018425   Pandiaraja D;Nagendran N A;Chandrasekaran S; Aditya R P (National Centre of Excellence, Statistical and Mathematical Modelling on Bioresources Management (MHR, Madurai-625 009, Email: pandiaraja@gmail.com) : Graph theoretical modelling and analysis of fragile honey bee pollination network. Curr Sci 2014, 107(12), 1988-96.

Due to environmental stress honey bees frequently make foraging shifts. Encounter with any nonflowering agent during such shifts leads to colony collapse. To assess the impact of non-flowering agents in the pollination network, we have modelled the pollination network as polligraphs using graph theoretical tools. Based on the outcome of the model we have extracted a few new network parameters and characterized the stability of the pollination network.

10 illus, 40 ref

018424   Jain R;Sinha D (NO, Center for Mathematical Sciences, Banasthali Univ, Banasthali-304 022, Email: ruchikajain29@gmail.com) : Non linear stability of L₄ in the restricted three-body problem when the smaller primary is a finite straight segment under resonance cases. Invertis J Sci Technol 2014, 7(4), 215-34.

Studied the non-linear stability of the triangular libration point L₄ in the restricted three-body problem when the smaller primary is a finite straight segment of length 21 under the presence of third and fourth order resonances. It is well known that most of the asteroids are irregularly shaped elongated bodies. We have taken these elongated bodies as a finite straight segment. We have used Markeev's theorem (1978) [I] to examine the non-linear stability for resonance cases 2:1 and 3:1. We have found that the triangular equilibrium solutions are always unstable in the third and fourth order resonance cases for 0…|<60> 0.05. We hove applied the results to the following solar systems (i) Jupiter -9 Metis (ii) Jupiter - 22 Kalliope (Hi) Jupiter -216 Kleopatra (iv) Jupiter - 243 Ida (v) Jupiter - 433 Eros (vi) Jupiter - 951 Gaspra.

3 illus, 1 table, 25 ref

018423   Bahl S;Mehta B (Statistics Dep, MDU, Rohtak, Research Scholar, MDU, Rohtak, Email: bhawna0111@gmail.com) : Ratio and product type exponential estimators. Ann agric Res 2014, 35(4), 465-70.

This paper proposes new ratio and product type estimators for estimating the mean of finite population using information on the auxiliary variable. The Bias and the Mean Square error (M.S.E) of these estimators are calculated. These estimators are compared for their precision with usual mean per unit, ratio and product estimators and are found to be more efficient in many practical situations.

2 tables, 4 ref

017465   Singh N P;Upadhyay V;Agrawal A K;Gupta K (NO, , 236, Durga Nagar, Firozabad-283 203, Email: aksinghnpsingh@rediffmail.com) : Hydromagnetic radiative convection flow in a vertical channel with temperature dependent viscosity and viscous dissipation and heat generation/absorption. Ultra Scient phys Sci-Sect B 2014, 26(2), 159-73.

Fully developed radiative convection flow of an electrically conducting, incompressible viscous liquid in a long vertical channel consisting of two parallel impermeable plates is investigated. The flow exists under constant pressure gradient, temperature dependent viscosity, viscous dissipation and in the presence of transversely applied uniform magnetic field. To obtain the solutions of the coupled non-linear system of equations, the regular perturbation technique is used. The effects of different physical parameters on velocity field, temperature distribution, skin-friction and rate of heat transfer are numerically evaluated, presented graphically and discussed.

7 illus, 16 ref

017464   Singh K D;Garg B P;Bansal A K (NO, , Applied Mathematics, Wexlow Building, Lower Kaithu, Shimla-171 003, Email: kdsinghshimla@gmail.com) : Hall current effect on visco-elastic MHD oscillatory convective flow through a porous medium in a vertical channel with heat radiation. Proc Indian Natn Sci Acad 2014, 80(2), 333-43.

Hall current effect on visco-elastic MHD oscillatory convective flow through a porous medium in a vertical channel with heat radiation is investigated. An oscillatory MHD convection flow of visco-elastic, incompressible, electrically conducting fluid in a vertical channel filled with porous medium in the presence of Hall currents is studied analytically. A magnetic field of uniform strength is applied in the direction normal to the planes of the plates. The temperature of one of the plates varies periodically and the temperature difference of the plates is high enough to induce heat transfer due to radiation. A closed form solution of the problem is obtained. The effects of various parameters on the velocity profiles, the skinfriction in terms of the amplitude and the phase angle are shown graphically and discussed in detail.

