009375   Sive Kota Reddy P;Subramanya M S (Mathematics Dep, Rajeev Institute of Technology, Industrial Area, B-M Bypass Road, Hassan-573 201, Email: reddy_math@yahoo.com) : Signed graph equation L<. Int J mathl Combinatorics 2009, 4(Jan), 84-8.

A Smarandachely k-signed graph (Smarandachely k-marked graph) is an ordered pair S = (G,σ) (S = (G, μ,)), whore G = (V, E) is a. graph culled the underlying graph of S and σ : E → (e₁, e₂, ..., e_k) (μ : V → (e₁, e₂, ..., e_k)) is a function, where each e, ∈ { +, - }. Particularly, a Smarandachely 2-singed graph or 2-markod graph is called abbreviated to a singed graph or a marked graph. We characterize signed graphs S for which L (S) ~, S, S ~ CE(S) a.nd L^k (S) ~ S. wliere ~ denotes switching equivalence and L(S). S and C_E(S) are denotes line signed graph, complementary signed Graph and common-edge signed graph of S respectively.

009374   Singh T;Chaubey R (Applied Mathematics Dep, Institute of Technology, Banaras Hindu Univ, Varanasi-221 005, Email: yahoo_raghav@rediffmail.com) : Bianchi type-I universe with wet dark fluid. Pramana J Phys 2008, 71(3), 447-58.

The Bianchi Type-I Universe filled with dark energy from a wet dark fluid has been considered. A new equation of state for the dark energy component of the Universe has been used. It is modeled on the equation of state p = γ(ρ - ρ*) which can describe a liquid, for example water. The exact solutions to the corresponding field equations are obtained in quadrature form. The solution for constant deceleration parameter have been studied in detail for both power-law and exponential forms. The cases γ = 1 and γ = 0 have also been analysed.

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009373   Singh K R;Singh A;Agrawal V K (Mathematics Dep, Meerut College, Meerut, Uttar Pradesh, Email: kaviraj_singh@yahoo.com) : Flow of a non-newtonian reiner-rivlin fluid between two enclosed counter torsionally oscillatin discs with different permeability. Int J appl mathl Analysis Applic 2009, 4(1), 19-30.

Problem of the flow of an incompressible non-Newtonian Reiner-Rivlin fluid between two enclosed counter torsionally oscillating discs with different permeability has been discussed. The flow functions H, G, L and M are expanded in the powers of the amplitude E (taken small) of the oscillations. The steady and unsteady parts of radial, transverse and axial velocities have been calculated successfully. The behaviours of the radial, transverse and axial velocities at different values of Reynolds number R, phase difference τ and cross-viscous parameter τ have been studied and shown graphically. The transverse shearing stress and moment on the lower and upper discs have also been obtained.

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009372   Singh J P;Tiwari R K (Mathematical Sciences Dep, A.P.S. Univ, Rewa-486 003, Email: jpsinghmp@lycos.com) : Perfect fluid bianchi type-I cosmological models with time varying G and Λ. Pramana J Phys 2008, 70(4), 565-74.

Bianchi Type-I cosmological models containing perfect fluid with time varying G and Λ have been presented. The solutions obtained represent an expansion scalar θ bearing a constant ratio to the anisotropy in the direction of space-like unit vector A. Of the two models obtained, one has negative vacuum energy density, which decays numerically. In this model, we obtain A ~ H², A ~ R₄₄/R and A ~ T^-1 (T is the cosmic time) which is in accordance with the main dynamical laws for the decay of A. The second model reduces to a static solution with repulsive gravity.

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009371   Singh C P (Applied Mathematics Dep, Delhi College of Engineering, Bawana Road, Delhi-110 042, Email: cpsphd@rediffmail.com) : Bulk viscous cosmology in early universe. Pramana J Phys 2008, 71(1), 33-48.

The effect of bulk viscosity on the early evolution of Universe for a spatially homogeneous and isotropic Robertson-Walker model is considered. Einstein's field equations are solved by using 'gamma-law' equation of state p = (γ - 1) ρ, where the adiabatic parameter gamma (γ) depends on the scale factor of the model. The 'gamma' function is defined in such a way that it describes a unified solution of early evolution of the Universe for inflationary and radiation-dominated phases. The fluid has only bulk viscous term and the coefficient of bulk viscosity is taken to be proportional to some power function of the energy density. The complete general solutions have been given through three cases. For flat space, power-law as well as exponential solutions are found. The problem of how the introduction of viscosity affects the appearance of singularity, is briefly discussed in particular solutions. The deceleration parameter has a freedom to vary with the scale factor of the model, which describes the accelerating expansion of the Universe.

