002068   Sarkar R P;Thangavelu S (Stat-Math Unit, Indian Statistical Institute, 203 B. T. Rd., Calcutta-700 108, Email: rudra@isical.ac.in) : Analogue of the Wiener Tauberian theorem for the Heisenberg motion group. J Indian Inst Sci 2007, 87(4), 467-74.

The Wiener Tauberian property holds for the Heisenberg Motion group. This is a special case of the same result for a wider class of groups. However, our exposition is almost self contained and the techniques used in the proof are relatively simple.

^iia12 ref

002067   Salunke J N;Gotmare A R (School of Mathematical Sciences, North Maharashtra Univ, Jalgaon, Email: drjnsalunke@gmail.com) : On groups and rings. Vidarbha J Sci 2008, 3(2), 12-6.

Every non empty countable set can be considered as a cyclic group. If a, b, c are three distinct elements of a countable set S then there is a binary operation * on S such that (S, *) is a cyclic group with identity a and b, c are inverses of each other. If d is an element of a countable set S then S can be considered as a cyclic group generated by d. Every nonempty countable set can be considered as a commutative ring with unity. Every countably infinite set can be considered as a field.

3 ref

002066   Patil V R;Pawar D D;Deshmukh A G (Mathematics Dep, Arts, Science & Commerce College, Chikhaldara Dist., Amravati-444 807, Email: vrpatil2007@rediffmail.com) : Plane wave solution of Einstein-maxwell equations coexisting with null fluid and null current in space-time V₅. Vidarbha J Sci 2008, 3(2), 28-34.

Obtained the solution of Einstein-Maxwell equations in the presence of null fluids and null currents in higher dimensional space-time V₅ for Z - (z - t) -type plane wave and also discussed some particular cases.

8 ref

002065   Nalatore H;Truccolo W;Rangarajan G (Applied Research International, , New Delhi) : Fast robust pattern classification algorithms for real time neuro-motor prosthetic applications. J Indian Inst Sci 2007, 87(4), 497-509.

A brief review of pattern classification algorithms based on discriminant analysis. Then applies these algorithms to classify movement direction based on multivariate local field potentials recorded from a microelectrode array in the primary motor cortex of a monkey performing a reaching task. Obtains prediction accuracies between 55% and 90% using different methods which are significantly above the chance level of 12.5%.

^iia9 illus, 25 ref

002064   Lyer S K (Mathematics Dep, Indian Institute of Science, Bangalore) : Branching particle systems and superprocess. J Indian Inst Sci 2007, 87(4), 491-6.

Describes a system of particles that perform independent random motions in space and at the end of their lifetimes give birth to a random number of offspring. Shows that the system in the large density, small mass, rapid branching or long time scale limit converges to a measure-valued diffusion called the superprocess.

^iia18 ref

002063   Kandalkar S P;Gaikwad M N;Wasnik A P;Khade P P (Mathematics Dep, Govt. Vidarbha Institute of Science and Humanities, Amravati-444 604, Email: spkandalkar2004@yahoo.com) : String cosmological model with electromagnetic field. Vidarbha J Sci 2008, 3(2), 51-5.

Paper Kantowski Sach's string cosmological model and the solution of the field equations are obtained in the presence of electromagnetic field. The physical and geometrical properties of the model are studied.

12 ref

002062   George R K;Shah T P (Mathematics Dep, Indian Institute of Space Science and Technology, Trivandrum-695 022, Email: rkg.iist@gmail.com) : Steering control of semilinear discrete dynamical system. J Indian Inst Sci 2007, 87(4), 485-9.

Investigates the controllability property of a class of semilinear non-autonomous system described by the difference equation x(t+1) = A(t)x(t)+B(t)u(t)+f(t,x(t)), t ∈ N₀ = {0, 1, 2, ....} under the assumption that its linear part is controllable and the nonlinear function/satisfies Lipschitz condition. Also gives an algorithm to compute steering control for the above system. Numerical example is given to illustrate the result.

