-
Bil: 1/2012
Title : K-Means Clustering in Data Analysis Speaker : Prof. C.
Loganathan Principal, Maharaja Arts and Science College, Tamil
Nadu, India Date : 13 January 2012 (Friday) Time : 10am – 11am
Venue : MM3, Institute of Mathematical Sciences
Abstract
The lecture is intended to give a brief explanations about the
clustering, a traditional
unsupervised method for data analysis. In the presentation the
Hierarchical clustering and
K-means clustering are elaborated. The two types of Hierarchical
clustering namely (i)
Agglomerative; and (ii) Divisive will be explained. Also the
importance of clustering are going to be highlighted in the fields
of Biological
Science, Health Science, Business and Marketing, Social network
analysis, Computer
Science, Crime analysis, Climatology and Mathematical
Sciences.
SEMUA DIJEMPUT HADIR
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA SIRI KOLOKIUM
-
Bil: 2/2012
Title : Numerical solution of elliptic partial differential
equations by
Haar wavelet operational matrix method Speaker : Cik Nor
Artisham Che Ghani MSc Candidate, Institute of Mathematical
Sciences, University of Malaya Date : 19 January 2012 (Thursday)
Time : 10am – 11am Venue : MM3, Institute of Mathematical
Sciences
Abstract
The purpose of this study was to establish a simple numerical
method based on the Haar wavelet operational matrix of integration
for solving two dimensional elliptic’s partial differential
equation (PDE) of the form, ),(),(),(2 yxfyxkuyxu =+∇ with the
Dirichlet boundary conditions. To achieve the target, we have
studied the Haar wavelet series, which came from the expansion for
two dimensional functions,
∑= )()(),( yhxhcyxu jiij or compactly written as )()(),(
yCHxHyxu T= , where C is the
coefficient matrix. Wu (2009) had previously used this expansion
to solve first order PDE, and we have extended the problem solving
for second order PDE. The main point for solving the second order
or higher order partial differential equations is the determination
of the coefficient matrix, C. If the function ),( yxu is known,
then C can
be easily computed as THUH . However, if function ),( yxu
appears as the dependent variable in the elliptic equation, we
first expand the highest partial derivative as Haar
wavelet series, for example, )()( yDHxHu Txx = , and the
coefficient matrix D usually can be solved by using Lyapunov or
Sylvester type equation. Then the solution ),( yxu can
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA SIRI KOLOKIUM
-
easily be obtained through Haar operational matrix. The key to
this is the identification for the form of coefficient matrix when
the function is separable. Three types of elliptic equations solved
by new method are demonstrated and the results are then compared
with exact solution. For the beginning, the computation was carried
out for lower resolution, 8=m . As expected, the more accurate
results can be obtained by increasing the resolution and the
convergence are faster at collocation points. This research is our
preliminary work on two dimensional space elliptic equation via
Haar wavelet operational matrix method. After it has been
successfully proved, we hope to
expand this method for solving diffusion equation, uktu
2∇=∂∂
and wave equation,
uctu 222
2
∇=∂∂ .
SEMUA DIJEMPUT HADIR
-
Bil: 3/2012
Title : A New Cryptographic Algorithm Based on Decomposition
Problem in Elliptic Curve Cryptography Speaker : Hilyati Hanina
Zazali MSc Candidate, Institute of Mathematical Sciences,
University of Malaya Date : 26 January 2012 (Thursday) Time : 10:00
am – 11:00 am Venue : MM3, Institute of Mathematical Sciences
Abstract This study describes three algorithms for efficient
implementations in Elliptic Curve Cryptography (ECC). The first
algorithm determines an approach of performing key exchanges
between two subgroups for Decomposition Problem and three subgroups
for Triple Decomposition Problem. The algorithms work by arranging
parameters using finite field group in elliptic curve E. It is a
new approach, which performs core operation using multiplication of
points based in ECC. The algorithm explores computational
advantages of computing cofactor number of points on E and it is
computationally infeasible to obtain if the cofactor are large
enough. The second algorithm deals with the use of Decomposition
Problem in encryption scheme for ECC. We introduce two concepts of
splitting messages using the scheme in El-Gamal and Massey-Omura
algorithms. The messages can be split either before or after the
user sends the messages to the receiver. The third algorithm
describes the application of Decomposition Problem to the signing
and verifying digital messages in ECC. Since sub exponential time
algorithm is known for ordinary discrete logarithm problem and
integer factorization problem and not for elliptic curve discrete
logarithm problem, the algorithm presented for the digital
signature in this study has substantially greater strength per key
bit than in other digital signature algorithm.
