007973   Udayakumar S;Gurumoorthy A (Mathematics Dep, AVVM Sri Pushpam College, Autonomous, Poondi, Thanjavur) : Study of Problems by parents of children with disability using Fuzzy cognitive maps model. Ultra Scient phys Sci-Sect B 2015, 27(1), 61-5.

In this paper the stress and social stigma suffered by parents of disabled children are analysed using Fuzzy Cognitive Maps (FCMs) model. Such study is new for researchers have studied only the problems faced by disabled children using mathematical models. However study of the problems faced by those parents using fuzzy models is absent in literature. Here the study is carried out by a pilot survey of 50 odd parents who have been interviewed for this purpose.

6 ref

007972   Thulukkanam K;Vasuki R (Maths Dep, Dr. Ambedkar Govt Arts College, Chennai-39, Email: thulukkanamk@gmail.com) : Two new fuzzy models using fuzzy cognitive maps model and Kosko hamming distance. Ultra Scient phys Sci-Sect B 2015, 27(1), 43-55.

In this paper for the first time two new fuzzy models viz Merged Fuzzy Cognitive Maps (MFCMs) models and Specially Merged Linked Fuzzy Cognitive Maps (SMLFCMs) are introduced. To compare the experts opinion a new techniques called Kosko Hamming distance and Kosko Hamming weight are introduced.

18 illus, 13 ref

007971   Thulukkanam K;Vasuki R (Maths Dep, Dr. Ambedkar Govt Arts College, Chennai-39, Email: thulukkanamk@gmail.com) : Analysis of the General Hazards and Health Hazards Suffered by the locals of Kodungaiyur using specially linked merged fuzzy cognitive Maps (SLMFCMs) Model. Ultra Scient phys Sci-Sect B 2015, 27(1), 25-32.

In this paper we use the Specially Merged Linked Fuzzy Cognitive Maps (SMLFCMs) model to study all problems faced by the Kodungaiyur locals like poverty, ecological imbalance, soil water pollution, problems faced by local rag pickers, literacy rate, health hazards suffered by locals so on.

s, 34 ref

007970   Sukparungsee S (Applied Statistics Dep, Faculty of Applied Sciences, King Mongkut's Univ of Technology North, Thailand-10800, Email: swns@kmutnb.ac.th) : Comparison of performance of CUSUM and EWMA with parametric and nonparametric for exponential data. Far East J mathl Sci 2014, 95(2), 249-58.

The nonparametric CUSUM and EWMA control charts are proposed to study the performance in order to detect the deviation from the target value. These nonparametric control charts are effective alternatives to parametric control charts. The performance of the nonparametric control charts are compared with parametric CUSUM and EWMA control charts when observations are from exponential distribution. The numerical results found from Monte Carlo simulation with repeated 10 times. We find that the performance of nonparametric control charts are superior to parametric CUSUM and EWMA control charts. Furthermore, the nonparametric EWMA performs better than nonparametric CUSUM for all magnitudes of shift.

2 tables, 13 ref

007969   Simanihuruk M (Mathematics Dep, Bengkulu Univ Jalan W R Supratman, Kandanglimun-383 71, Email: mudinsimanihuruk@yahoo.com.au) : On defective colorings of triangle free graphs with prescribed maximum degree. Far East J mathl Sci 2015, 96(3), 285-301.

Let m be a positive integer and let k be a non-negative integer. The assigns to the vertices of G such that the maximum degree of the subgraph induced on vertices receiving the same color is at most k. Let f(m, k) be the smallest order of a triangle-free G with χ<35>(G) = m. The determination of f(m, k) is an open problem even for the case k = 0. It is known that f(3, k) ≤ 4k + 5 and /(3, k) = 4k + 5 for k = 1, 2. Moreover, it had been characterized all the triangle-free graphs of order f(3, k) for k = 1, 2. This paper shows that if G is a triangle-free G of order 4k + 5 with Δ(G) ≥ 3k + 1, then χk(G) = 3 if and only if k = 0 or 1. If k = 0, then G ≅ C₅. If k = 1, then G ≅ G₄ in Figure 1.

