020310   Koshy T (NO, Framingham State Univ, Framingham, MA 01701-9101, USA, Email: tkoshy@framingham.edu) : Catalan identities revisited. J Indian Acad Math 2015, 37(1), 137-42.

The ubiquitous Catalan numbers have been studied for over two centuries. This article develops some interesting Catalan identities and extracts from one of them a formula discovered by C. Rousseau in 2010.

12 ref

020309   Kim Y K;Min W K (Mathematics Dep, Myiongji Univ, Youngin 449-728, Korea, Email: ykkim@mju.ac.kr) : On weak structures and w-Spaces. Far East J mathl Sci 2015, 97(5), 549-62.

We introduce the notions of weak structures and w-spaces, and study basic properties for them. We also introduce the notions of W-continuity, W -continuity and W-compactness on w-spaces, and investigate characterizations of such notions.

15 ref

020308   Kim C B (Mathematics Dep, Kookmin Univ, Seoul-136 702, South Korea, Email: cbkim@kookmin.ac.kr) : Fuzzy linear maps over the fuzzy space of linear maps. Far East J mathl Sci 2015, 97(8), 969-89.

In this paper, we study various properties of linear maps over the module of linear maps. Also we investigate a fuzzy R-module and a fuzzy linear map, and we obtain some exact sequences relative to them.

10 ref

020307   Kihcman A;Algabishi G O;Bichi S L (Mathematics Dep, Faculty of Science, Univ Putra Malaysia (UPM)-43400 UPM, Serdang, Selangor, Malaysia) : On classifications of non-constant linear second order PDEs and double convolution product. Far East J mathl Sci 2015, 97(8), 1031-42.

The present research work focuses on different types of second order partial differential equations (PDEs) with non-constant coefficients and studies their classifications. The convolutions of these partial differential equations (PDEs) are obtained and later classified. Some Maple programs are developed to achieve the various classifications in both cases before and after the convolution. Examples are tested by using the developed Maple code for classifications of these PDEs before and after the convolution and the results are presented for the polynomial types of convolution function in two variables. The results provide the bases for similarities and as such same method of solution for non-constant partial differential equations (PDEs) can be applied both before and after the convolution.

2 tables, 8 ref

020306   Jung-In S;Suk-Bok K;Kwang-Mo H;Sol-Ji N (Statistics Dep, Yeungnam Univ, 280 Daehak-ro, Gyeongsan-712 749, Republic of Korea, Email: sbkang@yu.ac.kr) : Hierarchical Bayesian estimation method for the type-II generalized logistic distribution based on progressively type-II censored samples. Far East J mathl Sci 2015, 97(8), 1013-22.

This paper estimates unknown parameters of the Type-II generalized logistic distribution based on progressively Type-II censored samples. For robust estimation, the hierarchical, structure of a conjugate prior distribution is considered. An estimation method for deriving Bayes estimators of unknown parameters that do not depend on hyperparameters is developed. Finally, a real data set is employed to examine the robustness of Bayes estimators based on the hierarchical prior considered.

1 illus, 3 tables, 15 ref

020305   Joshi S B;Joshi S S;Pawar H H (Mathematics Dep, Walchand College of Engineering, Sangli-416 415, Email: joshisb@hotmail.com) : On a subclass of starlike functions with fixed points. J Indian Acad Math 2015, 37(1), 101-11.

A subclass T*_n (α, β, γ) consisting of functions of the form f(z)= z Σ_k=2^∞ a_k z^k, a_k ≥ 0 are considered. The subclass T*_n(α,β,γ,z₀ ) for which f(z₀) = z₀ or f'(z₀) = 1, z₀ real, is examined. The coefficient estimates, distortion theorem, radius of convexity and closure property are obtained for this class.

5 ref

020304   Jitjagr P;Viriyapong C;Boonpok C (Mathematics Dep, Faculty of Science, Mahasarakhan Univ, Mahasarakham-44150, Thailand, Email: promlikhit18@gmail.com) : Regular generalized closed sets in generalized topological spaces. Far East J mathl Sci 2015, 97(5), 635-43.

The purpose of this paper is to introduce the concepts of μ.-regular generalized closed sets and μ-regular generalized open sets in generalized topological spaces and investigate some of their properties.

