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1.
We consider the question whether, given a countable family of lattices in a locally compact abelian group G, there exist functions such that the resulting generalized shift-invariant system is a tight frame of . This paper develops a new approach to the study of generalized shift-invariant system via almost periodic functions, based on a novel unconditional convergence property. From this theory, we derive characterizing relations for tight and dual frame generators, we introduce the system bandwidth as a measure of the total bandwidth a generalized shift-invariant system can carry, and we show that the so-called Calderón sum is uniformly bounded from below for generalized shift-invariant frames. Without the unconditional convergence property, we show, counter intuitively, that even orthonormal bases can have arbitrary small system bandwidth. Our results show that the question of existence of frame generators for a general lattice system is rather subtle and depends on analytical and algebraic properties of the lattice system. 相似文献
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Philomena Schlexer Anton Bay Andersen Bela Sebok Ib Chorkendorff Jakob Schitz Thomas W. Hansen 《Particle & Particle Systems Characterization》2019,36(3)
Nanoparticles have an immense importance in various fields, such as medicine, catalysis, and various technological applications. Nanoparticles exhibit a significant depression in melting point as their size goes below ≈10 nm. However, nanoparticles are frequently used in high temperature applications such as catalysis where temperatures often exceed several 100 degrees which makes it interesting to study not only the melting temperature depression, but also how the melting progresses through the particle. Using high‐resolution transmission electron microscopy, the melting process of gold nanoparticles in the size range of 2–20 nm Au nanoparticles combined with molecular dynamics studies is investigated. A linear dependence of the melting temperature on the inverse particle size is confirmed; electron microscopy imaging reveals that the particles start melting at the surface and the liquid shell formed then rapidly expands to the particle core. 相似文献
4.
CH Oxidation of Ingenanes Enables Potent and Selective Protein Kinase C Isoform Activation 下载免费PDF全文
Dr. Yehua Jin Dr. Chien‐Hung Yeh Dr. Christian A. Kuttruff Dr. Lars Jørgensen Dr. Georg Dünstl Dr. Jakob Felding Dr. Swaminathan R. Natarajan Prof. Dr. Phil S. Baran 《Angewandte Chemie (International ed. in English)》2015,54(47):14044-14048
Ingenol derivatives with varying degrees of oxidation were prepared by two‐phase terpene synthesis. This strategy has allowed access to analogues that cannot be prepared by semisynthesis from natural ingenol. Complex ingenanes resulting from divergent C? H oxidation of a common intermediate were found to interact with protein kinase C in a manner that correlates well with the oxidation state of the ingenane core. Even though previous work on ingenanes has suggested a strong correlation between potential to activate PKCδ and induction of neutrophil oxidative burst, the current study shows that the potential to activate PKCβII is of key importance while interaction with PKCδ is dispensable. Thus, key modifications of the ingenane core allowed PKC isoform selectivity wherein PKCδ‐driven activation of keratinocytes is strongly reduced or even absent while PKCβII‐driven activation of neutrophils is retained. 相似文献
5.
Explicit constructions and properties of generalized shift-invariant systems in $L^{2}(\mathbb {R})$
Ole Christensen Marzieh Hasannasab Jakob Lemvig 《Advances in Computational Mathematics》2017,43(2):443-472
Generalized shift-invariant (GSI) systems, originally introduced by Hernández et al. and Ron and 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 Calderón sum is not necessarily bounded by the lower frame bound. We identify a technical condition implying that the Calderón 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 Hernández 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). 相似文献
6.
Prof. Dr. Tunga Salthammer Friederike Monegel Nicole Schulz Dr. Erik Uhde Prof. Dr. Stefan Grimme Jakob Seibert Prof. Dr. Uwe Hohm Dr. Wolf-Ulrich Palm 《Chemistry (Weinheim an der Bergstrasse, Germany)》2021,27(3):1046-1056
The chemical background of olfactory perception has been subject of intensive research, but no available model can fully explain the sense of smell. There are also inconsistent results on the role of the isotopology of molecules. In experiments with human subjects it was found that the isotope effect is weak with acetone and D6-acetone. In contrast, clear differences were observed in the perception of octanoic acid and D15-octanoic acid. Furthermore, a trained sniffer dog was initially able to distinguish between these isotopologues of octanoic acid. In chromatographic measurements, the respective deuterated molecule showed weaker interaction with a non-polar liquid phase. Quantum chemical calculations give evidence that deuterated octanoic acid binds more strongly to a model receptor than non-deuterated. In contrast, the binding of the non-deuterated molecule is stronger with acetone. The isotope effect is calculated in the framework of statistical mechanics. It results from a complicated interplay between various thermostatistical contributions to the non-covalent free binding energies and it turns out to be very molecule-specific. The vibrational terms including non-classical zero-point energies play about the same role as rotational/translational contributions and are larger than bond length effects for the differential isotope perception of odor for which general rules cannot be derived. 相似文献
7.
