012061   Goyal S;Sreenadh K (Mathematics Dep, Indian Institute of Technology Delhi, Hauz Khas, New Delhi-110 016, Email: sarika.iitd@gmail.com) : Nehari manifold for non-local elliptic operator with concave-convex nonlinearities and sign-changing weight functions. Proc Indian Acad Sci-Mathl Sci 2015, 125(4), 545-58.

In this article, we study the existence and multiplicity of non-negative solutions of the following p-fractional equation. Authors show the existence and multiplicity of solutions by minimization on the suitable subset of Nehari manifold using the fibering maps. We find that there exists λ₀ such that for λ ∈ (0, λ₀), it has at least two non-negative solutions.

24 ref

012060   Goswami D (NO, Indian Statistical Institute, 203, B T Road, Kolkata-700 108, Email: goswamid@isical.ac.in) : Quadratic independence of coordinate functions of certain homogeneous spaces and action of compact quantum groups. Proc Math Sci 2015, 125(1), 127-38.

Let G be one of the classical compact, simple, centre-less, connected Lie groups of rank n with a maximal torus T, the Lie algebra G and let [E_i, F_i, H_i, i = 1, ..., n] be the standard set of generators corresponding to a basis of the root system. Consider the adjoint-orbit space M = {Ad_g(H₁), g ∈ G}, identified with the homogeneous space G/L where L = {g ∈ G : Ad_g (H₁) = H₁}. We prove that the coordinate functions f_i(g) : = λ_i(Ad_g(H₁)), i = 1, ..., n, where [λ₁, ..., λ_n] is basis of G' are 'quadratically independent' in the sense that they do not satisfy any nontrivial homogeneous quadratic relations among them. Using this, it is proved that there is no genuine compact quantum group which can act faithfully on C(M) such that the action leaves invariant the linear span of the above coordinate functions. As a corollary, it is also shown that any compact quantum group having a faithful action on the noncommutative manifold obtained by Rieffel deformation of M satisfying a similar 'linearity' condition must be a Rieffel-Wang type deformation of some compact group.

18 ref

012059   Ghosh D;Chakraborty D (Mathematics Dep, Indian Institute of Technology Kharagpur, Kharagpur-721 302, Email: debjani@maths.iitkgp.ernet.in) : A direction based classical method to obtain complete pareto set of multi-criteria optimization problems. Opsearch 2015, 52(2), 340-66.

This paper provides a direction based parameter dependent classical method to find entire Pareto set of multi-criteria optimization problems. Proposed method is non-gradient based and parameter of the technique essentially lies on the unit sphere in the criterion space. Sequentially solving a set of problems, corresponding to each particular parameter vector on the unit sphere, entire Pareto set of the problem is captured. It is obtained that the method bears a necessary and sufficient condition for Pareto optimality. It is also shown that a simple modification on the constraint set of the formulated problem can ensure general D-Pareto optimality of the outcome solutions, where D is any pointed convex cone. In specific, proposed method can extract ∈-Pareto optimal points. As at any ∈-Pareto point, trade-off between any two Objectives are bounded, outcome solution set of the studied method can facilitate decision maker for final selection of solution. Proposed technique and its illustrations are supported by several numerical and pictorial representations.

18 illus, 4 tables, 22 ref

012058   Gezer A;Altunbas M (Mathematics Dep, Faculty of Science, Ataturk Univ, 25240 Erzurum, Turkey, Email: agezer@atauni.edu.tr) : On the (1, 1)-tensor bundle with Cheeger-Gromoll type metric. Proc Indian Acad Sci-Mathl Sci 2015, 125(4), 569-76.

The main purpose of the present paper is to construct Riemannian almost product structures on the (1, 1)-tensor bundle equipped with Cheeger-Gromoll type metric over a Riemannian manifold and present some results concerning these structures.

17 ref

012057   Foruzanfar Z;Mostaghim Z (School of Mathematics, Iran Univ of Science and Technology, P O Box 1684613114, Narmak, Tehran, Iran, Email: mostaghim@iust.ac.ir) : Classification of non solvable groups with a given property. Proc Math Sci 2015, 125(1), 29-36.

In this paper, authors classify the finite non-solvable groups satisfying the following property P₅ : their orders of representatives are set-wise relatively prime for any 5 distinct non-central conjugacy classes.

16 ref

012056   Fathali J (Mathematics Dep, Shahrood Univ of Technology, Univ Blvd., Shahrood, Iran, Email: fathali@shahroodut.ac.ir ) : Backup multifacility location problem with l_P norm. Opsearch 2015, 52(2), 382-91.

