Charles Critchfield is a mathematician known for his contributions in the fields of applied mathematics and mathematical physics, particularly in the area of differential equations and dynamical systems. However, without additional context, it's challenging to pinpoint a specific individual since there may be multiple notable figures with that name.

A Yao graph is a specific type of geometric graph used primarily in the field of computational geometry and computer science, particularly in the context of network design and algorithms. It was introduced by Andrew Yao in the 1980s. The Yao graph is constructed based on a set of points in a Euclidean space, usually in two or three dimensions.

Firstly, it's actually legal in the US to yell fire in a theatre, and their theatres seem fine. Anyway, theatres just legally requiring customers not to make disruptions would have the exact same effect as the government banning it.

The Adian–Rabin theorem is a result in the field of mathematical logic, specifically in the area of decidability and the theory of algebraic structures. It addresses the properties of certain classes of roots of equations and relies on concepts from algebra and logic. In basic terms, the theorem states that for any given sequence of rational numbers, it is possible to find a computably enumerable sequence of algebraic numbers that has roots within those rational numbers.

Asymptotic dimension is a concept from geometric topology and metric geometry that provides a way to measure the "size" or "dimension" of a metric space in a manner that is sensitive to the space's large-scale structure. It was introduced by the mathematicians J. M. G. B. Connes and more extensively developed by others in the context of spaces that arise in analysis, algebra, and topology.

The Curve Complex is a mathematical structure used in the field of low-dimensional topology, particularly in the study of surfaces. It provides a combinatorial way to study the mapping class group of a surface, which is the group of isotopy classes of homeomorphisms of the surface.

Flexagon is a term that can refer to a few different concepts, depending on the context. However, it is most commonly recognized in the following ways: 1. **In Mathematics**: A flexagon is a type of flexible polygonal structure that can be manipulated to reveal different faces.

A Vandermonde polynomial is a type of polynomial that arises in various areas of mathematics, particularly in interpolation and number theory.

Vieta's formulas are a set of relations in algebra that relate the coefficients of a polynomial to sums and products of its roots. They are particularly useful in the context of polynomial equations.

The term "free factor complex" often arises in the context of group theory, particularly in the study of free groups and their actions. A free group is a group that has a basis such that every element can be uniquely expressed as the product of finitely many basis elements and their inverses.

This is an unsolvable problem because there's no way to extract large amounts of value from a person without cruelty, and even with cruelty, there's a limit to how much you can extract.

A Følner sequence is a concept from the field of mathematical analysis, particularly in ergodic theory and group theory. It is named after the mathematician Ernst Følner. A Følner sequence provides a way to study the asymptotic behavior of actions of groups on sets and is often used in the context of amenable groups.

A geometric group action is a specific type of action by a group on a geometric space, which can often be thought of in terms of symmetries or transformations of that space. More formally, if we have a group \( G \) and a geometric object (often a topological space or manifold) \( X \), a geometric group action is defined when \( G \) acts on \( X \) in a way that respects the structure of \( X \).

Greedy coloring is a graph coloring algorithm used to assign colors to the vertices of a graph such that no two adjacent vertices share the same color. The goal of graph coloring is to minimize the number of colors used, and greedy coloring serves as a heuristic method for this purpose. ### Basic Procedure The greedy coloring algorithm typically follows these steps: 1. **Order the Vertices**: Start by ordering the vertices of the graph.

Price fixing would require every single company selling something to cooperate. And if they do, another person sick of them can start a new company and undercut them. Price fixing would also destroy any goodwill towards these companies and many customers wouldn't patronize them even if they lowered their prices again.

The Grushko theorem is a result in the field of group theory, particularly concerning free groups and their subgroups. It provides a criterion to establish whether a given group is free and helps characterize the structure of free groups.

In mathematics, "outer space" typically refers to a certain type of geometric space associated with free groups and their actions. The most common reference is to "Outer space" denoted as \( \mathcal{O}(F_n) \), which is the space of marked metric graphs that correspond to the free group \( F_n \) of rank \( n \).

The term "Rips machine" could refer to several things, but in a common context, it often relates to a "Rips" machine used for a specific purpose in various industries. Here are some possibilities: 1. **Rips Software**: In computational topology, Rips complexes are used to study metric spaces. A machine or software that implements Rips complexes allows researchers to analyze the structure and properties of data using topological methods.