009325   Ismailov V E (Mathematics and Mechanics Institute, Azerbaijan National Academy of Sciences, Az-1141, Baku, Azerbaijan, Email: vugaris@mail.ru) : On the theorem of M Golomb. Proc Indian Acad Sci-Mathl Sci 2009, 119(1), 45-52.

Let X₁, ..., X_n be compact spaces and X - X₁ x ... x X_n. Consider the approximation of a function f ∈ C(X) by sums g₁(x₁) +...+g_n(x_n), where g_i ∈ C(X_i), i = 1, ..., n. In [8], Golomb obtained a formula for the error of this approximation in terms of measures constructed on special points of X, called 'projection cycles'. However, his proof had a gap, which was pointed out by Marshall and O'Farrell [15]. But the question if the formula was correct, remained open. The purpose of the paper is to prove that Golomb's formula holds in a stronger form.

18 ref

009324   Isidro J M (Analisis Matematico Dep, Facultad de Matematics, Universidade de Santiago de Compostela, Spain, Email: jm.isidro@usc.es) : On linear isometries of Banach lattices in C₀(Ω)-spaces. Proc Indian Acad Sci-Mathl Sci 2009, 119(5), 635-45.

Considers the space C₀(ΩQ) endowed with a Banach lattice-norm || . || that is not assumed to be the usual spectral norm || . ||_∞ of the supremum over Ω. A recent extension of the classical Banach-Stone theorem establishes that each surjective linear isometry U of the Banach lattice (C₀(Ω), ||.||) induces a partition Π of Ω into a family of finite subsets S ⊂ Ω along with a bijection T: Π → Π which preserves cardinality, and a family [u(S): S ∈ Π] of surjective linear maps u(S): C(T(S)) → C(S) of the finite-dimensional C*-algebras C(S) such that (U f)|_τ(S) = u(S)(f|_s) ∀f ∈ C₀(Ω) ∀S ∈ Π. Here we endow the space Π of finite sets S ⊂ Ω with a topology for which the bijection T and the map u are continuous, thus completing the analogy with the classical result.

5 ref

009323   Iscan M;Salimov A A (Faculty of Art and Science, Mathematics Dep, Ataturk Univ, Erzurum, Turkey, Email: miscan@atauni.edu.tr) : On kahler - Norden manifolds. Proc Indian Acad Sci-Mathl Sci 2009, 119(1), 71-80.

Concerned with the problem of the geometry of Norden manifolds. Some properties of Riemannian curvature tensors and curvature scalars of Kahler-Norden manifolds using the theory of Tachibana operators is presented.

21 ref

009322   Goswami D (Stat-Math Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata-700 108, Email: goswamid@isical.ac.in) : On equivariant embedding of Hilbert C<. Proc Indian Acad Sci-Mathl Sci 2009, 119(1), 63-70.

It is proved that an arbitrary (not necessarily countably generated) Hilbert G - A module on a G - C* algebra A admits an equivariant embedding into a trivial G - A module, provided G is a compact Lie group and its action on A is ergodic.

7 ref

009321   Gezer A (Mathematics Dep, Faculty of Science and Arts, Ataturk Univ, 25240, Erzurum, Turkey, Email: gezeraydin@hotmail.com) : On infinitesimal conformal transformations of the tangent bundles with the synectic lift of a Riemannian metric. Proc Indian Acad Sci-Mathl Sci 2009, 119(3), 345-50.

The purpose of the present article is to investigate some relations between the Lie algebra of the infinitesimal fibre-preserving conformal transformations of the tangent bundle of a Riemannian manifold with respect to the synectic lift of the metric tensor and the Lie algebra of infinitesimal projective transformations of the Riemannian manifold itself.

8 ref

009320   Germina K A;Koshy B (PG and Research Dep of Mathematics, Kannur Univ, Mary Matha Arts & Science College, Vemon P.O., Mananthavady-670 645, Email: srgerminaka@gmail.com) : Independent complementary distance pattern uniform garphs. Int J mathl Combinatorics 2009, 4(Jan), 63-74.

A graph G = (V, E) is called to he Smarandachely uniform graph, for an integer K ≥ 1 if there exists M₁M₂, ..., M_k ⊂ V(G) such that f_M (u) = {d(u,v) : v ∈ M_i} for ∀μ ∈ V (G) - M_i is independent of the choice of u ∈ V(G) - M_i and integer i, 1 ≤ i ≤ k, Each such set M_i, 1 ≤ i ≤ k is cailed a CDPU set [6, 7]. Particularly, for k = 1, a Smarandachely uniform 1-graph is abbreviated to a complementary distance pattern uniform graph, i.e., CDPU graphs. This paper studies independent GDPU graphs.

