Download COMMUTING GRPAH OF PRIME ORDER ELEMENTS IN FINITE

INSPEM WEEKLY SEMINAR (1/2016)
DATE
TIME
VENUE
:
:
:
PRESENTER:
8 January 2016 (Friday)
3.15 pm
Al-Farabi Seminar Room, INSPEM
1) SUZILA MOHD KASIM (GS42647)
(Supervisor: Dr. Athirah Nawawi)
2) YUSRA SALLEH (GS42936)
(Supervisor: Assoc. Prof. Dr. Ibragimov Gafurjan)
3) NURUL AMIRAH SIHABUDIN (GS42902)
(Supervisor: Assoc. Prof. Dr. Siti Hasana Sapar)
4) NUR ADAWIAH ALI (GS43058)
(Supervisor: Dr. Faridah Yunos)
TOPIC
:
1) COMMUTING GRPAH OF PRIME ORDER ELEMENTS IN
FINITE GROUPS
2) CONSTRUCTION OF EVASION STRATEGY IN MULTI
PURSUERS DIFFERENTIAL GAME WITH COORDINATEWISE INTEGRAL CONTRAINTS
3) ON SIMULTANEOUS PELL EQUATIONS
and
‘
4) MAXIMUM AND MINIMUM NORMS FOR t-NAF
EXPANSION ON KOBLITZ CURVE
COMMUTING GRPAH OF PRIME ORDER ELEMENTS
IN FINITE GROUPS
Suppose G is a finite group and X is a subset of G. Then the commuting graph on X, denoted
C(G,X), is a graph whose vertex set is X, with any two points connected by an edge if and
only if they commute. If the set X is a conjugacy class of involutions then we call the graph
C(G,X) the commuting involution graph for G with respect to X. These graphs have been
studied by many different authors. This research studies the structure of commuting graphs
C(G,X) such as the connectivity, diameter and disc sizes of the graph including the number of
CG(t)-orbits and their representatives when G as some finite groups and X are conjugacy
classes of elements of prime order.
CONSTRUCTION OF EVASION STRATEGY IN MULTI PURSUERS
DIFFERENTIAL GAME WITH COORDINATE-WISE INTEGRAL CONSTRAINTS
We study evasion differential game in multi pursuers against single evader with coordinatewise and control functions of all players are subjected to integral constraints. Assuming that
the total resource of the pursuers does not exceed that of the evader, we solve the game by
presenting explicit strategy for the evader which guarantees evasion.
ON SIMULTANEOUS PELL EQUATIONS
and
This project is to find the integral solutions to the simultaneous Pell equations
and
where
is square free and
an odd prime. In order to find the
fundamental solutions, we will consider the continued fractions expansion of
. By looking
at the pattern of solutions, some lemmas and theorems will be constructed.
MAXIMUM AND MINIMUM NORMS FOR t-NAF EXPANSION
ON KOBLITZ CURVE
The scalar multiplication in Elliptic Curve Cryptosystems (ECC) is the dominant operation of
computing integer multiple for an integer n and a point P on elliptic curve. In 1997, Solinas
introduced the τ -adic non-adjecent form (τ -NAF) expansion of an element n of ring Z(τ ) on
Koblitz Curve. However in 2000, Solinas estimated the length of τ -NAF expansion by using
maximum and minimum norms that obtained by direct evaluation method. In 2014, Yunos et.
al introduced the formula of norm for every τ -NAF to improve this method. However, a lot
of combination of norm should be considered when length of expansion is more than 15. To
avoid this problem, we need the formula to calculate the number of maximum and minimum
norms for τ -NAF occurring among of all elements in Z(τ ). With this formulas, we can
estimate the length of τ -NAF expansion more accurately.