12 illus, 1 table, 29 ref

017463   Prakash J;Bala R;Vaid K (Mathematics and Statistics Dep, Himachal Pradesh Univ, Shimla-171 005, Email: jpsmaths67@gmail.com) : On the characterization of nonoscillatory motions in magnetorotatory triply diffusive convection. Proc Indian Natn Sci Acad 2014, 80(2), 197-209.

^iia23 ref

017462   Nellai Murugan A;Victor Emmanuel G (Mathematics Dep, V.O. Chidambaram College, Thoothukudi-628 008, Email: anellai.vocc@gmail.com) : Complete n- domination number of union of n copies of certain edge deleted subgraphs. Ultra Scient phys Sci-Sect B 2014, 26(2), 123-32.

The concept of complete graphs with real life application was introduced. A. Nellai Murugan et. al., was introduced the concept of complete dominating number of a graph. In this paper, We introduce a new domination parameter called complete n-domination number of the union of n copies of certain edge deleted subgraphs of K₄ with edges in common. That is n images of complete graphs with edges in common. A subset S of V of a non trivial graph G is called a dominating set of G if every vertex in V-S is adjacent to at least one vertex in S. The domination number γ(G) of G is the minimum cardinality taken over all dominating set in G. A subset S of V of a nontrivial graph G is said to be complete dominating set, If Choose v∈ V(G) and put S ={v}; For every v we have N_G(S) = V- S denoted by S' is the complete dominating set. The minimum cardinality taken over all complete dominating set is called the complete domination number and is denoted by γ_n(G)^{14. A subset S of V of a nontrivial graph G is said to be complete n-domination number if every vertex in V is dominated by exactly n vertices of S and complete. The minimum cardinality of a complete n-dominating set is the complete n-domination number of G is denoted by nγ_n(G). We determine this number for some standard graphs and obtain bounds for general graphs. Its relationship with other graph theoretical parameters are also investigated.}

6 illus, 18 ref

017461   Murty M N (Physics Dep, National Institute of Science and Technology, Palur Hills, Berhampur-761 008) : Recursive implementation of type-IV discrete cosine transform using type-II discrete sine transform. Ultra Scient phys Sci-Sect B 2014, 26(2), 133-8.

This paper presents a novel recursive algorithm for implementation of type-IV discrete cosine transform (DCT-IV) of any general length using type-II discrete sine transform (DST-II). The recursive algorithms apply to arbitrary length algorithms and are suitable for VLSI implementation.

1 illus, 17 ref

017460   Maity B (NO, Pingla Thana Mahavidyalaya, Maligram, Paschim Medinipur, West Bengal-721 140, Email: barunmaity1986@gmail.com) : Technology in mathematics education presentation of materail developed for first year calculus topics-formal definition of limit. Int J Geosci Technol 2014, 2(2), 38-44.

Set of interactive class notes and a library of computer demonstration designed to be used in and out of material developed for first year calculus classroom are presented. The maximum area of this are explained by the modern technology. The demonstration are coded in Maple and designed to give geometric understanding to challenging calculus concepts. The interactive notes were first implemented in the fall 2010 semester, in a class of approximately 600 students were designed to be used during 34 one hour classes. Also the notes were 60%-80% complete with the remaining to be filled in by students in class and were fully executable, meaning that every problem could be answered using the software. The class materials are all developed in Maple and available on the CD provided. lt is important to note that the discussion in this paper only give some suggestions on the use of these programs and that if instructors choose to utilize these tools, they will likely find other uses the better fit their own teaching style and course to maximize the potential benefit. This Paper will give insight info the uses and benefits of computer- aided instruction (CAT) in a mathematics classroom.

4 illus, 16 ref

017459   Maity B (Mathematics Dep, Pigla Thana Mahavidyalaya, Maligram, Paschim Medinipur, West Bengal-721 140, Email: barunmaity1986@gmail.com) : Technology in mathematics education implementation and assessment analysis of data of winter 2010 data. Int J Aquatic Sci Technol 2014, 2(2), 22-31.

Use of technology has become highly popular in mathematics education. Instructors have implemented technology into classroom lessons, as well as various applications outside of class room. The data analysis of the online quizzes focuses on two years of five year study.Linear regression techniques are employed to investigate the relationship between find exam grades and both how a student interacts with and performs on the outline quizzes. The testing system was utilized to provide students with regular formative quizzes. Based on techniques learned through the literature search, the data analysis focuses on how students interact with the testing system students interact with the testing system and not necessarily just their performance on the online quizzes. The availability of information such as the number of times a student attempted each quiz and the date on which the student first attempted each quiz allows our data analysis to test the effect of how the student interacts with the system in ways not found in the literature. Student attitude towards the online testing is assessed through survey results.

