Continuous mappings | Complex analysis | Topology of function spaces
In mathematics, with special application to complex analysis, a normal family is a pre-compact subset of the space of continuous functions. Informally, this means that the functions in the family are not widely spread out, but rather stick together in a somewhat "clustered" manner. Note that a compact family of continuous functions is automatically a normal family.Sometimes, if each function in a normal family F satisfies a particular property (e.g. is holomorphic),then the property also holds for each limit point of the set F. More formally, let X and Y be topological spaces. The set of continuous functions has a natural topology called the compact-open topology. A normal family is a pre-compact subset with respect to this topology. If Y is a metric space, then the compact-open topology is equivalent to the topology of compact convergence, and we obtain a definition which is closer to the classical one: A collection F of continuous functions is called a normal family if every sequence of functions in F contains a subsequence which converges uniformly on compact subsets of X to a continuous function from X to Y. That is, for every sequence of functions in F, there is a subsequence and a continuous function from X to Y such that the following holds for every compact subset K contained in X: where is the metric of Y. (Wikipedia).
We are – almost all of us – deeply attracted to the idea of being normal. But what if our idea of ‘normal’ isn’t normal? A plea for a broader definition of an important term. If you like our films, take a look at our shop (we ship worldwide): https://goo.gl/ojRR53 Join our mailing list: h
From playlist SELF
The Normal Distribution (1 of 3: Introductory definition)
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From playlist The Normal Distribution
Everyone assumes that they are the only one to be freakish. In fact, of course, it’s very normal to be abnormal. Please subscribe here: http://tinyurl.com/o28mut7 If you like our films take a look at our shop (we ship worldwide): http://www.theschooloflife.com/shop/all/ Brought to you by h
From playlist SELF
Abstract Algebra | Normal Subgroups
We give the definition of a normal subgroup and give some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
Alternatives To a Standard Relationship
People tend to assume that if they're going to be in a relationship, it has to be a monogamous, long-term kind. Though that might have been true in many places for many years, there are an array of other options to consider. Sign up to our new newsletter and get 10% off your first online
From playlist RELATIONSHIPS
Elephant Family - Safari Sunday
We take a quick look at elephant families in this week's Safari Sunday.
From playlist Safari Sunday
Alice And Her Six Dads (Family Documentary) | Real Stories
A warm hearted and emotional film, following 22-year-old Alice as she searches for her real dad. During Alice's life there have been six different men that she's thought of as being her dad - some meant more to her than others. But there's one of these men Alice has no memory of - her bio
From playlist Family Documentaries
Determining values of a variable at a particular percentile in a normal distribution
From playlist Unit 2: Normal Distributions
I Gave Birth To My Grandchild | Strange Pregnancies | Real Families
This one-hour special focuses on three women whose extraordinary pregnancies defied science and logic. Doctors, anaesthesiologists, neonatologist, surgeons, and nurses were stunned as these mothers pushed their bodies to the brink in order to bring their babies into the world. After surviv
From playlist Our Favourite Videos
Colloque d'histoire des sciences "Gaston Darboux (1842 - 1917)" - Barnabé Croizat - 17/11/17
En partenariat avec le séminaire d’histoire des mathématiques de l’IHP Ovales, cyclides et surfaces orthogonales : les premières amours géométriques de Darboux Barnabé Croizat, Laboratoire Paul Painlevé, Université Lille 1 & CNRS À l’occasion du centenaire de la mort de Gaston Darboux, l
From playlist Colloque d'histoire des sciences "Gaston Darboux (1842 - 1917)" - 17/11/2017
Martin Taylor - The nonlinear stability of the Schwarzschild family of black holes - IPAM at UCLA
Recorded 26 October 2021. Martin Taylor of the Imperial College London presents "The nonlinear stability of the Schwarzschild family of black holes" at IPAM's Workshop II: Mathematical and Numerical Aspects of Gravitation. Abstract: I will present a theorem on the full finite codimension n
From playlist Workshop: Mathematical and Numerical Aspects of Gravitation
Adlai E Stevenson High School (Team #14485) Presentation
Adlai E Stevenson High School from Lincolnshire, Illinois was a Finalist in MathWorks Math Modeling Challenge 2021! On April 26, 2021, finalist teams presented their solution papers via Zoom to a panel of judges. Learn more about the 2021 Challenge problem topic and the winners: https://m3
From playlist M3 Challenge
DEFCON 14: Hunting for Metamorphic Engines
Speakers: Mark Stamp, Assistant Professor, Department of Computer Science, San Jose State University Wing H. Wong, Student, San Jose State University Abstract: Metamorphism has been touted as a way to generate undetectable viruses and worms, and it has also been suggested as a potential s
From playlist DEFCON 14
Stanford CS229: Machine Learning | Summer 2019 | Lecture 6 - Exponential Family & GLM
For more information about Stanford’s Artificial Intelligence professional and graduate programs, visit: https://stanford.io/3Eb7mIi Anand Avati Computer Science, PhD To follow along with the course schedule and syllabus, visit: http://cs229.stanford.edu/syllabus-summer2019.html
From playlist Stanford CS229: Machine Learning Course | Summer 2019 (Anand Avati)
Some algebro-geometric aspects of limiting mixed Hodge structure - Phillip Griffiths
Phillip Griffiths Professor Emeritus, School of Mathematics December 16, 2014 This will be an expository talk, mostly drawn from the literature and with emphasis on the several parameter case of degenerating families of algebraic varieties. More videos on http://video.ias.edu
From playlist Mathematics
Generalized Linear Model (Part A)
Regression Analysis by Dr. Soumen Maity,Department of Mathematics,IIT Kharagpur.For more details on NPTEL visit http://nptel.ac.in
From playlist IIT Kharagpur: Regression Analysis | CosmoLearning.org Mathematics
The Beautiful Mathematics of the Coffee Cup Caustics
0:00 Introduction and Problem formulation 7:10 Deriving the general formula 10:55 Solving the problem and deriving the parametric equation 15:15 Demonstration with Desmos In this video, I show how to derive the parametric equations for the coffee cup caustics. A beautiful mathematical pro
From playlist Summer of Math Exposition Youtube Videos
Normal functions and the geometry of moduli spaces of curves - Richard Hain
Richard Hain Duke University; Member, School of Mathematics January 13, 2015 In this talk, I will begin by recalling the classification of normal functions over g,nMg,n, the moduli space of nn-pointed smooth projective curves of genus gg. I'll then explain how they can be used to resolve
From playlist Mathematics
Young Carers: Looking After Mum (Family Documentary) | Real Stories
The unsung, unseen heroes of society, young carers provide emotional and physical care for disabled and sick parents in a complete reversal of the child/parent role. Want to watch more full-length Documentaries? Click here: http://bit.ly/1GOzpIu Follow us on Twitter for more - https://t
From playlist Family Documentaries
Mikhail Lyubich: Story of the Feigenbaum point
HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 23, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Luca Récanzone Find this video and other talks given by worldwide mathematicians on CIRM's Audi
From playlist Dynamical Systems and Ordinary Differential Equations