009319   Ganesh V;Subbiah M (Mathematics Dep, Rajiv Gandhi College of Engineering and Technology, Kirumampakkam, Pondicherry-607 402, Email: malaisubbiah@yahoo.com) : On upper bounds for the growth rate in the extended taylor goldstein problem of hydropynamic stability. Proc Indian Acad Sci-Mathl Sci 2009, 119(1), 119-35.

For the extended Taylor-Goldstein problem of hydrodynamic stability governing the stability of shear flows of an inviscid, incompressible but density stratified fluid in sea straits of arbitrary cross-section a new estimate for the growth rate of an arbitrary unstable normal mode is given for a class of basic flows. Furthermore the Howard's conjecture, namely, the growth rate kc_i → 0 as the wave number k → ∞ is proved for two classes of basic flows.

19 ref

009318   Fu K A;Yang X R (School of Statistics and Mathematics, Zhejiang Gongshang Univ, Hangzhou-310 018, China, Email: stazju@tom.com) : Moment convergence rates in the law of the logarithm for dependent sequences. Proc Indian Acad Sci-Mathl Sci 2009, 119(3), 387-400.

12 ref

009317   Fasihi M A;Jafarizadeh M A;Rezaei M (Physics Dep, Azarbijan Univ of Tarbiat Moallem, Tabriz 53714-161, Iran, Email: ma-fasihi@azaruniv.edu) : Approach to one-dimensional elliptic quasi-exactly solvable models. Pramana J Phys 2008, 70(4), 575-85.

One-dimensional Jacobian elliptic quasi-exactly solvable second-order differential equations are obtained by introducing the generalized third master functions. It is shown that the solutions of these differential equations are generating functions for a new set of polynomials in terms of energy with factorization property. The roots of these polynomials are the same as the eigenvalues of the differential equations. Some one-dimensional elliptic quasi-exactly quantum solvable models are obtained from these differential equations.

1 table, 24 ref

009316   Ebadi K (Studies in Mathematics of Univ of Mysore Dep, , Manasagangotri, Mysore-5700 06, Karnataka) : Smarandachely bondage number of a graph. Int J mathl Combinatorics 2009, 4(Jan), 9-19.

A dominating set D of a graph G is called a Smarandachely dominating S-set if for an integer s. each vertex v in V - D is adjacent to a vertex u ∈ D such that degu + s = degv. The minimum cardinality of Siriarandachely dominating -s-set in a graph G is called the Smarandachely dominationg s - number of G. denoted by γ^s_S(G). Such a set with minimum cardinality is called a Smarandachely dominating s-set. The Smarandtichely bondage s-number b^s_S(G) of a, graph G is defined to be the minimum cardinality among all sets of edges E C E such that γ^s_S (G - E') > γ^s_S(G). Particularly, the set with minimum Smarandachely bondage s-numher for all integers s ≥ 0 or s ≤ 0 is called the strong or weak dominating number of G, denoted by γ_s(G) or γ_w (G), respectively. In this paper. we present some bounds on b_s(G) and b_w(G) and give exact values for b_s (G) and b_w(G) for complete graphs. paths, wheels and bipartite complete graphs. Some general bounds are also given.

009315   Dutt P;Lamba S S (Mathematics Dep, Indian Institute of Technology, Kanpur-208 016, Email: pravir@iitk.ac.in) : Domain decomposition methods for hyperbolic problems. Proc Indian Acad Sci-Mathl Sci 2009, 119(2), 231-49.

Developed a method for solving hyperbolic initial boundary value problems in one space dimension using'domain decomposition, which can be extended to problems in several space dimensions. We minimize a functional which is the sum of squares of the L^{2 norms of the residuals and a term which is the sum of the squares of the L2 norms of the jumps in the function across interdomain boundaries. To make the problem well posed the interdomain boundaries are made to move back and forth at alternate time steps with sufficiently high speed. We construct parallel pre-conditioners and obtain error estimates for the method. The Schwarz waveform relaxation method is often employed to solve hyperbolic problems using domain decomposition but this technique faces difficulties if the system becomes characteristic at the inter-element boundaries. By making the inter-element boundaries move faster than the fastest wave speed associated with the hyperbolic system we are able to overcome this problem.}

2 illus, 13 ref

009314   Divaani-Aazar K (Department of Mathematics, Az-Zahra University, Vanak, Post Code 19834, Tehran, Iran) : Vanishing of the top local cohomology modules over noetherian rings. Proc Indian Acad Sci-Mathl Sci 2009, 119(1), 23-35.

