Search results
Results From The WOW.Com Content Network
Kraft's inequality limits the lengths of codewords in a prefix code: if one takes an exponential of the length of each valid codeword, the resulting set of values must look like a probability mass function, that is, it must have total measure less than or equal to one. Kraft's inequality can be thought of in terms of a constrained budget to be ...
McMillan was born in Minneapolis, Minnesota, in 1915, the only child of Franklin Richardson McMillan, a civil engineer, and Luvena Lucille Brockway McMillan, a schoolteacher. [3] He received his B.S. in 1936 and a Ph.D. 1939 from Massachusetts Institute of Technology (MIT) on a thesis entitled The calculus of discrete homogenous chaos ...
The name Desmos came from the Greek word δεσμός which means a bond or a tie. [6] In May 2022, Amplify acquired the Desmos curriculum and teacher.desmos.com. Some 50 employees joined Amplify. Desmos Studio was spun off as a separate public benefit corporation focused on building calculator products and other math tools. [7]
There are three inequalities between means to prove. There are various methods to prove the inequalities, including mathematical induction, the Cauchy–Schwarz inequality, Lagrange multipliers, and Jensen's inequality. For several proofs that GM ≤ AM, see Inequality of arithmetic and geometric means.
The Shannon–McMillan–Breiman theorem, due to Claude Shannon, Brockway McMillan, and Leo Breiman, states that we have convergence in the sense of L1. [2] Chung Kai-lai generalized this to the case where X {\displaystyle X} may take value in a set of countable infinity, provided that the entropy rate is still finite.
Grönwall's inequality is an important tool to obtain various estimates in the theory of ordinary and stochastic differential equations. In particular, it provides a comparison theorem that can be used to prove uniqueness of a solution to the initial value problem; see the Picard–Lindelöf theorem. It is named for Thomas Hakon Grönwall (1877 ...
This would contradict the Baire category theorem: because the reals form a complete metric space, they form a Baire space, which cannot be meager in itself. A variant of Thomae's function can be used to show that any F σ subset of the real numbers can be the set of discontinuities of a function.
Main page; Contents; Current events; Random article; About Wikipedia; Contact us