In this paper we consider the backup multifacility location problem. The multifacility location problem asks to find location of a number of facilities in the plane such that the sum of weighted distances between new facilities to existing facilities and each pair of new facilities is minimized. In the backup case some facilities may fail with a given probability. When a facility fails, the other facilities should serve its clients. We consider the case that the distances in the plane are measured by the l_p norm and propose an iterative method which is a generalization of the Weiszfeld algorithm for solving the problem.

6 tables, 18 ref

012055   Etemad S;Ettefagh M (Young Researchers and Elite Club, Tabriz Branch, Islamic Azad Univ, Tabriz, Iran, Email: sina.etemad@azaruniv.ac.ir) : (2n-1)-ideal amenability of triangular banach algebras. Proc Math Sci 2015, 125(2), 199-207.

Let A and B be two unital Banach algebras and let M be an unital Banach A, B-module. Also let T = [A M/B] be the corresponding triangular Banach algebra. Forrest and Marcoux (Trans. Amer. Math. Soc. 354 (2002) 1435-1452) have studied the rc-weak amenability of triangular Banach algebras. In this paper, we investigate (2n - 1)-ideal amenability of T for all n ≥ 1. We introduce the structure of ideals of these Banach algebras and then, we show that (2n - 1)-ideal almenability of T depends on (2n - 1)-ideal amenability of Banach algebras A and B.

9 ref

012054   Dutt P;Akhlaq H;Murthy A S V;Upadhyay C S (Mathematics & Statistics Dep, Indian Institute of Technology, Kanpur-208 016, Email: pravir@iitk.ac.in) : h-p spectral element methods for three dimensional elliptic problems on non-smooth domains, part-I: regularity estimates and stability theorem. Proc Math Sci 2015, 125(2), 239-70.

This is the first of a series of papers devoted to the study of h-p spectral element methods for solving three dimensional elliptic boundary value problems on non-smooth domains using parallel computers. In three dimensions there are three different types of singularities namely; the vertex, the edge and the vertex-edge singularities. In addition, the solution is anisotropic in the neighbourhoods of the edges and vertex-edges. To overcome the singularities which arise in the neighbourhoods of vertices, vertex-edges and edges, we use local systems of coordinates. These local coordinates are modified versions of spherical and cylindrical coordinate systems in their respective neighbourhoods. Away from these neighbourhoods standard Cartesian coordinates are used. In each of these neighbourhoods we use a geometrical mesh which becomes finer near the corners and edges. The geometrical mesh becomes a quasi-uniform mesh in the new system of coordinates. We then derive differentiability estimates in these new set of variables and state our main stability estimate theorem using a non-conforming h-p spectral element method whose proof is given in a separate paper.

10 illus, 32 ref

012053   Du Changmin;Guo L;Leng G (Mathematics Dep, Shanghai Univ, Shanghai 200 444, China, Email: adu860110@163.com) : Volume inequalities for Orlicz mean bodies. Proc Math Sci 2015, 125(1), 57-70.

In this paper, the Orlicz mean body H_φK of a convex body K is introduced. Using the notion of shadow system, we establish a sharp lower estimate for the volume ratio of H_φK and K.

38 ref

012052   Dewanji A;Basak G K;Biswas A (Applied Statistics Unit, Indian Statistical Institute, Kolkata) : Nonparametric estimation of Maximum Tolerated Dose(MTD)in the context of phaseV I clinical trials. Calcutta Statist Ass Bull 2015, 67(Mar-Jun), 15-34.

With the advent of technology, as there seems to be no reason not to implement a trial with a continuous domain of doses and varying step sizes, we provide a non-parametric methodology for such trials that aims to estimate Maximum Tolerated Dose (MTD) in the phase I clinical trials. We further provide extensive simulations for logistic and probit models with various parameter values to obtain a pseudo sample size for better design of the trials. We also illustrate a bootstrap method to obtain an estimate of the variance and the bias of our estimator.

1 illus, 5 tables, 32 ref

012051   Datta A;Jaggi S;Varghese C;Varghese E (NO, Indian Agricultural Statistics Research Institute, New Delhi) : Some series of row-column designs with multiple units per cell. Calcutta Statist Ass Bull 2015, 67(Mar-Jun), 89-99.

Row-column designs with multiple units per cell are used when the number of treatments is substantially large with limited number of replicates controlling heterogeneity in two directions. Here, some methods of constructing row-column designs with multiple units per cell with equal/ unequal cell sizes have been developed that are structurally complete, i.e. all the cells corresponding to the intersection of row and column receive at least two treatments. Properties of these classes of designs have been studied and all the methods result in designs in which the elementary contrasts of treatment effects are estimated with same variance. One series of row-column designs with unequal replications has also been obtained. Efficiency of the designs obtained has also been worked out.

3 tables, 16 ref

012050   Chitescu I;Ioana L;Miculescu R;Nita L (Faculty of Mathematics and Computer Science, Bucharest Univ, Bucharest, Academiei Str., 14, 010014, Romania, Email: ionchitescu@yahoo.com) : Sesquilinear uniform vector integral. Proc Math Sci 2015, 125(2), 187-98.

