A Van Kampen diagram is a combinatorial tool used in group theory, particularly in the study of the word problem for groups. It is named after the Dutch mathematician Egbert van Kampen. The diagram is often employed in the context of the word problem for finitely presented groups and the geometrical interpretation of group presentations. In general, a Van Kampen diagram is a specified type of two-dimensional polygonal diagram that represents a relation in a group presentation.

A colored matroid is a generalization of the concept of a matroid that incorporates additional structure based on colors. In a standard matroid, the focus is on independent sets of elements with certain combinatorial properties, typically defined via rank and independence axioms. A colored matroid extends this framework by assigning colors to the elements.

A **shortest-path tree** is a type of data structure used in graph theory that represents the shortest paths from a single source vertex to all other vertices in a weighted graph. The shortest-path tree is a subtree of the graph and satisfies the property that for any vertex in the tree, the path from the source vertex to that vertex is the shortest possible path in the graph. ### Key Characteristics: 1. **Source Vertex**: The node from which the shortest paths originate.

A Dudeney number is a special kind of integer that is both a perfect cube and the sum of its digits equals the cube root of the number itself. In mathematical terms, a Dudeney number \( n \) satisfies the condition: \[ n = a^3 \quad \text{and} \quad \text{sum of the digits of } n = a \] where \( a \) is a positive integer.

A "uniform tree" can refer to a couple of different concepts depending on the context, but generally, it often relates to structures in mathematics and computer science. 1. **In Graph Theory:** A uniform tree can refer to a type of tree graph where all levels of the tree (except possibly the last one) have the same number of children (uniform branching). For example, a binary tree is uniform because each node has exactly 2 children.

"Ars Magna Lucis et Umbrae," which translates to "The Great Art of Light and Shadow," is a treatise written by the 17th-century German Jesuit scholar Athanasius Kircher. Published in 1671, it focuses on optical science and the principles of light, shadow, and perspective. The work combines elements of philosophy, theology, and science, reflecting Kircher's fascination with various fields of knowledge and his efforts to explain the natural world.

"Oedipus Aegyptiacus" is a work by the German philosopher and cultural historian Georg Wilhelm Friedrich Hegel, published in the early 19th century. It deals with the representation of Egyptian culture and its influence on the development of Western thought and civilization. The title plays on the figure of Oedipus from Greek mythology, who is often associated with themes of fate, knowledge, and identity, and it connects these themes to the ancient Egyptian context.

The Brusselator is a mathematical model used to describe a reaction-diffusion system, particularly in the context of chemical kinetics. It was introduced by the Belgian physicists Ilya Prigogine and his collaborators in their studies of nonlinear dynamic systems. The Brusselator model is a simplified representation of autocatalytic reactions, where the autocatalytic processes lead to the emergence of complex behaviors such as oscillations and pattern formation.

In graph theory, a **clique cover** of a graph is a partition of the vertex set into cliques. A **clique** is a subset of vertices that forms a complete subgraph, meaning every pair of vertices within the subset is connected by an edge. Therefore, a clique cover is a way to divide the graph's vertices into groups where each group is a clique.

In graph theory, a **dominating set** for a graph \( G = (V, E) \) is a subset \( D \subseteq V \) of the vertices such that every vertex not in \( D \) is adjacent to at least one vertex in \( D \).

"Nonblocker" can refer to different concepts depending on the context in which it is used. However, it is not a widely recognized term in a specific field. Here are some potential interpretations: 1. **In Computing**: It could refer to a system or component that doesn't block the execution of processes or threads, allowing multiple operations to occur simultaneously without waiting for previous ones to finish. This concept is often important in non-blocking algorithms or asynchronous programming.

Spatial bifurcation refers to a phenomenon in dynamical systems where the stability and structure of solutions change as parameters vary, specifically within spatially extended systems. This concept is widely used in fields such as physics, biology, and ecology, where the spatial distribution of a system's components plays a crucial role in its behavior. In a typical bifurcation scenario, the system might exhibit different behaviors or patterns (such as periodic structures, waves, or steady states) in different regions of space.

An Arnold tongue is a concept from dynamical systems and theoretical physics, particularly in the study of nonlinear systems and bifurcations. It describes the regions of stability for periodic orbits in a nonlinear dynamical system as a function of two parameters, typically representing frequency and amplitude of a driving force. The term "Arnold tongue" is named after the mathematician Vladimir Arnold, who explored these systems.

BC Brno is a basketball club based in Brno, Czech Republic. The team has a history of participating in various international competitions, including tournaments such as the FIBA EuroCup, the Champions League, and others that include clubs from across Europe. BC Brno has a notable presence in the Czech basketball league and has been competitive on the international stage as well. The club's involvement in these competitions provides opportunities for showcasing talent and gaining experience against a variety of teams from different countries.

Diastole is the phase of the cardiac cycle during which the heart muscle relaxes and the chambers of the heart fill with blood. It occurs after systole, which is the phase when the heart muscles contract to pump blood out of the heart. Diastole is crucial for ensuring that the heart has enough blood to pump out during the next contraction.