014585   Sukanya M;Choi J;Rathie A K (Mathematics Dep, School of Mathematical and Physical Sciences, Central Univ of Kerala, Tejaswini Hills, Periye P.O., Kasaragod, 671316, Kerala State, Email: sukanyam981@gmail.com) : Note on two results involving products of generalized hypergeometric functions. Far East J mathl Sci 2017, 101(1), 119-23.

The objective of this note is to provide an elementary proof of two very interesting and useful results due to Bailey involving products of generalized hypergeometric functions.

3 ref

014584   Sriraj M A (Mathematics Dep, Vidyavardhaka College of Engineering, Mysuru-570 002, Email: masiraj@gmail.com) : Bounds for the largest color eigenvalue and the color energy. Int J mathl Combinatorics 2017, 1(1), 127-34.

In [1] Chandrashekar Adiga et al. introduced the matrix of a vertex colored graph and studied their eigenvalues called color eigenvalues. Further, defined the color energy of the graph and obtained some results. In this paper, we obtain bounds for the largest color eigenvalue and the color energy.

8 ref

014583   Somashekar D D;Shalini S L;Vidya N (Studies in Mathematics Dep, Mysore Univ, Manasagangotri, Mysuru-576 006, Email: dsomashekara@yahoo.com) : On transformationa and summation formulas for some basic hypergeomatric series. Int J mathl Combinatorics 2017, 1(1), 22-35.

In this paper, we give an alternate and simple proofs for Sear's three term ₃φ₂ transformation formula, Jackson's ₃φ₂ transformation formula and for a nonterminating form of the q-Saalschutz sum by using q-exponential operator techniques. We also give an alternate proof for a nonterminating form of the q-Vandermonde sum. We also obtain some interesting special cases of all the three identities, some of which are analogous to the identities stated by Ramanujan in his lost notebook.

15 ref

014582   Solouma E M;Wageeda M M (Mathematics Dep, Faculty of Science, Beni-Suef Univ, Egypt, Email: emadms74@gmail.com) : Special smarandache curves according to bishop frame in euclidean spacetime. Int J mathl Combinatorics 2017, 1(1), 1-9.

In this paper, authors introduce some special Smarandache curves according to Bishop frame in Euclidean 3-space E^{3. Also, we study Frenet-Serret invariants of a special case in E3. Finally, we give an example to illustrate these curves.}

5 illus, 10 ref

014581   Shukla H S;Pandey O P;Manda K (Mathematics & Statistics Dep, DDu Gorakhpur Univ, Gorakhpur, Email: profhsshuklagkp@rediffmail.com) : The β-change of special finsler spaces. Int J mathl Combinatorics 2017, 1(1), 78-87.

Authors have considered the β-change of Finsler metric L given by L* = f(L, β), where f is any positively homogeneous function of degree one in L and β. We have obtained the β-change of C-reducible Finsler spaces, S3-like Finsler spaces and T-tensor. Particular case when b_i in β is concurrent vector field has been studied.

7 ref

014580   Senyurt S;Cahskan A;Celik U (Faculty of Arts and Sciences, Mathematics Dep, Ordu Univ, Ordu, Turkey, Email: senyurtsuleyman@hotmail.com) : N*C* - smarandache curve of bertrand curves pair according to frenet frame. Int J mathl Combinatorics 2016, 1(1), 1-7.

In this paper, let (α, α*) be Bertrand curve pair, when the unit Darboux vector of the α* curve are taken as the position vectors, the curvature and the torsion of Smarandache curve are calculated. These values are expressed depending upon the α curve. Besides, we illustrate example of our main results.

2 illus, 14 ref

014579   Selvaraj B;Raju M (Science and Humanities Dep, Nehru Institute of Engineering and Technology, Coimbatore-641 105, Email: professorselvaraj@gmail.com) : Oscillatory solutions to certain second order neutral difference equations with quasi difference. Far East J mathl Sci 0000, 99(8), 1271-81.

This paper is concerned with some sufficient conditions for oscillatory solutions of the second order neutral difference equation of the form Δ(a_nΔ(x_n - p_nx_n-1)) + q_nf(x_n-τ) = 0, n ∈ N(a), a = max(1, τ). The result is obtained by transforming the second order neutral difference equation into third order non-neutral difference equation with some suitable substitutions.

7 ref

014578   Sato I (NO, Oyama National College of Technology, Oyama, Tochigi 323-0806, Japan, Email: isato@oyama-ct.ac.jp) : The matrix-weighted product distance matrix of a tree. Far East J mathl Sci 2017, 101(1), 25-37.

Recently, Bapat and Sivasubramanian [2] presented formulas for the determinant and the inverse of the product distance matrix of a tree. We introduce the product distance matrix of a tree with matrix weights and present formulas for its determinant and its inverse.

