007633   Azad K K (Mathematics Dep, Allahabad Univ, Allahabad, Uttar Pradesh) : On wavelet sets. J Indian Acad Math 2009, (Spl), 10-18.

40 ref

007632   Ayyaoppan G;Velmurugan S (Mathematics Dep, Pondicherry Engineering College, Puducherry-605 014) : A nonpreemptive priority multiserver queueing system with accessible and non-accessible bulk service and heterogeneous arrivals. Int Rev pure appl Math 2008, 4(2), 233-4.

In this paper a multi server non-preemptive priority queueing system consisting of two types of customer units with Poisson arrival and exponential service time distribution is analysed. The lower priority units are served by a bulk service rule. This rule admits each batch served to have not less than 'a' and not more than `b' customers such that the arriving customers can enter service station without affecting the service time if the size of the batch being served is less than `d' (a ≤ d ≤ b). The higher priority units have non-preemptive priority over lower priority units. The higher priority units are served singly. The steady state probability vectors of the number of customers in the queue are obtained using the modified matrix geometric method. The stability condition and mean queue length of customers are obtained. Numerical results are also presented.

7 ref

007631   Arun Kumar T;Anand Babu L;Shivani B (Mathematics Dep, Osmania Univ, Hyderabad-500 007, Email: oumaths@gmail.com) : Heat and mass transfer effect on free convective MHD flow past an infinite vertical plate using finite element method. J Indian Acad Math 2010, 32(1), 181-94.

A finite element technique is implemented for the free convection effects on MHD stokes problem. The numerical values for concentration, velocity and temperature under various physical situations are obtained and have been analyzed graphically. The numerical results are compared with analytical solution and established the validity of finite element technique (Ritz method).

10 illus, 3 tables, 10 ref

007630   Arora L K;Saha U K (Mathematics Dep, North Eastern Regional Institute of Science and Technology, Nirjuli (Itanagar), Arunachal Pradesh) : Integrals involving hypergeometric functions and H-function. J Indian Acad Math 2010, 32(1), 243-9.

Evaluates two finite integrals, first one involving hypergeometric function and the second, product of hypergeometric function & H-function which includes three results as its special cases, which seems to be new.

4 ref

007629   Anitha R;Sangavai K (Mathematics and Computer Applications Dep, PSG College of Technology, Coimbatore, Email: anitha_nadarajan@mail.psgiech.ac.in) : A quick survey on the solutions of degree constrained minimum spanning tree problem. Int Rev pure appl Math 2008, 4(2), 179-82.

A spanning tree of a graph such that each node in the tree has degree at most d is called a degree constrained spanning tree. The problem of finding the degree constrained spanning tree of minimum cost in an edge weighted graph is NP-complete for every d, in the range [2, n - 2], where n denotes the number of nodes. In this paper author give a brief summary on the solutions of this problem.

9 ref

007628   Anil Kumar;Varshney C L;Lal S (Applied Mathematics Dep, Dronacharya College of Engineering, Greater Noida, Uttar Pradesh, Email: dranilkumar06@yahoo.co.in) : Finite difference technique for three dimensional MHD flow through a porous medium bounded by an infinite vertical porous plate. J Indian Acad Math 2009, (Spl), 147-160.

Objective of this paper is to study the MHD three dimensional free convective flow of a viscous incompressible fluid through a porous medium. The porous medium is bounded by an infinite vertical porous plate. The governing equations have been solved by using Finite difference technique. The expressions for temperature profile, concentration profile and skin friction at the porous plate have been numerically worked out for various values of parameters involved in the solutions.

9 illus, 28 ref

007627   Amit Singh;Dimri R C;Gairola U C (Mathematics Dep, H.N.B. Garhwal University, Srinagar (Gharwal)-246 174, Email: Singhamit841@gmail.com) : Fixed point theorem for near-hybrid contraction. J Natn Acad Math India 2008, 22, 11-22.

In the present paper author proved a fixed point theorem by using near-hybrid contractive type condition for a pair of single-valued and a pair of multi valued mappings in complete metric spaces. This result extend the main result of Mbarki and others.

22 ref

007626   Amit Prakash (Applied Science Dep, Azad Institute of Engineering & Technology Natkur, Bangla Bazar Road, Lucknow, Email: apoct0185@rediffmail.com) : Special quarter-symmetric recurrent-metric connection in a Lorentzian para-sasakian manifolds. J Indian Acad Math 2009, (Spl), 120-28.

