In category theory, the concept of a **pushout** is a specific type of colimit that generalizes the idea of "gluing" objects together along a shared substructure. The pushout captures the idea of taking two objects that have a common part and combining them to form a new object.

Amari distance is a concept from information geometry and is used to measure the difference between two probability distributions. It is particularly relevant in the context of statistical inference and machine learning. The Amari distance is derived from the notion of the Bhattacharyya distance and employs the idea of the Fisher information metric. In a more formal sense, the Amari distance can be defined as a generalization of the Kullback-Leibler divergence.

Alexandre-Théophile Vandermonde (1735–1796) was a French mathematician known for his contributions to various fields, including algebra, combinatorics, and matrix theory. He is perhaps best known for the Vandermonde determinant and Vandermonde polynomial. The Vandermonde matrix is a type of matrix with the terms of a geometric progression in each row.

Isotypical representation is a concept that originates from category theory, particularly in the realm of algebraic topology and homotopy theory. It often relates to the study of morphisms and transformations between mathematical structures, allowing us to analyze the properties of these structures in a way that abstracts from their specific details. In a more concrete context, isotypical representations can refer to representations of algebraic structures (like groups) that are isomorphic in some sense, meaning that they exhibit similar properties or behaviors.

Hans Schneider is a noted mathematician known primarily for his work in linear algebra, matrix theory, and numerical analysis. He has made significant contributions to various areas of mathematics, including the study of matrices and their applications. Schneider has published numerous papers and has co-authored textbooks that are widely used in the field. Born in 1926, Schneider has had a long academic career, including positions at several universities.

The term "wild problem" typically refers to a type of problem that is complex, ill-defined, and difficult to solve using traditional methods. These problems often have uncertain or changing parameters, involve multiple stakeholders with differing perspectives, and may have no clear or definitive solutions. In a broader sense, "wild problems" can be linked to concepts in systems thinking, where interdependencies and feedback loops complicate problem-solving.

Gottfried Wilhelm Leibniz (1646–1716) was a prominent German polymath and philosopher known for his contributions to various fields, including philosophy, mathematics, and science. He is best known for co-developing calculus independently of Isaac Newton, and he introduced important concepts such as infinitesimal calculus, the notion of the derivative, and the integral.

Ivar Otto Bendixson (1861–1935) was a Norwegian mathematician known for his contributions to real analysis and calculus, particularly in the field of measure theory and the theory of functions of real variables. He is perhaps best known for the Bendixson-Debever theorem in the theory of differential equations and for his work on the properties of continuous functions. Bendixson's research laid important groundwork in areas that later influenced mathematical analysis and topology.

James Joseph Sylvester (1814–1897) was a prominent English mathematician known for his contributions to various fields, including algebra, matrix theory, and number theory. He played a pivotal role in the development of invariant theory and is credited with the introduction of several important concepts, such as Sylvester's law of inertia and the Sylvester matrix. Sylvester was also known for his work on determinants and his role in the early formation of the theory of linear transformations.

Moral conviction refers to the strong belief that a particular moral or ethical proposition is fundamentally and universally true, leading individuals to feel compelled to act according to that belief. It is characterized by an unwavering sense of right and wrong that deeply influences a person's thoughts, feelings, and behaviors. When people experience moral conviction, they often view their beliefs as non-negotiable and may feel a sense of duty to advocate for their values, sometimes even in the face of opposition.

In algebraic geometry, the notion of a morphism of finite type is a crucial concept used to describe the relationship between schemes or algebraic varieties. It gives a way to define morphisms that are "nice" in a certain sense, particularly in terms of the structure of the spaces involved.

The term "Butcher group" primarily refers to the mathematical structure known as the "Butcher group" in the context of numerical analysis, particularly in the field of solving ordinary differential equations (ODEs) using Runge-Kutta methods. Runge-Kutta methods are iterative techniques used to obtain numerical solutions to ODEs. The Butcher group specifically deals with the coefficients and structure of these methods. Named after the mathematician John C.

Multi-objective optimization is a type of optimization problem that involves simultaneously optimizing two or more conflicting objectives. Unlike single-objective optimization, where the goal is to find the best solution that maximizes or minimizes a single criterion, multi-objective optimization involves trade-offs between different objectives, as improving one objective may worsen another.

Multiple Displacement Amplification (MDA) is a method used to amplify DNA, particularly useful for generating large quantities of DNA from a small initial sample. This technique is especially valuable in fields such as genomics, forensics, and single-cell analysis, where starting material is often minimal.

The multiplicative group of integers modulo \( n \), often denoted as \( (\mathbb{Z}/n\mathbb{Z})^* \) or \( U(n) \), is the set of integers that are relatively prime to \( n \) under the operation of multiplication, with the multiplication performed modulo \( n \).

Multispectral optoacoustic tomography (MSOT) is an advanced imaging technique that combines optical and ultrasound technologies to provide detailed information about tissue composition and physiology. This method exploits the photoacoustic effect, where light is absorbed by tissue and subsequently converted into sound waves.

Municipalities in Croatia are the basic units of local self-government. As of the most recent administrative divisions, Croatia is divided into several tiers: counties (17 in total), cities (cities with special status, including the capital Zagreb), and municipalities. 1. **Counties**: Croatia is divided into 21 counties, which serve as the primary administrative subdivisions. They have their own governments and responsibilities.

Municipalities of Spain, known as "municipios" in Spanish, are the basic administrative divisions within the country. Spain is divided into 50 provinces, and each province is further divided into multiple municipalities. The municipalities are the third level of government, below the national and regional governments, and they play a crucial role in local administration and governance.

A musical clock is a type of clock that not only tells time but also plays music at specific intervals or on certain occasions. These clocks often include mechanical movements that allow them to chime or play melodies, usually on the hour or at other programmed times. They can be powered by mechanical means (like winding) or electrically. Musical clocks often feature intricate designs and craftsmanship, making them popular as decorative items as well as functional timepieces.

Charles Baudelaire, a prominent French poet best known for his collection "Les Fleurs du mal" ("The Flowers of Evil"), has inspired many composers and musicians over the years. Numerous musical settings of his poems can be found in various forms, including art songs (melodie), choral works, and orchestral pieces.