016496   Portal X R D (Applied Economics Dep, Lleida Univ, Campus de Cap Pont C. de Jaume II, 73-25001 Lleida, Spain, Email: rportal@econap.udl.cat) : Dealing with monotonicity constraints in screening probolems: The principal-agent model. Far East J mathl Sci 2017, 101(2), 215-59.

This paper contains two parts clearly differentiated: a survey study about the use of monotonicity constraints in screening problems, and a research work extending the space of solutions in agency theory to non-smooth or even discontinuous action profiles. Specifically, we first systematize and compare, under a wide variety of assumptions on the endogenous variables of the model, existing approaches used for the derivation of necessary conditions in screening problems containing monotonicity constraints. Then, after identifying the most robust methods to generalize previous results, the paper derives a complete characterization of optimum contracts in the model of Jullien [18], without resorting to the usual continuity and smoothness assumptions on allocation functions. In this way, we conclude that most results in Jullien [18] continue holding if, instead of the mentioned assumptions, the endogenous variables of the problem satisfy some weak regularity condition. Moreover, when the reservation utility fails to be type-dependent, as happens for instance in Guesnerie and Laffont [14], the characterization of optimal contracts still holds - 37 - without the need of imposing the referred regularity condition.

50 ref

016495   Patra P;Dash R B (Mathematics Dep, Ravenshaw Univ, Cuttack-753 003, Email: pritikanta@yahoo.com) : Mixed quadrature rule by blending clenshaw-curtis and gauss-legendre quadrature rules for approximate evaluation of real definite integrals in two dimensions. Ultra Scient phys Sci-Sect A 2016, 28(5-7), 278-85.

A mixed quadrature rule, blending Clenshaw-Curtis five point rule in two dimensions and Gauss-Legendre three point rule in two dimensions, is formed. The mixed rule has been imposed with some test integrals and found to be more effective than that of its constituent rules.

1 table, 15 ref

016494   Parida P K;Sahoo S K;Behera B (Mathematics Dep, C.V. Raman College of Engineering, Bhubaneswar, Email: prashanta_math@yahoo.co.in) : Multi-criteria decision making models using fuzzy TOPSIS technique. Ultra Scient phys Sci-Sect A 2016, 28(5-7), 286-93.

In this paper Authors propose Multi-criteria decision making (MCDM) models using fuzzy technique for order performance by similarity to ideal solution (Fuzzy TOPSIS) is used to choose among a group of decision makers. Concerning the MCDM, the value of a fuzzy number is greater than or equal to another fuzzy number, a new distance measure. Here we described the TOPSIS technique and expansion of fuzzy TOPSIS techniques and lastly we discussed fuzzy TOPSIS for group decision making, which is applied to measure the distance of each fuzzy number from both fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS). Then which is simultaneously closer to FPIS and farther from FNIS will be selected as the best choice.

27 ref

016493   Mathew G (Mathematics Dep, BCM College, Kottayam-686 001, Email: gmathew5616x@gmail.com) : Equivalent circulant graphs associated with a binary cyclic code. Ultra Scient phys Sci-Sect A 2016, 28(5-7), 251-8.

Various papers have been written on the theory of circulant graphs. Also graphs with circulant adjacency matrices is discussed in. Circulant graphs have important applications to the theory of designs and error correcting codes. The relationship between directed circulant graphs and binary linear - 36 - codes is established in. Each binary cyclic code corresponds to an equivalence class of directed circulant graphs. This paper discusses the method of determining the equivalent circulant graphs associated with a binary cyclic code.

13 ref

016492   Marskole S;Shrivastava S S (NO, Govt. P. G. College Seoni, Madhya Pradesh, Email: seema.marskole@yahoo.com) : Multivariable H-function and problem related to Flux condition. Ultra Scient phys Sci-Sect A 2016, 28(5-7), 232-4.

The aim of this research paper is to derive the solution of a problem related to flux condition involving the multivariable H-function.

4 ref

016491   Malviya A (Mathematics Dep, V.S.S.D. (P.G.) College, Kanpur, Email: alok92nov@rediffmail.com) : Control modelling effect of primary and secondary toxicnts oin the survival orExtinction of resource based population in aquatic environment: A qualitative approach. Ultra Scient phys Sci-Sect B 2017, 29(1-4), 35-9.