4 illus, 11 ref

007968   Silagadze Z (NO, Budker Institute of Nuclear Physics SB RAS and Novosibirsk State Univ, Novosibirsk-630 090, Email: Z.K.Silagadze@inp.nsk.su) : Sums of genealized harmonic series. Resonance 2015, 20(9), 822-43.

Examine here of the author the remarkable connection, first discovered by Beukers, Kolk and Calabi, between ζ(2n), the value of the Rlemann Zeta-function at an even positive integer, and the volume of some 2n-dimensional polytope. It can be shown that this volume is equal to the trace of a compact self-adjoint operator. Authors provide an explicit expression for the kernel of this operator in terms of Euler polynomials. This explicit expression mattes it easy to calculate the volume of the poly-tope and hence ζ(2n). In the case of odd positive integers, Authors rediscover an integral representa-tion for ζ(2n + 1), obtained by a different method by Cvijovic and Klinowski. Finally, authors indicate that the origin of the miraculous Beukers-Kolk- Calabi change of variables in the multidimensional integral, which is at the heart of this circle of ideas, can be traced to the amoeba associated with the certain Laurent polynomial. The article is dedicated to the memory of Vladimir Arnold (1937-2010).

24 ref

007967   Shirali S A (NO, Sahyadri School Tiwai Hill, Rajgurunagar, Pune-410 513, Email: shailesh.shirali@gmail.com) : Counting your way to the sum of squares formula. Resonance 2015, 20(10), 880-92.

In this article, we use combinatorial reasoning to derive a formula for the sum of the first n squares: I^{2 + 22 + 32 + ... + n2. Following this we do the same for the formula for the sum of the first n cubes. Then we look at the problem more generally.}

2 illus, 3 ref

007966   Shah D A;Desai A K (Mathematics Dep, CU Shah Univ, Wadhwan City-363 030) : Symmetry in Plane. Ultra Scient phys Sci-Sect A 2015, 27(1), 49-54.

In this article we study symmetries of plane figures. We start with the definition of isometry of a metric space. For the better understanding of all the isometries of R^{R, we present the known results in form of a flow chart. And then using this idea of isometry, we define symmetry group of a subset of RR. With the use of this definition we determine symmetry groups of the capital Alphabets of English. We also describe the symmetry group of a regular n-gon which is known as D_n. We also describe subsets of RR where symmetry group is the cyclic group of order n which is denoted usually by C_n.}

1 illus, 3 table, 2 ref

007965   Sethuraman G;Sujasree M (Mathematics Dep, Anna Univ, Chennai-600 025, Email: sethu@annauniv.edu) : On γ-labeling on the almost-bipartite graph (P_m x P_n) ⊕ P₄. Far East J mathl Sci 2014, 95(2), 143-57.

4 illus, 5 ref

007964   Selvaraj C;Biju V;Udhayakumar R (Mathematics Dep, Periyar Univ, Salem-636 011, Email: selvavlr@yahoo.com) : Stability of gorenstein FI-flat modules. Far East J mathl Sci 2014, 95(2), 159-68.

3 illus, 10 ref

007963   Selvachandran G;Salleh A R (Actuarial Science and Applied Statistics Dep, Faculty of Business and Information Science UCSI Univ, Jalan Menara Gading, 56000 Cheras Kuala Lumpur, Malaysia, Email: ganeshsree86@yahoo.com) : Intuitionistic fuzzy linguistic variables and intuitionistic fuzzy hedges. Far East J mathl Sci 2014, 95(2), 221-33.

In this paper, we introduce the concepts of intuitionistic fuzzy linguistic variables and intuitionistic fuzzy linguistic hedges which are the generalizations of the corresponding concepts in fuzzy set theory. The behavior of intuitionistic fuzzy sets after the application of these intuitionistic fuzzy linguistic hedges as well as some of the important properties of these concepts are also studied and discussed.

11 ref

007962   Sarkar J;Sinha B K (NO, Indian Univ-Purdue Universitym Inadianpolis, USA, Email: jsarkar@iupui.edu) : Sudoku squaress as experimental designs. Resonance 2015, 20(9), 788-802.

