When do fractional differential equations have solutions bounded by the Mittag-Leffler function?
When do fractional differential equations have solutions bounded by the Mittag Leffler function? New research into this question! http://www.degruyter.com/view/j/fca.2015.18.issue-3/fca-2015-0039/fca-2015-0039.xml?format=INT Fract. Calc. Appl. Anal. 18, no. 3 (2015), 642-650. DOI: 10.15
From playlist Mathematical analysis and applications
I define one of the most important constants in mathematics, the Euler-Mascheroni constant. It intuitively measures how far off the harmonic series 1 + 1/2 + ... + 1/n is from ln(n). In this video, I show that the constant must exist. It is an open problem to figure out if the constant is
From playlist Series
This lecture is part of an online course on rings and modules. We continue the previous lecture on complete rings by discussing Hensel's lemma for finding roots of polynomials over p-adic rings or over power series rings. We sketch two proofs, by slowly improving a root one digit at a tim
From playlist Rings and modules
The Cotangent's Series Expansion Derivation using FOURIER SERIES [ Mittag-Leffler Theorem ]
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From playlist Fourier Series
Gronwall's inequality & fractional differential equations
Several general versions of Gronwall's inequality are presented and applied to fractional differential equations of arbitrary order. Applications include: yielding a priori bounds and nonumultiplicity of solutions. This presentation features new mathematical research. http://projecteucli
From playlist Mathematical analysis and applications
Lagrange Polynomials for function approximation including simple examples. Chapters 0:00 Intro 0:08 Lagrange Polynomials 0:51 Visualizing L2 1:00 Numeric Example 1:11 Example Visualized 1:27 Why Lagrange Works 1:47 Lagrange Accuracy 2:12 Error 2:59 Error Visualized 3:20 Error Bounds 4:08
From playlist Numerical Methods
Laguerre's method for finding real and complex roots of polynomials. Includes history, derivation, examples, and discussion of the order of convergence as well as visualizations of convergence behavior. Example code available on github https://www.github.com/osveliz/numerical-veliz Chapte
From playlist Root Finding
Banach fixed point theorem & differential equations
A novel application of Banach's fixed point theorem to fractional differential equations of arbitrary order. The idea involves a new metric based on the Mittag-Leffler function. The technique is applied to gain the existence and uniqueness of solutions to initial value problems. http://
From playlist Mathematical analysis and applications
Irreducibility and the Schoenemann-Eisenstein criterion | Famous Math Probs 20b | N J Wildberger
In the context of defining and computing the cyclotomic polynumbers (or polynomials), we consider irreducibility. Gauss's lemma connects irreducibility over the integers to irreducibility over the rational numbers. Then we describe T. Schoenemann's irreducibility criterion, which uses some
From playlist Famous Math Problems
This lecture is part of an online course on rings and modules. We discuss when taking limits of modules preserves exactness. In particular we give the Mittag-Leffler condition that ensures that taking inverse limits of modules preserves exactness. For the other lectures in the course see
From playlist Rings and modules
Hermitian and Non-Hermitian Laplacians and Wave Equaions by Andrey shafarevich
Non-Hermitian Physics - PHHQP XVIII DATE: 04 June 2018 to 13 June 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore Non-Hermitian Physics-"Pseudo-Hermitian Hamiltonians in Quantum Physics (PHHQP) XVIII" is the 18th meeting in the series that is being held over the years in Quantum Phys
From playlist Non-Hermitian Physics - PHHQP XVIII
logarithm of a matrix. I calculate ln of a matrix by finding the eigenvalues and eigenvectors of that matrix and by using diagonalization. It's a very powerful tool that allows us to find exponentials, sin, cos, and powers of a matrix and relates to Fibonacci numbers as well. This is a mus
From playlist Eigenvalues
Sum of Polynomial Coefficients Challenge
Solution on Lemma: https://www.lem.ma/-K (and additional challenges) Tangentially related good read: http://bit.ly/PascalsTri Twitter: https://twitter.com/PavelGrinfeld
From playlist Problems, Paradoxes, and Sophisms
This is the second part of a proof of the Riemann Roch theorem. In it we prove Roch's part of the theorem ("Serre duality") which states that i(D) = l(K-D). We first work over the complex numbers where we can use the residue calculus. This gives two key points: a 1-form has a well defined
From playlist Algebraic geometry: extra topics
This talk is the first of two talks that give a proof of the Riemann Roch theorem, in the spacial case of nonsingular complex plane curves. We divide the Riemann-Roch theorem into 3 pieces: Riemann's theorem, a topological theorem identifying the three definitions of the genus, and Roch'
From playlist Algebraic geometry: extra topics
Commutative algebra 48: Limits and exactness
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We discuss when the limit of exact sequences is exact. We show this happens whenever the "Mittag-Leffler condition" is satisfi
From playlist Commutative algebra
Advice for research maths | The joy of maxel number theory and Gegenbauer polynomials | Wild Egg
We extend our Legendre polynomial maxel approach to the larger more general situation of Gegenbauer polynomials and their maxels. Now these depend on a parameter r, which is directly related to the dimension of the corresponding sphere on which the hypergroup structure gives characters whi
From playlist Maxel inverses and orthogonal polynomials (non-Members)
Lennart Carleson - The Abel Prize interview 2006
0:00 Glimpses of the Abel Prize ceremony made for Norwegian television 05:00 Interview proper starts (Norwegian) 07:46 (English) Almost-everywhere convergence of Fourier series for square-integrable (L^2) functions 10:08 Interesting example of need to have conviction about outcome before c
From playlist The Abel Prize Interviews