014395   Michel J;Rodriguez J M;Sigarreta J M;Villeta M (Matematicas Universidad Carlos III de Madrid, Av. de la Universidad 30, 28911 Leganes, Madrid, Spain, Email: jomaro@math.uc3m.es) : Gromov hyperbolicity in Cartesian product graps. Proc Indian Acad Sci-Mathl Sci 2010, 120(5), 593-609.

If X is a geodesic metric space and xi₁, x₂, x₃,∈ X, a geodesic triangle T = {x₁, x₂, x₃} is the union of the three geodesies [x₁x₂], [x₁x₂] and [x₂x₃] in X. The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δ-neighborhood of the union of the two other sides, for every geodesic triangle T in X. If X is hyperbolic, we denote by δ(X) the sharp hyperbolicity constant of X, i.e. δ(X) = inf {δ ≥ 0: X is δ-hyperbolic}. In this paper we characterize the product graphs G₁ x G₂ which are hyperbolic, in terms of G₁ and G₂: the product graph G₁ x G₂ is hyperbolic if and only if G₁ is hyperbolic and G₂ is bounded or G₂ is hyperbolic and G₁ is bounded. We also prove some sharp relations between the hyperbolicity constant of G₁ x G₂, δ(G₁), δ(G₂) and the diameters of G₁ and G₂ (and we find families of graphs for which the inequalities are attained). Furthermore, we obtain the precise value of the hyperbolicity constant for many product graphs.

30 ref

014394   Mahurpawar V;Ronghe A K (Mathematics Dep, Govt. P.G. College, Chhindawara) : Perfect fluid distribution in cylindrically symmetric inhomogenious universe in bimeyric relativity. Ultra Scient phys Sci 2010, 22(2), 397-400.

Authors to investigate the behavior of the perfect fluid in the cylindrically symmetric inhomogeneous cosmological model in bimetric theory of gravitation.

22 ref

014393   Mahmoudi M G (Mathematical Sciences Dep, Sharif Technology Univ, P. O. Box 11155-9415, Tehran, Iran, Email: mmahmoudi@sharif.ir) : Orthogonal symmetries and clifford algebras. Proc Indian Acad Sci-Mathl Sci 2010, 120(5), 535-61.

Involutions of the Clifford algebra of a quadratic space induced by orthogonal symmetries are investigated.

21 ref

014392   Liu S;Fang X (Mathematical Science School, Qufu Normal Univ, Qufu 273165, China, Email: ishd008!163.com) : K-theory for certain extension algebras of purely infinite simple CΘ-algebras. Proc Indian Acad Sci-Mathl Sci 2010, 120(4), 409-15.

Considers extension algebras of unital purely infinite simple C*-algebras by purely infinite simple stable C*-algebras. AT-theory of such extension algebras is described.

23 ref

014391   Li J;Wang Y (Mathematics and Physics Dep, Shijiazhuag Railway Institute, Shijiazhuang, 050043, Peoples' Republic of China, Email: yanjinglee@163.com) : (Z_Z)κ-actions with fixed point set of constnt codimension 2κ + 8<. Indian J pure appl Math 2010, 41(4), 607-23.

The ideal J_*,k^{2k + 8 of cobordism classes in the unoriented cobordism ring MO_*, containing a representative admitting a (Z₂)k-action with fixed point set of constant codimension 2k + 8 is determined for k ≥ 4.}

23 ref

014390   Leach P G L;Waren R R;Caister N;Naicker V; Euler N (School of mathematical Sciences, Kwazulu-Natal Univ, P.O. Box X54001 Durban 4000, Republic of South Africa, Email: leachp@ukzn.ac.za ) : Symmetries, integrals and solutions of ordinary differential equations of maximal symmetry. Proc Indian Acad Sci-Mathl Sci 2010, 120(1), 113-30.

Second- and third-order scalar ordinary differential equations of maximal, symmetry in the traditional sense of point, respectively contact, symmetry are examined for the mappings they produce in solutions and fundamental first integrals. The properties of the 'exceptional symmetries', i.e. those not considered to be generic to scalar equations of maximal symmetry, can be recast into a form which is applicable to all such equations of maximal symmetry. Some properties of these symmetries are demonstrated.

26 ref

014389   Krishna M (Institute of Mathematical Sciences, Taramani, Chennai-600 113, Email: krishna@imsc.res.in) : Regularity of the interband light absorption coefficient. Proc Indian Acad Sci-Mathl Sci 2010, 120(3), 351-62.

In this paper we consider the interband light absorption coefficient (ILAC), in a symmetric form, in the case of random operators on the d-dimensional lattice. We show that the symmetrized version of ILAC is either continuous or has a component which has the same modulus of continuity as the density of states.