11 ref

014577   Santhimaheswari N R (Mathematics Dep, G.Venkataswamy Naidu College, Kovilpatti-628 502, Email: nrsmaths@yahoo.com) : On (r,m,k)-regular fuzzy graphs. Int J mathl Combinatorics 2016, 1(1), 18-26.

In this paper, (r,m, k)- regular fuzzy graph and totally (r,m, k)- regular fuzzy graph are defined and compared through various examples. A necessary and sufficient condition under which they are equivalent is provided. Also (r,m, k)-regularity on some fuzzy graphs whose underlying crisp graph is a cycle is studied with some specific membership functions.

1 illus, 17 ref

014576   Saluja G S (Mathematics Dep, Govt Nagarjuna P.G College of Science, Raipur-492 010, Email: saluja1963@gmail.com) : Fixed point results under generalized contraction involving rational expression in complex valued metric spaces. Int J mathl Combinatorics 2017, 1(1), 53-62.

The aim of this paper is to study common fixed point under generalized contraction involving rational expression in the setting of complex valued metric spaces. The results presented in this paper extend and generalize several results from the existing literature.

8 ref

014575   Saluja G S (Mathematics Dep, Govt. Nagarjuna P.G. College of Science, Raipur-492 010, Email: saluja1963@gmail.com) : On common fixed point theorems with rational expressions in cone b-metric spaces. Int J mathl Combinatorics 2016, 1(1), 65-75.

In this paper, we establish some common fixed point theorems for rational contraction in the setting of cone b-metric spaces with normal solid cone. Also, as an application of our result, we obtain some results of integral type for such mappings. The results extend and generalize several known results from the existing literature.

16 ref

014574   Salah J Y (Basic Sciences, College of Applied Sciences, A'Sharqiyah Univ, Ibra, Oamn, Email: damous73@yahoo.com ) : Closed-to-convex criterion associated to the modified caputo's fractional calculus derivative operator. Far East J mathl Sci 2017, 101(1), 55-9.

In this paper, an open problem on the theory of univalent functions is evoked by the means of a fractional calculus derivative operator; that is a modification of the Caputo's fractional operator. A connection between functions belonging to the class of analytic functions and special case of the modified Caputo's derivative operator are also provided.

7 ref

014573   Riyas A;Geetha K (Mathematics Dep, T.K.M College of Engineering, Kollam-691 005, Email: riyasmaths@gmail.com) : study on cayley graphs over dihedral groups. Int J mathl Combinatorics 2017, 1(1), 63-70.

Let G be the dihedral group D_n and Cay(G, S) is the Cayley graph of G with respect to S, and let C_G(x) is the centralizer of an element x in G and x(bar) is the orbit of x in G. In this paper, we prove that if G act on G by conjugation, the vertex induced subgraph with vertex set C_G(x) of the Cayley graph Cay(G, x(bar) is either Hamiltonian or it contain Hamiltonian decompositions. But if n is prime, it is always Hamiltonian.

7 ref

014572   Renganathan N G;Udayabaskaran S;Lalitha D (NO, School of Basic Sciences Vel Tech Rangarajan Dr. Sagunthala R&D Insti, Chennai-600 062) : Stochastic analysis of HIV infection in the presence of therapeutic intervention. Far East J mathl Sci 2016, 99(8), 1119-139.

In this paper, a stochastic model of human immunodeficiency virus (HIV) dynamics is proposed and analysed in the presence of therapeutic intervention. The population of cells and HIV is divided into three compartments, one compartment is recognizable and the other two are unrecognizable by the therapy. Based upon the non-availability of improved therapy, the progression of HIV in the population is studied. The mean number of HIVs which escape therapy recognition at any time t is obtained. A discussion on the amount of toxin produced by the HIV population is also provided. A numerical study is provided to highlight the impact of the therapy on the HIV population. It is further shown that the three compartmental model generates a probability density function of cell death times. The behaviour of the proposed model is compared with those available in cancer treatment models.

6 illus, 16 ref

014571   Raheem A;Baig A Q (Mathematics Dep, COMSATS Institute of Information Technology, Islamabad, Pakistan, Email: rahimciit7@gmail.com) : Super edge-antimagic labeling of subdivided star trees. Int J mathl Combinatorics 2016, 1(1), 27-33.

Let G be a graph with V (G) and E(G) as the vertex set and the edge set respectively. An (a, d)-edge-antimagic total labeling of a graph G is a bijection λ from the set V (G) ∪ E(G) → {1, 2, 3, ..., |V(G)| + |E(G)|} such that the set of edge-weights {λ(x) + λ(xy) + λ(y) : xy ∈ E(G)} is equal to {a, a+d, a+2d, ..., a+(|E(G)|-1)d} where the integers a <62> 0 and d ≥ 0. An (a, d)-edge-antimagic total labeling of a graph G is called super (a, d)-EAT labeling if the smallest possible labels are assigned to the vertices of the graph G.