Sudoku is a popular combinatorial puzzle. We give a brief overview of some mathematical features of a Sudoku square. Then we focus on interpreting Sudoku squares as experimental designs in order to meet a practical need.

11 illus, 20 ref

007961   Sangaroon K;Ieosanurak W;Klongdee W (Risk and Insurance Research Group Mathematics Dep, Faculty of Science Khonkaen Univ, Khonkaen, 40002, Thailand) : Necessary condition for lower finite-time ruin probability under XL-reinsurance in the discrete-time risk process with exponential claims. Far East J mathl Sci 2014, 95(2), 133-42.

Author consider the discrete-time risk process in insurance in the case of excess-of-loss (XL-reinsurance) as the following: U_n(u, b) = u + nc(b) - ∑min{6, Y_k}, n = 1, 2, 3, ..., k = 1 where {Y_n : n ∈ N} is an independent and identically distributed claim process such that Y_n is a random variable indicating claim severity at time n, c(b) is a net income rate for one unit time with the retention level b of XL-reinsurance, and u ≥ 0 is an initial capital. We obtain a necessary condition for reducing the finite-time ruin probability in the case of Y_n has an exponential distribution and c(b) is calculated by the expected value principle. To illustrate these results some numerical examples are included.

2 illus, 9 ref

007960   Sane S S (Mathematics Dep, Indian Institute of Technology, Bombay, Mumbai-400 076, Email: sane@math.iitb.ac.in) : Shrikhande Graph. Resonance 2015, 20(10), 903-18.

Questions in mathematical statistics led to the discovery of some elegant mathematical structures and the Shrikhande graph is a beautiful example of the case in point. This article is an attempt to discuss the Shrikhande graph along with its connections in algebra, group theory and topology.

7 illu, 11 ref

007959   Ryu J H;Kim W K (Mathmatics Education Dep, Chungbuk National Univ, Cheongju-362-763, Email: rjh8805@daum.net) : Formula on powern of 2 x 2 matrics. Far East J mathl Sci 2015, 96(3), 365-77.

In this paper, we will investigate general formulae for power n of 2x2 matrices using the eigenvalues of A, and give some examples of Excel programming using general formulae for power n of 2x2 matrices. Those formulae will enhance the efficiency of computer programming for matrix multiplication computations and applications.

6 illus, 4 ef

007958   Rad N J (Mathematics Dep, Shahrood Univ of Technology, Shahrood, Iran, Email: n.jafarirad@gmail.com) : Note on neighborhood total domination in graphs. Proc Indian Acad Sci-Mathl Sci 2015, 125(3), 271-6.

Let G = (V, E) be a graph without isolated vertices. A dominating set S of G is called a neighborhood total dominating set (or just NTDS) if the induced subgraph G[N(S)] has no isolated vertex. The minimum cardinality of a NTDS of G is called the neighborhood total domination number of G and is denoted by γnt(G). In this paper, we obtain sharp bounds for the neighborhood total domination number of a tree. We also prove that the neighborhood total domination number is equal to the domination number in several classes of graphs including grid graphs.

7 ref

007957   Prasad K R;Sreedhar N;Srinivas M A S (Applied Mathematics Dep, Andhra Univ, Visakhapatnam-530 003, Email: rajendra92@rediffmail.com) : Existence of positive solutions for systems of second order multi-point boundary value problems on time scales. Proc Indian Acad Sci-Mathl Sci 2015, 125(3), 353-70.

In this paper, authors establish the existence of positive solutions for systems of second order multi-point boundary value problems on time scales by applying Guo-Krasnosel'skii fixed point theorem.

20 ref

007956   Ponnusamy S;Kaliraj A S (NO, Indian Statistical Institute (ISI), Chennai Centre, SETS (Society for Electronic Transactions and Security), MGR Knowledge City, CIT Campus, Taramani, Chenn, Email: samy@isichennai.res.in) : On the coefficient conjecture of clunie and sheil-small on univalent harmonic mappings. Proc Indian Acad Sci-Mathl Sci 2015, 125(3), 277-90.

