A Hermite ring, often related to the field of number theory and algebra, typically refers to a certain type of algebraic structure that has properties akin to those of Hermite polynomials or Hermitian matrices, although the precise definition may vary depending on the context in which the term is used. In a broader sense, a Hermite ring may refer to a ring of numbers or polynomials that uphold specific symmetries or characteristics reminiscent of Hermite functions or polynomials.

"Arithmetica" typically refers to a work by the ancient Greek mathematician Diophantus, who is often known as the "father of algebra." The full title of the work is "Arithmetica," and it is a collection of books that primarily deals with equations and number theory. Diophantus's methods involve finding integer solutions to polynomial equations, which is a major contribution to algebra.

Mathematically, we can decide if two events are timelike-separated or spacelike-separated by just looking at the sign of the spacetime interval between them.

On the light cone, these are events on the left/right part of the cone.

Different observers might not agree on the order of two spacelike-separated events.

Further discussion at Section "Light cone".

The opposite of those events are timelike-separated events.

Application of radiation pressure.

First live example: en.wikipedia.org/wiki/IKAROS

Slack tide refers to the short period of time between the changing of tides when the water is relatively calm and there is little to no horizontal water movement. It occurs at the transition between high tide and low tide, as well as between low tide and high tide. During slack tide, the water level is at its highest or lowest point before starting to rise or fall again.

Spectral music is a compositional technique and style that emerged in the late 20th century, primarily in the 1970s. It is characterized by its focus on the analysis and manipulation of sound spectra—essentially, the frequency content of sound. Composers in this genre analyze the harmonic and timbral characteristics of sounds, often employing computer technology to examine and synthesize these elements.

"Martian Time-Slip" is a science fiction novel written by Philip K. Dick, first published in 1964. The story is set on a colonized Mars and explores themes of reality, perception, and time.

Bayesian Structural Time Series (BSTS) is a framework used for modeling and forecasting time series data that incorporates both structural components and Bayesian methods. The BSTS framework is particularly useful for analyzing data with complex patterns, such as trends, seasonality, and irregularities, while also allowing for the incorporation of various types of uncertainty. ### Key Components of Bayesian Structural Time Series: 1. **Structural Components**: - **Trend**: Captures long-term movements in the data.

Secular variation refers to the long-term changes or trends observed in a particular phenomenon over an extended period, typically spanning decades to centuries. This term is commonly used in various fields, such as geology, paleoclimatology, and even economics, to describe gradual changes that are not tied to periodic cycles (like seasonal or annual changes). In the context of geology and geomagnetism, secular variation may refer to the gradual changes in the Earth's magnetic field intensity and direction over time.

A **graph manifold** is a class of 3-dimensional manifolds characterized by their geometric structure, specifically how they can be decomposed into pieces that look like typical geometric shapes (in this case, they resemble a torus and other types of three-manifolds).

In the context of topology and abstract algebra, an **extension** of a topological group refers to a way of constructing a new topological group from a known one by incorporating additional structure. This often involves creating a new group whose structure represents a combination of an existing group and a simpler group.

A homogeneous space is a mathematical structure that exhibits a high degree of symmetry. More formally, in the context of geometry and algebra, a homogeneous space can be defined as follows: 1. **Definition**: A space \(X\) is called a homogeneous space if for any two points \(x, y \in X\), there exists a symmetry operation (usually described by a group action) that maps \(x\) to \(y\).

A **monothetic group** is a term used in the context of taxonomy and systematics, particularly in the classification of organisms. It refers to a group of organisms that are united by a single common characteristic or a single attribute that defines that group. This characteristic is often a specific trait or combination of traits that all members of the group share, distinguishing them from organisms outside the group.

Cartan's theorems A and B are fundamental results in the theory of differential forms and the classification of certain types of differential equations, particularly within the context of differential geometry and the theory of distributions.

A relativistic particle refers to a particle that is moving at speeds close to the speed of light, where the effects of Einstein's theory of relativity become significant. In the realm of classical physics, particles are described by Newtonian mechanics, which assumes that velocities are much less than the speed of light. However, when particles approach relativistic speeds (typically a significant fraction of the speed of light, denoted as \(c\)), their behavior can no longer be accurately described by classical mechanics.

A Universal Linear Accelerator (ULA) is a type of particle accelerator that uses electromagnetic fields to accelerate charged particles, such as electrons, protons, or ions, in a straight line. The term "universal" suggests that this type of accelerator can be adapted for various applications and can accelerate different kinds of particles.