6 illus, 4 tables, 16 ref

017458   Humad V;Shrimali S (NO, Mewar Univ, Chittorgarh, Rajasthan) : LRS bianchi type - V string dust cosmological model in general relativity. Ultra Scient phys Sci-Sect B 2014, 26(2), 149-52.

Authors have investigated LRS Bianchi Type - V cosmological model with string dust as the source of gravitational field. For the complete determination of the model, we assume that rest energy density (ξ) is equal to the string tension density (λ). Some physical and geometrical features of the model are also discussed.

21 ref

017457   Humad V;Shrimali S (NO, Mewar Univ, Chittorgarh, Rajasthan) : Bianchi type - I string cosmological models with bulk viscous fluid in general relativity. Ultra Scient phys Sci-Sect B 2014, 26(2), 139-42.

Authors have investigated Bianchi Type - I string cosmological model with Bulk Viscous fluid in general relativity. To obtain a determinate model of the universe, we assumed that (i) 3ξθ = p, where ξ is the coefficient of bulk viscosity, 6 is the scalar of expansion and p is the energy density (ii) relation between metric potential B = A^{n. Some physical properties of the model are also discussed.}

17 ref

017456   Gupta B K;Aloney M R (Mathematics Dep, Bhagwant Univ, Ajmer, Rajasthan) : Quasi-pure W-projective modules and dimension. Ultra Scient phys Sci-Sect B 2014, 26(2), 117-22.

In this paper, we generalize the notion of projective, injective and flat modules and dimension. Hence, we introduce and study the notion of Quasi-pure W-projective modules and dimension.

11 ref

017455   Ellulu M (Nutrition and Dietetics Dep, Faculty of Medicine and Health Sciences, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia, Email: mohdsubhilulu@gmail.com) : Use of statistical agreement to run logistic regression. Hlth Agenda 2015, 3(1), 27-9.

Objective: To run logistic regression after merging two variables of raters depending on percent of agreement. Percent of agreement identifies quantitative expression of observer variation between two raters. Correct identification of abnormal and normal subjects depends on terms of sensitivity and specificity. Merging of two variables to have one variable is a crucial step to identify the only diseased/abnormal subjects by two raters. Thereby, logistic regression takes place to evaluate whether risk factors are associated with a defined condition. Using of statistical agreement to run logistic regression can help researchers to assess strong risk factors for one disease diagnosed and agreement by two raters for the same subjects by one step.

1 illus, 2 tables, 4 ref

017454   Elangovan R;Ramajayam R (Statistics Dep, Annamalai Univ, Annamalai Nagar-608 002, Email: srelangovan@rediffmail.com ) : Estimation of HIV infectivity through two modes of transmission. Ultra Scient phys Sci-Sect B 2014, 26(2), 103-16.

It is now known that the immunodeficiency virus (HIV) can be transmitted through a variety of contact mechanisms that include homosexual intercourse, heterosexual intercourse and needle sharing among intravenous drug abusers. The level of infectivity plays a major role in applying epidemic models to project the spread of the virus and in evaluating various intervention strategies. As a retrovirus HIV shows application error rate and leads to the creation of distinct viral genomes with different immunological properties. This character of HIV is called antigenic diversity. Every contact contributes to the transmission of some HIV which in turn contributes of the increase of antigenic diversity. Total damage crosses the threshold of any one transmission then the HIV infected person reaches the threshold level. Most of the behavior in the stochastic model for the expected time strongly depends on initial conditions. In this paper the expected time and variance of the estimated threshold level through two modes of transmission using three parameter Generalized Rayleigh Distribution has been derived. The analytical results are substantiated with suitable numerical illustrations.

4 illus, 4 tables, 8 ref

017453   Dhal D R;Mishra P K (Mathematics Dep, ITER, SOA, BBSR, Odisha) : Level crossings of a random trigonometric polynomial. Int J latest Technol Engng Mgmt appl Sci 2015, 4(2), 131-3.

