016012   Srivastava A;Arora P (Mathematics Dep, D.S.B. Campus, Kumaun Univ, Nainital, Email: asriv_123@rediffmail.com) : Randers change of m<. Indian J pure appl Math 2012, 43(1), 37-48.

Deals with a Randers metric that has been derived after a particular β-change in the mth root metric. Various geometers such as [71, [9], [10] etc. have studied the mth root metric and its transformations. Obtained some tensors and theorems holding the relation between the Finsler space equipped with the mth root metric and the one obtained after its Randers change.

10 ref

016011   Sophia Porchelvi R;Vasanthi L;Irene Hepzibah R (Mathematics Dep, A.D.M. College for Women, Nagapattinam-611 001, Email: sophiaporchelvi@gmail.com) : On solving a multiobjective linear programming problem using modified arithmetic. Int Rev Fuzzy Math 2012, 7(1), 21-5.

An iterative goal programming approach for solving fuzzy multi objective linear programming problem is considered. The problem involves fuzzy aspiration levels of objectives and moreover, fuzzy parameters are used both in objective functions and constraints. The concept of α-level set of fuzzy parameters is applied for getting a crisp bound of the constraints. The solution is obtained for various values of α using modified arithmetic operation on interval numbers and is verified by means of a numerical example.

5 ref

016010   Sophia Porchelvi R;Vasanthi L (Mathematics Dep, A.D.M. College for Women, Nagapattinam-611 001, Email: sophiaporchelvi@gmail.com) : On solving a fuzzy linear programming problem using simplex procedure with symmetric trapezoidal fuzzy numbers. Int Rev Fuzzy Math 2012, 7(2), 59-64.

A new method for solving a fuzzy linear programming problem using Simplex procedure with symmetric trapezoidal fuzzy numbers is proposed and moreover a linear ranking function is directly used here. A numerical example is provided to illustrate the feasibility of the proposed method.

4 ref

016009   Singh H K;Singh T B (Mathematics Dep, Delhi Univ, Delhi-110 007, Email: hksinghdu@gmail.com) : Cohomology of orbit spaces of certain free circle group actions. Proc Indian Acad Sci-Mathl Sci 2012, 122(1), 79-86.

Suppose that G = S¹ acts freely on a finitistic space X whose (mod p) cohomology ring is isomorphic to that of a lens space L^2m-1 (p; q₁, ..., q_m) or S¹ x CP^m-1. The mod p index of the action is defined to be the largest integer n such that αⁿ <128><153> 0, where α ∈ H² (X/G; Z_p) is the nonzero characteristic class of the S¹-bundle S¹ → X → X/G. Show that the mod p index of a free action of G on S¹ x CP^m-1 is p - 1, when it is defined. Using this, we obtain a Borsuk-Ulam type theorem for a free G-action on S¹ x CP^m-1. It is note worthy that the mod p index for free G-actions on the cohomology lens space is not defined.

15 ref

016008   Sharma P K (P.G. Mathematics Dep, D.A.V. College, Jalandhar, Punjab, Email: pksharma@davjalandhar.com) : Intuitionistic fuzzy relation on modules. Int Rev Fuzzy Math 2012, 7(1), 13-20.

Author extend the idea of fuzzy relations on modules as discussed by Erosy and Ralescu in to intuitionistic fuzzy relations on modules and give some characterization of intuitionistic fuzzy image and pre-image of modules.

17 ref

016007   Sharma P K (Mathematics Dep, D.A.V. College, Jalandhar City, Punjab, Email: pksharma@davjalamdhar.com) : α- anti fuzzy subgroup. Int Rev Fuzzy Math 2012, 7(2), 47-58.

On the basis of fuzzy sets introduced by LA. Zadeh, we first gave the definition of α-anti fuzzy set and then defined α-anti fuzzy subgroups and α-anti fuzzy normal subgroups and finally, defined quotient group of the α-anti fuzzy cosets of an α-anti fuzzy normal subgroup. This paper proves a necessary and sufficient condition of α-anti fuzzy subgroup (normal subgroup) to be anti fuzzy subgroup (normal subgroup). Some properties of quotient group of α-anti fuzzy normal subgroups are also discussed.

10 ref

016006   Senbagam K;Seshaiah C V (Mathematics Dep, Sri Ramakrishna Engineering College, Coimbatore) : Stochastic delay for video teleconference service traffic. Int Rev pure appl Math 2012, 8(1), 13-35.