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009370   Shah J B;Patel M N (Statistics Dep, R.J. Tibrewal College, Vastrapur, Ahmedabad-380 015, Email: Jayesh782@gmail.com ) : Bayes estimation under asymmetric loss functions from multiply type II cencored Rayleigh data. J Indian Statist Ass 2008, 46(1), 67-78.

Obtained Bayes estimator of the parameter of Rayleigh distribution under squared error loss function, general entropy loss function and linex loss function based on proper and improper priors under multiply Type-II censored data. Sensitivity analysis and simulated study are carried out to assess the performance of the estimator.

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009369   Seshadri H (Mathematics Dep, Indian Institute of Science, Bangalore-560 012, Email: harish@math.iisc.ernet.in ) : Elementary approach to gap theorems. Proc Indian Acad Sci-Mathl Sci 2009, 119(2), 197-201.

Using elementary comparison geometry, authour prove: Let (M, g) be a simply-connected complete Riemannian manifold of dimension > 3. Suppose that the sectional curvature K satisfies -1 - s(r) ≤ K ≤ - 1, where r denotes distance to a fixed point in M. If lim_r→∞ e^sr s(r) = 0, then (M, g) has to be isometric to Hⁿ. The same proof also yields that if K satisfies -s(r) ≤ K ≤ 0 where lim_r→∞r² s(r) = 0, then (M, g) is isometric to Rⁿ, a result due to Greene and Wu. The second result is a local one: Let (M, g) be any Riemannian manifold. For a ∈ R, if K ≤ a on a geodesic ball B_p(R) in M and K = a on εB_p(R), then K = a on B_p(R).

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009368   Sencimen C;Pehlivan S (Faculty of Arts and Sciences, Mathematics Dep, Mehmet Akif Ersoy Univ, Burdur, Turkey, Email: sencimen@mehmetakif.edu.tr) : Strong ideal convergence in probabilistic metric spaces. Proc Indian Acad Sci-Mathl Sci 2009, 119(3), 401-10.

Introduced the concepts of strongly ideal convergent sequence and strong ideal Cauchy sequence in a probabilistic metric (PM) space endowed with the strong topology, and establish some basic facts. Next, defines the strong ideal limit points and the strong ideal cluster points of a sequence in this space and investigate some properties of these concepts.

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009367   Seehta Lekshmi V;Pathiyil M;Jose K K (Statistics Dep, Nirmala College, Muvattupuzha-686 661) : Integer valued skew laplace processes and stress-strength models. Sci Soc 2009, 7(1), 37-48.

Discrete skew Laplace (DSL) distribution introduced by Kozubowski and Inusah (2006) is reviewed. A first order Integer Valued Autoregressive (INAR (1)) processes with a DSL marginal distributions are developed and various properties are investigated. Application of DSL distribution in stress-strength modeling is discussed. Stress-strength reliability is estimated using different methods and simulation studies are made to validate the results.

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009366   Sampathkumar E;Siva Kota Reddy P;Subramanya M S (Studies in Mathematics Dep, Mysore Univ, Manasagangotri, Mysore-570 006, Email: csampathkumar@eth.net) : Directionally n-signed graphs-II. Int J mathl Combinatorics 2009, 4(Jan), 89-98.

Let G = (V, E) be a graph. Let V be a vector space of dimensional n. A Smarandachely labeling on a graph G is labeling an edge uv ∈ G K(G) by an vector v ∈ V on (u, v) and - v on (v, u). Then turn the conception directional labeling as a special case to Smarandachely labeling. By directional labeling (or d-labeling) of an edge x = uv of G by an ordered n-tuple (a₁ a₂, αn), mean labeling of the edge x such that, consider the label on uv as (0,1,0,2,..., a_n) in the direction from u to v and the label on x as (α, a_n-11, ..., α₁) in the direction from v to u. Study graphs called (n, d)-sigraphs, in which every edge, is D-labeled by an n-tuple (a₁, a₂. ..., a_n), where m, a_n ∈ { +, - }, for 1 ≤ k ≤ n. In this paper author obtained another characterization of i-balanced (n, d)-sigraphs, introduced the notion of path balance arid generalized the notion of local balance in sigraphs.

