016964   Liang Z (School of Economic Mathematics, Southwestern Finance and Economics Univ, Chengdu-611 130, China, Email: zhilei0592@gmail.com) : Critical exponents for the evolution p-laplacian equation with a localized reaction. Indian J pure appl Math 2012, 43(5), 535-58.

This paper deals with the large time behavior of nonnegative solutions to the equation u_t = div(|∇_u|^p-2 ∇_u)+a(x)u^q, (x.,t) ∈ R^N x (0,T), where p <62> 2, q <62> 0, and the function a(x) ≥ 0 has a compact support. And obtain the critical exponent for global existence q₀ and the Fujita exponent q_c. In one-dimensional case N = 1, authors have q₀ = [2(p-1)/p and q_c = 2(p-1). Particularly, all solutions are global in time if 0 <60> q ≤ q₀, but blow up if q₀ <60> q ≤ q_c; while if q <62> q_c both blowing up solutions and global solutions exist. However, for the case N ≥ p <62> 2, these two critical exponents are exactly the same. Namely, q₀ = p - 1 = q_c.

19 ref

016963   Lakshmi S;Tamilselvi G (Mathematics Dep, K.N. Govt. Arts College for Women, Thanjavur) : Degradation-threshold-shock models in mathematics for the origin of HPA axis dysfunction in psychiatric patients. Int J mathl Sci 2012, 11(1-2), 55-60.

There are general classes of Mathematical & Stochastic models in reliability and survival analysis for degradation and failure data of subjects operating in a dynamic environment. The degradation process represents the deterioration of markers of health status and quality of life data in medical settings. A part of a body is regarded as failed when degradation first crosses a critical threshold level or when a censoring traumatic event occurs and may be recouped in negligible time upon each failure and possibly preventively at regular inspection times. For example, in medical settings the degree of HPA axis dysfunction predicts both sleep disturbance and the persistence of the HPA axis dysregulation. These findings provide support for the hypothesis that HPA axis dysfunction is central to the pathophysilogy of major depressive disorder and that it is important therapeutic target.

1 illus, 8 ref

016962   Lakshmi S;Saiva Raju N;Kavitha N (Mathematics Dep, K.N. Govt. Arts College for Women, Thanjavur) : Mathematical model for inhaled corticosteroid during long-term treatment in asthmatic children. Int J mathl Sci 2012, 11(1-2), 113-19.

In this paper, a shock model for the effect of stress in terms of corticosteroid is studied. Assume that shocks arrive according to a Poisson Process. For a deteriorating stress authors assume that the successive threshold value and geometrically non-decreasing after giving the dosage of methacholine and the consecutive recoup times after inhalant allergen. From an increasing geometric process to improve inhalation they assume that the successive threshold values are geometrically decreasing after suppression by dosage of methacholine. A change of dosage in Nth shock is adopted by which we shall change the dosage of methacoline by an identical new one (for example FEV1 and sECP) at the time following the Nth failure.

6 illus, 10 ref

016961   Lakshmi S;Karthik R (NO, K.N. Govt. Arts College for Women, Thanjavur, Tamilnadu, Email: lakshmi291082@yahoo.co.in ) : Mathematical model of four secretion hormones in healthy male subjects. Int J appl mathl Analysis Applic 2012, 7(1), 17-31.

Authors study the effects of acute oral administration of the selective noradrena- line reuptake inhibitor reboxetine on the cortisol (COR), ACTH, gonadotropin release hormone (GnRH) and prolactin (PRL) secretion were examined in 12 healthy male volunteers. In a randomized order, the subjects received placebo or reboxetine (4 mg) at 0800 h on two different days. After insertion of an intravenous catheter, blood samples were drawn 1 hour prior to the adminis- tration of placebo or reboxetine, at time of administration, and during the time of 5 hours thereafter at periods of 30 minutes. Serum concentrations of COR, GnRH, and PRL as well as plasma levels of ACTH were determined in each blood sample by means of double antibody RIA, uoroimmunoassay and chemiluminescence immunometric assay methods. The area under the curve value (AUC) was used as parameter for the COR, ACTH, GnRH, and PRL response. We proposed mathematical model to statistical analysis revealed significant stimulatory effects of reboxetine on COR, ACTH, GnRH, and PRL secretion compared to placebo. The results suggest that besides COR, ACTH and GnRH secretion, the release of PRL is also under the control of the noradrenergic systems in man. The mathematical model is to find out the results and is well discussed in section 5 of this paper.

