The Unique Homomorphic Extension Theorem is a result in the field of algebra, particularly concerning rings and homomorphisms. It typically states that if you have a ring \( R \) and a subring \( S \), along with a homomorphism defined on \( S \), then there exists a unique (in the case of certain conditions) homomorphic extension of this mapping up to the whole ring \( R \).

The Whitney extension theorem is a fundamental result in the field of analysis and differential geometry, concerning the extension of functions defined on a subset of a Euclidean space to the entire space while preserving certain properties.

In computational complexity theory, a theorem typically refers to a proven statement or result about the inherent difficulty of computational problems, particularly concerning the resources required (such as time or space) for their solution.

Friedman's SSCG (Stochastic Simulation and Control Game) function is a concept used in the context of economics and decision theory, particularly related to dynamic programming and optimal control. The SSCG function is often utilized to model and analyze strategic interactions and decisions under uncertainty. The exact formulation of the SSCG function can vary, but it typically involves aspects of stochastic processes, where outcomes depend not only on the current state and action but also on random events that can influence future states.

The Poincaré–Bendixson theorem is a fundamental result in the field of dynamical systems, particularly concerning the behavior of continuous dynamical systems in two dimensions. It addresses the long-term behavior of trajectories in a planar (2-dimensional) system described by a set of ordinary differential equations.

Blichfeldt's theorem is a result in the field of number theory, specifically in the study of lattice points and their distributions. Named after the mathematician A.B. Blichfeldt, the theorem deals with the packing of points in a convex geometry context.

The Hyperbolization Theorem is a result in the field of topology and geometric group theory, specifically concerning the characteristics of 3-manifolds. It states that any compact, orientable 3-manifold that contains a certain type of submanifold (specifically, a “reducible” submanifold or one that can be "hyperbolized") can be decomposed into pieces that exhibit hyperbolic geometry.

The Barwise Compactness Theorem is a result in model theory, specifically concerning first-order logic and structures. It extends the concept of compactness, which states that if every finite subset of a set of first-order sentences has a model, then the entire set has a model. The Barwise Compactness Theorem applies this idea to certain kinds of structures known as "partial structures.

Sharkovskii's theorem is a result in the field of dynamical systems, particularly concerning the behavior of continuous functions on the unit interval \([0, 1]\) and the periodic points of these functions. The theorem provides a remarkable ordering of natural numbers that relates to the existence and types of periodic points in continuous functions.

Geometric inequalities are mathematical statements that establish relationships between different geometric quantities, such as lengths, areas, angles, and volumes. These inequalities often provide useful bounds or constraints on these quantities and can be applied in various fields, including geometry, optimization, and analysis. Some common types of geometric inequalities include: 1. **Triangle Inequalities**: In any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Hirschberg's algorithm is a dynamic programming approach used for finding the longest common subsequence (LCS) of two sequences. It is particularly notable for its efficiency in terms of space complexity, using only linear space instead of the quadratic space that naive dynamic programming approaches require. ### Overview of the Algorithm: Hirschberg's algorithm is based on the principle of dividing and conquering.

Theorems in plane geometry are propositions or statements that can be proven based on axioms, definitions, and previously established theorems. Plane geometry deals with flat, two-dimensional surfaces and includes the study of points, lines, angles, shapes (such as triangles, quadrilaterals, and circles), and their properties.

As of my last knowledge update in October 2023, "Discoveries" by Hannes Bachleitner does not appear to be widely recognized or referenced in prominent sources.

Theorems about curves cover a vast range of topics in mathematics, particularly in geometry, calculus, and topology. Here are some key theorems and concepts associated with curves: 1. **Fermat's Last Theorem for Curves**: While Fermat's Last Theorem primarily concerns integers, there are generalizations and discussions about elliptic curves in number theory that relate deeply to the properties of curves.

A cubic centimetre (cm³ or cc) is a unit of volume that is commonly used in the metric system. It is defined as the volume of a cube that has sides measuring one centimetre in length. 1 cubic centimetre is equivalent to: - 1 millilitre (mL) - \(10^{-6}\) cubic metres (m³) - Approximately 0.

Pappus's centroid theorem, named after the ancient Greek mathematician Pappus of Alexandria, is a principle concerning the geometry of figures in relation to their centroids (or centroids). It actually consists of two related theorems, often referred to as Pappus's centroid theorems.

The Petersen–Morley theorem is a result in graph theory that concerns the structure of certain types of graphs. It states that for every sufficiently large graph, if it contains no complete subgraph \( K_n \) of size \( n \), then the graph can be colored with \( n-1 \) colors such that no two adjacent vertices share the same color. The theorem is particularly relevant when discussing the properties of planar graphs and colorability.

The term "bridging model" can refer to different concepts in various fields, including sociology, education, and business, among others. Below are a few contexts where the bridging model might be applied: 1. **Sociology and Social Networks**: In social network theory, a bridging model refers to how certain individuals (or nodes) act as bridges between different groups or communities.

The Riemannian Penrose inequality is a result in differential geometry and general relativity that relates the total mass of a Riemannian manifold with boundary to the area of its boundary. It is an extension of the classical Penrose inequality, which is a key result in the theory of general relativity regarding the mass of gravitational systems.