9 ref

020303   Jain D K;Jain R;Thakur A (Applied Mathematics Dep, Madhav Institute of Technology & Science, Gwalior-474 005, Email: jain_dkj@yahoo.co.in) : Pathway fractional integral images of product of some generalized hypergeometric functions. J Indian Acad Math 2015, 37(1), 113-26.

The proposed paper works out the pathway fractional integral images of product of I-functions, Mittag-Leffler function and Bessel function. The objective of this paper is to study of pathway fractional integral operator associated with the pathway model and pathway probability density for a certain product of special functions with general argument.

17 ref

020302   Isaac P;Neelima C A (Centre for Post Graduate Studies and Research, Mathematics Dep, Bharata Mata College, Thrikkakara, Kochi-682 021, Email: pibmct@gmail.com) : Rough subrings and their properties. Int J mathl Sci 2015, 14(1-2), 99-110.

In this paper, authors shall review the concept of rough ring, introduce the concept of rough subring, rough ring homomorphism and give some properties of them.

10 ref

020301   Imnukulkit P;Ratanaprasert C (Mathematics Dep, Faculty of Science, Silpakorn Univ, Nakhon Pathom, 73000, Thailand, Email: p741008@hotmail.com) : Finite generating sets for varieties of commutative unary algebras. Far East J mathl Sci 2015, 97(7), 857-69.

In universal algebra, we always look for algebras which are finitely axiomatizable and try to construct some bases for them. Kartashov [6] showed that every variety of commutative unary algebras of finite type has a finite basis of identities. In this paper, we give new proofs for all cases of non-regular and regular identities. Especially, we show a finite set of generators for the variety of cyclic commutative unary algebras.

6 ref

020300   Im Y B;Lee J S;Cho Y D (College of Dharma, Dongguk Univ, Seoul-10 715, Korea, Email: philpen@dongguk.edu) : Fuzzy strongly α-continuous mappings. Far East J mathl Sci 2015, 97(8), 949-57.

Define and characterize a fuzzy strongly α-continuous mapping and a fuzzy strongly α-open mapping on a fuzzy topological space. Besides, some interesting properties of those mappings are given.

11 ref

020299   Hazama F (Tokyo Denki Univ Hatoyama, Hiki-Gun Saitama, Japan, Email: hazama@mail.dendai.ac.jp) : Mathematical analysis of melodies: slope and discrete frechet distance. Far East J mathl Sci 2015, 97(5), 583-615.

A directed graph, called an M-graph, is attached to every melody. Our chief concern in this paper is to investigate: (1) how the positivity of the slope of the M-graph is related to singability of the melody, (2) when the M-graph has a symmetry, and (3) how we can detect a similarity between two melodies. For the third theme, we introduce the notion of transposed discrete Frechet distance, and show its relevance in the study of similarity detection among an arbitrary set of melodies.

8 illus, 11 tables, 3 ref

020298   Hakami A H (Mathematics Dep, King Khalid Univ, P.O. Box 9004, Abha, Postal Code:61431, Saudi Arabia, Email: aalhakami@kku.edu.sa) : Small zeros of quadratic form mod P<. Int J mathl Sci 2015, 14(1-2), 39-47.

Let Q(x) - Q(x₁, x₂,..., x_n) be a quadratic form over Z,p be an odd prime, and A = - (- 1)^n/2 detAQ_Q/p. A solution of the congruence Q(X) = 0 (mod p^m) is said to be a primitive solution if p | x_i for some i. We prove that if this congruence has a primitive solution then it has a primitive solution with || x || ≤ max {6^1/n p^m[(1/2) + (1/n)], 2^2(n+1)/(n-2 ) 3^2/(n-2), provided that n is even, n <62> m and n ≥ 2.

16 ref

020297   Goo Y H (Mathematics Dep, Hanseo Univ Seosan, Chungnam, 356-706, Republic of Korea, Email: yhgoo@hanseo.ac.kr) : Boundedness in the perturbed functional differential systems VIA t_∞ -similarity. Far East J mathl Sci 2015, 97(6), 763-80.

This paper, is to investigate bounds for solutions of the perturbed functional differential systems using the notion of t_∞ -similarity.

