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Category: Issue 4

Characterizaton and Theorems on Quaternion Doubly Stochastic Matrices

GUNASEKARAN K.
Department of Mathematics, Government Arts College (Autonomous), Kumbakonam, Tamilnadu, India
SEETHADEVI R. (seethadevir1@gmail.com)

ABSTRACT:

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

KEYWORDS: Doubly stochastic matrix, quaternion symmetric doubly stochastic matrix, quaternion orthogonal symmetric doubly stochastic matrix, centro doubly stochastic matrix, Subject code classification:15B99, 15A51


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

q- k – Hermitian doubly Stochastic, q- s – Hermitian Doubly Stochastic and q- s- k Hermitian Doubly Stochastic Matrices

GUNASEKARAN K.
Department of Mathematics, Government Arts College (Autonomous), Kumbakonam, Tamilnadu, India
SEETHADEVI R. (seethadevir1@gmail.com)
Department of Mathematics, Government Arts College (Autonomous), Kumbakonam, Tamilnadu, India

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.


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...

A study on limit cycle and non-homoclinic orbits for FitzHugh-Nagumo System

ALI E.M. SAEED (alikeria_math@yahoo.co.uk)
Department of Mathematics, Alzaem Alazhari University, Sudan

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


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....

M-Polynomials of Penta-chains

P. GAYATHRI ( pgayathrisundar@gmail.com)
Department of Mathematics, A.V.C. College (Autonomous), Mannampandal (India)
U. PRIYANKA
Department of Mathematics, A.V.C. College (Autonomous), Mannampandal (India)
S. SANDHIYA
Department of Mathematics, VELS University, Chennai (India)
S. SUNANDHA
Department of Mathematics, Vivekananda Arts and Science College for Women, Sirkali (India)
K.R. SUBRAMANIAN
Department of Computer Applications,Shrimati Indira Gandhi College, Trichy (India)

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


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...

Lipschitz Condition in the Controlled Convergence Theorem

SANDY MAE S. DOCDOC (sundaymay.docdoc@gmail.com)
Department of Mathematics and Statistics, College of Science and Mathematics, MSU-Iligan Institute of Technology, 9200 Iligan City, Lanao del Norte, Philippines
JULIUS V. BENITEZ (julius.benitez@g.msuiit.edu.ph)
Department of Mathematics and Statistics, College of Science and Mathematics, MSU-Iligan Institute of Technology, 9200 Iligan City, Lanao del Norte, Philippines

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


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...

New Types of Continuity Via gpc-Closed Sets

C. SANTHINI
Department of Mathematics, V.V. Vanniaperumal College for Women Virudhunagar (India)
R. GOMATHI (gomathiradha2@gmail.com)
Department of Mathematics, V.V. Vanniaperumal College for Women Virudhunagar (India)

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


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...

On the I -Integral of Graphs Under Some Binary Operations

RANDY L. CAGA-ANAN (randy.caga-anan@g.msuiit.edu.ph)
Department of Mathematics and Statistics College of Science and Mathematics Mindanao State University-Iligan Institute of Technology Iligan City 9200, Philippines

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


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 )...

Simple Properties of PUL-Stieltjes Integral in Banach Space

GREIG BATES C. FLORES (greigbates. ores@g.msuiit.edu.ph)
Department of Mathematics and Statistics, MSU-Ilingan Institute of Technology, 9200 Iligan City, Philippines
JULIUS V. BENITEZ (julius.benitez@g.msuiit.edu.ph)
Department of Mathematics and Statistics, MSU-Ilingan Institute of Technology, 9200 Iligan City, Philippines

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


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...