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Full-Text Articles in Physical Sciences and Mathematics
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 …