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https://nsuworks.nova.edu/mathematics_colloquium/ay_2022-2023/events
Recent Events in en-usMon, 24 Oct 2022 07:46:27 PDT3600One iteration for the second boundary condition for the nonlinear one dimensional Monge-Ampere equation
https://nsuworks.nova.edu/mathematics_colloquium/ay_2022-2023/events/2
https://nsuworks.nova.edu/mathematics_colloquium/ay_2022-2023/events/2Thu, 03 Nov 2022 12:30:00 PDT
The design of lenses and mirrors, in free form i.e. with no a priori symmetry assumption, has a long list of applications including materials processing, energy concentrators, medicine, antennas, computing lithography, laser weapons, optical data storage, imaging etc. The design process can be reduced to solving a generalized Monge-Ampere equation where the unknown is a function with a convexity property and subject to a constraint that a generalized gradient maps a given domain onto a prescribed one. The latter type of constraint is known as second boundary condition. The model one dimensional Monge-Ampere equation is nonlinear in the first order derivatives. We show that, although the discrete problem is nonlinear in the first order derivative, it can be solved with just one iteration. We also illustrate how the second boundary condition is reformulated in terms of the asymptotic cone of a convex extension.
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Gerard AwanouOn the Linear Independence of Finite Gabor and Wavelet Systems
https://nsuworks.nova.edu/mathematics_colloquium/ay_2022-2023/events/1
https://nsuworks.nova.edu/mathematics_colloquium/ay_2022-2023/events/1Thu, 15 Sep 2022 12:30:00 PDT
Gabor and Wavelet Systems are some of the most important families of integrable functions with great potential in applications. Those applications include numerical analysis, signal processing (sound, images), and many other areas of physics and engineering. In this talk, we will present some partial results on a conjecture that states each finite Gabor system is linearly independent. We will also present cases of linearly independent and cases of linearly dependent finite wavelet systems.
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Abdelkrim Bourouihiya