3 illus, 9 ref

016960   Lakshmi S;Christy Raj I (Mathematics Dep, Kundavai Nachiaar Govt. Arts College for Women, Thanjavur, Tamilnadu, Email: lakshmi291082@yahoo.co.in) : Three parameter weibull probablity distribution model for acute activation of NHE3 dexamethasone with SGK1 and requires a functional glucocorticoid receptor. Int J appl mathl Analysis Applic 2012, 7(1), 33-8.

Weibull probability distribution has numerous applications in various areas such as life expectancy, survival analysis and animal bioassay. Successful application of the Weibull distribution depends on having acceptable statistical estimates of the three parameters. We examined a changes of the three parameters mRNA, activity and protein in SGK1 and NHE3 induced by Glucocorticoids using human cells. We found that dexamethasone rapidly stimulates the variables. This application part is fitted to the three parameter Weibull distribution and concludes that the overall sample data fits well with our distribution due to the changes of the three parameters mRNA, activity and protein.

2 illus, 12 ref

016959   Krishna M (NO, Institute of Mathematical Sciences, Taramani, Chennai-600 113, Email: krishna@imsc.res.in) : Absolutely continuous spectrum and spectral transition for some continuous random operators. Proc Indian Acad Sci-Mathl Sci 2012, 122(2), 243-55.

In this paper, author consider two classes of random Hamiltonians on L² (R^d): one that imitates the lattice case and the other a Schrodinger operator with non-decaying, non-sparse potential both of which exhibit a.c. spectrum. In the former case we also know the existence of dense pure point spectrum for some disorder thus exhibiting spectral transition valid for the Bethe lattice and expected for the Anderson model in higher dimension.

26 ref

016958   Kranz R;Lenski W;Szal B (Zielona Gora Univ, Faculty of Mathematics, Computer Science and Econometrics, 65-516 Zielona Gora, ul. Szafrana 4a, Poland, Email: R.Kranz@wmie.uz.gora.pl) : Approximation of functions from L<. Indian J pure appl Math 2012, 43(5), 475-94.

Formulates some special conditions for the integrable functions and moduli of continuity. Authors give the results on rate of approximation of such functions by matrix means of their Fourier series, where the entries of the rows of the matrix generate the sequences belonging to the classes MRBVS and MHBVS. Also present some results on norm approximation for functions from the generalized integral Lipschitz classes.

10 ref

016957   Kitada H (Graduate School of Mathematical Sciences, Tokyo Univ, Komaba, Meguro, Tokyo 153-8914, Japan) : Timeless system, superluminal phenomena, Dark matter and big bang. Int J mathl Sci 2012, 11(1-2), 141-51.

With the notion of flavor-oscillation clock of Ahluwalia et. al. or the notion of local time introduced by the author, authors will consider a quantum mechanical local system that forms a bound state with respect to the local Hamiltonian of the system. They will see that such a local system is considered timeless and hence the principles of relativity do not apply to those timeless systems. As application and will suggest a possibility of the faster-than-light phenomena and a possible explanatroh of dark matter and Big Bang phenomenon consistent with the theory of relativity and the conservation law of matter.

15 ref

016956   Kirubaharan D R;Nirmala G (NO, Monomaniam Sundaranar Univ, Thirunelveli, Tamil Nadu, Email: jagkans@yahoo.com) : MFICN algorithm for transport graph from NDA to SRJ. Int Rev pure appl Math 2012, 8(2), 87-92.

In all scientific disciplines, researchers are always making trade-off between the generality and the specificity of their results. As the algorithms MFICN/S/D become narrower, available results often become refined and more powerful, algorithms for shortest path and maximum problems have very attractive worst-case and empirical behavior. This algorithm grows rather slowly in the number of underlying constraints and decision variables.