In this paper, a non-linear control mathematical model is proposed and analyzed to study the effect of primary and secondary toxicants on the survival or the extinction of resource based population in aquatic environment. The model is formulated by using system of non-linear ordinary differential equations. In the analysis, all the feasible equilibrium points of the system have been obtained. The conditions for local and non-linear stability of the non-trivial equilibrium points have been carried out using a suitable Lyapunov function. It may be observed from the stability conditions that the density of the resource biomass (zooplankton population) and resource based biological species (fish population) would co-exist if their growth rates were more than the death (removal) rates of both the species due to toxicants both primary and secondary and also when their carrying capacities are positive.

17 ref

016490   Mahagaonkar P (Mathematics Dep, Ballari Institute of Technology and Management, Ballari Karnataka-583 104, Email: pralahadpralhad@yahoo.com) : On b-chromatic number fora certain triangular line graphs. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 11-14.

The b-Chromatic number of a graph is the maximum number of k of colors that can be used to color the vertices of G. Let us consider the color classes for differentline graphs, where every line graphs with i has a representative (the color i dominating vertex) that is able to communicate with all the other line graphs. Further we investigate the b-chromatic number for certain triangular graphs such as triangular snake graphs, triangular fan graphs, triangular cylindrical graphs andwe also generalized some of the results based on these graphs.

3 illus, 14 ref

016489   Liu X;Xu T (Science Dep, Hebei Univ of Engineering Handan, 056038, P.R. China, Email: 470596294@qq.com) : Finite extension of a finitely generated torsion-free nilpotent group with regular automorphisms of order p<. Far East J mathl Sci 2017, 101(2), 321-8.

Let G be a finite extension of a finitely generated torsion-free nilpotent group and α be a - 35 - regular automorphism of order p² of G, where p is a prime. If the map ϕ: G → G defined by g^ϕ = [g, α] is surjective, then G is soluble and C_G(α²) is nilpotent. Moreover, if p = 2 then G is centre-by-metabelian and C_G(α² is abelian.

8 ref

016488   Lellis Thivagar M;Sutha Devi V (School of Mathematics, Madurai Kamaraj Univ, Madurai-625 021, Email: vsdsutha@yahoo.co.in) : Nano quotient mappings. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 58-65.

The purpose of this study is to introduce, define and study several classes of nano quotient map in nano topological spaces. Authors have initiated the several types of mappings such as nano α -quotient map, nano strongly α - quotient map and nano α*-quotient map in nano topological space and its properties are discussed. Also we have made comparisions among them.

8 ref

016487   Lellis Thivagar M;Kavitha J (School of Mathematics, Madurai Kamaraj Univ, Madurai, Tamil Nadu, Email: mlthivagar@yahoo.co.in) : Irresoluteness via binary supra topological spaces. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 40-5.

In this paper we introduce the new class of functions called binary supra α-irresolute functions and deals with the concrete examples. The purpose of the present note is to introduce a strong form of binary supra continuity called binary supra strongly α-irresolute which is stronger than binary supra α-irresolute. Basic and some comparitive properties of these fuctions are studied in this paper.

10 ref

016486   Lellis Thivagar M;Arockia Dasan M;Ramesh V (School of Mathematics, Madurai Kamaraj Univ, Madurai-625 021, Email: dassfredy@gmail.com) : Computation of separation axioms in N-topology. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 77-82.

In this paper Authors introduce and characterize Nτg -open sets and derive that this class of Nτg -open sets forms a topology on X. We also define the necessary and sufficient condition for a set to be Nτg -open set. Further we induce various kinds of spaces in N-topology and its applications.

10 ref

016485   Kwon N (Mathematics Dep, Daegu Univ, Gyeongsan, Gyeongbuk, Republic of Korea, Email: nkwon@daegu.ac.kr) : Bosonic-fermionic realizations of queer lie superalgebras. Far East J mathl Sci 2017, 101(2), 429-41.

The author construct the queer Lie superalgebras using the generators of the Clifford superalgebras.