Let R be a (not necessarily local) Noetherian ring and M a finitely generated R-module of finite dimension d. Let a be an ideal of R and M denote the intersection of all prime ideals p ∈ Supp_R H^d_a(M). It is shown that where for an Artinian R-module A authour put (M) A = ∩_n∈NMⁿ A. As a consequence, it is proved that for all ideals a of R, there are only finitely many non-isomorphic top local cohomology modules H^d_a(M) having the same support. In addition, they establish an analogue of the Lichtenbaum-Hartshorne vanishing theorem over rings that need not be local.

18 ref

009313   Deshpande M N;Rattihalli R N;Sreehari M (Statistics Dep, Institute of Science, Nagpur-440 001) : Discrete model based constant conditional probabilities. J Indian Statist Ass 2008, 46(1), 17-22.

It is known that a positive integer valued random variable X has the geometric waiting time distribution if and only if P(X = kX ≥ k) = θ for k ≥ 1. Here, we propose a two-parameter model by specifying P(X = 1)= p and P(X = kX ≥ k - 1) = θ for k = 2,3,... The problem of interest is to find the natural parameter space and study some distributional properties of the proposed model. If θ = p(1 - p), it yields the geometric waiting time distribution.

1 illus, 2 ref

009312   Datta M;Islam M R (Statistics and Mathematics Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata-700 108, Email: mahuya@isical.ac.in) : Smooth maps of a foliated manifold in a symplectic manifold. Proc Indian Acad Sci-Mathl Sci 2009, 119(3), 333-43.

Let M be a smooth manifold with a regular foliation F and a 2-form ω which induces closed forms on the leaves of F in the leaf topology. A smooth map f: (M, F) → (N, σ) in a symplectic manifold (N, σ) is called a foliated symplectic immersion if restricts to an immersion on each leaf of the foliation and further, the restriction of f*σ is the same as the restriction of σ on each leaf of the foliation. If is a foliated symplectic immersion then the derivative map D_f gives rise to a bundle morphism F: TM → TN which restricts to a monomorphism on TF ⊆ TM and satisfies the condition F*σ = ω on TF. A natural question is whether the existence of such a bundle map F ensures the existence of a foliated symplectic immersion. As we shall see in this paper, the obstruction to the existence of such an/is only topological in nature. The result is proved using the h-principle theory of Gromov.

6 ref

009311   Dalawat C S (NO, Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad-211 019, Email: dalawat@gmail.com) : Congruent numbers, elliptic curves, and the passage from the local to the global. Resonance 2009, 14(12), 1183-205.

The ancient unsolved problem of congruent numbers has been reduced to one of the major questions of contemporary arithmetic: the finiteness of the number of curves over Q which become isomorphic at every place to a given curve. We give an elementary introduction to congruent numbers and their conjectural characterisation, discuss local-to-global issues leading to the finite-ness problem, and list a few results and conjectures in the arithmetic theory of elliptic curves.

18 ref

009310   Crasmareanu M;Hretcanu C E (Al. I. Cuza Univ, Faculty of Mathematics, , Iasi 700506, Romania, Email: mcrasm@uaic.ro) : Last multipliers on Lie algebroids. Proc Indian Acad Sci-Mathl Sci 2009, 119(3), 287-96.

In this paper author extended the theory of last multipliers as solutions of the Liouville's transport equation to Lie algebroids with their top exterior power as trivial line bundle (previously developed for vector fields and mulivectors). Defines the notion of exact section and the Liouville equation on Lie algebroids. The aim of the present work is to develop the theory of this extension from the tangent bundle algebroid to a general Lie algebroid (e.g. the set of sections with a prescribed last multiplier is still a Gerstenhaber subalgebra). Presents some characterizations of this extension in terms of Witten and Marsden differentials.

32 ref

009309   Chin A Y M (Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia, Email: aymc@pc.jaring.my) : Clean elements in abelian rigns. Proc Indian Acad Sci-Mathl Sci 2009, 119(2), 145-8.

Let R be a ring with identity. An element in R is said to be clean if it is the sum of a unit and an idempotent. R is said to be clean if all of its elements are clean. If every idempotent in R is central, then R is said to be abelian. In this paper we obtain some conditions equivalent to being clean in an abelian ring.

