System bandwidth and the existence of generalized shift-invariant frames

We consider the question whether, given a countable family of lattices ${({\mathrm{\Gamma }}_j)}_{j\in J}$ in a locally compact abelian group G, there exist functions ${(g_j)}_{j\in J}$ such that the resulting generalized shift-invariant system ${(g_j(??\gamma ))}_{j\in J,\gamma \in {\mathrm{\Gamma }}_j}$ is a tight frame of $L^2(G)$. 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.     

In situ green synthesis of Cu‐Ni bimetallic nanoparticles supported on reduced graphene oxide as an effective and recyclable catalyst for the synthesis of N‐benzyl‐N‐aryl‐5‐amino‐1H‐tetrazoles

In the present work, for the first time we have designed a novel approach for the synthesis of N‐benzyl‐N‐aryl‐5‐amino‐1H‐tetrazoles using reduced graphene oxide (rGO) decorated with Cu‐Ni bimetallic nanoparticles (NPs). In situ synthesis of Cu/Ni/rGO nanocomposite was performed by a cost efficient, surfactant‐free and environmentally benign method using Crataegus azarolus var. aronia L. leaf extract as a stabilizing and reducing agent. Phytochemicals present in the extract can be used to reduce Cu²⁺ and Ni²⁺ ions and GO to Cu NPs, Ni NPs and rGO, respectively. Analyses by means of FT‐IR, UV–Vis, EDS, TEM, FESEM, XRD and elemental mapping confirmed the Cu/Ni/rGO formation and also FT‐IR, NMR, and mass spectroscopy as well as elemental analysis were used to characterize the tetrazoles. The Cu/Ni/rGO nanocomposite showed the superior catalytic activity for the synthesis of N‐benzyl‐N‐aryl‐5‐amino‐1H‐tetrazoles within a short reaction time and high yields. Furthermore, this protocol eliminates the need to handle HN₃.     

A classification of continuous wavelet transforms in dimension three

This paper presents a full catalogue, up to conjugacy and subgroups of finite index, of all matrix groups $H<\mathrm{GL}(3,\mathbb{R})$ that give rise to a continuous wavelet transform with associated irreducible quasi-regular representation. For each group in this class, coorbit theory allows to consistently define spaces of sparse signals, and to construct atomic decompositions converging simultaneously in a whole range of these spaces. As an application of the classification, we investigate the existence of compactly supported admissible vectors and atoms for the groups.     

Redox and Acid–Base Properties of Binuclear 4‐Terphenyldithiophenolate Complexes of Nickel

This work reports on the redox and acid–base properties of binuclear complexes of nickel from 1,4‐terphenyldithiophenol ligands. The results provide insight into the cooperative electronic interaction between a dinickel core and its ligand. Donor/acceptor contributions flexibly adjust to stabilize different redox states at the metals, which is relevant for redox reactions like proton reduction. Proton transfer to the [S₂Ni₂] core and Ni?H bond formation are kinetically favored over the thermodynamically favored yet unproductive proton transfer to ligand.     

Structure and spectroscopic properties of the dimeric copper(I) N‐heterocyclic carbene complex [Cu2(CNCt‐Bu)2](PF6)2

In recent years, the use of copper N‐heterocyclic carbene (NHC) complexes has expanded to fields besides catalysis, namely medicinal chemistry and luminescence applications. In the latter case, multinuclear copper NHC compounds have attracted interest, however, the number of these complexes in the literature is still quite limited. Bis[μ‐1,3‐bis(3‐tert‐butylimidazolin‐2‐yliden‐1‐yl)pyridine]‐1κ⁴C²,N:N,C^2′;2κ⁴C²,N:N,C^2′‐dicopper(I) bis(hexafluoridophosphate), [Cu₂(C₁₉H₂₅N₅)₂](PF₆)₂, is a dimeric copper(I) complex bridged by two CNC, i.e. bis(N‐heterocyclic carbene)pyridine, ligands. Each Cu^I atom is almost linearly coordinated by two NHC ligands and interactions are observed between the pyridine N atoms and the metal centres, while no cuprophilic interactions were observed. Very strong absorption bands are evident in the UV–Vis spectrum at 236 and 274 nm, and an emission band is observed at 450 nm. The reported complex is a new example of a multinuclear copper NHC complex and a member of a compound class which has only rarely been reported.     