21 ref

014388   Kong Q (Mathematics Dep, Tianjin Polytechnic Univ, Tianjin 300160, People's Republic of China, Email: tjkqi1978@163.com) : Two camina's theorems on conjugacy class sizes. Proc Indian Acad Sci-Mathl Sci 2010, 120(2), 139-40.

Let G be a finite group. Authours mainly investigate how certain arithmetical conditions on conjugacy class sizes of some elements of biprimary order of G influence the structure of G. Some known results are generalized.

6 ref

014387   Kirsch W;Krishna M (Fakultat fur Mathematik and Informatik, Fern Universitat in Hagen, 58084 Hagen, Germany, Email: krishna@imsc.res.in) : Lifshitz tails for the interband light absorption coefficient. Proc Indian Acad Sci-Mathl Sci 2010, 120(4), 465-79.

In this paper we consider the interband light absorption coefficient (ILAC) for various models. We show that at the lower and upper edges of the spectrum the Lifshitz tails behaviour of the density of states implies similar behaviour for the ILAC at appropriate energies. The Lifshitz tails property is also exhibited at some points corresponding to the internal band edges of the spectrum.

2 illus, 26 ref

014386   Khashyarmanesh K (Pure Mathematics Dep, Center of Excellence in Analysis on Algebraic Structures, Ferdowsi Mshhad Univ, P.O. Box 1159-91775, Mashhad. Iran, Email: khashyar@ipm.ir) : On the matlis duals of local cohomology modules and modules of generalized fractions. Proc Indian Acad Sci-Mathl Sci 2010, 120(1), 35-43.

Let (R, m) be a commutative Noetherian local ring with non-zero identity, a a proper ideal of R and M a finitely generated R-module with a M ≠ M. Let D(-) := Hom_R(-, E) be the Matlis dual functor, where E := E (R/m) is the injective hull of the residue field R/m. In this paper, by using a complex which involves modules of generalized fractions, we show that, if x₁, ..., x_n is a regular sequence on M contained in a, then Hⁿ_{(x1,....xn)rD(H<&>na}(M))) is a homomorphic image of D(M), where Hⁱ_b(-) is the i-th local cohomology functor with respect to an ideal b of R. By applying this result, we study some conditions on a certain module of generalized fractions under which D (Hⁿ(x₁, ...., x_n)_R (D(Hⁿ_a (M)))) @ D(D(M)).

15 ref

014385   Kamyabi Gol R A;Tousi R R (Mathematics Dep, Ferdowsi Univ, P.O. Box 1159, Ashhad 91775, Iran, Email: kamyabi@ferdowsi.um.ac.ir) : Some equivalent multiresolution conditions on locally compact abelian groups. Proc Indian Acad Sci-Mathl Sci 2010, 120(3), 317-31.

Conditions under which a function generates a multiresolution analysis are investigated. The definition of the spectral function of a shift invariant space is generalized from Rⁿ to a locally compact abelian group and the union density and intersection triviality properties of a multiresolution analysis are characterized in terms of the spectral functions. Finally, all multiresolution analysis conditions are characterized in terms of the scaling and the spectral functions.

22 ref

014384   Juluru N;Srinivasa Rao A S R (NO, , 5th Floor, PSU, R.A. Fisher Building Indian Statistical Institute, 203 B.T. Road, Kolkata-700 108, Email: ami@isical.ac.in) : Mahlburg's work on crank functions, Ramanujan's partitions revisited. Resonance 2010, 15(3), 232-43.

Karl Mahlburg brilliantly showed the importance of crank functions in partition congruences that were originally guessed by Freeman Dyson. Ra-manujan's partition functions are the centre of these works. Not only for the theory on cranks, but for many other researchers in India Ramanu- jan's work inspired their career in mathematics.

13 ref

014383   Jin D H (Mathematics Dep, Dongguk Univ, Kyongju-780 714 Korea, Email: jindh@dongguk.ac.kr) : Geometry of lightlike hypersurfaces of an indefinite Sasakian manifold. Indian J pure appl Math 2010, 41(4), 569-81.

Study the geometry of lightlike hypersurfaccs of an indefinite Sasakian manifold. The main result is to prove three characterization theorems for such a lightlike hypersurface. In addition to these main theorems, we study the geometry of totally geodesic light-like hypersurfaces of an indefinite Sasakian manifold.

