Convex analysis | Mathematical analysis
In convex analysis, a non-negative function f : Rn → R+ is logarithmically concave (or log-concave for short) if its domain is a convex set, and if it satisfies the inequality for all x,y ∈ dom f and 0 < θ < 1. If f is strictly positive, this is equivalent to saying that the logarithm of the function, log ∘ f, is concave; that is, for all x,y ∈ dom f and 0 < θ < 1. Examples of log-concave functions are the 0-1 indicator functions of convex sets (which requires the more flexible definition), and the Gaussian function. Similarly, a function is log-convex if it satisfies the reverse inequality for all x,y ∈ dom f and 0 < θ < 1. (Wikipedia).
Graphing a logarithmic function with two reflections
👉 Learn how to graph logarithmic functions. The logarithmic function is the inverse of the exponential function. To graph a logarithmic function, it is usually very useful to make the table of values of the function. This is done by choosing a range of values of x and then plug the x-value
From playlist How to Graph Logarithmic Functions in Different Bases
Learn how to graph a logarithm with reflections over x and y axis
👉 Learn how to graph logarithmic functions. The logarithmic function is the inverse of the exponential function. To graph a logarithmic function, it is usually very useful to make the table of values of the function. This is done by choosing a range of values of x and then plug the x-value
From playlist How to Graph Logarithmic Functions in Different Bases
Graphing the logarithmic equation with a horizontal & vertical translation
👉 Learn how to graph logarithmic functions involving vertical shift. The logarithmic function is the inverse of the exponential function. To graph a logarithmic function, it is usually very useful to make the table of values of the function. This is done by choosing a range of values of x
From playlist How to Graph Logarithmic Functions with Vertical Shift
Emanuel Milman: 1 D Localization part 4
The lecture was held within the framework of the Hausdorff Trimester Program: Optimal Transportation and the Workshop: Winter School & Workshop: New developments in Optimal Transport, Geometry and Analysis
From playlist HIM Lectures 2015
Complex Brunn–Minkowski theory and positivity of vector bundles – Bo Berndtsson – ICM2018
Geometry | Analysis and Operator Algebras Invited Lecture 5.2 | 8.2 Complex Brunn–Minkowski theory and positivity of vector bundles Bo Berndtsson Abstract: This is a survey of results on positivity of vector bundles, inspired by the Brunn–Minkowski and Prékopa theorems. Applications to c
From playlist Geometry
Determining the x intercept of a logarithmic equation
👉 Learn how to graph logarithmic functions. The logarithmic function is the inverse of the exponential function. To graph a logarithmic function, it is usually very useful to make the table of values of the function. This is done by choosing a range of values of x and then plug the x-value
From playlist How to Graph Logarithmic Functions in Different Bases
MIT RES.6-012 Introduction to Probability, Spring 2018 View the complete course: https://ocw.mit.edu/RES-6-012S18 Instructor: John Tsitsiklis License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu
From playlist MIT RES.6-012 Introduction to Probability, Spring 2018
Worldwide Calculus: The Natural Logarithm
Lecture on 'The Natural Logarithm' from 'Worldwide Differential Calculus' and 'Worldwide AP Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Worldwide Single-Variable Calculus for AP®
How to use a table to graph logarithmic function
👉 Learn how to graph logarithmic functions. The logarithmic function is the inverse of the exponential function. To graph a logarithmic function, it is usually very useful to make the table of values of the function. This is done by choosing a range of values of x and then plug the x-value
From playlist How to Graph Logarithmic Functions in Different Bases
Lec 11 | MIT 18.01 Single Variable Calculus, Fall 2007
Lecture 11: Max-min problems View the complete course at: http://ocw.mit.edu/18-01F06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.01 Single Variable Calculus, Fall 2006
Bo’az Klartag: On Yuansi Chen’s work on the KLS conjecture II
The Kannan-Lovasz-Simonovits (KLS) conjecture is concerned with the isoperimetric problem in high-dimensional convex bodies. The problem asks for the optimal way to partition a convex body into two pieces of equal volume so as to minimize their interface. The conjecture suggests that up to
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
PreCalculus - Logarithmic Function (1 of 23) What is an Logarithmic Function?
Visit http://ilectureonline.com for more math and science lectures! In this video I will define and give examples of logarithmic functions. Next video can be seen at: http://youtu.be/uLRiUMyDf64
From playlist Michel van Biezen: PRECALCULUS 1-5 - ALGEBRA REVIEW
Transcendental Functions 3 Examples using Properties of Logarithms.mov
Examples using the properties of logarithms.
From playlist Transcendental Functions
Variational Methods: How to Derive Inference for New Models (with Xanda Schofield)
This is a single lecture from a course. If you you like the material and want more context (e.g., the lectures that came before), check out the whole course: https://sites.google.com/umd.edu/2021cl1webpage/ (Including homeworks and reading.) Xanda's Webpage: https://www.cs.hmc.edu/~xanda
From playlist Computational Linguistics I
Peter Pivovarov: Random s-concave functions and isoperimetry
I will discuss stochastic geometry of s-concave functions. In particular, I will explain how a ”local” stochastic isoperimetry underlies several functional inequalities. A new ingredient is a notion of shadow systems for s-concave functions. Based on joint works with J. Rebollo Bueno.
From playlist Workshop: High dimensional spatial random systems
Graphing logarithmic equations
👉 Learn how to graph logarithmic functions. The logarithmic function is the inverse of the exponential function. To graph a logarithmic function, it is usually very useful to make the table of values of the function. This is done by choosing a range of values of x and then plug the x-value
From playlist How to Graph Logarithmic Functions in Different Bases
Alina Stancu: Some comments on the fundamental gap of the Dirichlet Laplacian in hyperbolic space
I will present some results on the fundamental gap of convex domains in hyperbolic space for different types of convexity. The results are in contrast with the behaviour of the fundamental gap in Euclidean space and I will make some comments on the aspects of the problem that are different
From playlist Workshop: High dimensional measures: geometric and probabilistic aspects
Graphing logarithmic equations
👉 Learn how to graph logarithmic functions. The logarithmic function is the inverse of the exponential function. To graph a logarithmic function, it is usually very useful to make the table of values of the function. This is done by choosing a range of values of x and then plug the x-value
From playlist How to Graph Logarithmic Functions in Different Bases
Graphing logarithmic equations
👉 Learn how to graph logarithmic functions. The logarithmic function is the inverse of the exponential function. To graph a logarithmic function, it is usually very useful to make the table of values of the function. This is done by choosing a range of values of x and then plug the x-value
From playlist How to Graph Logarithmic Functions in Different Bases