In this paper, authors first prove the coefficient conjecture of Clunie and Sheil-Small for a class of univalent harmonic functions which includes functions convex in some direction. Next, we prove growth and covering theorems and some related results. Finally, we propose two conjectures, an affirmative answer to one of which would then imply, for example, a solution to the conjecture of Clunie and Sheil-Small.

2 illus, 16 ref

007955   Parameswari C (Mathematics Dep, A P C Mahalaxmi College For Women, Thoothukudi-628 002, Email: parameswari60@gmail.com) : Fuzzy soft hyper K-subalgebra. Ultra Scient phys Sci-Sect A 2015, 27(1), 31-8.

In this paper, the notion of fuzzy soft hyper K-subalgebra is given and the level subset, union, intersection & some basic results of fuzzy hyper K-subalgebra are studied. We also state a characterization for a fuzzy soft hyper K-subalgebra in terms of iths level hyper K-subalgebra.

8 ref

007954   Oshah A;Darus M (NO, School of Mathematical Sciences Faculty of Science and Technology Univ, Bangi, Selangor, Malaysia, Email: anessa.oshah@yahoo.com) : Inclusion relationships of certain subclasses of analytic functions defined by new generalized derivative operator. Far East J mathl Sci 2014, 95(2), 203-19.

In this paper, new subclasses of analytic functions defined using new generalized derivative operator are introduced. Several inclusion relationships and some other interesting properties of these classes are discussed. In addition, inclusion relationships of these classes involving the generalized Bernardi-Libera-Livington integral operator are also considered.

19 ref

007953   Muddebihal M H;Gaffar A;Ahmed S (Mathematics Dep, Gulbarga Univ, Gulbarga-585 106, Email: mhmuddebihal@yahoo.co.in) : Regular number of subdivision of a graph. Ultra Scient phys Sci-Sect A 2015, 27(1), 1-6.

For any (p, q) graph G, a subdivision graph S(G) is obtained from G by subdividing each edge of G. The regular number of a S(G) is the minimum number of subsets into which the edge set of S(G) should be partitioned so that the subgraph induced by each subset is regular and is denoted by r_s(G). In this paper some results on regular number of r_s(G) were obtained and expressed in terms of elements of G.

2 ref

007952   Liu D;Zhao P (School of Mathematics and Statistics, Lanzhou Univ, Lanzhou 730000, People's Republic of China, Email: liuduchao@gmail.com) : Soliton solutions for a quasilinear schrodinger equation via morse theory. Proc Indian Acad Sci-Mathl Sci 2015, 125(3), 307-21.

In this paper, Morse theory is used to show the existence of nontrivial weak solutions to a class of quasilinear Schrodinger equation of the form -Δ_pu - (p/2p-1)uΔ_p(u^{2) = f(x, u), in a bounded smooth domain Ω ⊂ RN with Dirichlet boundary condition.}

29 ref

007951   Lee J R;Park C;Shin D Y (Mathematics Dep, Daejin Univ, Kyeonggi 487-711, Email: jrlee@daejin.ac.kr) : Functional equations in matrix normed spaces. Proc Indian Acad Sci-Mathl Sci 2015, 125(3), 399-412.

Using the fixed point method, we prove the Hyers-Ulam stability of the Cauchy additive functional equation and the quadratic functional equation in matrix normed spaces.

46 ref

007950   Kherd A;Saaban A (Faulty of Computer Science and Engineering, AL- Ahgaff Univ Mukalla, Hadramout, Yemen, Email: as_kherd@hotmail.com) : Positivity preserving odd degree-n Wang-ball boundary curves on rectangular grid using partial differential equation. Far East J mathl Sci 2015, 96(3), 265-83.

In this paper, the sufficient condition for the positive preservation of boundary curves for each edge of odd degree-n rectangular Wang-Ball patches will be discussed. With the use of polynomial solution of fourth order linear elliptic PDEs, these curves are defined on rectangular grid for the purpose of enhancing the positivity preservation of the interpolating surface. Through an independent adjustment of the lower boundary of edge Wang-Ball ordinates, a sufficient condition on boundary curves for individual edge of odd degree-n rectangular Wang-Ball patches is derived. By employing well known test function, finding reveals that the approach proposed is appropriate with regard to positive preservation of boundary curves and that there is improvement in the positive preservation of the whole interpolating surfaces.