^iia1 illus

002061   Gadgil S (Mathematics Dep, Indian Institute of Science, Bangalore-560 012, Email: gadgil@math.iisc.ernet.in) : On the proof of the poincare conjecture. J Indian Inst Sci 2007, 87(4), 451-6.

^iia10 ref

002060   Datta B (Mathematics Dep, Indian Institute of Science, Bangalore-560 012, Email: dattab@math.iisc.ernet.in) : Minimal triangulations of manifolds. J Indian Inst Sci 2007, 87(4), 429-49.

Finding vertex-minimal triangulations of closed manifolds is a very difficult problem. Except for spheres and two series of manifolds, vertex-minimal triangulations are known for only few manifolds of dimension more than 2. Presents a brief survey on the works done in last 30 years on the following: (i) Finding the minimal number of vertices required to triangulate a given pl manifold, (ii) Given positive integers n and d, construction of n-vertex triangulations of different d-dimensional pl manifolds, (iii) Classifications of all the triangulations of a given pl manifold with same number. Presentes a very brief history of triangulations of manifolds. Presentes examples of several vertex-minimal triangulations. Gives some interesting results on triangulations of manifolds. States the Lower Bound Theorem and the Upper Bound Theorem. States several results on minimal triangulations without proofs. Proofs are available in the references mentioned there. Also presentes some open problems/conjectures.

^iia71 ref

000099   Robinson D W;Sikora A (NO, Centre for Mathematics and its Applications, Mathematical Sciences Ins, Australian National Univ, Canberra, ACT 0200, Australia, Email: Derek.Robinson@anu.edu.au) : Degenerate elliptic operators: capacity, flux and separation. J Ramanujan Mathl Soc 2007, 22(4), 385-408.

Let S = (S_t}_t ≥ 0 be the semigroup generated on L₂(R^d) by a self-adjoint, second-order, divergence-form, elliptic operator H with Lipschitz continuous coefficients. Further let Ω be an open subset of R^d with Lipschitz continuous boundary ∂Ω. Authors proved that S leaves L₂(Ω) invariant if, and only if, the capacity of the boundary with respect to H is zero or if, and only if, the energy flux across the boundary is zero.

21, ref

000098   Mukherjee S P;Dasgupta N (NO, Calcutta Univ, Kolkatta) : Prediction interval for the rayleigh distribution. IAPQR Trans 2007, 32(1), 57-63.

Attempt was made to find a prediction interval based on type - II censored sample from the Rayleigh distribution that will contain at least m out of k future sample observations.

3 tables, 4 ref

000097   Masoom Ali M;Nadarajah S (NO, Ball State Univ, USA) : Normal posterior bessel distribution. IAPQR Trans 2007, 32(1), 65-73.

Posterior distribution for the shape parameter of the Bessel function distribution is obtained by deriving the distribution of the ratio XI Y, when X and Y are normal and Bessel function random variables distributed independently of each other.

1 illus, 11 ref

000096   Gyan Prakash;Pandey B N (NO, Harishchandra P.G. College, Varanasi) : Shrinkage estimation for logarithm of variance of a normal distribution under linex loss function. IAPQR Trans 2007, 32(1), 43-56.

Performance of some shrinkage testimators for logarithm of variance of a Normal distribution when a prior point guess value is available, under the invariant version of the LINEX loss function has studied. Comparison has been made with improved estimator.

4 tables, 10 ref

000095   Gajjar K A;Shah Jarodwala K K (NO, Mainagar Science College, Ahmedabad) : Bayesian reliability analysis of certain types of systems with descrete failure time. IAPQR Trans 2007, 32(1), 75-85.

When lifetime data on a complete system are not available, it is desirable to make use of the operational data on its components. Pursuing this approach, Bayesian reliability analysis of a k-out of n-system and a cold standby system are considered when failure time is discrete. Some simulated results are discussed for illustration.

4 tables, 11 ref

000094   Gadre M P (NO, Mundhoji College, Phaltan) : Multi-attribute modified group runs control chart to identify process deterioration. IAPQR Trans 2007, 32(1), 1-20.