Introduce and study an integral of Hilbert valued functions with respect to Hilbert valued measures. The integral is sesquilinear (bilinear in the real case) and takes scalar values. Basic properties of this integral are studied and some examples are introduced.

11 ref

012049   Chen Y;Chen G (School of Mathematics and Statistics, Southwest Univ, Chongqing 400715, People's Republic of China, Email: math_yan@126.com) : Characterization of PGL (2, p) by its order and one conjugacy class size. Proc Indian Acad Sci-Mathl Sci 2015, 125(4), 501-6.

Let p be a prime. In this paper, we do not use the classification theorem of finite simple groups and prove that the projective general linear group PGL(2, p) can be uniquely determined by its order and one special conjugacy class size. Further, the validity of a conjecture of J. G. Thompson is generalized to the group PGL(2, p) by a new way.

25 ref

012048   Chaurasia S N;Sundar S;Singh A (School of Computer Information Sciences, Hyderabad Univ, Hyderabad-500 046, Email: alok@uohyd.ac.in) : A hybrid evolutionary approach for set packing problem. Opsearch 2015, 52(2), 271-84.

In this paper, we present a hybrid approach comprising an evolutionary algorithm with guided mutation (EA/G) and a local search to solve the set packing problem (SPP). EA/G is a recently proposed evolutionary algorithm that can be considered as a cross between genetic algorithms (GAs) and estimation of distribution algorithms (EDAs) and that tries to overcome the shortcomings of both. Guided mutation in EA/G generates offsprings through a probability model based on a combination of global statistical information and location information of the solutions found so far. We have compared our approach with the state-of-the-art approaches. Computational results show the effectiveness of our approach.

1 illus, 4 tables, 15 ref

012047   Chatterjee A K;Mateen A;Chakraborty A (Operation Management Group, Indian Institute of Management, Calcutta, Joka, Diamond Harbor Road, Kolkara-700 104, Email: arqumm@iimk.ac.in) : On the equivalence of some supply chain coordination models. Opsearch 2015, 52(2), 392-400.

Existing literature on supply chain coordination considers various mechanisms such as joint economic lot size, quantity discount and vendor managed inventory as distinct and disparate entities. In this paper, we establish their equivalence through simple models and show that the said mechanisms lead to the same optimal solution under any given set of parameters of the system. Comments on the applicability of these models have also been provided.

1 illus, 1 table, 15 ref

012046   Chang-Jian Z (Mathematics Dep, China Jiliang Univ, Hanghou 310018, People's Republic of China, Email: chjzhao@163.com) : Volume sums of polar Blaschke-Minkowski homomorphisms. Proc Math Sci 2015, 125(2), 209-19.

In this article, we establish Minkowski and Aleksandrov-Fenchel type inequalities for the volume sum of polars of Blaschke-Minkowski homomorphisms.

48 ref

012045   Bhurjee A K;Panda G (Research Scholar, Indian Institute of Technology Kharagpur, Kharagpur-721 302, Email: ajaybhurji@gmail.com) : Multi-objective interval fractional programming problems : an approach for obtaining efficient solutions. Opsearch 2015, 52(1), 156-67.

This paper addresses a general multi-objective fractional programming problem whose parameters in the objective functions and constraints are intervals. Existence of the efficient solution of dais model is studied. A methodology is developed to determine its efficient solutions. This methodology is illustrated through a numerical example.

15 ref

012044   Bhowmik B (Mathematics Dep, Indian Institute of Technology Kharagpur, Kharagpur-721 302, Email: bappaditya@maths.iitkgp.ernet.in) : Regions of variability for a class of analytic and locally univalent functions defined by subordination. Proc Indian Acad Sci-Mathl Sci 2015, 125(4), 511-19.

In this article, we consider a family C(A, B) of analytic and locally uni-valent functions on the open unit disc D = [z : |z| <60> 1] in the complex plane that properly contains the well-known Janowski class of convex univalent functions. In this article, we determine the exact set of variability of log(f(z₀)) with fixed Z0 ∈ B and f"(O) whenever f varies over the class C(A, B).

6 ref

012043   Bhatnagar A;Shrivastav R K;Singh A K (Applied Sciences Dep, Faculty of Engineering and Technology, Agra College, Agra, Uttar Pradesh) : Effect of slip velocity on blood flow through composite stenosed arteries: A Herschel-Bulkley fluid model. Natn Acad Sci Lett 2015, 38(3), 251-5.