5 illus, 2 table, 10 ref

007949   Katemee N;Yasuwan R (Mathematics and Statistics Dep, Faulty of Science and Agricultural Technology, Rajamangala University, TAK-63000, Thailand, Email: ss@hotmail.com) : Control charts for the generalized poisson process. Far East J mathl Sci 2015, 96(3), 353-64.

This study developed a new cumulative sum chart (CUSUM chart) based on the generalized Poisson (GP) process. The chart could be used to detect the mean of nonconformities (λ) shifts. The developed chart was called the λ_GP -CUSUM chart. Moreover, the study researched the influence of the CUSUM chart based on GP distribution; also called the λ_or -CUSUM chart and Exponentially Weighted Moving Average (EWMA-chart) based on GP distribution. The EWMA_GP -chart was called to monitor the parameter λ in GP process. The λ_GP -CUSUM chart, λ_or-CUSUM chart and EWMA_GP -chart were compared with the c-chart based on GP distribution (^{CGP -chart. Performance was considered from the average run length (ARL). The findings showed that when there was a shift in λ, all levels of parameters, the λ_GP -CUSUM chart and EWMA_GP -chart performed for all levels of the shift.}

1 illus, 4 tables, 14 ref

007948   Jayshree K;Gajivaradhan P (Mathematics Dep, Pachaiyappa's College, Chennai-600 030) : Study of Semigroup semirinings using chain lattices as semirings. Ultra Scient phys Sci-Sect A 2015, 27(1), 77-89.

In this paper we study semigroup semirings using chain lattices as semirings. Such study is new and innovative. Condition for these semigroup semirings to contain special elements like zero divisors, units and idempotents are obtained.

6 ref

007947   Jayshree K;Gajivaradhan P (Mathematics Dep, Pachaiyappa's College, Chennai-600 030) : Special elements in semigroups. Ultra Scient phys Sci-Sect A 2015, 27(1), 71-6.

This paper defines the notion of special elements like Smarandache zero divisors, Smarandache units, Smarandache idempotents and Smarandache nilpotnents for semigroups. This is the first time such study has been carried out on semigroups.

4 ref

007946   Harne S;Badshah V H;Pal S (Mathematics Dep, Govt. Holkar Science College, Indore, Madhya Pradesh) : Linearly Recursive sequences of Fibonacci Numbers. Ultra Scient phys Sci-Sect B 2015, 27(1), 21-4.

The Fibonacci sequence is based on an additive relationship between any term and the three preceding terms. We shall make it a linear dependence and it will involve the preceding r terms. Here and throughout, q will note the general additive sequence.

9 ref

007945   Gupta B K;Aloney M R (Mathematics Dep, Bhagwant Univ, Ajmer, Rajasthan) : Pseudo weakly finitely Quasi injective modules. Ultra Scient phys Sci-Sect A 2015, 27(1), 26-30.

In this paper, we generalize the concepts of pseudo weakly-injective (PW-injective for: short) modules and weakly-finitely-quasi-injective (iWFQ-injective for short) modules to pseudo-weakly-finitely-quasi-injective (PWFQ-injective for short) modules. Our main goal in this work is to study the basic properties of these concepts, characterizations of pseudoiweakly-finitely-quasi-injective modules.

11 ref

007944   Gour K;singh R (NO, B N P G College, Udaipur, Rajasthan) : Products of modified multivariable H-function and general class of polynomial on a Boundary value problem and its solution. Ultra Scient phys Sci-Sect B 2015, 27(1), 9-16.

In this paper, we construct a model of a boundary value problem and then obtain its solution involving Product General Class of Polynomials and Modified Multivariable H-function.

13 ref

007943   Garg M;Agarwal S (Mathematics Dep, Nehru P G College, Chhibramau, Kannauj, Uttar Pradesh, Email: manojshikha@rediffmail.com) : On g'0S*- Homeomorphism in Topological Spaces. Ultra Scient phys Sci-Sect A 2015, 27(1), 90-4.