9 ref

016484   Kwon N (Mathematics Dep, Daegu Univ, Gyeongsan, Gueongbuk, Korea, Email: nkwon@daegu.ac.kr) : On free field realizations of affine lie superalgebras of type D(m, n)<. Far East J mathl Sci 2017, 101(2), 415-27.

Authors construct free field realizations of the affine orthosymplectic Lie superalgebras arising from vertex representations of the affine general linear Lie superalgebras.

11 ref

016483   Kusmayadi T A;Kuntari S;Fikri A F;Rahmadi D; Pradana H C (Mathematics Dep, Faculty of Mathematics and Natural Sciences, Sebelas Maret Univ, Surakarta, 57126, Indonesia, Email: tri.atmojo.kusmayadi@gmail.com) : The metric dimension of sunflower, t-fold wheel, and (K₁ + (P_n ⋅ P_m). Far East J mathl Sci 2016, 99(5), 687-98.

Let G be a connected simple graph with vertex set V(G) = (v₁, v₂, ..., v_n) and edge set E(G) = {e₁, e₂, ..., e_n}. For an ordered set W = {w₁, w₂, ..., w_k} of vertices and a vertex v in G, the representation of v with respect to W is the ordered k-tuples r(v|W) = (d(v, w₁), d(v, w, ..., d(v, w_k)), where d(x,y) represents the distance between the vertices x and y. The set W is called a resolving set for G if every two vertices of G have distinct representations. A resolving set containing a minimum number of vertices is called a basis for G. The metric dimension of G, denoted by dim(G), is the number of vertices in a basis of G. In this paper, we determine the metric dimensions of some graphs, namely sunflower, t-fold wheel, and K₁ + (P_n ⋅ P_m).

3 illus, 15 ref

016482   Kulli V R (Mathematics Dep, Gulbarga Univ, Gulbarga-585 106, Email: vrkulli@gmail.com) : Some new multiplicative geometric-arithmetic indices. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 52-7.

In this paper, authors propose some new topological indices: second, third, fourth and fifth multiplicative geometricarithmetic indices of a molecular graph. A topological index is a numeric quantity from the structural graph of a molecule. Here, we compute the fifth multiplicative geometric arithmetic index of line graphs of subdivision graphs of 2D-lattice, nanotube and nanotorus of TUC₄C₈[p,q].

3 illus, 16 ref

016481   Kulli V R (Mathematics Dep, Gulbarga Univ, Gulbarga-585 106, Email: vrkulli@gmail.com) : Multiplicative connectivity indices of nanostructures. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 1-10.

A single number that can be used to characterize some property of the graph of a molecular is called a topological index for that graph. In this paper, we compute several topological indices of linear [n]-anthracene, V-anthracene nanotube and nanotori: multiplicative Zagreb, multiplicative hyper-Zagreb, multiplicative sum connectivity, multiplicative product connectivity, general multiplicative Zagreb, multiplicative ABC and multiplicative GA indices.

4 illus, 17 ref

016480   Kulli V R (Mathematics Dep, Gulbarga Univ, Gulbarga-585 106, Email: vrkulli@gmail.com) : Equality of secure domination and inverse secure domination numbers. Ultra Scient phys Sci-Sect A 2016, 28(5-7), 294-8.

Let G = (V, E) be a graph. Let - 33 - D be a minimum secure dominating set of G. If V - D contains a secure total dominating set D' of G, then D' is called an inverse secure dominating set with respect to D. The smallest cardinality of inverse secure dominating set of G is the secure domination number γ_s^-1(G) of G. In this paper, we obtain some graphs for which γ_s(G) = γ_s^-1(G) and establish some results on this respect. Also we obtain some graphs for which γ_s(G) = γ_s^-1(G) = p/2, p where p is the number of vertices of G.

3 illus, 24 ref

016479   Khalil A;Ahmad A G B (School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia, Email: k.sakita@yahoo.ca) : Fiber homotopy equivalence for β-fibrations in the homotopy theory of polish semigroups. Far East J mathl Sci 2017, 101(2), 361-73.

In [1], Cerin introduced the homotopy theory for topological semigroups and the concept of the S-fibration. The lifting function for the S-fibration was given in [7]. In this paper, we build upon these results and introduce the concept of B-fiber homotopy equivalence for B-fibrations in the homotopy theory of Polish semigroups. This is applied to obtain a version of a theorem due to Tulley on strong fiber homotopy equivalence. In addition, we show that the notions of B-fiber homotopy and strong B-fiber homotopy are the same in the category of Polish semigroups.

