Integrals | Summability methods
In mathematics, Hadamard regularization (also called Hadamard finite part or Hadamard's partie finie) is a method of regularizing divergent integrals by dropping some divergent terms and keeping the finite part, introduced by Hadamard . Riesz showed that this can be interpreted as taking the meromorphic continuation of a convergent integral. If the Cauchy principal value integral exists, then it may be differentiated with respect to x to obtain the Hadamard finite part integral as follows: Note that the symbols and are used here to denote Cauchy principal value and Hadamard finite-part integrals respectively. The Hadamard finite part integral above (for a < x < b) may also be given by the following equivalent definitions: The definitions above may be derived by assuming that the function f (t) is differentiable infinitely many times at t = x for a < x < b, that is, by assuming that f (t) can be represented by its Taylor series about t = x. For details, see Ang. (Note that the term − f (x)/2(1/b − x − 1/a − x) in the second equivalent definition above is missing in Ang but this is corrected in the errata sheet of the book.) Integral equations containing Hadamard finite part integrals (with f (t) unknown) are termed hypersingular integral equations. Hypersingular integral equations arise in the formulation of many problems in mechanics, such as in fracture analysis. (Wikipedia).
Ingrid Daubechies - 2/4 Time-Frequency Localization and Applications
Abstract: In this 250th anniversary year of the birth of Joseph Fourier, it behoves us to talk of frequency and spectral analysis! The lectures shall visit a number of different techniques that have been developed and applied in the last 30 years, to carry out what engineers and applied m
From playlist Hadamard Lectures 2018 - Ingrid DAUBECHIES - Time-Frequency Localization and Applications
Ingrid Daubechies - 4/4 Time-Frequency Localization and Applications
Abstract: In this 250th anniversary year of the birth of Joseph Fourier, it behoves us to talk of frequency and spectral analysis! The lectures shall visit a number of different techniques that have been developed and applied in the last 30 years, to carry out what engineers and applied m
From playlist Hadamard Lectures 2018 - Ingrid DAUBECHIES - Time-Frequency Localization and Applications
Ingrid Daubechies - 1/4 Time-Frequency Localization and Applications
Abstract: In this 250th anniversary year of the birth of Joseph Fourier, it behoves us to talk of frequency and spectral analysis! The lectures shall visit a number of different techniques that have been developed and applied in the last 30 years, to carry out what engineers and applied m
From playlist Hadamard Lectures 2018 - Ingrid DAUBECHIES - Time-Frequency Localization and Applications
Database Normalisation: Introduction
This is the first in a series of videos about database normalisation. It defines database normalisation and outlines the benefits of normalising a database. It also includes definitions of the first three normal forms of a relational database. The videos that follow explain the first thr
From playlist Database Normalisation
Ingrid Daubechies - 3/4 Time-Frequency Localization and Applications
Abstract: In this 250th anniversary year of the birth of Joseph Fourier, it behoves us to talk of frequency and spectral analysis! The lectures shall visit a number of different techniques that have been developed and applied in the last 30 years, to carry out what engineers and applied m
From playlist Hadamard Lectures 2018 - Ingrid DAUBECHIES - Time-Frequency Localization and Applications
Christian Bär: Local index theory for Lorentzian manifolds
HYBRID EVENT We prove a local version of the index theorem for Dirac-type operators on globally hyperbolic Lorentzian manifolds with Cauchy boundary. In case the Cauchy hypersurface is compact, we do not assume self-adjointness of the Dirac operator on the spacetime or of the associated el
From playlist Mathematical Physics
Deutsch Jozsa Algorithm - Quantum Computer Programming w/ Qiskit p.3
Exploring our first quantum algorithm, the Deutsch-Jozsa algorithm. Quantum Playlist: Part 1: https://www.youtube.com/watch?v=aPCZcv-5qfA&list=PLQVvvaa0QuDc79w6NcGB0pnoJBgaKdfrW&index=2 Text-based tutorial and sample code: https://pythonprogramming.net/Deutsch-jozsa-hadamard-quantum-comp
From playlist Quantum Computer Programming w/ Qiskit
Klaus Fredenhagen - Quantum Field Theory and Gravitation
The incorporation of gravity into quantum physics is still an essentially open problem. Quantum field theory under the influence of an external gravitational field, on the other side, is by now well understood. I is remarkable that, nevertheless, its consistent treatment required a careful
From playlist Trimestre: Le Monde Quantique - Colloque de clôture
DDPS | Entropy stable schemes for nonlinear conservation laws
High order methods are known to be unstable when applied to nonlinear conservation laws with shocks and turbulence, and traditionally require additional filtering, limiting, or artificial viscosity to avoid solution blow up. Entropy stable schemes address this instability by ensuring that
From playlist Data-driven Physical Simulations (DDPS) Seminar Series
Discrete Structures: Quantum Computing
Learn a little bit about quantum computing. I had to trim out the TED talk that was originally shown in the live stream.
From playlist Discrete Structures
The quantum computers are coming - talk
Many people may not know it, but we live in a time where the first quantum computers have been created - and they're pretty damn cool. Why? Because while regular bits are limited to only two boring values, QBITs can take near infinite values and operate singularly or in harmony with each o
From playlist Talks
Fixed Effects and Random Effects
Brief overview in plain English of the differences between the types of effects. Problems with each model and how to overcome them.
From playlist Experimental Design
Linear regression (6): Regularization
Lp regularization penalties; comparing L2 vs L1
From playlist cs273a
The Normal Distribution (1 of 3: Introductory definition)
More resources available at www.misterwootube.com
From playlist The Normal Distribution
Lec 23 | MIT 6.451 Principles of Digital Communication II
Lattice and Trellis Codes View the complete course: http://ocw.mit.edu/6-451S05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 6.451 Principles of Digital Communication II
C Programming: Quantum Computing
Learn a bit about one of the next waves in computer science: quantum computing. What kinds of problems can it solve more efficiently? We'll discuss some of the basic quantum operations and write a simulator in C.
From playlist C Programming
Random and systematic error explained: from fizzics.org
In scientific experiments and measurement it is almost never possible to be absolutely accurate. We tend to make two types of error, these are either random or systematic. The video uses examples to explain the difference and the first steps you might take to reduce them. Notes to support
From playlist Units of measurement
Qubits and Gates - Quantum Computer Programming w/ Qiskit p.2
Diving deeper into Qubits, what they really are, how to visually represent a qubit, and how quantum gates impact these qubits. Part 1: https://www.youtube.com/watch?v=aPCZcv-5qfA&list=PLQVvvaa0QuDc79w6NcGB0pnoJBgaKdfrW&index=2 Part 3: https://www.youtube.com/watch?v=_BHvE_pwF6E&list=PLQV
From playlist Quantum Computer Programming w/ Qiskit