Author present a novel control scheme that takes into account the fractal properties of video teleconference service traffic (VTST) flows. To this end, determined, the second central moment of the cumulative traffic processes as well as their wavelet energy across time scales, considering a multiplicative cascade model for the VTST traffic traces. In addition, derived an analytical expression for the effective bandwidth estimation of the fractal modeled traffic process, Use the proposed effective bandwidth equation to compute the effective envelope for fractal traffic flows for VTST. The development on the fractal traffic effective envelopment allows us to design a control scheme capable of efficiently guaranteeing quality of service in terms of effective envelope violation and delay probabilities for fractal traffic flows. Through simulations, we compare the admissible number of flows in connections under different types of scheduling algorithms as well as different traffic models, such as the monofractal fBm and the proposed fractal approach.

4 illus, 2 tables, 37 ref

016005   Selvakkumaraen N;Arjunan K (Mathematics Dep, Latha Mathavan Engineering College, Kidaripatti-625 301, Madurai, Email: sk291166@gmail.com) : Notes on intuitionistic L-fuzzy subhemirings of a hemiring. Int Rev pure appl Math 2012, 8(1), 1-7.

Author made an attempt to study the algebraic nature of an intuitionistic L-fuzzy subhemiring of a hemiring.

17 ref

016004   Sebastian P;Johnson T P (Mathematics Dep, Mary Matha Arts & Science College, Mananthavady, Kerala, Email: pamyseb@gmail.com) : Semigroup action on fuzzy subsets and the category of S-fuzzy subsets. Int Rev Fuzzy Math 2012, 7(1), 27-34.

Author defined S-Fuzzy subsets and S-Fuzzy morphisms for a semigroup S with identity and the category S-FSET. Defines a covariant functor from the category S-SET to the category S-FSET. and studied some special objects and morphisms in the object category S-FSETX.

7 ref

016003   Santhanam G (Mathematics and Statistics Dep, Indian Institute of Technology, Kanpur-208 016, Email: santhana@iitk.ac.in) : Isoperimetric upper bounds for the first eigenvalue. Proc Indian Acad Sci-Mathl Sci 2012, 122(3), 375-84.

Let M be a closed hypersurface in a simply connected space form M(k) where K = 0, 1 or -1. In this paper, authors give two isoperimetric upper bounds for the first eigenvalue of the Laplacian of M.

10 ref

016002   Saberi Najafi H;Edalatpanah S A (Mathematics Dep, Lihijan Branch, Islamic Azad Univ, Lahijan, Iran) : Preconditioning strategy to solve fuzzy linear systems (FLS). Int Rev Fuzzy Math 2012, 7(2), 65-80.

In this article, the preconditioning methods are used for fuzzy linear systems and especially some new preconditioners are introduced. Moreover, the preconditioned iterative methods are studied from the point of view of rate of convergence and the convergence properties of the proposed methods have been analyzed and compared with the classical methods. Finally, the methods are tested by numerical example that shows a good improvement on the convergence speed.

31 ref

016001   Rodriguez J M;Sigarreta J M (Matematicas Dep, Carlos III de Madrid Univ, Avenide de la 30 Univ, 28911 Leganes, Madrid, Spain, Email: jomaro@math.uc3m.es) : Bounds on gromov hyperbolicity constant in graphs. Proc Indian Acad Sci-Mathl Sci 2012, 122(1), 53-65.

If X is a geodesic metric space and x₁, x₂, x₃ ∈ X, a geodesic triangle T = [x₁, X₂, x₃} is the union of the three geodesies [x₁x₂], x₂x₃] and [x₃x₁] 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 two other sides, for every geodesic triangle T in X. If X is hyperbolic, authors denote by δ(X) the sharp hyperbolicity constant of X, i.e. δ(X) = inf{δ ≥ 0 : X is δ-hyperbolic). In this paper authors relate the hyperbolicity constant of a graph with some known parameters of the graph, as its independence number, its maximum and minimum degree and its domination number. Furthermore, they compute explicitly the hyperbolicity constant of some class of product graphs.

27 ref

016000   Ramachandran V V S (NO, B.V.C. College of Engineering, Rajahmundry, Andhra Pradesh) : Dynamics in groups. Int Rev pure appl Math 2012, 8(1), 9-11.

Author defined a dynamical system (G, f) where G is a Group and f is a homomorphism from to itself. It was established some properties of the set of fixed points and the set of periodic points. It was proved that the set of all fixed points is a subgroup of G and it is a strongly invariant subset of G.

2 ref

015999   Ram Murty M;Thangadurai R (Mathematics Dep, Queen's Univ, Kingston, Ontario K7L 3N6, Canada, Email: murty@mast.queensu.ca) : On a paper of S S Pillai. Proc Indian Acad Sci-Mathl Sci 2012, 122(1), 1-13.