9 ref

016478   Kannan K R;Elumalai N (Mathematics Dep, Annai College of Engineering and Technology, Kovilacheri, Tamil Nadu, Email: rakkirajesh1986@gmail.com) : k-symmetric circulant, s-symmetric circulant and s-k symmetric circulant matrices. Ultra Scient phys Sci-Sect A 2016, 28(5-7), 322-7.

The basic concepts and theorems of k-symmetric Circulant, s-symmetric Circulant and s-k-symmetric Circulant matrices are introduced with examples.

6 ref

016477   Joshi V N (NO, , SUNY Stony Brook USA, Email: vnjoshig@gmail.com) : General fuzzy mathematical expression for carrier of a genetic disorder. Ultra Scient phys Sci-Sect B 2017, 29(1-4), 97-8.

In this paper a general fuzzy mathematical model for any genetic disorder is proposed. A genetic disorder is caused in whole or in part by a change in the DNA sequence away from the normal sequence. A gene is associated with the disorder, e.g. FXN gene is associated with Friedreich's Ataxia, PRKN with Parkinson's disease, APOE with Alzheimer disease, HOXB with Breast and Prostate carcinoma etc.. We have attempted to present a carrier model of disorder based on fuzziness factor.

4 ref

016476   Jnajaroon A;Chaladgarn T;Haarsa P (NO, , Mathematics Dep, Srinakharinwirot, Bangko 10110, Thailand) : A bulge function on volterra integral equations of the second kind by using the elzaki transform. Far East J mathl Sci 2016, 99(5), 755-61.

In this paper, we study the Volterra integral equations of the second kind. By employing Elzaki transform, inverse Elzaki transform and the convolution theorem of Elzaki transform, we deal with the exact solution of the Volterra integral equations of the second kind.

1 illus, 1 table, 7 ref

016475   Hatada K (Mathematics Dep, Faculty of Education Gifu Univ, 1-1, Yanagido, Gifu City GIFU 501-1193, Japan, Email: hatada@gifu.u.ac.jp) : Equality in inequalities of rearrangements. Far East J mathl Sci 2017, 101(2), 407-14.

Let n be any positive integer larger than 2. Let {x_s}ⁿ_s=1 and {Y_s}ⁿ_s=1 be arbitrary real sequences of mild increase: namely x₁ ≤ x₂ ≤ x₃ ≤ ... ≤ x_n-1 ≤ x_n and y₁ ≤ y₂ ≤ y₃ ≤ ... ≤ y_n-1 ≤ y_n. Let S_n denote the symmetric group of degree n acting on {j ∈ Z|1 ≤ J ≤ n} in the usual way. Let σ ∈ S_n denote the substitution (1 2 3 ... ... n-1 n/2 3 4 ... ... n 1). Put τ = σ^-1 for short. In this paper, we give the following (1), (2) and (3): (1) Necessary and sufficient condition for ∑ⁿ_j=1 x_jy_n+1-j = ∑ⁿ_j=1 x_σ(j)y_{n+1-j; (2) Necessary and sufficient condition for ∑ⁿj=1 xjyn+1-j = ∑ⁿj=1 xτ(j)yn+1-j; (3) If ∑ⁿj=1 xjyn+1-j = ∑ⁿj=1 xσ(j)yn+1-j and ∑ⁿj=1 xjyn+1-j = - 32 - ∑ⁿj=1 xτ(j)yn+1-j then we have x1 = xn or y1 = yn. We treat also equality in inequalities (i) and (ii) below.}

2 ref

016474   Hatada K (Mathematics Dep, , Faculty of Education Gifu Univ, Email: hatada@gifu-u.ac.jp) : Minimum values of ∑<. Far East J mathl Sci 2017, 101(2), 395-406.

