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Articles 1 - 16 of 16
Full-Text Articles in Entire DC Network
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
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
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.
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
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
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
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
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
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.