13 ref

020296   Gomez-Calderon J (Mathematics Dep, The Pennsylvania State Univ, New Kensington, Pennsylvania-15068, USA, Email: jxg11@psu.edu) : Cyclotomic polynomials of the second kind. Part 2. Far East J mathl Sci 2015, 97(5), 573-82.

5 ref

020295   Gawande A;Raich V;Rai S (NO, Govt. Autonomous Holkar Science College, Indore, Madhya Pradesh, Email: gawandearchana@gmail.com) : Fuzzy matrix solution for the study of teacher's and student's evalution. J Indian Acad Math 2015, 37(1), 127-36.

Fuzzy set theory plays an important role in pattern recognition. It serves as an interface between linguistic variables and quantitative characterization. Fuzzy set membership value can be use to provide missing of incomplete information Fuzzy relation provides solutions of our daily life problems depend on two different situation. Teacher quality matters a great deal in terms of student learning. Therefore, teacher quality measurement is important. Even though performance of student i.e. Excellent, good, normal or bad will be depending on his/her own specialty. In this paper we will try to obtain conclusion about students performance and teachers quality using FMS and R/v technique by giving membership grades to their specialty from 0 to 1 in the fuzzy relation matrix Ro (an occurrence relation obtained by observations on sufficient number of student and teacher), R_c (a conformability relation confirmed by expert in education sector) and R_s (a matrix which contains degree of specialty seen by educationist for testing the model). We also compare the results obtained in both methods.

7 ref

020294   Fadail Z M;Ahmad A G B;Rad G S;Ozturk V; Radenovic S (School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia, Email: zaid_fatail@yahoo.com) : Some remarks on coupled, tripled and n-Tupled coincidence and fixed points theorems in ordered abstract metric spaces. Far East J mathl Sci 2015, 97(7), 809-39.

In this paper, we introduce the concept of monotone mappings and monotone mapping with respect to other mapping to obtain some coupled, tripled and n-tupled coincidence and fixed point results in partially ordered abstract/metric spaces. Our results generalize, extend, complement and improve various comparable results in the existing literature. The examples are given to illustrate the usability of our results.

60 ref

020293   Fadail Z M;Ahmad A G B;Ozturk V;Radenovic S (School of Mathamatical Sciences, Faculty of Science and Technology, Univ Kebangsaan Malaysia 43600 UKM Bangi, Selangor Darul Ehasan, Malaysia, Email: zaid_fatail@yahoo.com) : Some remarks on fixed point results of b₂-metric spaces. Far East J mathl Sci 2015, 97(5), 533-48.

This paper, is to consider, discuss and generalize some recent fixed point results for mappings in 2-metric and b₂ -metric spaces established by Mustafa et al. [31]. By using one new lemma all our results are with much shorter proofs. One example shows that our generalizations are genuine.

40 ref

020292   Dutta T K;Ghosh A (Pure Mathematics Dep, Calcutta Univ, 35, Ballygunge Circular Raod, Kolkata700 019, Email: duttatapankumar@yahoo.co.in) : Intuitionistic fuzzy prime ideals of semirings (II). Int Rev Fuzzy Math 2015, 11(1), 53-68.

In this paper authors have further studied.intuitionistic fuzzy prime ideal of semirings. Also we have introduced the notions of intuitionistic fuzzy completely prime ideal of semirings and studied them.

15 ref

020291   Dhanesh L;Murugesan P (NO, Sathyabama Univ, Chennai, Email: lavanyadhanesh2007@gmail.com) : Analyzing the WCET and improving the performance of the real-time system by implementing cyclic priority preemptive task scheduling algorithm. Far East J mathl Sci 2015, 97(6), 667-88.

The main objective of the research work is to improve the performance of the real time system by analyzing the worst case execution time (WCET), with the implementation of the new proposed algorithm. The proposed algorithm approximates the mean waiting time for a given class based on the higher and lower priority tasks, receiving service prior to the target and the mean residual service time experienced. Additional time caused by preemptions is estimated as part of mean request completion time for a given class and as part of the mean delay experienced due to jobs in execution, on an arrival. The algorithm is evaluated analytically and by simulation. Comparisons with other algorithms (such as first-come-first-served, round-robin, rate monotonic, EDF and non-preemptive priority order) reveal that CPPTS achieves a better balance among priority classes where high priority requests are favored while preventing lower priority requests from over starvation.