009365   Salimov A A;Akbulut K (Faculty of Sciences, Department of Mathematics, Ataturk University, Erzurum, Turkey, Email: asalimov@atauni.edu.tr) : Not on paraholomorphic Cheeger-Gromoll metric. Proc Indian Acad Sci-Mathl Sci 2009, 119(2), 187-95.

Aim of this note is to study a paraholomorphic Cheeger-Gromoll metric on the tangent bundle of Riemannian manifolds.

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009364   Saha R K;Chanda P K (Siliguri B.Ed. College, P.O. Kadamtala (Shivmandir), Dist. Darjeeling-734 01) : On some exact solutions of slightly variant forms of Yang's equations and their graphical representations. Pramana J Phys 2008, 70(5), 763-77.

The equations obtained by Yang while discussing the condition of self-duality of SU(2) gauge fields on Euclidean four-dimensional space have been generalized. Exact solutions and their graphical representations for the generalized equation (for some particular values of the parameters) have been reported. They represent interesting physical characteristics like waves with spreading solitary profile, spreading wave packets, waves with pulsating solitary profile (between zero and a maximum), waves with oscillatory solitary profile and chaos.

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009363   Sabu M C;Tikekar R (Mathematics Dep, St. Albert's College, Ernakulam, Kerala-682 018) : Anisotropic fluid sphere model in general relativity. Sci Soc 2009, 7(1), 9-16.

Relativistic model of a compact anisotropic fluid sphere with the feature that both radial and transverse pressures are continuous across the boundary surface is reported. The physical relevance of these models is examined and it is shown that it may be suitable to describe the interior of a neutron star.

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009362   Sabnia S V;Nair H (Mathematics Dep, IIT Bombay, Powai, Mumbai-400 076) : Reliability test plans for series system with discrete data. J Indian Statist Ass 2008, 46(1), 55-66.

Most of the reliability test plans that are available in the literature have been constructed for series/parallel systems and they assume continunous distribution such as exponential/gamma for lifetimes of components of a given system. The only exception is the reliability test plan developed by Easterling et al(1991) using one of the basic discrete distributions, namely, the binomial distribution. The objectives of this paper are to design optimal reliability test plans for a series system using scenarios that give rise to data representing geometric and negative binomial distributions. The notions such as majorization and Schur-convexity play crucial roles in designing reliability test plan based on negative binomial data. The relevant numerical results are also provided.

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009361   Ravindran R (Information Sci Dep, Atria Inst of Technol, Bangalore-560 002, Email: renrav@math.lisc.ernet.in) : Lighthill and his art of mathematical modelling. Resonance 2009, 14(1), 47-59.

Lighthill modeled the flow of blood through a narrow capillary involving the passage of individual red blood cells through it in a single file. The study involved the motion of relatively tightly fitting pellets of solid matter forced along distensible tubes. The equations governing the motion and suitable boundary conditions are formulated. The mathematical highlight of Lighthill's model is the use of the method of matched assymptotic expansion in six layers.

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009360   Rao T S S R K (Stat.-Math. Unit, Indian Statistical Institute, R.V. College Post, Bangalore-560 059, Email: tss@isibang.ac.in) : Riesz isomorphisms of tensor products of order unit Banach spaces. Proc Indian Acad Sci-Mathl Sci 2009, 119(3), 383-6.

Formulated and proved an order unit Banach space version of a Banach-Stone theorem type theorem for Riesz isomorphisms of the space of vector-valued continuous functions. Similar results were obtained recently for the case of lattice-valued continuous functions.

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009359   Rana M;Agarwal A K (Center for Advanced Study in Mathematics, Punjab Univ, Chandigarh-160 014, Email: aka@pu.ac.in) : On an extension of a combinatiorial identity. Proc Indian Acad Sci-Mathl Sci 2009, 119(1), 1-7.

Using Frobenius partitions we extend the main results of [4]. This leads to an infinite family of 4-way combinatorial identities. In some particular cases we get even 5-way combinatorial identities which give us four new combinatorial versions of Gollnitz-Gordon identities.

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009358   Prodinger H (Mathematics Dep, Stellenbosch Univ, 7602 Stellenbosch, South Africa, Email: hproding@sun.ac.za) : Sums of powers of Fibonacci polynomials. Proc Indian Acad Sci-Mathl Sci 2009, 119(5), 567-70.

Using the explicit (Binet) formula for the Fibonacci polynomials, a summation formula for powers of Fibonacci polynomials is derived straightforwardly, which generalizes a recent result for square.

