The AKNS system, short for the Ablowitz-Kaup-Newell-Segur system, refers to a well-known integrable system of nonlinear partial differential equations (PDEs) that arises in the context of fluid dynamics, optics, and other fields in applied mathematics and mathematical physics. The AKNS system is typically associated with the nonlinear Schrödinger equation and can be represented in a matrix form.

"Statistics stubs" generally refers to short or incomplete articles related to statistical concepts, methods, or data that are typically found on platforms like Wikipedia. These stubs usually contain minimal information about a topic, serving as a placeholder for more detailed content to be developed later. In the context of Wikipedia, a "stub" can encourage users to expand on the topic by providing additional information, references, and context.

In the context of Wikipedia and other collaborative encyclopedic platforms, a "stub" is a short or incomplete article that could be expanded to provide more detailed and comprehensive information. Stub templates are predefined snippets of code that editors can add to articles to indicate that the content is insufficient and invite users to contribute more information. Mathematics stub templates specifically refer to stubs related to mathematical topics. They are used to flag articles that need improvement in order to meet the standards of a full, informative entry.

Uniform tilings in the hyperbolic plane are arrangements of hyperbolic shapes that cover the entire hyperbolic plane without any gaps or overlaps while exhibiting a regular and repeating pattern. These tilings are characterized by their symmetry and regularity, often defined by their vertex configuration and the types of shapes used in the tiling. In mathematical terms, a uniform tiling can be described as a tessellation of the hyperbolic plane using polygonal shapes that can be generalized by their vertex configurations.

The Table of Lie Groups consists of a classification of Lie groups based on their dimension and properties. Lie groups are smooth manifolds that also have a group structure, and they play a significant role in various areas of mathematics and theoretical physics, particularly in the study of symmetries. There are several types of Lie groups, but they can generally be categorized into a few main classes. Here’s a simplified overview: 1. **Compact Lie Groups**: These groups are closed and bounded.

The outline of statistics typically refers to the organization and structure of statistical concepts, methods, and applications. Below is a general outline of statistics that encompasses its key areas: ### 1. Introduction to Statistics - Definition of Statistics - Importance of Statistics - Types of Statistics: Descriptive and Inferential ### 2. Data Collection - Types of Data: Qualitative vs.

Nikolay Bogolyubov was a prominent Soviet and Russian mathematician and theoretical physicist known for his contributions to various fields, including statistical mechanics, quantum field theory, and many-body physics. He authored or co-authored numerous papers, books, and articles throughout his career.

The philosophy of computer science is a branch of philosophy that examines the foundational concepts and implications of computer science, technology, and computational practices. It investigates questions not only about the nature of computation and algorithms but also their ethical, social, and epistemological dimensions. Here are some key areas of focus within this field: 1. **Nature of Computation**: Philosophers explore what it means for something to be computable.

The list of uniform polyhedra refers to a classification of polyhedra that are highly symmetrical, including both regular polyhedra (Platonic solids) and less regular forms that still exhibit a uniform structure. These polyhedra are defined by having faces that are composed of regular polygons and all vertices having the same type of arrangement of faces.

Systems theory is an interdisciplinary study that emphasizes the relationships and interactions within and between systems. It has applications in various fields, including biology, engineering, social sciences, environmental science, and management. Here’s a list of different types or branches of systems theory: 1. **General Systems Theory**: Proposed by Ludwig von Bertalanffy, it focuses on the common principles that govern all systems, regardless of their nature.

The term "list of transforms" can refer to various contexts, especially in mathematics, computer science, and signal processing. Below are some interpretations of what a "list of transforms" could entail: ### 1. Mathematical Transforms: - **Fourier Transform**: Converts a function of time (or space) into a function of frequency. - **Laplace Transform**: Used to analyze linear time-invariant systems, transforming a function of time into a complex frequency domain.

A **repunit** is a number consisting entirely of the digit 1. For example, the numbers 1, 11, 111, 1111, and so forth are repunits. The mathematical representation of a repunit \( R_n \) is given by: \[ R_n = \frac{10^n - 1}{9} \] where \( n \) is the number of digits (or "ones") in the repunit.

The properties of sets of real numbers encompass a variety of concepts from topology, measure theory, and real analysis. Here is a summary of some key properties and classifications of sets of real numbers: 1. **Countable vs. Uncountable**: - **Countable Set**: A set is countable if it is finite or can be put in a one-to-one correspondence with the natural numbers (e.g., the set of rational numbers).

Price indices are used to measure the relative change in the price level of a basket of goods and services over time. They are essential for economic analysis and inform various economic policies.

A list of polyhedral stellations refers to various polyhedra that can be created by extending the faces, edges, or vertices of a given polyhedron. Stellations can produce more complex shapes from simple ones, often resulting in fascinating geometric structures.

Planar symmetry groups refer to the mathematical groups that describe the symmetries present in two-dimensional shapes. These groups capture how a pattern can be transformed through rotations, translations, reflections, and glide reflections while preserving its overall structure. The main types of planar symmetry groups can be categorized into: 1. **Cyclic Groups (C_n)**: These consist of rotations about a point. For example, C_3 corresponds to a triangle where you can rotate the shape 120 degrees.

Numerical libraries are essential tools in programming that provide functions for numerical computing, data manipulation, and scientific calculations. Here’s a list of some popular numerical libraries across various programming languages: ### Python 1. **NumPy**: Fundamental package for numerical computations in Python. 2. **SciPy**: Builds on NumPy and provides additional functionality for optimization, integration, and statistics. 3. **Pandas**: Provides data structures for efficiently storing and manipulating large datasets.

Numerical analysis software encompasses a wide range of applications and programming environments used to perform numerical computations. Here’s a list of some popular numerical analysis software packages: 1. **MATLAB**: A high-level language and interactive environment for numerical computation, visualization, and programming. It includes numerous built-in functions for numerical analysis. 2. **NumPy/SciPy**: Open-source libraries for Python.

Relativity, both special and general, involves a variety of mathematical concepts and techniques. Here's a list of key mathematical topics commonly associated with relativity: ### 1. **Geometry** - **Differential Geometry**: Understanding curved spaces, manifolds, and tensors. - **Riemannian Geometry**: Study of curved surfaces and spaces, including concepts of curvature. - **Symplectic Geometry**: Sometimes used in the context of classical and quantum mechanics.

A hand pump is a manually operated device used to move fluids, typically water, from one place to another. It uses human effort to create a vacuum or pressure that allows fluids to be drawn up from a source, such as a well or a container, and transferred to another location. Hand pumps can vary in design, but they generally consist of the following components: 1. **Cylinder**: A chamber where the fluid is drawn in and expelled.