Defines and study a special quarter-symmetric recurrent-metric connection in a Lorentzian para-Sasakian manifold and prove its existence. The curvature tensor and the Ricci tensor of the special quarter-symmetric recurrent-metric connection are found. A necessary and sufficient condition has been deduced for the Ricci tensor of D to be skew-symmetric under certain conditions. Some properties of the conformal curvature tensor and Einstein tensor with respect to the special quarter-symmetric recurrent-metric connection in a Lorentzian para-Sasakian manifold is obtained.

5 ref

007625   Ahmed N;Kalita H (Mathematics Dep, Guwahati Univ, Guwahati-781 014, Email: saheel_nazib@yahoo.com) : Oscillatory MHD free convective flow through a porous with mass transfer, soret effect and chemical reaction. Indian J Sci Technol 2010, 3(8), 919-24.

An attempt is made to investigate the problem of an oscillatory MHD free convective flow through a porous medium with mass transfer, Soret effect and chemical reaction when the temperature as well as concentration at the plate varies periodically with time about a steady mean. Analytical solutions to the coupled non-linear equations governing the flow and heat and mass transfer are obtained by using regular perturbation technique. The influence of the different parameters entering in to the problem viz. the Hartmann number M, the Grashof number for heat transferG_r, the Grashof number for mass transfer G_m, Soret number S₀, the plate velocity U, chemical reaction C_h etc. on temperature distribution, species concentration, velocity distribution, skin-friction and the rates of heat and mass transfer at the plate are discussed graphically.

16 ref

007624   Agarwal M;Verma V S;Srivastava S (Mathematics & Astronomy Dep, Lucknow University, Lucknow-226 007) : Analytical approach to the problem of dispersion of an air pollutant with variable wind velocity. J Natn Acad Math India 2008, 22, 51-62.

The dispersion of an air pollutant emitted from a point source is studied by assuming that the wind velocity varies with downwind distance taken in the form of wave functions and by considering the rate of removal constant. It is further assumed that eddy diffusivities are constants. Then, an analytical solution to an unsteady state three-dimensional dispersion equation with a point source has been developed.

3 illus, 17 ref

006598   Zhang Z;Pang B (Mathematics Dep, Luoyang Teachers' College, Luoyang-471 002, Email: zhzhzhang-yang@163.com) : Several identities in the catalan triangle. Indian J pure appl Math 2010, 41(2), 363-78.

Authors first establish several identities for the alternating sums in the Catalan triangle whose (n,p) entry is defined by B_n,p = p/n(2n/n-p). Second, authors show that the Catalan triangle matrix C can be factorized by C = FY = ZF, where F is the Fibonacci matrix. From these formulas, some interesting identities involving B_{n, p} and the Fibonacci numbers F_n are given. As special cases, some new relationships between the well-known Catalan numbers C_n

13 ref

006597   Yousefi M S;Amini M;Sady F (Mathematics Dep, Faculty of Mathematical Sciences, Tarbiat Modares Univ, P.O. Box 14115 134, Tehran, Iran, Email: shams@modares.ac.ir) : Complete order amenability of the Fourier algebra. Indian J pure appl Math 2010, 41(3), 485-504.

Defines complete order amenability and first complete order coho-mology groups for quantized Banach ordered algebras and show that the vanishing of the latter is equivalent to the operator amenability for the Fourier algebra.

27 ref

006596   Speh B;Venkataramna T N (Mathematics Dep, 310 Moloott Hall Cornell Univ, Ithaca, NY-14853 4201, USA, Email: speh@math.cornell.edu) : Discrete components of some complementary series representations. Indian J pure appl Math 2010, 41(1), 145-51.

Authors show that the restriction of the complementary series representations of SO(n, 1) to SO (m, 1) (m <60> n) contains complementary series representations of SO (m, 1) discretely, provided that the continuous parameter is sufficiently close to the first point of reducibility and the representation of M- the compact part of the Levi- is a sufficiently small fundamental representation. Authors proves, as a consequence, that the cohomological representation of degree i of the group SO (n, 1) contains discretely, for i ≤ m/2, the cohomological representation of degree i of the subgroup SO(m, 1) if i ≤ m/2. As a global application, show that if G/Q is a semisimple algebraic group such that G(R) = SO(n, 1) up to compact factors, and if we assume that for all n, the tempered cohomological representations are not limits of complementary series in the automorphic dual of SO(n, 1), then for all n, non-tempered cohomological representations are isolated in the automorphic dual of G. This reduces conjectures of Bergeron to the case of tempered cohomological representations.

10 ref

006595   Singh J P (Mathematics and Computer Sciences Dep, Mizoram Univ, Aizawl-796 009, Email: jp_maths@rdiffmail.com) : On a semi-symmetric metric connexion on a Riemannaian manifold. Sci Vision 2010, 10(2), 62-5.

