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Articles 1 - 30 of 72
Full-Text Articles in Physical Sciences and Mathematics
Extensions Of Algebraic Frames, Papiya Bhattacharjee
Extensions Of Algebraic Frames, Papiya Bhattacharjee
Mathematics Colloquium Series
A frame is a complete lattice that satisfies a strong distributive law, known as the frame law. Frames are also known as Pointfree Topology, as every topology is a frame. Even though the concept of frames originated from topology, the idea has expanded to many other areas of mathematics and frames are now studied in their own merit. Given two frame L and M, we say M is an extension of L if L is a subframe of M. In this talk we will discuss different types of frames extensions, such as Rigid extension, r-extension, and r*-extension between two frames. …
Extensions Of Algebraic Frames, Papiya Bhattacharjee
Extensions Of Algebraic Frames, Papiya Bhattacharjee
Algebra Seminar
A frame is a complete lattice that satisfies a strong distributive law, known as the frame law. Frames are also known as Pointfree Topology, as every topology is a frame. Even though the concept of frames originated from topology, the idea has expanded to many other areas of mathematics and frames are now studied in their own merit. Given two frame L and M, we say M is an extension of L if L is a subframe of M. In this talk we will discuss different types of frames extensions, such as Rigid extension, r-extension, and r*-extension between two frames. …
Optimal Control Of Coefficients For The Second Order Parabolic Free Boundary Problems, Ali Hagverdiyev
Optimal Control Of Coefficients For The Second Order Parabolic Free Boundary Problems, Ali Hagverdiyev
Mathematics Colloquium Series
In this talk I will discuss Inverse Stefan type free boundary problem for the second order parabolic equation arising for instance, in modeling of laser ablation of biomedical tissues, where the information on the coefficients, heat flux on the fixed boundary, and density of heat sources are missing and must be found along with the temperature and free boundary. New PDE constrained optimal control framework is employed, where the missing data and the free boundary are components of the control vector, and optimality criteria are based on the final moment measurement of the temperature and position of the free boundary. …
The Heisenberg Lie Algebra And Its Role In The Quantum Mechanical Harmonic Oscillator, Angelina Georg
The Heisenberg Lie Algebra And Its Role In The Quantum Mechanical Harmonic Oscillator, Angelina Georg
Algebra Seminar
No abstract provided.
Irreducible Representations Of Sl(2,C), Della Medovoy
Irreducible Representations Of Sl(2,C), Della Medovoy
Algebra Seminar
No abstract provided.
Lie Algebras And Lie Groups, Nhi Nguyen
Lie Algebras And Lie Groups, Nhi Nguyen
Mathematics Colloquium Series
No abstract provided.
Irreducible Representations Of Sl(2,C), Della Medovoy
Irreducible Representations Of Sl(2,C), Della Medovoy
Mathematics Colloquium Series
No abstract provided.
The Heisenberg Lie Algebra And Its Role In The Quantum Mechanical Harmonic Oscillator, Angelina Georg
The Heisenberg Lie Algebra And Its Role In The Quantum Mechanical Harmonic Oscillator, Angelina Georg
Mathematics Colloquium Series
No abstract provided.
Lie Algebras And Lie Groups, Nhi Nguyen
1324-Avoiding (0,1)-Matrices, Megan Bennett
1324-Avoiding (0,1)-Matrices, Megan Bennett
Mathematics Colloquium Series
A 1324-avoiding (0,1)-matrix is an 𝑚×𝑛 matrix that does not contain the 1324-pattern. Our goal is to find the maximum number of 1’s that an 𝑚 × 𝑛 1324-avoiding (0,1)-matrix can contain. We build upon Brualdi and Cao’s recent work, where they characterized the 𝑚 × 𝑛 1234-avoiding matrices with the maximum number of 1’s. They found that these matrices can contain up to 3(𝑚 + 𝑛 − 3) 1’s. We originally conjectured that 1324-avoiding matrices must contain at most the same number of 1’s, as is the case with the six patterns formed by permutations of {1,2,3}. However, we …
Eigenvalue And Singular Value Inequalities Via Extreme Principles, Fuzhen Zhang
Eigenvalue And Singular Value Inequalities Via Extreme Principles, Fuzhen Zhang
Mathematics Colloquium Series
Given two square matrices of the same order, we consider the eigenvalues and singular values of the sum and product of the matrices. For example, what can be said about the sum of the largest and smallest eigenvalues of the product of two positive semidefinite matrices? This talk reviews some eigenvalue and singular value inequalities recently obtained via minimax principles. In particular, we present singular value inequalities of log-majorization type.
