Physical Sciences and Mathematics Commons^™

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

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

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. …

A Survey On Varieties Generated By Small Semigroups And A Companion Website, João Araújo, João Pedro Araújo, Peter J. Cameron, Edmond W. H. Lee, Jorge Raminhos

Mathematics Faculty Articles

This paper presents new findings on varieties generated by small semigroups and groups, and offers a survey of existing results. A companion website is provided which hosts a computational system integrating automated reasoning tools, finite model builders, SAT solvers, and GAP. This platform is a living guide to the literature. In addition, the first complete and justified list of identity bases for all varieties generated by a semigroup of order up to 4 is provided as supplementary material. The paper concludes with an extensive list of open problems.

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

Algebra Seminar

No abstract provided.

Lie Algebras And Lie Groups, Nhi Nguyen

Mathematics Colloquium Series

No abstract provided.

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

Mathematics Colloquium Series

No abstract provided.

Lie Algebras And Lie Groups, Nhi Nguyen

Algebra Seminar

No abstract provided.

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

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

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

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.

Propuesta De Un Modelo De Enseñanza En Las Matemáticas Enfocado En La Solución De Problemas En El Nivel Secundario En Puerto Rico, Carlos J. Colon Rivera

Theses and Dissertations

El propósito del estudio fue proponer un modelo educativo enfocado en la solución de problemas matemáticos en el nivel secundario, y se realizó la revisión sistemática para evaluarlo. El marco teórico incluyó teorías heurísticas y modelos educativos. La metodología de seis fases que se empleó en este estudio, incluyendo la formulación de preguntas investigativas, búsqueda de literatura, selección de investigaciones, levantamiento de información, análisis y resumen de resultados y exposición y discusión de estos. Se siguieron guías para revisiones sistemáticas y criterios de inclusión y exclusión para evaluar la efectividad de modelos didácticos en la disciplina de matemáticas con énfasis …

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).

Linking Mathematical Models And Trap Data To Infer The Proliferation, Abundance, And Control Of Aedes Aegypti, Jing Chen, Xi Huo, Andre B. B. Wilke, John C. Beier, Chalmers Vasquez, William Petrie, Robert Stephen Cantrell, Chris Cosner, Shigui Ruan

Mathematics Faculty Articles

Aedes aegypti is one of the most dominant mosquito species in the urban areas of Miami-Dade County, Florida, and is responsible for the local arbovirus transmissions. Since August 2016, mosquito traps have been placed throughout the county to improve surveillance and guide mosquito control and arbovirus outbreak response. In this paper, we develop a deterministic mosquito population model, estimate model parameters by using local entomological and temperature data, and use the model to calibrate the mosquito trap data from 2017 to 2019. We further use the model to compare the Ae. aegypti population and evaluate the impact of rainfall intensity …

A Permanent Inequality For Positive Semidefinite Matrices, Vehbi Emrah Paksoy

Mathematics Faculty Articles

In this paper, we prove an inequality involving the permanent of a positive semidefinite matrix and its leading submatrices. We obtain a result in the similar spirit of Bapat-Sunder per-max conjecture.

123-Forcing Matrices, Richard A. Brualdi, Lei Cao

Mathematics Faculty Articles

A permutation σ of {1, 2,...,n} contains a 123-pattern provided it contains an increasing subsequence of length 3 and, otherwise, is 123-avoiding. In terms of the n × n permutation matrix P corresponding to σ, P contains a 123-pattern provided the 3 × 3 identity matrix I3 is a submatrix of P. If A is an n × n (0, 1)-matrix, then A is 123-forcing provided every permutation matrix P ≤ A contains a 123-pattern. The main purpose of this paper is to characterize such matrices A with the minimum number of 0’s.

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

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

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

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

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

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

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

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.

Effectiveness And Safety Of Tranexamic Acid Use In Acute Traumatic Injury In The Prehospital And In-Hospital Settings: A Systematic Review And Meta-Analysis Of Randomized Controlled Trials, Scott Rowe, Amy Liu, Israel Zagales, Muhammad Awan, Radleigh Santos, Mark Mckenney, Adel Elkbuli

Mathematics Faculty Articles

Background and Objectives:

This systematic review and meta-analysis of randomized controlled trials (RCTs) aims to assess efficacy and safety of tranexamic acid (TXA) use in acute traumatic injuries.

Methods:

PubMed and Cochrane libraries were searched for relevant RCTs published between January 2011 and January 3, 2021. Cohen’s Q Test for heterogeneous effects was used to determine the appropriateness of fixed versus random effects models.

Results:

Twenty-two studies met inclusion criteria. Meta-analysis of relative risk of mortality between treatment and placebo groups in the in-hospital, and perioperative settings was not significant. However, the risk of mortality is significantly lower in the …

An Upper Bound On The Spectral P-Norms Of Tensors And Matrix Permanent, Killian J. Hitsman, Vehbi E. Paksoy

Mako: NSU Undergraduate Student Journal

No abstract provided.

Inhibition Of Aminoglycoside 6’-N-Acetyltransferase Type Ib [Aac(6′)-Ib]: Structure-Activity Relationship Of Substituted Pyrrolidine Pentamine Derivatives As Inhibitors, Kenneth Rocha, Jesus Magallon, Craig Reeves, Kimberly Phan, Peter Vu, Crista L. Oakley-Havens, Stella Kwan, Maria S. Ramirez, Travis Lavoi, Haley Donow, Prem Chapagain, Radleigh Santos, Clemencia Pinilla, Marc A. Giulianotti, Marcelo E. Tolmasky

Mathematics Faculty Articles

The aminoglycoside 6′-N-acetyltransferase type Ib [AAC(6′)-Ib] is a common cause of resistance to amikacin and other aminoglycosides in Gram-negatives. Utilization of mixture-based combinatorial libraries and application of the positional scanning strategy identified an inhibitor of AAC(6′)-Ib. This inhibitor’s chemical structure consists of a pyrrolidine pentamine scaffold substituted at four locations (R1, R3, R4, and R5). The substituents are two S-phenyl (R1 and R4), an S-hydroxymethyl (R3), and a 3-phenylbutyl (R5) groups. Another location, R2, does not have a substitution, but it is named because its stereochemistry was modified in some compounds utilized in this study. Structure-activity …