In the present study we have developed a mathematical model for analyzing the flow characteristics of blood through an atherosclerotic arterial segment taking the velocity slip condition at the arterial wall. Blood is considered as Herschel-Bulkley fluid flowing in a uniform right circular tube having a composite stenosis. The dimensionless expressions of wall shear stress, flow resistance, volumetric flow rate in the stenotic region, apparent viscosity and axial velocity have been derived. The graphical representations for the influence of flow behaviour index, slip velocity, axial length and stenosis height on wall shear stress, flow resistance, volumetric flow rate, apparent viscosity and axial velocity have been shown. It has been observed that volumetric flow rate and axial velocity increase but wall shear stress and apparent viscosity decrease with slip velocity at arterial wall.

16 ref

012042   Bhar S;Rajeev B (Stat. Math. Unit, Indian Statistical Institute, Bangalore, Email: suprio@isibang.ac.in) : Differential operators on Hermite sobolev spaces. Proc Math Sci 2015, 125(1), 113-25.

In this paper, authors compute the Hilbert space adjoint ∂* of the derivative operator ∂ on the Hermite Sobolev spaces S_q. We use this calculation to give a different proof of the 'monotonicity inequality' for a class of differential operators (L, A) for which the inequality was proved in Infin. Dimens. Anal. Quantum Probab. Relat. Top. 2(4) (2009) 515-591. We also prove the monotonicity inequality for (L, A), when these correspond to the Ornstein-Uhlenbeck diffusion.

10 ref

012041   Besma B (LA.R.E.QUAD, FSEGN, Univ of Carthage, Tunis, Tunisia, Email: besma.kaabi@isg.rnu.tn) : Employment measure in developing countries via minimum wage and poverty new fuzzy approach. Opsearch 2015, 52(2), 329-39.

New models of employment show that there are some cases in which a minimum wage can have positive effects on employment and social welfare. The effects depend ultimately on the prevailing market wage and the frictions in the market. Card and Krueger (Am. Econ. Rev. 90(5), 1397-1420 2000) for example, argue that raising minimum wages sometimes increases employment. Based on this finding, we propose in this paper, a new approach to measure an employment via a fuzzy poverty measure and a relative minimum wage. An application using individual well-being data from Tunisia households in 2010 is presented.

1 illus, 2 tables, 38 ref

012040   Ayyaswamy S K;Krishnakumari B;Natarajan C; Venkatakrishnan Y B (Mathematics Dep, SASTRA Univ, Tanjore-613 401, Email: devasenavk@gmail.com) : Bounds on the hop domination number of a tree. Proc Indian Acad Sci-Mathl Sci 2015, 125(4), 449-55.

A hop dominating set of a graph G is a set D of vertices of G if for every vertex of V(G)D, there exists u ∈ D such that d(u, v) = 2. The hop domination number of a graph G, denoted by γh,(G), is the minimum cardinality of a hop dominating set of G. We prove that for every tree T of order n with/leaves and s support vertices we have (n-l-s+4)/3 ≤ <85>h, (G) ≤ n/2, and characterize the trees attaining each of the bounds.

6 ref

012039   Arumugam S;Ebadi K;Manrique M (National Centre for Advanced Research in Discrete Mathematics, Kalasalingam Univ, Anand Nagar, Krishnankoil-626 126, Email: s.arumugam.klu@gmail.com) : Co-Roman domination in graphs. Proc Math Sci 2015, 125(1), 1-10.

Let G = (V, E) be a graph and let f : V → {0, 1, 2} be a function. A vertex u is said to be protected with respect to f if f(u) <62> 0 or f(u) = 0 and u is adjacent to a vertex with positive weight. The function f is a co-Roman dominating function (CRDF) if: (i) every vertex in V is protected, and (ii) each v ∈ V with f(v) <62> 0 has a neighbor u ∈ V with f(u) = 0 such that the function f_vu : V → {0, 1, 2}, defined by f_vu(u) = 1, f_vu(v) = f(v) - 1 and f_vu(x) = f(x) for x ∈ V[u, v] has no unprotected vertex. The weight of f is w(f) = ∑_v∈V f(v)- The co-Roman domination number of a graph G, denoted by γcr(G), is the minimum weight of a co-Roman dominating function on G. In this paper we initiate a study of this parameter, present several basic results, as well as some applications and directions for further research. We also show that the decision problem for the co-Roman domination number is NP-complete, even when restricted to bipartite, chordal and planar graphs.

15 ref

012038   Arora R;Arora S R (Mathematics Dep, Delhi Univ, Keshav Mahavidyalaya, Delhi, Email: ritunarora@yahoo.in) : A cutting plane approach for multi-objective integer indefinite quadratic programming problem. Opsearch 2015, 52(2), 367-81.

In this paper, an algorithm is developed to solve a Multi-Objective Integer Indefinite Quadratic Programming Problem (IQMPP). The cutting plane technique finds all the non-dominated p-tuples of the (IQMPP) problem. Since the objective functions of (IQMPP) problem are quasi-monotone, the cutting plane truncates a portion of the feasible region and enables us to find all the non-dominated p-tuples at extreme points of the remaining feasible region. The algorithm is explained with the help of an example.