In 1935, Erdos proved that all natural numbers can be written as a sum of a square of a prime and a square-free number. In 1939, Pillai derived an asymptotic formula for the number of such representations. The mathematical review of Pillai's paper stated that the proof of the above result contained inaccuracies, thus casting a doubt on the correctness of the paper. In this paper, authors re-examine Pillai's paper and show that his argument was essentially correct. Afterwards, we improve the error term in Pillai's theorem using the Bombieri-Vinogradov theorem.

8 ref

015998   Quaegebeur J;Sabbe M (Mathematics Dep, K.U. Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium, Email: johan.quaegebeur@wis.kuleuven.be) : Isometric coactions of compact quantum groups on compact quantum metric spaces. Proc Indian Acad Sci-Mathl Sci 2012, 122(3), 351-73.

Proposed a notion of isometric coaction of a compact quantum group on a compact quantum metric space in the framework of Rieffel, where the metric structure is given by a Lipnorm. Within this setting author studied the problem of the existence of a quantum isometry group.

18 ref

015997   Prasad K R;Kameswara Rao A;Nageswara Rao S (Applied Mathematics Dep, Andhra Univ, Visakhapatnam-530 003, Email: rajendra_92@rediffmail.com) : Existence of positive solutions for the system of higher order two-point boundary value problems. Proc Indian Acad Sci-Mathl Sci 2012, 122(1), 139-52.

In this paper, authors establish the existence of at least one and two positive solutions for the system 6f higher order boundary value problems by using the Krasnosel'skii fixed point theorem.

22 ref

015996   Porchelvi R S;Jamuna Devi P;Karthi R (Mathematics Dep, A.D.M. College for Women, Nagappattinam-611 001, Email: sophiaporchelvi@gmail.com) : Statistical survey and analysis report on people working in match box industry at Kovilpatti and their level of satisfaction towards the working environment and other aspects. Int Rev pure appl Math 2012, 8(1), 37-47.

This survey intends to capture the level of satisfaction of the people working in match box industry in Kovilpatti, towards the working environment and other aspects. The basic intention behind the survey is to find whether they are satisfied with their life style, and to know whether the government policies and schemes reach them and how far it helps them to improve their lifestyle and also to know about the satisfaction level in basic facilities they get. For this study the researcher opted 1000 respondents those who are working in various match box industry in Kovilpatti. The study reveals that the people are facing problems in the following areas: salary, housing, children's study, health condition, awareness towards the hazards of chemicals and finally some suggestions are given.

13 tables, 7 ref

015995   Pathak R S;Prasad A;Manish Kumar (Centre for Interdisciplinary Mathematical Sciences, Banaras Hindu Univ, Varanasi-221 005, Email: ramshankarpathak@yahoo.co.in) : n-dimensional pseudo-differential operator involving the Hankel transformation. Proc Indian Acad Sci-Mathl Sci 2012, 122(1), 99-120.

An n-dimensional pseudo-differential operator (p.d.o.) involving the n-dimensional Hankel transformation is defined. The symbol class H^m is introduced. It is shown that p.d.o.'s associated with symbols belonging to this class are continuous linear mappings of the n-dimensional Zemanian space H_<128><109>(Iⁿ) into itself. An integral representation for the p.d.o. is obtained. Using the Hankel convolution, it is shown that the p.d.o. satisfies a certain L¹-norm inequality.

7 ref

015994   Passi I B S (Centre for Advanced Study in Mathematics, Panjab Univ, Chandigarh-160 014, Email: ibspassi@yahoo.co.in ) : Group algebras. Indian J pure appl Math 2012, 43(2), 89-106.

Given a group G and a commutative ring k with identity, one can define an k-algebra k[G] called the group algebra of G over k. An element α ∈ k[G] is said to be algebraic if f(α) = 0 for some non-zero polynomial f(X) ∈ k[X}. Author will discuss some of the developments in the study of algebraic elements in group algebras.

58 ref

015993   Nandakumar R;Rao N R (Kovilet, Palace 41 Compund, Tripunithura-682 301, Email: nandacumar@gmail.com) : Fair partitions of polygons: an elementary introduction. Proc Indian Acad Sci-Mathl Sci 2012, 122(3), 459-67.

Introduces the question: Given a positive integer N, can any 2D convex polygonal region be partitioned into N convex pieces such that all pieces have the same area and the same perimeter? The answer to this question is easily 'yes' for N = 2. We give an elementary proof that the answer is 'yes' for N = 4 and generalize it to higher powers of 2.

9 ref

015992   Mo X (Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking Univ, Beijing-100 871, China, Email: moxh@pku.edu.cn) : Finsler metrics with constant (or scalar) flag curvature. Proc Indian Acad Sci-Mathl Sci 2012, 122(3), 411-27.