2 illus, 1 table, 19 ref

016955   Khedekar A S;Rajan C S (School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400 005, Email: arati@math.tifr.res.in) : On cohomology theory for topological groups. Proc Indian Acad Sci-Mathl Sci 2012, 122(2), 221-42.

Author Constructed some new cohomology theories for topological groups and Lie groups and study some of its basic properties. For example, Author introduce a coho- mology theory based on measurable cochains which are continuous in a neighbourhood of the identity. Author show that if G and A are locally compact and second countable, then the second cohomology group based on locally continuous measurable cochains as above parametrizes the collection of locally split extensions of G by A.

21 ref

016954   Khan S A (Engineering Dep, Salalah College of Technology, Post Box No. 608, Postal Code 211, Salalah, Sultanate of Oman, Email: rohelakhan@yahoo.com) : Farey sequences and resistor neworks. Proc Indian Acad Sci-Mathl Sci 2012, 122(2), 153-62.

In this article, author employ the Farey sequence and Fibonacci numbers to establish strict upper and lower bounds for the order of the set of equivalent resistances for a circuit constructed from n equal resistors combined in series and in parallel. The method is applicable for networks involving bridge and non-planar circuits.

24 ref

016953   Khan H (NO, Jagannant International MGMT School, Vasant Kunj, New Delhi-110 070) : Some fundamental operations on fuzzy set theory. Int J mathl Sci 2012, 11(1-2), 161-6.

Work in this paper is on the applications of fuzzy set theory operations introduced by Zadeh in 1965.

4 illus, 15 ref

016952   Kaya C (Mathematics Dep, Cankiri Karatekin Univ, 67149 Cankuri, Turkey, Email: celalettinkaya@gmail.com) : On lifting singular curves. Indian J pure appl Math 2012, 43(5), 423-8.

Aim of this note is to lift singular curves of a certain type to characteristic zero. The liftings are obtained as suitable pushouts and the corresponding relative jacobians are identified as rigidifed Picard functors.

8 ref

016951   Kaushal N;Tiwari M;Parihar C L (Mathematics Dep, Indore Institute of Science and Technology, Indore, Email: nams0053@gmail.com) : Lattice fixed point theorem with antimorphisms. Int J appl mathl Analysis Applic 2012, 7(1), 63-5.

Presents a short and constructive proof of a lattice fixed-point theorem having application in theory of games with strategic complementarities.

7 ref

016950   Kamalakar P V S;Rao D R V P;Rao R R (Mathematics Dep, S.B.I.T., Khammam, Andhra Pradesh) : Finite element analysis of chemical reaction effect on non-darcy convective heat and mass transfer flow through a porous medium in vertical channel with heat sources. Int J appl mathl Analysis Applic 2012, 7(1), 97-116.

Attempted to study thermo-diffusion effect on non-Darcy convective the and Mass transfer flow of a viscous fluid through a porous medium in a vertical channel with heat generating sources. The governing equations flow, heat and mass transfer are solved by using Galerkin finite element technique with quadratic polynomial approximations. The approximation solution is written directly as a linear combination of approximation functions with unknown nodal values as coefficients. Secondly, the approximation polynomials are chosen exclusively from the lower order piecewise polynomials restricted to contiguous elements. The velocity, temperature, concentration, shear stress and rate of Heat and Mass transfer are evaluated numerically for different variations of parameter.

12 illus, 12 tables, 15 ref

016949   Jain R;Jain D K;Ahmad F (School of Mathematics and Applied Sciences, Jiwaji Univ, Gwalior-475 011, Email: renujain3@rediffmail.com) : Basic hypergeometric transformation relating gauss, appell and srivastava-daoust functions. Int J appl mathl Analysis Applic 2012, 7(1), 67-75.

Obtained a basic integral formula for Appell's double basic Hypergeometric function Φ by making use of Laplace-type double integral technique. Also obtain Basic hypergeometric transformation formulas involving Appell's and Srivastava-Doaust functions.