Let k and r be arbitrary positive real numbers and let n be any positive integer. Let R₊ denote the set of all the positive real numbers. Put Ω(r, k, n) = {(x₁, x₂, ..., x_n) ∈ Rⁿ₊ | ∑ⁿ_j=1 x^r_j ≤ k}. We give minimum values of functions F(x₁, x₂, ..., x_n) = ∑ⁿ_j=1 (x_j + x^-1_j) and G(x₁, x₂, ..., x_n)=∏ⁿ_j=1 x_j + ∑ⁿ_j=1 x^-1_j on Ω(r, k, n) Corollaries are also given.

4 ref

016473   Hantomoto J (General Education, Tokyo National College of Technology, Kunugida 1220-2 Hachioji, Tokyo 193-0997, Japan, Email: hatomoto-jinn@tokyo-ct.ac.jp) : Polynomial lower bounds on large deviations for some partially hyperbolic diffeomorphisms. Far East J mathl Sci 2016, 99(5), 615-22.

In this paper we study a C^1+α-partially hyperbolic diffeomorphism f of which restriction on one dimensional center unstable direction behaves as Manneville-Pomeau map. We show that f satisfies polynomial lower bounds on large deviations associated with its unique SRB measure for some continuous functions.

20 ref

016472   Gunasekaran K;Seethadevi R (Mathematics Dep, Government Arts College, Kumbakonam, Tamilnadu, Email: seethadevir1@gmail.com) : q - k - hermitian doubly stochastic, q - s - hermitian doubly stochastic and q - s - k hermitian doubly stochastic matrices. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 144-55.

The basic concepts and theorems of q - k - hermitian doubly stochastic, q -s hermitian doubly stochastic and q -s - k - hermitian - 31 - doubly stochastic matrices are introduced with examples.

5 ref

016471   Gunasekaran K;Seethadevi R (Mathematics Dep, Government Arts College, Kumbakonam, Tamilnadu, Email: seethadevir1@gmail.com) : Characterization and theorems on quaternion doubly stochastic matrices. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 135-43.

The concepts of quaternion symmetric doubly stochastic are developed, basic theorems and some results for these matrices and characterization are analyzed with examples.

6 ref

016470   Gunasekaran K;Nandakumar S;Gunaseelan D (Ramanujan Research Centre, Mathematics PG and Research Dep, Government Arts College, Kumbakonam-612 001, Email: gngseelan86@gmail.com ) : Level operators over bipolar intuitionistic M-fuzzy group and anti M-fuzzy group. Ultra Scient phys Sci-Sect A 2016, 28(5-7), 370-82.

In this paper the concept of a Bipolar intuitionistic M fuzzy group and anti M fuzzy group is a new algebraic structure of a bipolar intuitionistic M fuzzy subgroup of a M fuzzy group and anti M fuzzy group are defined and related operators and level operators are investigated. The purpose of the study is to implement the fuzzy set theory and group theory of bipolar intuitionistic M fuzzy group and anti M fuzzy group. The relation between operation of level operators of bipolar intuitionistic M fuzzy group and bipolar intuitionistic anti M fuzzy group are established.

16 ref

016469   Gunasekaran K;Kannan K;Rahamathunisha M (Ramanujan Research Centre, Mathematics P.G. and Research Dep, Government Arts College (Autonomous), Kumabakonam-612 002, Email: srnisha.phdpmu@gmail.com) : On tricomplex representation methods of a matrix trace inequality. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 30-2.

In this paper, on tricomplex representation methods of a matrix trace inequality is introduced. A matrix trace inequality for positive semi definite Hermitian matrices A and B, 0≤tr (A*B)ⁿ≤(trA)ⁿ *(trB)ⁿ is established, where n is an integer. The above inequality improves the result given by Yang (J Math. Anal. Appl. 250 (2000), 372-374.

6 ref

016468   Govindarasu A;Sassicala S (Mathematics Dep, A.V.C. College (Autonomous), Mannampandal-609 305, Email: sasram10@gmail.com) : Characterizations of conjugate unitary matrices. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 33-9.

The concept of conjugate unitary matrices is introduced. Characterizations of conjugate unitary matrices are obtained and derived some theorems.

8 ref

016467   Gomathy S V (School of Mathematics, Madurai Kamaraj Univ, Madurai-625 021, Email: gomathybaskar@gmail.com) : Note on transformations of generalized burgers equations. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 116-25.