SEMUA DIJEMPUT HADIR
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA SIRI KOLOKIUM
-
Bil: 4/2012
Title : Characterizations via Regression of Generalized
Order
Statistics Speaker : Prof. Mirza Iftekhar Beg Department of
Mathematics and Statistics, University of Hyderabad, India (with M.
Ahsanullah, Ramesh C. Gupta) Date : 26 January 2012 (Thursday) Time
: 11:00 am – 12:00 noon Venue : MM3, Institute of Mathematical
Sciences
Abstract We present some characterizations of distributions
based on the regression ofgeneralized order statistics. In the case
of adjacent generalized order statistics, the conditional
expectation of one generalized order statistic given the other
one completely characterizes
distributions depending on the type of regression function. In
the case of non-adjacent
generalized order statistics, the characterization of
distributions using conditional expectations
becomes more complicated. The results presented in the paper
unify and extend some of the
existing results involving order statistics and record
values.
SEMUA DIJEMPUT HADIR
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA SIRI KOLOKIUM
-
Bil: 6/2012
Title : Optimal (s;S) Policies for Jump Inventory Models Speaker
: Prof. Lakdere Benkherouf Department of Statistics and Operations
Research, Kuwait University, Kuwait Date : 29 February 2012
(Wednesday) Time : 3:00 pm – 4:00 pm Venue : MM3, Institute of
Mathematical Sciences
Abstract
In this talk, a single item stochastic inventory model where
demand is driven by a
piecewise deterministic process, will be presented. The model
appears to be a natural
extension to some existing deterministic models. Then, the
optimal impulse control policy
which minimizes the inventory costs over an infinite horizon
will be discussed along with a
Quasi-Variational Inequality (QVI) formulation. It turns out
that the solution of the (QVI)
orresponds to the classical (s;S) policy.
SEMUA DIJEMPUT HADIR
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA
SIRI KOLOKIUM
-
Bil: 7/2012
Title : Differential Geometric Analysis of Radiation-particle
Interaction Speaker : Dr. Kwa Kiam Heong Department of Mathematics
Ohio State University, Columbus, OH U.S.A. Date : 14 March 2012
(Wednesday) Time : 3:00 pm – 4:00 pm Venue : MM3, Institute of
Mathematical Sciences
Abstract
On the basis of Lorentz equations of motion, we relate the
dynamics of particle orbits in a generic EM field with planar
symmetry to a curvature function and associated Jacobi fields
within a Lorentzian geometrical framework. The class of EM fields
with planar symmetry includes arbitrary plane-wave fields,
standing-wave fields, and EM fields of colliding waves. As
applications, we show that this reformulation of Lorentz equations
leads to (1) a demonstration of the integrability of particle
orbits in a plane-wave field as a result of the vanishing of the
curvature function and (2) a manifestation of the parametric
dependence of the dynamical response of particle orbits to the EM
field on the intensity parameter in terms of local stability and
the occurrence of parametric resonance. Note: The results have
recently been published in J. Phys. A: Math. Theor. 45 (2012)
105203 (22 pp)
(http://dx.doi.org/10.1088/1751-8113/45/10/105203).
SEMUA DIJEMPUT HADIR
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA
SIRI KOLOKIUM
-
Bil: 8/2012
Title : Classification of totally umbilical proper slant
submanifolds
of Kenmotsu manifolds Speaker : Dr. Siraj Uddin Institute of
Mathematical Sciences, University of Malaya Date : 26 March 2012
(Monday) Time : 11:00 am – 12:00 noon Venue : MM3, Institute of
Mathematical Sciences
Abstract The purpose of this talk is to classify totally
umbilical slant submanifolds of a
Kenmotsu manifold. We prove that a totally umbilical slant
submanifold of a Kenmotsu
manifold is either anti-invariant or the dimension of the
submanifold is 1. Moreover, we
find that every totally umbilical proper slant submanifold is
totally geodesic.