24 ref

014570   Ponraj R;Adaickalam M M;Kala R (Mathematics Dep, Sri Paramakalyani College, Alwarkurichi-627 412, Email: ponrajmaths@gmail.com) : Quotient cordial labeling of graphs. Int J mathl Combinatorics 2016, 1(1), 101-8.

In this paper we introduce quotient cordial labeling of graphs. Let G be a (p, q) graph. Let f : V (G) → {1, 2, ..., p} be a 1 - 1 map. For each edge uv assign the label [f(u)/f(v)] (or) [f(v)/f(u)] according as f(u) ≥ f(v) or f(v) <62> f(u). f is called a quotient cordial labeling of G if |e_f(0) - e_f(1)| ≤ 1 where e_f(0) and e_f(1) respectively denote the number of edges labelled with even integers and number of edges labelled with odd integers. A graph with a quotient cordial labeling is called a quotient cordial graph. We investigate the quotient cordial labeling behavior of path, cycle, complete graph, star, bistar etc.

4 illus, 3 tables, 5 ref

014569   Opio I;Mirumbe G I;Ssebuliba J;Mango J M (Mathematics Dep, Makerere Univ, P.O. Box 7062, Kampala, Uganda, Email: mirumbe@cnc.mak.ac.ug) : On the solution space of ordinary differential equations with polynomial coefficients. Far East J mathl Sci 2017, 101(1), 103-18.

Consider the ordinary differential equation with polynomial coefficients defined on R as follows: ty^{(n)(t) + (m-t)y(n-1)(t)-py(t) = 0. where t ∈ (-∞, ∞), n, p, m ∈ Z₊ and n ≥ 2. We prove in this paper that the values of m and p determine whether the solutions of the equation (1) are either classical, that is solutions in the space C(-∞, ∞) of continuous functions on R or distributional which are solutions in the space D' of distributions whose supports are bounded on the positive real half-line or both.}

9 ref

014568   Nayak N G (Mathematics and Statistics Dep, S.S Dempo College of Commerce and Economics, Goa, Email: nayaknutan@yahoo.com) : Spectra and energy of signed graphs. Int J mathl Combinatorics 2017, 1(1), 10-21.

The energy of a signed graph Σ is defined as ε(Σ) = ∑^{n_t=1 |λ_i|, where λ₁, λ₂, ..., λ_n are the eigenvalues of Σ. In this paper, we study the spectra and energy of a class of signed graphs which satisfy pairing property. We show that it is possible to compare the energies of a pair of bipartite and non-bipartite signed graphs on n vertices by defining quasi-order relation in such a way - 29 - that the energy is increasing. Further, we extend the notion of extended double cover of graphs to signed graphs to find the spectra of unbalanced signed bipartite graphs and also we construct non-cospectral equienergetic signed bipartite graphs.}

3 illus, 16 ref

014567   Nayak N G (Mathematics and Statistics Dep, S. S. Dampo College of Commerce and Economics, Goa, Email: nayaknutan@yahoo.com) : On net-regular signed graphs. Int J mathl Combinatorics 2016, 1(1), 57-64.

A signed graph is an ordered pair Σ = (G, σ), where G = (V,E) is the underlying graph of Σ and σ : E → {+1,-1}, called signing function from the edge set E(G) of G into the set {+1,-1}. It is said to be homogeneous if its edges are all positive or negative otherwise it is heterogeneous. Signed graph is balanced if all of its cycles are balanced otherwise unbalanced. It is said to be net-regular of degree k if all its vertices have same net-degree k i.e. k = d^{±_Σ(v) = d+_Σ(v) - d-_Σ(v), where d+_Σ(v)(d-_Σ(v)) is the number of positive(negative) edges incident with a vertex v. In this paper, we obtained the characterization of net-regular signed graphs and also established the spectrum for one class of heterogeneous unbalanced net-regular signed complete graphs.}

3 illus, 14 ref

014566   Narayankar K P;Lokesh S B (Mathematics Dep, Manglore Univ, Mangalagangothri, Manglore-574 199, Email: kishori_pn@yahoo.co.in) : Peripheral distance energy of graphs. Int J mathl Combinatorics 2017, 1(1), 88-101.

The peripheral distance matrix of a graph G of order n with k peripheral vertices is a square symmetric matrix of order k x k, denoted as D_p-matrix of G and is defined as D_p(G) = [d_ij], where d_ij is the distance between two peripheral vertices v_i and v_j in G. The peripheral distance energy of a graph G is the sum of the absolute values of the eigenvalues of D_p-matrix of G. The sum of the distances between all pairs of peripheral vertices is a peripheral Wiener index of a graph G. In this paper, we study some preliminary facts of D_p-matrix of G and give some bounds for peripheral distance energy of a graph G. Specially the bounds are presented for a graph of diameter less than 3. Bounds of peripheral distance energy in terms of peripheral Wiener index are also obtained for graphs of diam (G) ≤ 2.