Yano studied semi-symmetric connexion on a Riemannian manifold (Mⁿ,g} and Thompson introduced 2-recurrent Riemannian manifold. The author here studied the nature of the 2-recurrent Riemannian manifold that admits a semi-symmetric connexion and it is found that such a manifold (Mⁿ,g) is M-Projectively 2-recurrent.

2 ref

006594   Ram Murty M (Mathematics Dep, Queen's Univ, Kingston, Ontario, K7L 3N6, Canada, Email: murty@mast.queensu.ca) : Small solutions of polynomial congruences. Indian J pure appl Math 2010, 41(1), 15-23.

Let p be prime and q/p - 1. Suppose x^q ≡ a(mod p) has a solution. Estimates the size of the smallest solution x₀ with 0 <60> x₀ <60> p. Proved that |x₀| <60> p^3/2q^-1 log p. By applying the Burgess character sum estimates, and estimates of certain exponential sums due to Bourgain, Glibichuk and Konyagin, we derive refinements of our result.

13 ref

006593   Prakasa Rao B L S (Mathematics and Statistics Dep, Hyderabad Univ, Hyderabad-500 046, Email: blsprao@gmail.com) : Wavelet linear estimaation for derivatives of a density from observations of mixtures with varying mixing proportions. Indian J pure appl Math 2010, 41(1), 275-91.

A wavelet based linear estimator is proposed for the derivatives of a probability density function based on a sample from a finite mixture of components with varying mixing proportions. It extends the linear estimator of a probability density function proposed by Pokhyl'ko (Theor. Probability and Math. Statist, 70 (2005) 135-145). Upper bounds on L₂ and L∝ losses are obtained for such estimators.

24 ref

006592   Misra G (Mathematics Dep, Indian Institute of Science, Bangalore-560 012, Email: gm@math.iisc.ernet.in) : Bergman kernel function. Indian J pure appl Math 2010, 41(1), 189-97.

Authors point out that a large family of n x n matrix valued kernel functions defined on the unit disc D ⊆ C, which were constructed recently in [9], behave like the familiar Bergman kernel function on D in several different ways. Shows that a number of questions involving the multiplication operator on the corresponding Hilbert space of holomorphic functions on D can'be answered using this likeness.

12 ref

006591   Mikhailov R;Passi I B S (Algebra Dep, Steklov Mathematical Institute, Gubkina 8, Moscow-119 991, Russia, Email: romanum@mi.ras.ru) : Limits over categories of extensions. Indian J pure appl Math 2010, 41(1), 113-31.

Considers limits over categories of extensions and show how certain well-known functors on the category of groups turn out as such limits. Also discuss higher (or derived) limits over categories of extensions.

12 ref

006590   Mehdi S;Parthasarathy R (Laboratoire de Mathematiques, UMR 7122 du CNRS pde Metz Univ, Batiment A, Ile du Saulcy, 57045 Metz Cedex 1, France, Email: mehdi@univ-metz.fr) : Representation theoretic harmonic spinors for coherent families. Indian J pure appl Math 2010, 41(1), 133-44.

Coherent continuation π₂ of a representation π₁ of a semisimple Lie algebra arises by tensoring π₁ with a finite dimensional representation F and projecting it to the eigenspace of a particular infinitesimal character. Some relations exist between the spaces of harmonic spinors (involving Kostant's cubic Dirac operator and the usual Dirac operator) with coefficients in the three modules. For the usual Dirac operator we illustrate with the example of cohomological representations by using their construction as generalized Enright-Varadarajan modules. In [9] we considered only discrete series, which arises as generalized Enright-Varadarajan modules in the particular case when the parabolic subalgebra is a Borel subalgebra.

25 ref

006589   Martin Lindsay J;Sinha K B (Mathematics and Statistics Dep, Lancaster Univ, Lancaster LA1 4YF, Uk, Email: j.m.lindsay@lancaster.ac.uk) : Quantum stochastic lie- Trotter product formula. Indian J pure appl Math 2010, 41(1), 313-25.

A Trotter product formula is established for unitary quantum stochastic processes governed by quantum stochastic differential equations with constant bounded coefficients.

25 ref

006588   Ma Ming;Li Z (School of Mathematics and Computer Science, Northwest Nationalities Univ, Lanzhou-730 030, Peoples' Republic of China, Email: jsmm@xbmu.edu.cn) : Life behavior of censored α-shock model. Indian J pure appl Math 2010, 41(2), 401-20.