16 ref

014382   Jeta Ram;Chandak S (Mathematics and Statistics Dep, Jai Narain Vyas Univ, Jodhpur-342 005, Email: bishnoi_jr@yahoo.com) : Unified fractional derivative formulas for the Fox-Wright generalized hypergeometric function. Proc Natn Acad Sci India-Sect A 2009, 79(Pt1), 51-7.

Derives a generalized derivative formula involving the product of Fox-Wright generalized hypergeometric function _pψ_q and a general class of multivariable polynomials. On account of the general nature of the operator involving generalized polynomial set, as its Kernel, and due to presence of a Fox-Wright generalized hypergeometric function _pψ_q, the investigation provides interesting unification and extension of a number of known results. Some interesting special cases of the established results are also discussed.

17 ref

014381   Jain M;Pandey R (Mathematics Dep, I.B.S., Khandari, Agra-282 002, Email: madhujain@sancharnet.in) : Queueing analysis of state dependent M<. Proc Natn Acad Sci India-Sect A 2009, 79(Pt1), 99-107.

A single server queueing system with state dependent Pois-son bulk arrival, general bulk service and multiple vacations of alternate type and setup times is studied. The operator provides service in batches according to a general bulk service rule such that the service starts only when a minimum number of units, say a is present in the queue and the maximum service capacity of the batch is b. For the analysis purpose, we introduce a supplementary variable technique and then Laplace transforms and generating functions are used to obtain steady state formulae. The system size distribution and expected length of idle and busy periods are derived. Finally, we establish a condition under which the optimal stationary operating policy is achieved under a linear cost structure. A numerical illustration is provided to examine the effect of parameters on various performance indices.

6 illus, 1 table, 15 ref

014380   Huang M;Ponnusamy S;Wang X (Mathmatics Dep, Hunan Normal Univ, Changsha, Hunan 410081, People's Republic of China, Email: mzhuang79@yahoo.com.cn) : John disks, the apollonian metric, and min-max properties. Proc Indian Acad Sci-Mathl Sci 2010, 120(1), 83-96.

The main results of this paper are characterizations of John disks-the simply connected proper subdomains of the complex plane that satisfy a twisted double cone connectivity property. One of the characterizations of John disks is an analog of a result due to Gehring and Hag who found such a characterization for quasidisks. In both situations the geometric condition is an estimate for the domain's hyperbolic metric in terms of its Apollonian metric. The other characterization is in terms of an arc min-max property.

15 ref

014379   Huang J (Sciences College, North China Technology Univ, Beijing 100144, China, Email: hizheng@163.com) : Heat kernel version of cowling-price theorem for the Laguerre hypergroup. Proc Indian Acad Sci-Mathl Sci 2010, 120(1), 73-81.

In this paper, authors prove a heat kernel version of Cowling-Price theorem for the Laguerre hypergroup.

17 ref

014378   Hans Gill R J;Raka M;Sehmi R (Centre for Advanced Study in Mathematics, Panjab Univ, Chandigarh-160 014, Email: hansgill@pu.ac.in) : Estimaties on conjectures of Minkowski and Woods. Indian J pure appl Math 2010, 41(4), 595-606.

Let Rⁿ be the n-dimensional Euclidean space. Let A be a lattice of determinant 1 such that there is a sphere |X| <60> R which contains no point of A other than the origin O and has n linearly independent points of A on its boundary. A well known conjecture in the geometry of numbers asserts that any closed sphere in Rⁿ of radius √ n/4 contains a point of A. This is known to be true for n ≤ 8. Gives estimates on a more general conjecture of Woods for n ≥ 9. This leads to an improvement for 9 ≤ n ≤ 22 on estimates of Il'in (1991) to the long standing conjecture of Minkowski on product of n non-homogeneous linear forms.

2 tables, 36 ref

014377   Guo Y H (Mathematics Dep, Hexi Univ, Gansu, Zhangye 734000, People's Republic of China, Email: gyh7001@163.com) : n-Colour even self-inverse compositions. Proc Indian Acad Sci-Mathl Sci 2010, 120(1), 27-33.

An n-colour even self-inverse composition is defined as an n-colour self-inverse composition with even parts. In this paper, we get generating functions, explicit formulas and recurrence formulas for n-colour even self-inverse compositions. One new binomial identity is also obtained.

9 ref

014376   Gorain G C (Mathematics Dep, J.K. College, Purulia-723 101, Email: goraing@gmail.com) : Stabilization for the vibrations modeled by the 'standard linear model' of viscoelasticity. Proc Indian Acad Sci-Mathl Sci 2010, 120(4), 495-506.