In Euler’S Footsteps: The Enduring Appeal Of Special Functions And Special Problems, Lubomir Markov
In Euler’S Footsteps: The Enduring Appeal Of Special Functions And Special Problems, Lubomir Markov
Mathematics Colloquium Series
We denote the Euler-Riemann zeta function by ζ(x) and the dilogarithm by (x). The question of determining the exact value of ζ(2) (known as the Basel Problem), the one of obtaining as much information as possible about ζ(3), and a host of other related problems have been of unwavering interest for over 300 years. Several other special functions arise from the consideration of series similar to (x). Two of them are Ramanujan's inverse tangent integral and Legendre's chi-function . In our talk we shall derive the power series expansion for the function and use it to obtain several rapidly convergent …
Excursions In Vector Calculus, Diego Castano
Excursions In Vector Calculus, Diego Castano
Mathematics Colloquium Series
Vector calculus is an invaluable tool in much of physics – electromagnetism is a prime example. The use of vector calculus is highlighted in an exploration of the concept of inductance and a reconsideration of its calculation. A form of the standard equation for inductance that is more versatile is derived and applied in some examples.
Mean Value Theorems For Analytic Functions, Lubomir Markov
Mean Value Theorems For Analytic Functions, Lubomir Markov
Mathematics Colloquium Series
Questions related to the location of zeros and critical points of classes of functions (polynomial, entire, analytic in a certain domain, etc.) are fundamentally important in Analysis. In this talk, he will examine some interesting mean value theorems concerning real and complex analytic functions, focusing on the complex case. He will also present sharper versions of two known results. Part of the presentation will pay tribute to the remarkable contributions of several classical Bulgarian mathematicians to problems involving the distribution of zeros of a function and its derivative(s).
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.
Seizure Prediction In Epilepsy Patients, Gary Dean Cravens
Seizure Prediction In Epilepsy Patients, Gary Dean Cravens
NSU REACH and IPE Day
Purpose/Objective: Characterize rigorously the preictal period in epilepsy patients to improve the development of seizure prediction techniques. Background/Rationale: 30% of epilepsy patients are not well-controlled on medications and would benefit immensely from reliable seizure prediction. Methods/Methodology: Computational model consisting of in-silico Hodgkin-Huxley neurons arranged in a small-world topology using the Watts-Strogatz algorithm is used to generate synthetic electrocorticographic (ECoG) signals. ECoG data from 18 epilepsy patients is used to validate the model. Unsupervised machine learning is used with both patient and synthetic data to identify potential electrophysiologic biomarkers of the preictal period. Results/Findings: The model has shown states corresponding to …
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.
Classic/Quantum Harmonic Oscillator, Killian J. Hitsman
Classic/Quantum Harmonic Oscillator, Killian J. Hitsman
Mathematics Colloquium Series
A Harmonic Oscillator is an integral part of periodic motion in Classical and Quantum Theory. For systems with small fluctuations near stable points of equilibrium, the Harmonic Oscillator serves as a good approximation for measuring eigenstates and wave amplitudes of the particle(s). Aside from the classical version, this presentation will include the Lie Algebra of commutation relations as well as the ladder operators (Discrete and Continuous) as it pertains to a Quantum Harmonic Oscillator. After that, one of its' contributions to scalar fields in Quantum Field Theory, namely the Casimir Force, will be discussed. Whether it is a system of …
Quaternions And Matrices Of Quaternions, Fuzhen Zhang
Quaternions And Matrices Of Quaternions, Fuzhen Zhang
Mathematics Colloquium Series
Quaternions comprise a noncommutative division algebra (skew field). As part of contemporary mathematics, they find uses not only in theoretical and applied mathematics but also in computer graphics, control theory, signal processing, physics, and mechanics. Speaker, N S U Professor, Fuzhen Zhang reviews basic theory on quaternions and matrices of quaternions, presents important results, proposes open questions, and surveys recent developments in the area.