Gadre and Rattihali (2006) proposed a control chart called the 'Modified Group Runs (MGR) control chart' to identify increase in fraction non-conforming. Extends the concept of MGR chart to a multi-attribute case to detect process deterioration. It is shown that in the multi-attribute case also, the MGR chart gives a significant reduction in out-of control 'Average Time to Signal' (ATS) as compared to the other matched multi-attribute control charts (MACCs). In the steady state also, the performance of 'Multi-Attributes MGR' (MA-MGR) chart is better. The procedure of identifying the attribute causing signal is also described.

1 illus, 5 tables, 16 ref

000093   De Rango A (NO, , 347 Sarauren Ave., suit 222, Toronto, Ontario, M6R 2G5, Canada, Email: a.derango@1 staccess.ca ) : Crossed product C*-algebras associated with homeomorphisms of the unit circle. J Ramanujan Mathl Soc 2007, 22(4), 315-4.

Given a homeomorphism φ of the unit circle T, there is associated the C*-crossed product algebra of C(T) by the Z-action induced by φ. Author analyze the C*-crossed product algebras arising from those homeomorphisms that possess both cyclic and non-cyclic points, or are order-reversing. It is shown that upto compact perturbations, infinite-dimensional irreducible *-representations of algebras in this class can be expressed in terms of certain finite-dimensional irreducible *-representations. This relationship is used to recover the topological features of the underlying homeomorphisms upto inversion, and to construct a complete *-isomorphism invariant for these algebras. It is shown that two algebras with underlying homeomorphisms φ and ψ are *-isomorphic if and only if φ is conjugate to ψ or ψ^-1.

19 ref

000092   Banica T;Bichon J;Collins B (Mathematics Dep, Paul Sabatier Univ, 118 route de Narbonne, 31062 Toulouse, France, Email: banica@picard.ups-tlse.fr) : Hyperoctahedral quantum group. J Ramanujan Mathl Soc 2007, 22(4), 345-84.

Considers the hypercube in Rⁿ, and showed that its quantum symmetry group is a q-deformation of O_n at q = -1. Then authors consided the graph formed by n segments, and show that its quantum symmetry group is free in some natural sense. This latter quantum group, denoted H⁺_n, enlarges Wang's series S⁺_n, O⁺_n, U⁺_n.

36 ref

000091   Baier S (NO, Jacobs Univ Bremen, School of Engineering and Science, P.O. Box 750 561, 28725 Bremen, Germany, Email: s.baier@jacobs-university.de) : Lang-Trotter conjecture on average. J Ramanujan Mathl Soc 2007, 22(4), 299-314.

For an elliptic curve E over Q and an integer r let π^r_{E(x) be the number of primes p ≤ x of good reduction such that the trace of the Frobenius morphism of E/FP equals r. Consider the quantity π^rE(x) on average over certain sets of elliptic curves. More in particular, Established the following: If A, B > x^1/2+ε and AB > x^3/2+ε, then the arithmetic mean of π^rE(x) over all elliptic curves E : y² = x³ + ax + b with a, b ∈ Z, |a| ≤ A and |b| ≤ B is - Cr√x/log x, where Cr is some constant depending on r. This improves a result of C. David and F. Pappalardi. Also established an "almost-all" result on π^rE(x).}

9 ref

000090   Agarwal S;Agarwal M (NO, Delhi Univ, Delhi) : Redundancy optimization in multi-state complex systems with multi-state components: a heuristic approach. IAPQR Trans 2007, 32(1), 21-42.

Purpose of the paper is to develop a heuristic algorithm for redundancy optimisation in multi-state complex systems with multi-state components. The heuristic proposed is applicable, in general, to any coherent system with no restriction on objective and constraint functions, and requires the minimal path vectors of the system to be known. To illustrate the simplicity and ease of application of the algorithm, solutions of a flow network problem and a bridge structure with linear as well as nonlinear constraints are obtained.

2 illus, 8 tables, 19 ref