Proof-number search (PNS) is a method used in artificial intelligence, particularly in the domain of game playing and automated theorem proving. It is a search strategy that focuses on determining the strength or quality of a position in a game or a proof in a logic problem. PNS operates by evaluating the proof numbers and disproof numbers associated with different nodes in a search tree.
The Reverse-Delete algorithm is a graph algorithm used to find the minimum spanning tree (MST) of a connected and undirected graph. It is based on the concept of deleting edges and checking connectivity, which is a complement to the more commonly known Prim's and Kruskal's algorithms for finding MSTs. ### How the Reverse-Delete Algorithm Works: 1. **Initialization**: Start with the original graph, consisting of vertices and edges.
The **chromatic polynomial** is a polynomial that encodes the number of ways to color the vertices of a graph using a given number of colors such that no two adjacent vertices share the same color. Specifically, for a graph \( G \), the chromatic polynomial \( P(G, k) \) is defined as the number of ways to color the graph with \( k \) colors. ### Key Properties 1.
Complete coloring is a term primarily used in the context of graph theory, a branch of mathematics and computer science that studies the properties of graphs. In graph theory, a "coloring" of a graph is an assignment of colors to the vertices of the graph such that no two adjacent vertices share the same color. A "complete coloring" typically refers to a coloring where the number of colors used is equal to the maximum degree of the graph plus one.
In graph theory, a **tree** is a type of graph that has specific properties. Here are the key characteristics that define a tree: 1. **Acyclic**: A tree is acyclic, meaning it does not contain any cycles. In other words, there is no way to start at one vertex, travel along the edges, and return to the same vertex without retracing steps.
A threshold graph is a specific type of directed graph used in mathematics and computer science, particularly in the study of networks, social networks, and combinatorial optimization. It has a particular structure characterized by certain properties: 1. **Vertex Set**: A threshold graph is defined on a finite set of vertices. 2. **Edge Set**: The edges in a threshold graph are determined by a threshold value.
Bright Bricks is a UK-based company known for its expertise in constructing large-scale models and displays using LEGO bricks. Founded in 2011, the company specializes in creating custom LEGO builds for a variety of clients, including businesses, museums, and events. Their projects can range from intricate architectural models and promotional displays to life-sized sculptures and themed installations. Bright Bricks is recognized for its creativity and attention to detail, often employing professional builders and designers to ensure high-quality results.
"Canadian string theorists" typically refers to physicists from Canada who specialize in string theory, a theoretical framework in physics that aims to reconcile general relativity and quantum mechanics. String theory posits that the fundamental constituents of the universe are not point-like particles, but rather one-dimensional "strings" that can vibrate at different frequencies. The theory seeks to provide a unified description of all fundamental forces and particles in the universe.
Vizing's theorem is a result in graph theory that relates to the edge coloring of graphs. Specifically, it states that for any simple graph \( G \), the chromatic index (the minimum number of colors needed to color the edges of the graph so that no two adjacent edges share the same color) is either equal to the maximum degree \( \Delta(G) \) of the graph or \( \Delta(G) + 1 \).
In the context of mathematics, particularly in functional analysis and related fields, the term "Χ-bounded" (often written as X-bounded) refers to a property of a set or a family of functions. A set \( S \) of functions or operators is called X-bounded if it is uniformly bounded in the topology or structure defined by a space \( X \).
A bound graph is a concept primarily used in the context of graph theory, though the term can be related to various domains such as computer science, mathematics, and other related fields. However, "bound graph" may not refer to a widely recognized term with a single definition across various disciplines.
In graph theory, a modular graph is a concept related to the idea of module or modularity in the context of substructures of a graph. The term "modular graph" can sometimes be used in discussions of modular decomposition, which is a technique for breaking down a graph into simpler components based on the concept of modules.
A scale-free network is a type of network characterized by a particular property in its degree distribution. In such networks, the distribution of connections (or edges) among the nodes follows a power law, which means that a few nodes (often referred to as "hubs") have a very high number of connections, while the majority of nodes have relatively few connections.
The Graphene Flagship is a major European research initiative focused on the development and commercialization of graphene and related two-dimensional materials. Launched in 2013, it is one of the largest and most ambitious research projects supported by the European Commission under its Horizon 2020 program. Graphene is a single layer of carbon atoms arranged in a two-dimensional lattice.
Graphene lens refers to a lens technology that utilizes graphene, a single layer of carbon atoms arranged in a two-dimensional lattice, as part of its design or functionality. Graphene has unique optical properties, such as its high optical transparency and the ability to manipulate light in innovative ways.
Graphene nanoribbons (GNRs) are narrow strips of graphene, a single layer of carbon atoms arranged in a hexagonal lattice. They are typically characterized by their width, which can be on the order of a few nanometers, and come in two main types based on their edge configuration: armchair and zigzag.
Graphene plasmonics is a field of study that explores the interaction between graphene— a single layer of carbon atoms arranged in a two-dimensional lattice— and plasmons, which are coherent oscillations of electrons that occur at the surface of conductors and can propagate along metal-dielectric interfaces. ### Key Concepts: 1. **Plasmons**: Plasmons are quasi-particles resulting from the collective oscillations of free electrons in a material.
A graphene spray gun is a tool designed for applying graphene-based coatings or materials in a liquid form. Graphene, a single layer of carbon atoms arranged in a two-dimensional lattice, has remarkable properties such as high strength, electrical conductivity, and thermal conductivity. These properties make it suitable for various applications, including coatings that enhance the performance of surfaces.
HSMG can refer to a few different things depending on the context, but one prominent meaning is related to the **Handmade Soap & Cosmetic Guild**. This organization is dedicated to supporting and educating soap makers and cosmetic manufacturers, providing resources and fostering a community for those in the handmade soap and cosmetic industry.