Lie Classical Method is applied to find general transformations for two Generalized Burgers - 30 - Equations. Also transformations of Generalized Burgers Equation with time-dependent viscosity to another generalized Burgers equation with constant viscosity has been done.

11 ref

016466   Gayathri P;Priyanka U;Sandhiya S;Sunandha S; Subramanian K R (Mathematics Dep, A.V.C. College, Mannampandal, Email: pgayathrisundar@gmail.com) : M-polynomials of penta-chains. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 164-8.

Using the vertex degrees of the graphs, M- polynomials of several types of graphs consisting of concatenated pentagonal rings are obtained and studied in this paper. The vertex degree based indices like Randic, Geometric - Arithmetic, Sum Connectivity, Harmonic, First Zagreb, Second Zagreb, Second Modified Zagreb, Inverse Sum, Alberston, Atom - bond Connectivity, Symmetric - Division index and Augmented Zagreb indices etc., of penta-chains can be calculated easily by using the proposed M-Polynomials of the penta-chains for single, alternating and double-row pentachains of two types.

5 illus, 10 ref

016465   Garg M;Agarwal S (Mathematics P.G. Dep, Nehru Degree College, Chhibramau, Kannauj, Uttar Pradesh, Email: garg_manoj1972@yahoo.co.in) : On 0/g - closed sets in topological spaces. Ultra Scient phys Sci-Sect A 2016, 28(5-7), 235-44.

In this paper, authors introduce and study a new class of sets namely 0/g-closed sets which settled in between the class of g*-closed sets²¹ and the class of g-closed sets³ and then we study many basic properties of 0/g-closed sets together with the relationship of these sets with some other sets. As applications of 0/g -closes sets, we introduce some new separation properties, namely T⁰_1/2-spaces, ⁰T_1/2-spaces, T⁰_1/2-spaces and αT⁰_1/2-spaces. Further we introduce and study new types of continuous maps called 0/g-continuous maps and 0/g-irresolute maps.

2 illus, 37 ref

016464   Garg M (Mathematics P.G. Dep, Nehru (P.G.) College, Chhibramau, Kannauj, Uttar Pradesh, Email: garg_manoj1972@yahoo.co.in) : New type of generalized fixed point theorem on compact metric space. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 74-6.

In this paper, Authors prove a fixed point theorem for self mappings satisfying a new contractive type condition in a compact metric space.

7 ref

016463   Garg M (Mathematics P.G. Dep, Nehru (P.G.) College, Chhibramau, Kannauj, Uttar Pradesh, Email: garg_manoj1972@yahoo.co.in) : Generalized fixed point theorem in dislocated quasi-metric space. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 71-3.

In this work, Authors discuss the existence of fixed points of continuous contracting mappings defined on dislocated quasi-metric space. This work is a continuity of the previous works of Isufati.

6 ref

016462   Flores G B C;Benitez J V (Mathematics and Statistics Dep, MSU-Iligan Institute of Technology, 9200 Iligan City, Philippines, Email: greigbates.flores@g.msuiit.edu.ph) : Simple properties of PUL-stieltjes integral in banach space. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 126-34.

Using PUL integrals, Boonpogkrong in ²defined and discussed the Kurzweil-Henstock - 29 - integral on manifolds. In this paper, we introduce the PUL-Stieltjes integral of Banach- valued functions and give some simple properties of this integral. Moreover, a charac- terization of PUL-Stieltjes integral is also given by establishing the Cauchy criterion.

8 ref

016461   Elumalai N;Arthi B (Mathematics PG and Research Dep, A.V.C. College (Autonomous), Mannampandal, Tamil Nadu, Email: arthi9976963109@gmail.com) : Properties of k - centrohermitian and k - skew centrohermitian matrices. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 111-15.

The basic concepts and Theorems of k- Centrohermitian, k- Skew Centrohermitian matrices are introduced with examples.

8 ref

016460   Elumalai N;Anurdha R;Rajapriya R (NO, A.V.C. College (Autonomous), Mannampandal, Mayiladuthurai-609 305, Email: rajipriya325@gmail.com) : Relation meet and relation join matrices on posets. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 89-100.