Theorem 1. Let EN (T, Φ', Φ") denote the average number of real roots of the random trigonometric polynomial T =T_n(θ, ω) = ^{nΣ_k=1a_k ωcoskθin the interval (T, Φ', Φ") . Clearly, T can have at most 2n zeros in the interval (0, 2π). Assuming a_k(w)s to be mutually independent and identically distributed normal random variables. Dunnage has shown that in the interval 0 ≤θ≤2 π) all save a certain exceptional set of the functions . (T_n(<113w) have (2n/√3)+O{n11/13(log n)3/13>} zeros when n is large. We consider the same family of trigonometric polynomials and use the Kac-Rice formula for the exception of the number of real roots and obtain that EN(T;0,2π) <126> 2n/√6 + 0(log n). The result is better than that of Dunnage since our constants is (1/√2) times his constant and our error term is smaller. The proof is base on the convergence of an integral of which an asymptotic estimation is obtained.}

4 ref

016460   Suman Kumari;Kamini Kumar (Botany University Dep, Ranchi Univ, Ranchi, Jharkhand) : D<. Adv Pl Sci 2014, 27(2), 493-6.

D^{2 analysis among five species and varieties was studied with the help of karyotype analysis. The genotypes were grouped into three clusters based on D2 values. Clustering pattern indicated that the genetic diversity was due to genetic distance. The inter and intracluster constellation distance represent the index of genetic diversity among the constellations. The intra cluster distance between the constellation were 100.5, 0.00 and 0.00 respectivily. The inter-cluster distance between CI-CII, CII-CIII and CI-CIII was 29.32, 35.41 and 18.32 respectivily. Highest D2- value between the CII-CIII suggests that the genotype belonging to this constellation might be useful in a breeding programme for getting good and desirable segregants.}

1 illus, 1 table, 7 ref

016459   Singh N P;Rajput J S (Mathematics Dep, CL Jain (PG) College, Firozabad-283 203, Email: jsraput2684@gmail.com) : Combined effect of radiation, rotation and hall current on heat and mass transfer flow past an accelerated porous plate with suction/injection and internal heat generation/absorption. Ultra Scient phys Sci-Sect A 2014, 26(2), 159-72.

Combined effect of Hall current, rotation and radiation on unsteady heat and mass transfer flow of a viscous, electrically conducting, incompressible fluid past an accelerated porous plate is investigated analytically. The plate is subjected to suction and injection. The fluid is gray, absorbing-emitting but non-scattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The non-dimensional equations governing the flow are solved by the use of Laplace transform technique. Numerical computations for effects of different parameters on the velocity, the temperature, the concentration field, the skin-friction, the Nusselt number and the Sherwood number are obtained, shown graphically or presented in tabular form followed by detailed discussion.

10 illus, 2 tables, 35 ref

016458   Saxena K;Anita (NO, Govt. Motilal Vigyan Mahavidyalaya, Bhopal) : Study of the product summability (γ,r) (C,1) to derived fourier series. Ultra Scient phys Sci-Sect A 2014, 26(2), 131-40.

The object of the present note is to extend the theorems of Sachan (E,q) (C,1) summability, qγO of derived Fourier series.

7 ref

016457   Samanta K P;Samanta B (Mathematics Dep, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711 103, Email: bijoysamanta@yahoo.com) : On mixed trilateral generating relations for biorthogonal polynomials suggested by the Laguerre polynomials. Ultra Scient phys Sci-Sect A 2014, 26(2), 185-90.

In this note, authors have obtained some novel results on mixed trilateral generating relations involving the polynomials, Y_n+r^{a-nk (x; k) a modified form of Konhauser biorthogonal polynomials, Y_nn (x; k) by group theoretic method. As special cases, we have obtained the corresponding results on generalized Laguerre polynomials. Some applications of our results are also discussed.}

7 ref

016456   Sahoo L;Mahanti M (NO, Gopobandhu Science College, Athgarh, Cuttack, Odisha-754 029, Email: lokanath.math@gmail.com ) : Average number of points of inflection of a random sum of orthogonal polynomials. Ultra Scient phys Sci-Sect A 2014, 26(2), 173-84.

Let y = Σ^{n_k=o Y_k (t)ψ_k (t) be a random polynomial such that (Y₀(w), Y₁(w), Y_N(w)) is a sequence of mutually independent normally distributed random variables with mean zero and variance one; be a sequence of normalized Jacobi polynomials, orthogonal with respect to the interval (-1,1). It is proved that the average number of points of inflection of the random equation y=0 is asymptotic to √(5/7)n.}

12 ref

016455   Masuti S K;Verma J K (NO, The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai-600 113, Email: shreedevikm@imsc.res.in) : Two notes on normal hilbert polynomial of two ideals. Proc Indian Natn Sci Acad 2014, 80(3), 589-95.

6 ref

016454   Garg M (Mathematics Dep, Nehru (P.G.) College, Chhibramau, Kannauj, Uttar Pradesh, Email: garg_manoj1972@yahoo.co.in) : On Quasi **g-open and Quasi **g-closed functions. Ultra Scient phys Sci-Sect A 2014, 26(2), 154-8.