7 ref

016948   Iyengar T K V;Vani V G (Mathematics Dep, National Institute of Technologym, Warangal-506 004, Email: iyengar_nitw@yahoo.co.in) : Flow of an imcompressible micropolar fluid in the region between two slowly rotating confocal oblate spheroids. Int Rev pure appl Math 2012, 8(2), 93-119.

In this paper we study the steady flow of an incompressible micropolar fluid in the region between two confocal oblate spheroids, which are slowly rotating with different angular speeds about their common axis of symmetry. The toroidal velocity component and the microrotation components are determined in terms of Legendre, associated Legendre and spheroidal wave functions in infinite series form. The couple on the inner and outer spheroids is found and is numerically evaluated for diverse values of geometric parameter and material parameters of the fluid. The variation of the couple is displayed through graphs.

10 illus, 11 ref

016947   Gururaja H A (Mathematics Dep, St. Aloysius College, Mangalore-575 003, Email: gururaj.upadhya@gmail.com) : Ricci flow warped product metrics with positive isotropic curvature on S<. Proc Indian Acad Sci-Mathl Sci 2012, 122(4), 597-614.

Study the asymptotic behaviour of the ODE associated to the evolution of curvature operator in the Ricci flow of a doubly warped product metric on S^p+1 x S¹ with positive isotropic curvature.

11 ref

016946   Guo X (Mathematics Dep, Southwestern Finance and Economics Univ, Chengdu-611 130, People's Republic of China, Email: guoxunxiang@yahoo.com) : Multi-frame vectors for unitary systems. Indian J pure appl Math 2012, 43(4), 391-409.

The set of all complete multi-normalized tight frame vectors N F^T(U) with multiplicity r and the set of all complete multi-frame vectors F^T(U) with multiplicity r for a system U of unitary operators acting on a separable Hilbert space are characterized in terms of co-isometries and surjective operators in C_Ψr(U), the set of all operators which locally commute with U at Ψ^r, a fixed complete wandering r-tuple for U. Then author study the linear combinations of multi-frame vectors for U and establish some conditions under which these combinations are still the same type of multi-frame vectors for U. Finally, author established some interesting properties for multi-frame veer-tors when U is a unitary group. All these results have potential applications in the theory of multi-Gabor systems and multi-wavelet systems.

20 ref

016945   Fattahi A;Javanshiri H (Mathematics Dep, Razi Univ, Kermanshah, Iran, Email: hjavanshirigh@yahoo.com) : Discretization of continuous frame. Proc Indian Acad Sci-Mathl Sci 2012, 122(2), 189-202.

In this paper author consider the notion of continuous frame of subspaces and define a new concept of continuous frame, entitled continuous atomic resolution of identity, for arbitrary Hilbert space H which has a countable reconstruction formula. Among the other results, we characterize the relationship between this new concept and other known continuous frames. Finally, we state and prove the assertions of the stability of perturbation in this concept.

9 ref

016944   Edalatpanah S A;Shahabi S (Applied Mathematics Dep, Tonekabon Branch, Islamic Azad Univ, Tonekabon, Iran, Email: saedalatpanah@gmail.com) : New two-phase method for solving the fuzzy primal simplex algorithm. Int Rev pure appl Math 2012, 8(2), 157-64.

Recently, Nasseri et at., [1, 2] proposed fuzzy two-phase method involving fuzzy artificial variables and fuzzy big-M method to obtain an initial fuzzy basic feasible solution to solve the linear programming with fuzzy variables (FVLP) problems. In this paper, authors propose a new two-phase method for solving fuzzy linear programming. Our method needs not any artificial variables and has an advantage of the simple implementation. Furthermore this method is more effective and faster than above methods.

17 ref

016943   Dhorajia A M (Mathematics Dep, IIT Mumbai, Mumbai-400 076, Email: alpesh@math.iitb.ac.in) : Symplectic modules over overrings of polynomial rings. Indian J pure appl Math 2012, 43(4), 371-90.