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009357   Popa D (Department of Mathematics, University of Constanta, Bd. Mamaia 124, 8700 Constanta, Romania) : 2-Summing operators on C ([0,1],l_p) with values in l₁. Proc Indian Acad Sci-Mathl Sci 2009, 119(2), 221-30.

Let Ω be a compact Hausdorff space, X a Banach space, C (Ω, X) the Banach space of continuous X-valued functions on Ω under the uniform norm, U: C(Ω2, X) → Y a bounded linear operator and U³⁵., U₃₅ two natural operators associated to U. For each 1 ≤ s < ∞, let the conditions (α) U ∈ Π_s(C(Ω, X), Y); (β) U³⁵ ∈ Π,(C(Ω), Π_s(X, Y)); (γ) U₃₅ ∈ Π_s(X, Π_s(C(Ω), Y)). A general result, [10, 13], asserts that (α) implies (β) and (γ). In this paper, in case s = 2, we give necessary and sufficient conditions that natural operators on C([0, 1], l_p) with values in l₁ satisfies (α), (β) and (γ), which show that the above implication is the best possible result.

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009356   Petracovici B;Petracovici L;Zaharescu A (Mathematics Dep, Western Illinois Univ, Macomb, IL 61455, USA, Email: B-Petracovici@wiu.edu) : Divisors, measures and critical functions. Proc Indian Acad Sci-Mathl Sci 2009, 119(3), 351-68.

Introduced a new distance between Galois orbits over Q. Using generalized divisors, extended the notion of trace of an algebraic number to other transcendental quantities. Defines the critical function for a class of transcendental numbers, that generalizes the notion of minimal polynomial of an algebraic number. The results extend the results obtained by Popescu et al.

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009355   Peng Y Z;Krishnan E V;Feng H (School of Mathematics and Statistics, Wuhan Univ, Wuhan-430 072, Email: yanzepeng@163.com) : Travelling wave-like solutions of the Zakharov-Kuznetsov equation with variable coefficients. Pramana J Phys 2008, 71(1), 49-55.

Travelling wave-like solutions of the Zakharov-Kuznetsov equation with variable coefficients are studied using the solutions of Raccati equation. The solitary wave-like solution, the trigonometric periodic wave solution and the rational wave solution are obtained with a constraint between coefficients. The property of the solutions is numerically investigated. It is shown that the coefficients of the equation do not change the wave amplitude, but may change the wave velocity.

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009354   Padmanabhan T (IUCAA, Pune Univ Campus Geneshkhind, Pune-411 007, Email: paddy@iucaa.ernet.in) : Power of nothing. Resonance 2009, 14(2), 179-90.

The vacuum state of the electromagnetic field is far from trivial. Amongst other things it can exert forces that are measurable in the lab, in a curious phenomenon known as Casimir effect.

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009353   Ozkurt A;Donmez D (Department of Mathematics, Cukurova University, 01330-Adana, Turkey, Email: aozkurt@cu.edu.tr) : On the torus coboradant cohomology spheres. Proc Indian Acad Sci-Mathl Sci 2009, 119(1), 101-108.

Let G be a compact Lie group. In 1960, P A Smith asked the following question: "Is it true that for any smooth action of G on a homotopy sphere with exactly two fixed points, the tangent G-modules at these two points are isomorphic ?" A result due to Atiyah and Bott proves that the answer is 'yes' for Z_p and it is also known to be the same for connected Lie groups. In this work, authour prove that two linear torus actions on -Sⁿ which are c-cobordant (cobordism in which inclusion of each boundary component induces isomorphisms in Z-cohomology) must be linearly equivalent. As a corollary, for connected case, we prove a variant of Smith's question.

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009352   Obradovic M;Ponnusamy S;Vasundhra P (Mathematics Dep, Faculty of Civil Engineering, Bulevar Kralja Aleksandra 73, 11000 Belgrade, Serbia, Email: obrad@grf.ac.rs) : Univalence and starlikeness of nonlinear integral transform of certain class of analytic function. Proc Indian Acad Sci-Mathl Sci 2009, 119(5), 593-610.

Let U(λ, μ) denote the class of all normalized analytic functions in the unit disk |z| < 1 satisfying the condition f(z)/z ≠ 0 and |f'(z) (z/f(z))^μ+1 - 1| < λ, |z| < 1. For f ∈ U(λ, μ) with μ ≤ 1 and 0 ≠ μ₁ ≤ 1, and for a positive real-valued integrable function φ defined on [0, 1] satisfying the normalized condition ƒ¹₀ φ(t)dt-1.