1 illus, 33 ref

014565   Mueen Z;Ramli R;Zaibidi N Z (Decision Science Dep, School of Quantitative Science, Univ Utara Malaysia, Malaysia, Email: mueen.zeiana@gmail.com) : Minimizing waiting times using multiple fuzzy queueing model with supply priorities. Far East J mathl Sci 2016, 99(8), 1177-93.

This paper proposes to construct the membership function of the system characteristics of a multiple channel queueing model with two classes of priority in which arrival rates and service rates of customers are all fuzzy numbers. A crisp multiple channel with two classes of priority queueing system generalized to a fuzzy environment has been seen to adopted widely in previous literature, hence the motivation to transform a fuzzy queue with multiple channel and two class of priority into a family of conventional crisp queues with the application of alpha cut approach. A set of parametric nonlinear programs is developed to describe the family of crisp queues with multiple channels priority and a numerical example is solved successfully to demonstrate the validity of the proposed procedure. The developed mathematical formula in this article is expressed by membership functions rather than by crisp values and more focus is - 28 - placed on queueing systems encountered in real life with the aim of reducing the expected waiting time of customers in the queue for each priority class.

2 illus, 1 table, 20 ref

014564   Min W K;Kim Y K (Mathematics Dep, Kangwon National Univ, Chuncheon 200-701, Korea, Email: wkmin@kangwon.ac.kr) : On generalized w-closed sets in associated weak spaces. Far East J mathl Sci 2017, 101(1), 201-14.

The purpose of this note is to introduce the notion of generalized w_τ-closed (w_τ-open) sets in an associated w_τ-space and to study its properties. In particular, we find the conditions of continuous functions to preserve generalized w_τ-closed sets or generalized w_τ-open sets.

14 ref

014563   Makkala T;Leerawat U (Methematics Dep, Faculty of Science, Kasetsart Univ, Bangkok 10900, Thailand, Email: fsciut1@ku.ac.th) : Structure of Γ-generalized boolean semirings. Far East J mathl Sci 2017, 101(1), 39-53.

In this paper, we establish a generalization of Boolean semiring, namely Γ-generalized Boolean semiring. Moreover, we introduce the concept of ideal, quotient and homomorphism of Γ-generalized Boolean semiring and then some related properties are discussed.

9 ref

014562   Mahde S S;Mathad V (Mathematics Dep, Mysore Univ, Manasagangotri, Mysuru, Email: sultan.mahde@gmail.com) : Pure edge neighbor integrity of graphs. Int J mathl Combinatorics 2017, 1(1), 111-26.

In a communication network, several vulnerability measure s are used to determine the resistance of the network to disruption of operation after the failure of certain stations or communication links. This study introduces a new vulnerability parameter, pure edge-neighbor-integrity of graphs. The pure edge-neighbor-integrity of a graph G is defined to be PENI(G) = min_R⊆E(G){|R| + w_e(G/R)}, where R is any edge subversion strategy of G and w_e(G/R) is the number of edges in the largest component of G/R. A set R ⊆ E(G), is said to be a PENI-set of G if PENI (G) = |R| + w_e(G/R). In this paper, several properties and bounds on the PENI are presented over here and the relation between PENI with other parameters is investigated. The PENI of some classes of graphs is also computed.

11 illus, 18 ref

014561   Madhi M H;Mohamed N (Statistics Dep, Faculty of Science, Sebha Univ, Sebha, Libya, Email: hassan2000_2009@yahoo.com) : Modified grey model GM(1, 1) based on reconstruction of background value. Far East J mathl Sci 2017, 101(1), 189-99.

In recent years, the grey forecasting model has achieved good prediction accuracy with limited data and has been widely used in several research fields. However, the grey forecasting model sometimes yields large forecasting errors which need to be improved. It is found that background value is an important tool affecting the accuracy and adaptability of the GM(1,1) model. Thus, to minimize such errors, this paper develops an optimization model for the traditional GM(1,1) model based on reconstructing the background value. As a result, the comparison shows that the modified model provides significantly better performance than traditional grey model GM(1,1).

1 illus, 1 table, 13 ref

014560   Kowsalya V;Vernold Vivin J (Research & Developement Centre, Bharathiar Univ, Coimbatore-641 046, Email: vkowsalya09@gmail.com) : Note on acyclic coloring of sunlet graph families. Int J mathl Combinatorics 2017, 1(1), 135-8.