SEMUA DIJEMPUT HADIR
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA SIRI KOLOKIUM
-
Bil: 9/2012
Title : A direct approach for optimal stopping problems Speaker
: Dr. Erik Baurdoux Department of Statistics London School of
Economics, UK Date : 6 April 2012 (Friday) Time : 11:00 am – 12:00
noon Venue : MM3, Institute of Mathematical Sciences
Abstract In this talk we give a brief introduction and overview
of some classical optimal stopping problems such as the secretary
problem and the quickest detection problem. We then move
on to the example of the American put for Lévy processes and
show that it can be solved
using a so-called direct approach.
SEMUA DIJEMPUT HADIR
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA SIRI KOLOKIUM
-
Bil: 10/2012
Title : Some classification results on totally umbilical proper
slant
and hemi-slant submanifolds of a nearly Kenmotsu manifold
Speaker : Dr. Siraj Uddin Institute of Mathematical Sciences,
University of Malaya Date : 30 May 2012 (Wednesday) Time : 3:00 pm
– 4:00 pm Venue : MM3, Institute of Mathematical Sciences
Abstract In this talk we discuss slant and hemi-slant
submanifolds of a nearly Kenmotsu
manifold. We prove that every totally umbilical proper slant
submanifold of a nearly
Kenmotsu manifold is totally geodesic and derive the
integrability conditions of involved
distributions in the definition of a hemi-slant submanifold.
Finally, we obtain a classification
theorem on a totally umbilical hemi-slant submanifold of a
nearly Kenmotsu manifold.
SEMUA DIJEMPUT HADIR
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA SIRI KOLOKIUM
-
Bil: 11/2012
Title : Thoughts on mathematics teaching in 2012, and beyond
Speaker : Prof. Frank Uhlig Department of Mathematics and
Statistics, Auburn University, Auburn Date : 25 June 2012 (Monday)
Time : 3:00 pm – 4:00 pm Venue : MM3, Institute of Mathematical
Sciences
Abstract This talk approaches education and more specifically
math education holistically.
We look at the interaction of teachers and students, the
subjects and our teaching and
learning in the teaching process.
How should and could we use our mathematical knowledge base, the
teaching tools and
the applications of math for the problems of today, given our
individual and cultural history
and our times?.
SEMUA DIJEMPUT HADIR
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA SIRI KOLOKIUM
-
Bil: 12/2012
Title : Numerical Methods Based Computation and Analysis of
Interior Permanent Magnet Synchronous Motor Drive Speaker : Ms.
Shahida Pervin MSc. Candidate, Institute of Mathematical Sciences,
University of Malaya Date : 27 June 2012 (Wednesday) Time : 3:00 pm
– 4:00 pm Venue : MM3, Institute of Mathematical Sciences
Abstract Recently, the interior permanent magnet synchronous
motor (IPMSM) is getting
popular in industrial drives because of their advantageous
features such as high torque to
current ratio, high power to weight ratio, high efficiency, high
power factor, low noise, and
robustness. Among different permanent magnet (PM) synchronous
motors, the IPMSM
with magnets buried inside the rotor core shows excellent
properties such as mechanically
robust rotor, small effective air gap, and rotor physical
non-saliency. The vector control
technique is widely used for high performance control of an
IPMSM drive as the motor
torque and flux can be controlled separately in vector control.
Fast and accurate
response, quick recovery of speed from any disturbances and
insensitivity to parameter
variations are some of the important characteristics of high
performance drive system
used in electric vehicles, robotics, rolling mills, traction and
spindle drives.
Despite many advantageous features of IPMSM, precise control of
this motor at high-
speed conditions especially, above the rated speed remains an
engineering challenge. At
high speeds the voltage, current and power capabilities of the
motor exceed the rated
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA SIRI KOLOKIUM
-
limits. Consequently, the nonlinearity due to magnetic
saturation of the rotor core and
hence the variation of d,q axes flux linkages will be
significant. Thus, it severely affects the
performance of the drive at high speeds. The IPMSM drive can be
operated in above the
rated speed using the field-weakening (FW) technique. In an
IPMSM the flux/field can only
be weakened by the demagnetizing effect of d-axis armature
reaction current, id. Recently,
researchers developed sophisticated FW control algorithms but
often ignored the high
precision computation of the algorithm. Mostly they simplify the
equations of flux control
by ignoring the stator resistance and depend on Matlab/Simulink
library. This results in
improper flux weakening operation of IPMSM. However, the proper
flux computation is a
crucial issue for motor control particularly, at high speed
condition. Therefore, there is a
need to investigate the other computational methods.
In this work, accurate flux estimation for proper field
weakening operation of IPMSM is
developed by incorporating the stator resistance of the motor.