Let B be a commutative Noetherian ring of dimension d and let S be a set of all manic polynomials in B[X]. Let A be a subring of S^-1 B[X] which contains B[X]. Let P be a symplectic A-module of rank 2n ≥ d, n <62> 0. Then author proved that ESp(A² ⊥ P, (,)) acts transitively on Um (A² ⊕ P).

11 ref

016942   Deshmukh S (Mathematics Dep, College of Science, King Saud Univ, P.B. No. 2455, Riyadh 11451, Saudi Arabia, Email: shariefd@ksu.edu.sa) : Real hypersurfaces of a complex space form. Proc Indian Acad Sci-Mathl Sci 2012, 122(4), 629-34.

Author are interested in obtaining a condition under which a compact real hypersurface of a complex projective space CPⁿ is a geodesic sphere. Author, also g study the question as to whether the characteristic vector field of a real hypersurface of the complex projective space CPⁿ is harmonic, and show that the answer is in negative.

17 ref

016941   Das P K;Behera A (School of Applied Science (Math), KIIT Univ, Bhubaneswar-24, Orissa, Email: dasprasantkumar@yahoo.co.in) : (T,x)-η-invex function and x*-GDDVIP in H-differentiable manifolds and riemannian n-manifolds. Int J mathl Sci 2012, 11(1-2), 61-102.

Concepts of η-Lipschitz function of order α and η-uniformly Lipschitz function of order p are introduced and the order of a quasidomonotone and potential operator is studied. The subadditive and supersubtractive functions with respect to- the second component, weakly subadditive and weakly supersubtractive function, weakly bilinear function with respect to the second component associated with a functional are also introduced. Using weakly subadditive and weakly supersubtractive functions the existence theorems of the weakly bilinear function under addition and subtraction are proved. x* -generalized variational inequality problem in Sⁿ is established and the existence theorem is studied using the weakly bilinear function. Also x -generalized variational inequality problem and x*-generalized complementarity problem are established. The existence theorems of these problems are studied in H/-differentiable manifolds. The concept of T-η-invex function of second kind, i.e., (T, x*)-η-invex function in H-differentiable manifolds is introduced. The x* -generalized differential dominated variational inequality problem and x* -generalized differential dominated complementarity problem in H-differentiablc manifolds are established. Relation theorem between (T. x*)-η-invex function and x*-generalized differential dominated variational inequality problem is established. Some existence theorems of x* -generalized differential dominated variational inequality problems and x*-generalized differential dominated complementarity problems in Riemannian n-manifolds in the presence of fixed point inclusion are proved.

28 ref

016940   Cui H (Basic Dep, Guangdong Pharmaceutical Univ, Guangzhou-510 006, People's Republic of China) : The asymptotic behavior of solutions of an initial boundary value problem for the generalized Benjamin-Bona-Mahony equation. Indian J pure appl Math 2012, 43(4), 323-42.

The asymptotic behaviors of solutions of an initial-boundary value problem for the generalized BBM equation with non-convex flux are discussed. It is proved that under the conditions of constant boundary data and small perturbation for the initial data, the global solutions exist and converge time-asymptotically to a stationary wave or the superposition of a stationary wave and a rarefaction wave. The proof is given by a technical L^-2-weighted energy method.

30 ref

016939   Crasmareanu M (Faculty of Mathematics, "Al. l.Cuza" Univ, Iasi-700 506, Romania, Email: mcrasm@uaic.ro) : Parallel tensors and Ricci solutions in N(k)-quasi Einstein manifolds. Indian J pure appl Math 2012, 43(4), 359-69.

The Eisenhart problem of finding parallel and symmetric tensors is considered in the framework of N (k)-quasi Einstein manifolds and the result is connected with Ricci solitons. If the generator of the manifold provides a Ricci soliton then this is: i) shrinking on a class of conformally flat perfect fluid space-times and on quasi-umbilical hypersurfaces, in particular unit spheres; ii) expanding if the generator is of torse-forming type.