In this paper, authors find the acyclic chromatic number χ_a for the central graph of sunlet graph C(S_n), line graph of sunlet graph L(S_n), middle graph of sunlet graph M(S_n) and the total graph of sunlet graph T(S_n) for all n ≥ 3.

5 ref

014559   Kilicoglu S;Senyurt S (Mathematics Dep, Baskent Univ, Turkey, Email: senyurtsuleyman@hotmai.com) : On the second order mannheim partner curve in E<. Int J mathl Combinatorics 2017, 1(1), 71-7.

In this study first authors worked on the Mannheim curve pair {α, α₁} and Mannheim curve pair {α₁, α₂}. We called α₂ as the second order Mannheim partner curve of the Mannheim curve α. We examined the Frenet apparatus of second order Mannheim partner curve in terms of, Frenet apparatus of Mannheim curve α, with the offset property of second order Mannheim partner α₂. Further we examined third order Mannheim partner α₃ where {α₂, α₃} are Mannheim curve pair.

9 ref

014558   Goo Y H (Mathematics Dep, Hanseo Univ, Seosan, Chungnam-356 706, Republic of Korea, Email: yhgoo@hanseo.ac.kr) : h-Stability and boundedness in the functional differential systems. Far East J mathl Sci 0000, 99(8), 1215-31.

In this paper we show that the solutions to nonlinear perturbed differential system y' = f(t, y) + <91>^{t_t0 g(s, y(s))ds + h(t, y(t), Ty(t)), have h-stability and bounded property by imposing conditions on the perturbed part <91>t_t0 g(s, y(s))ds + h(t, y(t), Ty(t)) and on the fundamental matrix of the unperturbed system y' = f(t, y).}

16 ref

014557   Goo Y H (Mathematics Dep, Hanseo Univ, Seosan Chungnam-356 706, Republic of Korea, Email: yhgoo@hanseo.ac.kr) : Asymptotic property for nonlinear perturbed functional differential systems. Far East J mathl Sci 2016, 99(8), 1141-57.

In this paper, we show that the solutions to nonlinear perturbed functional differential system y' = f(t, y) + <91>^{t_t0 g(s, y(s), Ty(s))ds, have asymptotic property by imposing conditions on the perturbed part <91>t_t0 g(s, y(s), Ty(s)) ds and on the fundamental matrix of the unperturbed system y' = f(t, y).}

16 ref

014556   Ergun E;Bayram E (Ondokuz Mayis Univ, Carsamba Shamber of Commerce Vocational School, Carsamba, Samsun, Turkey, Email: eergun@omu.edu.tr) : Surface family with a common natural Geodesic lift. Int J mathl Combinatorics 2016, 1(1), 34-41.

In the present paper, authors find a surface family possessing the natural lift of a given curve as a geodesic. We express necessary and sufficient conditions for the given curve such that its natural lift is a geodesic on any member of the surface family. We present a sufficient condition for ruled surfaces with the above property. Finally, we illustrate the method with some examples.

5 illus, 8 ref

014555   Dobbs D E (Mathematics Dep, Tennessee Univ Knoxville, Tennessee 37996-1320, Email: dobbs@math.utk.edu) : When the relative integral closure is the only intyermediate ring. Far East J mathl Sci 2017, 101(1), 15-24.

Let A ⊂ B be (commutative) rings (with the same 1); let A* denote the integral closure of Ain B. Suppose that A ⊂ A* and A* ⊂ B are minimal ring extensions whose crucial maximal ideals are M and N, respectively. Then A* is the only ring Csuch that A ⊂ C ⊂ B if and only if N ∩ A = M. This generalizes a recent for integral domains due to Ben Nasr and Zeidi [2]. We give examples with nontrivial zero-divisors to illustrate both possibilities (i.e., where N ∩ A may or may not be M).

12 ref

014554   Dey S;Bhattacharyya A (Mathematics Dep, Jadavpur Univ, Kolkata-700 032, Email: santu.mathju@gmail.com) : Some curvature properties of LP-sasakian manifold with respect to quarter-symmetric metric connection. Int J mathl Combinatorics 2016, 1(1), 42-56.

The objective of the present paper is to study the curvature tensor of the quarter-symmetric metric connection - 25 - with respect to Lorentzian Para-Sasakian manifold (briefly, LP-Sasakian manifold). It is shown that if in the manifold M^{n, W₂ = 0, then the manifold Mn is locally isomorphic to Sn(1), where W₂ is the W₂-curvature tensor of the quarter-symmetric metric connection in a LP-Sasakian manifold. Next we study generalized projective φ-Recurrent LP-Sasakian manifold with respect to quarter-symmetric metric connection. After that φ-pseudo symmetric LP-Sasakian manifold with respect to quarter-symmetric metric connection is studied and we also discuss LP-Sasakian manifold with respect to quarter-symmetric metric connection when it satisfies the condition P(bar).S(bar) = 0, where P(bar) denotes the projective curvature tensor with respect to quarter-symmetric metric connection. Further, we also study ξ-conharmonically flat LP-Sasakian manifold with respect to quarter-symmetric metric connection. Finally, we give an example of LP-Sasakian manifold with respect to quarter-symmetric metric connection.}

18 ref

014553   Devendra Kumar;Choi J;Singh J;Sharma R P (Mathematics Dep, JECRC Univ, Jaipur-303 905, Email: devendra.maths@gmail.com) : Numerical solution of nonlinear fractional Camassa-Holm equation. Far East J mathl Sci 2017, 101(1), 125-35.