6 ref

009308   Chen A;Ma Z (School of Mathematics and Computing Science, Guilin Univ of Electronic Technology, Guilin, Guangxi, 541004, People's Republic of China, Email: aiyogchen@163.com) : Bifurcation methods of dynamical systems for generalized Kadomtsov-Petviashvili-Benjamin-Bona-Mahony equation. Pramana J Phys 2008, 71(1), 57-63.

By applying the bifurcation theory of dynamical system to the generalized KP-BBM equation, the phase portraits of the travelling wave system are obtained. It can be shown that singular straight line in the travelling wave system is the reason why smooth periodic waves converge to periodic cusp waves. Under different parametric conditions, various sufficient conditions to guarantee the existence of the above solutions are given. Some exact explicit parametric representations of the above waves are obtained.

4 illus, 5 ref

009307   Chadwick E;Hatam A (School of Computing, Science and Engineering, Salford Univ, Salford, M5 4WT, UK, Email: e.a.chadwick@salford.ac.uk) : Further note on he force discrepancy for wing theory in Euler flow. Proc Indian Acad Sci-Mathl Sci 2009, 119(5), 679-98.

Uniform steady potential flow past a wing aligned at a small angle to the flow direction is considered. The standard approach is to model this by a vortex sheet, approximated by a finite distribution of horseshoe vortices. In the limit as the span of the horseshoe vortices tends to zero, an integral distribution of infinitesimal horseshoe vortices over the vortex sheet is obtained. The contribution to the force on the wing due to the presence of one of the infinitesimal horseshoe vortices in the distribution is focused upon. Most of the algebra in the force calculation is evaluated using Maple software and is given in the appendices. It is shown that the normal force is half that expected. In this further note, in addition it is demonstrated that the axial force is infinite. The implications and reasons for these results are discussed.

24 ref

009306   Carriazo A;Fernandez L M;Rodriguez-Hidalgo A (Geometry and Topology Dep, Faculty of Mathematics, Sevilla Univ, Apartado de Correos 1160, 41080-Sevilla, Spain, Email: carriazo@us.es) : Submanifolds weakly associated with graphs. Proc Indian Acad Sci-Mathl Sci 2009, 119(3), 297-318.

Established an interesting link between differential geometry and graph theory by defining submanifolds weakly associated with graphs. Proved that, every submanifold satisfies such an association, and other general results. Finally, submanifolds associated with graphs either in low dimensions or belonging to some special families have been studied.

12 illus, 10 ref

009305   Brown J;Lakshmibai V (Mathematics Dep, Northeastern Univ, Boston, MA 02115, USA, Email: brown.justin1@neu.edu) : Wahl's conjecture for a minuscule G/P. Proc Indian Acad Sci-Mathl Sci 2009, 119(5), 571-92.

Shows that Wahl's conjecture holds in all characteristics for a minuscule G/P.

11 ref

009304   Bot R I;Dumitru A;Wanka G (Faculty of Mathematics, Chemnitz University of Technology, D-09107 Cheminitz, Germany, Email: radu.bot@mathematik.tu-chemnitz.de) : New fenchel dual problem in vector optimization. Proc Indian Acad Sci-Mathl Sci 2009, 119(2), 251-65.

New Fenchel dual has been introduced for vector optimization problems inspired by the form of the Fenchel dual attached to the scalarized primal multiobjective problem. For the vector primal-dual pair authour prove weak and strong duality. Furthermore, we recall two other Fenchel-type dual problems introduced in the past in the literature, in the vector case, and make a comparison among all three duals. Moreover, we show that their sets of maximal elements are equal.

15 ref

009303   Bhowmik M;Pal M (Mathematics Dep, V.T.T. College, Midnapore, Email: mono9ranjan_bhowmik@rediffmail.com) : Partition of generalized interval-valued intuitionistic fuzzy sets and some properties. Int J appl mathl Analysis Applic 2009, 4(1), 1-10.

Defines four partitions of generalized interval-valued intuitionistic fuzzy sets (GIVIFSs) have been defined. In fact, all interval-valued intuitionstic fuzzy sets (IVIFSs) are GIVIFSs but all GIVIFSs are not IVIFSs. Also, studies some properties of the four partitioned subsets of GIVIFSs.

009302   Bhat B V R (NO, Indian Statistical Institute, R V College Post, Bangalore-560 059, Email: bhat@isibang.ac.in ) : Wigner's semicircle law and free independence. Resonance 2009, 14(10), 970-7.

Free probability theory is a mathematical generalization of classical probability theory. For free central limit theorem we get the semicircle law as the limit law. EP Wigner came across this probability distribution while studying random matrices.