4 tables, 11 ref

012037   Amirthakodi M;Sivakumar B (School of Mathematics, Madurai Kamaraj Univ, Madurai, India, Email: amirthakodim@yahoo.com) : An invenory system with service facility and finite orbit size for feedback customers. Opsearch 2015, 52(2), 225-55.

In this article, we consider a continuous review inventory system with service facility consisting of finite waiting hall and a single server. The customers arrive according to a Poisson process and any arriving customer, who finds the waiting hall is full, is considered to be lost. The individual customer's unit demand is satisfied after a random time of service, which is assumed to be exponential distribution. After a customer is served, he/she will decide either to join the retrial group, which is of finite size, called orbit, for another service or leave the system according to a Bernoulli trial. The customers in the orbit, called feedback customers, compete for service according to classical retrial policy. The service times for these feedback customers are assumed to be independent and exponential distribution. The inventory is replenished according to an (s, S) inventory policy, and the replenishing times are assumed to be exponential. The joint probability distribution of the inventory level, the number of customers in the orbit, number of customers in the waiting hall and the status of the server is obtained in the steady state. Some important system performance measures in the steady state are derived, and the long-run total expected cost rate is also calculated. We have derived the Laplace-Stieljes transforms of waiting time distribution of both primary as well as the feedback customers. The sensitivity analysis has been carried out to examine the effect of different parameters and cost in the system.

7 illus, 2 tables, 24 ref

012036   Alp M;Davvaz B (Mathematics Dep, Nigde Univ, Nigde, Turkey, Email: muratalp@nigde.edu.tr) : Pullback and pushout crossed polymodules. Proc Math Sci 2015, 125(1), 11-20.

In this paper, authors introduce the concept of pullback and pushout crossed polymodules and we describe the construction of pullback and pushout crossed poly-modules. In particular, by using the notion of fundamental relation, we obtain a crossed module from a pullback crossed polymodule.

21 ref

012035   Aloui K (NO, Univ d' Aix-Marseille, Institut de Mathematiques de Marseille UMR 7373 CNRS, Campus de Luminy, Case 907, 13288 Marseille cedex 9, France, Email: karam.aloui@etu.univ-amu.fr) : On the order of magnitude of some arithmetical functions under digital constraint I. Proc Indian Acad Sci-Mathl Sci 2015, 125(4), 457-76.

Let q ≥ 2 be an integer and let S_q (n) denote the sum of the digits in base q of the positive integer n. We look for an estimate of the average of some multiplicative arithmetical functions under constraints on the arithmetical congruence of the integers and the sum of their digits.

11 ref

012034   Afrouzi G A;Ghaemi M B;Mir S (Mathematics Dep, Faculty of Mathematics Sciences, Mazandaran Univ, Babolsar, Iran, Email: mir@phd.pnu.ac.ir) : Three critical point theorem for non-smooth functionals with application in differential inclusions. Proc Indian Acad Sci-Mathl Sci 2015, 125(4), 521-35.

A variety of three-critical-point theorems have been established for non-smooth functionals, based on a minimax inequality. In this paper, a generalized form of a recent result due to Ricceri is introduced for non-smooth functionals and by a few hypotheses, without any minimax inequality, the existence of at least three critical points with a uniform bound on the norms of solutions, is obtained. Also, as an application, our main theorem is used to obtain at least three anti-periodic solutions for a second order differential inclusion.

18 ref

010981   Prabhakar M V;Bhate H (NO, College of Military Engineering, Pune-411 031, Email: hbhate@math.unipune.ac.in) : Commutation and darboux transformation. Pramana J Phys 2015, 85(5), 869-80.

In this paper we show that the Darboux transformation for a large class of nonlinear evolution equations arises due to factorization and commutation. The factorization and commutation has been pointed out earlier for Schrodinger operator. We show that it extends to a large class of nonlinear differential equations which admit Lax pairs including Boussinesq, Davey-Stewartson, Bogoyavlensky-Schiff and n-wave interaction equation.

14 ref

010980   Pankaj Kumar;Bhatia S S;Vijay Kumar (School of Mathematics and Computer Application, Thapar Univ, Patiala-147 001) : Generalized sequential convergence in fuzzy neighborhood spaces. Natn Acad Sci Lett 2015, 38(2), 161-4.

Present work deals with introducing and studying a generalized sequential convergence, namely statistical convergence in fuzzy neighborhood spaces. Some properties of statistical convergence on fuzzy neighborhood spaces are discussed.

