Search results for "C1"
showing 10 items of 3475 documents
On the Almost Everywhere Convergence of Multiple Fourier-Haar Series
2019
The paper deals with the question of convergence of multiple Fourier-Haar series with partial sums taken over homothetic copies of a given convex bounded set $$W\subset\mathbb{R}_+^n$$ containing the intersection of some neighborhood of the origin with $$\mathbb{R}_+^n$$ . It is proved that for this type sets W with symmetric structure it is guaranteed almost everywhere convergence of Fourier-Haar series of any function from the class L(ln+L)n−1.
Frame-related Sequences in Chains and Scales of Hilbert Spaces
2022
Frames for Hilbert spaces are interesting for mathematicians but also important for applications in, e.g., signal analysis and physics. In both mathematics and physics, it is natural to consider a full scale of spaces, and not only a single one. In this paper, we study how certain frame-related properties of a certain sequence in one of the spaces, such as completeness or the property of being a (semi-) frame, propagate to the other ones in a scale of Hilbert spaces. We link that to the properties of the respective frame-related operators, such as analysis or synthesis. We start with a detailed survey of the theory of Hilbert chains. Using a canonical isomorphism, the properties of frame se…
Frames and weak frames for unbounded operators
2020
In 2012 G\u{a}vru\c{t}a introduced the notions of $K$-frame and of atomic system for a linear bounded operator $K$ in a Hilbert space $\mathcal{H}$, in order to decompose its range $\mathcal{R}(K)$ with a frame-like expansion. In this article we revisit these concepts for an unbounded and densely defined operator $A:\mathcal{D}(A)\to\mathcal{H}$ in two different ways. In one case we consider a non-Bessel sequence where the coefficient sequence depends continuously on $f\in\mathcal{D}(A)$ with respect to the norm of $\mathcal{H}$. In the other case we consider a Bessel sequence and the coefficient sequence depends continuously on $f\in\mathcal{D}(A)$ with respect to the graph norm of $A$.
"Table 11" of "Dijet azimuthal correlations and conditional yields in $pp$ and $p$+Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV with the ATLAS det…
2020
Unfolded azimuthal angular correlation distributions (Delta p_{T} > 3). Black markers represent p+Pb, red markers p+p
"Table 10" of "Dijet azimuthal correlations and conditional yields in $pp$ and $p$+Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV with the ATLAS det…
2020
Unfolded azimuthal angular correlation distributions. Black markers represent p+Pb, red markers p+p
"Table 1" of "Dijet azimuthal correlations and conditional yields in $pp$ and $p$+Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV with the ATLAS dete…
2020
Unfolded azimuthal angular correlation distributions. Black markers represent p+Pb, red markers p+p
Sterile neutrinos as dark matter candidates
2021
In these brief lecture notes, we introduce sterile neutrinos as dark matter candidates. We discuss in particular their production via oscillations, their radiative decay, as well as possible observational signatures and constraints.
Ahlfors-regular distances on the Heisenberg group without biLipschitz pieces
2015
We show that the Heisenberg group is not minimal in looking down. This answers Problem 11.15 in `Fractured fractals and broken dreams' by David and Semmes, or equivalently, Question 22 and hence also Question 24 in `Thirty-three yes or no questions about mappings, measures, and metrics' by Heinonen and Semmes. The non-minimality of the Heisenberg group is shown by giving an example of an Ahlfors $4$-regular metric space $X$ having big pieces of itself such that no Lipschitz map from a subset of $X$ to the Heisenberg group has image with positive measure, and by providing a Lipschitz map from the Heisenberg group to the space $X$ having as image the whole $X$. As part of proving the above re…
Identification and characterization of aging products in the glyoxal/ammonium sulfate system – implications for light-absorbing material in atmospher…
2012
Abstract. In this study we report the identification of bicyclic imidazoles in aqueous aerosol mimics using HPLC-ESI-MS/MS. 2,2´-Biimidazole was identified to be a major contributor to the 280 nm absorbance band observed in mixtures of glyoxal and ammonium sulfate, despite the fact that its production rate is two orders of magnitude lower than the previously reported production rates of imidazole or imidazole-2-carboxaldehyde. The molar absorptivity of 2,2´-biimidazole was determined to be (36 690±998) M−1 cm−1. This demonstrates the necessity of molecular product identification at trace levels to enable a better understanding of relevant absorbing species. Additionally the forma…
Formation of 3-methyl-1,2,3-butanetricarboxylic acid via gas phase oxidation of pinonic acid – a mass spectrometric study of SOA aging
2012
Abstract. This paper presents the results of mass spectrometric investigations of the OH-initiated oxidative aging of α-pinene SOA under simulated tropospheric conditions at the large aerosol chamber facility AIDA, Karlsruhe Institute of Technology. In particular, the OH-initiated oxidation of pure pinic and pinonic acid, two well-known oxidation products of α-pinene, was investigated. Two complementary analytical techniques were used, on-line atmospheric pressure chemical ionization/mass spectrometry (APCI/MS) and filter sampling followed by liquid chromatography/mass spectrometry (LC/ESI-MS). The results show that 3-methyl-1,2,3-butanetricarboxylic acid (MBTCA), a very low volatile α-pine…