The Newton-Raphson
method (NRM) based numerical computation is used for high
precision computation of flux
component of stator current, id to enhance the performance of
the IPMSM drive over wide
speed range. For the complete drive the maximum torque per
ampere (MTPA) technique
is used below the rated speed and FW technique is used above the
rated speed. The
performance of the proposed NRM based computation of id for
IPMSM drive is evaluated
in simulation using Matlab/Simulink at different operating
conditions. The performance of
the IPMSM drive with the proposed NRM method is also compared
with the conventional
simplified computation of id. It has been found from the results
that the IPMSM drive with
proposed calculation of id provides better response as compared
to the conventional
calculation of id. Thus, the proposed method could be a
potential candidate for real-time
field weakening operation of IPM motor. If possible, the
proposed drive system will be
implementation in real-time using digital signal processor (DSP)
board DS-1104.
In the next step, different order Runge-Kutta methods (RKM) will
be used to solve the
motor differential equations and the performance of the IPMSM
drive will be tested and
compared with the Matlab/Simulink library motor model.
SEMUA DIJEMPUT HADIR
-
Bil: 13/2012
Title : Interactions between Interfacial Griffith Cracks in
Composite
Materials Speaker : Dr. S. Das Department of Applied
Mathematics, Institute of Technology,
Banaras Hindu University, India Date : 3 July 2012 (Tuesday)
Time : 3:00 pm – 4:00 pm Venue : MM3, Institute of Mathematical
Sciences
Abstract The article deals with the plane strain problem of
determining the interactions of a
pair of outer cracks on a central crack situated at the
interface of composite materials. The
mixed boundary value problem is reduced to solving a pair of
simultaneous singular
integral equations which have finally been solved numerically by
using Jacobi
polynomials. The analytical expressions for stress intensity
factors at the central crack tip
and the expression of the strain energy release rate have been
derived for general
loading. Numerical values of the interaction effects of the
outer cracks on the central crack
have been calculated through stress magnification factors. The
interaction effects are
either shielding or amplification depending on the size of the
outer cracks and their
spacing from the central crack.
SEMUA DIJEMPUT HADIR
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA SIRI KOLOKIUM
-
Bil: 14/2012
Title : New family of Archimedean copula Speaker : Ms. Azam
Pirmoradian PhD. Candidate, Institute of Mathematical Sciences,
University of Malaya Date : 11 July 2012 (Wednesday) Time : 10:00
am – 11:00 am Venue : MM3, Institute of Mathematical Sciences
Abstract The Archimedean copulas form an important family of
copulas, which have a
simple form with properties such as associativity and possess a
variety of dependence
structures. Specifically, the Archimedean copula for a bivariate
data set can be easily
constructed by a generator function. As a generator uniquely
determines an Archimedean
copula, different choices of generator yield many families of
copulas. As a consequence,
many dependence properties of such copulas are relatively easy
to establish because
they reduce to analytical properties of the generator. In this
talk we speak about the
Archimedean copula together with introducing some new bivariate
Archimedean copulas
with a one-parameter family, which we refer to as trigonometric
copulas. Dependence
properties of these copulas are analyzed. With reference to
their properties, some of them
are chosen to build multivariate copulas according to C-vine and
D-vine structure.
Illustrative examples are done to validate the theoretical part
of our research. Finally we
apply new copulas on hydrology data.
SEMUA DIJEMPUT HADIR
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA SIRI KOLOKIUM
-
Bil: 15/2012
Title : Natural Convection in an Inclined Square Enclosure
Subject
to Sinusoidal Temperature Profile on the Left Sidewall Speaker :
H. T. Cheong MSc. Candidate, Institute of Mathematical Sciences,
University of Malaya Date : 11 July 2012 (Wednesday) Time : 3:00 pm
– 4:00 pm Venue : MM3, Institute of Mathematical Sciences
Abstract A numerical study on natural convection in an inclined
square enclosure heated
and cooled with sinusoidal temperature profile on the left
sidewall has been considered.
The right wall of the enclosure is cooled with constant
temperature while the horizontal top
and bottom walls are adiabatic. The governing equations are
solved by using the Finite
Difference Method for different Rayleigh numbers and inclination
angles. The results are
presented in the forms of streamlines, isotherms and Nusselt
numbers. It was found that
the flow patterns are dependent on Rayleigh numbers and
inclination angles.