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009301   Behravesh H;Mousavi H (Faculty of Science, Deparment of Mathematics, University of Urmia, Urimia, Iran, Email: h.behravesh@mail.urmia.ac.ir) : Note on p-groups of ≤ p<. Proc Indian Acad Sci-Mathl Sci 2009, 119(2), 137-43.

Authors defined c(G), q(G) and p(G). In this paper it is shown that if G is a p-group, where p is an odd prime and |G| ≤ p^{4, then c(G) = q(G) = p(G). However, the question of whether or not there is a p-group G with strict inequality c(G) = q(G) < p(G) is still open.}

11 ref

009300   Ashrafi N (Mathematics Dep, Semnan Univ, Semnan, Iran, Email: nashrafi@semnan.ac.ir) : Finer classification of the unit sum number of the ring of integers of quadratic fields and complex cubicn fields. Proc Indian Acad Sci-Mathl Sci 2009, 119(3), 267-74.

The unit sum number, u(R), of a ring R is the least k such that every element is the sum of k units; if there is no such k then u(R) is ω or ∞ depending on whether the units generate R additively or not. Here authors introduce a finer classification for the unit sum number of a ring and in this new classification we completely determine the unit sum number of the ring of integers of a quadratic field. Further obtained some results on cubic complex fields which one can decide whether the unit sum number is ω or ∞. Presented some examples showing that all possibilities can occur.

3 ref

009299   Asgari M S (Mathematics Dep, Faculty of Science, Islamic Azad Univ, Cetral Tehran Branch, Simayeiran St., Farahzadi Ave., West Town, Tehran, Iran, Email: m_asgari@iauctb.ac.ir) : New characterizations of fusion frames (Frames of subspaces). Proc Indian Acad Sci-Mathl Sci 2009, 119(3), 369-82.

Authors gives new characterizations of fusion frames, on the properties of their synthesis operators, on the behavior of fusion frames under bounded operators with closed range, and on erasures of subspaces of fusion frames. Furthermore shows that every fusion frame is the image of an orthonormal fusion basis under a bounded surjective operator.

17 ref

009298   Alaeiyan M;Hosseinipoor M K (Mathematics Dep, Iran Univ of Science and Technology, Narmak, Tehran 16844, Iran, Email: alaiyan@iust.ac.ir) : Classifying cubic edge-transitive graphs of order 8p. Proc Indian Acad Sci-Mathl Sci 2009, 119(5), 647-53.

A simple undirected graph is said to be semisymmetric if it is regular and edge-transitive but not vertex-transitive. Let p be a prime. It was shown by Folkman that a regular edge-transitive graph of order 2p or 2p^{2 is necessarily vertex-transitive. In this paper, an extension of his result in the case of cubic graphs is given. It is proved that, every cubic edge-transitive graph of order 8p is symmetric, and then all such graphs are classified.}

1 illus, 1 table, 20 ref

009297   Aggarwal D (Statistics and Probability Dep, Michigan State Univ, MI 48823, U.S.A., Email: da.aggarwal@gmail.com) : Testing the equality of two distributions with current status data. J Indian Statist Ass 2008, 46(1), 1-15.

Paper deals with the problem of testing the equality of two distribution functions against the two sided alternative based on the current status data. It derives asymptotic distribution of the underlying test statistic both under the null hypothesis and under local alternatives. A simulation study is included to exhibit the finite sample level and power behavior. It also contains a finite sample comparison of the proposed test with the two sample Cramer-von Mises test based on nonparametric maximum likelihood estimators of the time to event distribution functions.

8 tables, 19 ref

009296   Agayev N;Ozen T;Harmanci A (Department of Pedagogy, Qafqaz University, Baku Azerbaijan, Email: nazsimagayev@qafqaz.edu.az) : On a class of semicommutative modules. Proc Indian Acad Sci-Mathl Sci 2009, 119(2), 149-58.

Let R be a ring with identity, M a right R-module and S = End_R (M). In this note, we introduce S-semicommutative, 5-Baer, S-q.-Baer and S-p.q.-Baer modules. Authour study the relations between these classes of modules. Also we prove if M is an S-semicommutative module, then M is an S-p.q.-Baer module if and only if M[x] is an S[,x]-p.q.-Baer module, M is an S-Baer module if and only if M[x] is an S[x]-Baer module, M is an 5-q.-Baer module if and only if M[x] is an S[x]-q.-Baer module.

10 ref

009295   Adhikari S D;Gun S;Rath P (NO, Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad-211 019, Email: adhikari@mri.ernet.in) : Remarks on some zero-sum theorems. Proc Indian Acad Sci-Mathl Sci 2009, 119(3), 275-81.

