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$\beta$-transformation, natural extension and invariant measure

Ergodic Theory and Dynamical Systems, 2000
For $\beta>1$, consider the $\beta$-transformation $T_\beta$. When $\beta$ is an integer, the natural extension of $T_\beta$ can be represented explicitly as a map on the unit square with an invariant measure: the corresponding two-dimensional Lebesgue measure.
Brown, Gavin, Yin, Qinghe
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From blocks to rocks: a natural extension of zoned namespaces

USENIX Workshop on Hot Topics in Storage and File Systems, 2021
Zoned namespaces (ZNS) is an emerging storage abstraction with the potential to supersede the conventional block abstraction for flash-based devices. ZNS constrains the writes to be sequential within each zone, thereby avoiding a costly translation in ...
Umesh Maheshwari
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The role of natural soundscape in nature-based tourism experience: an extension of the stimulus–organism–response model

Current Issues in Tourism, 2020
This paper echoes the call for multisensory tourism research from the perspective of auditory sensory experience. Based on an extended stimulus–organism–response (SOR) model, the natural soundscape is linked with tourists’ emotion and behaviour, and the ...
Jinde Jiang
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On natural Riemann extensions

Publicationes Mathematicae Debrecen, 2011
A natural Riemann extension is a natural lift of a manifold with a symmetric affine connection to its cotangent bundle. The corresponding structure on the cotangent bundle is a pseudo-Riemannian metric. The classical Riemann extension has been studied by many authors. The broader (two-parameter) family of all natural Riemann extensions was found by the
OLDRICH KOWALSKI, MASAMI SEKIZAWA
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Invariant Measures and Natural Extensions

Canadian Mathematical Bulletin, 2002
AbstractWe study ergodic properties of a family of intervalmaps that are given as the fractional parts of certain real Möbius transformations. Included are the maps that are exactly n-to-1, the classical Gauss map and the Renyi or backward continued fraction map.
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Constructing Natural Extensions of Propositional Logics

Studia Logica, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Two Natural Extensions of n-normality

Acta Mathematica Sinica, English Series, 2023
The author in this paper generalizes the classes of \(n\)-normal and quasinormal operators. He also establishes a Weyl-like theorem and shows the existence of a nontrivial invariant subspace for this new class.
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Nanotechnology – A shelf life extension strategy for fruits and vegetables

Critical reviews in food science and nutrition, 2020
Most harvested fruits and vegetables cannot be stored in natural conditions for a satisfactory shelf life duration due to their perishable nature.
Wenchao Liu, Min Zhang, B. Bhandari
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NOILC: Natural Extensions

2015
Following a discussion of the use of filtered signals, the chapter illustrates the wider interpretation of NOILC by considering its flexibility using multi-rate discrete time systems followed by an analysis of situations where variation of the initial conditions is possible and can be regarded as part of the input signal.
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Natural extensions of holomorphic motions

Journal of Geometric Analysis, 1997
This paper discusses the problem of natural extensions of holomorphic motions; it gives the following unique way of extensions. Let \(\overline{D}\) be the closed unit disc and \(\{X_z ; z\in \overline{D}\}\), a real analytic family of the real analytic plane Jordan curves \(X_z\).
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