The shock models play an important role in reliability theory. In a previous paper by Li et al., the δ-shock model, which is different from the classical shock model, was introduced and studied. In this paper, a censored δ-shock model is presented, which originates from the study of customer relationship management (CRM). Based on the underlying homogeneous Poisson process, we obtain the explicit distribution of system lifetime and other related properties, and demonstrate that this new system is superior to NBU. In addition, an exponential limit theorem is obtained. Finally, the application of this new system to evaluate customer lifetime values (CLV) is provided. These results are important to theory and applications.

3 illus, 26 ref

006587   Luukacova Medvid M;Morton K W (Institute of Numerical Simulation, Hamburg Technology Univ, Hamburg, Germany) : Finite volume evolution galerkin methods-a survey. Indian J pure appl Math 2010, 41(2), 329-61.

FVEG methods have been developed over the last dozen years to approximate unsteady hyperbolic equations in several space dimensions. In this survey the algorithmic origins of the methods are described. Then a detailed derivation of the methods is given, followed by evidence of their stability and accuracy. Finally several examples of their application are given.

4 illus, 31 ref

006586   Li J (Mathematics Dep, Rudan Univ, Room 202, No 20 Building, Guoding Road 700, Shanghai-200 433, People's Republic of China, Email: angelzcy@yahoo.cn) : Some limit results for probabilities estimates of Brownian motion with polynomial drift. Indian J pure appl Math 2010, 41(3), 425-42.

Let (B_t + f(t))_{t∈[0, + ∞]} be a Brownian motion with polynomial drift f(t), where f(t) is a polynomial. Some Limit Results for Lower tail and large deviation probabilities estimates, and Level crossing probabilities estimates of (B_t + f(t))_{t∈[0, + ∞]} are given in this paper.

6 ref

006585   Khanduja S K;Khassa R (Mathematics Dep, Punjab Univ, Chandigarh-160 014, Email: skhand@pu.ac.in) : Extension of a result of Zaharescu on irreducible polynomial. Indian J pure appl Math 2010, 41(1), 67-75.

It is well known that if f(x) is a monic irreducible polynomial of degree d with coefficients in a complete valued field (K, ||), then any monic polynomial of degree d over K which is sufficiently close to f(x) with respect to || is also irreducible over K. In 2004, Zaharescu proved a similar result applicable to separable, irreducible polynomials over valued fields which are not necessarily complete. In this paper, the authors extend Zaharescu's result to all irreducible polynomials without assuming separability.

5 ref

006584   Kannan V (Mathematics and Statistics Dep, Hyderabad Univ, Hyderabad-500 046, Email: vksm@uohyd.ernet.in) : Sets of periods of dynamical systems. Indian J pure appl Math 2010, 41(1), 225-40.

Authors presents a coherent, though not exhaustive, account of some well-known and some recent results of many mathematicians (including our own) on the following question: Given a "nice" class of dynamical systems, which subsets of N arise as the sets of periods of members of that class? While stating and explaining some elegant answers, proofs have been outlined or indicated occasionally.

1 table, 43 ref

006583   Jia Feng L;Jhi-Bing Z (Mathematics Dep, Ahejiang Normal Univ, Jinhua, Zhejiang-321 004, People's Republic of China, Email: jiafenglu@zjnu.edu.cn) : (p,λ)-Koszul algebras and modules. Indian J pure appl Math 2010, 41(3), 443-73.

In this paper, the notions of (p,λ)-Koszul algebra and (p,λ)-Koszul module are introduced. Some criteria theorems for a positively graded algebra A to be (p,λ)-Koszul are given. The notion of weakly (pλ)-Koszul module is defined as well and let Wκ^p_λ (A) denote the category of weakly (p,λ)-Koszul modules. Shows that M ∈ Wκ^p_λ(A) if and only if it can be approximated by (p,λ)-Koszul submodules, which is equivalent to that G(M) is a (p, λ)-Koszul module, where G(M) denotes the associated graded module of M. As applications, the relationships of the minimal graded projective resolutions of M, G(M) and (p, λ)-Koszul submodules are established. In particular, for a module M ∈ Wκ^p_λ (A) authors prove that ⊕_i≥o Extⁱ_A (M, A₀) ∈ gr_o(E(A)), also get as a consequence that the finitistic dimension conjecture is valid in Wκ^p_λ (A) under certain conditions.

15 ref

006582   Janakiram B;Davis M A;Soner N D (Planning Dep, , Bangalore-560 001) : Distance neighbourhood domination in graphs. Natn Acad Sci Lett 2009, 32(9-10), 287-90.

