In order theory, a branch of mathematics, the term "prime" can refer to a particular type of element within a partially ordered set (poset).

A **simplicial Lie algebra** is a mathematical structure that arises in the study of algebraic topology and differentiable geometry, particularly in the context of generalized symmetries and homotopy theory. It combines concepts from both Lie algebras and simplicial sets.

Tropical compactification is a mathematical technique used in algebraic geometry and related areas, particularly those involving tropical geometry. To understand tropical compactification, it's helpful to first grasp some concepts in both algebraic geometry and tropical geometry. ### Tropical Geometry: 1. **Tropical Semiring**: In tropical geometry, we typically work with a modified version of the arithmetic called the tropical semiring.

The Alon–Boppana bound is a result in the field of graph theory and spectral graph theory. It provides a lower bound on the largest eigenvalue (also known as the spectral radius) of a regular graph. More formally, let \( G \) be a \( d \)-regular graph on \( n \) vertices.

A distance-regular graph is a specific type of graph that has a high degree of regularity in the distances between pairs of vertices. Formally, a graph \( G \) is said to be distance-regular if it satisfies the following conditions: 1. **Regularity**: The graph is \( k \)-regular, meaning each vertex has exactly \( k \) neighbors.

Graph automorphism is a concept in graph theory that refers to a symmetry of a graph that preserves its structure. More specifically, an automorphism of a graph is a bijection (one-to-one and onto mapping) from the set of vertices of the graph to itself that preserves the adjacency relationship between vertices.

The Ihara zeta function is a mathematical object that arises in the study of finite graphs, particularly in the context of algebraic topology and number theory. It was introduced by Yoshio Ihara in the 1960s.

Sims' conjecture is a hypothesis in the field of algebraic topology and combinatorial group theory, specifically relating to the properties of certain types of groups. Named after mathematician Charles Sims, the conjecture primarily deals with the structure of finite groups and representation theory. While specific details or formulations may vary, Sims' conjecture is generally focused on establishing a relationship between the orders of groups and their representations or modules.

A strongly regular graph is a specific type of graph characterized by a regular structure that satisfies certain conditions regarding its vertices and edges. Formally, a strongly regular graph \( G \) is defined by three parameters \( (n, k, \lambda, \mu) \) where: - \( n \) is the total number of vertices in the graph.

A **vertex-transitive graph** is a type of graph in which, for any two vertices, there is some automorphism of the graph that maps one vertex to the other. In simpler terms, this means that the graph looks the same from the perspective of any vertex; all vertices have a similar structural role within the graph. ### Key Properties: 1. **Automorphism:** An automorphism is a bijection (one-to-one correspondence) from the graph to itself that preserves the edges.

David Eisenbud is a prominent American mathematician known for his work in algebraic geometry, commutative algebra, and related fields. He has made significant contributions to the study of singularities, mixed characteristic, and the interplay between algebra and geometry. Eisenbud has also been involved in various educational efforts and served in administrative roles, including as the director of the Mathematical Sciences Research Institute (MSRI) in Berkeley, California.

An **acylindrically hyperbolic group** is a type of group in geometric group theory that generalizes the concept of hyperbolic groups. These groups are characterized by a specific type of action they have on a $\textit{proper geodesic metric space}$.

Ann Cartwright is a name that could refer to several individuals, but in a prominent context, she is known as a philosopher of science, particularly recognized for her work on the philosophy of physics and the foundations of scientific theories. She has contributed significantly to discussions surrounding the nature of scientific explanations, causal relationships, and the interpretation of scientific theories.

The term "horn angle" can refer to different concepts depending on the context in which it is used. However, in scientific and mathematical contexts, it is often associated with the field of geometry and particularly with the study of shapes and angles in polyhedra or polyhedral surfaces. In a more specific context, the horn angle can refer to an angle formed by certain geometric constructs within a horn-like shape.

Adam Tanner was a Jesuit theologian and philosopher, known for his contributions to Jesuit education and thought. While specific details about his life and work may not be widely documented, Jesuit theologians typically engage with a range of theological, philosophical, and social issues, drawing from the rich tradition of Jesuit beliefs and education.

The term "adaptive machine" can refer to various concepts in different fields, particularly in technology and machine learning. Generally, it describes systems or algorithms that can adjust their behavior or outputs based on new data or changing conditions. Here are a few contexts in which "adaptive machine" might be used: 1. **Adaptive Machine Learning**: In this context, adaptive machines use algorithms that can learn and improve from experience.

An adiabatic invariant is a quantity that remains constant when changes are made to a system very slowly, or adiabatically, compared to the timescales of the system's dynamics. The concept is often discussed in the context of classical mechanics, quantum mechanics, and thermodynamics. ### In Classical Mechanics In classical mechanics, one of the most well-known adiabatic invariants is the action variable, which is defined in the context of a periodic motion.

The Erdős–Rado theorem is a result in combinatorial set theory that deals with families of sets and their intersections. It is named after mathematicians Paul Erdős and Richard Rado, who developed the theorem in the context of infinite combinatorics.

Adolfo del Campo can refer to a person or a specific concept depending on the context. However, as of my last update in October 2023, there is no widely recognized figure or term by that name in public discourse, literature, or notable events.

In astronomy, polar distance refers to the angular measurement of the distance from a celestial object to the celestial pole, typically expressed in degrees. The celestial pole is the point in the sky that corresponds to the Earth's North or South Pole. In a more specific sense, polar distance can be associated with the position of a star or other celestial object in the sky in relation to the celestial sphere.