Study the stabilization of vibrations of a flexible structure modeled by the 'standard linear model' of viscoelasticity in a bounded domain in Rⁿ with a smooth boundary. We prove that amplitude of the vibrations remains bounded in the sense of a suitable norm in a space X, defined explicitly in (22) subject to a restriction on the uncertain disturbing forces on X. We also estimate the total energy of the system over time interval [0, T] for any T <62> 0, with a tolerance level of the disturbances. Finally, when the input disturbances are insignificant, uniform exponential stabilization is obtained and an explicit form for the energy decay rate is derived, these results are achieved by a direct method under undamped mixed boundary conditions.

21 ref

014375   Gijo E V;Scaria J (SQC & OR Unit, Indian Statistical Institute, 8th Mile, Mysore Road, Bangalore-560 059, Email: gijo@isibang.ac.in) : Application of SARIMA model in demand forecasting. Sci Soc 2010, 8(1), 13-23.

A company involved in packaging of tea was interested in forecasting the monthly demand for tea from its depots across the country. Time series data on market demand in monthly frequency was available. This data were modeled by Box-Jenkins Seasonal ARIMA model. Adequacy of the fitted model has been tested using Ljung-Box test criteria followed by residual analysis. Thus, the most appropriate model was used to forecast the monthly demand of tea. This model has helped the organization to plan the production activities more efficiently so that on time availability of product in the market was ensured.

9 illus, 3 tables, 12 ref

014374   Gani A N;Dinagar D S (P.G. & Research Dep of Mathematics, Jamal Mohamed College, Tiruchirappalli-620 020, Email: ganijmc@yahoo.co.in) : Note on linear programming in fuzzy environment. Proc Natn Acad Sci India-Sect A 2009, 79(Pt1), 91-8.

The theoretical frame work of basic feasible solution, unbounded solution and optimality condition of the fuzzy linear programming problem (LPP) involving piecewise quadratic fuzzy numbers are given and an effective method of solving fuzzy LPP is introduced.

1 illus, 1 table, 7 ref

014373   Gadgil S;Pandit S (Mathematics Dep, Indian Institute of Science, Bangalore-560 012) : Splittings of groups, normal forms and partitions of ends. Proc Indian Acad Sci-Mathl Sci 2010, 120(2), 217-41.

Splittings of a free group correspond to embedded spheres in the 3-manifold M = <35>_kS² x S¹. These can be represented in a normal form due to Hatcher. In this paper, authour determine the normal form in terms of crossings of partitions of ends corresponding to normal spheres, using a graph of trees representation for normal forms. In particular, they give a constructive proof of a criterion determining when a conjugacy class in πT₂(M) can be represented by an embedded sphere.

31 ref

014372   Fu H P (Mathematics Dep, Nanchang Univ, Nanchang 330047, People's Republic of China, Email: mathfu@126.com) : Rigidity of minimal submanifolds with flat normal bundle. Proc Indian Acad Sci-Mathl Sci 2010, 120(4), 457-64.

Let Mⁿ (n ≥ 3) be an n-dimensional complete immersed n-2/n-super-stable minimal submanifold in an (n + p)-dimensional Euclidean space R^n+p with flat normal bundle. We prove that if the second fundamental form of M satisfies some decay conditions, then M is an affine plane or a catenoid in some Euclidean subspace.

13 ref

014371   Fu E A (School of Statistics and Mathematics, Zhejiang Gondshang Univ, Hangzhou 310018, China, Email: statzju@tom.com ) : Almost sure invariance principle for trimmed sums of random vectors. Proc Indian Acad Sci-Mathl Sci 2010, 120(5), 611-18.

Let {X_n; n ≥ 1} be a sequence of independent and identically distributed random vectors in R^p with Euclidean norm |.|, and let X^(r)_n = X_m if |X_m| is the r-th maximum of {|X_k|; k ≥ n}. Define S_n = Σ_k≥n X_k and ^(r)S_n = S_n - (X⁽¹⁾_n + ... + X^(r)_n). In this paper a generalized strong invariance principle for the trimmed sums (^(r)S_n is derived.

8 ref

014370   Dong Z;Tao J (Mathematics Dep, Zhejiang Univ, Hangzhou 310 027, China, Email: dongzhe@zju.edu.cn) : Nuclearity for dual operator spaces. Proc Indian Acad Sci-Mathl Sci 2010, 120(1), 105-11.

In this short paper, author studied the nuclearity for the dual operator space V* of an operator space V. It was shown that V* is nuclear if and only if V*** is injective, where V*** is the third dual of V. This is in striking contrast to the situation for general operator spaces. This result is used to prove that V* is nuclear if and only if V is nuclear and V** is exact.