5 illus, 2 tables, 12 ref

020290   Cho Y U (Mathematics Dep, College of Education Silla Univ, Pusan-617 736, Korea, Email: yucho@silla.ac.kr) : Characterization of distributive GSA. Far East J mathl Sci 2015, 97(7), 897-903.

Throughout this paper, we concern with some concepts of R-groups, where R is a near-ring, and their related algebraic structures, that is, group semiautomata and the distributive group semiautomata. The author already studied the 1st, 2nd and 3rd isomorphic theorems of group semiautomata. In this paper, we investigate a characterization of distributive group semiautomata.

7 ref

020289   Chitra S;Indhumathi B;Ramya S (Mathematics Dep, PSGR Krishnammmal College for Women, Coimbatore, Tamilnadu, Email: 3ugmaths@gmail.com) : Strong edge-magic total labelings of certain graphs. Int J mathl Sci 2015, 14(1-2), 89-97.

The aim of the paper is extending Strong edge- magic total labeling for, Cycles, Petersen, Harary, Star, Tietze's, 14-Cubic graphs, 28-Cubic graphs and Rower Snark which forms wonderful examples.

20 ref

020288   Chandra Sekhar K V (Mathematics Dep, K.L. Univ, Vaddeswaram-522 502, Email: kasulanati22@rediffmail.com) : Radiation effect with thermal mass diffusion in MHD convection flow from a porous vertical plate with ohmic heating. Int J chem Sci 2015, 13(3), 1163-72.

The effects of radiation on heat and mass transfer transfer in MHD mixed convection flow past an infinite vertical porous plate with Ohmic heating and viscous dissipation have been discussed. Solutions have been derived for the velocity, temperature field, and concentration profiles using multi-parameter perturbation technique. The results are analyzed graphically to observe the influence of various parameters like Schmidt number (Sc), Prandtl number (Pr), magnetic parameter (M), radiation parameter (F), and porosity (k).

8 illus, 6 ref

020287   Canadas A M;Angarita M A O;Salas Avilla W G (Mathematics Dep, National Univ of Colombia, Colombia) : Matrix problems to generated mosaic-based CAPTCHAs. Far East J mathl Sci 2015, 97(8), 991-1012.

Matrix problems and in particular matrix representations of partially ordered sets (posets) are used to formally define and generate emerging and multistable images. Images induced by such representations are mosaics which can be used to design different * types of Human Interaction Proofs (HIPs).

6 illus, 24 ref

020286   Busababodin P;Areepong Y;Sukparungsee S (Applied Statistics Dep, Faculty of Applied Science, King Mongkut's Univ of Technology North Bangkok, Bangkok 10800, Thailand, Email: sws@kmutnb.ac.th) : Analytical expression of ARL for AR(p) on exponential CUSUM procedure. Far East J mathl Sci 2015, 97(7), 905-24.

The Cumulative Sum (CUSUM) procedure has widespread applications in improving quality for manufacturing and service systems. The Average Run Length and Average Delay Times are traditional measurements of performance of control chart. In this paper, we study the CUSUM procedure when observations are from pth order autoregressive model AR(p) with exponential white noise. The aim of this paper is to derive explicit formulas for the Average Run Length and the Average Delay Times on CUSUM procedure. Numerical results obtained from explicit formulae and numerical integration approaches by using the Gauss-Legendre rule are presented for illustrative purposes. We have shown that the results obtained from the two approaches are in excellent agreement.

26 ref

020285   Biswas A;Verma S (Faculty of Mathematics, Applied Sciences Dep, TRUBA College of Engineering & Technology, Indore, Madhya Pradesh, Email: anitabiswas89@yahoo.com) : Optimality condition for linear fractional programming problem. J Indian Acad Math 2015, 37(1), 19-24.

Linear fractional programming is a generalization of linear programming. The objective functions in linear programs are linear functions while the objective function in a linear fractional program is a ratio of two linear functions. In this paper an attempt is made to solve the optimality in linear fractional programming problem, which states that if the convex set of feasible solution of AX ≤ b, X ≥ 0 is a convex polyhedron, then at least one of the extreme points gives an optimal solution and If the optimal solutions occur at more than one extreme point, the value of the objective function will be the same for all convex combinations of these extreme point.