World Statistics Day: Malaria And Its Effects On The World: A Statistical Look, Aysha Nuhuman, Pola Naguib
World Statistics Day: Malaria And Its Effects On The World: A Statistical Look, Aysha Nuhuman, Pola Naguib
Mathematics Colloquium Series
As October 20, 2020 is designated United Nations World Statistics Day, we look at an important statistical problem using a data set collected by researchers from the United Nations. We have all heard about Malaria and seen the effects it could have on friends and family. Still, while we ponder on the who and why this could have occurred, we are here to tell you about the what and how. The severity of this disease can be seen throughout the world. In this presentation, we will look at the number of reported cases of Malaria worldwide and how they affected …
Tensor Eigenvalue Problems And Modern Medical Imaging, Vehbi Emrah Paksoy
Tensor Eigenvalue Problems And Modern Medical Imaging, Vehbi Emrah Paksoy
Mathematics Colloquium Series
Tensors (or hypermatrices) are multidimensional generalization of matrices. Although historically they are studied from the perspective of combinatorics and (hyper)graph theory, recent progress in the subject shows how useful they are in more applied sciences such as physics and medicine. In this presentation, I introduce a few tensor eigenvalue problems and their application to higher order diffusion tensor imaging such as diffusion-weighted magnetic resonance imaging (DW-MRI) and higher angular resolution diffusion imaging (HARDI).
Soccer Tournament Matrices, Lei Cao
Soccer Tournament Matrices, Lei Cao
Mathematics Colloquium Series
In this talk, I will present a combinatorial object, soccer tournament matrices, which is understandable to undergraduate students and gives a taste of combinatorial matrix theory. Consider a round-robin tournament of n teams in which each team plays every other team exactly once and where ties are allowed. A team scores 3 points for a win, 1 point for a tie, and 0 point for a loss, then each particular result leads to a soccer tournament matrix. Let T(R, 3) denote the class of all soccer tournament matrices with the row sum vector R. In this talk, I will explore …
How Good Are Standard Copulas Anyway?, Dragan Radulovic
How Good Are Standard Copulas Anyway?, Dragan Radulovic
Mathematics Colloquium Series
First, we will raise a question: How good are standard copulas in capturing the dependency structure? To this end we will offer a series of simulated/numerical examples demonstrating that, more often than not, standard model copulas do not capture the underlying dependency structure. We believe that copula models, unlike other statistical tools, are too readily accepted by practitioners. Rigorous, goodness-of-fit tests are commonly replaced by off-hand statements like: “it works well”. To this end, the second part of the talk offers a theoretical result, an umbrella type theorem tailored for creating numerous Goodness of Fit tests for copulas.
Algebraic Frames And Ultrafilters, Papiya Bhattacharjee
Algebraic Frames And Ultrafilters, Papiya Bhattacharjee
Mathematics Colloquium Series
A frame, also known as pointfree topology, is a complete lattice that satisfies a strong distributive property, known as the 'frame law.' Originally, the study of frames began as studying topological spaces without points, hence the name pointfree topology. Due to this connection, different topological concepts can be generalized to frames, for example, compactness. In the first part of the talk, I will explain the basic notions of frames and their connection with topology. It turns out that we can find frame structure in other categories than topological spaces. For example, given a commutative ring R with identity, the lattice …