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https://nsuworks.nova.edu/mathematics_colloquium/ay_2023-2024/Events
Recent Events in en-usFri, 19 Apr 2024 05:47:41 PDT3600Extensions of Algebraic Frames
https://nsuworks.nova.edu/mathematics_colloquium/ay_2023-2024/Events/10
https://nsuworks.nova.edu/mathematics_colloquium/ay_2023-2024/Events/10Tue, 16 Apr 2024 12:30:00 PDT
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. We will show the relation between these extensions and how they are related to the prime elements of the frames.
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Papiya BhattacharjeeOptimal Control of Coefficients for the Second Order Parabolic Free Boundary Problems
https://nsuworks.nova.edu/mathematics_colloquium/ay_2023-2024/Events/9
https://nsuworks.nova.edu/mathematics_colloquium/ay_2023-2024/Events/9Thu, 11 Apr 2024 12:30:00 PDT
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. Some numerical results will be shared.
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Ali HagverdiyevMajorization Polytopes
https://nsuworks.nova.edu/mathematics_colloquium/ay_2023-2024/Events/8
https://nsuworks.nova.edu/mathematics_colloquium/ay_2023-2024/Events/8Thu, 15 Feb 2024 12:30:00 PST
Given two vectors of real components, we say that one vector (say u) majorizes or dominates the other vector (say v) if the components of u are more spread-out than the components of v. This idea of comparing vectors is used to analyze probability distributions and to formulate optimization problems in real life; and it leads to Majorization theory, a branch of mathematics that has applications in various fields, including inequalities, geometry, combinatorics, optimization, and statistics. A majorization polytope is a convex polytope associated with majorization. The classical Birkhoff polytope is a majorization polytope that consists of doubly stochastic matrices. The Birkhoff theorem states that this polytope is generated by permutation matrices. The concept of Birkhoff polytope has been extended to multi-dimensional arrays (aka hypermatrices or tensors). This talk summarizes the studies of the polytope of line- and plane- stochastic tensors. This is a joint work with Xiao-Dong Zhang.
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Fuzhen ZhangThe Heisenberg Lie Algebra and its role in the Quantum Mechanical Harmonic Oscillator
https://nsuworks.nova.edu/mathematics_colloquium/ay_2023-2024/Events/7
https://nsuworks.nova.edu/mathematics_colloquium/ay_2023-2024/Events/7Wed, 29 Nov 2023 12:00:00 PSTAngelina GeorgIrreducible representations of sl(2,C)
https://nsuworks.nova.edu/mathematics_colloquium/ay_2023-2024/Events/6
https://nsuworks.nova.edu/mathematics_colloquium/ay_2023-2024/Events/6Wed, 29 Nov 2023 12:00:00 PSTDella MedovoyLie Algebras and Lie Groups
https://nsuworks.nova.edu/mathematics_colloquium/ay_2023-2024/Events/5
https://nsuworks.nova.edu/mathematics_colloquium/ay_2023-2024/Events/5Wed, 29 Nov 2023 12:00:00 PSTNhi Nguyen1324-Avoiding (0,1)-Matrices
https://nsuworks.nova.edu/mathematics_colloquium/ay_2023-2024/Events/4
https://nsuworks.nova.edu/mathematics_colloquium/ay_2023-2024/Events/4Tue, 28 Nov 2023 12:30:00 PST
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 have found 1324-avoiding matrices that contain more 1’s than those that are 1234-avoiding, and we provide a conjecture for the maximum number of 1’s that a 1324-avoiding matrix can contain.
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Megan BennettEigenvalue and Singular Value Inequalities via Extreme Principles
https://nsuworks.nova.edu/mathematics_colloquium/ay_2023-2024/Events/3
https://nsuworks.nova.edu/mathematics_colloquium/ay_2023-2024/Events/3Thu, 02 Nov 2023 12:30:00 PDT
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.
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Fuzhen ZhangIN EULER’S FOOTSTEPS: THE ENDURING APPEAL OF SPECIAL FUNCTIONS AND SPECIAL PROBLEMS
https://nsuworks.nova.edu/mathematics_colloquium/ay_2023-2024/Events/2
https://nsuworks.nova.edu/mathematics_colloquium/ay_2023-2024/Events/2Thu, 26 Oct 2023 12:30:00 PDT
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 numerical series involving zeta values. An integral representation for ζ(2) similar to the one given by Margrethe Munthe Hjortnaes in 1953 for ζ(3) is also obtained, as well as a one-line solution to the Basel problem famously settled by Euler in 1734.
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Lubomir MarkovExcursions in Vector Calculus
https://nsuworks.nova.edu/mathematics_colloquium/ay_2023-2024/Events/1
https://nsuworks.nova.edu/mathematics_colloquium/ay_2023-2024/Events/1Thu, 28 Sep 2023 12:30:00 PDT
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.
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Diego Castano