Semi-continuity is a concept in mathematics, specifically in the field of topology and analysis, that describes a form of continuity for functions or sets. There are two main types of semi-continuity: lower semi-continuity and upper semi-continuity.

The concept of a **subderivative** arises in the context of convex analysis and nonsmooth analysis. It generalizes the idea of a derivative to non-differentiable functions. Here’s a brief overview of its key aspects: 1. **Context**: In classical calculus, the derivative of a function at a point measures the rate at which the function changes at that point.

Jarzynski equality is a result in statistical mechanics that provides a relationship between the work done on a system during a non-equilibrium process and the change in free energy of the system. It was formulated by Christopher Jarzynski in 1997.

Complexification is a term that can refer to various concepts across different fields, often denoting the process of adding complexity to a system, concept, or phenomenon. Here are a few contexts in which "complexification" is commonly used: 1. **Systems Theory and Complexity Science**: In this context, complexification refers to the process by which systems evolve from simpler to more complex forms.

Neptunium is a chemical element with the symbol Np and atomic number 93. It is a silvery, radioactive metal that belongs to the actinide series of the periodic table. Neptunium is notable for being the first transuranium element, meaning it was the first element discovered that has an atomic number greater than that of uranium (92). Neptunium was discovered in 1940 by Edwin McMillan and Philip H.

A vector space is a mathematical structure formed by a collection of vectors, which can be added together and multiplied by scalars. Here are some common examples of vector spaces: 1. **Euclidean Space (ℝⁿ)**: - The set of all n-tuples of real numbers.

A graded vector space is a specific type of vector space that is decomposed into a direct sum of subspaces, each associated with a specific degree or grading. This setup is often used in various areas of mathematics, including algebra, geometry, and theoretical physics.

Vehicle graveyards, often referred to as junkyards, scrap yards, or auto recyclers, are places where discarded, damaged, or end-of-life vehicles are collected and processed. These facilities serve several purposes: 1. **Scrap Metal Recovery**: Vehicle graveyards typically dismantle vehicles for parts and scrap metal. Valuable metals like steel, aluminum, and copper are extracted and sold to be recycled.

A **topological vector space** is a type of vector space that is equipped with a topology, which allows for the definition of concepts such as convergence, continuity, and compactness in a way that is compatible with the vector space operations (vector addition and scalar multiplication).

Vector calculus is a branch of mathematics that deals with vector fields and the differentiation and integration of vector functions. It combines concepts from calculus, linear algebra, and mathematical analysis to study fields in multiple dimensions, focusing particularly on the behavior of vectors in space. Key concepts in vector calculus include: 1. **Vectors**: A vector is a quantity defined by both magnitude and direction.

"Vehicle operators by vehicle type" typically refers to the categorization or classification of individuals or companies that operate different types of vehicles. This can include various modes of transportation, such as: 1. **Personal Vehicles**: - Cars - Motorcycles - Bicycles 2.

Vehicle retailers are businesses or establishments that sell vehicles to consumers or businesses. These retailers can offer a variety of vehicles, including: 1. **New Cars:** Brand new vehicles that are sold directly from manufacturers or dealerships. 2. **Used Cars:** Previously owned vehicles that are sold by dealerships or individual sellers. 3. **Motorcycles:** Retailers may also specialize in or include motorcycles in their inventories. 4. **Trucks and Commercial Vehicles:** Retailers that focus on larger vehicles for commercial purposes.

The eccentricity vector, often denoted as **e**, is a vector that describes the shape and orientation of an orbit in celestial mechanics. It is particularly relevant in the context of conic sections, which are used to describe orbits of celestial bodies (like planets, comets, and satellites) around other massive bodies.

The number 222 is an integer that comes after 221 and before 223. It is an even number and can be expressed in various contexts, such as mathematics or symbolism. In mathematics, 222 can be factored into prime numbers: \( 222 = 2 \times 3 \times 37 \). It is also sometimes considered a "palindromic" number, as it reads the same forwards and backwards when considered as a string of digits.

In geometry, equipollence refers to the concept of two figures or geometric objects being equivalent in certain properties, often in terms of their area, volume, or other measurable attributes, even if they are not congruent or identical in shape. This concept can apply in various contexts, such as in the study of similar figures, where the shapes may differ but have proportions that maintain certain ratios, or when comparing geometric figures that can be transformed into one another through operations like scaling or deformation.

An indicator vector (or indicator variable) is a vector used in statistics and machine learning to represent categorical data in a binary format. It is commonly used in contexts such as regression analysis, classification problems, and other areas where categorical variables need to be included in mathematical models. In an indicator vector: - Each category of a variable is represented as a separate binary dimension (0 or 1).

The Laplace–Runge–Lenz (LRL) vector is a fundamental concept in celestial mechanics and classical mechanics, particularly in the study of central force problems, such as the motion of planets and satellites around a central body (like the Sun). ### Definition The LRL vector \( \mathbf{A} \) is defined in the context of the motion of a particle under a central force, such as gravity.

A probability vector is a mathematical object that represents a probability distribution over a discrete set of outcomes. In simpler terms, it's a vector (an ordered list) where each element corresponds to the probability of a particular outcome occurring, and the sum of all the probabilities in the vector equals one. ### Key Characteristics of a Probability Vector: 1. **Non-negativity**: Each element of the probability vector must be non-negative. This means that the probability of any outcome cannot be less than zero.