Authors aim to present a numerical algorithm for solving a nonlinear fractional Camassa-Holm equation. The Camassa-Holm equation arises in shallow water waves. The fractional derivative is taken in Caputo sense. The numerical results are presented graphically. The results show that the analytical scheme is very effective and user-friendly for solving nonlinear fractional differential equations describing physical problems.

4 illus, 30 ref

014552   Chaubey V K;Mishra A;Pandey A K (Applied Sciences Dep, Buddha Institute of Technology, Gida, Gorakpur-273 209, Email: vkchaubey@outlook.com) : Some properties of a h-Randers finsler space. Int J mathl Combinatorics 2017, 1(1), 102-10.

The purpose of the present paper is to obtain the relation between imbedding class numbers of tangent Riemannian spaces to (M^{n, L) and (Mn, L*) where L*(x, y) is obtained from the transformation of L(x, y) is given by L*(x,y) → L(x,y) + b_i(x,y)yi.}

16 ref

014551   Charoenpol A;Ratanaprasert C (Mathematics Dep, Faculty of Science, Silpakorn Univ, Nakhon Pathom, 73000, Thailand, Email: aveya.c@gmail.com) : The lattice of all subvarieties of M_n. Far East J mathl Sci 2017, 101(1), 61-71.

Authors introduced a BDLC-algebra in [3] to be a lattice-based algebra (A; ∨, ∧, f, 0, 1) whose (A; ∨, ∧, 0, 1) is a bounded distributive lattice and f is a connected 0-endomorphism. We showed that for each n ∈ N, the class M_n of all BDLC-algebras whose the pre-period is less than or equal to n is a variety. In [4], we characterized all subdirectly irreducible algebras in M_n moreover, it can be generated by a single subdirectly irreducible algebra. In this paper, we apply the results in [3, 4] and [5] to describe the lattice of all subvarieties of M_n for all n ∈ N.

4 illus, 10 ref

014550   Chandrakala S B (NO, Nitte Meenakshi Institute of Technology, Bangalore) : Clique partition of transformation graphs. Int J mathl Combinatorics 2016, 1(1), 91-96.

A clique in a graph G is a complete subgraph of G. A clique partition of G is a collection C of cliques such that each edge of G occurs in exactly one clique in C. The clique partition number cp(G) is the minimum size of a clique partition of G. In this paper upper bounds for the clique partition number of the transformation graphs G^{++- and G+++ for some standard class of graphs is obtained.}

4 ref

014549   Chamidah N;Rifada M (Mathematics Dep, Faculty of Sciences and Technology, Airlangga Univ, Surabaya, Indonesia, Email: nur-c@fst.unair.ac.id) : Local linear estimation in BI-responce semiparametric regression model for estimating median growth charts of children. Far East J mathl Sci 2016, 99(8), 1233-44.

Measurement of growth in a child generally depends on anthropometric measure wherein weight and height (or length) are considered. In this paper, we investigate median growth charts of children ranging from birth to two years old taking their sex also in account. Thus, a bi-response semiparametric model based on local linear estimator is used in which weight and length are response variables, and sex as a parametric while the age as nonparametric predictor variables. The difference pattern of growth chart has been discussed for both boys as well as girls.

6 illus, 8 ref

014548   Chaluvaraju B;Boregowda H S;Kumbinarsaiah S (Mathematics Dep, Bangalore Univ, Janana Bharathi Campus, Bangalore-560 056, Email: bchaluvaraju@gmail.com) : Binding number of some special classes of trees. Int J mathl Combinatorics 2016, 1(1), 76-81.

The binding number of a graph G = (V,E) is defined to be the minimum of |N(X)|/|X| taken over all nonempty set X ⊆ V(G) such that N(X) ≠ V(G). In this article, we explore the properties and bounds on binding number of some special classes of trees.

8 ref

014547   Buvaneswari S;Rajendran P A (Mathematics Dep, Periyar Maniammai Univ, Vallam, Thanjavur-613 403, Email: buvaneswari@pmu.edu) : Products and coproducts in the category of graphs. Far East J mathl Sci 2016, 99(8), 1261-70.