A set S of vertices in a graph G = (V,E) is said to be a k-distance neighbourhood dominating set, if G = U_v∈S <60> N_k[v] <62>. The k-distance neighbourhood domination number is the minimum cardinality of a k-distance neighbourhood dominating set of G and is denoted by n_k(G). In this communication, besides obtaining some bounds on n_k(G), some interesting results on n_k(G) characterizations of k-distance neighbourhood dominating set and minimal k-distance neighbourhood dominating set are obtained.

5 ref

006581   Huda S;Mukerjee R (Statistics Dep, Faculty of Science, Kuwait Univ, P.O. Box-5969, Safat-13060, Kuwait, Email: shuda@kuc01.kuniv.edu.kw) : Minimax second-order designs over cuboidal regions for the difference between two estimated responses. Indian J pure appl Math 2010, 41(1), 303-12.

Minimization of the variance of the difference between estimated responses at two points, maximized over all pairs of points in the factor space, is taken as the design criterion. Optimal designs under this criterion are derived, via a combination of algebraic and numerical techniques, for the full second-order regression model over cuboidal regions. Use of a convexity argument and a surrogate objective function significantly reduces the computational burden.

2 tables, 9 ref

006580   Guo X;Guo Y;Shum K P (Mathematics Dep, Jiangxi Normal Univ, Nanchang, Jiangxi-330 022, People's Republic of China, Email: xjguo@jrnu.edu.cn) : Super rpp semigroups. Indian J pure appl Math 2010, 41(3), 505-33.

Study a class of special strongly rpp semigroups, namely, the class of super rpp semigroups. These super rpp semigroups are generalizations of both superabundant semigroups and Clifford semigroups within the class of rpp semigroups. In particular, we prove that a super rpp semigroup is a semilattice of D¹-simple strongly rpp semigroups. The result not only generalizes a well-known theorem of Clifford in the class of completely regular semigroups but also strengthens some structure theorems obtained by Ren-Shum for superabundant semigroups which are orthodox. Some special super rpp semigroups are considered and discussed.

33 ref

006579   Digernes T;Varadarajan V S (NO, Trondheim Univ, Trondheim, Norway, Email: digernes@math.ntnu.no) : Notes on Euler's work on divergent factorial series and their associated continued fractions. Indian J pure appl Math 2010, 41(1), 39-66.

Factorial series which diverge everywhere were first considered by Euler from the point of view of summing divergent series. He discovered a way to sum such series and was led to certain integrals and continued fractions. His method of summation was essentialy what we call Borel summation now. In this paper, we discuss these aspects of Euler's work from the modern perspective.

15 ref

006578   Das N (P.G. Mathematics Dep, Utkal Univ, Vanivihar, Bhubaneswar-751 004, Email: namitadas440@yahoo.co.in) : Asymptotic Toeplitz and Hankel operators on the Bergman space. Indian J pure appl Math 2010, 41(2), 379-400.

The concept of asymptotic Toeplitz and asymptotic Hankel operators on the Bergman space are introduced and properties of these classes of operators are studied. The importance of this notion is that it associates with a class of operators a Toeplitz operator and with a class of operators a Hankel operator where the original operators are not even Toeplitz or Hankel. Thus it is possible to assign a symbol to an operator that is not Toeplitz or Hankel and hence a symbol calculus is obtained. Further a relation between Toeplitz operators and little Hankel operators on the Bergman space is established in some asymptotic sense.

11 ref

006577   Dani S G (School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Raod, Colaba, Mumbai-400 005, Email: dani@math.tifr.res.in) : Convolution roots and embeddings of probability measure on locally compact groups. Indian J pure appl Math 2010, 41(1), 241-50.

Discusses some properties of nilpotent Lie groups and their application in proving the embedding theorem for infinitely divisible probability measures on locally compact groups.

9 ref

006576   Dales H G;Feinstein J F (Pure Mathematics Dep, Leeds Univ, Leeds LS2 9JT, UK, Email: garth@maths.leeds.ac.uk) : Normed algebras of differentiable functions on compact plane sets. Indian J pure appl Math 2010, 41(1), 153-87.

