In mathematics, the lower envelope or pointwise minimum of a finite set of functions is the pointwise minimum of the functions, the function whose value at every point is the minimum of the values of the functions in the given set. The concept of a lower envelope can also be extended to partial functions by taking the minimum only among functions that have values at the point. The upper envelope or pointwise maximum is defined symmetrically. For an infinite set of functions, the same notions may be defined using the infimum in place of the minimum, and the supremum in place of the maximum. For continuous functions from a given class, the lower or upper envelope is a piecewise function whose pieces are from the same class. For functions of a single real variable whose graphs have a bounded number of intersection points, the complexity of the lower or upper envelope can be bounded using Davenport–Schinzel sequences, and these envelopes can be computed efficiently by a divide-and-conquer algorithm that computes and then merges the envelopes of subsets of the functions. For convex functions or quasiconvex functions, the upper envelope is again convex or quasiconvex. The lower envelope is not, but can be replaced by the lower convex envelope to obtain an operation analogous to the lower envelope that maintains convexity. The upper and lower envelopes of Lipschitz functions preserve the property of being Lipschitz. However, the lower and upper envelope operations do not necessarily preserve the property of being a continuous function. (Wikipedia).
Resolution of the two envelope fallacy
I talk about a very simple solution to the two envelope fallacy. Watch this video first: https://youtu.be/OqVFKY504X0
From playlist Puzzles and Riddles
Understanding Work Envelopes of Robots!
Robots are designed based on the work envelope requirement. The volume the end effector of this robot is able to reach is known as the work envelope. For example, for this robot shown, the blue shade volume is the work envelope. Let’s learn more about this crucial concept of robotics. Be
From playlist Robotics
Solve The Two Envelopes Fallacy
A fallacy arising from a surprisingly simple situation. Can you figure out what the problem is with this reasoning?
From playlist Puzzles and Riddles
Will It Fit? What Size Box is Needed to Package Smaller Boxes (Ex 1)
This video explains how to determine if a certain number of smaller boxes will fit inside a larger box.
From playlist Mathematics General Interest
Will It Fit? What Size Box is Needed to Package Smaller Boxes (Ex 2)
This video explains how to determine if a certain number of smaller boxes will fit inside a larger box.
From playlist Mathematics General Interest
Envelopes - Applied Cryptography
This video is part of an online course, Applied Cryptography. Check out the course here: https://www.udacity.com/course/cs387.
From playlist Applied Cryptography
Predict what will happen when these two balloons are connected
Make a prediction about how the air will move between these two baloons. Visit my blog here: http://stevemould.com Follow me on twitter here: http://twitter.com/moulds Buy nerdy maths things here: http://mathsgear.co.uk
From playlist Experiments
Show Me Some Science! Balloon Buoyancy
There’s nothing intrinsically “floaty” about helium. You can make a helium balloon that sinks, if it’s cold enough, as we see in this video. At normal room temperature, a helium balloon will rise, as you know. The weight of the rubber balloon plus the gas inside is less than that weight o
From playlist Show Me Some Science!
How to draw a box and whisker plot
From playlist Mr Arnold's Unit 1 Higher Revision
Lie groups: Poincare-Birkhoff-Witt theorem
This lecture is part of an online graduate course on Lie groups. We state the Poincare-Birkhoff Witt theorem, which shows that the universal enveloping algebra (UEA) of a Lie algebra is the same size as a polynomial algebra. We prove it for Lie algebras of Lie groups and sketch a proof of
From playlist Lie groups
Michela Mapelli - Astrophysical models of binary compact objects - IPAM at UCLA
Recorded 16 November 2021. Michela Mapelli of the University of Padova presents "Astrophysical models of binary compact objects: open questions and main uncertainties" at IPAM's Workshop III: Source inference and parameter estimation in Gravitational Wave Astronomy. Abstract: Currently, we
From playlist Workshop: Source inference and parameter estimation in Gravitational Wave Astronomy
Stability of the set of quantum states - S. Weis - Workshop 2 - CEB T3 2017
Stephan Weis / 26.10.17 Stability of the set of quantum states A convex set C is stable if the midpoint map (x,y) - (x+y)/2 is open. For compact C the Vesterstrøm–O’Brien theorem asserts that C is stable if and only if the barycentric map from the set of all Borel probability measures to
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Pedagogical Lectures on Stellar Theory - 2 by Dipankar Bhattacharya
PROGRAM VIRTUAL MEETING ON COMPACT STARS AND QCD 2020 (ORIGINALLY "COMPACT STARS IN THE QCD PHASE DIAGRAM VIII: THE ERA OF MULTI-MESSENGER ASTRONOMY") ORGANIZERS: Manjari Bagchi, Sarmistha Banik, Sudip Bhattacharyya, Prashanth Jaikumar, V. Ravindran and Sayantan Sharma DATE: 17 August
MIT Electronic Feedback Systems (1985) View the complete course: http://ocw.mit.edu/RES6-010S13 Instructor: James K. Roberge License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT Electronic Feedback Systems (1985)
V. Guedj - Quasi-psh envelopes and supersolutions
Using and extending an approximation process due to Berman, we show that the quasi-psh envelope of a viscosity super-solution is a pluripotential super-solution of a given complex Monge-Ampère equation. We apply these ideas to Kahler-Einstein geometry (joint work with H.C.Lu and A.Zeriahi)
From playlist Complex analytic and differential geometry - a conference in honor of Jean-Pierre Demailly - 6-9 juin 2017
Lecture 7.1: Josh McDermott - Introduction to Audition, Part 1
MIT RES.9-003 Brains, Minds and Machines Summer Course, Summer 2015 View the complete course: https://ocw.mit.edu/RES-9-003SU15 Instructor: Josh McDermott The study of sound textures and high level goals of auditory processing. Anatomy and structure of the auditory system, frequency tunin
From playlist MIT RES.9-003 Brains, Minds and Machines Summer Course, Summer 2015
Climate Science, Waves, and PDE's for the Tropics ( 1 ) - Andrew J. Majda
Lecture 1: Climate Science, Waves, and PDE's for the Tropics: Observations, Theory, and Numerics Abstract: Geophysical flows are a rich source of novel problems for applied mathematics and the contemporary theory of partial differential equations. The reason for this is that many physical
From playlist Mathematical Perspectives on Clouds, Climate, and Tropical Meteorology
Jere Koskela: Inference for coalescent and diffusion models in genetics (3/3)
Abstract: Mathematical models in population genetics frequently come in pairs: a diffusion process describes the forward-in-time evolution of allele frequencies in a population, and a branching-coalescing particle system describes the random genetic ancestry of a sample on sequences from t
From playlist Summer School on Stochastic modelling in the life sciences
Cover for basement entrance 1a
Green cover is a connecting rod of an ellipse mechanism of two pink sliders. Driving force from fixed cylinder is applied to the connecting rod via a pinion rack drive (instead of to pink lower slider) ensures smooth motion of the mechanism even at death position when the connection rod is
From playlist Mechanisms