Symmetric convolution is a specific type of convolution operation that maintains symmetry in its kernel or filter. In general, convolution is a mathematical operation that combines two functions to produce a third function. It is commonly used in signal processing, image processing, and various fields of mathematics and engineering.

In topology and algebra, a **topological homomorphism** generally refers to a mapping between two topological spaces that preserves both algebraic structure (if they have one, like being groups, rings, etc.) and the topological structure. The term is often used in the context of topological groups, where the objects involved have both a group structure and a topology.

A **pseudo-functor** is a generalization of the concept of a functor in category theory, designed to handle situations where some structure is retained but strictness is relaxed. In formal category theory, functors map objects and morphisms from one category to another while preserving the categorical structure (identity morphisms and composition of morphisms). Pseudo-functors, however, allow for certain flexibility in this structure.

A weak order, in the context of mathematics and decision theory, refers to a type of preference relation that is characterized by a transitive and complete ordering of elements, but allows for ties. In the context of utility and choice theory, weak orders enable the representation of preferences where some options may be considered equally favorable. A weak order unit typically refers to the elements or alternatives that are being compared under this ordering system.

Crystallography is the scientific study of crystals and their structures. It involves analyzing the arrangement of atoms within solid materials, particularly in crystalline substances where atoms are arranged in a highly ordered, repeating pattern. Crystallography plays a crucial role in various fields, including chemistry, physics, biology, and materials science. Key aspects of crystallography include: 1. **X-ray Diffraction**: This is one of the primary techniques used in crystallography.

In category theory, an **amnestic functor** is a type of functor that exhibits a specific relationship with respect to the preservation of certain structures. The concept may not be as widely recognized as other notions in category theory, and it's important to clarify that terms might differ slightly based on the context in which they are used.

Wetzel's problem is a question in mathematical logic and set theory, specifically related to the properties of functions and sets. It was posed by the mathematician David Wetzel in the context of exploring the properties of certain types of functions.

In the context of computer science, a **functor** is a design pattern that originates from category theory in mathematics. It is a type that can be mapped over, which means it implements a mapping function that applies a function to each element within its context. ### In Programming Languages 1.

In category theory, the Hom functor is a fundamental concept used to describe morphisms (arrows) between objects in a category. Specifically, given a category \(\mathcal{C}\), the Hom functor allows us to examine the set of morphisms between two object types. ### Definition 1.

Lenticular galaxies are a type of galaxy that possess features of both spiral and elliptical galaxies. They are characterized by a central bulge and a disk-like structure but lack the distinct spiral arms typically found in spiral galaxies. Lenticular galaxies are categorized as "S0" in the Hubble sequence of galaxy classification.

Ring galaxies are a type of galaxy characterized by a prominent ring-like structure surrounding a central core. These galaxies typically have a distinct, well-defined ring of stars, gas, and dust that forms either as a result of gravitational interactions during collisions or mergers with other galaxies or as a result of internal processes.

A1689-zD1 is a distant galaxy that has garnered significant attention in astronomical studies due to its remarkable properties. It is located in the galaxy cluster Abell 1689, which is about 2.2 billion light-years away from Earth. The designation "zD1" refers to its redshift, which is a measure of how much the light from the galaxy has been stretched due to the expansion of the universe.

Sergei Odintsov is likely a reference to a prominent Russian researcher and scientist known for his work in theoretical physics, particularly in the fields of cosmology and gravitation. He has contributed to various studies related to dark energy, modified theories of gravity, and cosmological models.

DLA0817g, also known as DLA0817g-1, is a distant astronomical object classified as a quasar, which is an extremely luminous active galactic nucleus powered by a supermassive black hole. It was discovered in 2018 and is notable for being one of the most distant quasars known, with a redshift of approximately 7.54. This implies that the light we observe from DLA0817g has taken around 13.

A dark matter halo is a theoretical structure that surrounds galaxies and galaxy clusters, comprising a significant portion of their total mass. Dark matter, which does not emit, absorb, or reflect light and is therefore invisible to electromagnetic observations, is inferred to exist based on its gravitational effects on visible matter.

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.

Sergey Gulev is a prominent Russian oceanographer known for his contributions to the field of marine science, particularly in areas such as ocean circulation, climate change, and the study of marine ecosystems. He has been involved in research related to the dynamics of the world's oceans and their impact on global climate systems.

Lists of galaxies are compilations of galaxies categorized and organized based on various criteria such as their type, location in the sky, or other characteristics. These lists can include well-known galaxies, like the Milky Way and Andromeda, as well as more obscure ones. Here are a few common ways galaxies are organized in lists: 1. **By Type**: Galaxies can be classified into types based on their shape and structure, such as: - Spiral galaxies (e.g.

NGC 5501 is a spiral galaxy located in the constellation Ursa Major. It is part of a larger group known as the NGC 5500 group of galaxies. NGC 5501 is characterized by its bright nucleus and well-defined spiral structure, which makes it a subject of interest for astronomers studying galaxy formation and evolution. This galaxy is roughly 70 million light-years away from Earth and has a diameter of about 100,000 light-years.