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009351   Nitsure N (School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400 005, Email: nitsure@math.tifr.res.in) : Sign (di) lemma for dimension shifting . Proc Indian Acad Sci-Mathl Sci 2009, 119(2), 179-86.

There is a surprising occurrence of some minus signs in the isomorphisms produced in the well-known technique of dimension shifting in calculating derived functors in homological algebra. We explicitly determine these signs. Getting these signs right is important in order to avoid basic contradictions. Authour illustrate the result - which we call as the sign lemma for dimension shifting - by some de Rham cohomology and Chern class considerations for compact Riemann surfaces.

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009350   Neamaty A;Haghaieghy S (Mathematics Dep, Faculty of Basic Sciences, Mazandaran Univ, Babolsar, Iran, Email: namaty@umz.ac.ir) : On the asymptotic of an eigenvalue problem with 2n interior singularities. Proc Indian Acad Sci-Mathl Sci 2009, 119(5), 619-27.

Considers the linear differential equation of the form -y"(x) + q(x) y(x) = λy(x), - ∞ < a < x < b < ∞. where y satisfies Dirichlet boundary conditions and q is a real- valued function which has even number of singularities at c₁, ..., C_2n ∈ (a, b). Studied the asymptotic eigenvalue near the singularity points.

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009349   Nayak S S;Kunichi M C (Statistics Dep, Gulbarga Univ, Gulbarga-585 106) : Some characterizations using equidistribution of functions of generalized order statistics. J Indian Statist Ass 2008, 46(1), 43-53.

Authors obtain characterizations of distributions through the equidistribution of some functions of generalized order statistics.

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009348   Nayak S S;Kunichi M C (Statistics Dep, Gulbarga Univ, Gulbarga-585 106) : On Density convergence of record values. J Indian Statist Ass 2008, 46(1), 31-42.

Considered the local uniform convergence of the density of record values under linear and power normalizations. A uniform criterion and necessary and sufficient conditions for the density convergence are also presented.

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009347   Natarajan P N (NO, , Old No.2/3, New No.3/3 Second Main Road, R. A. Puram, Chennai-600 028) : Some more results on the algebra (C₀,C₀) of infinite matrices in non-Archimedean fields. Int J appl mathl Analysis Applic 2009, 4(1), 105-8.

Some more results regarding the algebra (C0, c₀) of infinite matrices in complete, non-trivially valued, non-archimedean fields have been recorded briefly.

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009346   Nassif C (Centro Brasileiro de Pesquisas Fisicas, Rua Dr. Xavier Sigaud 150, 22290-180, Rio de Janeiro, R.J., Brazil, Email: cnassif@cbpf.br) : Deformed special relativity with an invariant minimum speed and its cosmological implications. Pramana J Phys 2008, 71(1), 1-13.

Aims to introduce a new symmetry principle in the space time geornetry through the elimination of the classical idea of rest and by including a universal minimum speed limit in the subatomic world. Such a limit, unattainable by particles, represents the preferred reference frame associated with a universal background field that breaks Lorentz symmetry. Thus, the structure of space-time is extended due to the presence of a vacuum energy density, which leads to a negative pressure at cosmological scales. The tiny values of the cosmological constant and the vacuum energy density shall be successfully obtained, which are in good agreement with current observational results.

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009345   Nadkarni M G;Rajeev B (Mathematics Dep, Mumbai Univ, Kalina, Mumbai-400 098, Email: mgnadkarni@gmail.com) : Measure free martingales and martingale measures. Proc Indian Acad Sci-Mathl Sci 2009, 119(5), 655-67.

Let T ⊂ R be a countable set, not necessarily discrete. Let f_t, t ∈ T, be a family of real-valued functions defined on a set Ω. Discusses conditions which imply that there is a probability measure on Ω under which the family f_t t ∈ T, is a martingale.

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009344   Mukherjea A;Restrepo R (Mathematics Dep, The Univ of Texas-Pan American, 1201 West Univ Drive, Edinburg TX 78539, USA, Email: arunava.mukherjea@gmail.com) : Upper packing dimension of a measure and the limit distribution of products of i.i.d. stochastic matrices. Proc Indian Acad Sci-Mathl Sci 2009, 119(5), 669-77.

This article gives sufficient conditions for the limit distribution of products of i.i.d. 2 x 2 stochastic matrices to be continuous singular, when the support of the distribution of the individual random matrices is countably infinite. It extends a previous result for which the support of the random matrices is finite. The result is based on adapting existing proofs in the context of attractors and iterated function systems to the case of infinite iterated function systems.

