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
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.
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).