Numerical analysis | Numerical differential equations
In numerical mathematics, the boundary knot method (BKM) is proposed as an alternative boundary-type meshfree distance function collocation scheme. Recent decades have witnessed a research boom on the meshfree numerical PDE techniques since the construction of a mesh in the standard finite element method and boundary element method is not trivial especially for moving boundary, and higher-dimensional problems. The boundary knot method is different from the other methods based on the , such as boundary element method, method of fundamental solutions and singular boundary method in that the former does not require special techniques to cure the singularity. The BKM is truly meshfree, spectral convergent (numerical observations), symmetric (self-adjoint PDEs), integration-free, and easy to learn and implement. The method has successfully been tested to the Helmholtz, diffusion, convection-diffusion, and Possion equations with very irregular 2D and 3D domains. (Wikipedia).
This step by step guide demonstrates tying 15 types: 00:36 Overhand 01:22 Square 02:36 Figure Eight 03:40 Bowline, 05:29 Running 06:19 Half, 07:45 Timber, 09:42 Rolling, 10:43 Clove Hitches 11:30 Cat's Paw 12:58 Single, 14:40 Double Sheet or Becket Bends 15:30 Fisherman's, 17:09 Doubl
From playlist How To Tutorials
This knot is very useful for adjusting tie downs quickly and easily. For example, a tarp could be held down by a series of these knots and be made very tight so the wind cannot make it rise, and easily be removed simply by sliding the knots later. A taut line knot is also used to keep larg
From playlist Practical Projects & Skills
Knots and surfaces II | Algebraic Topology | NJ Wildberger
In the 1930's H. Siefert showed that any knot can be viewed as the boundary of an orientable surface with boundary, and gave a relatively simple procedure for explicitly constructing such `Seifert surfaces'. We show the algorithm, exhibit it for the trefoil and the square knot, and then di
From playlist Algebraic Topology
I saw that one day on Korean TV. With little practice, it takes about half the time than the normal method. Actually, I'm rather slow on this video. I can do it in around 7 seconds.
From playlist Other...
Gluing is a good method to construct new topological spaces from known ones. Here a rectangles is glued along the edges to form a torus. Often the fundamental group of the glued object can be calculated from the pieces (here a rectangles) and the glue (here two intersecting circles). Th
From playlist Algebraic Topology
How to Tie the Most Useful Knot in the World (Bowline)
This is a short video to help those who have seen many of my past videos where I use a bowline knot. This is the most useful knot you will ever learn. It will not slip when in use, and comes undone easily even after being tightened under thousands of pounds. #NightHawkInLight -~-~~-~~~-~~
From playlist Practical Projects & Skills
Make A Combination Lock - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Untangling the beautiful math of KNOTS
Visit ► https://brilliant.org/TreforBazett/ to help you learn STEM topics for free, and the first 200 people will get 20% off an annual premium subscription. Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://www.beautifulequation.com/pages/trefor Suppose yo
From playlist Cool Math Series
Link: https://www.geogebra.org/m/a72HSgzU
From playlist Geometry: Challenge Problems
Knotty Problems - Marc Lackenby
Knots are a familiar part of everyday life, for example tying your tie or doing up your shoe laces. They play a role in numerous physical and biological phenomena, such as the untangling of DNA when it replicates. However, knot theory is also a well-developed branch of pure mathematics.
From playlist Oxford Mathematics Public Lectures
Joel Hass - Lecture 1 - Algorithms and complexity in the theory of knots and manifolds - 18/06/18
School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects (http://geomschool2018.univ-mlv.fr/) Joel Hass (University of California at Davis, USA) Algorithms and complexity in the theory of knots and manifolds Abstract: These lectures will introduce algorithmic pro
From playlist Joel Hass - School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects
Marc Lackenby - Using machine learning to formulate mathematical conjectures - IPAM at UCLA
Recorded 14 February 2023. Marc Lackenby of the University of Oxford presents "Using machine learning to formulate mathematical conjectures" at IPAM's Machine Assisted Proofs Workshop. Abstract: I will describe how machine learning can be used as a tool for pure mathematicians to formulate
From playlist 2023 Machine Assisted Proofs Workshop
Kai Smith: Character Varieties of Tangles and Singular Instanton Homology
Kai Smith, Indiana University Title: Character Varieties of Tangles and Singular Instanton Homology Singular Instanton Homology ($I^\natural$) is a knot homology theory defined by Kronheimer and Mrowka which has been instrumental in proving fundamental facts about Khovanov homology. Unfort
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Ed Witten -- From Gauge Theory to Khovanov Homology Via Floer Theory
Edward Witten lecture entitled "From Gauge Theory to Khovanov Homology Via Floer Theory" as part of the Banff International Research Station conference "Perspectives on Knot Homology". The Banff International Research Station will host the "Perspectives on Knot Homology" workshop in Banf
From playlist Research Lectures
Jessica Purcell - Lecture 3 - Knots in infinite volume 3-manifolds
Jessica Purcell, Monash University Title: Knots in infinite volume 3-manifolds Classically, knots have been studied in the 3-sphere. However, many examples of knots arising in applications lie in broader classes of 3-manifolds. These include virtual knots, which lie within thickened surfa
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Knot contact homology and partially wrapped Floer homology - Lenhard Ng
Workshop on Homological Mirror Symmetry: Methods and Structures Speaker:Lenhard Ng Title: Knot contact homology and partially wrapped Floer homology Affilation: Duke Date: November 7, 2016 For more vide, visit http://video.ias.edu
From playlist Workshop on Homological Mirror Symmetry: Methods and Structures
Algebraic topology: Fundamental group of a knot
This lecture is part of an online course on algebraic topology. We calculate the fundamental group of (the complement of) a knot, and give a couple of examples. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52yxQGxQoxwOtjIEtxE2BWx
From playlist Algebraic topology
The Computational Complexity of Geometric Topology Problems - Greg Kuperberg
Greg Kuperberg University of California, Davis September 24, 2012 This talk will be a partial survey of the first questions in the complexity theory of geometric topology problems. What is the complexity, or what are known complexity bounds, for distinguishing n-manifolds for various n? Fo
From playlist Mathematics
Differential Equations: Separation of Variables
This video provides several examples of how to solve a DE using the technique of separation of variables. website: http://mathispower4u.com blog: http://mathispower4u.wordpress.com
From playlist First Order Differential Equations: Separation of Variables
Results on abundance of global surfaces of section - Umberto Hryniewicz
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Results on abundance of global surfaces of section Umberto Hryniewicz Date: October 15, 2021
From playlist Mathematics