10 ref

020284   Bidyarani S;Tomba I (Mathematics Dep, Manipur Univ, Imphal, Manipur, Email: sbidya77@gmail.com) : Migration aspects in the states of the North Eastern region, India. J Indian Acad Math 2015, 37(1), 31-46.

Migration is an important factor for influencing the social and economic development of a place but the exact data of migration is generally not available and therefore different methods are used. The technique developed by Tomba (1991/2010) is applied here for estimation of prior male migrants (OL), settled migrants and for migration analysis taking the sex ratio and growth rate of some standard population. As suggested by Patterson and Greenwood (1960/1969), in migration theory, prior migrants play an important role. The flow of migration and the net opportunity analysis are studied with the use of migration indices, male migrants (OL) and settled migrants. The states in the North Eastern Region (NER) of India show inhomogeneous growth rates ranging from -0.6 to 27.9 in 2001-11.

1 illus, 7 tables, 10 ref

020283   Bhatt S K;Shrivastava R (Mathematics Dep, Govt. N.P.G. College of Science, Raipur (C.G), Email: skbhatt28@rediffmail.com) : Application of I-Function in one-dimensional heat equation. J Indian Acad Math 2015, 37(1), 25-9.

As an example of the application of I-function in applied mathematics, in this paper, authors shall consider the problem of determining the temperature in a slab of homogeneous material bounded by the planes x = 0 and x - π having an initial temperature u = f(x), varying only with the distance from the faces and with its two faces kept at zero temperature.

4 ref

020282   Beceren Y;Noiri T (Mathematics Dep, Faculty of Science, Selcuk Univ Kampus, Konya, 42031, Turkey, Email: ybeceren@selcuk.edu.tr) : On some irresolute functions concerning semi-open sets. Far East J mathl Sci 2015, 97(6), 781-92.

In this paper, authors introduce and study new classes of generalizations of some irresolute functions via the weak forms of semi-open sets in topological spaces. Also, we give some of their properties and have a decomposition of semi αlc-irresoluteness.

17 ref

020281   Aramaki J (Science Div, Faculty of Science and Engineering, Tokyo Denki Univ, Hatoyama-Machi, Saitama-350 0394, Japan, Email: aramaki@mail.dendai.ac.jp) : The stability of the twisted nematic critical state in the liquid crystal theory. Far East J mathl Sci 2015, 97(8), 959-68.

Considerd the weak stability of a twisted nematic critical state of the Oseen-Frank energy functional under the exterior magnetic field. We show that if the degree of twist and strength of the magnetic field are both small, then the twisted state is weakly stable.

7 ref

020280   Appa Rao B V;Prasad K A S N V (Mathematics Dep, K.L. Univ, Vaddeswaram, Guntur-522 502, Email: bvardr2010@kluniversity.in) : Study of controllability of matrix integro- Differential equations on time scales. Int J chem Sci 2015, 13(3), 1324-32.

In this paper, first we develop the method of variation of parameters formula for integro-differential system on time scales in terms of resolvent kernals and then offer sufficient conditions for the complete controllability of the first order matrix integro-differential system on time scales. 2000 Mathematics subject classification: 49K15, 93B05 and 37N35.

8 ref

020279   Anyanwu M C;Oruh B I (Mathematics Dep, Michael Okpara Univ of Agriculture Umudike, Abia State, Nigeria, Email: manyanwu71@yahoo.com) : Estimating the price of pure discount bond: Eigenfunction expansion approach. Far East J mathl Sci 2015, 97(8), 1043-57.

This paper develops an eigenfunction expansion procedure for estimating the price of a pure discount bond. Under the assumption that the stochastic interest rate in the market follows a mean-reverting process, the infinitesimal generator of the pricing semi-group is systematically transformed to the operator of the simple harmonic oscillator. The result shows that the bond prices calculated using the eigenfunction expansion procedure approximates very closely the bond price calculated using the reduction to the Riccati equation.

2 illus, 8 ref

020278   Adam F;Hassan N (School of Mathematical Sciences, Faculty of Science and Technology, Univ Kebangsaan Malaysia 43600 UKM Bangi, Selangor D.E Malaysia, Email: nas@ukm.edu.my) : Multi Q-fuzzy soft set and its application. Far East J mathl Sci 2015, 97(7), 871-81.