By finding Killing vector fields of general Bryant's metric we give a lot of new Finsler metrics of constant (or scalar) flag curvature and determine their scalar curvature.

14 ref

015991   Mishra M K;Kamli S (NO, ECG PEC, Nagapattinum) : Fuzzy supper continuity. Int Rev Fuzzy Math 2012, 7(2), 43-6.

Author studied and explore the concept of fuzzy supper continuity and characterized relating to several other well-known variations of fuzzy continuity, in fuzzy topology.

14 ref

015990   Lu J;Pang L (Mathematics Dep, Guangxi Normal Univ, Guangxi, Guilin-541 004, People's Republic of China, Email: jklu@mailbox.gxnu.edu.cn) : Note on TI-subgroups of finite groups. Proc Indian Acad Sci-Mathl Sci 2012, 122(1), 75-7.

Subgroup H of a finite group G is called a TI-subgroup if H <128><167> H^x = 1 or H for any x ∈ G. In this short note, the finite groups all of whose nonabelian subgroups are Tl-subgroups are classified.

5 ref

015989   Kong Q (Mathematics Dep, Tianjin Polytechnic Univ, Tianjin-300 160, People's Republic of China, Email: tjkqj1978@163.com) : Finite groups with three conjugacy class sizes of some elements. Proc Indian Acad Sci-Mathl Sci 2012, 122(3), 335-7.

Let G be a finite group. Proves as follows: Let G be a p-solvable group for a fixed prime p. If the conjugacy class sizes of all elements of primary and biprimary orders of G are {1, p^a, n} with a and n two positive integers and (p, n) = 1, then G is p-nilpotent or G has abelian Sylow p-subgroups.

10 ref

015988   Kanhere A (Homi Bhabha Center for Science Education, Tata Institute of Fundamental Research, V.N. Purav Marg, Mankhurd, Mumbai-400 088, Email: aalokakanhere@gmail.com) : Resolution of veronese embedding of plane curves. Indian J pure appl Math 2012, 43(2), 155-78.

Let C be a smooth (irreducible) curve of degree d in P². Let P² → P⁵ be the Veronese embedding and let I_c denote the homogeneous ideal of C on P⁵. In this note we explicitly write down the minimalfree resolution of I_c for d ≥ 2.

9 rfe

015987   Jyothi P;Pradeep Kumar T V (Laqshya Institute of Technology and Sciences, , Khammam, Andhra Pradesh, Email: jyothi.puligadda.77@gmail.com) : Regular polynomial near rings. Int Rev Fuzzy Math 2012, 7(1), 1-5.

The main aim of this paper is to investigate the fundamental structures of Regular polynomial near rings, the concept of degree, least degree and symbolically zero polynomials. Also obtained results related to the degree, least degree and symbolically zero polynomials.

9 ref

015986   Jiao X;Xu Z;Xu X (School of Mathematicas, Sciences, Graduate Chinese Academy of Sciences Univ, Beijing-100 049, People's Republic of China, Email: xxj@gucas.ac.cn) : Holomorphic two-spheres in the complex grassmann manifold G(k,n). Proc Indian Acad Sci-Mathl Sci 2012, 122(3), 399-409.

Study the non-degenerate holomorphic S² in the complex Grassmann manifold G(k, n), 2k ≤ n, by the method of moving frame. For a non-degenerate holomorphic one, there exists globally defined positive functions λ₁, ..., λ_k on S². Authors first show that the holomorphic S² in G(k, 2k) is totally geodesic if these λ_i are all equal. Conversely, for any totally geodesic immersion f from S² into G(k, n), authors prove that λ₁/(S²) <128><172> G(k, 2k) up to U(n)-transformation, λ_i = 1/<128><182>k, the Gaussian curvature K = 4/k and f is given by (Z₀, z₁) → (z₀I_k, z₁I_k, 0) in terms of homogeneous coordinate.

12 ref

015985   Jia-Feng L (Mathematics Dep, Zhejiang Normal Univ, Jinhua, Zhejiang-321 004, Peoples' Republic of China, Email: jiafenglv@gmail.com) : Nonpure piecewise-Koszul algebras. Indian J pure appl Math 2012, 43(1), 1-23.

The notions of nonpure piecewise-Koszul algebra and nonpure piecewise-Koszul module are introduced, which are the "nonpure" version of piecewise-Koszul algebras and modules first introduced in [19]. Some criteria for a standard graded algebra to be nonpure piecewise-Koszul are given. Also discusses some basic properties of nonpure piecewise-Koszul modules. Gave a sufficient condition to be true in terms of nonpure piecewise-Koszul modules.