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009343   Mortini R (Mathematiques Dep, LMAM, UMR 7122, Universite Paul Verlaine, Ile du Saulcy, F-57045 Metz, France, Email: mortini@poncelet.univ-metz.fr) : Distinguished real Banach algebra. Proc Indian Acad Sci-Mathl Sci 2009, 119(5), 629-4.

Presents a new and elementary approach to characterize the maximal ideals and their associated multiplicative linear functionals for a classical real Banach algebra of analytic functions.

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009342   Meiss J D (Applied Mathematics Dep, Colorado Univ, Boulder, CO 80309-0526, Email: James.Meiss@colorado.edu) : Visual explorations of dynamics: the standard map. Pramana J Phys 2008, 70(6), 956-88.

The Macintosh application Std Map allows easy exploration of many of the phenomena of area-preserving mappings. This tutorial explains some of these phenomena and presents a number of simple experiments centered on the use of this program.

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009341   Mehta V B;Trivedi V (School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400 005, Email: vikram@math.tifr.res.in) : On some frobenius restriction theorems for semistable sheaves. Proc Indian Acad Sci-Mathl Sci 2009, 119(1), 109-18.

Version of an effective Frobenius restriction theorem for semistable bundles in characteristic p has been proved. The main novelty is in restricting the bundle to the p-fold thickening of a hypersurface section. The base variety is G/P, an abelian variety or a smooth projective tone variety.

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009340   Mathews J (NO, , 2230 Hamilton Drive, Ames, IA 50014, USA, Email: mathews@iastate.edu) : George Andrews' game. Resonance 2009, 14(2), 172-8.

Show is how Zeck-endorf's Theorem (every positive integer can be represented in one and only one way as the sum of non-consecutive Fibonacci numbers) can be used to construct a number-guessing game invented by Professor George Andrews.

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009339   Martin Antonio J Calderon (Deparamento de Mathematicas, Universidad de Cadiz, 11510 Puerto Real, Cadiz, Spain, Email: ajesus.calderon@uca.es) : On split lie triple systems. Proc Indian Acad Sci-Mathl Sci 2009, 119(2), 165-77.

Study of arbitrary split Lie triple systems by focussing on those with a coherent 0-root space. Show that any such triple systems T with a symmetric root system is of the form T = U + ∑_j I_j with U a subspace of the 0-root space T₀ and any I_j a well described ideal of T, satisfying [I,, T, I_k] = 0 if j ≠ k. Under certain conditions, it is shown that T is the direct sum of the family of its minimal ideals, each one being a simple split Lie triple system, and the simplicity of T is characterized. The key tool in this job is the notion of connection of roots in the framework of split Lie triple systems.

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009338   Marti A C;Ponce M;Masoller C (Instituto de Fisica, Facultad de Ciencias, , Universidad de la Republica, Email: arturomarti@gmail.com) : Dynamics of delayed-coupled chaotic logistic maps: influence of network topology, connectivity and delay times. Pramana J Phys 2008, 70(6), 1117-25.

Reviews recent work on the synchronization of a network of delay-coupled maps, focusing on the interplay of the network topology and the delay times that take into account the finite velocity of propagation of interactions. Asumes that the elements of the network are identical (N logistic maps in the regime where the individual maps, without coupling, evolve in a chaotic orbit) and that the coupling strengths are uniform throughout the network. Shows that if the delay times are sufficiently heterogeneous, for adequate coupling strength the network synchronizes in a spatially homogeneous steady state, which is unstable for the individual maps without coupling. This synchronization behavior is referred to as 'suppression of chaos by random delays' and is in contrast with the synchronization when all the interaction delay times are homogeneous, because with homogeneous delays the network synchronizes in a state where the elements display in-phase time-periodic or chaotic oscillations. We analyze the influence of the network topology considering four different types of networks: two regular (a ring-type and a ring-type with a central node) and two random (free-scale Barabasi-Albert and small-world Newman-Watts). We find that when the delay times are sufficiently heterogeneous the synchronization behavior is largely independent of the network topology but depends on the network's connectivity, i.e., on the average number of neighbors per node.

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009337   Mafi A (Deparment of Mathematics, University of Kurdistan, P.O.Box 416, Sanandaj, Iran, Email: a_mafi@ipm.ir ) : Generalization of the finiteness problem in local cohomology modiules. Proc Indian Acad Sci-Mathl Sci 2009, 119(2), 159-64.

