Shellac is an American rock band formed in 1992, known for their distinctive sound that blends elements of post-hardcore and noise rock. They feature a minimalist style with concise song structures and a rhythmic, percussive approach to guitar and bass. The band consists of Steve Albini (vocals, guitar), Bob Weston (bass, vocals), and Todd Trainer (drums, vocals).
William Crookes (1832–1919) was a prominent English chemist and physicist known for his work in a variety of fields, including chemistry, physics, and the study of psychic phenomena. He is perhaps best known for the invention of the Crookes tube, an early experimental electrical discharge tube that played a significant role in the development of atomic physics and the study of cathode rays, which eventually led to the discovery of electrons by J.J. Thomson.
"We Be the Echo" is a creative collective and community-focused initiative that aims to amplify the voices and stories of marginalized communities, particularly those in urban environments. It serves as a platform for artists, activists, and community members to share their experiences and challenges, fostering dialogue and collaboration. The collective often utilizes various forms of media, including art, music, and public events, to engage audiences and promote social change.
A bilinear quadrilateral element is a type of finite element used in numerical methods for solving partial differential equations (PDEs) in two dimensions. It is particularly popular in the finite element method (FEM) for structural and fluid problems. The key characteristics of bilinear quadrilateral elements include: ### Shape and Nodes - **Geometry**: A bilinear quadrilateral element is defined in a rectangular (quadrilateral) shape, typically with four corners (nodes).
The Bishop–Phelps theorem is a result in functional analysis that addresses the relationship between the norm of a continuous linear functional on a Banach space and the structure of the space itself. More specifically, it deals with the existence of points at which the functional attains its norm.
The Bohr–Favard inequality is a result in analysis that applies to integrable functions. It is named after the mathematicians Niels Henrik Abel and Pierre Favard. The inequality concerns the behavior of functions and their integrals, particularly in the context of convex functions and the properties of the Lebesgue integral.
Borchers algebra refers to a mathematical framework introduced by Daniel Borchers in the context of quantum field theory. It arises notably in the study of algebraic quantum field theory (AQFT), where the focus is on the algebraic structures that underpin quantum fields and their interactions. In Borchers algebra, one typically deals with specific types of algebras constructed from the observables of a quantum field theory. These observables are collections of operators associated with physical measurements.
The Favard operator is an integral operator used in the field of functional analysis and approximation theory. It is typically associated with the approximation of functions and the study of convergence properties in various function spaces. The operator is used to construct a sequence of polynomials that can approximate continuous functions, particularly in the context of orthogonal polynomials. The Favard operator can be defined in a way that it maps continuous functions to sequences or series of polynomials by integrating against a certain measure.
The Fekete–Szegő inequality is a result in complex analysis and functional analysis concerning analytic functions. It is primarily related to bounded analytic functions and their behavior on certain domains, particularly the unit disk.
Fernique's theorem is a result in probability theory, particularly in the context of Gaussian processes and stochastic analysis. It deals with the continuity properties of stochastic processes, specifically the continuity of sample paths of certain classes of random functions.
Hadamard's method of descent, developed by the French mathematician Jacques Hadamard, is a technique used in the context of complex analysis and number theory, particularly for studying the growth and distribution of solutions to certain problems, such as Diophantine equations and modular forms. The method relies on the concept of reducing a problem in higher dimensions to a problem in lower dimensions (hence the term "descent").
A holomorphic curve is a mathematical concept from complex analysis and algebraic geometry. Specifically, it refers to a curve that is defined by holomorphic functions. Here’s a breakdown of what this means: 1. **Holomorphic Functions**: A function \( f: U \rightarrow \mathbb{C} \) is called holomorphic if it is complex differentiable at every point in an open subset \( U \) of the complex plane.
William Eccles (1903–1998) was an English physicist known for his contributions to the fields of physics and engineering, particularly in the study of electrical circuits and equipment. He is perhaps best recognized for his work on the development of the concept of the "Eccles-Jordan trigger circuit," which he co-developed with his colleague F. W. Jordan.
Cyclic reduction is a mathematical and computational technique primarily used for solving certain types of linear systems, particularly those that arise in numerical simulations and finite difference methods for partial differential equations. This method is particularly effective for problems that can be defined on a grid and involve periodic boundary conditions. ### Key Features of Cyclic Reduction: 1. **Matrix Decomposition**: Cyclic reduction typically involves breaking down a large matrix into smaller submatrices.
The Denjoy–Luzin–Saks theorem is a significant result in the field of real analysis, particularly in the theory of functions and their integrability. The theorem deals with the conditions under which a measurable function can be approximated by simple functions.
A **differential manifold** is a mathematical structure that generalizes the concept of curves and surfaces to higher dimensions, allowing for the rigorous study of geometrical and analytical properties in a flexible setting. Each manifold is locally resembling Euclidean space, which means that around each point, the manifold can be modeled in terms of open subsets of \( \mathbb{R}^n \).
Drinfeld reciprocity is a key concept in the field of arithmetic geometry and number theory, particularly in the study of function fields and their extensions. It is named after Vladimir Drinfeld, who introduced it in the context of his work on modular forms and algebraic structures over function fields. The concept can be viewed as an analogue of classical reciprocity laws in number theory, such as the law of quadratic reciprocity, but applied to function fields instead of number fields.
The Drinfeld upper half-plane is a mathematical construct that arises in the context of algebraic geometry and number theory, particularly in the study of modular forms and Drinfeld modular forms. It is an analogue of the classical upper half-plane in the theory of classical modular forms but is defined over fields of positive characteristic. ### Definition 1.
The Eden growth model, also known as the Eden process or the Eden model, is a concept in statistical physics and mathematical modeling that describes the growth of clusters or patterns in a stochastic (random) manner. It was first introduced by the physicist E. D. Eden in 1961.