@iastate.edu) : Entropy maximization. Proc Indian Acad Sci-Mathl Sci 2009, 119(4), 531-9.

It is shown that (i) every probability density is the unique maximizer of relative entropy in an appropriate class and (ii) in the class of all pdf f that satisfy f fh_i dμ = λ_i for i = 1,2, k the maximizer of entropy is an f₀ that is proportional to exp (∑c_ih_i) for some choice of c_i. An extension of this to a continuum of constraints and many examples are presented.

010366   Athreya J S (Mathematics Dep, Yale Univ, New Haven, CT, USA, Email: jathreya@gmail.com) : Logarithm laws and shrinking target properties. Proc Indian Acad Sci-Mathl Sci 2009, 119(4), 541-52.

Survey some of the recent developments in the study of logarithm laws and shrinking target properties for various families of dynamical systems. We discuss connections to geometry, diophantine approximation and probability theory.

31 ref

010365   Ahmed S (Mathematics Dep, Govt. Degree College, Thanna Mandi-185 212, Email: Shakeelar2002@yahoo.co.in) : Some properties of order of an element in topological spaces. J Indian Acad Math 2009, 31(1), 289-93.

Studied some more properties of Order of an Element in Topological Spaces.

10 ref

010364   Age C T;Salunke J N (Mathematics Dep, School of Mathematical Sciences, North Maharashtra Univ, Jalgaon-425 001, Email: caage17@gmail.com) : Fixed point theorem for continuous densifying mapping in complete metric space. J Indian Acad Math 2009, 31(1), 31-5.

Presents a fixed point theorem and it is an extension of the fixed point theorem of S. Khan.

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009381   Vilcu G E (Mathematics and Computr Science Dep, Petroleum-Gas Univ of Ploiesti, Bulevardul Bucuresti, Nr. 39, Ploiesti 100680, Romania, Email: gvilcu@mail.upg-ploiesti.ro) : Riemannian foliations on quaternion CR-submanifolds of an almost quaternion Kahler product manifold. Proc Indian Acad Sci-Mathl Sci 2009, 119(5), 611-18.

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009380   Vasuki K R;Sharath G (Studies in Mathematics Dep, Mysore Univ, Manasagangotri, Mysore-570 006) : Bilateral hypergeometric series summation formulas. Int J mathl Combinatorics 2009, 4(Jan), 41-8.

H. Exton has recorded two 3 ψ 3 basic bilateral hypergeometric scries Mnnination formula without proof oil page 305 of his book entitled q- hypergeometric functions and applications.

009379   Tamizh Chelvam T;Mutharasu S (Mathematics Dep, Manomaniam Sundaranar Univ, Tirunelveli-627 012) : Efficient domination in Bi-Cayley graphs. Int J mathl Combinatorics 2009, 4(Jan), 56-62.

A Cayley graph is constructed out of a. group V and its general ing set A ami it ih denoted by C(T, X). A Smarandachely n-Cayley graph, is defined to be C = ZC*(T. X), when; V(G) = Γ X Z_n and E(G) = {((x, 0). (y,1))_a, ((.x, 1), (y, 2))_a, ... ((x, n. - 2), (y,n - 1))_a : x, y ∈ Γ a ∈ X such that y = x * a}. Particularly, a Smarandachely 2-Caylev graph is called as a Bi-Cayley graph, denoted by BC(Γ, X). Necossary and sufficient conditions lor the existence of an efficient dominating set a.nd an efficient open dominating set. in Bi-Cayley graphs are determined.

009378   Sury B (NO, Indian Statistical Institute, 8th Mile Mysore Road, Bangalore-560 059, Email: sury@isibang.ac.in) : When are complex zeroes on a roll(e)?. Resonance 2009, 14(9), 872-81.

It is quite common for the same material to crystallize in different arrangements of the molecules in the crystal. This phenomenon is referred to as polymorphism and it happens for elements, Pharmaceuticals, biological compounds and proteins. In this article we present a brief review of bolymor-phism, stressing its physical aspects, types and applications, We discuss why it is important to understand the phenomenon, and the need to develop ways of controlling it. Also outline some legal issues related to it.

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009377   Storch U (Uwe Storch, Fakultat fur Mathematik, Ruhr Universitat Bochum, D-44780 Bochum, Germany, Email: uwe.storch@rub.de) : Pythagoras and diophantus. Resonance 2009, 14(7), 691-703.

Theorem of Pythagoras is employed as a starting point for discussing the irrationality of the square root of 2 and its implications in Mathematics and culture. It motivates to consider the equation of the circle over the field of rational numbers and other fields which leads in a natural way to the use of modular arithmetic for Diophantine equations.

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009376   Somashekara D D;Veena C R (Studies in Mathematics Dep, Mysore Univ, Manasagangothri, Mysore-570 006, Email: dsomashekara@yahoo.com) : On smarandachely harmonic graphs. Int J mathl Combinatorics 2009, 4(Jan), 75-83.

Graph G is said to be Sraarandachely harmonic graph with property P if its vertices can be labeled 1,2, ..., n such that the function f p : A → Q defined by is injective. Particularly, if A is the collection of all paths of length 1 in G (That is. A = E(G)), then a. Smarandachely harmonic graph is called Strongly harmonic gia]>h. In this paper we show that, all cycles, wheels, trees a.nd grids are strongly harmonic graphs. Also we give a.n upper bound a.nd a. lower bound for μ(n), the niaxinmin number of edges in a strongly harmonic graph of order n.