SEMUA DIJEMPUT HADIR
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA SIRI KOLOKIUM
-
Bil:16/2012
Title : Maintenance of deteriorating non-exponential single
server
queue Speaker : Ms. Koh Siew Khew PhD Candidate, Institute of
Mathematical Sciences University of Malaya Date : 18 July 2012
(Wednesday) Time : 10:00 am – 11:00 am Venue : MM3, Institute of
Mathematical Sciences
Abstract
Consider the single server queue in which the system capacity is
infinite and the customers are served on a first come, first served
basis. We first treat the case of a system without deterioration in
which the service time and interarrival time distributions are
assumed to have a constant asymptotic rate. We derive the
stationary queue length distribution and the stationary waiting
time distribution for the system. The results found are verified by
using simulation. We next apply the similar method of deriving the
stationary queue length distribution to a system in which the
server would deteriorate due to random shocks and the seriously
affected server will be sent for repair. The customer’s
interarrival time (service time) is assumed to have a constant
asymptotic rate while the service time (interarrival time) remains
exponentially distributed. From the stationary queue length
distribution, we can find the sojourn time distribution of a
customer who arrives when the queue is in a stationary state, and
the expected length of the duration between two successive repair
completions. From these distributions and expected length, we find
the value of the specified maintenance level such that the long run
average cost is minimized.
SEMUA DIJEMPUT HADIR
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA SIRI KOLOKIUM
-
Bil:17/2012
Title : The integrated inventory and production planning for
time
varying demand process Speaker : Siti Suzlin Bt Supadi Institute
of Mathematical Sciences, University of Malaya Date : 23 July 2012
(Monday) Time : 3:00 pm – 4:00 pm Venue : MM3, Institute of
Mathematical Sciences
Abstract
In the literature, integrated inventory model has received a lot
of attention. Most previous
works on this topic have been based on the assumption of
constant demand rate.
However this assumption is not reliable in the reality; it is
either increasing or decreasing
with time.
We considered the model which consists of a single vendor who
manage the production
and deliver to a single buyer with a linearly decreasing demand
rate over a finite time
horizon. Costs are attached to manufacturing set up, the
delivery of a shipment and
stockholding at the vendor and buyer. The objective is to
determine the number of
shipments and size of those shipments which minimize the total
system cost - assuming
the vendor and buyer collaborate and find a way of sharing the
consequent benefits.
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA SIRI KOLOKIUM
-
We begin with the integrated inventory policy for shipping a
vendor's final production batch
to a single buyer under linearly decreasing demand. The first
case considered here is the
holding cost at the vendor is less than at the buyer. We solve
this model with equal
shipment size policy, equal shipment period policy and unequal
shipment size and period
policy. Then, we develop a mathematical model when the unit
holding cost is higher at the
vendor rather than at the buyer (consignment stock problem). For
this case, we also
consider equal shipment size policy, equal shipment period
policy, and unequal shipment
size and period as in the previous case policy.
It is followed by an integrated inventory model with n
production batches which consists of
the final batch at the end of the production cycle. This model
also considers the case of
the buyer's holding cost being greater than the vendor's and
vice versa. We consider this
model with equal cycle time and unequal cycle time for both
policies. We show the
solution policies when the shipment sizes are equal and when
they are unequal.
We illustrate all the policies with numerical examples and
sensitivity analysis. Then we
make some comparison of the model. Lastly we end the thesis with
conclusion and some
recommendations for further research.
SEMUA DIJEMPUT HADIR
-
Bil:18/2012
Title : Formulation of invariants for discrete Tchebichef
moments
and image classification Speaker : Pee Chih Yang PhD Candidate,
Institute of Mathematical Sciences University of Malaya Date : 25
July 2012 (Wednesday) Time : 3:00 pm – 4:00 pm Venue : MM3,
Institute of Mathematical Sciences
Abstract
Due to the discrete nature and the orthogonality of the basis
functions, discrete Tchebichef moments are superior global features
extractor. However, the moments cannot be directly used by
recognition system as the object images might already being
deformed in various ways. Invariants that are insensitive to
particular deformation and provide enough discrimination power to
distinguish objects belonging to different classes are therefore
important to help simplify classification system and enhance
recognition performance. Two major types of invariant that are
widely used by recognition systems are being studied. They are
anisotropic scale and translation (AST) invariants, and
translation, rotational and scale (TRS) invariants. Current
proposed algorithms on discrete Tchebichef moments are reviewed and
new invariants algorithms which are numerically efficient and with
better discrimination power are proposed. An empirical study showed
that the propose algorithms are robust to noisy conditions.They
also give better recognition performance on discriminating sets of
very similar Chinese handwritten characters.
