In mathematics, a filtration F {\displaystyle {\mathcal {F}}} is, informally, like a set of ever larger Russian dolls, each one containing the previous...

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

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

(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...

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:...

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

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

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

}])} where: J v {\displaystyle J_{v}} is the trans endothelial solvent filtration volume per second. [ P c − P i ] − σ [ π p − π g ] {\displaystyle [P_{\mathrm...

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...

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

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

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

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

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

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

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

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...

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...

production, pre-filtration in active carbon treatments and membrane systems; Iron-removal from groundwater using aeration and sand filtration. Final purification...

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...

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

used in obstruction theory, to construct spectral sequences by means of filtrations, and generally to make inductive arguments. They are particularly important...

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 mathematics, chromatic homotopy theory is a subfield of stable homotopy theory that studies complex-oriented cohomology theories from the "chromatic"...

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...