Jakob Heller Tobias F. Pascher Dr. Christian van der Linde Dr. Milan Ončák Prof. Dr. Martin K. Beyer 《Chemistry (Weinheim an der Bergstrasse, Germany)》2021,27(66):16367-16376
Hydrated aluminium cations have been investigated as a photochemical model system with up to ten water molecules by UV action spectroscopy in a Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer. Intense photodissociation was observed starting at 4.5 eV for two to eight water molecules with loss of atomic hydrogen, molecular hydrogen and water molecules. Quantum chemical calculations for n=2 reveal that solvation shifts the intense 3s–3p excitations of Al+ into the investigated photon energy range below 5.5 eV. During the photochemical relaxation, internal conversion from S1 to T2 takes place, and photochemical hydrogen formation starts on the T2 surface, which passes through a conical intersection, changing to T1. On this triplet surface, the electron that was excited to the Al 3p orbital is transferred to a coordinated water molecule, which dissociates into a hydroxide ion and a hydrogen atom. If the system remains in the triplet state, this hydrogen radical is lost directly. If the system returns to singlet multiplicity, the reaction may be reversed, with recombination with the hydroxide moiety and electron transfer back to aluminium, resulting in water evaporation. Alternatively, the hydrogen radical can attack the intact water molecule, forming molecular hydrogen and aluminium dihydroxide. Photodissociation is observed for up to n=8. Clusters with n=9 or 10 occur exclusively as HAlOH+(H2O)n-1 and are transparent in the investigated energy range. For n=4–8, a mixture of Al+(H2O)n and HAlOH+(H2O)n-1 is present in the experiment. 相似文献
8.
Photo‐Wolff Rearrangement of 2‐Diazo‐1,2‐naphthoquinone: Stern–Volmer Analysis of the Stepwise Reaction Pathway 下载免费PDF全文
2‐Diazo‐1,2‐naphthoquinone (1) and its derivatives are the photoactive components in Novolak photoresists. A femtosecond infrared study has established that the photoreaction of 1 proceeds largely by a concerted Wolff rearrangement yielding the ketene 1H‐inden‐1‐ylidene‐methanone (3) within 300 fs after excitation, but earlier trapping studies gave evidence for a minor reaction path via a carbene intermediate 1‐oxo‐2(1H)‐naphthalenylidene (2) with a lifetime of about 10 ps. Here, we provide a quantitative assessment of the stepwise pathway by Stern–Volmer analysis of the trapping of 2 by methanol to yield 2‐methoxy‐1‐naphthol (4). We conclude that the lifetime of the carbene 2 is at least 200 ps. Moreover, [3 + 2]cycloaddition of 2 and acetonitrile yielding 2‐methylnaphth[2,1‐d]oxazole (5) was observed. A comparison of the yields of 5 formed upon photolysis and upon thermolysis of 1 in acetonitrile provides evidence that a substantial part of the hot nascent carbene 2 formed photolytically rearranges to the ketene 3 during its vibrational relaxation (hot ground‐state reaction). 相似文献
9.
Thorsten vomStein Tim denHartog Julien Buendia Spas Stoychev Jakob Mottweiler Carsten Bolm Jürgen Klankermayer Walter Leitner 《Angewandte Chemie (Weinheim an der Bergstrasse, Germany)》2015,127(20):5957-5961
Ruthenium–triphos complexes exhibited unprecedented catalytic activity and selectivity in the redox‐neutral C C bond cleavage of the β‐O‐4 lignin linkage of 1,3‐dilignol model compounds. A mechanistic pathway involving a dehydrogenation‐initiated retro‐aldol reaction for the C C bond cleavage was proposed in line with experimental data and DFT calculations. 相似文献
10.