Investigates the completeness and completions of the normed algebras (D⁽¹⁾(X), ||.||) for perfect, compact plane sets X. In particular, construct a radially self-absorbing, compact plane set X such that the normed algebra (D⁽¹⁾(X), ||.||) is not complete. This solves a question of Bland and Feinstein. Also prove that there are several classes of connected, compact plane sets X for which the completeness of (D⁽¹⁾ (X), ||.||) is equivalent to the pointwise regularity of X. For example, this is true for all rectifiably connected, polynomially convex, compact plane sets with empty interior, for all star-shaped, compact plane sets, and for all Jordan arcs in C. In an earlier paper of Bland and Feinstein, the notion of an F-derivative of a function was introduced, where F is a suitable set of rectifiable paths, and with it a new family of Banach algebras D⁽¹⁾_F (X) corresponding to the normed algebras D⁽¹⁾(X). In the present paper, we obtain stronger results concerning the questions when D⁽¹⁾(X) and D⁽¹⁾_F (X) are equal, and when the former is dense in the latter. In particular, show that equality holds whenever X is 'F-regular'. An example of Bishop shows that the completion of (D⁽¹⁾(X), ||.|| need not be semisimple. Shows that the completion of (D⁽¹⁾(X), ||.||) is semisimple whenever the union of all the rectifiable Jordan arcs in X is dense in X. Proves that the character space of D⁽¹⁾(X) is equal to X for all perfect, compact plane sets X, whether or not (D⁽¹⁾X), ||.||) is complete. In particular, characters on the normed algebras (D⁽¹⁾(X), ||.||) are automatically continuous.

9 illus, 19 ref

006575   Chatterjee K;Dey A (Statistics Dep, Visva Bharati Univ, Santiniketan, Birbhum-731 235, Email: alok.dey@gmail.com) : Class of saturated row column designs. Indian J pure appl Math 2010, 41(1), 293-302.

A new class of saturated, binary row-column designs is proposed. It is shown that these designs are treatment connected in the sense that these permit the estimability of all contrasts among treatment effects.

6 ref

006574   Brijlall D;Baboolal D (School of Science, Mathematics and Technology Education, KwaZulu- Natal Univ, Private Bag X54001, Durban 4000, South Africa, Email: brijlalld@ukzn.ac.za) : Katetov Morita theorem for the dimension of metric frames. Indian J pure appl Math 2010, 41(3), 535-53.

The results which appear here are devoted to the dimension theory of metric frames. We begin by characterizing the covering dimension dim of metric frames in terms of special sequences of covers and then prove the fundamental Katetov-Morita Theorem asserting that Ind L = dimL for every metric frame L. Next, establish two characterizations of the dimension function Ind in metric frames, one in terms of special bases and another in terms of decompositions into subspaces of dimension zero. These characterizations yield a sum theorem.

12 ref

006573   Bhatia R (NO, Indian Statistical Institute, New Delhi-110 016, Email: rbh@isid.ac.in) : Modulus of continuity of the matrix absolute value. Indian J pure appl Math 2010, 41(1), 99-111.

Lipschitz continuity of the matrix absolute value |A| = (A* A)^1/2 is studied. Let A and B be invertible, and let M₁ = max(||A||, ||B||), M₂ = max (||A^-1||, ||B^-1||). Then it is shown that, || |A| - |B| || ≤ (1 + log M₁M₂) ||A-B||. A proof is given for the well-known theorem that there is a constant c(n) such that for any two n x n matrices A and B || |A| - |B| || ≤ c(n) ||A - B|| and the best constant in this inequality is O(log n).

18 ref

006572   Bapat R B;Gupta S (NO, Indian Statistical Institute, New Delhi-110 016, Email: rbb@isid.ac.in) : Resistance distance in wheels and fans. Indian J pure appl Math 2010, 41(1), 1-13.

The wheel graph is the join of a single vertex and a cycle, while the fan graph is the join of a single vertex and a path. The resistance distance between any two vertices of a wheel and a fan is obtained. The resistances are related to Fibonacci numbers and generalized Fibonacci numbers. The derivation is based on evaluating determinants of submatrices of the Laplacian matrix. A combinatorial argument is also illustrated. A connection with the problem of squaring a rectangle is described.

2 illus, 19 ref

006571   Bandyopadhyay S;Bose A;Sengupta D (DKDIS SET Labs, Infosys Technologyies Ltd., Hyderabad-500 032, Email: subhadip_b@infosys.com) : Nonparametric estimation of multivariate density with direct and auxiliary data and application. Indian J pure appl Math 2010, 41(1), 251-74.

Considers the problem of multivariate density estimation, using samples from the distribution of interest as well as auxiliary samples from a related distribution. Assumes that the data from the target distribution and the related distribution may occur individually as well as in pairs. Using nonparametric maximum likelihood estimator of the joint distribution, authors derive a kernel density estimator of the marginal density. Shows theoretically, in a simple special case, that the implied estimator of the marginal density has smaller integrated mean squared error than that of a similar estimator obtained by ignoring dependence of the paired observations. Establishes consistency of the marginal density estimator under suitable conditions. Demonstrates small sample superiority of the proposed estimator over the estimator that ignores dependence of the samples, through a simulation study with dependent and non-normal populations. The application of the density estimator in nonparametric classification is also discussed. It is shown that the misclassification probability of the resulting classifier is asymptotically equivalent to that of the Bayes classifier. We also include a data analytic illustration.

