Conjectures that have been proved | Planar graphs
In mathematics, Scheinerman's conjecture, now a theorem, states that every planar graph is the intersection graph of a set of line segments in the plane. This conjecture was formulated by E. R. Scheinerman in his Ph.D. thesis , following earlier results that every planar graph could be represented as the intersection graph of a set of simple curves in the plane. It was proven by Jeremie Chalopin and Daniel Gonçalves. For instance, the graph G shown below to the left may be represented as the intersection graph of the set of segments shown below to the right. Here, vertices of G are represented by straight line segments and edges of G are represented by intersection points. Scheinerman also conjectured that segments with only three directions would be sufficient to represent 3-colorable graphs, and conjectured that analogously every planar graph could be represented using four directions. If a graph is represented with segments having only k directionsand no two segments belong to the same line, then the graph can be colored using k colors, one color for each direction. Therefore, if every planar graph can be represented in this way with only four directions,then the four color theorem follows. and proved that every bipartite planar graph can be represented as an intersection graph of horizontal and vertical line segments; for this result see also . proved that every triangle-free planar graph can be represented as an intersection graph of line segments having only three directions; this result implies Grötzsch's theorem that triangle-free planar graphs can be colored with three colors. proved that if a planar graph G can be 4-colored in such a way that no separating cycle uses all four colors, then G has a representation as an intersection graph of segments. proved that planar graphs are in 1-STRING, the class of intersection graphs of simple curves in the plane that intersect each other in at most one crossing point per pair. This class is intermediate between the intersection graphs of segments appearing in Scheinerman's conjecture and the intersection graphs of unrestricted simple curves from the result of Ehrlich et al. It can also be viewed as a generalization of the circle packing theorem, which shows the same result when curves are allowed to intersect in a tangent. The proof of the conjecture by was based on an improvement of this result. (Wikipedia).
Dealing with Schrodinger's Equation - The Hamiltonian
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. Schrodinger's
From playlist Quantum Mechanics
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From playlist Quantum Physics
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From playlist Schrödinger's equation
Physics - Ch 66 Ch 4 Quantum Mechanics: Schrodinger Eqn (13 of 92) Time & Position Dependencies 2/3
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From playlist PHYSICS 66.1 QUANTUM MECHANICS - SCHRODINGER EQUATION
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From playlist Mathematical Physics II - Youtube
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We've talked about the quantum state plenty- but what happens to it over time? That's exactly the question the Schrodinger equation solves. This video we talk about 'Linearity'. In the next video we discuss the equation itself and its derivation. Click here fore that: https://youtu.be/DEgW
From playlist Quantum Mechanics (all the videos)
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From playlist Mathematics
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From playlist Schrödinger's equation
Recent developments in non-commutative Iwasawa theory I - David Burns
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From playlist Mathematics
Giles Gardam: Kaplansky's conjectures
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From playlist Global Noncommutative Geometry Seminar (Americas)
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From playlist Talks of Mathematics Münster's reseachers
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From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
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From playlist Mathematics
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Lillian Ratliff - Learning via Conjectural Variations - IPAM at UCLA
Recorded 15 February 2022. Lillian Ratliff of the University of Washington presents "Learning via Conjectural Variations" at IPAM's Mathematics of Collective Intelligence Workshop. Learn more online at: http://www.ipam.ucla.edu/programs/workshops/mathematics-of-intelligences/?tab=schedule
From playlist Workshop: Mathematics of Collective Intelligence - Feb. 15 - 19, 2022.
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From playlist Perfectoid Spaces 2019
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Visit http://ilectureonline.com for more math and science lectures! In this video I will show how to use the Schrodinger's equation, part 2/2. Next video in this series can be seen at: https://youtu.be/kO9JZgVXqyU
From playlist PHYSICS 66.1 QUANTUM MECHANICS - SCHRODINGER EQUATION
Jochen Koenigsmann : Galois codes for arithmetic and geometry via the power of valuation theory
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