Let a be an ideal of a commutative Noetherian ring R with non-zero identity and let N be a weakly Laskerian R-module and M be a finitely generated R-module. Let t be a non-negative integer. It is shown that if Hⁱ_a (N) is a weakly Laskerian R-module for all i < t, then Hom_R(R/a, H^t_a (M, N)) is weakly- Laskerian R-module. Also, we prove that Extⁱ_R(R/a, H^t_a(N)) is weakly Laskerian R-module for all; = 0, 1. In particular, if SuppflC/^CAO) is a finite set for all i < t, then Extⁱ_R(R/a, H^t_a(N)) is weakly Laskerian R-module for all i =0, 1.

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009336   Korkee I;Haukkanen P (Mathematics Dep, Statistics and Philosophy, Tampere Univ, FI-33014, Finland, Email: ismo.korkee@uta.fi) : Meet and join matrices in the poset of exponential divisors. Proc Indian Acad Sci-Mathl Sci 2009, 119(3), 319-32.

It is well-known that (Z₊, I) = (Z₊, GCD, LCM) is a lattice, where | is the usual divisibility relation and GCD and LCM stand for the greatest common divisor and the least common multiple of positive integers. The number d = Π^r_k=1 P_k^d(k) is said to be an exponential divisor or an e-divisor of n = Π^r_k=1 Pk_k^n(k) (n > 1), written as d I_e n, if d^{(k) | n(K) for all prime divisors p_k of n. It is easy to see that (Z₊{1}, |_e) is a poset under the exponential divisibility relation but not a lattice, since the greatest common exponential divisor (GCED) and the least common exponential multiple (LCEM) do not always exist. In this paper authors embed this poset in a lattice. As an application author study the GCED and LCEM matrices, analogues of GCD and LCM matrices, which are both special cases of meet and join matrices on lattices.}

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009335   Kohnen W;Weib C (Mathematisches Institut der Universitat Heidelberg, INF 288, D-69120 Heidelberg, Germany, Email: winfried@mathi.uni-heidelberg.de) : Orthogonality and Hecke oerators. Proc Indian Acad Sci-Mathl Sci 2009, 119(3), 283-6.

Analyzed orthogonality relations between old forms and the connection to the theory of Hecke operators.

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009334   Katore S D;Thakare S V;Adhao K S (PGTD of Mathematics, Rajsthan Aryan Mahavidyalaya, Washim 444 505, Email: katoresd@rediffmail.com) : Bianchi type-I cosmological mesonic stiff fluid models in Lyra's geometry. Pramana J Phys 2008, 71(1), 15-22.

Bianchi Type-I cosmological models in Lyra's geometry are obtained when the source of gravitational field is a perfect fluid coupled with massless mesonic scalar field. Some physical and kinematical properties of the models are also discussed.

21 ref

009333   Kannan S S;Sardar P (Chennai Mathematical Institute, Plot H1, SIPCOT IT Park, Padur Post Office, Siruseri-603 103, Email: kannan@cmi.ac.in) : Torus quotients of homogeneous spaces of the general linear group and the standard representation of certain symmetric groups. Proc Indian Acad Sci-Mathl Sci 2009, 119(1), 81-100.

Stratification of the GIT quotient of the Grassmannian G_2,n modulo the normaliser of a maximal torus of S L_n (k) with respect to the ample generator of the Picard group of G_2,n has been given. Authour also prove that the flag variety G L_n (k) / B_n can be obtained as a GIT quotient of G L_n+1(k)/B_n+1 modulo a maximal torus of S L_n+1 (k) for a suitable choice of an ample line bundle on GL_n+1(k)/B_n+1.

10 ref

009332   Juriaans S O;Passi I B S;Souza Filho A C (Instituto de Matematica e Estatistica, Universidade de Sao Paulo (IME-USP), Caixa Postal 66281, Sao Paulo, CEP 05315-970, Brasil, Email: ostanley@ime.usp.br) : Hyperbolic unit groups and quaternion algebras. Proc Indian Acad Sci-Mathl Sci 2009, 119(1), 9-22.

Quadratic extensions K = Q[√d] and the finite groups G for which the group ring o_K [G] of G over the ring OK of integers of K has the property that the group U₁ (OK [G]) of units of augmentation 1 is hyperbolic. Authour also construct units in the Z-order H(OK) of the quaternion algebra H(K) = (-1, -1/K), when it is a division algebra.