In this paper, we introduce a new type of open function namely quasi **g-open function. Further we obtain its characterizations and its basic properties.

5 ref

016453   Ganapathy Raman R (Mathematics Dep, Pachaiyappa's College, Chennai) : Circular chromatic number of some products. Ultra Scient phys Sci-Sect A 2014, 26(2), 115-18.

Of interest in this theory is the question of determining the circular chromatic number of product graphs. There are four kinds of graph products: (i) Cartesian Product (G x H), (ii) Direct Product (GxH), (iii) Lexicographic Product (G. H) and (iv) Strong product (G x H).

9 ref

016452   Dorsett C (NO, Texas A&M Univ-Commerce, Texas, (USA)) : Open set and closed set subspaces and the T₁ separation axiom. Ultra Scient phys Sci-Sect A 2014, 26(2), 119-22.

Within this paper, questions concerning open set and closed set subspaces of T₁ spaces are investigated and resolved.

2 ref

016451   Das R K;Sah M (Mathematics Post Graduate Dep, S.K.M. Univ, Dumka, Jharkhand) : Role of fuzzy stacks on extended topology. Ultra Scient phys Sci-Sect A 2014, 26(2), 149-53.

The paper is addressed to the introduction of some fuzzy stacks as to how they play an important role on extended fuzzy topology and its results.

7 ref

016450   Chugh R;Rekha Rani;Sanjay Kumar (Mathematics Dep, Maharshi Dayanand Univ, Rohtak-124 001, Email: rekhadalal93@gmail.com) : Weak convergence theorem for nonexpansive and monotone, lipschitz continuous mappings. Proc Indian Natn Sci Acad 2014, 80(3), 583-8.

In this paper, authors shall prove a weak convergence theorem for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for a monotone, Lipschitz continuous mapping. With the help of a numerical example, we shall show the existence of a fixed point and find a solution of a variational inequality problem using C++. Further, we consider the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of a monotone, Lipschitz continuous mapping.

1 table, 12 ref

016449   Chandra S;Saajan Kumar (Mathematics Dep, S.M. Post-Graduate College, Chandausi-244 412) : On generalized norlung summability factors of infinite series. Ultra Scient phys Sci-Sect A 2014, 26(2), 141-8.

In this paper author have proved a theorem on generalized Norlund summability Factors of infinite series, which generalizes various known results.

8 ref

015451   Jawad A J M;Mirzazadeh M;Biswas A (Computer Engineering Technique Dep, Al-Rafidain Univ, College, Baghdad, Iraq, Email: mirzazadehs2@guilan.ac.ir) : Solitary wave solutions to nonlinear evolution equations in mathematical physics. Pramana J Phys 2014, 83(4), 457-71.

This paper obtains solitons as well as other solutions to a few nonlinear evolution equations that appear in various areas of mathematical physics. The two analytical integrators that are applied to extract solutions are tan-cot method and functional variable approaches. The soliton solutions can be used in the further study of shallow water waves in (1+1) as well as (2+1) dimensions.

25 ref

014532   Zhao X;Liu C (NO, School of Science, Jiangnan Univ, Wuxi-214 122, Email: zxp032@gmail.com) : Time periodic solution of a 2D fourth order nonlinear parabolic equation. Proc Indian Acad Sci-Mathl Sci 2014, 124(3), 349-64.

By using the Galerkin method, authors study the the existence and uniqueness of time-periodic generalized solutions and time-periodic classical solutions to a fourth-order nonlinear parabolic equation in 2D case.

21 ref

014531   Wu B Y (Mathematics Dep, Minjiang Univ, Fuzhou, Fujiang-350 121, Email: 569405943@qq.com) : Growth of fundamental group for Finsler manifolds with integral Ricci curvature bound. Proc Indian Acad Sci-Mathl Sci 2014, 124(3), 411-17.

An upper bound on the growth of fundamental group for a class of Finsler manifolds with integral Ricci curvature bound is given. This generalizes the corresponding results with pointwise Ricci curvature in literature.

16 ref

014530   Tugores F;Tugores L (Mathematics Dep, Universidade de Vigo, 32004 Ourense, Spain, Email: ftugores@uvigo.es) : Interpolation for a subclass of H<. Proc Indian Acad Sci-Mathl Sci 2014, 124(3), 343-8.

