The S-procedure is a mathematical technique used in convex optimization and control theory, specifically in the context of robust control and system stability analysis. It provides a way to transform certain types of inequalities involving quadratic forms into conditions that can be expressed in terms of linear matrix inequalities (LMIs).

Singular Value Decomposition (SVD) is a mathematical technique in linear algebra used to factorize a matrix into three other matrices. It is particularly useful for analyzing and reducing the dimensionality of data, solving linear equations, and performing principal component analysis.

Spinors are mathematical objects used in physics and mathematics, particularly in the context of quantum mechanics and the theory of relativity. In three dimensions, spinors can be understood as a generalization of the notion of vectors and can be associated with the representation of the rotation group, specifically the special orthogonal group SO(3). ### Definition and Representation In three-dimensional space, spinors are typically expressed in relation to the group of rotations SO(3).

Split-complex numbers, also known as hyperbolic numbers or null numbers, are a type of number that extends the real numbers similarly to how complex numbers extend them. They are defined as numbers of the form: \[ z = x + yj \] where \( x \) and \( y \) are real numbers, and \( j \) is a unit with the property that \( j^2 = 1 \).

The term "star domain" can refer to different concepts depending on the context. Here are a few interpretations: 1. **Astronomy and Astrophysics**: In the context of stars and celestial bodies, a "star domain" could refer to a region of space that includes a group of stars or star systems. This could pertain to a section of a galaxy or a cluster of stars that share certain characteristics or are gravitationally bound.

Near-parabolic comets are comets whose orbits are close to parabolic, indicating that they are on the verge of escaping the Sun's gravitational influence. These comets typically have orbital eccentricities close to 1, which means their paths are elongated but not quite sufficient to be classified as hyperbolic (eccentricity greater than 1).

A Z-order curve, also known as a Z-ordering or Morton order, is a spatial filling curve that is used to map multi-dimensional data (like two-dimensional coordinates) into one-dimensional data while preserving the spatial locality of the points. This means that points that are close together in the multi-dimensional space will remain close together in the one-dimensional representation. The Z-ordering works by interleaving the binary representations of the coordinates of the points.

Zech's logarithm, denoted as \( z \), is a mathematical construct used primarily in the field of finite fields and combinatorial structures, such as in coding theory and cryptography. It arises in relation to the concepts of logarithms in finite fields, specifically in the context of operations involving powers of elements in these fields.

Lists of minor planets by number refer to an organized collection or catalog of minor planets (also known as asteroids) that have been assigned a numerical designation based on their order of discovery. The Minor Planet Center (MPC), which is affiliated with the International Astronomical Union (IAU), is responsible for tracking and cataloging these objects.

Lists of unnumbered minor planets refer to catalogues or compilations of minor planets (also known as asteroids) that have been officially discovered and observed but have not yet been assigned a permanent number by the International Astronomical Union (IAU). In the context of celestial objects, minor planets are typically those that are smaller than planets and don't dominate their orbital zones.

A list of Earth-crossing asteroids refers to a collection of asteroids whose orbits bring them into close proximity to Earth's orbit. These asteroids are classified as "near-Earth objects" (NEOs), and more specifically, some of them are categorized as "Atira" (no close approaches to Earth) or "Apollo" and "Aten" asteroids, which do cross Earth's orbit.

A list of Uranus-crossing minor planets includes those asteroids and other small celestial bodies that have orbits that cross the orbit of Uranus. These objects are a subset of the broader group of near-Earth objects and can include centaurs, trans-Neptunian objects, and asteroids.

The list of Venus-crossing minor planets includes a group of small celestial bodies whose orbits bring them close to the orbit of Venus. These minor planets are typically asteroids, and their classifications are based on the paths they take around the Sun, specifically those that intersect with Venus's orbital path. A minor planet is considered a "Venus-crossing" object if it has a semimajor axis and eccentricity that allows its orbit to intersect with that of Venus.

Pluto has five known moons. The most notable of these are: 1. **Charon**: This is the largest moon of Pluto and is almost half the size of Pluto itself, making it the largest moon in relation to its parent planet in the Solar System. Charon and Pluto are sometimes considered a double dwarf planet system due to their size and the way they orbit each other.

Loop quantum gravity (LQG) is a theoretical framework that aims to reconcile general relativity and quantum mechanics, primarily focused on the quantization of spacetime itself. The field has attracted a number of researchers over the years. Here’s a list of some prominent figures associated with loop quantum gravity: 1. **Carlo Rovelli** - One of the founding figures of loop quantum gravity, he has made significant contributions to the theory and its interpretation.

A direct proof is a method of demonstrating the truth of a mathematical statement by straightforward logical deductions from accepted axioms, definitions, and previously established results. In a direct proof, you begin with known facts and apply logical reasoning to arrive directly at the conclusion you are trying to prove. Here are some key characteristics of direct proofs: 1. **Logical Sequence**: Direct proofs rely on a clear sequence of logical steps, where each step follows directly from the previous one or from an established theorem or definition.

A "truth-bearer" is a philosophical term that refers to entities that can be said to be true or false. In essence, truth-bearers are statements, propositions, beliefs, or sentences that possess a truth value. The concept is important in discussions of truth in philosophy, particularly in debates about the nature of truth, the conditions under which a belief or statement is true, and how truth relates to reality.

"Four Epigraphs after Escher" is a composition for solo piano by the American composer and pianist *Ned Rorem*. Written in 1998, the piece is inspired by the works of the Dutch graphic artist M.C. Escher, known for his mathematically inspired artwork that explores patterns, symmetry, and impossible constructions.