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Simply Science
France
Приєднався 21 жов 2022
A channel dedicated to simple explanations of basic science. Mathematics and physics are made accessible to the layman, the beginning apprentice or the eternal student. If you have suggestions for topics, feel free to pass them on, e.g. in the comments sections.
The Symmetric Group Algebra
We introduce the group algebra for the symmetric group that permutes the elements of a finite set. In the group algebra, we identify the center. We compute a few example structure constants for the multiplication in the center of the symmetric group algebra and indicate a few general questions about the structure constants that have occupied mathematicians for decades.
Переглядів: 10
Відео
Quelles Fractions Sont Décimales ?
Переглядів 2419 годин тому
Quelles fractions sont des nombres décimales et lesquelles ne le sont pas ? On répond à cette question en généralité et on vérifie notre compréhension à l'aide d'exemples.
Co-adjoint Orbit Quantisation : SU(2) Part 2
Переглядів 48Місяць тому
In this second part on orbit quantisation we discuss the path integral quantisation of a particle that sits still on a co-adjoint orbit of the SU(2) group. The particle lives on a sphere and we can perform the path integral calculation of the character of the corresponding SU(2) representation explicitly.
La Valeur Absolue et la Composition de Fonctions
Переглядів 23Місяць тому
Nous définissons la valeur absolue comme une fonction composée. On contraste une fonction composée, toujours bien définie, avec le problème de définir une fonction inverse, par exemple pour le carré.
La Racine, le Carré et leurs Graphs
Переглядів 691Місяць тому
On discute comment lier le graphique pour le carré avec celui de la racine. On apprend le concept de fonction inverse et comment trouver son graph à partir du graph de la fonction.
Une Racine est un Nombre Irrationnel
Переглядів 703 місяці тому
On démontre que la racine d'un nombre entier qui n'est pas un carré (d'un nombre entier) est irrationnelle. La preuve par contradiction est élementaire et courte. Elle utilise une compréhension de la factorisation des nombres entiers en nombres premiers.
Les Valeurs Interdites
Переглядів 813 місяці тому
Nous rappelons la définition de fonction et comment elle est essentielle pour comprendre les valeurs interdites. Puis, on fait des exercises standards et un exercice piège pour bien tester notre compréhension.
Inégalités: Comprendre les Règles de Calcul
Переглядів 866 місяців тому
On raisonne pour comprendre les règles de calcul pour les inégalités ou les inéquations.
Puissances: Comprendre les Règles de Calcul
Переглядів 367 місяців тому
On définit les puissances d'un nombre. A partir de la définition, nous dérivons simplement les règles de calcul qui deviennent facile à retenir.
The Wallpaper Groups
Переглядів 737 місяців тому
We discuss all the possible symmetries of wallpaper patterns. The classifications is based on the possible crystallographic lattices and their extra discrete symmetries. We discuss the seventeen groups using illustrative examples. Errata: the centred rectangular example should be properly glide reflected and the point groups could also be of the type Z3, Z4 or Z6.
The Crystallographic Lattices
Переглядів 137 місяців тому
We discuss the possible shapes of two-dimensional crystallographic lattices and render the classification comprehensible through the analysis of vector length inequalities. This is a preparation for understanding the crystallographic groups in two dimensions, namely, the wallpaper groups.
The Crystallographic Angles
Переглядів 447 місяців тому
We review a crystallographic restriction theorem which determines the orders of possible rotation symmetries that are members of the point group of a crystallographic symmetry group of a pattern in space. The theorem is elementary yet of crucial importance in crystallography.
Frieze Groups
Переглядів 778 місяців тому
We discuss the seven symmetry groups of friezes. These are simple examples of crystallographic groups. They are the symmetries of a pattern in two-dimensional space with a one-dimensional translation subgroup. We list all seven groups, draw patterns with these symmetries and explain why the seven groups suffice.
One-dimensional Crystallography
Переглядів 78 місяців тому
We discuss the space groups or crystallographic groups in one dimension. These are the symmetry patterns of one-dimensional crystals. It is a very much simplified version of the classification of crystallographic groups in three-dimensional euclidean space. We go through the classification of the groups as well as the patterns of which they are. the symmetries. In one dimension, the whole proce...
Euler's Totient Function and Möbius Inversion
Переглядів 768 місяців тому
We discuss properties of the Euler's totient function and how it interfaces with Dirichlet convolution and the Möbius function. The totient function equals the convolution of the identical function with the Möbius function, as proven by Gauss.
