Explicit constructions and properties of generalized shift-invariant systems in L2(R)L^2(\mathbb{R})

Generalized shift-invariant (GSI) systems, originally introduced by Hern\'andez, Labate & Weiss and Ron & Shen, provide a common frame work for analysis of Gabor systems, wavelet systems, wave packet systems, and other types of structured function systems. In this paper we analyze three important aspects of such systems. First, in contrast to the known cases of Gabor frames and wavelet frames, we show that for a GSI system forming a frame, the Calder\'on sum is not necessarily bounded by the lower frame bound. We identify a technical condition implying that the Calder\'on sum is bounded by the lower frame bound and show that under a weak assumption the condition is equivalent with the local integrability condition introduced by Hern\'andez et al. Second, we provide explicit and general constructions of frames and dual pairs of frames having the GSI-structure. In particular, the setup applies to wave packet systems and in contrast to the constructions in the literature, these constructions are not based on characteristic functions in the Fourier domain. Third, our results provide insight into the local integrability condition (LIC).Comment: Adv. Comput. Math., to appea

Countable dense homogeneous filters and the Menger covering property

In this note we present a ZFC construction of a non-meager filter which fails to be countable dense homogeneous. This answers a question of Hern\'andez-Guti\'errez and Hru\v{s}\'ak. The method of the proof also allows us to obtain a metrizable Baire topological group which is strongly locally homogeneous but not countable dense homogeneous.Comment: 8 page

Global Warming and the Sweetness of Life : A Tar Sands Tale | Matt Hern

Lecture, October 18, 2018. 6:15 pm, Room 521, College Building. The Liberal Arts division and the department of History, Philosophy + the Social Sciences welcome writer/activist Matt Hern for a talk called Global Warming and the Sweetness of Life: A Tar Sands Tale. Hern is co-author of the recent book Global Warming and the Sweetness of Life (MIT, 2018), which charts multiple trips through the tar sands of northern Alberta and documents the effects of global warming on indigenous communities. Hern and co-creators Am Johal and Joe Sacco offer new forms of thinking about global warming and ecological perils in the context of class and de-colonial politics and seek new definitions of the word ecology. Matt Hern is a community organizer, independent scholar, writer and activist based in East Vancouver, British Columbia (Coast Salish Territories). He is known for his work in radical urbanism, community development, ecology and alternative forms of education. He is currently the co-founder and co-director of a creative production cooperative with and for refugees and recently arrived youth called Solid State Industries. Hern teaches at multiple universities, lectures globally and is widely-referenced in radical political and social discourses. His writing has been published on six continents and translated into 14 languages. He holds a PhD in Urban Studies from the Union Institute & University.https://digitalcommons.risd.edu/liberalarts_ncss_events/1007/thumbnail.jp

Chiral Symmetry and N*(1440) -> N pi pi Decay

The N*(1440) -> N pi pi decay is studied by making use of the chiral reduction formula. This formula suggests a scalar-isoscalar pion-baryon contact interaction which is absent in the recent study of Hern{\'a}ndez et al. The contact interaction is introduced into their model, and is found to be necessary for the simultaneous description of g_{RN pi pi} and the pi-pi and pi-N invariant mass distributions.Comment: 12 page