A new proof of a weighted generalization of a result of Gao in a particular case has been given. Also gives new methods for determining the weighted Davenport constant and another similar constant for some particular weights.

11 ref

009294   Adhami A Y;Bari A;Rabbani Q (Statistics and Operations Research Dep, Aligarh Muslim Univ, Aligarh, Email: yusufstats@gmail.com) : Extended kth-best approach for solving bilevel linear integer programming. Int J appl mathl Analysis Applic 2009, 4(1), 11-17.

NAZ cut and A-T cut are applied to the extended Kth-best approach for linear bilevel programming to solve the bilevel programming problem for integer variables. An example is given in the end to illustrate the procedure.

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009293   Abu-Falahah I;Macias R A;Segovia C;Torrea J L (Deparamento de Matematicas, Facultad de Ciencias, Universidad Autonoma de Madrid, 28049 Madrid, Spain, Email: ibraheem.abufalahah@uam.es ) : Transferring strong boundedness among Laguerre orthogonal systems. Proc Indian Acad Sci-Mathl Sci 2009, 119(2), 203-20.

Given the family of Laguerre polynomials, it is known that several ortho-normal systems of Laguerre functions can be considered. Prove that an exhaustive knowledge of the boundedness in weighted L^{p of the heat and Poisson semigroups, Riesz transforms and g-functions associated to a particular Laguerre orthonormal system of functions, implies a complete knowledge of the bounded-ness of the corresponding operators on the other Laguerre orthonormal system of functions. As a byproduct, new weighted Lp boundedness are obtained. The method also allows us to get new weighted estimates for operators related with Laguerre polynomials.}

1 illus, 17 ref

008336   Yadav R K;Nirwan P (Mathematics and Statistics Dep, J.N.V. Univ, Jodhpur-342 005, Email: rkmdyadav@yahoo.co.in) : Some results involving generalized Weyl fractional q-integrals of certain basic multiple hypergeometric functions. Bull pure appl Math 2009, 3(2), 263-75.

Evaluates a the generalized Weyl type fractional q-integrals of basic multiple hypergeometric functions. The generalized Weyl fractional q-integrals of basic Lauricella functions, basic Kampe de Feriet functions, basic Appell functions, q-Horn's functions and basic confluent hypergeometric functions have been evaluated as applications of the main results.

12 ref

008335   Xu X;Jiao X (School of Mathematical Sciences, Graduate University of Chinese Academy of Sciences, Bejing 100049, China, Email: xwxu04@mails.gucas.ac.cn) : Holomorphic two-spheres in complex grassmann manifold G(2,4). Proc Indian Acad Sci-Mathl Sci 2008, 118(3), 381-8.

Use the harmonic sequence to study the linearly full holomorphic two-spheres in complex Grassmann manifold G (2, 4). Shows that if the Gaussian curvature K (with respect to the induced metric) of a non-degenerate holomorphic two-sphere satisfies K ≤ 2 (or K ≥ 2), then K must be equal to 2. Simultaneously, we show that one class of the holomorphic two-spheres with constant curvature 2 is totally geodesic. Concerning the degenerate holomorphic two-spheres, if its Gaussian curvature K ≤ 1 (or K ≥ 1), then K = 1. Moreover, we prove that all holomorphic two-spheres with constant curvature 1 in G(2, 4) must be U (4)-equivalent.

6 ref

008334   Wei C (School of Mathematical Sciences, Ocean University of China, Qingdao 266071,People's Republic of China, Email: weicgqd@yahoo.com.cn) : On ideals and quotients of AT-algebras. Proc Indian Acad Sci-Mathl Sci 2008, 118(4), 517-24.

Some results on AT-algebras are given. Study the problem when ideals, quotients and hereditary subalgebras of AT-algebras or AT-algebras or AT-algebras, and give a necessary and sufficient condition of a hereditary subalgebra of an A T-algebra being an AT-algebra.

11 ref

008333   Vij I;Mittal S K;Singh T P (Maths Dep, S.M.S. Khalsa College, Barara, (Ambala) Haryana) : Optimal flow time in open shop scheduling including weights and transportation time. Ultra Scient phys Sci 2009, 21(2M), 566-70.

Deals with n x 2 open shop scheduling problem in which the processing time of jobs on machines, transportation time of each job from one machine to another and weightage to jobs is considered. The objective of the study is to find an optimal sequence of jobs which minimizes total weighted mean production time. The algorithm is derived to find out the optimal sequence and is demonstrated with numerical illustration.

