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2nd conference of ICMSA was held in 2006 at Penang, Malaysia.
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Articles 8 Documents
 1 
Search results for , issue "Vol 2, No 1 (2006): Pure Maths : ICMSA 2006" : 8 Documents clear
ON THE CARDINALITY OF THE SET OF SOLUTIONS TO CONGRUENCE EQUATION ASSOCIATED WITH QUINTIC FORM Siti Hasana Sapar
Proceedings of ICMSA Vol 2, No 1 (2006): Pure Maths : ICMSA 2006
Publisher : Proceedings of ICMSA

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Abstract

The exponential sum associated with f is defined aswhere the sum is taken over a complete set of residues modulo q and let x = (x1, x2, ... , xn) be a vector in the space Zn with Z ring of integers and q be a positive integer, f a polynomial in x with coefficients in Z. The value of S(f; q)has been shown to depend on the estimate of the cardinality |jV|, the number of elements contained in the setwhere fx is the partial derivative of f with respect to x = (x1, x2, ..., xn). This paper will give an explicit estimate of |V| for polynomial f(x; y) in Zp[x; y] of degree five. Earlier authors have investigated similar polynomials of lowerdegrees. The polynomial that we consider in this paper is as follows:The approach is by using p-adic Newton Polyhedron technique associated with this polynomial.
EXPONENTS OF PRIMITIVE GRAPHS CONTAINING TWO DISJOINT ODD CYCLES Indra Syahputra
Proceedings of ICMSA Vol 2, No 1 (2006): Pure Maths : ICMSA 2006
Publisher : Proceedings of ICMSA

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Abstract

A connected graph G is primitive provided there exists a positive integer k such that for each pair of vertices u and v in G there is a walk of length k connecting u and v. The smallest of such positive integer k is the exponent of G. A primitive graph is said to be odd primitive graph if it has an odd exponent. It is known that if G is an odd primitive graph then G contains two disjoint odd cycles. This paper discusses exponents of a class of primitivegraphs containing of exactly two disjoint odd cycles. For such graphs we characterize the odd and even primitive graphs.
AN ALTERNATIVE CONSTRUCTION OF THE MOUFANG LOOP M(G, 2) Andrew Rajah
Proceedings of ICMSA Vol 2, No 1 (2006): Pure Maths : ICMSA 2006
Publisher : Proceedings of ICMSA

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Abstract

In [3], Orin Chein defined and constructed a class of Moufang loops called the M(G, 2) with a product rule which is rather complicated. We provide an alternative definition ofM(G, 2) with a much simpler product rule.
NEWTON POLYHEDRA AND ESTIMATION TO EXPONENTIAL SUMS Kamel Arifin Mohd Atan
Proceedings of ICMSA Vol 2, No 1 (2006): Pure Maths : ICMSA 2006
Publisher : Proceedings of ICMSA

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Abstract

The classical Newton polygon is a device for computing the fractional power series expansions of algebraic functions. Newton gave a number of examples of this process in his ”Method of Fluxions” which amount to a general method. However, it was not till much later that Puiseux proved that every branch of a plane algebraic curve defined by a polynomial equation f(x, y) = 0 has an expansionin a neighbourhood of a point (x0, y0) on the curve. In practice, the integers a, b and q can be read off from the Newton polygon and the coefficients cj can be determined successively with ever-increasing labour.
A VISUAL MODEL FOR COMPUTING SOME PROPERTIES OF U(n) AND Zn Nor Muhainiah Mohd Ali
Proceedings of ICMSA Vol 2, No 1 (2006): Pure Maths : ICMSA 2006
Publisher : Proceedings of ICMSA

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Abstract

A computer program is developed using Microsoft Visual C++ in theWindows environment. This program focuses on two specific finite Abelian groups, which are the group Zn under addition modulo n and the group U(n) under multiplication modulo n, where n is any positive integer less than or equal to 120. Computations of the properties of the two groups get more tedious and time consuming as the value of n increases. Therefore a program that couldassist in the computation would indeed be of great help. This program in C++ is written relating to some properties of Zn and U(n). It enables the user to enter any positive integer n (n · 120) to generate answers to some properties of these two groups. A lattice diagram can be obtained for any groups of Zn and, for groups of U(n) which are cyclic.
SYMMETRY ANALYSIS ON Jessada Tanthanuch
Proceedings of ICMSA Vol 2, No 1 (2006): Pure Maths : ICMSA 2006
Publisher : Proceedings of ICMSA

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Abstract

Equationis a delay partial differential equation with an arbitrary functional G. Group analysis method is applied to find symmetries of the equation and to make group classification. Representations of analytical solutions and reduced equations are obtained from the symmetries.
NEWTON POLYHEDRA AND ESTIMATION TO EXPONENTIAL SUMS Kamen Ariffin Mohd Atan; J.H Loxton
Proceedings of ICMSA Vol 2, No 1 (2006): Pure Maths : ICMSA 2006
Publisher : Proceedings of ICMSA

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Abstract

The classical Newton polygon is a device for computing the fractional power series expansions of algebraic functions. Newton gave a number of examples of this process in his ”Method of Fluxions” which amount to a generalmethod.
-BACKBONE COLORING NUMBERS OF SPLIT GRAPHS WITH TREE BACKBONES A.N.M. Salman
Proceedings of ICMSA Vol 2, No 1 (2006): Pure Maths : ICMSA 2006
Publisher : Proceedings of ICMSA

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Abstract

In the application area of frequency assignment graphs are used to model the topology and mutual interference between transmitters. The problem in practice is to assign a limited number of frequency channels in aneconomical way to the transmitter in such a way that interference is kept at an acceptable level. This has led to various different types of coloring problem in graphs. One of them is a -backbone coloring. Given an integer 2, a graph G = (V,E) and a spanning subgraph H of G (the backbone of G), a -backbone coloring of (G,H) is a proper vertex coloring V ! {1, 2, . . .} of G in which the colors assigned to adjacent vertices in H differ by at least . The -backbone coloring number BBC(G,H) of (G,H) is the smallest integer ` for which there exists a -backbone coloring f : V - {1, 2, . . . , l}. In this paper we consider the -backbone coloring of split graphs. A split graph is a graph whose vertex set can be partitioned into a clique (i.e. a set of mutually adjacent vertices) and an independent set (i.e. a set of mutually non adjacent vertices), with possibly edges in between. We determine sharp upper bounds for -backbone coloring numbers of split graphs with tree backbones.

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