The Poincaré inequality is a fundamental result in mathematical analysis and partial differential equations. It provides a bound on the integral of a function in terms of the integral of its derivative.
Herbrand's theorem is an important result in mathematical logic, particularly in the field of model theory and proof theory. It connects syntactic properties of first-order logic formulas to semantic properties of their models. There are several formulations of Herbrand's theorem, but one of the most common versions concerns the existence of models for a set of first-order logic sentences. ### Herbrand's Theorem (Informal Statement) 1.
Novikov's Compact Leaf Theorem is a result in the field of differential topology, particularly in the study of foliations on smooth manifolds. It addresses the existence of compact leaves in a certain class of foliations, which are decompositions of a manifold into disjoint submanifolds called leaves.
The Flajolet Prize is an award given in recognition of outstanding contributions to the field of algorithmic research, specifically in the area of combinatorial algorithms and analysis of algorithms. It is named after Philippe Flajolet, a prominent researcher known for his work in combinatorics and algorithms. The prize is typically awarded at the International Conference on Analysis of Algorithms (ALA), where leading researchers in the field gather to present their work.
A formal language is a set of strings composed of symbols from a defined alphabet that follows specific syntactical rules or grammar. Unlike natural languages, which are used for everyday communication and can be ambiguous and variable, formal languages are precise and unambiguous. They are often used in mathematical logic, computer science, linguistics, and theoretical computer science. Key characteristics of formal languages include: 1. **Alphabet**: The basic set of symbols from which strings are formed.
Ellen Gould Zweibel is an American intellectual property attorney and a prominent figure in the field of intellectual property law. She is known for her expertise in various areas including patent law, copyright, and trademark issues. In addition to her legal practice, Zweibel has contributed to legal scholarship and education in intellectual property, often engaging with issues at the intersection of law and emerging technologies.
Ellen S. Stewart (1919–2011) was a notable American theater producer and the founder of La MaMa Experimental Theatre Club in New York City. Established in 1961, La MaMa became an influential venue for avant-garde and experimental theater, showcasing a diverse range of artists and productions. Stewart was known for her commitment to nurturing new talent and providing a platform for innovative works that often addressed social issues and varied cultural perspectives.
Ana Claudia Arias is an American professor and researcher known for her work in the fields of materials science and engineering, specifically in areas related to nanotechnology and nanomaterials. She is associated with the University of California, Los Angeles (UCLA), where she conducts research and teaches. Arias's work often focuses on applications of nanomaterials in various fields, including energy, electronics, and biotechnology.
Amos Dolbear is a name associated with several significant achievements, primarily in the fields of science and technology. Most notably, Amos Emerson Dolbear (1837–1910) was an American inventor, physicist, and educator. He is best known for his work in electricity and telecommunications, especially for his contributions to the development of the telephone.
The Fraňková–Helly selection theorem is a result in the field of functional analysis and topology, specifically concerning the selection of points from family of sets. It builds upon the classical Helly's theorem, which deals with finite intersections of convex sets in Euclidean spaces. The Fraňková–Helly selection theorem provides conditions under which one can extract a sequence from a family of sets that converges in a certain sense.
Fuchs' theorem is a result in the field of complex analysis, particularly in the study of ordinary differential equations with singularities. The theorem provides conditions under which a linear ordinary differential equation with an irregular singular point can be solved using power series methods. Specifically, Fuchs' theorem states that if a linear differential equation has only regular singular points, then around each regular singular point, there exist solutions that can be expressed as a Frobenius series.
The Gaussian integral refers to the integral of the function \( e^{-x^2} \) over the entire real line.
Godunov's theorem is a result in the field of numerical analysis, specifically related to the numerical solution of hyperbolic partial differential equations (PDEs). It is named after the Russian mathematician S. K. Godunov, who contributed significantly to the development of finite volume methods for solving these types of equations.
Holmgren's uniqueness theorem is a result in the theory of partial differential equations (PDEs), particularly concerning elliptic equations. It addresses the uniqueness of solutions to certain boundary value problems.
Jensen's inequality is a fundamental result in convex analysis and probability theory that relates to convex functions.
The Khintchine inequality is a result in mathematical analysis, particularly in the study of probability theory and functional analysis. It pertains to the properties of sums of independent random variables, specifically regarding their expected values and moments.
Komlós' theorem, also known as Komlós' conjecture, is a result in combinatorial mathematics, specifically in the field of graph theory. The theorem deals with the concept of almost perfect matchings in large graphs.
The Lagrange reversion theorem is a result in mathematical analysis and combinatorics that relates to the coefficients of a power series. More specifically, it provides a method to express the coefficients of the inverse of a power series in terms of the coefficients of the original series.
Malmquist's theorem, also known as the Malmquist interpolation theorem, is a result in the field of complex analysis and functional analysis that pertains to the behavior of holomorphic functions. Specifically, it addresses the existence of holomorphic functions defined on a certain domain that agree with prescribed values on a collection of points.
The Peano existence theorem, often referred to in the context of ordinary differential equations (ODEs), is a fundamental result that provides conditions under which solutions to certain initial value problems exist.