• Seminars, 2009
  • December 28, 2009
    Some open problems of sliding mode control theory
    Professor L. M. Fridman, Engineering Faculty, National University of Mexico (UNAM)

    The talk will start with the historical revision of sliding modes(SM) controllers and problems arise during SM controllers developments. Than the higher order sliding mode concept will be revisited. Connecting the above mentioned tutorial 10 open problems which are studying in UNAM SM Lab will be presented:

    1. Liapunov based approach to Super twisting second order SM controllers
    2. Adaptation of the gain of SOSMs
    3. Singular perturbed approach for robustness of HOSMs
    4. Design of the filters for HOSM to adjust the chattering
    5. HOSM based control for the systems with unmatched perturbation
    6. HOSMs finite time observation and identification
    7. Output HOSM based control
    8. Output integral SM based LQ control
    9. Generation of Autuoscillations via 2 relay controllers
    10. HOSM based observation and identification of hybrid systems
  • December 21, 2009
    Optimal Traffic Control for Isolated Intersection: Optimal Control Synthesis
    Professor Ilya Ioslovich, Faculty of Civil and Environmental Engineering, Technion


    A simplified traffic model of isolated controlled intersection is considered. The continuous model of dynamical process is derived in order to find and analyze an optimal control policy to minimize total delay. An analytical solution of the optimal control problem with constrained signal light control is presented. The optimal synthesis is found for all the cases of the control constraints.
    The previous results from sixties and seventies are discussed.
    This is a joint work with Jack Haddad, Per-Olof Gutman and David Mahalel.

  • November 23, 2009
    Mathematical methods in digital image processing. Image filtering
    Dr. Irina Karelin, Senior Algorithm Developer, Generic Imaging Company


    Mathematical methods are widely used in digital image processing. Image filtering is one of the most important methods used for noise removing, sharpening contrast, adjusting the dynamic range of the image, for image segmentation.
    Bilateral filters are non-linear filters used for image smoothing with edge preserving. Whereas many filters are convolution in the image domain bilateral filters are operates in the image’s range- pixel values. Different types of filters will be discussed.

  • July 9, 2009
    Boundary interpolation problems for analytic self-maps of the unit disk
    Professor Vladimir Bolotnikov, Department of Mathematics, College of William and Mary


    The characterization of analytic self-maps of the unit disk in terms of their Taylorcoefficients at the origin is due to I. Schur. In the talk, we will discuss the boundary analogue of this result: we will chracterize analytic self-maps of the unit disk in terms of angular boundary derivatives.

  • June 29, 2009
    The free will theorem
    Dr. Ofer Eyal, Department of Physics, ORT Braude College


    Quantum mechanics predicts for the square of spin measurements some discrete values. How do these values depend on the spatial angle of the measuring instrument? The answer is that there is no explicit function that can tell us these values (the Kochen-Specker paradox). This fact, together with space-time locality imply the free will theorem about the decision of the particle which outcome to show in the measurement.

  • April 20, 2009
    New Tools for Research, Teaching and Tutoring Mathematics
    Omer Yagel, Representative of Maplesoft, VP Business Development DigiSec


    The science of Computer Algebra System (CAS) has stupendously developed over the last 3 decades, since the introduction of the first commercial systems in the 70s. Nowadays CAS is an important tool in the toolbox of almost every scientist with Maple by Maplesoft being the world’s CAS top application.
    The Maple tool chain is used to formulate mathematical models, solve and analyse complex systems in a variety of science and engineering disciplines. Maple is the first stop in formulating a model and in most cases also the last, offering full analysis and report tool. At the base of the new Maple tool chain stands Maple 12, which seamlessly combines advanced symbolic algebra capabilities with the most powerful numeric algorithms, top graphic engine and a document interface to create reports and write in a natural 2D math form. On top of the Maple engine are found:

    Physical modelling, multi-domain simulation environment that produces symbolic equations out of the blocks model, automatically simplifies and mathematically reduces the system, numerically simulate it and fully connected to the Maple infrastructure for further analysis.

    A server application that enables presenting a Maple worksheet on the Internet / Intranet, were the client only needs a Java enabled web browser.

    Maple Teacher Assistant – a Maple base application that may automatically create exams and home assignments out of templates, evaluates the results (numerically, symbolically the textually) and grade the student’s performance.
    Out of the box Maple is a reach application, containing 5 codes generators and over 100 packages covering a wide variety of discipline, exempli gratia:

    • Algebra
    • Advanced Linear Algebra
    • Discrete Algebra
    • Geometry
    • Plots
    • Calculus
    • Advanced Calculus
    • Tensor Calculus
    • Differential Equations
    • Variations Methods
    • Topology
    • Graph Theory
    • Group Theory
    • Units
    • Programming

    Maple tool chain is not only a FULL and COMLETE substitute for MATLAB, it betters the numeric only application in every way. Sceptic MATLAB users are more than welcome and invited to try and challenge this statement!
    An introductory lecture, briefly presenting the tools and environment of the Maple tool chain is to be given a power user of Maple in both academy and commercial duties and currently the VP Business Development for DigiSec, Maplesoft ‘s local representative.

  • April 6, 2009
    Free probability with applications to connections with complex analysis and combinatorics
    Professor Marek Bozejko, Instytut Matematyczny, Uniwersytet Wroclawski


    The main topics of my talk are following:

    1. Introduction to free probability of Voiculescu.
    2. A Complex Burger equation as heat equation in free probability.
    3. Nevanlinna-Pick functions and free infinitely divisible laws .
    4. Combinatorics of non-crossing partitions ,Delannoy triangle in free probability.
    1. M.Bozejko,On \Lambda(p) sets with minimal constant in discrete noncommutative groups, Proc.AMS,51(1975),402-412.
    2. M.Bozejko,M.Leinert,R.Speicher,Convolution and limit theorems for conditionally free random variables,Pacific J.Math.,175,357-388,(1996).
    3. M.Bozejko,W.Bryc,On a class of free Levy laws related to regression problem,J.Functional Analysis,236(2006),59-77.
    4. M.Bozejko,E.Lytvynov,Meixner lass of non-commutative generalized stochastic processes with freely independent values I.A characterization, appear in Comm.Math.Phys.(2009).
    5. S.Belinschi,M.Bozejko,F.Lehner,R.Speicher, The Normal Distribution is free infinitely divisible,Preprint 2009.
    6. F.Hiai,D.Petz,The Semicicle Law,Free Random Variables and Entropy, AMS 2000.
    7. A.Nica,R.Speicher,Lectures on the Combinatorics of Free Probability,Cambridge UP 2006.
    8. D.Voiculescu,K.Dykema and A.Nica, Free random Variables, AMS 1992.