Authors define relation meet and relation join matrices on two different posets R and S of a lattice with respect to a complex-valued function f on P by (X,Y)_f = (f(x_i ∧ y_i)) and [X,Y]_f = (f [x_i ∨ y_i]) respectively. Also we present some examples for the determinant and inverse of(X, Y)_f and [X,Y]_f.

9 ref

016459   Dubey S S;Shrivastava S S (NO, ITM Univ, Raipur, Chhattisgarh, Email: sss.math@yahoo.co.in) : On double integral involving generalized I-function of two variables. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 104-7.

The aim of this research paper is to evaluate a double integral involving generalized I-function of two variables.

4 ref

016458   Dolas U (Mathematics Dep, C.S.A.P.G. College, Sehore-466 001, Email: udolas@gmail.com) : On coincidence points in pseudocompact tichonov spaces. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 101-3.

In this paper, Authors are proving a Certain common fixed point theorem for pairs of selfmaps on a Pseudocompact topological space and pairs as well as families of selfmaps on a compact metric space. Authors improve the results of Fisher¹, Harinath², Jain and Dixit³.

9 ref

016457   Docdoc S M S;Benitez J V (Mathematics and Statistics Dep, College of Science and Mathematics, MSU-Iligan Institute of Technology, 9200 Iligan City, Lanao del Norte, Philippines, Email: julius.benitez@g.msuiit.edu.ph) : Lipschitz condition in the controlled convergence theorem. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 169-75.

The Lebesgue integral is noted for its - 28 - powerful convergence theorems - the Monotone Con- vergence Theorem (MCT) and Dominated Convergence Theorem (DCT). In⁵ and ⁸, these two convergence theorems were proved for the Henstock integral. Nakanishi in ⁹ and Lee and Yyborny in ⁸ consider yet another but more powerful convergence theorem, called the Con- trolled Convergence Theorem (CCT), that includes the monotone and dominated convergence theorems. Paredes and Chew in ¹¹ studied a controlled convergence theorem for Banach space valued HL-integrals. Generalized absolute continuity (ACG) plays a very significant role in CCT. On the other hand, it is known that if a function satisles a Lipschitz condition then it is ACG. It is the objective of this study to investigate some Lipschitz condition in the Controlled Convergence Theorem.

14 ref

016456   Dixit S (Mathematics Dep, V.S.S.D. College, Kanpur, Uttar Pradesh, Email: sd0408@rediffmail.com) : Batch service vacation model (M/G<. Ultra Scient phys Sci-Sect B 2017, 29(1-4), 40-1.

In this chapter Authors discuss the batch service vacation model. In such system, customers arrive according to a Poisson process and are served in batches of maximum size b and minimum thre shold a. The server takes a single vacation when it finds less than a customers after the service completion.

7 ref

016455   Dixit S (Mathematics Dep, V.S.S.D. College, Kanpur, Uttar Pradesh, Email: sd0408@rediffmail.com) : Vacation model (M<. Ultra Scient phys Sci-Sect A 2016, 28(5-7), 304-8.

In this paper Authors discuss the batch arrival vacation model appear in many situations such as computer communication systems. The common method of studying the batch arrival queueing system with vacations is by using supplementary variables.

11 ref

016454   Dhiman S (Mathematics Dep, Govt. Science College, Rewa, Madhya Pradesh, Email: sdhimanjee@gmail.com) : Distribution of the sum of mixed independent random variables involving generalized H-functions of two variables. Ultra Scient phys Sci-Sect A 2016, 28(5-7), 299-303.

The aim of this section is to obtain the distribution of mixed sum of two independent random variables with different probability density functions. One with probability density function defined in finite range and the other with probability density function defined in infinite range and associated with product of general class of polynomials and generalized H-function of two variables. The method used is based on Laplace transform and it's inverse. The result obtained here is quite general in nature and is capable of yielding a large number of corresponding new and known results merely by specializing the parameters involved therein. To illustrate, some special cases of our main result are also given.

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016453   Dhaiban A K (Apparatus of Supervision and Scientific Evaluation, Ministry of Higher Education and Scientific Research, Iraq, Email: ali_alzubiadi@yahoo.com) : Comparison between linear programming model and optimal control model of production-inventory system. Curr Sci 2017, 112(9), 1855-63.