14 ref

014369   DE Filippis V (DI.S.I.A., Faculty of Engineering, Messina Univ, 98166 Messina, Italy, Email: defilippis@unime.it) : Power cocentralizing generalized derivations on prime rings. Proc Indian Acad Sci-Mathl Sci 2010, 120(3), 285-97.

Let R be a prime ring, U the Utumi quotient ring of R, C = Z(U) the extended centroid of R, L a non-central Lie ideal of R, H and G non-zero generalized derivations of R. Suppose that there exists an integer n ≥ 1 such that (H(u)u - uG(u))ⁿ = 0, for all u e L, then one of the following holds: (1) there exists c e U such that H(x) = xc, G(x) = ex; (2) R satisfies the standard identity s₄ and char(R) = 2; (3) R satisfies s₄ and there exist a, b, c ∈ U, such that H(x) = ax+xc, G(x) = cx+xb and (a - b)ⁿ = 0.

13 ref

014368   Chang-Jian Z;Cheung W S (Information and Mathematics Sciences Dep, College of Science, China Jiliang Univ, Hangzhou 310018, People's of China, Email: chjzhao@yahoo.com.cn) : L_p -mixed intersection bodies and star duality. Proc Indian Acad Sci-Mathl Sci 2010, 120(4), 429-40.

The paper extends the two notions of the dual mixed volumes and L_p-intersection body to q-dual mixed volumes and L_p-mixed intersection body, respectively. Inequalities for the star dual of L_p-mixed intersection bodies are established.

34 ref

014367   Chanchal Kumar;Singh P (Mathematics Dep, Jammu Univ, Jammu-180 006, Email: chanchal_jammu@yahoo.com) : Deficiently extremal cohen-macaulay algebras. Proc Indian Acad Sci-Mathl Sci 2010, 120(2), 163-8.

The aim of this paper is to study homological properties of deficiently extremal Cohen-Macaulay algebras. Eagon-Reiner showed that the Stanley-Reisner ring of a simplicial complex has a linear resolution if and only if the Alexander dual of the simplicial complex is Cohen-Macaulay. An extension of a special case of Eagon-Reiner theorem is obtained for deficiently extremal Cohen-Macaulay Stanley-Reisner rings.

9 ref

014366   Cao T B;Xu H Y;Zhu C X (Mathematics Dep, Nanchang Univ, Nanchang 330031, China, Email: tbcao@ncu.edu.cn) : Complex oscillation of differential polynomials generated by meromorphic solutions of differential equations in the unit disc. Proc Indian Acad Sci-Mathl Sci 2010, 120(4), 481-93.

In this paper, we investigate the complex oscillation of differential polynomials generated by meromorphic solutions of differential equations f^(k) + A(z) f = 0, k ≥ 2, where the coefficient A is meromorphic in the unit disc D = {z: |z| <60> 1}.

28 ref

014365   Calderon Martin A J;Forero Piulestan M (Matematicas Dep, Universidad de Cadiz, 11510 Puerto Real, Cadiz, Spain, Email: ajesus.calderon@uca.es) : On split lie triple systems II. Proc Indian Acad Sci-Mathl Sci 2010, 120(2), 185-98.

In [4] it is studied that the structure of split Lie triple systems with a coherent 0-root space, that is, satisfying [T₀, T0, T] = 0 and [T₀, T_α, T0] ≠ 0 for any nonzero root a and where TO denotes the 0-root space and T_α the a-root space, by showing that any of such triple systems T with a symmetric root system is of the form T = U + Σ_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_j, T, I_k] = 0 if j ≠ k. It is also shown in [4] that under certain conditions, a split Lie triple system with a coherent 0-root space 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. In the present paper we extend these results to arbitrary split Lie triple systems with no restrictions on their 0-root spaces.

12 ref

014364   Buyukasik E;Demirci Y M (Mathematics Dep, Izmir Institute of Tehcnology, 35430, Urla, Izmir, Turkey, Email: enginbuyukasik@iyte.edu.tr) : Weakly distributive modules. applications to supplement submodules. Proc Indian Acad Sci-Mathl Sci 2010, 120(5), 525-34.

Authors define and study weakly distributive modules as a proper generalization of distributive modules. prove that, weakly distributive supplemented modules are amply supplemented. In a weakly distributive supplemented module every submodule has a unique coclosure. This generalizes a result of Ganesan and Vanaja. We prove that ;π-projective duo modules, in particular commutative rings, are weakly distributive. Using this result we obtain that in a commutative ring supplements are unique. This generalizes a result of Camillo and Lima. also prove that any weakly distributive ⊕-supplemented module is quasi-discrete.