Introduce and characterize two types of interpolating sequences in the unit disc D of the complex plane for the class of all functions being the product of two analytic functions in D, one bounded and another regular up to the boundary of D, concretely in the Lipschitz class, and at least one of them vanishing at some point of D.

5 ref

014529   Shah H M (NO, Harish Chandra Research Institute, Chhatnag Road, Jhusi-211 019, Email: hemangimshah@hri.res.in) : New proof of the theorem: harmonic manifolds with minimal horospheres are flat. Proc Indian Acad Sci-Mathl Sci 2014, 124(3), 419-25.

In this note authors reprove the known theorem: Harmonic manifolds with minimal horospheres are flat. It turns out that our proof is simpler and more direct than the original one. We also reprove the theorem: Ricci flat harmonic manifolds are flat, which is generally affirmed by appealing to Cheeger-Gromov splitting theorem. We also confirm that if a harmonic manifold M has same volume density function as R^{n, then M is flat.}

6 ref

014528   Qi F;BoYan X (College of Mathematics, Inner Mongolia Univ for Nationalities, Tonliao City, Inner Mongolia Autonomous Region-028 043, Email: qifeng618@hotmail.com) : Some Hermite Hadamard type inequalities for geometrically quasi-convex functions. Proc Indian Acad Sci-Mathl Sci 2014, 124(3), 333-42.

In the paper, we introduce a new concept 'geometrically quasi-convex function' and establish some Hermite-Hadamard type inequalities for functions whose derivatives are of geometric quasi-convexity.

26 ref

014527   Ocak F;Salimov A A (Mathematics Dep, Faculty of Sciences, Karadeniz Technical Univ, 61080 Travzon, Turkey, Email: filiz_math@hotmail.com) : Geometry of the cotangent bundle with Sasakian metrics and its applications. Proc Indian Acad Sci-Mathl Sci 2014, 124(3), 427-36.

Main aim of this paper is to study paraholomorpic Sasakian metric and Killing vector field with respect to the Sasakian metric in the cotangent bundle.

16 ref

014526   Nikseresht A;Sepasdar Z;Shirdareh Haghighi M H (Mathematics Dep, College of Science Shiraz Univ, 71457-44776, Shiraz, Iran, Email: ashkan_nikseresht@yahoo.com) : Kirchhoff index of graphs and some graph operations. Proc Indian Acad Sci-Mathl Sci 2014, 124(3), 281-9.

Let T be a rooted tree, G a connected graph, x, y ∈ V(G) be fixed and G_i's be |V(T)| disjoint copies of G with x_i and y_i denoting the corresponding copies of x and y in G_i, respectively. We define the T-repetition of G to be the graph obtained by joining y_i to x_j for each i ∈ V(T) and each child 7 of i. In this paper, we compute the Kirchhoff index of the T-repetition of G in terms of parameters of T and G. Also we study how Kf(G) behaves under some graph operations such as joining vertices or subdividing edges.

3 illus, 9 ref

014525   Mushtaq Q;Yousaf A (Mathematics Dep, Quaid-e-Azam Univ 45320, Islamabad-144 000, Email: pir_qmushtaq@yahoo.com ) : Diagrams for certain quotients of PSL (2,Z[i]). Proc Indian Acad Sci-Mathl Sci 2014, 124(3), 291-9.

Actions of the Picard group PSL(2, Z[i]) on PL(F_p), where p ≡ 1 (mod 4), are investigated through diagrams. Each diagram is composed of fragments of three types. A technique is developed to count the number of fragments which frequently occur in the diagrams for the action of the Picard group on PL(F_p). The conditions of existence of fixed points of the transformations are evolved. It is further proved that the action of the Picard group on PL(F_p) is transitive. A code in Mathematica is developed to perform the calculation.

11 ref

014524   Mial Y;Xu W;Chen S;Adler A (NO, College of Mathematics and Information Science, Henan Normal Univ, Henan Province-453 007, Email: yumiao728@gmail.com) : Some limit theorems for negatively associated random variables. Proc Indian Acad Sci-Mathl Sci 2014, 124(3), 447-56.

Let {X_n, n ≥ 1} be a sequence of negatively associated random variables. The aim of this paper is to establish some limit theorems of negatively associated sequence, which include the L^{p-convergence theorem and Marcinkiewicz-Zygmund strong law of large numbers. Furthermore, we consider the strong law of sums of order statistics, which are sampled from negatively associated random variables.}

11 ref

014523   Maity S (Mathematics Dep, Indian Institute of Science, Bangalore-560 012, Email: somamaity@math.iisc.ernet.in) : On the stability of the L<. Proc Indian Acad Sci-Mathl Sci 2014, 124(3), 383-409.

