Joram Lindenstrauss, David Preiss, Tiˇser Jaroslav · Princeton University Press eBooks · 2012
This chapter describes the modulus of smoothness of a function in the direction of a family of subspaces and the much simpler notion of upper Fréchet differentiability. It also considers the notion of spaces admitting bump functions smooth in the direction of a family of subspaces with modulus controlled by ω(<italic>t</italic>). It shows that this notion is related to asymptotic uniform smoothness, and that very smooth bumps, and very asymptotically uniformly smooth norms, exist in all asymptotically <italic>c</italic>₀ spaces. This allows a new approach to results on Γ-almost everywhere Frechet differentiability of Lipschitz functions. The chapter concludes by explaining an immediate consequence for renorming of spaces containing an asymptotically <italic>c</italic>₀ family of subspaces.
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Emily Clader, Dustin Ross · Undergraduate texts in mathematics · 2025
There is a very good chance that the pictures of affine varieties that we have depicted in this book have taken you back to your days of calculus.
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2023
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Kim Nguyen · 2011
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Jacek Wojtkiewicz · 2014
The ground state energy of the anisotropic XY chain in transverse magnetic field: explicite expression and
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Arthur G. Werschulz · 2008
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Edmund Burke · Cambridge University Press eBooks · 2014
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Torsten Asselmeyer-maluga, Carl H. Brans, See Profile et al. · 2015
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Kim Nguyen · 2025
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Arpita Mal, Kallol Paul, Debmalya Sain · Infosys science foundation series · 2024
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Arjen K. Lenstra · 2006
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Aditya Goenkaa, Manh-hung Nguyenb · 2009
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Aditya Goenkaa, Manh-hung Nguyenb · 2009
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Vedad Hulusić, Kurt Debattista, Alan Chalmers · The Visual Computer · 2012
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Hulusic, V., Debattista, K., Chalmers, A. · Bournemouth University Research Online (Bournemouth University) · 2013
Despite the complexity of the Human Visual System (HVS), research over the last few decades has highlighted a number of its limitations. These limitations can be exploited in computer graphics to significantly reduce computational cost and thus required rendering time, without a viewer perceiving any difference in resultant image quality. Furthermore, crossmodal interaction between different modalities, such as \nthe influence of audio on visual perception, has also been shown as significant both in psychology and computer graphics. In this paper we investigate the effect of beat rate on temporal visual perception, i.e. frame rate \nperception. For the visual quality and perception evaluation, \na series of psychophysical experiments was conducted and the data analysed. The results indicate that beat rates in some cases do affect temporal visual perception and that certain beat rates can be used in order to reduce the amount of rendering required to achieve a perceptual high quality. This is another step towards a comprehensive understanding of auditory-visual crossmodal interaction and could be potentially used in highfidelity interactive multi-sensory virtual environments.
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Peter K. Friz · Cambridge University Press eBooks · 2010
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Linden, W., Dose, V., Toussaint, U. · MPG.PuRe (Max Planck Society) · 2014
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Fairchild Books · 2021
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Yurii Kolomoitsev, Sergey Tikhonov · arXiv (Cornell University) · 2019
We provide a comprehensive study of interrelations between different measures of smoothness of functions on various domains and smoothness properties of approximation processes. Two general approaches to this problem have been developed: the first based on geometric properties of Banach spaces and the second on Littlewood-Paley and Hörmander type multiplier theorems. In particular, we obtain new sharp inequalities for measures of smoothness given by the $K$-functionals or moduli of smoothness. As examples of approximation processes we consider best polynomial and spline approximations, Fourier multiplier operators on $\mathbb{T}^d$, $\mathbb{R}^d$, $[-1, 1]$, nonlinear wavelet approximation, etc.
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Étienne Matheron, Armel Primot, Pascal Lefèvre · HAL (Le Centre pour la Communication Scientifique Directe) · 2013
We isolate various su cient conditions for a Banach space X to have the so-called Blum-Hanson property. In particular, we show that X has the Blum-Hanson property if either the modulus of asymptotic smoothness of X has an extremal behaviour at in nity, or if X is uniformly G^ateaux smooth and embeds isometrically into a Banach space with a 1-unconditional nite-dimensional decomposition.
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