27 ref

015984   Jebaraj J (Mathematics Dep, Vivekanandha College of Engineering for Women, Trichengodu, Tamil Nadu, Email: je06ba@yahoo.co.in) : Improving mathematical modeling in bio-science research- a case study on biological research scholars in Coimbatore city. Res J biol Sci 2011, 3(4), 28-35.

The advent of new mathematical modeling technologies has significantly influenced the direction of biological research. Initially, the focus was on adoption, but with the emergence of new mathematical modeling technologies, it is now considered the responsibility of research organizations to adopt mathematical modeling technologies in their curriculum. As a result, current research in biological sciences is mainly concerned with the implementation of mathematical modeling in the research process. The innovation process in research organization is considered successful only if it leads to the implementation and possible institutionalization of mathematical modeling. This article examines the relationship between the independent innovative variables (Bio-logical biological research scholars" competence and complexity of mathematical modeling) and dependent variables (research scholars' satisfaction and utilization of mathematical modeling). Four hypotheses were formulated to examine the relationship between the variables. Using regression analyses it is discovered that the four hypotheses were not supported. The results demonstrate that the implementation of mathematical modeling has not been successful. This failure can be attributed more to the negligence of modeling techniques by research organizations. More specifically, the findings emphasize that the degree of implementation of mathematical modeling is a critical variable in biological-research. Research-organizations could organize workshops/seminars on Mathematical-modeling technical skills for biological science research scholars. Active interaction of research scholars who are users with non users is a practical means of moving the mathematical modeling initiative forward. A cadre of biological science research scholars motivated by the potential of mathematical modeling techniques can ignite the interest of other users.

3 illus, 3 tables, 10 ref

015983   Jasiulis-Goldyn B;Kula A (Institute of Mathematics, Wroclaw Univ, pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland, Email: jasiulis@math.uni.wroc.pl) : Urbanik generalized convolutions in the non-commutative probability and a forgotton method for constructing generalized convolution. Proc Indian Acad Sci-Mathl Sci 2012, 122(3), 437-58.

Deals with the notions of weak stability and weak generalized convolution with respect to a generalized convolution, introduced by Kucharczak and Urbanik. Study properties of such objects and give examples of weakly stable measures with respect to the Kendall convolution. Moreover, we show that in the context of non-commutative probability, two operations: the q-convolution and the (q, 1)-convolution satisfy the Urbanik's conditions for a generalized convolution, interpreted on the set of moment sequences. The weak stability reveals the relation between two operations.

24 ref

015982   Iyigun E (Mathematics Dep, Uludag Univ, Faculty of Arts and Science, 16059, Bursa Turkey, Email: esen@uludag.edu.tr ) : Harmonic curvatures and curvature centres in L<. J Analysis Computn 2012, 8(1), 9-20.

Author gave harmonic functions, harmonic cur-vatures and curvature centers of a non-null curve of osculating order 5 in Lorentzian 5-space L⁵. Also, by de.ning a general helix of rank 3 we obtain some results in L⁵. In the final part, by using the definition of a vector prod uct of four vectors in I; from [8], Calculates 2nd; 3rd; 4'h and 5th curvature centers of a special curves.

8 ref

015981   Govindarajan R;Lavanya S (D.G. Vaishnav College, Madras Univ, Chennai, Tamil Nadu) : Effective fuzzy graphs and effective fuzzy coloring. Int Rev Fuzzy Math 2012, 7(1), 7-12.

The concept of effective fuzzy graph is defined and the effective fuzzy subgraph of a fuzzy graph is found. All the basic definitions of fuzzy coloring are clearly given and the concept of fuzzy coloring has been introduced to the effective fuzzy subgraph. It has been shown that fuzzy chromatic number of the fuzzy graph and that of the effective subgraph are equal. But the fuzzy edge chromatic number and the fuzzy total chromatic number of a fuzzy graph is greater than or equal to that of the effective subgraph. Also it is proved that the effective edge coloring of a fuzzy graph G is not equivalent to the effective vertex coloring of its line graph.

8 ref

015980   Ghaffarzadeh G;Abbaspour M H (Mathematics Dep, Islamic Azad Univ, Khoy Branch, Khoy, Iran, Email: gh.ghaffarzadeh@iaukhoy.ac.ir) : Minimal degrees of faithful quasi-permutation representations for direct products of p-groups. Proc Indian Acad Sci-Mathl Sci 2012, 122(3), 329-34.

In [2], the algorithms of c(G), q(G) and p(G), the minimal degrees of faithful quasi-permutation and permutation representations of a finite group G are given. The main purpose of this paper is to consider the relationship between these minimal degrees of non-trivial p-groups H and K with the group H x K.