SEMUA DIJEMPUT HADIR
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA SIRI KOLOKIUM
-
Bil: 19/2012
Title : Pricing of Interest Rate Derivatives Speaker : Khor Chia
Ying (Ph.D. Candidate, Institute of Mathematical Sciences,
University of Malaya) Date : 16 August 2012 (Thursday) Time :
11am – 12pm Venue : MM3, Institute of Mathematical Sciences
Abstract A numerical method is proposed to find the bond price
of a zero-coupon bond at time t with maturity time T under the CIR
model of which distributions of the increments are symmetrical and
having fat-tails. The numerical results thus found arefairly close
to the corresponding theoretical values in the original CIR model.
The similar numerical method is next applied to evaluate the bond
price of a zero-coupon bond with maturity time T under the Chan,
Karolyi, Longstaff and Sanders (CKLS) interest rate model that is
described by a Levy process. The numerical results obtained show
that the bond price decreases slightly when the parameter γ in the
CKLS model increases, and the variation of the bond price is slight
as the non-normality of the underlying distribution in the Levy
process is varied. A method is also proposed for pricing the
European call option with maturity T and strike price K written on
a zero-coupon bond with maturity S > T. The numerical results
thus found show that the option price decreases as the parameter γ
in the CKLS model increases, and the variation of the option price
is slight when the underlying distribution of the increment departs
from the normal distribution. So far, the parameters in the
interest rate models that used in finding the bond price and the
European call option price are assumed to be constants. The
restriction on constant parameters is lifted by describing the
parameters as ones which follow a multivariate non-normal
distribution. The corresponding bond price and option price for the
CKLS model are obtained by using simulation.
SEMUA DIJEMPUT HADIR
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA SIRI KOLOKIUM
-
Bil: 20/2012
Title : A Study on Sufficient Conditions and Numerical Solutions
of Oscillatory Nonlinear Ordinary Differential Equations of Second
Order Speaker : Ms. Mastora Jaber Saad (Ph.D. candidate, Institute
of Mathematical Sciences, University of Malaya)
Date : 24 August 2012 (Friday) Time : 10:00 am – 11:00 am Venue
: MM3, Institute of Mathematical Sciences
Abstract
We study oscillation of solutions of the second order non-linear
ordinary
differential equations of the forms
)2())(),(,())())(()()),((()()()()())(()(
)1())(,())()()),((()()()(
txtxtHtxtxtrtxgtqtxthtxtxtr
txtHtxtrtxgtqtxtr
•••••
•••
=ΨΦ++
Ψ
=Φ+
where hr , and q are continuous functions on the interval [ )
),(,0,, 00 +∈Ψ≥∞ RRCtt and
)(tr is a positive function. g is continuously differentiable
function on the real line R except
possibly at 0 with 0)( >xxg and 0)( >≥′ kxg for all ,0≠x Φ
is a continuous function on
RxR with 0),( >Φ vuu for all u 0≠ and ),(),( vuvu Φ=Φ λλλ for
any ),0( ∞∈λ and H is a
continuous function on [ )∞,0t ×R×R with )())(())(),(,(
tptxgtxtxtH ≤•
for all ≠x 0 and
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA
SIRI KOLOKIUM
-
0tt ≥ .
Throughout this study, we restrict our attention only to the
solutions of the differential
equations (1) and (2) which exist on some ray[ )∞,xt . A
solution x(t) of the differential
equations (1) and (2) is said to be oscillatory if it has
arbitrary large zeros. Otherwise it is
said to be non-oscillatory. Equations (1) and (2) are called
oscillatory if all its solutions are
oscillatory. Otherwise it are called non oscillatory. Numerical
examples are also
demonstrated.
