Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 8 of 8
Full-Text Articles in Physical Sciences and Mathematics
One Iteration For The Second Boundary Condition For The Nonlinear One Dimensional Monge-Ampere Equation, Gerard Awanou
One Iteration For The Second Boundary Condition For The Nonlinear One Dimensional Monge-Ampere Equation, Gerard Awanou
Mathematics Colloquium Series
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 …
On The Linear Independence Of Finite Gabor And Wavelet Systems, Abdelkrim Bourouihiya
On The Linear Independence Of Finite Gabor And Wavelet Systems, Abdelkrim Bourouihiya
Mathematics Colloquium Series
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.
A Novel Tcr Clustering Method For Sars-Cov-2 Epitopes, Naziba A. Nuha
A Novel Tcr Clustering Method For Sars-Cov-2 Epitopes, Naziba A. Nuha
Mathematics Colloquium Series
T-cell epitopes are peptides generated from antigens that are presented by MHC class I and class II molecules to T-cells. These epitopes are usually identified by T-cell receptors (TCRs) of CD4 T-cells which then causes transformation of CD4 T-cells to helper or regulatory T cells. Recently, there has been growing interest in the role of T cells and their involvement in various ailments including SARS-COV-2, cancer, autoimmune diseases and other infectious diseases. However, the mechanism of TCR epitope recognition by Tcell receptors (TCRs) of CD4 T-cells at a repertoire level is still not fully understood. In this project, we reviewed …
A Weighted Probability Measure For Objects In Euclidean Space, Alessandro Xello
A Weighted Probability Measure For Objects In Euclidean Space, Alessandro Xello
Mathematics Colloquium Series
Since we were little kids, we developed our own sense dimension as a measure of some kind of extent. Whether it be length, width, or height, we intuitively understand how these features fit in the three-dimensional world we live in, and how to measure it. Nevertheless, mathematicians have found themselves dealing with objects, like fractals, and spaces, like R4 , that challenge our intuitive and self-developed definition of measure, to the point that it is not sufficient anymore. Lebesgue measure and Harsdorf measure for example are ways of assigning a measure to objects that belong to n-dimensional Euclidean spaces, in …
Modeling And Simulation Of Microscopic Fibers In A Viscous Fluid, William Mitchell
Modeling And Simulation Of Microscopic Fibers In A Viscous Fluid, William Mitchell
Mathematics Colloquium Series
In biology, the movements of tiny structures often rely on the mechanical properties of long, thin tubes. For example, bacteria swim by rotating their flagella, and in cell division (mitosis) the two copies of the DNA must be pulled apart by microtubules. To understand these processes it is very tempting to take advantage of the large aspect ratio of the thin structures, for example by modeling them as one-dimensional curves rather than as more complicated objects with volume and surface area. This kind of shortcut saves a lot of work! I will describe one standard and widely used tool known …
How Prey Defense Patterns Predator-Prey Distributions, Evan Haskell
How Prey Defense Patterns Predator-Prey Distributions, Evan Haskell
Mathematics Colloquium Series
In ecology, predator and prey species share a common interest in survival. However, this common interest places these species at odds with each other. Predators need to consume prey for their survival. Prey, on the other hand, do not survive if they are consumed. To meet their needs, predators engage in foraging or prey-taxis behaviors whereby they seek areas of high prey density. For prey there are numerous defense strategies to engage including aposematic mechanisms to advertise they are not worth the predator’s while, attacking the predator through chemical or community defense mechanisms, and alarm calls to seek assistance from …
Numerical Schemes For Integro-Differential Equations Related To Alpha-Stable Processes, Xiaofan Li
Numerical Schemes For Integro-Differential Equations Related To Alpha-Stable Processes, Xiaofan Li
Mathematics Colloquium Series
The mean first exit time, escape probability and transitional probability densities are utilized to quantify dynamical behaviors of stochastic differential equations with non-Gaussian, α-stable type Lévy motions. Taking advantage of the Toeplitz matrix structure of the time-space discretization, a fast and accurate numerical algorithm is proposed to simulate the nonlocal Fokker-Planck equations on either a bounded or infinite domain. Under a specified condition, the scheme is shown to satisfy a discrete maximum principle and to be convergent. The numerical results for two prototypical stochastic systems, the Ornstein-Uhlenbeck system and the double-well system are shown.
From Derivation To Error Analysis Of Splitting Methods—A Contemporary Review, Qin Sheng
From Derivation To Error Analysis Of Splitting Methods—A Contemporary Review, Qin Sheng
Mathematics Colloquium Series
Splitting methods, with representative examples such as ADI (alternating-direction implicit) method and LOD (local one-dimensional) method, have been playing a significant role for the numerical solution of differential equations. In this talk, we will start from a seemed-to-be obvious issue as an introduction of the modern splitting methods. Historical roots of the literature will be mentioned. We will then use a splitting approach for solving a semi-linear Kawarada partial differential equation which is extremely important to numerical combustion, environmental protection, and biomedical research. Finally, the concept of global error and its estimates will be discussed and extended.