2 tables, 18 ref

006570   Argac N;Filippis V D (Mathematics Dep, Ege Univ, Science Faculty 35100, Bornova, Izmir, Turkey, Email: nurcan.argac@ege.edu.tr) : Cocentralizing derivations and nilpotent values on lie ideals. Indian J pure appl Math 2010, 41(3), 475-83.

Let R be a prime ring with char R ≠ 2, L a non-central Lie ideal of R, d, g non-zero derivations of R, n ≥ 1 a fixed integer. Proves that if (d = 0 for all x ∈ L, then either d = g = 0 or R satisfies the standard identity s₄ and d, g are inner derivations, induced respectively by the elements a and b such that a + b ∈ Z(R).

13 ref

006569   Akbary A;Murty Kumar V (Mathematics and Computer Science, Lethbridge Univ, Lethbridge, Alberta, T1K 3M4, Canada, Email: amir.akbary@uleth.ca) : Analogue of the Siegel-Walfisz theorem for the cyclicity of CM elliptic curve mod_p. Indian J pure appl Math 2010, 41(1), 25-37.

Let E be a CM elliptic curve defined over Q and of conductor N. Established an asymptotic formula, uniform in N and with improved error term, for the counting function of primes p for which the reduction mod p of E is cyclic. Result resembles the classical Siegel-Walfisz theorem regarding the distribution of primes in arithmetic progressions.

14 ref

006568   Agarwal P;Jain S (Mathematics Dep, Global Institute of Technology, Jaipur-302 017, Email: goyal_praveen2000@yahoo.co.in) : On unified finit integrals involving a multivariable polynomial and a generalized mellin barnes type of contour integral having general argument. Natn Acad Sci Lett 2009, 32(9-10), 281-6.

Evaluates unified finite integrals involving a multivariable polynomial Sm1n1, ..., Smrnr [x] and a generalized Mellin Barnes type of contour integral having general argument H [z]. The values of the integrals are obtained in terms of Ψ (z) (the logarithmic derivative of Γ (z)). A large number of new and known finite integrals involving simpler special function and polynomials follow as special cases of which Wright hyper geometric function, generalized Wright-Bessal function and generalized hyper geometric function are believed to be new.

10 ref

006567   Adimurthi;Veerappa Gowda G D (NO, T.I.F.R. Centre for Applicable Mathematics, P.B. No. 6503 Harada Nagar, Bangalore-560 065, Email: aditi@tifrbng.res.in) : Neumann boundary condition for a non-autonomous Hamiltion-Jacobi equation in a quarter plane. Indian J pure appl Math 2010, 41(1), 199-224.

Considers Hamilton-Jacobi equation u_t + H(u, u_x) = 0 in the quarter plane and study initial boundary value problems with Neumann boundary condition on the line x = 0. Authors assume that p → H(u, p) is convex, positively homogeneous of degree one. In general, this problem need not admit a continuous viscosity solution when s → H(s, p) is non increasing. In this paper, explicit formula for a viscosity solution of the initial boundary value problem is given for the cases s → H(s,p) is non decreasing as well as s → H(s, p) is non increasing.

3 illus, 14 ref

006566   Abhyankar S S (Mathematics Dep, Purdue Univ, West Lafayette, In 47907, USA, Email: ram@cs.purdue.edu) : Dicritical divisors and Jacobian problem. Indian J pure appl Math 2010, 41(1), 77-97.

The dicritical divisor coming out of integrable holonomic systems gets miraculously married to the jacobian problem of algebraic geometry.

34 ref

005531   Yang L;Chang S S (Mathematics Dep, South West Science and Technology Univ, Mianyang, Sichuan-621 002, China, Email: yanglizxs@yahoo.com.cn) : Algorithms for solving quasi-variational inclusion problem and fixed point problem. Indian J Math 2009, 51(3), 567-83.

The purpose of this paper is by using a new iterative scheme for finding a common element of the set of solutions for the quasi-variational inclusion problem with multi-valued maximal monotone mapping and iuverse-stroiigly monotone mapping and the set of fixed points of non-expansive mapping in Hilbert space. Under suitable conditions, some strong convergence theorems for approximating to this common element are proved. The results presented in the paper extend and improve some recent results in Chang-Lee-Chan.

