Results 291 to 300 of about 95,031 (330)
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Algebra Universalis, 1995
The author studies the endomorphism monoid of independence algebras. By an independence algebra she means an algebra where the subalgebra closure operator satisfies the Exchange Property and endomorphisms can be arbitrarily prescribed on any basis. Notable examples for independence algebras are: vector spaces, sets, free \(G\)-sets.
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The author studies the endomorphism monoid of independence algebras. By an independence algebra she means an algebra where the subalgebra closure operator satisfies the Exchange Property and endomorphisms can be arbitrarily prescribed on any basis. Notable examples for independence algebras are: vector spaces, sets, free \(G\)-sets.
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Journal of Symbolic Logic, 1981
This paper is concerned with algebraic independence in structures that are relatively simple for their size. It is shown that for κ a limit cardinal, if a structure of power at least κ is ∞ω-equivalent to a structure of power less than κ, then must contain an infinite set of algebraically independent elements. The same method of proof yields the fact
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This paper is concerned with algebraic independence in structures that are relatively simple for their size. It is shown that for κ a limit cardinal, if a structure of power at least κ is ∞ω-equivalent to a structure of power less than κ, then must contain an infinite set of algebraically independent elements. The same method of proof yields the fact
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Simultaneous Approximation and Algebraic Independence
The Ramanujan Journal, 1997Rappelons la notion de mesure d'approximation simultanée (MAS): soit \(\theta= (\theta_1,\dots,\theta_n)\in \mathbb{C}^n\); une application \(\varphi: \mathbb{N}\times [0,+\infty[\to [0,+\infty]\) est une MAS pour \(\theta\) si il existe \(D_0\in\mathbb{N}\) et \(h_0\geq 1\) tels que, pour tout entier \(D\geq D_0\), tout nombre réel \(h\geq h_0\) et ...
Roy, Damien, Waldschmidt, Michel
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Independence in Operator Algebras
Foundations of Physics, 1999Various notions of independence of observables have been proposed within the algebraic framework of quantum field theory. We discuss relationships between these and the recently introduced notion of logical independence in a general operator-algebraic context. We show that C*-independence implies an analogue of classical independence.
StanisŁaw Goldstein +2 more
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Algebraic independent component analysis
IEEE International Conference on Robotics, Intelligent Systems and Signal Processing, 2003. Proceedings. 2003, 2004We present extended results of our recent algorithm for ICA of overcomplete mixtures, namely, the algebraic independent component analysis (AICA). This algorithm is based entirely on algebraic operations and vector-distance measures. AICA retains the stability and convergence properties of the previously proposed geometric ICA (geo-ICA) algorithms but ...
K. Waheed, F.M. Salem
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ON ALGEBRAIC INDEPENDENCE OF ALGEBRAIC POWERS OF ALGEBRAIC NUMBERS
Mathematics of the USSR-Sbornik, 1985This paper contains a complete proof of the following theorem. Let \(\alpha\neq 0,1\) be algebraic, let \(\beta\) be algebraic of degree \(d\geq 2\), and let t be the transcendence degree over \({\mathbb{Q}}\) of the field generated by the numbers (*) \(\alpha^{\beta},...,\alpha^{\beta^{d- 1}}\).
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Algebra Universalis, 1998
Let \((A,P)\) be a pair where \(A\) is an algebra and \(P\subseteq A\) is a poset with order relation \(\leq \). A set \(X\subseteq A\) is said to be independent if, for all \(x\in X\), we have \(x\notin \text{Sg}(X\setminus \{x\})\). The definition of order-independence algebra is introduced by abstracting some properties of chains in finite Boolean ...
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Let \((A,P)\) be a pair where \(A\) is an algebra and \(P\subseteq A\) is a poset with order relation \(\leq \). A set \(X\subseteq A\) is said to be independent if, for all \(x\in X\), we have \(x\notin \text{Sg}(X\setminus \{x\})\). The definition of order-independence algebra is introduced by abstracting some properties of chains in finite Boolean ...
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Huffman Algebras for Independent Random Variables
Proceedings. IEEE International Symposium on Information Theory, 1994zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chang, Cheng-Shang, Thomas, Joy A.
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On algebraic independence of dirichlet series
Communications on Pure and Applied Mathematics, 1986The authors make a thorough study of algebraic independence (over suitable subrings) in the ring \(A\) of the ring of all formal Dirichlet series which is isomorphic to the ring of arithmetical functions with Dirichlet convolution. In particular, they study algebraic independence and transcendence over \(C(Z)\), the smallest subring of \(A\) containing
Shapiro, Harold N., Sparer, Gerson H.
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Algebraic independence of exponents
Mathematical Notes of the Academy of Sciences of the USSR, 1975Three theorems are obtained for the algebraic independence of some numbers related to exponential functions. Theorems 1 and 3 are extensions of the well-known Gelfond results.
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