Existence, Gevrey regularity, and decay properties of solutions to Active models in critical spaces

Author(s):  
Hantaek Bae ◽  
Woojae Lee
2019 ◽  
Vol 12 (1) ◽  
pp. 1-17
Author(s):  
Amy Cross ◽  
Cherie Allan ◽  
Kerry Kilner

This paper examines the effects of curatorial processes used to develop children's literature digital research projects in the bibliographic database AustLit. Through AustLit's emphasis on contextualising individual works within cultural, biographical, and critical spaces, Australia's literary history is comprehensively represented in a unique digital humanities space. Within AustLit is BlackWords, a project dedicated to recording Australia's Aboriginal and Torres Strait Islander storytelling, publishing, and literary cultural history, including children's and young adult texts. Children's literature has received significant attention in AustLit (and BlackWords) over the last decade through three projects that are documented in this paper. The curation of this data highlights the challenges in presenting ‘national’ literatures in countries where minority voices were (and perhaps continue to be) repressed and unseen. This paper employs a ‘resourceful reading’ approach – both close and distant reading methods – to trace the complex and ever-evolving definition of ‘Australian children's literature’.


2020 ◽  
Vol 30 (10) ◽  
pp. 5544-5559 ◽  
Author(s):  
Jonathan D Power ◽  
Charles J Lynch ◽  
Babatunde Adeyemo ◽  
Steven E Petersen

Abstract This article advances two parallel lines of argument about resting-state functional magnetic resonance imaging (fMRI) signals, one empirical and one conceptual. The empirical line creates a four-part organization of the text: (1) head motion and respiration commonly cause distinct, major, unwanted influences (artifacts) in fMRI signals; (2) head motion and respiratory changes are, confoundingly, both related to psychological and clinical and biological variables of interest; (3) many fMRI denoising strategies fail to identify and remove one or the other kind of artifact; and (4) unremoved artifact, due to correlations of artifacts with variables of interest, renders studies susceptible to identifying variance of noninterest as variance of interest. Arising from these empirical observations is a conceptual argument: that an event-related approach to task-free scans, targeting common behaviors during scanning, enables fundamental distinctions among the kinds of signals present in the data, information which is vital to understanding the effects of denoising procedures. This event-related perspective permits statements like “Event X is associated with signals A, B, and C, each with particular spatial, temporal, and signal decay properties”. Denoising approaches can then be tailored, via performance in known events, to permit or suppress certain kinds of signals based on their desirability.


Author(s):  
SANJIV KUMAR GUPTA ◽  
KATHRYN E. HARE

Abstract Let $G/K$ be an irreducible symmetric space, where G is a noncompact, connected Lie group and K is a compact, connected subgroup. We use decay properties of the spherical functions to show that the convolution product of any $r=r(G/K)$ continuous orbital measures has its density function in $L^{2}(G)$ and hence is an absolutely continuous measure with respect to the Haar measure. The number r is approximately the rank of $G/K$ . For the special case of the orbital measures, $\nu _{a_{i}}$ , supported on the double cosets $Ka_{i}K$ , where $a_{i}$ belongs to the dense set of regular elements, we prove the sharp result that $\nu _{a_{1}}\ast \nu _{a_{2}}\in L^{2},$ except for the symmetric space of Cartan class $AI$ when the convolution of three orbital measures is needed (even though $\nu _{a_{1}}\ast \nu _{a_{2}}$ is absolutely continuous).


1984 ◽  
Vol 12 (1) ◽  
pp. 105-116 ◽  
Author(s):  
A. Corma ◽  
V. Fornés ◽  
J.B. Monton ◽  
A.V. Orchilles
Keyword(s):  

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 841
Author(s):  
Toshiaki Hishida

In this expository paper, we study Lq-Lr decay estimates of the evolution operator generated by a perturbed Stokes system in n-dimensional exterior domains when the coefficients are time-dependent and can be unbounded at spatial infinity. By following the approach developed by the present author for the physically relevant case where the rigid motion of the obstacle is time-dependent, we clarify that some decay properties of solutions to the same system in whole space Rn together with the energy relation imply the desired estimates in exterior domains provided n≥3.


2008 ◽  
Vol 77 (3) ◽  
Author(s):  
J. M. Gates ◽  
M. A. Garcia ◽  
K. E. Gregorich ◽  
Ch. E. Düllmann ◽  
I. Dragojević ◽  
...  
Keyword(s):  

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