Papers

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

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.

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.
 

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.

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.

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.

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.

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.