INSTITUT SAINS MATEMATIK UNIVERSITI MALAYA SIRI ... series/Past...INSTITUT SAINS MATEMATIK...

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



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

∇=∂∂ .


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.




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.




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.



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).



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.




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.




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.




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?.




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



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.


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.




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.




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.




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.




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.



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.


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.




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.




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


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.


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




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.




Bil:23/2012


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.


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.




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