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Chemical bonding concepts emerge naturally from maximally entangled atomic orbitals. [PDF]
Nat CommunDing L, Matito E, Schilling C.
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Australian & New Zealand Journal of Statistics, 2014
SummaryA Bayes linear space is a linear space of equivalence classes of proportional σ‐finite measures, including probability measures. Measures are identified with their density functions. Addition is given by Bayes' rule and substraction by Radon–Nikodym derivatives. The present contribution shows the subspace of square‐log‐integrable densities to be
Boogaart, K. Gerald van den +2 more
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SummaryA Bayes linear space is a linear space of equivalence classes of proportional σ‐finite measures, including probability measures. Measures are identified with their density functions. Addition is given by Bayes' rule and substraction by Radon–Nikodym derivatives. The present contribution shows the subspace of square‐log‐integrable densities to be
Boogaart, K. Gerald van den +2 more
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Proceedings of the London Mathematical Society, 1988
In a recent paper by \textit{V. D. Milman} and the author [Isr. J. Math. 54, 139-158 (1986; Zbl 0611.46022)] the notion of weak cotype 2 and weak type 2 Banach spaces were introduced. In the present paper the author considers the class of Banach spaces which are both of weak type 2 and weak cotype 2.
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In a recent paper by \textit{V. D. Milman} and the author [Isr. J. Math. 54, 139-158 (1986; Zbl 0611.46022)] the notion of weak cotype 2 and weak type 2 Banach spaces were introduced. In the present paper the author considers the class of Banach spaces which are both of weak type 2 and weak cotype 2.
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Behavioral and Brain Sciences, 2013
AbstractUse of quantum probability as a top-down model of cognition will be enhanced by consideration of the underlying complex-valued wave function, which allows a better account of interference effects and of the structure of learned and ad hoc question operators.
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AbstractUse of quantum probability as a top-down model of cognition will be enhanced by consideration of the underlying complex-valued wave function, which allows a better account of interference effects and of the structure of learned and ad hoc question operators.
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SIAM Review, 1973
Summary: A resolution space, recently introduced for the study of causality in an operator theoretic setting, is employed to formulate an abstract state concept which generalizes the state space theory commonly used in the study of finite-dimensional dynamical systems.
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Summary: A resolution space, recently introduced for the study of causality in an operator theoretic setting, is employed to formulate an abstract state concept which generalizes the state space theory commonly used in the study of finite-dimensional dynamical systems.
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SIAM Review, 1970
A new formalism, termed the resolution space, is presented within which the theory of causal systems may be unified and extended. The resulting formalism, which is defined as a Hilbert space together with a resolution of the identity, readily includes the commonly encountered function and sequence space causality concepts yet is sufficiently ...
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A new formalism, termed the resolution space, is presented within which the theory of causal systems may be unified and extended. The resulting formalism, which is defined as a Hilbert space together with a resolution of the identity, readily includes the commonly encountered function and sequence space causality concepts yet is sufficiently ...
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On the Performance of Clustering in Hilbert Spaces
IEEE Transactions on Information Theory, 2008Based on randomly drawn vectors in a separable Hilbert space, one may construct a k-means clustering scheme by minimizing an empirical squared error. We investigate the risk of such a clustering scheme, defined as the expected squared distance of a random vector X from the set of cluster centers.
Biau, Gérard, Devroye, L., Lugosi, G.
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Mathematika, 2010
A covering \((C_n)\) of a Banach space is said to be a \textit{tiling} if the interiors of \(C_n\) are pairwise disjoint. Answering a question originating from the work of \textit{V.\,Klee} [Math.\ Ann.\ 257, 251--260 (1981; Zbl 0453.41021)], the author proves that a separable Hilbert space has a tiling by closed convex sets whose outer radii are ...
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A covering \((C_n)\) of a Banach space is said to be a \textit{tiling} if the interiors of \(C_n\) are pairwise disjoint. Answering a question originating from the work of \textit{V.\,Klee} [Math.\ Ann.\ 257, 251--260 (1981; Zbl 0453.41021)], the author proves that a separable Hilbert space has a tiling by closed convex sets whose outer radii are ...
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1998
Let \(K\) be a field complete with respect to some valuation 1.1 and let \(E=(E,\|\cdot \|)\) be a \(K\)-Banach space. \(K\)-Banach spaces \(E\) such that for each closed subspace \(D\) there exists a linear surjective projection \(P:E\to D\) satisfying \(\| Px\|\leq\| x\|\) for all \(x\in E\) are called norm Hilbert spaces (NHS). The authors introduce
Ochsenius, H., Schikhof, W.H.
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Let \(K\) be a field complete with respect to some valuation 1.1 and let \(E=(E,\|\cdot \|)\) be a \(K\)-Banach space. \(K\)-Banach spaces \(E\) such that for each closed subspace \(D\) there exists a linear surjective projection \(P:E\to D\) satisfying \(\| Px\|\leq\| x\|\) for all \(x\in E\) are called norm Hilbert spaces (NHS). The authors introduce
Ochsenius, H., Schikhof, W.H.
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