7 ref

015979   Fu K;Chen J (School of Statistics and Mathematics, Zhejiang Gongshang Univ, Hangzhou-310 018, China, Email: fukeang@hotmail.com) : Precise asymptotics for complete moment convergence in Hilbert spaces. Proc Indian Acad Sci-Mathl Sci 2012, 122(1), 87-97.

Let [X, X_n;n ≥ 1} be a sequence of i.i.d. random variables taking values in a real separable Hilbert space (H, ||.||) with covariance operator <128><83>. Set S_n = <128><83>_i=1ⁿ X_i, n ≥ 1. Authors prove that for 1 <60> p <60> 2 and r <62> 1 + p/2, Q where Y is a Gaussian random variable taking value in a real separable Hilbert space with mean zero and covariance operator <128><83>, and <128><115>² is the largest eigenvalue of <128><83>.

16 ref

015978   El-Kholy E M;Lashin E S R;Daoud S N (Mathematics Dep, Faculty of Science, Tanta Univ, Tanta, Egypt) : Operations on graphs and folding of some special graphs. J Analysis Computn 2012, 8(1), 47-58.

Author studied examining the relation between folding of a given graph and folding of new graphs generating from this graph by some known operations like line, dual, clique, closure and kth power of this graph. Also we discussed folding of some special graphs like, Hamiltonian, perfect, and triangulated graphs.

12 illus, 4 ref

015977   Dubey U V;Prasad A;Singla P (The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai-600 113, Email: dubey@imsc.res.in) : Cartan matrix of a centralizer algebra. Proc Indian Acad Sci-Mathl Sci 2012, 122(1), 67-73.

Centralizer algebra of a matrix consists of those matrices that commute with it. authors investigate the basic representation-theoretic invariants of centralizer algebras, namely their radicals, projective indecomposable modules, injective indecomposable modules, simple modules and Cartan matrices. With the help of our Cartan matrix calculations we determine their global dimensions. Many of these algebras are of infinite global dimension.

6 ref

015976   Dhara B (Mathematics Dep, Belda College, Belda, Paschim Medinipur-721 424, Email: basu_dhara@yahoo.com) : Annihilating power values of co-commutators with generalized derivations. Proc Indian Acad Sci-Mathl Sci 2012, 122(1), 121-8.

Let R be a prime ring with its Utumi ring of quotient U, H and G be two generalized derivations of R and L a noncentral Lie ideal of R. Suppose that there exists 0 <128><153> a ∈ R such that a(H(u)u - uG(u))ⁿ = 0 for all u ∈ L, where n ≥ 1 is a fixed integer. Then there exist b', c' ∈ U such that H(x) = b'x + xc', G(x) = c'x for all x ∈ R with ab' = 0, unless R satisfies S₄, the standard identity in four variables.

25 ref

015975   Desai A R (Mathematics Dep, S.D.M. College of Engg & Tech., Dharwad-580 002, Email: ardesai69@rediffmail.com) : New subclasses of meromorphic close-to convex functions. J Analysis Computn 2012, 8(2), 85-9.

Let f(z) be regular function defined in the punctured disk 0 <60> |z| <60> 1 with a simple pole at z = Q for which Re[-z²f'(z)-1/(2λ-1)]^μ [1 + zf'(z)/f'(z) + λ]^γ <62> 0, where μ and γ are real. The author show that for certain values of μ and γ the function is meromorphically close-to-convex. AMS1991 Subject Classifications: Primary 30C45.

4 ref

015974   Daher R;Hamad S L;Kawazoe T;Shimeno N (Mathematics Dep, Faculty of Sciences of Ain Chock, Hassan II Univ, Casablanca, Morocco, Email: ra_daher@yahoo.fr) : Uncertainty principles for the cherednik transform. Proc Indian Acad Sci-Mathl Sci 2012, 122(3), 429-36.

Investigates two uncertainty principles for the Cherednik transform on the Euclidean space a; Miyachi's theorem and Beurling's theorem. Authors give an analogue of Miyachi' theorem for the Cherednik transform and under the assumption that a has a hypergroup structure, an analogue of Beurling's theorem for the Cherednik transform.

13 ref

015973   Chu Y M;Wang M K;Qiu S L (Mathematics and Computing Science Dep, Hunan City Univ, Yiyang-413 000, China, Email: chuyuming@hutc.zj.cn) : Optimal combinations bounds of root-square and arithmetic means for toader mean. Proc Indian Acad Sci-Mathl Sci 2012, 122(1), 41-51.