Considered the Riemannian functional R_p(g) = ∫_M|R(g)|^{p dv_g defined on the space of Riemannian metrics with unit volume on a closed smooth manifold M where R(g) and dv_g denote the corresponding Riemannian curvature tensor and volume form and p ∈ (0, ∞). First we prove that the Riemannian metrics with non-zero constant sectional curvature are strictly stable for R_p for certain values of p. Then we conclude that they are strict local minimizers for R_p for those values of p. Finally generalizing this result we prove that product of space forms of same type and dimension are strict local minimizer for R_p for certain values of p.}

9 ref

014522   Li H (College of Arts and Science, Shanghai Maritime Univ, Shanghai-201 306, Email: lihongxia_2002@163.com) : Periodic diffeomorphisms on homotopy E(4) surfaces. Proc Indian Acad Sci-Mathl Sci 2014, 124(3), 437-45.

In this paper, we study the periodic diffeomorphisms on homotopy E(4) surfaces. Under some conditions, we prove the non-existence of periodic diffeomorphisms of odd prime order that act trivially on the cohomology of elliptic surfaces E (4). Besides, we give an application of our main theorem.

1 table, 13 ref

014521   Keskin R;Siar Z (NO, Sakarya Univ, Merkezi, 54180 Sakarya, Turkey, Email: rkeskin@sakarya.edu.tr) : Positive integer solution of the diophantine equation x₂-L_nxy + (-1)<. Proc Indian Acad Sci-Mathl Sci 2014, 124(3), 301-3.

Consider the equation x^{2 - L_nxy + (-1)ny2 = ±5r and determine the values of n for which the equation has positive integer solutions x and y. Moreover, we give all positive integer solutions of the equation x2 - L_nxy + (-1)ny2 = ±5r when the equation has positive integer solutions.}

8 ref

014520   Karandikar R;Rao B V (NO, Chennai Mathematical Institute, H1, SIPCOT IT Park, Siruseri-603 103, Email: rlk@cmi.ac.in) : On quadratic variation of martingales. Proc Indian Acad Sci-Mathl Sci 2014, 124(3), 457-69.

Authors give a construction of an explicit mapping Ψ: D([0, ∞), R) → D([0, ∞), R), where D([0, ∞), R) denotes the class of real valued r.c.1.1. functions on [0, ∞) such that for a locally square integrable martingale (M_t) with r.c.1.1. paths, gives the quadratic variation process (written usually as [M, M]_t) of (M_t). We also show that this process (At) is the unique increasing process (B_t) such that M_t^{2 - B_t is a local martingale, B0 = 0 and P((ΔB)_t = [(ΔM)_t]2, 0 <60> t <60> ∞) = 1. Apart from elementary properties of martingales, the only result used is the Doob's maximal inequality. This result can be the starting point of the development of the stochastic integral with respect to r.c.1.1. martingales.}

11 ref

014519   Gurjar S;Nitsure N (NO, School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400 005, Email: sgurjar@math.tifr.res.in) : Schematic Harder Narasimhan stratification for families of principal bundles and a modules. Proc Indian Acad Sci-Mathl Sci 2014, 124(3), 315-32.

Let G be a reductive algebraic group over a field k of characteristic zero, let X → S be a smooth projective family of curves over k, and let E be a principal G bundle on X. The main result of this note is that for each Harder-Narasimhan type τ there exists a locally closed subscheme S^{τ (E) of S which satisfies the following universal property. If ƒ : T → S is any base-change, then ƒ factors via Sτ (E) if and only if the pullback family ƒ*E admits a relative canonical reduction of Harder-Narasimhan type τ. As a consequence, all principal bundles of a fixed Harder-Narasimhan type form an Artin stack. We also show the existence of a schematic Harder-Narasimhan stratification for flat families of pure sheaves of A-modules (in the sense of Simpson) in arbitrary dimensions and in mixed characteristic, generalizing the result for sheaves of O-modules proved earlier by Nitsure. This again has the implication that A-modules of a fixed Harder-Narasimhan type form an Artin stack.}

12 ref

014518   Chung J;Hunt H;Perkins A;Sahoo P K (Mathematics Dep, Kunsan National Univ, Kunsan-573 701, Email: jychung@kunsan.ac.kr) : Stability of a simple levi civita functional equation on non unital commutative semigroups. Proc Indian Acad Sci-Mathl Sci 2014, 124(3), 365-81.