9 tables, 10 ref

008332   Tripathi V N;Pal S (Mathematics Dep, S.B.P.G. College Baragaon, Varanasi, Uttar Pradesh) : On unifrom T(C, I) summability of legendre series. Ultra Scient phys Sci 2009, 21(2M), 553-8.

Deals with a thereom on uniform T(C, I) Summability of Legendre series under very general condition. It generalizes a very recently known result due to Tripati and Yadav^{3 on uniform (Np,q) (C,l) Summability of Legendre series under similar condition. It may be noted that the (Np, q) Summability is a particular T-Summability method.}

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008331   Thangavelu P;Sheiba Grace J (Mathematics Dep, Aditanar College, Tiruchendur-628 216, Email: ptvelu12@gmail.com) : E-Convex programmings. Ultra Scient phys Sci 2009, 21(2M), 455-8.

Youness introduced the concepts of E-convex sets and E-convex functions and studied their properties. Following this Xiusu Chen and Suneja, Lalitha and Govil studied the applications of E-convex functions. Shows that Theorem 3.1 of Youness [J. Optim. Theory Appl. 102(2)(I999), 439--150] is incorrect by giving some counter examples. Modifies-Theorem 3.1 of Youness and apply this to solve an E-convex programming problem.

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008330   Tak S S;Mathur R (Mathematics and Statisitics Dep, JNV Univ, Jodhpur, Rajasthan, Email: sstak@rediffmail.com) : Numerical solution of transient free convective flow past a vertical porous plate with viscous dissipation and radiation. Ultra Scient phys Sci 2009, 21(2M), 443-50.

Combined effect of viscous dissipation and radiation on transient free convection flow past an infinite vertical porous plate has been studied numerically using Crank Nicolson finite difference scheme. It is found that the steady-state solution is reached after time t_s = 8.5. It is also observed that due to greater viscous dissipative heat or the presence of radiation, there is a rise in the skin friction and a fall in the Nusselt number.

7 illus, 28 ref

008329   Sreedhar Babu M;Bhaskar Reddy N;Subba Reddy M V (Mathematics Dep, S V Univ, Tirupati-517 502, Email: drmvsubbreddy@yahoo.co.in) : Effect of variable viscosity on the peristaltic motion of a jeffrey fluid in a symmetric channel. Ultra Scient phys Sci 2009, 21(2), 395-402.

The peristaltic motion of an incompressible Jeffrey fluid with variable viscosity in a two-dimensional symmetric channel under the long wavelength and low Reynolds number assumptions is investigated. Analytical solutions are obtained for axial velocity and axial pressure gradient. The effects of viscosity parameter a, material parameter λ₁ and amplitude ratio φ on the pumping characteristics and the friction force are studied through graphs in detail.

9 illus, 10 ref

008328   Sreeda K N;Sattanathan R (NO, Vinayaka Missions Univ, Salem, Email: sreeda.arun@gmail.com) : Model for TOPSIS method based on intuitionistic fuzzy sets. Ultra Scient phys Sci 2009, 21(2M), 365-70.

Multicriteria decision making (MCDM) analysis may involve problems dealing with incomplete information. In such instances, the performance ratings of the criteria may be expressed in terms of Intuitionistic fuzzy values. These intuitionistic fuzzy values may then be utilized along with the traditional Technique for Order Performance by Similarity to Ideal Solution [TOPSIS] method so as to arrive at the decision where incomplete weight information are given. Using this method, the ranking of order of all alternatives are obtained by calculating the distances to both Intuitionistic fuzzy positive ideal solution (IFPIS) and the Intuitionistic fuzzy negative ideal solution (IFNIS) simultaneously. In this paper, we have discussed the use of Intuitionistic fuzzy sets (IFS) in multicriteria decision making (MCDM) analysis and its application to a practical problem in combination with the TOPSIS method.

3 tables, 15 ref

008327   Sonjun L V;Leng G (College of Mathematics and Computer Science, Chongqing Normal Univ, Chongqing 400047, People's Republic of China, Email: lvsongjun@126.com) : L_P-curvature images of convex bodies and L_P-projection bodies. Proc Indian Acad Sci-Mathl Sci 2008, 118(3), 413-24.

Associated with the L_p-curvature image defined by Lutwak, some inequalities for extended mixed p-affine surface areas of convex bodies and the support functions of L_p-projection bodies are established. As a natural extension of a result due to Lutwak, an L_p-type affine isoperimetric inequality, whose special cases are L_p-Busemann-Petty centroid inequality and L_p-affine projection inequality, respectively, is established. Some L_p-mixed volume inequalities involving L_p-projection bodies are also established.