11 ref

014363   Borah G;Hazarika G C (NO, Joya Gogoi College P.O. Khumtai, Dist.-Golaghat) : Effect of variable viscosity & thermal conductivity on steady laminr free convection flow of an electrically conducting fluid along a porous hot vertical plate in the presence of heat source/sink. Ultra Scient phys Sci 2010, 22(1), 183-90.

Steady Laminar free convection flow of an electrically conducting fluid along a porous hot vertical plate in the presence of heat source/sink under variable viscosity & thermal conductivity is' investigated. The problem is studied numerically, applying Runge -Kutta Shooting method. The velocity and temperature distribution are shown graphically. It is observed that the variable viscosity & thermal conductivity effects are significant on the problem.

4 illus, 9 ref

014362   Biswas I (Mathematics Dep, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400 005, Email: indranil@math.tifr.res.in) : Atiyah bundle and connections on a principal bundle. Proc Indian Acad Sci-Mathl Sci 2010, 120(3), 299-316.

Let M be a C^{∞ manifold and G a Lie a group. Let Eg be a C∞ principal G-bundle over M. There is a fiber bundle C(E_G) over M whose smooth sections correspond to the connections on E_G. The pull back of EG to C(E_G) has a tautological connection. We investigate the curvature of this tautological connection.}

5 ref

014361   Barman R;Baruah N D (Mathematical Sciences Dep, Tezpur Univ, Papaam-784 028, Email: rupamb@tezu.ernet.in) : Theta function identities associated with Ramanujan's modular equations of degree 15. Proc Indian Acad Sci-Mathl Sci 2010, 120(3), 267-84.

Presents alternative proofs of some of Ramanujan's theta function identities associated with the modular equations of composite degree 15. Along the way we also find some new theta-function identities. We also give simple proofs of his modular equations of degree 15.

7 ref

014360   Baishun Lai;Luo Q (Institute of Contemporary Mathematics, Henan Univ, Kaifeng 475004, People's Republic of China, Email: laibaishun@henu.edu.cn) : Uniqueness of singular solution of semilinear elliptic equation. Proc Indian Acad Sci-Mathl Sci 2010, 120(5), 583-91.

Study asymptotic behavior of solution near 0 for a class of elliptic problem. The uniqueness of singular solution is established.

11 ref

014359   Azad H;Biswas I (Mathematics and Statistics Dep, King Fahd Univ, Saudi Arabia, Email: hassanaz@kfupm.edu.sa) : A note on the tangent bundle of G/P. Proc Indian Acad Sci-Mathl Sci 2010, 120(1), 69-71.

Let P be a Parabolic subgroup Linnear algebraic group G. authour prove that the tangent bundle T (G/P) is stable.

6 ref

014358   Athreya K B;Athreya S R;Iyer S K (Mathematics and Statistics Dep, Iowa State Univ, Ames, Iowa 50011, USA, Email: kba@iastate.edu) : Critical age-dependent branching markov processes and their scaling limits. Proc Indian Acad Sci-Mathl Sci 2010, 120(3), 363-85.

This paper studies: (i) the long-time behaviour of the empirical distribution of age and normalized position of an age-dependent critical branching Markov process conditioned on non-extinction; and (ii) the super-process limit of a sequence of age-dependent critical branching Brownian motions.

17 ref

014357   Ashisha Kumar;Ray S K (Mathematics and Statistics Dep, Indian Institute of Technology Kanpur, Kanpur-208 016, Email: ashishak@iitk.ac.in) : Mixed norm estimate for radon transform on weighted L<. Proc Indian Acad Sci-Mathl Sci 2010, 120(4), 441-56.

Discusses about the mapping property of Radon transform on L^p spaces with power weight. It will be shown that the Pitt's inequality together with the weighted version of Hardy-Littlewood-Sobolev lemma imply weighted inequality for the Radon transform.

29 ref

014356   Alzer H (NO, , Morsbacher Str. 10, D-51545 Waldbrol, Cermany, Email: h.alzer@gmx.de) : Integral inequalities for self-reciprocal polynomials. Proc Indian Acad Sci-Mathl Sci 2010, 120(2), 131-7.

Let n ≥ 1 be an integer and let P_n be the class of polynomials P of degree at most n satisfying zⁿP(1/z) = P(z) for all z ∈ C. Moreover, let r be an integer with 1 ≤ r ≤ n. Then we have for all P ∈ P_n: α_n(r) ∫^2π₀ |P(e^it)|²dt ≤ ∫^2π₀ |P^(r)(e^it)|²dt ≤ β_n(r) ∫^2π₀ |P(e^it)|²dt with the best possible factors.