In this paper we introduce a new class of closed maps namely g^{0 (s)-closed maps also introduce a new class of homeomorphisms called g0(s)* -homeomorphisms. Further we show that the set of all g0 (s)*- homeomorphisms form a group under the operation composition of maps.}

5 ref

007942   Garg M (Mathematics Dep, Nehru College, Chhibramau, Kannauj, Uttar Pradesh, Email: garg_manoj1972@yahoo.in) : Gprsg-Homeomorphism and Sggr-Homeomorphisms in Topological spaces. Ultra Scient phys Sci-Sect A 2015, 27(1), 43-8.

In the present paper we introduce two new types of mappings called gprsg-homeomorphism and sggpr-homeomorphism and then shown that one of these mapping has a group structure. Further we investigate some properties of these two homeomorphisms.

18 ref

007941   Ganapathyraman R (Mathematics Dep, Pachiyappa's College, Chennai-600 030) : Lattice on Fuzzy implication. Ultra Scient phys Sci-Sect A 2015, 27(1), 39-42.

In this paper we present some Boolean algebras in the form of lattice by using the fuzzy implication. We show that these methods lead to various and much richer algebraic structures on the set of all fuzzy implications than obtained in the literature.

7 ref

007940   Gaketem T (Mathematics Dep, School of Science, Phayao Univ, Phayao, 56000, Thailand, Email: newtonisaac41@yahoo.com) : On semi-prime and quasi-semi-prime ideals in Γ-AG-rings. Far East J mathl Sci 2014, 95(2), 169-79.

In this paper, authors introduce the notion of semi-prime and quasi-semi-prime ideals in Γ-AG-rings. Finally, we study properties of semi-prime and quasi-semi-prime ideals in Γ-AG-rings.

13 ref

007939   Dutt P;Husain A;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-II: proof of stability theorem. Proc Indian Acad Sci-Mathl Sci 2015, 125(3), 413-47.

This is the second of a series of papers devoted to the study of h-p spectral element methods for three dimensional elliptic problems on non-smooth domains. The present paper addresses the proof of the main stability theorem. We assume that the differential operator is a strongly elliptic operator which satisfies Lax-Milgram conditions. The spectral element functions are non-conforming. The stability estimate theorem of this paper will be used to design a numerical scheme which give exponentially accurate solutions to three dimensional elliptic problems on non-smooth domains and can be easily implemented on parallel computers.

4 illus, 14 ref

007938   Duraphe S (Mathematics Dep, M V M, Bhopal, Email: duraphe_sus65@rediffmail.com) : New approach to solve balanced transportation problem. Ultra Scient phys Sci-Sect B 2015, 27(1), 71-3.

In this paper we have introduced a new method to obtain an initial basic feasible solution. Further, we illusrtate by suitable example.

7 ref

007937   Dorsett C (Mathematics Dep, Texas A and M Univ-Commerce, Commerce, Texas-754 29) : New characterization of T2 spaces using semi open set, feebly open set, Regular semi open set, and other related set subspaces. Ultra Scient phys Sci-Sect A 2015, 27(1), 19-25.

Within this paper, T2 spaces are further characterized using semi open set, feebly open set, regular semi open set, and other related set subspaces.

24 ref

007936   Choi J;Parmar R K (Mathematics Dep, Dongguk Univ, Gyeongju-780 714, Republic of Korea, Email: junesang@mail.dongguk.ac.kr) : Incomplete lauricella and fourth appell functions. Far East J mathl Sci 2015, 96(3), 315-28.

Recently, Srivastava et al. [18] introduced the incomplete Pochhammer symbol and studied some fundamental properties and characteristics of a family of potentially useful incomplete hypergeometric functions. Here we introduce the incomplete Lauricella function γ_C^{(n) and Γ_C(n) of n variables, and investigate certain properties of the incomplete Lauricella functions, for example, their various integral representations, differential formula and recurrence relation, in a rather systematic manner. Some interesting special cases of our main results are also considered.}

25 ref

007935   Charoenpanitseri W;Poonyakanok O (Mathematics Dep, Faculty of Information Technology Rangsit Univ, Pathumthani 12000, Thailand, Email: wongsakorn.c@rsu.ac.th) : Characterization of small 3-colorable graphs. Far East J mathl Sci 2014, 95(2), 235-48.