17 ref

009331   Jose K K;Naik S R (Statistics Dep, St. Thomas College, Pala Center for Mathematical Sciences, Pala Campus, Pala, Email: kkjstc@gmail.com) : Overview of Mathai's entropy and Pathway model. Sci Soc 2009, 6(1), 89-96.

Brief account of classical entropy measures has been given namely, the Boltzmann-Gibbs and the Shannon entropy measures as well as their generalization due to Tsallis (1988). Mathai's pathway model and entropy measure are also reviewed and its relevance in the context of reaction rates, Mittag-Leffler functions and inaccuracy measures is established.

9 ref

009330   Jose K K;Jayamol K V (Statistics Dep, St. Thomas College, Pala-686 574) : Some characterizations of geometric law within G* class of lifetime distributions. J Indian Statist Ass 2008, 46(1), 23-30.

Analyzed the relations between alternating-probability generating function (a.p.g.f.)s and moments of the parent and derived distributions. characterized geometric distribution within G* class. Also gave some other characterizations of geometric law using coefficient of variation and length biased random variable.

8 ref

009329   Jimenez-Vargas A;Navarro M A (Deparamento de Algebra y Analisis Matematico, Universidad de Almeria, 04120, Almeria, Spain, Email: ajimenez@ual.es) : Holder seminorm preserving linear bijections and isometries. Proc Indian Acad Sci-Mathl Sci 2009, 119(1), 53-62.

Let (X, d) be a compact metric and 0<a.<1. The space Lip f(X) of Holder functions of order a is the Banach space of all functions/from X into K such that ||Hf|| = max {||f|| ∞, L(f)} < ∞, where L(f) = sup{|f(x) - f(y)|/d^{α(x, y): x,y ∈X, x ≠ y} is the Holder seminorm of f. The closed subspace of functions f such that lim |f(x)-f(y)|/dα(x, y) = 0 d(x,y)→0 is denoted by lipα (X). Authour determine the form of all bijective linear maps from lipα (X) onto lipα(Y) that preserve the Holder seminorm.}

10 ref

009328   Janardhan S;Saraykar R V (Mathematics Dep, St. Francis De Sales College, Nagpur-440 006, Email: sujata_jana@yahoo.com ) : K-causal structure of space-time in general relativity. Pramana J Phys 2008, 70(4), 587-601.

Using K-causal relation introduced by Sorkin and Woolgar [1], generalize results of Garcia-Parrado and Senovilla [2,3] on causal maps. Also introduce causality conditions with respect to K-causality which are analogous to those in classical causality theory and prove their inter-relationships. We introduce a new causality condition following the work of Bombelli and Noldus [4] and show that this condition lies in between global hyperbolicity and causal simplicity. This approach is simpler and more general as compared to traditional causal approach [5,6] and it has been used by Penrose et al [7] in giving a new proof of positivity of mass theorem. C°-space-time structures arise in many mathematical and physical situations like conical singularities, discontinuous matter distributions, phenomena of topology-change in quantum field theory etc.

4 illus, 28 ref

009327   Jain V K (Mathematics Dep, Indian Institute of Technology, Kharagpur-721 302, Email: vkj@maths.iitkgp.ernet.in) : On the zeros of a polynomial. Proc Indian Acad Sci-Mathl Sci 2009, 119(1), 37-43.

For a polynomial of degree n, authour have obtained an upper bound involving coefficients of the polynomial, for moduli of its p zeros of smallest moduli, and then a refinement of the well-known Enestrom-Kakeya theorem (under certain conditions).

3 ref

009326   Jabeen Z;Gupte N (NO, Institute of Mathematics Sciences, CIT Campus, Taramani, Chennai-600 113, Email: gupte@physics.iitm.ac.in) : Probabilistic signatures of spatiotemporal intermittency in the coupled sine circle map lattice. Pramana J Phys 2008, 70(6), 1055-61.

The phase diagram of the coupled sine circle map system exhibits a variety of interesting phenomena including spreading regions with spatiotemporal intermittency, non-spreading regions with spatial intermittency, and coherent structures termed solitons. A spreading to non-spreading transition is seen in the system. A cellular automaton version of the coupled system maps the spreading to non-spreading transition to a transition from a probabilistic to a deterministic cellular automaton. The solitonic sector of the system shows spatiotemporal intermittency with soliton creation, propagation and absorption. A probabilistic cellular automaton mapping is set up for this sector which can identify each one of these phenomena.

2 illus, 1 table, 18 ref