Mathematical analysis | Approximation theory

Fekete problem

In mathematics, the Fekete problem is, given a natural number N and a real s ≥ 0, to find the points x1,...,xN on the 2-sphere for which the s-energy, defined by for s > 0 and by for s = 0, is minimal. For s > 0, such points are called s-Fekete points, and for s = 0, logarithmic Fekete points (see ).More generally, one can consider the same problem on the d-dimensional sphere, or on a Riemannian manifold (in which case ||xi −xj|| is replaced with the Riemannian distance between xi and xj). The problem originated in the paper by Michael Fekete who considered the one-dimensional, s = 0 case, answering a question of Issai Schur. An algorithmic version of the Fekete problem is number 7 on the list of problems discussed by . (Wikipedia).

Video thumbnail

Complex Magnitude Equation with Geometric Interpretation

A response to Fematika's video about complex loci.

From playlist Challenge Problems

Video thumbnail

Making ferrofluid from scratch

Back in October, I tried making ferrofluid but I kept failing and I ended up giving up for a while. Months later though, I got inspired, and I spent an insane amount of time researching ferrofluid and trying to make it. It was a very messy and sometimes frustrating process, but I was event

From playlist Long Projects (25 min+)

Video thumbnail

Teach Astronomy - Solutions to the Fermi Paradox

http://www.teachastronomy.com/ The Fermi Paradox starts with the simple question, where are they? It's based on the huge number of potential sites for life and the large amount of time in the history of the universe for intelligent civilizations that can travel in space to have developed.

From playlist 28. Interstellar Travel, SETI, and the Rarity of Life

Video thumbnail

I'm Not THAT Bad At Fermi Problems!

Fermi was a smart cookie, how smart of a cookie is this recent physics graduate at solving Fermi problems? Try for yourself!: http://www.fermiquestions.com/play

From playlist Fun Physics Quizes!

Video thumbnail

Python for Digital Humanities (24: Storing Data - XML Files)

If you enjoy this video, please subscribe. I provide all my content at no cost. If you want to support my channel, please donate via PayPal: https://www.paypal.com/cgi-bin/webscr?cmd=_donations&business=AZ73QW52SUX8N¤cy_code=USD&source=url Patreon: https://www.patreon.com/WJBMatting

From playlist An Introduction to Python for the Digital Humanities

Video thumbnail

The nature of matter

If there’s one thing that we think we understand, it’s matter.  After all, matter makes up everything around us; it even makes up you.  However, all is not as it seems.  Over the last century, scientists have learned about the building blocks of matter, starting with atoms.  It turns out t

From playlist Fermilab Featured Videos

Video thumbnail

Problem #24 Circuit with Five Resistors

Problem #24 Circuit with Five Resistors

From playlist Bi-weekly Physics Problems

Video thumbnail

[BOURBAKI 2018] 20/10/2018 - 2/4 - Romain DUJARDIN

Romain DUJARDIN Théorie globale du pluripotentiel, équidistribution et processus ponctuels, d'après Berman, Boucksom, Witt-Nyström, etc. La théorie du pluripotentiel est un analogue dans Cn de la théorie classique du potentiel dans C, qui prend ses racines dans l’électrostatique. Sa vers

From playlist BOURBAKI - 2018

Video thumbnail

What Does It Mean to Be Intelligent? - with Howard Gardner

Howard Gardner's landmark theory of multiple intelligences called into question the value of the IQ test and the notion that someone's intelligence is dominated by a single, measurable general ability. Howard's memoir 'A Synthesizing Mind' is available now: https://geni.us/qkhl Watch the

From playlist Livestreams

Video thumbnail

The Hunt for New Batteries - with Serena Corr

Serena Corr looks at the science behind batteries, discusses why we are hunting for new ones and investigates what tools we use to pave this pathway to discovery. Watch the Q&A: https://youtu.be/lZjqiR0czLo The hunt is on for the next generation of batteries that will power our electric v

From playlist Livestreams

Video thumbnail

Serfaty Sylvia "In search of the Abrikosov lattice"

Résumé This question is at the interface between mathematical analysis, condensed matter physics, statistical mechanics, and even a little bit of number theory. In superconductors, one observes in certain regimes the emergence of densely packed point vortices forming perfect triangular la

From playlist Colloque Scientifique International Poincaré 100

Video thumbnail

A Series of Fortunate Events – with Sean B. Carroll

Is simple chance the source of all the beauty and diversity we see in the world? Sean B. Carroll tells the story of the awesome power of chance. Sean's book "A Series of Fortunate Events" is available now: https://geni.us/mPPrdQH Watch the Q&A: https://youtu.be/adrqThhSgYg Why is the worl

From playlist Livestreams

Video thumbnail

Where Do New Viruses Come From?

Where do new viruses come from and how do they end up infecting humans? One way this can happen is via zoonosis - when a disease jumps from an animal to a human via a spillover event. Subscribe for regular science videos: http://bit.ly/RiSubscRibe --- A very special thank you to our Patre

From playlist Ri Shorts

Video thumbnail

My TIG Is Breaking Up With Me

My oscilloscope and I pick up on what my TIG welder is laying down. The news doesn't look good.

From playlist All Uploads

Video thumbnail

How Do Pandemics Get Around the World?

Most outbreaks of diseases area localised events but some such as Black Death, chikungunya and the swine flu break the norm and become worldwide pandemics. How do they travel around the world and how do scientists map them? Subscribe for regular science videos: http://bit.ly/RiSubscRibe -

From playlist Ri Shorts

Video thumbnail

Affine and mod-affine varieties in arithmetic geometry. - Charles - Workshop 2 - CEB T2 2019

François Charles (Université Paris-Sud) / 24.06.2019 Affine and mod-affine varieties in arithmetic geometry. We will explain how studying arithmetic versions of affine schemes and their bira- tional modifications leads to a generalization to arbitrary schemes of both Fekete’s theorem on

From playlist 2019 - T2 - Reinventing rational points

Video thumbnail

Quasi-Fermi Levels Explained

https://www.patreon.com/edmundsj If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible. Quasi-Fermi l

From playlist Electronics I: Semiconductor Physics and Devices

Video thumbnail

How Do Our Brains Perceive the World Around Us? - with Anil Seth

How does our brain translate visual signals into a conscious experience? Watch Anil's talk on the same topic: https://youtu.be/qXcH26M7PQM Anil's new book "Being You" is available now: https://geni.us/anil Anil Seth is Professor of Cognitive and Computational Neuroscience at the Universit

From playlist Ri Shorts

Related pages

Issai Schur | Mathematics | Riemannian manifold