K-coloring of a graph is a mapping f : V(G) → {1, 2, ..., k}. A k-coloring is proper if adjacent vertices receive distinct colors. A graph is called k-colorable if it has a proper k-coloring. It is well-known that a graph is 2-colorable if and only if it does not contain any odd cycles as a subgraph. However, there is no result about forbidden subgraphs for 3-colorable graph. In this paper, we/show nine non-3-colorable graphs and prove that a graph with at most eight vertices is 3-olorable if and only if it does not contain the nine graphs as a subgraph.

11 illus, 7 ref

007934   Charkrit S (Mathematics Dep, Maejo Univ, Chiang Mai 50290, Thailand, Email: sita_char@yahoo.com) : Analytical and numerical studies on solutions of n-order singular partial differential equations. Far East J mathl Sci 2014, 95(2), 181-203.

In this paper, authors propose some new differential operators for solving the n-order singular initial value problems (IVPs) based on the Lane-Emden type in two types of partial differential equations (PDEs). The IVPs are converted into integral equations by the new inverse operators. By the combination of the modified Adomian decomposition method (ADM) and these new operators, the convergent series solution is obtained efficiently while the standard ADM cannot be used for proposed equations. Furthermore, the advantage of the two-step Adomian decomposition method (TSADM) is demonstrated to avoid noise terms and the difficulty of computations.

17 ref

007933   Chandra S;Saxena M (Mathematics Dep, S M Post-Graduate College, Chandausi-244 412, Email: satishchandra111960@gmail.com) : On the Harmonic summability of Double fourier series. Ultra Scient phys Sci-Sect A 2015, 27(1), 55-64.

In this paper we have proved a theorem on the harmonic summability of double Fourier series, which generalizes various known results.

7 ref

007932   Chandel R S;Dolas U;Tiwari R (Mathematics Govt. Dep, Geetanjali Girls College, Bhopal, Email: rs_chandel2009@yahoo.co.in) : On common fixed point theorem in complete metric space for mapping of Compatible type Y. Ultra Scient phys Sci-Sect A 2015, 27(1), 13-18.

In this paper author prove a unique common fixed point theorem for pair of self-mappings of weakly compatible maps in a complete metric space for mappings satisfying compatibility of type γ.

5 ref

007931   Campos S;Saal L (NO, Universidad Nacional de Cordoba, Cordoba, Argentina, Email: silcampos@famaf.unc.edu) : Some spherical analysis related to the pairs (U (n), H_n) and (U (p,q), H_n), P + q = n. Proc Indian Acad Sci-Mathl Sci 2015, 125(3), 371-97.

In this paper authors define the normalized spherical transform associated with the generalized Gelfand pair (U(p, q), H_n), where H_n is the Heisenberg group 2n + 1 -dimensional and p+ q = n. We show that the normalized spherical transform F(f) of a Schwartz function f on H_n restricted to the spectrum of the Gelfand pair (U(n), H_n) is the Gelfand transform g of a radial Schwartz function g on H_n. Moreover, by the Godement-Plancherel inversion formula the function g can be recovered explicitly from F(f).

12 ref

007930   Balasubramanian S;Chaitanya Ch (Mathematics Dep, Government Arts College (A), Karur-639 005, Email: mani55682@rediffmail.com) : Contra ag-Closed and almost contra ag-closed mapping. Ultra Scient phys Sci-Sect A 2015, 27(1), 95-106.

The aim of this paper is to introduce and study the concepts of contra αg-closed and almost contra αg-closed mappings and the interrelationship between other contra-closed maps.

36 ref

007929   Auria N A D (Mathematics and Applications R. Caccioppoli, Univ of Naples Federico II, Via Claudia-80125 Naples, Italy, Email: nudauria@unina.it) : Well posed minty quasi variational inequalities. Far East J mathl Sci 2015, 96(3), 379-91.

