An **integral domain** is a specific type of algebraic structure in the field of abstract algebra. It is defined as a non-zero commutative ring with certain properties.

A Puiseux series is a type of power series that allows for fractional exponents and is used in algebraic geometry and the study of singularities. It can be thought of as a generalization of the Taylor series or Laurent series.

Stanley decomposition is a concept related to combinatorial geometry and enumerative combinatorics, specifically in the context of polyhedral combinatorics. It is named after Richard P. Stanley, a prominent mathematician who has made significant contributions to these fields. The Stanley decomposition provides a way to express a polyhedron, especially a convex polytope, as a combination of combinatorial objects, typically through the use of face lattices.

The Price of Anarchy (PoA) is a concept from game theory, particularly in the context of auctions and other competitive scenarios. It measures how the efficiency of a given outcome in a strategic game (where players act out of self-interest) compares to the optimal outcome that could be achieved if all players acted in a cooperative manner.

Geometry in computer vision refers to the study and application of geometric principles to understand, interpret, and manipulate visual data captured from the real world. It plays a crucial role in various tasks and algorithms that involve shape, position, and the three-dimensional structure of objects. Here are some key aspects of how geometry is applied in computer vision: 1. **Image Formation**: Geometry helps in understanding how a three-dimensional scene is projected onto a two-dimensional image sensor. This includes knowledge about camera models (e.

Random graphs are mathematical structures used to model and analyze networks where the connections between nodes (vertices) are established randomly according to specific probabilistic rules. They are particularly useful in the study of complex networks, social networks, biological networks, and many other systems where the relationships between entities can be represented as graphs. ### Key Concepts in Random Graphs: 1. **Graph Definition**: A graph consists of nodes (or vertices) and edges (connections between pairs of nodes).

A Narcissistic number, also known as a pluperfect digital invariant (PDI), is a number that is equal to the sum of its own digits each raised to the power of the number of digits. In simpler terms, for a number \( n \), it can be expressed as: \[ n = d_1^p + d_2^p + d_3^p + ... + d_k^p \] where \( d_1, d_2, ...

"Beef Trust" is a burlesque show that typically revolves around themes of meat or butchery, often incorporating humor, satire, and various performance art elements. Burlesque itself is a style of theatrical entertainment that combines comedy, music, dance, and striptease, usually with a playful and risqué twist.

Béla Szőkefalvi-Nagy (1928–2018) was a Hungarian mathematician known for his contributions to functional analysis, particularly in the area of operator theory. He is recognized for his work on the theory of unbounded operators and spectral theory, as well as for the development of various mathematical concepts and techniques.

square, cube. 4D case known as tesseract.

Convex hull of all $\{-1,1{\}}^D$ (Cartesian product power) D-tuples, e.g. in 3D:

From this we see that there are $2^D$ vertices.

Two vertices are linked iff they differ by a single number. So each vertex has D neighbors.

Belgrade is the capital and largest city of Serbia, located at the confluence of the River Sava and the River Danube. It has a rich history that dates back to prehistoric times, and it has been a significant cultural, economic, and political center in the region for centuries. Belgrade's architecture reflects its diverse history, featuring a mix of historic buildings, such as those from the medieval and Ottoman periods, alongside modern structures.

The non-regular version of the hypercube.

Dragonfly 44 is a galaxy located about 330 million light-years away from Earth in the constellation Coma Berenices. It gained attention in the astronomical community due to its unusual characteristics; specifically, it is a massive, nearly invisible galaxy that contains a very large amount of dark matter. Dragonfly 44 was discovered in 2016 as part of the Dragonfly Telephoto Array project, which aimed to identify faint, diffuse galaxies.

GLASS-z12 is a distant galaxy that was identified in a study related to the GLASS (Gravitational Lensing Australian Space Observatory) project. This galaxy is significant because it is one of the earliest known galaxies observed, believed to have formed just 400 million years after the Big Bang. Researchers consider it to be a key object of study for understanding galaxy formation and evolution in the early universe.