This study compares two models of the production-inventory system-optimal control and linear pro-gramming. We derived the optimality conditions of optimal control model and formulated the linear pro-gramming model. A new method to determine the theoretical solution of the boundary value problem has been suggested. Our numerical results suggest that control on the inventory level was realized at the end of the planning period, depending on the optimal control model, while in the linear programming model, it was realized from the beginning of the plan-ning period. Also, the method to determine the theo-retical solution of the boundary value problem has proven to be efficient.

7 illus, 2 tables, 30 ref

016452   Darti I;Suryanto A (Mathematics Dep, Brawijaya Univ, Jl. Veteran-Malang 65145, Indonesia) : Dynamics preserving nonstandard finite difference method for the modified leslie-gower predator-prey model with holling-type II functional response. Far East J mathl Sci 2016, 99(5), 719-33.

In this paper, we propose a discrete modified Leslie-Gower predator-prey model with Holling-type II functional response derived from the nonstandard finite difference (NSFD) method. It is shown that the NSFD scheme preserves the dynamics of the corresponding continuous model such as the positivity solutions, equilibria and the local stability properties. The dynamical consistence of the discrete model is independent of time-step size. To confirm the analytical results, some numerical simulations are presented.

2 illus, 25 ref

016451   Chouhan C P S;Dulawat M S;Parihar J S (Mathematics & Statistics Dep, Bhupal Nobles' Univ, Udaipur, Email: chandrapal.singh1982@gmail.com) : Method of construction of triangular designs. Ultra Scient phys Sci-Sect A 2016, 28(5-7), 358-60.

This paper describes a new method of construction of triangular designs. Consequently, a new series of truly self-dual triangular design is obtained.

4 ref

016450   Chouhan C P S;Dulawat M S;Parihar J S (Mathematics & Statistics Dep, Bhupal Nobles' Univ, Udaipur, Email: dulawat_ms@rediffmail.com) : Method of construction of group divisible designs. Ultra Scient phys Sci-Sect A 2016, 28(5-7), 354-7.

In this paper, Authors have presented a new method of construction of regular group divisible design. We also characterized a particular design of the series v = b = 4t + 3, r = k= 2t+1, λ = t viz., v = b = 31, r = k = 15, λ = 7, considering nice block structure.

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016449   Cerin Z;Gianella G M (NO, , Kopernikova 7, 19919 Zagreb, Croatia, Email: cerin@math.hr) : Identities for products and squares of (S, T)-fibonacci and (S, t)-lucas numbers. Far East J mathl Sci 2016, 99(5), 743-54.

For products and squares of (s, t)-Fibonacci and (s, t)-Lucas numbers that generalize Fibonacci and Lucas numbers we describe several identities that extend the Cusumano identity for Fibonacci numbers stated long ago as a problem in the journal Fibonacci Quarterly.

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016448   Caga-Anan R L (Mathematics Dep, Statistics College of Science and Mathematics Mindanao State Univ-Ilig, Iligan City 9200, Philippines, Email: randy.caga-anan@g.msuiit.edu.ph) : On the I -integral of graphs under some binary operations. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 183-91.

Let G = (V (G), E(G)) be an undirected connected graph and let X be a subset of V (G). Furthermore, let I (X ) and B(X ) denote the set of isolates and the boundary set of X, respectively. - 26 - The inner boundary number of X, denoted by β_i(X ) is β_i(X) = max{|Y |:Y ⊆ X and B(XY)Y = B(X)}. The outer boundary number of X, denoted by β_o(X ) is β_o(X ) =|V(G) N[X ]|. The I -integral of X is I ∫_I(X ) = β_i(X ) β_o(X ) | I(X ) | and the I -integral of G is I ∫_I(G) = min{∫_I ⊆(X ) : X V(G)}I. In this paper, we determine the I -integral of graphs resulting from some binary operations such as the join, corona, composition, and cartesian product of graphs.

4 ref

016447   Beg M;Shrivastava S S (NO, VITS, Satna, Madhya Pradesh, Email: sss.math@yahoo.co.in) : Partial derivatives involving generalized H-function of two variables. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 108-10.

The aim of this paper is to derive partial derivatives involving generalized H-function of two variables.

3 ref