Category: Issue 4

ABSTRACT:

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

KEYWORDS: q -k - hermitian Doubly Stochastic, q -s - hermitian Doubly Stochastic, q-s -k - hermitian doubly stochastic matrices, Subject code classification:15B99, 15A51.

ABSTRACT:

In this paper we investigate the complete FitzHugh-Nagumo System with I  0 . Based on the result in1,2 we discuss the non-existence of homoclinic orbits of the system. Further, we prove that the system has unique limit cycle under the conditions of existence of homoclinic orbits.

KEYWORDS: Li euf0a2nard equation, FitzHugh-Nagumo System, Limit cycle, Homoclinic orbits

ABSTRACT:

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.

KEYWORDS: M-Polynomial, Topological indices, Molecular graph, Penta-chain

ABSTRACT:

The Lebesgue integral is noted for its powerful convergence theorems – the Monotone Con- vergence Theorem (MCT) and Dominated Convergence Theorem (DCT). In 5 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 signicant role in CCT. On the other hand, it is known that if a function satises a Lipschitz condition then it is ACG. It is the objective of this study to investigate some Lipschitz condition in the Controlled Convergence Theorem.

KEYWORDS: uniform u000e-Lipschitz, UACG*, Controlled Convergence Theorem, 2010 Mathematics Subject Classifcation: 26A24, 26A06, 26A39, 26A42

ABSTRACT:

The aim of this paper is to introduce several continuous functions via gpc-closed sets in topological spaces namely gpc-continuous function, (gpc)*-continuous functions, minimal gpc-continuous function, maximal gpc-continuous function and study their properties. Furthermore, a decomposition of continuity is obtained.

KEYWORDS: Paracontinuous functions, *-paracontinuous functions, gpc-continuous functions, (gpc)*-continuous functions, minimal gpc-continuous function and maximal gpc-continuous function, MSC: 54C08, 54C05

ABSTRACT:

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. The inner boundary number of X, denoted by (X ) i is (X) = max{|Y |:Y X and B(X Y) Y = B(X)}. i   The outer boundary number of X, denoted by (X ) o  is (X ) =|V(G) N[X ]| . o  The I -integral of X is I  (X ) = (X ) (X ) | I(X ) | i o     and the I -integral of G is 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.

KEYWORDS: I -integral, isolates, boundary, Mathematics Subject Classification: 05C69

ABSTRACT:

Using PUL integrals, Boonpogkrong in 2 dened and discussed the Kurzweil-Henstock 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.

KEYWORDS: Banach Space, PUL-Stieltjes