17 ref

010979   Pan X (NO, Institute of Plant Quarantine, Chinese Academy of Inspection and Quarantine Beijing, 100029, China) : Reconstruct species-area theory using set theory. Natn Acad Sci Lett 2015, 38(2), 173-7.

Species-area theory (SAT) is an important research platform for ecology and biodiversity conservation. Traditionally, the SAT is described using the algebra method, without considering taxonomic characteristic differences between species. Here, we use the branch of mathematics known as set theory to reformulate the SAT, including the species-area relationship, endemic-area relationship, overlap-area relationship, and alpha, beta, and gamma diversity. Then fundamental equations are derived by this method: (1) the number of species in one area can be divided into two parts: species (endemic species) in only this area, and species (overlapping species) in both the focal and neighboring area. The total number of species in these two areas is equal to the sum of the number of species in one of the two areas and the number of species existing only in the other area. (2) A new definition of beta diversity is proposed to describe the overlapping species distribution among the local alpha diversity in the whole gamma diversity. Therefore, gamma diversity is the union of all alpha diversity or the union of all beta diversity.

15 ref

010978   Mayil Vaganan B;Emily Priya E (Applied Mathematics and Statistics Dep, School of Mathematics, Madurai Kamaraj Univ, Madurai-625 021, Email: vkbmv66@gmail.com) : Generalized cole-hopf transformations for generalized burgers equations. Pramana J Phys 2015, 85(5), 861-7.

Detailed review of the invention of Cole-Hopf transformations for the Burgers equation and all the subsequent works which include generalizations of the Burgers equation and the corresponding developments in Cole-Hopf transformations are documented.

21 ref

010977   Krzywkowski M;Venkatakrishnan Y B (Mathematics Dep, Johannesburg Univ, Johannesburg, South Africa) : Bipartite theory of graphs: outer-independent domination. Natn Acad Sci Lett 2015, 38(2), 169-72.

Let G=(V,E) be a bipartite graph with partite sets X and Y. Two vertices of X are X-adjacent if they have a common neighbor in Y, and they are X-independent otherwise. A subset D⊆X is an X-outer-independent dominating set of GG if every vertex of XD has an X-neighbor in D, and all vertices of XD are pairwise X-independent. The X-outer-independent domination number of G, denoted by γ_x^{oi(G), is the minimum cardinality of an X-outer-independent dominating set of G. We prove several properties and bounds on the number γ_Xoi(G).}

6 ref

010976   Krishna D V;Reddy T R (Mathematics Dep, GIT, GITAM Univ, Visakhapatnam-530 045) : Coeffient inequality for certain subclasses of analytic fuctions associated with Hankel determinant. Indian J pure appl Math 2015, 46(1), 91-106.

The objective of this paper is to obtain an upper bound to the functional | a₂a₄ - a₃^{2| for the function / and its inverse belonging to certain subclasses of analytic functions, using Toeplitz determinants.}

40 ref

010975   Kim D S;Kim T (Mathematics Dep, Sogang Univ, Seoul 121 742 Republic of Korea, Email: dskim@sogang.ac.kr) : Symmetry identities of q-bernoulli polynomials of the second kind. Indian J pure appl Math 2015, 46(1), 85-90.

In this paper, authors give identities of symmetry for the q-Bernoulli polynomials which are derived from the symmetric properties of the p-adic invariant integrals on Z_p.

17 ref

010974   Jiao Z;Li Q (School of Science, Hanzhou Dianzi Univ, Hangzhou, Zhejiang, 310018, P R China, Email: jzhenhua@163.com) : The liouville's theorem of harmonic functions on alexandrov spaces with nonnegative ricci curvature. Indian J pure appl Math 2015, 46(1), 51-8.

In this paper, the authors prove the Liouville's theorem for harmonic function on Alexandrov spaces by heat kernel approach, which extends the Liouville's theorem of harmonic function from Riemannian manifolds to Alexandrov spaces.

15 ref

010973   Ghorbel M;Farah M B (Laboratoire De Probabilites et Statistique, Faculte Des Sciences de Sfax, Univ de Sfaz, B P 802, 3018 Safax, Tunisia, Email: ghorbel@math.univ.paris13.fr) : Dirichlet partition on symmetric matrices. Indian J pure appl Math 2015, 46(1), 73-83.

In this work, author study the Dirichlet partition on symmetric matrices. For this, we give some main properties of the Dirichlet distribution. Next, the result of Huillet and Martinez (2003) which gives a remarkable representation of the mean expected value of many functionals of Dirichlet distributions in terms of the mean of independent gamma random variables will be extended on positive definite symmetric matrices.

14 ref

010972   Fujisawa Y (Graduate School of Mathematics, Nagoya Univ, Furocho, Chikusa-ku, Nagoya-464 8602, Email: fujisawa_gifu@yahoo.co.jp) : On sums of generalized Ramanujan sums. Indian J pure appl Math 2015, 46(1), 1-10.

