Department of Mathematics & Statistics
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Mathematics


Seminars 2015-2016 | Seminars 2014-2015 | Seminars 2013-2014 | Seminars 2012-2013 | Conferences | Workshops

October 23rd, 2013, 10:00 a.m., Science Conference Room.
Title: Differential forms and Applications
Speaker: Dr. Joseph Malkoun (NDU - Louaize, Lebanon)
Abstract: We introduce the language of differential forms and the exterior derivative, i.e. the d operator. This ultimately enables to unify various theorems of calculus 4 such as the divergence theorem and Green's theorem into a single theorem, namely Stoke's theorem. We will also see, time permitting, how this enables us to write the electromagnetic field as a 2-form containing both the electric and magnetic field. Maxwell's equations can then be written using the d-operator in a very simple way.

November 20th, 2013, 10:00 a.m., Science Conference Room.
Title: Stratified Monte Carlo for integration and simulation
Speaker: Dr. Rami El Haddad (USJ - Mansourieh, Lebanon)
Abstract : Monte Carlo (MC) methods are probabilistic simulation methods using random numbers to solve on computers problems from applied sciences and techniques. Their principle is based on the use of the central limit theorem: One estimates a parameter, written as the expected value of a random variable, by repeated and independent evaluations of the variable. The error of the method is approximated through the variance of the estimator. One way to improve the convergence is to reduce the order of the variance of the estimators. In this talk, we analyze variance reduction methods and we test their efficiency for numerical integration and for solving differential equations.

December 18th, 2013, 10:00 a.m., Science Conference Room.
Title: The local-global approach to Diophantine equations
Speaker: Dr. Martin Bright (AUB, Lebanon)
Abstract: The problem of finding integer or rational solutions to equations has been studied since ancient times.  It has long been realised that studying solutions modulo an integer m is a useful tool: if an equation has no solutions modulo m, then it certainly has no integer solutions.  However, there are some equations which have no integer solutions despite having solutions modulo every integer m.  To understand this phenomenon, we can study p-adic ("local") solutions to the equation, and try to understand where the integer ("global") solutions lie inside the "local" ones.

January 22th, 2014, 10:00 a.m., Science Conference Room.(Canceled)
Title: T.B.A.
Speaker: Dr. Youssef Raffoul (University of Dayton, Ohio, USA)
Abstract: T.B.A.

March 3rd, 2014, 10:00 a.m., Science Conference Room.
Title: Fixed Point Or Lyapunov Functionals?
Speaker: Dr. Youssef Raffoul (University of Dayton, Ohio, USA)
Abstract: Lyapunov functions and functionals have been successfully used to obtain boundedness, stability and the existence of periodic solutions of ordinary differential equations, differential equations with functional delays and Volterra integrodifferential equations. In the study of differential equations with functional delays, when using
Lyapunov functionals, many difficulties arise if the delay is unbounded or if the differential equation in question has unbounded terms. In this talk we explore the use of fixed point theory to overcome some of the difficulties. In particular we concentrate on the stability of the trivial solution of the nonlinear neutral differential equations with unbounded delay,
x' (t)= -a(t)x(t)+ c(t) x' (t-g(t))+ q(x(t),x(t-g(t)))
We will provide several examples in which comparison between the two methods is considered. Several Open Problems will be presented at the end of the talk.

March 24th, 2014, 10:00 a.m., Science Conference Room.
Title: Boundedness And Exponential Stability In Highly Nonlinear Stochastic Differential Equations
Speaker: Dr. Youssef Raffoul (University of Dayton, Ohio, USA)
Abstract: Download (PDF format)

April 10, 2014, 12:30 p.m., Science Conference Room.

Title: Ashtekar-Lewandowski measure as a restriction of the product one.
Speaker: Dr. Tamer Tlas (American University of Beirut)
Abstract: I will describe the importance of finding a measure on the space of connections for topological quantum field theory. Then the A-L measure will be constructed and shown to be closely related to the product one.

May 7th, 2014, 10:00 a.m., Science Conference Room.

Title: Decomposition of the Chi-square Test in Non-Equiprobable Cases
Speaker: Dr. Abbas Hakim (American University of Beirut)
Abstract: The goodness-of-fit test for the multinomial model, introduced by Pearson in 1900, is still one of the most popular tests that have withstood the test of time. In recent literature, there has been some attempts to decompose this test into basic components that are asymptotically independent and each of them contains information about some distinct aspects of the underlying distribution. This was done in the case of equiprobable cell probabilities with k cells, k being a power of two, using a sub-matrix of a Hadamard matrix. In this presentation, we explain the inherent relevance of Hadamard matrices to this problem. We then propose a method to generalize the decomposition to non-equiprobable cells as well as to an arbitrary number k of cells (not necessarily a power of two). An appropriately chosen linear transformation of the vector of multinomial cell counts renders the variance-covariance matrix of this transformed vector into an idempotent matrix. We perform a spectral decomposition of this matrix by directly presenting a suitable “new” orthogonal matrix of the generalized Hadamard-type.

May 15th, 2014, 12:30 p.m., Abou Khater Auditorium
Title: Medical Insurance and How to Measure its Performance
Speaker: Mr. Samih Geha Fellow in the Society of Actuaries and Founder of Actuscope (Riyadh and Lebanon)

June 4th, 2014, 12:00 p.m., Science Conference Room.
Title: Latest Trends in Business Analytics
Speaker: Mr. Nehme Tawk (Founder & CEO of Soft Solutions)

June 9th, 2014, 10:00 a.m., Science Conference Room.
Title:  Pedestrians - footbridge synchronization: analytical study of a macroscopic model
Speaker: Dr. Joanna Bodgi
Abstract: Through recent instances, several footbridges have exhibited a proven sensitivity to the lateral force generated by walking pedestrians. A synchronization phenomenon between the crowd and the footbridge was confirmed by experimental studies. In recent literature, a substantial number of studies aim to model this phenomenon, but they often fall short to reproduce it in an accurate physical and mathematical environment. In this talk, a macroscopic crowd-structure model is presented, where the synchronization phenomenon is accounted for in the equation governing the evolution of the pedestrian's walking frequency. First, the mathematical developments are presented and the resulting synchronization equation is shown to be similar to the Kuramoto one. A subsequent analytical study allows us then to determine the critical number of pedestrians for which synchronization may be triggered, and the displacement amplitude of the footbridge when the crowd-structure system has reached a stationary state. Finally, experimental application to real footbridges confirms the accuracy of this model in predicting crowd-footbridge behavior.