Molodtsov introduced the concept of soft set as a general mathematical tool for dealing with uncertainty. In this work, we introduce the notion of a multi Q-fuzzy soft set and the basic operations associated with it, namely, complement, union, intersection, OR and AND operations, along with illustrative examples. Basic properties of the operations are also given. Finally, we define a multi Q-fuzzy soft-aggregation operator that allows constructing more efficient decision making methods.

26 ref

019150   Patel A B;Shekhawat M P (Mathematics Dep, Sardar Patel Univ, Vallabh Vidyanagar-388 120, Email: abp1908@gmail.com) : Hypo-EP operators. Indian J pure appl Math 2016, 47(1), 73-84.

In this paper we study closed range operators on a Hilbert space such that the range is contained in the range of its adjoint. Some results pertaining to these operators and operator matrices are discussed.

11 ref

019149   Liu Y;Sun W (School of Science, Shandong Univ of Technology, Zibo, 255 049, Shandong Province, P.R.China, Email: yjliu98@126.com) : Elementary wave interactions in magnetogasdynamics. Indian J pure appl Math 2016, 47(1), 33-57.

This paper is mainly concerned with the interactions of the elementary waves for the one-dimensional ideal Magnetogasdynamics with transverse magnetic field. By applying the method of the characteristic analysis, we obtain constructively the solutions of the all possible wave interactions when the initial data are three piecewise constant states. We find that the result is very different from that of the corresponding case of the conventional gas dynamics. However, the result is consistent with that of the corresponding case for Euler equations when the magnetic field vanishes.

14 illus, 19 ref

019148   Kamath S S;Kolake P (Mathematical and Computational Sciences Dep, National Institute of Technology Karnataka, Surathkal, Srinivasnagar, Mangalore-575 025, Email: shyam.kamath@gmail.com) : Neighborhood contraction in graphs. Indian J pure appl Math 2016, 47(1), 97-110.

Let G be a graph and v be any vertex of G. Then the neighborhood contracted graph G_v of G, with respect to the vertex v, is the graph with vertex set V - N(v), where two vertices u,w ∈ V - N(v) are adjacent in G_v if either w = v and u is adjacent to any vertex of N(v) in G or u,w ∉ N[v] and u,w are adjacent in G. The properties of the neighborhood contracted graphs are discussed in this paper. The neighborhood contraction in some special class of graphs, the domination in a graph and the neighborhood contracted graphs are discussed in the paper.

3 illus, 7 ref

019147   Huang R Z;Liu X G (School of Mathematical Sciences and LPMC, Nankai Univ, Tianjin-300 071, P.R. China, Email: hrzsea@mail.nankai.edu.cn) : Non-triviality of a product in the Adams E₂-Term. Indian J pure appl Math 2016, 47(1), 59-72.

Let p be a prime greater than five and A the mod p Steenrod algebra. In this paper, we prove that h_nh_mδ_s+4Ext_A^{s+6,t(s,n,m)+s< D>A(Z/p,Z/p) is nontrivial in the Adams E₂} non super scripta-term when m ≥ n + 2 ≥ 7 and 0 ≤ s <60> p - 4, and trivial in the Adams E₂-term when m ≥ n + 2 = 6 and 0 ≤ s <60> p - 4, where δ_s+4 stands for the fourth Greek letter element and t(s, n, m) = 2(p - 1)[(s + 1) + (s + 2)p + (s + 3)p² + (s + 4)p³ + pⁿ + p^m].

7 ref

019146   Dhara B;Argac N;Pradhan K G (Mathematics Dep, Belda College, Belda, Paschim Medinipur-721 424) : Annihilator condition of a pair of derivations in prime and semiprime rings. Indian J pure appl Math 2016, 47(1), 111-24.

Let n be a fixed positive integer, R be a prime ring, D and G two derivations of R and L a noncentral Lie ideal of R. Suppose that there exists 0 ≠ a ∈ R such that a(D(u)uⁿ-uⁿG(u)) = 0 for all u ∈ L, where n ≥ 1 is a fixed integer.

24 ref

019145   Das S (Mathematics Dep, Indian Institute of Science, Bangalore-560 012, Email: somu@math.iisc.ernet.in) : Cuspidality and the growth of fourier coefficients of modular forms. Indian J pure appl Math 2016, 47(1), 9-22.