In category theory the definition of a product of objects was first given by Maclane in the 1950's and it is probably the earliest example of category theory being used to define a fundamental mathematical notion by giving a universal mapping property (UMP) which determines the structure uniquely. In this article, we investigate which of the products among the so many products defined in graph theory such as the Cartesian product, the strong product, the Tensor product, etc., actually satisfy the universal mapping property (UMP) in the category of graphs.

5 ref

014546   Boonsanyos C;Anantayasethi A;Saengsura K (Mathematics Dep, Faculty of Science, Mahasarakham Univ, Thailand, Email: kittisak.s@msu.ac.th) : Maximal clones of co-operations on {0,1,2}. Far East J mathl Sci 0000, 99(8), 1159-75.

In this paper, authors characterize all maximal clones of co-operations on {0, 1, 2}.

4 ref

014545   Basavanagoud B;Desai V R (NO, Mathematics Karnatak Univ Dep, Dharwad-580 003, Email: b.basavanagoud@gmail.com) : On the wiener index of quasi-total graph and its complement. Int J mathl Combinatorics 2016, 1(1), 82-90.

The Wiener index of a graph G denoted by W(G) is the sum of distances between all (unordered) pairs of vertices of G. In practice G corresponds to what is known as the molecular graph of an organic compound. In this paper, we obtain the Wiener index of quasi-total graph and its complement for some standard class of graphs, we give bounds for Wiener index of quasi-total graph and its complement also establish Nordhaus-Gaddum type of inequality for it.

12 ref

014544   Alhamedi A A;Ibrahim K;Alodat M T;Masseran N (Statistics Program School of Mathematical Sciences, Faculty of Scienc, Kebangsaan Malaysia Univ, Malaysia, Email: obideeali@gmail.com) : Bayesian inference for multiple linear regression model under extended skew normal errors. Far East J mathl Sci 2017, 101(1), 171-87.

In this paper, we conduct a study on the Bayesian inference for the multiple linear regression model when errors are assumed to follow the independent extended skew normal distribution. In the Bayesian inference, a hierarchal representation of the prior parameters is adopted in order to take advantage of the flexibility in the Bayesian methods. Then, we derive the posterior and full conditional posterior distribution. Furthermore, we conduct a simulation study to compare the parameter estimates found under the assumption that errors follow the extended skew normal distribution with their counterparts when the errors follow the multivariate normal distribution. Finally, we apply our findings to Australian Athletes data.

2 illus, 4 tables, 12 ref

014543   Akhbari M H (Mathematics Dep, Estahban Branch Islamic Azad Univ, Estahban, Iran) : Probabilistic bounds on weak and strong total domination in graphs. Int J mathl Combinatorics 2016, 1(1), 97-100.

A set D of vertices in a graph G = (V,E) is a total dominating set if every vertex of G is adjacent to some vertex in D. A total dominating set D of G is said to be weak if every vertex v ∈ V - D is adjacent to a vertex u ∈ D such that d_G(v)≥d_G(u). The weak total domination number _γwt(G) of G is the minimum cardinality of a weak total dominating set of G. A total dominating set D of G is said to be strong if every vertex v ∈ V - D is adjacent to a vertex u ∈ D such that d_G(v) ≤ d_G(u). The strong total domination number _γst(G) of G is the minimum cardinality of a strong total dominating set of G. We present probabilistic upper bounds on weak and strong total domination number of a graph.

10 ref

013501   Zong Z;Hu F (School of Statistics, Qufu Normal Univ, Qufu, Shandong 273165, China, Email: hufengpf@163.com) : L<. Proc Math Sci 2016, 126(3), 433-60.

In this paper, by using L^p (1<60> p ≤ 2) weak convergence method on backward stochastic differential equations (BSDEs) with non-uniformly Lipschitz coefficients, we obtain the limit theorem of gg-supersolutions. As applications of this theorem, we study the decomposition theorem of ε_g-supermartingale, the nonlinear decomposition theorem of Doob-Meyer's type and so on. Furthermore, by using the decomposition theorem of ε-supermartingale, we - 31 - provide some useful characterizations of an ε-evaluation by the generating function g(t;ω;y;z) without the assumption that gg is continuous with respect to tt. Our results generalize the known results in Ph. Briand et al., Electronic Commun. Probab. 5 (2000) 101-117; L Jiang, Ann. Appl. Probab. 18 (2008) 245-258; S Peng, Probab. Theory Relat. Fields 113 (1999) 473-499; S Peng, Modelling derivatives pricing with their generating functions (2006) http://arxiv.org/abs/math/0605599 and E Rosazza Gianin, Insur. Math. Econ. 39 (2006) 19-34.

31 ref

013500   Zhang J;Miao L;Tang J (School of Mathematical Sciences, Yangzhou Univ, Yangzhou 225002, People's Republuic of China, Email: lmiao@yzu.edu.cn) : M*-supplemented subgroups of finite groups. Proc Math Sci 2016, 126(2), 187-97.