23 ref

016938   Chen S H;Ponnusamy S;Wang X (Mathematics Dep, Hunan Normal Univ, Changsha, Hunan-410 081, People's Republic of China, Email: sclchen1982@yahoo.com.cn) : Equivalent moduli of continuity, Bloch's theorem for pluriharmonic mappings in B<. Proc Indian Acad Sci-Mathl Sci 2012, 122(4), 583-95.

Author first establish a Schwarz-Pick type theorem for plurihar-monic mappings and then author apply it to discuss the equivalent norms on Lipschitz-type spaces. Finally, waobtain several Landau's and Bloch's type theorems for plurihar-monic mappings.

26 ref

016937   Chen H (Mathematics Dep, School of Science, Nanchang Univ, Nanchang-330 031, Email: chb_00721@126.com) : Asymptotic behavior of stochastic two-dimensional navier-stokes equations with delays. Proc Indian Acad Sci-Mathl Sci 2012, 122(2), 283-95.

Paper proves the L²-exponential stability of weak solutions of two-dimensional stochastic Navier-Stokes equations in the presence of delays. The results extend some of the existing results.

14 ref

016936   Chadwick E;El-Mazuzi R (School of Computing Science and Engineering, Salford Univ, Salford M5 4WT, UK, Email: e.a.chadwick@salford.ac.uk) : Coupled far-field formulation for time-periodic numerical problems in fluid dynamics. Proc Indian Acad Sci-Mathl Sci 2012, 122(4), 661-72.

Consider uniform flow past an oscillating body generating a time-periodic motion in an exterior domain, modelled by a numerical fluid dynamics solver in the near field around the body. A far-field formulation, based on the Oseen equations, is presented for coupling onto this domain thereby enabling the whole space to be modelled. In particular, examples for formulations by boundary elements and infinite elements are described.

3 illus, 28 ref

016935   Basu M;Kodiyalam V;Sunder V S (The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai-600 113, Email: madhushree@imsc.res.in) : From graphs to free products. Proc Indian Acad Sci-Mathl Sci 2012, 122(4), 547-60.

Investigate a construction (from Kodiyalam Vijay and Sunder V S, J. Fund. Anal. 260 (2011) 2635-2673) which associates a finite von Neumann algebra M(Γ μ) to a finite weighted graph (Γ, μ). Pleasantly, but not surprisingly, the von Neumann algebra associated to a 'flower with n petals' is the group on Neumann algebra of the free group on n generators. In general, the algebra M(Γ, μ) is a free product, with amalgamation over a finite-dimensional abelian subalgebra corresponding to the vertex set, of algebras associated to subgraphs 'with one edge' (or actually a pair of dual edges). This also yields 'natural' examples of (i) a Fock-type model of an operator with a free Poisson distribution; and (ii) C ⊕ C-valued circular and semi-circular operators.

1 illus, 11 ref

016934   Baruah N D;Bora J;Ojah K K (Mathematical Sciences Dep, Tezpur Univ, Napaam-784 028, Email: nayan@tezu.ernet.in) : Ramanujan's modular equations of degree 5. Proc Indian Acad Sci-Mathl Sci 2012, 122(4), 485-506.

Provided alternative derivations of theta function identities associated with modular equations of degree 5. Authors then use the identities to derive the corresponding modular equations.

21 ref

016933   Barakat H M;El-Adll M E (Mathematics Dep, Faculty of Science, Zagazig Univ, Zagazig, Egypt, Email: hbarakat2@hotmail.com) : On the limit distribution of lower extreme generalized order statistics. Proc Indian Acad Sci-Mathl Sci 2012, 122(2), 297-311.

In a wide subclass of generalized order statistics (gOs), which contains most of the known and important models of ordered random variables, weak convergence of lower extremes are developed. A recent result of extreme value theory of m-gOs (as well as the classical extreme value theory of ordinary order statistics) yields three types of limit distributions that are possible in case of linear normalization. In this paper a similar classification of limit distributions holds for extreme gOs, where the parameters γ_j, j = 1, ..., n, are assumed to be pairwise different. Two illustrative examples are given to demonstrate the practical importance for some of the obtained results.

