In mathematics, a filtration F {\displaystyle {\mathcal {F}}} is an indexed family ( S i ) i ∈ I {\displaystyle (S_{i})_{i\in I}} of subobjects of a given...

usual hypotheses or the usual conditions. Natural filtration Filtration (mathematics) Filter (mathematics) Klenke, Achim (2008). Probability Theory. Berlin:...

point of an ultrafilter is a limit point. Filtration (mathematics) – Indexed set in mathematics Filtration (probability theory) – Model of information...

(stochastic processes), a mathematical model for a number of filtering problems in signal processing and the like. Filtration (mathematics), an indexed set of...

processes in mathematics and statistics, the generated filtration or natural filtration associated to a stochastic process is a filtration associated to...

corresponds to the ordering ( 0 , 1 , 2 ) {\displaystyle (0,1,2)} . Filtration (mathematics) Flag manifold Grassmannian Matroid Kostrikin, Alexei I. and Manin...

known as glomerular filtration. A major measure of kidney function is the glomerular filtration rate (GFR). The glomerular filtration rate is the flow rate...

algebra of a group with a length function is a filtered algebra. Filtration (mathematics) Length function Abe, Eiichi (1980). Hopf Algebras. Cambridge:...

thoracic duct which empties into the great veins close to the heart. Filtration from plasma to interstitial (or tissue) fluid occurs in microvascular...

filtration known as Čech filtration. A similar construction uses a nested sequence of Vietoris–Rips complexes known as the Vietoris–Rips filtration....

In mathematics, a Hodge structure, named after W. V. D. Hodge, is an algebraic structure at the level of linear algebra, similar to the one that Hodge...

respect to an underlying filtration. BSDEs naturally arise in various applications such as stochastic control, mathematical finance, and nonlinear Feynman-Kac...

Gravity filtration is a method of filtering impurities from solutions by using gravity to pull liquid through a filter. The two main kinds of filtration used...

In mathematical representation theory, a good filtration is a filtration of a representation of a reductive algebraic group G such that the subquotients...

In mathematics, especially in the area of algebraic topology known as stable homotopy theory, the Adams filtration and the Adams–Novikov filtration allow...

The offset filtration (also called the "union-of-balls" or "union-of-disks" filtration) is a growing sequence of metric balls used to detect the size...

theorem Fundamental theorem on homomorphisms Universal property Filtration (mathematics) Category theory Monoidal category Groupoid Group object Coalgebra...

In representation theory, a Jantzen filtration is a filtration of a Verma module of a semisimple Lie algebra, or a Weyl module of a reductive algebraic...

In topological data analysis, the Vietoris–Rips filtration (sometimes shortened to "Rips filtration") is the collection of nested Vietoris–Rips complexes...

of the stem and limbs of a plant into smaller ones Ramification group, filtration of the Galois group of a local field extension Ramification theory of...

dictatorship Boris Weisfeiler allegedly drowned. He is known for the Weisfeiler filtration, Weisfeiler–Leman algorithm and Kac–Weisfeiler conjectures. Weisfeiler...

holomorphic vector bundle may be built from stable ones using Harder–Narasimhan filtration. Stable bundles were defined by David Mumford in Mumford (1963) and later...

In mathematics, the Moy–Prasad filtration is a family of filtrations of p-adic reductive groups and their Lie algebras, named after Allen Moy and Gopal...

all basic topological notions and results. Filtration (mathematics) – Indexed set in mathematics Filtration (probability theory) – Model of information...

specifically in local class field theory, the ramification groups are a filtration of the Galois group of a local field extension, which gives detailed information...

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n {\displaystyle n} -dimensional...

production, drinking water preparation, pre-filtration in active carbon treatments and membrane systems, and the filtration of swimming pool water. Iron-removal...

convergence that is found in general topology Filtration (mathematics) – Indexed set in mathematics Filtration (probability theory) – Model of information...

In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly...

acid-base balance, various electrolyte concentrations, and removal of toxins. Filtration occurs in the glomerulus: one-fifth of the blood volume that enters the...