Structure and Biosynthesis of Crocagins: Polycyclic Posttranslationally Modified Ribosomal Peptides from Chondromyces crocatus

Secondary metabolome mining efforts in the myxobacterial multiproducer of natural products, Chondromyces crocatus Cm c5, resulted in the isolation and structure elucidation of crocagins, which are novel polycyclic peptides containing a tetrahydropyrrolo[2,3-b]indole core. The gene cluster was identified through an approach combining genome analysis, targeted gene inactivation in the producer, and in vitro experiments. Based on our findings, we developed a biosynthetic scheme for crocagin biosynthesis. These natural products are formed from the three C-terminal amino acids of a precursor peptide and thus belong to a novel class of ribosomally synthesized and post-translationally modified peptides (RiPPs). We demonstrate that crocagin A binds to the carbon storage regulator protein CsrA, thereby inhibiting the ability of CsrA to bind to its cognate RNA target.     

Light-Driven Catalyst-Free Access to Phthalazines: Entry to Antiviral Model Drugs by Merging Domino Reactions**

We report the development of a metal-free four-step one-pot synthetic strategy to access high-value functionalized phthalazines using o-methyl benzophenones as starting compounds. Combining a light-mediated enolization of o-methyl benzophenones/Diels-Alder reaction domino process with a subsequent deprotection/aromatization domino reaction in one-pot leads to sustainable and efficient organic synthesis. The tangible advantages, i. e., absence of catalysts or additives, utilization of commercially available and/or easily accessible substrates, mild reaction conditions, simplicity, and single work-up procedure, make this combined process highly appealing for the direct construction of various 1-aryl-phthalazines. Importantly, in vitro bioactivity evaluation of these newly prepared heterocyclic compounds demonstrated a strong antiviral efficacy against major human pathogens like HCMV and SARS-CoV-2.     

Tannin-Mordant Coloration with Matcha (camelia sinensis) and Iron(II)-Lactate on Human Hair Tresses

The aim of this work was to optimize our natural hair dyeing system which we described in our previous work and to compare with other dyeing systems. Therefore, we investigated concentration limits of matcha and mordant and compared this new dyeing method with commercial permanent systems on the market. Completely unpigmented hair tresses were dyed with matcha powder (camelia sinensis) and iron(II)-lactate. To investigate the wash fastness and concentration limits, the differently dyed hair tresses were spectrophotometrically measured. The comparison of the damage potential for which cysteic acid is an indicator was measured by NIR. The concentration of matcha and mordant are responsible for the intensity of the color results. The higher the matcha or the mordant concentration, the darker the color results of the dyed hair tresses. Hair damage of matcha mordant dyeing is comparable with results of commercial permanent hair coloration systems. Moreover, the results of wash fastness of matcha mordant dyed hair tresses is comparable and even better by tendency to permanent colored hair tresses.     

Phosphine-Stabilized Pnictinidenes

The reaction of the intramolecular germylene-phosphine Lewis pair (o-PPh₂)C₆H₄GeAr* ( 1 ) with Group 15 element trichlorides ECl₃ (E=P, As, Sb) was investigated. After oxidative addition, the resulting compounds (o-PPh₂)C₆H₄(Ar*)Ge(Cl)ECl₂ ( 2 : E=P, 3 : E=As, 4 : E=Sb) were reduced by using sodium metal or LiHBEt₃. The molecular structures of the phosphine-stabilized phosphinidene (o-PPh₂)C₆H₄(Ar*)Ge(Cl)P ( 5 ), arsinidene (o-PPh₂)C₆H₄(Ar*)Ge(Cl)As ( 6 ) and stibinidene (o-PPh₂)C₆H₄(Ar*)Ge(Cl)Sb ( 7 ) are presented; they feature a two-coordinate low-valent Group 15 element. After chloride abstraction, a cyclic germaphosphene [(o-PPh₂)C₆H₄(Ar*)GeP] [B(C₆H₃(CF₃)₂)₄] ( 8 ) was isolated. The ³¹P NMR data of the germaphosphene were compared with literature examples and analyzed by quantum chemical calculations. The phosphinidene was treated with [iBu₂AlH]₂, and the product of an Al−H addition to the low-valent phosphorus atom (o-PPh₂)C₆H₄(Ar*)Ge(H)P(H)Al(C₄H₉)₂ ( 9 ) was characterized.