18 ref

008326   Somasundaram S;Nagarajan A;Mahadevan G (Mathematics Dep, Manonmaniam Sundaranar Univ, Tirunelveli-627 012, Email: nagarajan.voc@gmail.com) : Edge and vertex intersection of paths in a graph. Ultra Scient phys Sci 2009, 21(2M), 315-18.

Investigates some parameters μ₀, μ₁ (μ'₀ μ'₁) for vertex (edge) intersection of paths in a graph G. μ0(G) μ1(G)) is the minimum number of vertices (edges) of all graphs H such that G is the intersection graph of some path cover of a graph H. μ'₀, μ'₁ are define analogously for edge intersection graph.

2 illus, 6 ref

008325   Somasimdaram S;Nagarajan A;Mahadevan G (Mathematics Dep, Manonmaniam Sundaranar Univ, Tirunelveli-627 012, Email: nagarajan.voc@gmail.com) : On randomly K_n - packable graphs. Ultra Scient phys Sci 2009, 21(2M), 353-6.

Graph G is said to be packable by the graph F if its edges can be partitioned into copies of F. It is randomly packable if what remains of deletion of edges of a proper subgraph that is F packable is also F-packable. Investigates the proerties of Ω (Ψ) where Ψ is a unique K_n - packing of a graph.

4 illus, 3 ref

008324   Shukla S (Mathematics Dep, Allahabad Univ, Allahabad-211 002, Email: Complex_geometry@yahoo.co.in) : On Kenmotsu manifold. Ultra Scient phys Sci 2009, 21(2M), 485-90.

In 1926, H. Levy proved that a second order symmetric parallel non singular tensor on a space of constant curvature is a constant multiple of the metric tensor. R. Sharma generalized Levy's result and studied second order parallel tensor on a Kahler space of constant holomorphic sectional curvature as well as on a acompact K-contact manifold without boundary. U.C. De and Debasish tarafdar showed that for a P-Sasakian manifold M with a symmetric parallel lensor of type (0,2) is also a constant multiple of the metric tensor and there is no parallel 2-form on M.

8 ref

008323   Shukla S (Mathematics Dep, Allahabad Univ, Allahabad-211 002, Email: complex_geometry@yahoo.co.in) : Analytic vector field on an almost hyperbolic Hermitian manifold. Ultra Scient phys Sci 2009, 21(2M), 469-76.

Discusses an analytic vector field on an almost hyperbolic Hermitian manifold and to obtain certain expressions of the curvature tensor on an almost hyperbolic Hermitian manifold admitting semi-symmetric metric connection assuming analytic vector field to be killing and affine.

11 ref

008322   Shantharaju C V;Mathad V (Mathematics Dep, REVA Institute of Technology & Management, Kattigenahalli, Yelahanka, Bangalore-560 064, Email: shnthraju@yahoo.co.in) : Algorithm to determine the chromatic number of a graph. Ultra Scient phys Sci 2009, 21(2M), 577-9.

Coloring of a graph is an assignment of colors to its vertices so that no two adjacent vertices receive the same color. An n-coloring of a graph G uses n colors. The chromatic number x(G) of a graph G is the minimum n for which G has an n-coloring. Gives an algorithm to determine the chromatic number of a graph.

3 illus, 1 ref

008321   Sapna (Mathematics Dep, H.B. Technological Institute, Kanpur-208 002, Email: aapna1980jan@rediffmail.com) : Analysis of non-newtonian fluid flow in a stenosed artery. Ultra Scient phys Sci 2009, 21(2), 307-14.

The numerical illustration presented at the end of the paper provides the results for the resistance to flow, apparent viscosity and the wall shear stress through their graphical representations. It has been shown that the resistance to flow, apparent viscosity and wall shear stress increases with the size of the stenosis but these increases is comparatively small due to non-Newtonian behavior of the blood indicating the usefulness of its rheological character in the functioning of the diseased arterial circulation. Few comparisons with the existing results have been made in order to validate the applicability of the present model.

9 illus, 22 ref

008320   Santhanam G (Mathematics and Statistics Dep, Indian Institute fo Technology, Kanpur-208 016, Email: santhana@iitk.ac.in) : Hypersurfaces in simply connected space forms. Proc Indian Acad Sci-Mathl Sci 2008, 118(4), 569-72.

Let M be a hypersurface in a simply connected space form M(K). Author proves some rigidity results for M in terms of lower bounds on the Ricci curvature of the hypersurface M.

3 ref