The dot product, also known as the scalar product, is a mathematical operation that takes two vectors and returns a single scalar (a real number). It is used extensively in geometry, physics, and various fields of engineering.

In mathematics, a scalar is a single number used to measure a quantity. Scalars are often contrasted with vectors, which have both magnitude and direction. Scalars can represent various quantities such as temperature, mass, energy, time, and speed, among others. Some key characteristics of scalars include: 1. **Magnitude Only**: Scalars have only magnitude; they do not have a direction associated with them.

Tricomi–Carlitz polynomials are a class of polynomials that arise in the study of $q$-analogues in the context of basic hypergeometric series and combinatorial identities. They are named after the mathematicians Francesco Tricomi and Leonard Carlitz, who studied these polynomials in relation to $q$-series. These polynomials can be defined through various generating functions and properties related to $q$-binomial coefficients.

A dipole graph is a specific type of graph used in physics and mathematics to represent a system featuring two opposing charges or poles, typically illustrated in the context of electric or magnetic fields. In the context of electrostatics, for example, a dipole consists of two point charges of equal magnitude and opposite sign separated by a distance.

The Ellingham-Horton graph is a thermodynamic reference tool used in metallurgy and materials science. It provides a visual representation of the standard free energy changes (ΔG) of various metal oxides as a function of temperature. Named after the researchers Sir Harold Ellingham and J. H. Horton, the graph is primarily used to analyze the stability of metal oxides and their tendency to reduce (or be reduced to their elemental form) at given temperatures.

A Livingstone graph is a type of mathematical graph used in the field of graph theory, specifically in relation to the study of networks and topological structures. It is named after the mathematician William Livingstone, though the term may not be widely recognized in all mathematical literature. Livingstone graphs are characterized by certain properties unique to their structure, often being studied for their applications in biology, chemistry, and network design.

A Moore graph is a special type of undirected graph that has particular properties related to its diameter, degree, and the number of vertices. Specifically, a Moore graph is defined as a regular graph of degree \( k \) with diameter \( d \) that has the maximum possible number of vertices for those parameters.

A supply chain refers to the entire system of organizations, people, activities, information, and resources involved in the production and delivery of a product or service from suppliers to customers. It encompasses all stages of a product's lifecycle, including sourcing raw materials, manufacturing, transportation, warehousing, and distribution. Key components of a supply chain include: 1. **Suppliers**: Provide the raw materials or components needed for production. 2. **Manufacturers**: Transform raw materials into finished goods.

RFPolicy can refer to various concepts depending on the context in which it is used, and it may not correspond to a single, widely recognized term. However, it is often associated with "Radio Frequency Policy" or policies related to radio frequency allocations and management, particularly in telecommunications and broadcasting. 1. **Radio Frequency Policy**: This refers to the regulatory framework governing the use of radio frequencies for various applications, including telecommunications, broadcasting, and wireless communications.

In signal processing, normalized frequency is a dimensionless quantity that provides a way to express frequency in a scaled form relative to a reference frequency. Normalization helps simplify the analysis and comparison of signals, especially in contexts like digital signal processing, filter design, and system analysis.

A **normal number** is a real number whose individual digits, and in broader terms, digits of any base, are uniformly distributed. More formally, a number is said to be normal in base \( b \) if, in its expansion in that base, all digits from \( 0 \) to \( b-1 \) appear with equal frequency in the limit as you consider more and more digits.

Norman Feather is best known as a psychologist and researcher who has contributed to the fields of social psychology and the study of attitudes, motivation, and consistency in human behavior. One of his notable contributions is the development of the "Feather's Theory of the Need for Achievement," which explores how personal motives influence people's attitudes and decisions in various contexts.

The norm of reciprocity is a social principle or norm that suggests that individuals are more likely to respond to positive actions with positive actions and to negative actions with negative ones. In essence, it is the idea that people feel a social obligation to return favors, gifts, or acts of kindness they receive from others. This norm plays a significant role in building social relationships and cooperation, as it encourages mutual support and balance in interpersonal exchanges.

The North American Maglev Transport Institute (NAMTI) is an organization focused on promoting and advancing magnetic levitation (maglev) transportation technology in North America. Maglev trains use powerful magnets to lift and propel vehicles at high speeds, offering a potentially more efficient and faster alternative to traditional rail systems. NAMTI aims to facilitate research, development, and deployment of maglev systems, collaborating with governmental, educational, and industrial partners.

Not-All-Equal 3-Satisfiability (NAE-3-SAT) is a variation of the standard 3-Satisfiability (3-SAT) problem in the field of computational complexity and logic. In general, the 3-SAT problem involves determining whether there is an assignment of truth values to variables in a boolean formula written in conjunctive normal form (CNF), such that the entire formula evaluates to true.

Norwegian nuclear physicists are scientists from Norway who specialize in the study of nuclear physics, which focuses on the components and behavior of atomic nuclei. This field encompasses various subjects, including nuclear structure, nuclear reactions, radioactivity, and applications of nuclear technology, such as nuclear energy and medical imaging. Norway has contributed to nuclear physics through research institutions, universities, and collaborative projects.

A Perkel graph is a special type of graph used in the study of graph theory and combinatorial designs. It is defined based on a recursive structure. Specifically, a Perkel graph is constructed from an initial set of vertices and uses certain rules to add edges based on the properties of those vertices.

The Schläfli graph is an interesting and well-studied graph in the field of graph theory, particularly in relation to polyhedra and higher-dimensional polytopes. It is defined as the graph whose vertices correspond to the regular polyhedra (in 3D) and regular polytopes (in higher dimensions), and where edges connect pairs of polyhedra that share a common face.

A table of simple cubic graphs provides a list of cubic graphs, which are graphs where every vertex has a degree of exactly 3 (i.e., each vertex is connected to exactly three edges). Simple cubic graphs have no loops or multiple edges between the same pair of vertices. These graphs are also known as 3-regular graphs. A common way to organize and present simple cubic graphs is by their number of vertices (usually denoted as \( n \)).

A triangle graph, often referred to in the context of graph theory, can denote different concepts based on context, but generally it refers to a type of graph structure that contains a specific relationship resembling triangles. 1. **Triangle in Graph Theory**: In a general mathematical graph, a triangle is a complete subgraph consisting of three vertices, where each vertex is connected to the other two. This means there are three edges that form a triangle shape.