In this paper, authors present a survey of the recent results on the characterization of the cuspidality of classical modular forms on various groups by a suitable growth of their Fourier coefficients.

26 ref

019144   Coriasco S;Toft J (Di Matematica Dep, Univ degli Studi di Torino, Torino, Italy) : Calculus of fourier integral operators with inhomogeneous phase functions on R<. Indian J pure appl Math 2016, 47(1), 125-66.

We construct a calculus for generalized SG Fourier integral operators, extending known results to a broader class of symbols of SG type. In particular, we do not require that the phase functions are homogeneous. An essential ingredient in the proofs is a general criterion for asymptotic expansions within the Weyl-Hormander calculus. We also prove the L²(R^d)-boundedness of the generalized SG Fourier integral operators having regular phase functions and amplitudes uniformly bounded on R^2d.

28 ref

019143   Bandyopadhyay S;Raha S;Nayak P K (Mathematics Dep, Visva Bharati, Santiniketan-731 235, Email: sibasisbanerjee@rediffmail.com) : Profit allocation among rational players in a cooperative game under uncertainty. Sadhana 2015, 40(4), 1077-89.

In this paper, a cooperative game has been considered, where there is a coalition between rational players in an uncertain environment. The uncertainty occurs in terms of the quality of the raw material. The pay-offs of the players are influenced by the degree of satisfaction. Pay-offs are considered as interval numbers. A multisection technique has been applied to obtain a rational solution. In the process, it has been found that the degree of satisfaction of the rational players converges to its optimum value with the convergence of the iterations. A comparative study has been made with methods existing in the literature.

2 illus, 17 ref

019142   Alimohammady M;Ramazannejad M (Mathematics Dep, Faculty of Mathematical Sciences, Univ of Mazandaran, Babolsar, Iran, 47416-1468, Email: m.alimohammady@gmail.com) : Inertial proximal algorithm for difference of two maximal monotone operators. Indian J pure appl Math 2016, 47(1), 1-8.

In this note, a new algorithm is presented for finding a zero of difference of two maximal monotone operators T and S, i.e., T - S in finite dimensional real Hilbert space H in which operator S has local boundedness property. This condition is weaker than Moudafi's condition on operator S in [13]. Moreover, applying some conditions on inertia term in new algorithm, one can improve speed of convergence of sequence.

17 ref

019141   Akbar M A;Alam M N;Hafez M G (Applied Mathematics Dep, Rajshahi Univ, Bangladesh, Email: ali_math74@yahoo.com) : Application of the novel (G'/G)-expansion method to construct travelling wave solutions to the positive Gardner-KP equation. Indian J pure appl Math 2016, 47(1), 85-96.

The novel (G'/G)-expansion method is one of the powerful methods accredited at the present time for establishing exact traveling wave solutions to nonlinear evolution equations (NLEEs). In this article, the method has been implemented to find the traveling wave solutions to the positive Gardner-KP equation. The efficiency of this method for finding exact and traveling wave solutions has been demonstrated. The obtained solutions have been compared with the solution obtained by other methods. The solutions have also been demonstrated by figures. It has been shown that the method is straightforward and an effective tool for solving NLEES that occur in applied mathematics, mathematical physics, and engineering.

5 illus, 35 ref

019140   Abdmouleh F (Univ de Sfax, Institut Superieur de Gestion Industrielle de Sfax Route de Tunis km 1, B. P. 1164-3000 Sfax, Tunisie, Email: faical_abdmouleh@yahoo.fr) : B-Essential and B-Weyl spectra of sum of two commuting bounded operators. Indian J pure appl Math 2016, 47(1), 23-31.

In this paper, we devote our research to the B-essential spectra of the sum of two bounded linear operators defined on a Banach space by means of the B-essential spectra of each of the two operators where their products are finite rank operators.

16 ref

018154   Ver,a J K (Mathematics Dep, Govt. P. G. College, Panna, Madhaya Pradesh, Email: jk.verma87@yahoo.co) : Fixed points on two complete D- metric spaces. Asian J Adv Basic Sci 2015, 4(1), 25-7.

