Research Centers CRAMS (Center of Research in Applied Mathematics & Statistics)

    CRAMS (Its history, mission, achievements, future goals):

    AUL Center for Research in Applied Mathematics and Statistics "CRAMS” was established in 2002 as an international interdisciplinary research center dedicated to supporting cooperative applied research in the mathematical and statistical sciences.

    The main activities of CRAMS are theoretical and computational studies of  deterministic and stochastic processes which model real-life problems or have a potential for doing so.  These include differential and integral equations, SDE’s and SIE’s (basically nonlinear).  And to develop new numerical methods for solving such problems.  New methodologies include e.g. wavelets and frames, Markov-chain Monte Carlo methods, spatio-temporal techniques, neural networks methods, etc.

    Typical CRAMS interests in numerical mathematics have included solution of ordinary and partial differential equations, BVP’s, integral equations, and optimization. In computational stochastics the typical interests have been on statistical characterization and prediction, computational inference in molecular population genetics, turbulent flow in fluids and the environment, molecular dynamics in chemistry and bioinformatics, economic dynamics and control and pricing American Options in finance. Some projects of CRAMS have been supported by the Lebanese NCSR and by other international organizations.

    As its first International research activity, CRAMS hosted in 2005 the International Symposium on Applied Non-harmonic Fourier Analysis at AUL, Lebanon. A Symposium organized in honor of the Riemann-Lebesgue Lemma Centennial.

    Professor Nassar Haidar, who is the head of the center, is also the Managing Editor of the Journal ofNumerical Mathematics and Stochastics:

    Director of CRAMS participating in ICNFAA-2004, at Kyungnam University, South Korea

    CRAMS-05 International Symposium on Applied Non-harmonic Fourier Analysis, in 2005 at AUL
    Upper L: CRAMS-05 Scientific Committee, headed by H. G. Feichtinger;
    Lower R: Granting N. H. S. Haidar a medal of the President of the Lebanon

    At the plenary session of the CRAMS-05 Symposium

    L: Seminar at CRAMS; R: Seminar at the African Institute for Mathematical Sciences AIMS in Dakar

    Some of CRAMS publications:

    N. H. S. Haidar,  An amplitude spectral  tonometer,  Computers  &  Mathematics with  Applications, 46 (5-6) : 959-969, 2003.

    Nassar H.S. HAIDAR, Adnan M. HAMZEH, Soumaya M. HAMZEH and Edward El-NAKAT, On martingales invoked by stochastic exponential and monomial densities, Random Operators and Stochastic Equations, Vol. 12, No. 4, 349–360, 2004.

    Nassar H. S. Haidar, Adnan M. Hamzeh and Soumaya M. Hamzeh, DECOMPOSITION PRINCIPLE FOR THE

    RECIPROCAL OF THE FACTORIAL, Applied Mathematics E-Notes, 5, 44-51, 2005.

    Haidar, N.H.S., Hamzeh, A. M. and Hamzeh S. M. Comparative stationarity of stochastic exponential and monomial densities. Random Operators & Stochastic Equations, 14 (4) : 303-310, 2006.

    NASSAR H. S. HAIDAR, A scale-frequency harmonic series, Integral Transforms and Special Functions, Vol. 17, No. 4, 275–283, 2006.

    Haidar , N.H.S.  On a symmetrized definite integration, Applied Mathematics & Computation,186, 70-73, 2007.

    Nassar H. S. Haidar, Real analysis proofs for the double Parametrized Riemann-Lebesgue Lemma, International Journal of Mathematics and Computer Science, 2, no. 4, 327–332, 2007.

    Nassar H. S. Haidar, Closed Divisibility of Integer Sequences under Summation of Digits, International Mathematical Forum, 3, no. 25, 1229 – 1232, 2008.

    N. H. S. Haidar, A. M. Hamzeh and S. M. Hamzeh,  Comparative Stationarity of stochastic exponential and monomial densities and related  nonlinear approximations, Nonlinear Functional Analysis and Applications, 1, 165–173, 2009.

    N. H. S. Haidar, Oscillatory spherical travelling-wave-type solutions to the cardiac BVP, Numerical Functional Analysis and Optimization, 30 (7–8),751–772, 2009.

    N. H. S. HAIDAR, On a Randomized Romberg Integration Method, Journal of Numerical Mathematics and Stochastics,1 (1) : 11-23, 2009.

    N. H. S. Haidar, On the Riemann-Lebesgue lemma with a nonharmonic kernel, Journal of Mathematical Sciences: Advances and Applications, 4(1), 9-26, 2010.

    Haidar, N.H.S. A geometric note on integration, Computers &  Mathematics  with  Applications, 59 (9), 3130-3136, 2010.

    N. H. S. Haidar, Applied scale-frequency analysis,  Advances and Applications in Mathematical Sciences, 7(2), 141-175, 2010.

    Haidar, N.H.S. On a finite asymptotic integral transform. J. Inv. & Ill-posed Problems, 19, 429-451, 2011.