A subgroup H of a group GG is said to be M*-supplemented in G if there exists a subgroup K of G such that G = H K and H ∩ K is M-supplemented in G. In this paper, we prove as follows: Let E be a normal subgroup of a group G. Suppose that every maximal subgroup of every non-cyclic Sylow subgroup P of F*(E) is M*-supplemented in G, then E ≤ Z_Uφ(G).

18 ref

013499   Zhang H (School of Mathematics Science, Huaiyin Normal Univ, 111 Changjiang West Road, Huaian, Jiangsu 223300, China, Email: hhzh@hytc.edu.cn) : (3, 1)*-choosability of graphs of nonnegative characteristic without intersecting short cycles. Proc Math Sci 2016, 126(2), 159-65.

A graph G is called (k, d)*-choosable if for every list assignment L satisfying |L(v)| ≥ k for all v ∈ V(G), there is an L-coloring of G such that each vertex of G has at most d neighbors colored with the same color as itself. In this paper, it is proved that every graph of nonnegative characteristic without intersecting i-cycles for all i = 3, 4, 5 is (3, 1)*-choosable.

1 illus, 17 ref

013498   Zamora A (NO, Instituto de Ciencias Mathematicas (CSIC-UAM-UC3M-UCM), Nicolas Cabera 13-15, Campus Cantoblanco UAM, 28049 MAdrid, Spain, Email: alfonsozamora@icmat.es) : Harder-narasimhan filtration for rank 2 tensors and stable coverings. Proc Math Sci 2016, 126(3), 305-27.

The authors construct a Harder--Narasimhan filtration for rank 2 tensors, where there does not exist any such notion a priori, as coming from a GIT notion of maximal unstability. The filtration associated to the 1-parameter subgroup of Kempf giving the maximal way to destabilize, in the GIT sense, a point in the parameter space of the construction of the moduli space of rank 2 tensors over a smooth projective complex variety, does not depend on a certain integer used in the construction of the moduli space, for large values of the integer. Hence, this filtration is unique and we define the Harder--Narasimhan filtration for rank 2 tensors as this unique filtration coming from GIT. Symmetric rank 2 tensors over smooth projective complex curves define curve coverings lying on a ruled surface, hence we can translate the stability condition to define stable coverings and characterize the Harder--Narasimhan filtration in terms of intersection theory.

1 illus, 15 ref

013497   Xu H;Yang D (Center of Mathematical Sciences, Zhejiang Univ, Hangzhou 310027, People's Republic of China, Email: xuhw@cms.zju.edu.cn) : Rigidity theorem for willmore surfaces in a sphere. Proc Math Sci 2016, 126(2), 253-60.

Let M² be a compact Willmore surface in the (2 + p)-dimensional unit sphere S^2+p. Denote by H and S the mean curvature and the squared length of the second fundamental form of M², respectively. Set p² = S - 2H². In this note, we proved that there exists a universal positive constant C, such that if ||ρ²||₂ <60> C, then ρ² = 0 and M² is a totally umbilical sphere.

10 ref

013496   Sutopo;Wijayanti I E;Wahyuni S (Mathematics Dep, Universitas Gadjah Mada, Yogyakarta, Indonesia, Email: sutopo_mipa@ugm.ac.id) : Some results on graded N-prime numbers. Far East J mathl Sci 2016, 99(9), 1399-1408.

In this paper, we consider graded N-prime submodules as introduced by Sanh, and investigate their properties besides characterizations. For example, we prove that (i) if X is a fully invariant graded submodule of M, then the residual ideal of X by M is a graded ideal of S, and (ii) if M is a graded quasi-projective module, X is a graded N-prime submodule of M and Y ⊂ X is a fully invariant graded submodule of M, then X/Y is a graded N-prime submodule of M/Y.

7 ref

013495   Sohn B K (Mathematics Dep, Inje Univ, Kimhae, Kyungnam-621 749, Korea, Email: mathsohn@inje.ac.kr) : Distibutional boundary values in beurling ultradistributions. Far East J mathl Sci 2016, 99(9), 1421-41.

Let D'_(ω)(R^N) be the space of Beurling ultradistributions in the sense of [5] and Z'_(ω)(R^N) be the space of the Fourier transform of D'_(ω)(R^N). We define certain analytic functions in tubes in C^N which are defined by growth conditions and obtain distributional boundary value properties of the analytic functions in Z'_(ω)(R^N). Also, we recover analytic functions by Fourier-Laplace transforms. Further, we show that Beurling ultradistributions of L_p -growth generate the analytic functions which satisfy a boundedness condition and have distributional boundary values in D'_(ω)(R^N).

24 ref