SEMUA DIJEMPUT HADIR
-
Bil:21/2012
Title : On Fredholm Index, Transversal Approximations and
Quillen’s Geometric Complex Cobordism of Hilbert Manifolds
with some Applications to Flag Varieties of Loop Groups Speaker
: Prof. Dr. Cenap Ozel
AIBU Mathematics Department Bolu, Turkey Date : 19 September
2012 (Wednesday) Time : 3:00 pm – 4:00 pm Venue : MM3, Institute of
Mathematical Sciences
Abstract By using Fredholm index we developed a version of
Quillen's geometric cobordism theory for infinite dimensional
Hilbert manifolds. This cobordism theory has a graded group
structure under topological union operation and has push-forward
maps for complex orientable Fredholm maps. In this work, by using
Quinn's Transversality Theorem , it will be shown that this
cobordism theory has a graded ring structure under transversal
intersection operation and has pull-back maps for smooth maps. It
will be shown that the Thom isomorphism in this theory will be
satisfied for finite dimensional vector bundles over separable
Hilbert manifolds and the projection formula for Gysin maps will be
proved. After we discuss the relation between this theory and
classical cobordism, we describe some applications to the complex
cobordism of flag varieties of loop groups and we do some
calculations
SEMUA DIJEMPUT HADIR
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA SIRI KOLOKIUM
-
Bil:22/2012
Title : Pricing of Interest Rate Derivatives Speaker : Ms. Khor
Chia Ying (Ph.D. candidate, ISM, UM) Date : 21 September 2012
(Friday) Time : 10:00 am – 11:00 am Venue : MM3, Institute of
Mathematical Sciences
Abstract A numerical method is proposed to find the bond price
of a zero-coupon bond at time t with maturity time T under the CIR
model of which distributions of the increments are symmetrical and
having fat-tails. The numerical results thus found are fairly close
to the corresponding theoretical values in the original CIR model.
The similar numerical method is next applied to evaluate the bond
price of a zero-coupon bond with maturity time T under the Chan,
Karolyi, Longstaff and Sanders (CKLS) interest rate model that is
described by a Levy process. The numerical results obtained show
that the bond price decreases slightly when the parameter γ in the
CKLS model increases, and the variation of the bond price is slight
as the non-normality of the underlying distribution in the Levy
process is varied. A method is also proposed for pricing the
European call option with maturity T and strike price K written on
a zero-coupon bond with maturity S > T. The numerical results
thus found show that the option price decreases as the parameter γ
in the CKLS model increases, and the variation of the option price
is slight when the underlying distribution of the increment departs
from the normal distribution. So far, the parameters in the
interest rate models that used in finding the bond price and the
European call option price are assumed to be constants. The
restriction on constant parameters is lifted by describing the
parameters as ones which follow a multivariate non-normal
distribution. The corresponding bond price and option price for the
CKLS model are obtained by using simulation.
SEMUA DIJEMPUT HADIR
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA SIRI KOLOKIUM
-
Bil:23/2012
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA
PhD Conversion Seminar
Title : Engel Elements in Groups Speaker : Quek Shio Gai
(SGP110001)
Date : 30 November 2012 (Friday) Time : 3:00 pm – 4:00 pm Venue
: MM3, Institute of Mathematical Sciences
Abstract
Let G be a group and ,, 21 xx … mx G . The commutator of 1x and
2x is
21
1
2
1
121 ],[ xxxxxx and a simple commutator of weight 2m is defined
recursively as
],],,,,[[],,,[ 12121 mmm xxxxxxx where by convention . Let . A
useful
shorthand notation is , where by convention ][],[ 0 xyx . An
element
Gg is called a left Engel element, if for each Gx ,there is a
positive integer ),( xgnn such
that 1],[ gx n . The set of all left Engel elements is denoted
by )(GL . Right Engel elements is
defined similarly. In this talk, we shall discuss some
properties of Engel elements.
SEMUA DIJEMPUT HADIR
Research Group : Algebraic & Analytic Methods in
Mathematical Sciences
-
Bil: 12/2012
Title : Preserver Problems and Quantum Information Science
Speaker : Professor Dr. Chi-Kwong Li
Ferguson Professor of Mathematics, The College of William &
Mary Williamsburg, VA 23187-8795, USA
Date : 9 February 2012, Thursday Time : 10:00 am - 11:00 am
Venue : MM3, Institute of Mathematical Sciences, University of
Malaya
Abstract
. In this talk, we will describe some recent results on
preserver problems related to quantum information science including
the preservers of decomposable states, product numerical ranges,
higher rank numerical ranges, convex structure of states, etc. Open
problems and current work will be mentioned.
SEMUA DIJEMPUT HADIR
INSTITUT SAINS MATEMATIK
UNIVERSITI MALAYA SIRI KOLOKIUM