Ramanujan sums have been studied and generalized by several authors. For example, Nowak [8] studied these sums over quadratic number fields, and Grytczuk [4] defined that on semigroups. In this note, we deduce some properties on sums of generalized Ramanujan sums and give examples on number fields. In particular, we have a relational expression between Ramanujan sums and residues of Dedekind zeta functions.

9 ref

010971   Dinesh Kumar;Sanjay Kumar (Mathematics Dep, Delhi Univ, Delhi-110 007, Email: dinukumar680@gmail.com) : The dynamics of semigroups of transcendental entire functions I. Indian J pure appl Math 2015, 46(1), 11-24.

Author consider the dynamics associated with an arbitrary semigroup of transcendental entire functions. Fatou-Julia theory is used to investigate the dynamics of these semigroups. Several results of the dynamics associated with iteration of a transcendental entire function have been extended to transcendental semigroup case. We also investigate the dynamics of conjugate semigroups, abelian transcendental semigroups and wandering and Baker domains of transcendental semigroups.

22 ref

010970   Caglar M;Orhan H (Mathematics Dep, Faculty of Science and Letters, Kafkas Univ, TR 36100 Kars, Turkey, Email: mcaglar25@gmail.com) : Sufficient condition for univalence and quasiconformal extensions. Indian J pure appl Math 2015, 46(1), 41-50.

In this paper, we obtain some sufficient conditions for the univalence. In particular, as special cases, our results imply certain known univalence criteria. Also, we refine the result to a quasi-conformal extension criterion with the help of Becker's method.

23 ref

010969   Behboodi M;Eskandari G B (Mathematical Science Dep, Isfahan Univ of Technology, P O Box 84156 83111, Isfahan, Iran, Email: mbehbood@cc.iut.ac.ir) : Local duo rings whose finitely generated modules are direct sums of cyclics. Indian J pure appl Math 2015, 46(1), 59-72.

In this paper, we give an answer to the following question of Kaplansky [14] in the local case: For which duo rings R is it true that every finitely generated left R-module can be decomposed as a direct sum of cyclic modules? More precisely, we prove that for a local duo ring R, the following are equivalent: (i) Every finitely generated left R-module is a direct sum of cyclic modules; (ii) Every 2-generated left. R-module is a direct sum of cyclic modules; (Hi) Every factor module of R^{R ⊕ R is a direct sum of cyclic modules; (iv) Every factor module of RR ⊕ R is serial; (v) Every finitely generated left. R-module is serial; (vi) R is uniserial and for every non-zero ideal I of R, R/I is a linearly compact left R-module; (vii) R is uniserial and every indecomposable injective left R-module is left uniserial; and, (viii) Every finitely generated right R-module is a direct sum of cyclic modules.}

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010968   Aksoyak F K;Yayli Y (Ahi Evran Univ, Elementary Mathematics Teacher Education, Kirsehir, Turkey, Email: ferdag.aksoyak@ahievran.edu.tr) : General rotational surfaces with pointwise 1-type gauss map in pseudo-euclidean space E₂<. Indian J pure appl Math 2015, 46(1), 107-18.

In this paper, we study general rotational surfaces in the 4- dimensional pseudo-Euclidean space E₂^{4 and obtain a characterization of flat general rotation surfaces with pointwise 1-type Gauss map in E₂4 and give an example of such surfaces.}

20 ref

010967   Abouelaz A;Daher R (Mathematics and Computer Science Dep, Hassan II of Casablanca Univ, Faculty of Science Ain Chock, Route d'El Jadida, Km 8, B P 5366, Maarif 20100 Casablanca, Morocco, Email: a.abouelaz@fsac.ac.ma) : Holomorphic extension of certain discrete functions on Z<. Indian J pure appl Math 2015, 46(1), 25-40.

In this paper, authors construct an holomorphic extension of certain functions on Z^{n. We deduce a discrete Gutzmer's formula for the discrete Fourier transform (see Theorem 4.4). In addition, we prove the Hardy-Littlewood inequality for the classical Radon transform on Rn (see Theorem 4.7). In this work, we use the techniques of the diophantine integral geometry and the estimate method in certain weighted L2- spaces.}

9 ref

009982   Upadhyay S K;Tripathi A (Applied Mathematics Dep, Indian Institute of Technology, Banaras Hindu University, Varanasi-221 005, Email: sk-upadhyay2001@yahoo.com) : Calderon's reproducing formula for Watson wavelet transform. Indian J pure appl Math 2015, 45(3), 269-77.

In this paper the inverse Watson wavelet transform is investigated, the Calderon reproducing formula of Watson convolution is obtained by generalizing the results of [6]. Some applications associated with Calderon's reproducing formula of Watson convolution are given.