In this paper, authors study the Hyers-Ulam stability of a simple Levi-Civita functional equation ƒ(x + y) = ƒ(x)h(y) + ƒ(y) and its pexiderization ƒ(x + y) = g (x) h (y) + k (y) on non-unital commutative semigroups by investigating the functional inequalities |ƒ(x + y) - ƒ(x)h(y) - ƒ(y)| ≤ ∈ and |ƒ(x+y) - g(x)h(y) - k(y)| ≤ ∈, respectively. We also study the bounded solutions of the simple Levi-Civita functional inequality.

15 ref

013501   Surender Kumar;Goel P (NO, JJT Univ, Jhunjhunu, Rajasthan, Email: surendergarg26004@gmail.com) : Availability analysis of two different units system with a standby having imperfect switch over device in banking industry. Arya Bhatta J Math Inf 2014, 6(2), 299-304.

The availability analysis of a banking industry with two unit redundant system having imperfect switch using Regenerative point Graphical Technique (RPGT) is discussed. Initially two non identical units are operative and one unit if kept as standby. The standby put online with the help of an imperfect switch. The failure and repair rates are taken as exponential and system is discussed with the help of tables.

1 illus, 4 tables, 7 ref

013500   Singh T P;Tyagi A (Mathematics Dep, Yamuna Instt. of Engg. & Tech., Gadholi-Yamuna Nagar) : Cost analysis of a queue system with impatient customers. Arya Bhatta J Math Inf 2014, 6(2), 309-12.

The paper deals the cost analysis of M/M/1/N queuing system with impatient customers. We assume that the arriving customers balk with some probability and reneging follow negative exponential distribution. The Markov process techniques have been applied to develop the steady state probability. Matrix form solution is given along with some performance measures. A cost model has been developed to find the optimal service rate. To demonstrate the use of the model, different parametric values have been specified and lucid illustration has been presented with the help of table and graphs.

2 tables, 11 ref

013499   Shrivastava R;Mishra P P (Mathematics Dep, Govt. Indira Gandhi Home Science Girls College, Shahdol, Madhya Pradesh, Email: workshopshahdol@yahoo.com) : Application of product of chebyshev hermite polynomials, I- function and M- series in heat conduction. Asian J Adv Basic Sci 2014, 3(1), 74-7.

As an example of the application of I-function in applied mathematics, in this paper first author establish two integrals involving the product of I-function, M-series and Chebyshev Hermite polynomials and then we make its application to solve a boundary value problem on heat conduction.

9 ref

013498   Shikha D;Hari Kishan;Megha Rani (Mathematics Dep, D.N. College, Meerut) : Ordering policy for items with variable deterioration under trade credit and time discounting. Arya Bhatta J Math Inf 2014, 6(2), 275-82.

An inventory model has been developed for deteriorating items under the assumptions of trade credit and time discounting. The deterioration rate has been considered as linear function of time, i.e. θt. The demand rate has been considered as linear function of time. Shortages are not allowed.

1 illus, 16 ref

013497   Sharma S;Miglani E S;Singh T P (CSE, Hindustan Institute of Tech. & Management, Dheen, Ambala, Email: sachinsharma.one@gmail.com) : Effect of total disk access time using zoned-bit recording technology by placing more frequently used data at outer zone. Arya Bhatta J Math Inf 2014, 6(2), 357-64.

In the present communication, we have explored new mechanism to place most frequently used data at outer zone of tracks over hard disk. The effect on transfer time has been observed using Zoned-Bit Recording Technology An attempt has been made to minimize the seek time through scheduling techniques on track requests. Our efforts have shown that transfer time gets reduced with reasonable difference on applying this technique.

2 illus, 4 tables, 18 ref

013496   Sharma P R;Shukla S (Mathematics Dep, Rajasthan Univ, Jaipur, Email: shailjpr@yahoo.com) : Advance technique for solving assignment problems. Asian J expl Sci 2013, 27(2), 57-71.

Assignment problem is a typical combinatorial optimization problem. Classical Assignment Problem (AP) is a well-known topic world-wide. In this problem G_IJ denotes the cost for assigning the jth job to the ith person. This cost is usually deterministic in nature. But in realistic situations, it may not be practicable to know the precise values of these costs. We consider many classical problems from location theory which may serve as theoretical models for several logistic problems such that some linear or quadratic function attains its minimum. It turns out that linear objective function yields a linear assignment problem, which can be solved easily by several primal-dual methods like Hungarian method, Shortest augmenting path method etc. Aim of the paper is to investigate a new approach to solve assignment problems of different types. This method proposes momentous advantages over similar methods.

11 illus, 1 table, 7 ref