Finds the greatest values α₁ and α₂, and the least values β₁ and β₂, such that the double inequalities α₁S(a, b) + (1 - α₁)A(a, b) <60> T(a, b) <60> β₁S(a, b) + (1 - β₁)A(a,b) and S^α₂(a,b)A^1-α₂(a, b) <60> T(a,b) <60> S^β₂(a, b)A^1-β₂(a, b) hold for all a, b <62> 0 with a <128><153> b. As applications, get two new bounds for the complete elliptic integral of the second kind in terms of elementary functions. Here, 5(a, b) = [(a² + b²)/2]^1/2, A(a,b) = (a + b)/2, and T(a,b) = 2/π <128><134>^π/2₀ <128><182>a²cos² <128><113> + b²sin² <128><113> d<128><113> denote the root-square, arithmetic, and Toader means of two positive numbers a and b, respectively.

2 tables, 22 ref

015972   Chintamani M N;Moriya B K (Harish-Chandra Research Institute, , Chhatnag Road, Jhunsi, Allahabad-211 019, Email: chintamani@mri.ernet.in) : Generalizations of some zero sum theorems. Proc Indian Acad Sci-Mathl Sci 2012, 122(1), 15-21.

Given an abelian group G of order n, and a finite non-empty subset A of integers, the Davenport constant of G with weight A, denoted by D_A(G), is defined to be the least positive integer t such that, for every sequence (x₁, ..., x_t) with x_i ∈ G, there exists a non-empty subsequence (x_j1, ..., X_jl) and a_i ∈ A such that <128><83>^l_i=1 a_ix_ji. = 0. Similarly, for an abelian group G of order n, E_A(G) is defined to be the least positive integer t such that every sequence over G of length t contains a subsequence (x_{j1, ..., Xjn) such that <128><83>i=1ⁿ aixji = 0, for some ai ∈ A. When G is of order n, one considers A to be a non-empty subset of {1, ..., n - 1). If G is the cyclic group Z/nZ, author denote EA(G) and DA(G) by EA(n) and DA(n) respectively. In this note, authors extend some results of Adhikari et al (Integers 8 (2008) Article A52) and determine bounds for DRn(n) and ERn(n), where Rn = {x² : x ∈ (Z/nZ)*}. Authors follow some lines of argument from Adhikari et al (Integers 8 (2008) Article A52) and use a recent result of Yuan and Zeng (European J. Combinatorics 31 (2010) 677-680), a theorem due to Chowla (Proc. Indian Acad. Sci. (Math. Sci.) 2 (1935) 242-243) and Kneser's theorem (Math. Z. 58 (1953) 459-484; 66 (1956) 88-110; 61 (1955) 429-434).}

15 ref

015971   Chatterjee T (NO, The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai-600 113, Email: tapasc@imsc.res.in) : On the dimension of Chowla-Milnor space. Proc Indian Acad Sci-Mathl Sci 2012, 122(3), 313-7.

In a recent work, Gun, Murty and Rath defined the Chowla-Milnor space and proved a non-trivial lower bound for these spaces. They also obtained a conditional improvement of this lower bound and noted that an unconditional improvement of their lower bound will lead to irrationality of ζ(k)/π^k for odd positive integers k <62> 1. In this paper, author give an alternate proof of their theorem about the conditional lower bound.

2 ref

015970   Chami F E (Mathematics Dep, Lebanese Univ, Faculty of Sciences II, B.P. 90656, Fanar-Maten, Lebanon, Email: fchami@ul.edu.lb) : Branching law from Sp(n) to Sp(q) x Sp(n-q) and an application to laplace operator spectra. Indian J pure appl Math 2012, 43(1), 71-86.

Author gave a branching law from the group Sp(n) to the subgroup Sp(q) x Sp(n-q). Proposeed an application of this result to compute the Laplace spectrum on the forms of the manifold Sp(n)/Sp(q) x vSp(n-q), using the "identification" of the Laplace operator with the Casimir operator in symmetric spaces.

11 ref

015969   Burcu Bozkurt S;Adiga C;Bozkurt D (Mathematics Dep, Science Faculty, Selcuk Univ, 42075, Campus, Konya, Turkey, Email: sbbozkurt@selcuk.edu.tr) : On the energy and Estrada index of strongly quotient graphs. Indian J pure appl Math 2012, 43(1), 25-36.

Author considered the strongly quotient graphs and obtained some better results for the energy and Estrada index of these graphs, as well as some relations between Estrada index and the graph energy.

18 ref

015968   Bharathidass S (NO, Periyar E.V.R. College, Tiruchirappalli-620 023) : Multiple servers state dependent queue with. J Analysis Computn 2012, 8(1), 21-30.

