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Planar graph by

A **planar graph** is a type of graph that can be embedded in the plane, meaning that it can be drawn on a flat surface such that its edges intersect only at their endpoints (vertices) and do not cross each other. In other words, a graph is planar if it can be represented in such a way that no two edges overlap except at their endpoints.

Self-complementary graph by

A self-complementary graph is a type of graph that is isomorphic to its own complement. In graph theory, for a given graph \( G \), the complement graph \( \overline{G} \) is formed by taking the same vertex set as \( G \) but including only those edges that are not present in \( G \).

Strongly chordal graph by

A **strongly chordal graph** is a specific type of graph that combines properties of both chordal graphs and certain restrictions on the structure of its cliques. 1. **Chordal Graph**: A graph is defined as chordal (or "circular" or "perfectly triangulated") if every cycle of four or more vertices has a chord. A chord is an edge that is not part of the cycle but connects two vertices of the cycle.

Lindenbaum's lemma by

Triangle-free graph by

A **triangle-free graph** is a type of graph that does not contain any cycles of length three, which means it does not have any set of three vertices that are mutually connected by edges. In other words, if you pick any three vertices in the graph, at least one pair of those vertices will not be directly connected by an edge. Triangle-free graphs can be characterized using graph theory, and they have significant implications in various areas, including combinatorics, algorithm design, and social networks.

Butterfly graph by

A butterfly graph is a type of network graph that resembles the shape of a butterfly when visualized. It is often used to represent parallel computations in computer science, particularly in the context of networks and interconnection systems. The butterfly graph has specific properties that make it useful for various applications, including: 1. **Structure**: A butterfly graph is typically defined recursively, meaning that it is constructed in layers.

Truncated tetrahedron by

A truncated tetrahedron is a type of Archimedean solid that is formed by truncating (or cutting off) the corners (vertices) of a regular tetrahedron. This process involves slicing off each of the four vertices of the tetrahedron, resulting in a new solid with additional faces.

Operator algebras by

Operator algebras is a branch of functional analysis and mathematics that studies algebras of bounded linear operators on a Hilbert space. These algebras are typically closed in a specific topology (usually the operator norm topology or the weak operator topology), which makes them particularly amenable to the tools of functional analysis, topology, and representation theory.

Bipolar theorem by

The term "bipolar theorem" is often used in the context of convex analysis and mathematical optimization. Specifically, it relates to the relationships between sets and their convex cones.

C*-algebra by

A C*-algebra is a type of algebraic structure that arises in functional analysis and is fundamental to the study of operator theory and quantum mechanics.

Complemented subspace by

In functional analysis and related fields of mathematics, a **complemented subspace** is a type of subspace of a vector space that has a certain structure with respect to the entire space. More specifically, consider a vector space \( V \) and a subspace \( W \subseteq V \).

Constructive quantum field theory by

Constructive quantum field theory (CQFT) is a branch of theoretical physics that aims to provide rigorous mathematical foundations to quantum field theory (QFT). Traditional approaches to QFT often involve perturbative techniques and heuristic arguments, which can sometimes lead to ambiguities or inconsistencies. In contrast, CQFT seeks to establish a solid mathematical framework for QFT by developing and rigorously proving results using techniques from advanced mathematics, such as operator algebras, functional analysis, and topology.

Alexa Beiser by

As of my last update in October 2023, there is no widely recognized figure or entity named Alexa Beiser. It is possible that she is a private individual or someone who may have gained prominence after that date.

Functional square root by

The term "functional square root" generally refers to a concept in mathematics where one function is considered the square root of another function. More formally, if \( f(x) \) is a function, then a function \( g(x) \) can be considered a functional square root of \( f(x) \) if: \[ g(x)^2 = f(x) \] for all \( x \) in the domain of interest.

Hadamard space by

A **Hadamard space** is a specific type of metric space that generalizes the concept of non-positive curvature. More formally, a Hadamard space is a complete metric space where any two points can be connected by a geodesic, and all triangles in the space are "thin" in a sense that closely resembles the behavior of triangles in hyperbolic geometry.

Markushevich basis by

The Markushevich basis is a concept in functional analysis and specifically in the context of Banach spaces. It is a type of basis used in the study of nuclear spaces, which are a kind of topological vector space characterized by the property that every continuous linear functional on the space can be expressed in terms of a countable linear combination of the basis elements.

Order complete by

"Order complete" typically refers to the status of a transaction or purchase in which all aspects of the order have been fulfilled. This means that the customer has successfully placed an order, the payment has been processed, and the items have been shipped or delivered. This status is commonly used in e-commerce and retail settings to indicate that there are no outstanding issues with the order and that the customer can expect their items as agreed.

Pettis integral by

The Pettis integral is a generalization of the Lebesgue integral that is used to integrate functions taking values in Banach spaces, rather than just in the real or complex numbers. It is particularly significant when dealing with vector-valued functions and weakly measurable functions. In more formal terms, let \( X \) be a Banach space, and let \( \mu \) be a measure on a measurable space \( (S, \Sigma) \).

Quasi-interior point by

The term "quasi-interior point" is used in the context of convex analysis and optimization, specifically in relation to sets and their boundaries. While the exact definition can vary slightly depending on the specific mathematical context, it generally refers to a point in the closure of a convex set that is not on the boundary of the set, but rather "near" the interior.