Measures of nearness between two or more objects with respect to a specific characteristic are parameter of the nearness. In D-metric space thereby which it has been possible to determine the geometrical nearness, generalized metric D is a slight variant of two metric. Fisher^{4 & 5} obtained related fixed point theorems on two complete metric spaces. Inspired by his work, in this paper we prove a related fixed point theorem on two complete D-metric spaces.

11 ref

018153   Myla J;Nandhini S (NO, Baktavatsalam Memorial College for Women, Korattur, Chennai-80, Email: jayapalmyla@gmail.com) : Isolation and identification of microflora from Indian currency notes and evaluation of virulence of pathogens using PCR. Scient Trans Envir Technovation 2015, 8(4), 185-8.

Currency note contamination is of important to public health as it can provide a vehicle for easy transmission of pathogen between handlers. An attempt has been made to isolate bacterial and fungal pathogens from different categories of Indian currency notes and evaluation of potential pathogens ad its virulence have been determinedusing PCR.

6 illus, 16 ref

018152   Deo S D;Punwatkar G S;Patil U M (Mathematics Dep, N. S. Science & Arts College, Bhadrawati, Dist.Chandrapur, Maharashtra) : Bianchi type -III cosmological model electromagnetic field with cosmic strings in general theory of relativity. Archiv appl Sci Res 2015, 7(1), 48-53.

Bianchi type -III Cosmological model filled with a magnetized Cosmic strings is investigated in general relativity. Here we assume that F₂₃ is only non-vanishing component of electromagnetic field tensor F_ij. We obtain exact solution by assuming that the expansion θ in the model is proportional to the shear σ which leads to C=Bⁿ where B and C are functions of time only. The physical and geometrical behaviour of cosmological model are discussed.

11 ref

017112   Vasavi C;Suresh Kumar G;Murthy M S N (Mathematics Dep, Koneru Lakshmaiah Univ, Vaddeswaram, Guntur, Andhra Pradesh, Email: vasavi.klu@gmail.com) : Fuzzy dynamic equations on time scales under second type Hukuhara delta derivative. Int J chem Sci 2016, 14(1), 49-66.

In this paper, we introduce and study the properties of second type Hukuhara delta derivative denoted by (Δ_SH-derivative) for fuzzy set-valued functions on time scales whose values are normal, convex, upper semicontinuous and compactly supported fuzzy sets in R^{n. We establish the existence and uniqueness criteria for fuzzy dynamic equations on time scales using Banach contraction principle. For an application, we consider the radioactive decay problem and illustrate the advantage of (Δ_SH-derivative).}

1 illus, 33 ref

017111   Nageswara Rao B;Ramakrishna N;Eswarlal T (Mathematics Dep, Coastal Institute of Technology and Management, Narapam, Kothavalasa, Vizinagaram, Andhra Pradesh, Email: nageswararao.mathes@gmail.com) : Application of translates of vague sets in carier decission making. Int J chem Sci 2016, 14(1), 372-80.

Vague set is very useful in providing of a flexible model to elaborate uncertainty and vagueness involved in decision making. In this paper, we reviewed the concept of vague set and apply translates operators on vague set, also proposed its application for carrier determination by using the translate of eulclidence distance method. To measure the each student and each carrier respectively. Its solution is obtained by looking shortest distance between each student and each carrier.

3 tables, 10 ref

017110   Hemalatha K;Kameswaran P K;Madhavi M V D N S (Mathematics Dep, V.R. Siddhartha Engineering College, Vijayawada-520 007, Email: perikamesh@gmail.com) : Mixed convective heat transfer from a vertical plate embedded in a saturated non-darcy porous medium with concentration and melting effect. Sadhana 2015, 40(2), 455-65.

Effect of melting and solute dispersion on heat and mass transfer in non-Darcy fluid flow over a vertical surface has been studied numerically in the present article. The flow is assumed to be laminar and steady state. Using similarity transformations, the governing boundary layer equations are transformed into self-similar nonlinear ordinary differential equations, which are then solved by using boundary value problem solver. A comparison with the numerical results made for different Ra / pe values in the absence of some particular parameters. The velocity and concentration inside the boundary layer are observed to be influenced by the parameters like Ra / Pe, L, B, M. The flow heat and mass transfer coefficients are discussed through the plots.

8 illus, 3 tables, 13 ref