13 ref

016932   Bahadur S (Mathematics & Astronomy Dep, Lucknow Univ, Lucknow-226 007, Email: swarnimabahadur@ymail.com) : (0;0,2)-interpolation on the unit circle. Int J mathl Sci 2012, 11(1-2), 103-11.

In this paper, study the explicit representation and convergence of Pal-type weighted (0; 0, 2)-interpolation on the unit circle on two pairwise disjoint sets of nodes obtained by projecting vertically the zeros of (1 - x²)P_n(x) and P'_n(x) respectively on the unit circle, where P_n (x) stands for nth Legendre polynomial.

15 ref

016931   Baghani O;Gachpazan M;Baghani H (Applied Mathematics Dep, Faculty of Mathematical Sciences, Ferdowsi Mashhad Univ, Iran, Email: omid.baghani@gmail.com) : Existence, uniqueness and stability of solutions for a class of nonlinear integral equations under generalized lipschitz condition. Indian J pure appl Math 2012, 43(4), 309-21.

Authors proved the existence, uniqueness and the stability of solutions for some nonlinear functional-integral equations by using generalized Lips-chitz condition. Authors proved a fixed point theorem to obtain the mentioned aims in Banach space X :- C([a.b], R). As-application authors study some Volterra integral equations with linear, nonlinear and singular kernel.

19 ref

016930   Azhari M E (Ecole Normale Superieure, Avenue Oued Akreuch, Takaddoum, BP 5118, Robat, Morocco, Email: mohammed.elazhari@yahoo.fr) : Real seminorm with square property is submultiplicative. Indian J pure appl Math 2012, 43(4), 303-7.

A seminorm with square property on a real associative algebra is submulti-plicative.

7 ref

016929   Arunkumar M;Vijayanandhraj G;Vijayalakshmi C (Mathematics Dep, Government Arts College, Tiruvannamalai-606 603, Email: annarun2002@yahoo.co.in) : Stability of a recuiprocal functional equation in menger probabilistic normed spaces. Int Rev pure appl Math 2012, 8(2), 71-8.

In this paper, the authors has established the generalized Ulam-Hyers stability of a Reciprocal functional equation f(2y) = f(y+z)f(y-z)/[f(y+z) + f(y-z)] in Menger Probabilistic Normed Space.

24 ref

016928   Arumugam S;Bagga J;Chandrasekar K R (National Centre for Advanced Research in Discrete Mathematics (n-CARD, Kalasalingam Univ, Anand Nagar, Krishnankoli-626 126, Email: s.arumugam.klu@gmail.com) : On dominator colorings in graphs. Proc Indian Acad Sci-Mathl Sci 2012, 122(4), 561-71.

Dominator coloring of a graph G is a proper coloring of G in which every vertex dominates every vertex of at least one color class. The minimum number of colors required for a dominator coloring of G is called the dominator chromatic number of G and is denoted by χ_d(G). In this paper we present several results on graphs with χ_d(G) = χ(G) and χ_d(G) = γ(G) where χ(G) and γ(G) denote respectively the chromatic number and the domination number of a graph G. Also prove that if μ(G) is the Mycielskian of G, then χ_d(G) + 1 ≤ χ_d(μ(G)) ≤ χ_d(G) + 2.

2 illus, 19 ref

016927   Anuradha S;Sumathi K (Mathematics Dep, Huindusthan College of Arts & Science, Coimbatore-641 002, Email: anu.prasanthi@gmail.com) : Effect of hall current on MHD flow and heat transfer along a porous plate with temperature varying cosinusoidally with time. Int J appl mathl Analysis Applic 2012, 7(1), 83-95.

Unsteady free convective flow of a viscous incompressible and electrically conducting fluid along an infinite vertical porous plate is investigated with Hall current. The flow is oriented vertically upward along the x*-axis. The entire system is assumed to be rotating with angular velocity Ω* about z*-axis. The fluid is injected with the constant velocity w₀l through the porous plate. The Species Concentration at the plate and temperature of the plate are assumed to be varying cosinusoidally with time. In order to attain a physical insight into the problem, primary velocity field, Secondary velocity field, temperature field, concentration field, rate of heat and mass transfer are calculated numerically for different non-dimensional numbers.