Dirichlet Convolution and Möbius Inversion
Переглядів 828 місяців тому
Dirichlet Convolution and Möbius Inversion
The Jordan-Hölder Theorem for Finite Groups
Переглядів 599 місяців тому
The Jordan-Hölder Theorem for Finite Groups
The Third Isomorpism Theorem for Groups
Переглядів 89 місяців тому
The Third Isomorpism Theorem for Groups
Le Coefficient Directeur, la Tangente et un Exercice
Переглядів 459 місяців тому
Le Coefficient Directeur, la Tangente et un Exercice
The Second Isomorphism Theorem for Groups
Переглядів 1299 місяців тому
The Second Isomorphism Theorem for Groups
The First Isomorphism Theorem for Groups
Переглядів 1710 місяців тому
The First Isomorphism Theorem for Groups
The Hom and Ext Functors in the BGG Category O
Переглядів 2410 місяців тому
The Hom and Ext Functors in the BGG Category O
The First Structural Properties of the BGG Category O
Переглядів 2111 місяців тому
The First Structural Properties of the BGG Category O
Résoudre une Équation Quadratique par Symétrie
Переглядів 2011 місяців тому
Résoudre une Équation Quadratique par Symétrie
Center, Characters and Linked Weights
Переглядів 2711 місяців тому
Center, Characters and Linked Weights
Fonctions Affines et Géometrie Eucildienne
Переглядів 1811 місяців тому
Fonctions Affines et Géometrie Eucildienne
Finite Dimensional and Verma Modules of sl(2,C)
Переглядів 8111 місяців тому
Finite Dimensional and Verma Modules of sl(2,C)
Thanks ❤❤❤
Converse: If there exist integers x and y such that ax + by = 1 then gcd(a,b) = 1 Prf: Let d = gcd(a,b) If 1 = bx + ay then 1 = d( b/d)x + d ( a/d)y or 1 = d( xb/d + ay/d) The quantity in brackets is an integer for b/d and a/d are integer; this tells us that d|1 or d=1 so that gcd(a,b) = 1
At 5:38, do you mean lambda is not smaller than mu?
Yes, thanks for the specification. See also Humphrey's book on Representations of Semisimple Lie algebras, subsection 3.1. The stronger condition is implied by the other assumptions though.
Morbius function: One of the functions of all time
Prof des grands maths
Can you provide a good reference for this
Unfortunately, there is no good reference for the exact content of the video. There are some standard references on the topic, including Alekseev, Faddeev and Shatashvili, ``Quantization of symplectic orbits of compact Lie groups by means of the functional integral,'' J. Geom. Phys. 5 (1988), 391-406 doi:10.1016/0393-0440(88)90031-9 and the book on the orbit method by Kirillov. These will neither contain this exact explanation nor are they strictly speaking the original references. Moreover, my point of view is slightly different. But, these are good entry points for further literature searches.
@@Simply_Science Also do you know of a good reference for phase space quantization ( don't confuse it for Dirac quantization ) ?
@@Slayer-bh7yd Good keywords to look for are Geometric Quantization (e.g. the book by Woodhouse) and Symplectic Quantization (e.g. references by Weinstein).
Any good reference for this
www.physics.rutgers.edu/~gmoore/695Fall2015/TopologicalFieldTheory.pdf by Greg Moore, or the book by Koch might be useful starting points depending on your background.
@@Simply_Science Thanks
Merci pour cette explication❤
Merci beaucoup pour cette explication❤
Black holes are based on a mathematical misconception. Most people don't know that Einstein said that singularities are not possible. In the 1939 journal "Annals of Mathematics" he wrote- "The essential result of this investigation is a clear understanding as to why the Schwarzchild singularities (Schwarzchild was the first to raise the issue of General Relativity predicting singularities) do not exist in physical reality. Although the theory given here treats only clusters (star clusters) whose particles move along circular paths it does seem to be subject to reasonable doubt that more general cases will have analogous results. The Schwarzchild singularities do not appear for the reason that matter cannot be concentrated arbitrarily. And this is due to the fact that otherwise the constituting particles would reach the velocity of light." He was referring to the phenomenon of dilation (sometimes called gamma or y) mass that is dilated is smeared through spacetime relative to an outside observer. "Time dilation" is one aspect of dilation. General Relativity does not predict singularities when you factor in dilation. What we see in modern astronomy has been known since 1925. This is when the existence of galaxies was confirmed. It was clear that there should be an astronomical quantity of light emanating from our own galactic center, but there isn't. The modern explanation for this is because gravitational forces there are so strong that not even light can escape, even though the mass of the photon is zero. The original and correct explanation is because the mass there is dilated relative to an Earthbound observer. In other words that mass is all around us. Television and movies popularized black holes starting in the 1960's.
Bravo 👍