5 ref

014355   Alexandru V;Popescu N;Vajaitu M;Zaharescu A (Mathematics Dep, Bucharest Univ, Romania Institute of Mathematics of the Romaian Academ, P.O. Box 1-764, Bucharest 014700, Romania, Email: marian.vajaitu@imar.ro) : On the Iwasawa algebra associated to normal element of C_p. Proc Indian Acad Sci-Mathl Sci 2010, 120(1), 45-55.

Given a prime number p and the Galois orbit O (x) of a normal element x of C_p, the topological completion of the algebraic closure of the field of p-adic numbers, we study the Iwasawa algebra of O(x) with scalars drawn from Q_p and relate it with QP-distributions and functionals.

12 ref

014354   Alaeiyan M;Tavallaee H A;Onagh B N (Mathematics Dep, Iran Science and Technology Univ, Narmak, Tehran 16844, Iran, Email: alaeiyan@iust.ac.ir) : Semisymmetric cubic graphs of order 16P<. Proc Indian Acad Sci-Mathl Sci 2010, 120(1), 19-26.

An undirected graph without isolated vertices is said to be semisymmetric if its full automorphism group acts transitively on its edge set but not on its vertex set. In this paper, authors inquire the existence of connected semisymmetric cubic graphs of order 16 p². It is shown that for every odd prime p, there exists a semisymmetric cubic graph of order 16 p² and its structure is explicitly specified by giving the corresponding voltage rules generating the covering projections.

2 illus, 16 ref

014353   Akka D G;Waradn S (NO, , Nadgir institute of Engineering and Technology, H. H. 4. Jindal Nagar) : Super magic strength of a graph. Indian J pure appl Math 2010, 41(4), 557-68.

By G(p, q) we denote) a graph having p vertices and q edges, by V and E the vertex set and edge set of G respectively. A graph G(p, q) is said to have an edge magic labeling (valuation) with the constant (magic number) c(f) if there exists a one-to-one and onto function f : V ∪ E → {1,2, ...., p + q} such that f(u) + f(v) + f(uv) = c(f) for all uv ∈ E. An edge magic labeling f of G is called a super magic labeling if f(E) ={1, 2, ...., q}. The concepts of the super magic and super magic strength of a graph are introduced. The super magic strength (sms) of a graph G is defined as the minimum of all constants c' (f) where the minimum is taken over all super magic labeling of G and is denoted by sms(G). This minimum is defined only if the graph has at least one such super magic labeling. In this paper, the super magic strength of some well known graphs P_2n, P_2n+1, K_1,n, B_n,n, <60> K_1,n : 2 <62>, P_n² and (2n + 1) P₂, C_n and W_n are obtained, where P_n is a path on n vertices, K_1,n is a star graph on n + 1 vertices, n-bistar n_n,n is the graph obtained from two copies of K_1,n by joining the centres of two copies of K_1,n by an edge e, if e is subdivided then B_n,n becomes <60> K_1,n : 2 <62>, (2n + 1) P₂ is 2n + 1 disjoint copies of P₂, P_n² is a square graph of P_n. C_n is a cycle on n vertices and W_n = C_n + K₁ is wheel on n + 1 vertices.

10 illus, 6 ref

014352   Adhikari S D;Ambily A A;Sury B (Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad-211 019, Email: adhikari@mri.ernet.in) : Zero-sum problems with subgroup weights. Proc Indian Acad Sci-Mathl Sci 2010, 120(3), 259-66.

Generalized some theorems on zero-sums with weights from [1], [4] and [5] in two directions. In particular, we consider Z^d_p for a general d and subgroups of Z*_p as weights.

14 ref

013223   Singh K D;Rakesh Kumar (Mathematics Dep, HP Univ, Shimal-171 005) : Soret and Hall current effects on heat and mass transfer in MHD flow of a viscous fluid through porous medium with variable suction. Proc Indian Natn Sci Acad 2009, 75(3), 119-26.

An unsteady free convective flow through porous media of a viscous, incompressible, electrically conducting fluid past an infinite porous, non-conducting, vertical piate is analyzed. A strong uniform magnetic field is applied perpendicular to the plane of the plate which is subjected to a variable suction velocity. It is assumed that the free stream, plate temperature, species concentration oscillates about a non-zero mean and the concentration level of the diffusing species is small compared with other concentrations. Taking Hall current into account, equations of motion, energy and concentration are solved by perturbation technique. The effects of the various parameters, entering into the problem, on the primary and secondary velocity are shown graphically while the skin friction coefficient, Nusselt number and Sherwood number obtained in terms of amplitudes and phase angles are listed in tabular form and discussed.

