A Mackey space, named after George W. Mackey, is a concept in the field of functional analysis, particularly in relation to topological vector spaces. It is primarily defined in the context of locally convex spaces and functional analysis. A locally convex space \( X \) is called a Mackey space if the weak topology induced by its dual space \( X' \) (the space of continuous linear functionals on \( X \)) coincides with its original topology.
Maharam's theorem is a result in the field of measure theory, specifically dealing with the structure of measure spaces. It states that every complete measure space can be decomposed into a direct sum of a finite number of nonatomic measure spaces and a countably infinite number of points, which correspond to Dirac measures. In more specific terms, this theorem emphasizes the classification of complete σ-finite measures.
Mahler's inequality is a result in the field of functional analysis, particularly in relation to the norms of sequences and the behavior of sums in certain mathematical spaces.
The Mandelbox is a type of fractal, specifically a 3D fractal that is an extension of the Mandelbrot set. It was discovered by artist and mathematician Bert Wang. The Mandelbox fractal is generated using a combination of simple transformations and complex mathematical rules, primarily involving iterations of mathematical functions. The structure of the Mandelbox is notable for its intricate, self-similar shapes and the depth of detail that can be found within it, which can be zoomed into indefinitely.
The Mazur–Ulam theorem is a fundamental result in the field of functional analysis and geometry. It deals with the structure of isometries between normed spaces.
The Measurable Riemann Mapping Theorem is a result in complex analysis that deals with the existence of a conformal (angle-preserving) mapping from a domain in the complex plane onto another domain.
The Meyers–Serrin theorem is a result in the field of partial differential equations, specifically concerning weak solutions of parabolic equations. It provides conditions under which weak solutions exist and are defined in a specific sense. More precisely, the theorem establishes criteria for the existence of weak solutions to the initial boundary value problem for nonlinear parabolic equations. It relates to the properties of the spaces involved, particularly Sobolev spaces, and the concept of weak convergence.
Minlos's theorem is a result in the field of mathematical physics, particularly in the study of classical and quantum statistical mechanics. It concerns the existence of a certain kind of measure and the characterization of the states of a system described by a Gaussian field or process. More formally, Minlos's theorem provides conditions under which a Gaussian measure on the space of trajectories (or functions) can be constructed.
Mixed boundary conditions refer to a type of boundary condition used in the context of partial differential equations (PDEs), where different types of conditions are applied to different parts of the boundary of the domain. Specifically, a mixed boundary condition can involve both Dirichlet and Neumann conditions, or other types of conditions, imposed on different sections of the boundary.
The Mixed Finite Element Method (MFEM) is an extension of the standard finite element method (FEM) that allows for the simultaneous approximation of multiple variables, often with different types of equations or fields. This method is particularly useful in problems where the physical phenomena being modeled can be described by both scalar and vector quantities, or where certain variables are more conveniently expressed as functions that are not directly compatible with the usual finite element framework.
The Modified Korteweg-de Vries–Burgers (mKdV-Burgers) equation is a mathematical model that combines features of both the Korteweg-de Vries (KdV) equation, which is used to describe shallow water waves and other phenomena in fluid dynamics, and the Burgers equation, which accounts for viscous effects and is often used in the study of shock waves and turbulence.
The Modified Morlet wavelet is a commonly used wavelet in time-frequency analysis and signal processing, particularly in the context of analyzing non-stationary signals. A wavelet is a mathematical function that can be used to represent a signal at various scales and positions, allowing for the detection of localized features in time and frequency. ### Key Features of the Modified Morlet Wavelet: 1. **Structure**: The Modified Morlet wavelet is essentially a complex exponential modulated by a Gaussian function.
In the context of nonstandard analysis, a *monad* is a concept that generally relates to the ideas of "infinitesimals" and "restricted quantities." Nonstandard analysis is a branch of mathematics that extends standard analysis by introducing a rigorous way to handle infinitesimal and infinite quantities using structures called *hyperreal numbers*.
The Monge equation, often referred to in the context of optimal transport theory and differential geometry, describes the relationship between a function and its gradient in terms of a specific type of geometric problem. Specifically, in the context of optimal transport, the Monge-Ampère equation is one of the key equations studied.
The Monodromy matrix arises in the context of differential equations, particularly in the study of linear differential equations or systems of linear differential equations. It provides valuable information about the behavior of solutions as they are analytically continued along paths in the complex plane. ### Key Concepts: 1. **Differential Equations**: Consider a linear ordinary differential equation (ODE) or a system of linear differential equations.
Morrey–Campanato spaces are function spaces that generalize several important concepts in analysis, particularly in the study of differentiability properties of functions and partial differential equations. They are named after the mathematicians Carlo Morrey and Mario Campanato, who contributed to their development.
The Moseley snowflake is a type of fractal structure derived from a simple geometric process. It's named after the mathematician who studied its properties. Like other fractals, the Moseley snowflake is created by repeatedly applying a set of geometric rules. The construction of a typical snowflake fractal begins with a simple shape, such as a triangle. In each iteration of the process, smaller triangles are added to the sides of the existing shape, resulting in an increasingly complex and intricate design.
Motz's problem is a question in recreational mathematics named after mathematician John Motz. The problem typically asks whether it is possible to distribute a given number of objects (often identified in the context of combinatorial games or puzzles) in such a way that certain conditions or constraints are satisfied. One common formulation of Motz's problem involves partitioning a set of items or arranging them in configurations that follow specific rules, often leading to intriguing and complex patterns.
"N-jet" can refer to several things depending on the context, but it is often associated with a specific term in physics, particularly in high-energy particle physics and astrophysics. In particle physics, "N-jets" describes a situation in collider experiments where multiple jets of particles are produced in a single collision event.
The term "N-transform" can refer to different concepts depending on the context, such as in mathematics, engineering, or signal processing. However, one notable reference is to the **N-transform** used in the context of mathematical transforms, particularly in control theory and system analysis. Here are some possible interpretations of N-transform: 1. **Numerical Methods**: N-transform may refer to algorithms or methods for numerical solutions, particularly when dealing with differential equations or numerical integration.