Consider a muli-server Markovian queue in which machine repair problem has been analysed. If any operating machine fails, it is replaced by a spare machine and submitted for repair. It is assumed that the life time and repair time are exponentially distributed. The failed machines may or may not enter the queue depends on the number of failed machines waiting for service. Likewise, service rate also depends on the number of failed machines which are to be repaired. The values of failure and service rates are stated according to the situations of the system. An additional repair man is utilised whenever it is necessary and some other queueing characters are also included for analysing this model. The steady-state probabilities for the number of failed machines, waiting for service are derived in different situations. The expressions for the expected number of failed machines in the system are derived.

6 ref

015967   Berisha N S;Berisha F M (Faculty of Mathematics and Nature Sciences, Prishtina Univ, Mother Theresa Av.5, 10000 Prishtina, Kosovo, Email: nimete-berisha@hotmail.com) : Approximating generalised lipschitz classes of functions by means of algebraic polynomials. Int Rev pure appl Math 2012, 8(1), 49-69.

Approximation by means of algebraic polynomials of generalised Lipschitz classes of functions is considered. These classes of functions are defined by a generalised modulus of smoothness and operators of differentiation of these functions. Gives structural characteristics of classes of functions defined by the order of best approximation by algebraic polynomials.

13 ref

015966   Bastani M;Salkuyeh D K (Mathematics Dep, Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran, Email: salkuyeh@gmail.com ) : Highly accurate method to solve fisher's equation. Pramana J Phys 2012, 78(3), 335-46.

In this study, authors present a new and very accurate numerical method to approximate the Fisher's-type equations. Firstly, the spatial derivative in the proposed equation is approximated by a sixth-order compact finite difference (CFD6) scheme. Secondly, we solve the obtained system of differential equations using a third-order total variation diminishing Runge-Kutta (TVD-RK3) scheme. Numerical examples are given to illustrate the efficiency of the proposed method.

5 illus, 4 tables, 35 ref

015965   Basavanagoud B;Patil P V;Hosamani S K M (Mathematics Dep, Karnatak Univ, Dharwad-580 003, Email: b.basavanagoud@gmail.com) : Domination in degree splitting graphs. J Analysis Computn 2012, 8(1), 1-8.

Let G = (V, E) be a graph with V=S₁ ∪ S₁ ∪, ..., ∪ S_t, ∪ T where each S. is a set of vertices having at least two vertices and having the same degree and T = V∪S₁. The degree splitting graph of G is denoted by DS(G) is obtained from G by adding vertices w₁, w₂, ..., w_t and joining w. to each vertex of S. (1 ≤ i ≤ t). Let the vertices and the edges of a graph G are called the elements of G. Studied the variation in domination from the graph G to the degree splitting graph DS(G). Also established many bounds on γ (DS(G)) in terms of elements of G but not in terms of elements of DS(G).

1 illus, 5 ref

015964   Babitha S;Baskar Babujee J (Mathematics Dep, Anna Univ, Chennai-600 025, Email: babi_mit@yahoo.co.in) : On square sum labeling in graphs. Int Rev Fuzzy Math 2012, 7(2), 81-7.

In this paper author studied square sum labeling introduced by Ajitha, Arumugam, and Germina in 2009. Exhibited square sum labeling for Kite graph, Jellyfish graph J(m, n), Book graph, Uniform t-ply graph P_t (u, v) and Triangular snake graph. Also provides some new construction of square sum labeling.

9 ref

015963   Anand S;Agarwal A K (Centre for Advanced Study in Mathematics, Panjab Univ, Chandigarh-160 014, Email: shivani.bedi.maths@gmail.com) : New class of lattice paths and partitions with n copies of n. Proc Indian Acad Sci-Mathl Sci 2012, 122(1), 23-39.

Agarwal and Bressoud (Pacific J. Math. 136(2) (1989) 209-228) defined a class of weighted lattice paths and interpreted several q-series combinatorially. Using the same class of lattice paths, Agarwal (Utilitas Math. 53 (1998) 71-80; ARS Com-binatoria 76 (2005) 151-160) provided combinatorial interpretations for several more q-series. In this paper, a new class of weighted lattice paths, which we call associated lattice paths is introduced. It is shown that these new lattice paths can also be used for giving combinatorial meaning to certain q-series. However, the main advantage of our associated lattice paths is that they provide a graphical representation for partitions with n + t copies of n introduced and studied by Agarwal (Partitions with n copies of n, Lecture Notes in Math., No. 1234 (Berlin/New York: Springer-Verlag) (1985) 1-4) and Agarwal and Andrews (J. Combin. Theory A45(l) (1987) 40-49).

2 illus, 12 ref