17 illus, ref

016926   Anastassiou G A;Mezei R A (Mathematical Sciences Dep, The Memphis Univ, Memphis, TN-38152, U.S.A, Email: ganastss@memphis.edu) : L_p convergence with rates of smooth poisson-cauchy type singular operators. Int J mathl Sci 2012, 11(1-2), 1-26.

In this article authors continue the study of smooth Poisson-Cauchy Type singular integral operators on the line regarding their convergence to the unit operator with rates in the L_p norm, p ≥ 1. The related established inequalities involve the higher order L_p modulus of smoothness of the engaged function or its higher order derivative.

16 ref

016925   Alaeiyan M;Razzaghmaneshi B (Mathematics Dep, Islamic Azad Karaj Branch Univ, Karaj, Iran, Email: alaeiyan@iust.ac.ir ) : Permutation groups with bounded movement having maximum orbits. Proc Indian Acad Sci-Mathl Sci 2012, 122(2), 175-9.

Let G be a permutation group on a set Ω with no fixed points in Ω and let m be a positive integer. If no element of G moves any subset of Ω by more than m points (that is, |Γ^gΓ| ≤ m for every Γ ⊆ Ω and g Ξ G), and also if each G-orbit has size greater than 2, then the number t of G-orbits in Ω is at most 1/2 (3m - 1). Moreover, the equality holds if and only if G is an elementary abelian 3-group.

5 ref

016924   Aithal V T;Kulkarni R S (UM-DAE Centre for Excellence in Basic Sciences, Mumbai-Kalina Campus Univ, Santacruz (E), Mumbai-400 098, Email: vikram@cbs.ac.in) : On existence of invariant measures. Indian J pure appl Math 2012, 43(4), 343-58.

Let G be a Lie group, H ≤ G a closed subgroup and M ≈ G/H. Andre Weil gave a necessary and sufficient condition for the existence of invariant measures on homogeneous spaces of arbitrary locally compact groups. For Lie groups using the structure theory author a neater necessary and sufficient condition for the existence of a G-invariant measure on M.

15 ref

016923   Aithal A R;Raut R (Mathematics Dep, Mumbai Univ, Vidyanagari, Mumbai-400 098, Email: aithal86@gmail.com) : On the extrema of Dirichlet's first eigenvalue of a family of punctured regular polygons in two dimensional space forms. Proc Indian Acad Sci-Mathl Sci 2012, 122(2), 257-81.

Let ℘₁, ℘₀ be two regular polygons of n sides in a space form M² (K) of constant curvature K = 0, 1 or - 1 such that ℘₀ ⊂ ℘₁i and having the same center of mass. Suppose ℘₀ is circumscribed by a circle C contained in ℘₁. Author fix ℘₁ and vary ℘₀ by rotating it in C about its center of mass. Put Ω = (℘₁℘_{0>D>)⁰, the interior of ℘1℘0 in M²(k). It is shown that the first Dirichlet's eigenvalue λ1 (Ω) attains extremum when the axes of symmetry of ℘0 coincide with those of ℘1.}

13 ref

016922   Abhyankar S;Heizner W (Mathematics Dep, Purdue Univ, West Lafayette, IN 47907, USA, Email: ram@cs.purdue.edu) : Rees valuations. Proc Indian Acad Sci-Mathl Sci 2012, 122(4), 525-46.

Study dicritical divisors and Rees valuations.

27 ref

016019   Zhong-Xue L;Liu Z;Yao C (School of Mathematical Science, Xuzhou Normal Univ, Xuzhou-221 116, Peoples' Republic of China, Email: lvzx1@tom.com) : L<. Indian J pure appl Math 2012, 43(1), 49-70.

Author considered the blow-up solutions of Cauchy problem for two-coupled nonlinear Schrodinger equations with harmonic potential. Establish the lower bound of blow-up rale. Furthermore, the L² concentration for radially symmetric blow-up solutions is obtained.

36 ref