13 ref

009981   Titus P;Iyappan K (NO, University College of Engineering Nagercoil, Anna University, Tirunelveli Region, Nagercoil-629 004, Email: titusvino@yahoo.com) : Forcing vertex monophonic number of a graph. Int J mathl Combinatorics 2015, 1, 86-95.

For any vertex x in a connected graph G of order p ≥ 2, a set S_x ⊆ V (G) is an x-monophonic set of G if each vertex v ∈ V (G) lies on an x - y monophonic path for some element y in S_x. The minimum cardinality of an x-monophonic set of G is the x-monophonic number of G and is denoted by m_x(G). A subset T_x of a minimum x-monophonic set S_x of G is an x-forcing subset for S_x if S_x is the unique minimum x-monophonic set containing T_x. An x-forcing subset for S_x of minimum cardinality is a minimum x-forcing subset of S_x. The forcing x-monophonic number of S_x, denoted by fm_x (S_x), is the cardinality of a minimum x-forcing subset for S_x. The forcing x-monophonic number of G is fm_x (G) = min{fm_x (S_x)}, where the minimum is taken over all minimum x-monophonic sets S_x in G. We determine bounds for it and find the forcing vertex monophonic number for some special classes of graphs. It is shown that for any three positive integers a, b and c with 2 ≤ a ≤ b <60> c, there exists a connected graph G such that fm_x (G) = a, m_x(G) = b and cm_x(G) = c for some vertex x in G, where cm_x(G) is the connected x-monophonic number of G.

5 illus, 1 table, 13 ref

009980   Sun L;Wang W;Zhou J (NO, College of Science, Harbin Engineering University, Harbin-150 001, P R China, Email: zhoujiang04113112@163.com) : Laplacian spectral characterization of some graph join. Indian J pure appl Math 2015, 45(3), 279-86.

For two disjoint graphs G and H, the join of G and H, denoted by G ν H, is the graph obtained from G ∪ H by joining each vertex of G to each vertex of H. A graph is said to be DLS if there is no other non-isomorphic graph with the same Laplacian spectrum. For a connected DLS graph G with a cut vertex, we prove that G ν K _r is DLS, where K_r is a complete graph. For a disconnected DLS graph G with n ≥ 10 vertices and m ≤ n - 4 edges, we show that G ν (K _r - e) is DLS, where K_r - e is the graph obtained by deleting one edge of K _r . Applying these results we can obtain new DLS graphs.

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009979   Sugirtha P;Vasuki R;Venkateswari J (Mathematics Dep, Dr.Sivanthi Aditanar College of Engineering, Tiruchendur-628 215, Email: p.sugisamy28@gmail.com) : Skolem difference odd mean labeling of H-graphs. Int J mathl Combinatorics 2015, 1, 96-106.

Graph G with p vertices and q edges is said to have a skolem difference odd mean labeling if there exists an injective function ƒ : V (G) → {1, 2, 3, ..., 4q - 1} such that the induced map ƒ ^{* : E(G) → {1, 3, 5, ..., 2q - 1} defined by ƒ *(uv) = <91><157>ƒ(u)-<134>(v))<157>/2<93> is a bijection. A graph that admits skolem difference odd mean labeling is calle a skolem difference odd mean graph. In this paper, we investigate skolem difference odd mean labeling of some H-graphs.}

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009978   Sharma V;Manchanda P (Mathematics Dep, Guru Nanak Dev Univ, Amritsar-143 005, Email: vikramsharma6898@gmail.com) : Nonuniform wave packet frames in L<. Indian J ind appl Math 2015, 6(2), 139-52.

In this paper, we construct wave packet frames in L^{2 over a translation set A, which is not necessarily a group. We call it nonuniform wave packet frame. We present a necessary and sufficient condition for the wave packet system to be a frame for L2}

19 ref

009977   Senyurt S;Caliskan A (Faculty of Arts and Sciences, Mathematics Dep, Ordu University, 52100, Ordu/Turkey, Email: senyurtsuleyman@hotmail.com) : N<. Int J mathl Combinatorics 2015, 1, 1-13.

In this paper, when the unit Darboux vector of the partner curve of Mannheim curve are taken as the position vectors, the curvature and the torsion of Smarandache curve are calculated. These values are expressed depending upon the Mannheim curve. Besides, we illustrate example of our main results.

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009976   Senyurt S;Bilici M;Caliskan M (Mathematics Dep, Faculty of Arts and Sciences, Ordu University, 52100, Ordu/Turkey, Email: senyurtsuleyman@hotmail.com) : Some characterizations for the involute curves in dual space. Int J mathl Combinatorics 2015, 1, 113-25.

In this paper, we investigate some characterizations of involute - evolute curves in dual space. Then the relationships between dual Frenet frame and Darboux vectors of these curves are found.

1 illus, 13 ref