22 ref

005530   Tripathi A;Datta S (Mathematics Dep, Lucknow Univ, Lucknow-226007, Email: sv.datta@gmail.com) : Mathematical modeling of fluid flow through a wavy walled square pipe in environmental studies: non-orthogonal coordinates. Res Envir Life Sci 2009, 2(3), 157-64.

In this paper authors consider the steady flow of a viscous fluid through a rectilinear pipe bounded by four sinusoidally varying plates in same phase with opposite plates separated by a mean distance 2 h. For the non-varying rectilinear pipe with rectangular cross section, the classical velocity profile for the fully developed flow is well known. In the present research an attempt is made to analyze the flow in a generalized non-orthogonal coordinate system that renders the wavy pipe as plane walled pipe. Continuity equation and Navier-stokes equations are presented in the generalized coordinate system and simplified through use of small perturbation under small Reynolds number approximation. Flow characteristics such as centerline velocity have been evaluated and discussed. The results of the paper have possible applications in flow of air pollutants in stakes and waste water through pipes and also in life sciences.

005529   Tripathi A;Datta S (Mathematics Dep, Lucknow Univ, Lucknow-226 007, Email: nivelesh@rediffmail.com) : Flow through a pipe bounded by four sinusoidally varying with opposite plates differing in phase by and separated by a constant mean distance. Res Envir Life Sci 2009, 2(4), 223-30.

Considered the steady flow of a viscous fluid through a rectilinear pipe bounded by four sinusoidally varying with opposite plates differing in phase by and separated by a mean distance. For the non-varying rectilinear pipe with rectangular cross section, the classical velocity profile for the fully developed flow is well known. An attempt here is made to analyze the flow in a generalized non-orthogonal coordinate system that renders the wavy pipe as plane walled pipe. Continuity equation and Navier-Stokes equations are presented in the generalized coordinate system and simplified through use of small perturbation under small Reynolds number approximation. Flow characteristics such as centerline velocity have been evaluated and discussed. The results of the paper have possible applications in developing and designing environment pollution control related equipments and also in modeling.

005528   Sulaiman W T (Computer Engineering Dep, College of Engineering, Mosul Univ, Mosul, Iraq, Email: waadsulaiman@hotmail.com) : Two new mappings in connection to Hadamard's inequality. Indian J Math 2009, 51(3), 627-36.

In this paper author point out to two new inequalities of the Hadamard type on the lines of Dragomir. Established main properties including convexity, monotonicity and boundedness using a simple new technique in the proof.

2 ref

005527   Suchithra K;Adolf Stephen B;Gangadharan A; Sivasubramanian S (Applied Mathematics Dep, Sri Venkateswara College of Engineering Sriperumbudur, Chennai-602 105, Email: suchithravenkat@yahoo.co.in) : Fekete-szego inequality for certain subclass of analytic functions related to complex order. Indian J Math 2009, 51(3), 453-61.

In the present investigation, the authors obtain Fekete-Szego inequality for certain normalized analytic function f(z) defined on the open unit disk for which 1 + 1/b [{αβz³f"'(z) + (2αβ + α - βz² f" (z) + zf'(z)/αβz²f" (z)+ (α - β zf'(z) + (1 - α + β f(z)}-1] (0 ≤ β ≤ α ≤ 1, b ≠ 0, a complex number) lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions of complex order defined by convolution are given. As a special case of our result, we obtain Fekete-Szego inequality for a class of functions defined through fractional derivatives.

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005526   Stella Irene Mary J (Mathematics Dep, PSG College of Arts and Science, Coimbatore-641 014, Email: stellairenemary@gmail.com) : Spectra of composition operators and their aluthge transforms. Indian J Math 2009, 51(3), 549-55.

In this paper, the normal approximate point spectrum, approximate point spectrum of composition operators and that of their generalized Aluthge transformations as weighted composition operators have been characterized.

5 ref

005525   Rokibul Islam M;Habibur Rahman M;Ali Akbar M (Mathematics Discipline, Khulna Univ, Khulna-9208, Bangladesh) : Analytical approximate solution of fourth order more critically damped nonlinear systems. Indian J Math 2009, 51(3), 611-26.

In this article, the Krylov-Bogoliubov-Mitropolskii (KBM) method has been extended for obtaining the solution of fourth order non-oscillatory nonlinear systems characterizing more critically damped systems. The results obtained by the presented method agree with those obtained by the numerical method nicely. An example is solved to illustrate and verify the method.

3 illus, 19 ref