3 tables, 18 ref

013222   Singh K D;Mathew A (Mathematics Dep, ICDEOL, Himachal Pradesh Univ, Summer Hill, Shimla-171 005, Email: kdsinghshimla@gmail.com) : Heat transfer in three dimensional MHD flow between two parallel porous plates moving in oposite directions with transpiration cooling. Proc Natn Acad Sci India-Sect A 2009, 79(PtIII), 291-302.

The laminar flow of an electrically conducting viscous incompressible fluid flow between two infinite parallel porous plates moving in opposite directions is presented in the presence of viscous dissipative heat. The upper porous plate moving in the positive direction of χ'-axis is subjected to a transverse sinusoidal suction velocity whereas the lower porous plate is subjected to a constant injection velocity. The flow becomes three-dimensional due to this type of suction velocity. The mathematical analysis is presented for the hydromagnetic field. The results are obtained for velocity, temperature, Nusselt number and skin friction. The effects of different parameters like Reynolds number (Re), Prandtl number (Pr), Eckert number (Ec), Hartmann number (M), suction parameter (λ) and the pressure parameter (G) have been shown graphically and discussed in detail.

8 illus, 6 ref

013221   Patel B P;Ibrahim S M;Nath Y (Applied Mechanics Dep, Indian Institute of Technology, Delhi Hauz Khas, New Delhi-110 016) : Periodic response of nonlinear dynamical system with large number of degrees of freedom. Sadhana 2009, 34(6), 1033-7.

In this paper, a methodology based on shooting technique and New-mark's time integration scheme is proposed for predicting the periodic responses of nonlinear systems directly from solution of second order equations of motion without transforming to double first order equations. The proposed methodology is quite suitable for systems with large number of degrees of freedom such as the banded system of equations from finite element discretization.

1 illus, 10 ref

013220   Malik S C;Barak M S (Statistics Dep, M.D. Univ, Rohtak-124 001, Email: sc_malik@rediffmail.com) : Reliability and economic analysis of a system operating under different weather conditions. Proc Natn Acad Sci India-Sect A 2009, 79(PtII), 205-13.

This paper considers a single-unit system operating under two weather conditions : normal and abnormal. Two reliability models are developed in which unit may fail completely either directly from normal mode or via partial failure. The unit is inspected to examine the feasibility of its repair at complete and partial failure in models 1 and 2 respectively. If repair of the unit is not feasible, it is replaced by new one. However, repair of the unit at its partial and complete failure is done without inspection in models 1 and 2 respectively. The operation, inspection and repair of the unit are stopped in abnormal weather. The distributions of failure time and change of weather conditions follow negative exponential while that of inspection and repair times are taken as arbitrary with different probability density function (pdf). All random variables are mutually independent and uncorrelated. Expressions for reliability and economic measures of system effectiveness are derived by using semi-Markov process and regenerative point technique. Numerical results are also obtained for a particular case.

4 illus, 1 table, 6 ref

013219   Konwar J (Mathematics Dep, Manohari Devi Kanoi Girls College, Dibrugarh-786 001, Email: konwar_i@yahoo.co.in) : A mathematical model for HIV infections in Assam. Bull Life Sci 2009, 15(Mar), 17-24.

The infection of HIV (Human Immunodeficiency Virus) is a global threat to human health. AIDS (Acquired Immune Deficiency Syndrome) is the consequence of the infection of this deadly virus. Mathematical models can serve as tools for understanding the epidemiology of HI V and AIDS if they are constructed carefully. They may be very important and helpful to the clinicians and policy makers in taking decision for the most effective course of action at the time of confrontation with the problems associated with HIV or AIDS. But research oriented works in this area are very limited till now. In this paper, a mathematical model regarding the transmission of HIV in Assam is proposed. This model is based on Linear Programming Problem (LPP) and here, five major routes of transmission namely sexual, injectable drug user, blood and blood product, perinatal and others of HIV/AIDS are considered. For easy understanding of the model a simple example considering only three routes of transmission and three districts of Assam is also added here.

3 tables, 10 ref

013218   Khare B B;Kumar S (Statistics Dep, Faculty of Science, Banaras Hindu University, Vsaranasi-221 005, Email: bbkhare56@yahoo.com) : Utilization of coefficient of variation in the estimation of population mean using auxiliary character in the presence of non-response. Natn Acad Sci Lett 2009, 32(7-8), 235-42.

The ratio, product and regression type estimators of population mean in the presence of non-response using coefficient of variation of the study character are found to be more efficient than the relevant estimators.

^ssc2 tables, 18 ref