A concept of well-posedness for quasi-variational inequalities of Minty type with one or more than one solution is presented. Characterizations and sufficient conditions are given in Banach spaces.

17 ref

007928   Aloney M R;Sahu G (NO, Bhagwant Univ, Ajmer, Rajshthan) : Almost relative strongly M-flat modules. Ultra Scient phys Sci-Sect A 2015, 27(1), 7-12.

Throughout this paper we have defined a new concept of almost strongly M-flat modules^{11 and we are motivated10. And given several properties of them13. This paper concept introduced as a generalization of flat modules. There are two part in discussion In first part we study Almost strongly M-flat modules and in second section we study about the homomorphism θ_X : A Σ_R⊗ Hom_R(XJ, NJ)→ Hom_A (A Σ_R⊗ XJ, A Σ_R⊗NJ) Where A is an R-algebra, XJ and NJ is R-modules. And last result we prove M be almost strongly M-flat modules then following statement are equivalent. a) Any finitely generated ideal I is almost M-projective b) Every submodule of M is almost strongly M-flat modules. c) Every flat module is almost strongly M-flat module.}

2 illus, 24 ref

007927   Al-Khazaleh A M H;Al Wadi S;Ababneh F (Mathematics Dep, Faulty of Science, Al-Albayt Univ Al-Mafraq, Jordan, Email: ahmed_2005kh@yahoo.com) : Wavelet transform asymmetric winsorized mean in detecting outlier values. Far East J mathl Sci 2015, 96(3), 339-51.

One of the main problems in large datasets is outlier detection, the outliers are detected using Z-score, box plot method, statistical measures and asymmetric Winsorized mean. This paper has a novel method for detecting the outlier values by combining the asymmetric Winsorized mean with the famous spectral analysis function which is wavelet transform (WT). As a result, after comparing the new technique with the previous mentioned methods using financial data from Amman Stock Exchange (ASE), we have found the wavelet transform asymmetric Winsorized mean (WTAWM) is the best method in outlier detections.

1 illus, 3 table, 19 ref

007926   Agarwal P;Rogosin S V;Trujillo J J (Mathematics Dep, Anand International College of Engineering, Jaipur-303 012, Email: praveen.agarwal@anandice.ac.in) : Certain fractional integral operators and the generalized multi-index mittag-leffler functions. Proc Indian Acad Sci-Mathl Sci 2015, 125(3), 291-306.

In this paper, authors obtain formulas of fractional integration (of Marichev-Saigo-Maeda type) of the generalized multi-index Mittag-Leffler functions E_{y, k} [(α_j, β_j)m; z] generalizing 2m-parametric Mittag-Leffler functions studied by Saxena and Nishimoto (J. Fract. Calc. 37 (2010) 43-52). Some interesting special cases of our main results are considered too.

54 ref

007925   Abdelkarim A A (NO, Jerash Private Univ, Jerash, Jordan) : Properly separable defferential equations. Far East J mathl Sci 2015, 96(3), 329-37.

A differential or integral equation is called properly separable if it can be written as y^{(n) = ⇔₁ a_nyn, yn = ⇔₁ a_nDn(y), In(y) = ⇔ a_nyn or yn = ⇔₁ a_nIn(y). In this note, we give solutions for some cases of these equations.}

1 ref

007924   Abbas S;Kavitha V;Murugesu R (School of Basic Sciences, Indian Institute of Technology Mandi, Mandi-175 001, Email: abbas@iitmandi.ac.in) : Stepanov-like weighted pseudo almost automorphic solutions to fractional order abstract integro-differential equations. Proc Indian Acad Sci-Mathl Sci 2015, 125(3), 323-51.

In this article, we study the concept of Stepanov-like weighted pseudo almost automorphic solutions to fractional order abstract integro-differential equations. We establish the results with Lipschitz condition and without Lipschitz condition on the forcing term. An interesting example is presented to illustrate the main findings. The results proven are new and complement the existing ones.

44 ref