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1. Ergodic Theory: Ergodic Theory is the mathematical theory of well-behaved randomness. The random variables can occur discretely or continuously, but the total probability over the time period is always 1 so that the end of the time period, the random event ... [100%] 2023-02-22 [Mathematics]
2. Ergodic theory: metric theory of dynamical systems 1) In the "abstract" or "general" part of ergodic theory one examines measurable dynamical systems. In the most general sense this is a triple $(W,G,F)$, where $W$ is a measurable space (the "phase ... (Mathematics) [100%] 2023-12-21 [Ergodic theory]
3. Ergodic theory: Ergodic theory is a branch of mathematics that studies statistical properties of deterministic dynamical systems; it is the study of ergodicity. In this context, "statistical properties" refers to properties which are expressed through the behavior of time averages of various ... (Branch of mathematics that studies dynamical systems) [100%] 2024-06-17 [Ergodic theory]
4. Ergodic Ramsey theory: Ergodic Ramsey theory is a branch of mathematics where problems motivated by additive combinatorics are proven using ergodic theory. Ergodic Ramsey theory arose shortly after Endre Szemerédi's proof that a set of positive upper density contains arbitrarily long arithmetic ... [81%] 2023-12-20 [Ergodic theory] [Ramsey theory]...
5. Systems theory: Systems theory is the interdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent components that can be natural or human-made. (Interdisciplinary study of systems) [75%] 2023-09-21 [Systems theory] [Systems science]...
6. Systems theory (engineering): In engineering and mathematics, systems theory or mathematical systems theory refers broadly to the mathematical study of (complex) systems in engineering and interconnections among such systems. Systems in this context refers to dynamical systems. (Engineering) [75%] 2023-09-21
7. Maximal ergodic theorem: If $ T $ is an endomorphism of a measure space $ ( X , \mu ) $, if $ f \in L _ {1} ( X , \mu ) $ and if $ E $ is the set of $ x \in X $ for which $$ \sup _ {n \geq 0 } \sum_{i=0} ^ { n ... (Mathematics) [71%] 2024-01-12 [Ergodic theorems, spectral theory, Markov operators]
8. Multiplicative ergodic theorem: Oseledets's multiplicative ergodic theorem, Oseledec's multiplicative ergodic theorem Consider a linear homogeneous system of differential equations $$ \tag{a1 } \dot{x} = A ( t) x ,\ \ x ( 0 ; x _ {0} ) = x _ {0} \in \mathbf R ^ {n} ,\ \ t \geq 0 ... (Mathematics) [71%] 2023-10-17
9. Operator ergodic theorem: A general name for theorems on the limit of means along an unboundedly lengthening "time interval" $ n = 0 \dots N $, or $ 0 \leq t \leq T $, for the powers $ \{ A ^ {n} \} $ of a linear operator $ A $ acting on a Banach ... (Mathematics) [71%] 2024-01-12 [General theory of linear operators]
10. Gallagher ergodic theorem: Let $f(q)$ be a non-negative function defined on the positive integers. Gallagher's ergodic theorem, or Gallagher's zero-one law states that the set of real numbers $x$ in $0\leq x\leq1$ for which the Diophantine ... (Mathematics) [71%] 2023-09-15
11. Birkhoff ergodic theorem: One of the most important theorems in ergodic theory. For an endomorphism $ T $ of a $ \sigma $-finite measure space $ (X,\Sigma,\mu) $, Birkhoff’s ergodic theorem states that for any function $ f \in {L^{1}}(X,\Sigma,\mu) $, the limit ... (Mathematics) [71%] 2023-09-18 [Ergodic theorems, spectral theory, Markov operators]
12. Maximal ergodic theorem: The maximal ergodic theorem is a theorem in ergodic theory, a discipline within mathematics. Suppose that \displaystyle{ (X, \mathcal{B},\mu) }[/math] is a probability space, that \displaystyle{ T : X\to X }[/math] is a (possibly noninvertible) measure-preserving transformation ... [71%] 2023-12-30 [Probability theorems] [Ergodic theory]...
13. Ergodic theory, non-commutative: A branch of the theory of operator algebras in which one studies automorphisms of $C^*$-algebras from the point of view of ergodic theory. The range of questions considered in non-commutative ergodic theory and the results obtained so far ... (Mathematics) [70%] 2023-10-17
14. Biomatrix systems theory: Biomatrix systems theory claims to be an integrated systems theory. It was developed through an interdisciplinary PhD programme at the University of Cape Town. [61%] 2023-12-19 [Systems theory]
15. Biochemical systems theory: Articles Most recent articles on Biochemical systems theory Most cited articles on Biochemical systems theory Review articles on Biochemical systems theory Articles on Biochemical systems theory in N Eng J Med, Lancet, BMJ Media Powerpoint slides on Biochemical systems theory ... [61%] 2024-01-02 [Systems biology]
16. World-systems theory: World-systems theory (also known as world-systems analysis or the world-systems perspective) is a multidisciplinary approach to world history and social change which emphasizes the world-system (and not nation states) as the primary (but not exclusive) unit ... (Approach emphasizing the world-system as the primary unit of social analysis) [61%] 2023-09-20 [Sociological theories] [Theories of history]...
17. Grammar systems theory: Grammar systems theory is a field of theoretical computer science that studies systems of finite collections of formal grammars generating a formal language. Each grammar works on a string, a so-called sequential form that represents an environment. (Field of theoretical computer science) [61%] 2023-12-05 [Formal languages] [Theoretical computer science]...
18. Dynamical systems theory: Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. (Area of mathematics used to describe the behavior of complex dynamical systems) [61%] 2023-12-12 [Dynamical systems] [Complex systems theory]...
19. Dynamical systems theory: Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. (Area of mathematics used to describe the behavior of complex dynamical systems) [61%] 2023-12-19 [Dynamical systems] [Complex systems theory]...
20. Abstract Systems Theory: This article discusses systems in the context of general systems theory. For systems in the sense of logics, see formal systems. (Mathematics) [61%] 2023-12-23