Greedy wavelet projections are bounded on BV

Let be the space of functions of bounded variation on with . Let , , be a wavelet system of compactly supported functions normalized in , i.e., , . Each has a unique wavelet expansion with convergence in . If is the set of indicies for which are largest (with ties handled in an arbitrary way), then is called a greedy approximation to . It is shown that with a constant independent of . This answers in the affirmative a conjecture of Meyer (2001).

     

Electrostatically Self-Assembled Multilayers of Chitosan and Xanthan Studied by Atomic Force Microscopy and Micro-Interferometry

The thickness and surface morphology of electrostatically self-assembled films of chitosan and xanthan (persistence length of ∼120nm) have been studied using dual-wavelength Reflection Interference Contrast Microscopy (DW-RICM) and tapping mode Atomic Force Microscopy (AFM). The multilayers were prepared at two ionic strengths (5mM and 150mM). When the multilayers were assembled at 150 mM a network like morphology was observed after one bilayer. This structure was found to be of large influence in the further growth of the multilayers, with the same kind of network structure being observed at all number of bilayers. A lack of swelling behaviour, as well as the network structure and the poresize of the network, is suggested to originate from the high chain stiffness of xanthan.     

l-Arginine Improves Solubility and ANTI SARS-CoV-2 Mpro Activity of Rutin but Not the Antiviral Activity in Cells

The COVID-19 pandemic outbreak prompts an urgent need for efficient therapeutics, and repurposing of known drugs has been extensively used in an attempt to get to anti-SARS-CoV-2 agents in the shortest possible time. The glycoside rutin shows manifold pharmacological activities and, despite its use being limited by its poor solubility in water, it is the active principle of many pharmaceutical preparations. We herein report our in silico and experimental investigations of rutin as a SARS-CoV-2 Mpro inhibitor and of its water solubility improvement obtained by mixing it with l-arginine. Tests of the rutin/l-arginine mixture in a cellular model of SARS-CoV-2 infection highlighted that the mixture still suffers from unfavorable pharmacokinetic properties, but nonetheless, the results of this study suggest that rutin might be a good starting point for hit optimization.     

On upper bounds for high order Neumann eigenvalues of convex domains in Euclidean space

We derive sharp upper bounds for eigenvalues of the Laplacian under Neumann boundary conditions on convex domains with given diameter in Euclidean space. We use the Brunn-Minkowski theorem in order to reduce the problem to a question about eigenvalues of certain classes of Sturm-Liouville problems.

     

Spiro[4.4]nonatetraene and its Positive and Negative Radical Ions: Molectronic Structure Investigations

The electronic structure of spiro[4.4]nonatetraene 1 as well as that of its radical anion and cation were studied by different spectroscopies. The electron‐energy‐loss spectrum in the gas phase revealed the lowest triplet state at 2.98 eV and a group of three overlapping triplet states in the 4.5 – 5.0 eV range, as well as a number of valence and Rydberg singlet excited states. Electron‐impact excitation functions of pure vibrational and triplet states identified various states of the negative ion, in particular the ground state with an attachment energy of 0.8 eV, an excited state corresponding to a temporary electron attachment to the 2b₁ MO at an attachment energy of 2.7 eV, and a core excited state at 4.0 eV. Electronic‐absorption spectroscopy in cryogenic matrices revealed several states of the positive ion, in particular a richly structured first band at 1.27 eV, and the first electronic transition of the radical anion. Vibrations of the ground state of the cation were probed by IR spectroscopy in a cryogenic matrix. The results are discussed on the basis of density‐functional and CASSCF/CASPT2 quantum‐chemical calculations. In their various forms, the calculations successfully rationalized the triplet and the singlet (valence and Rydberg) excitation energies of the neutral molecule, the excitation energies of the radical cation, its IR spectrum, the vibrations excited in the first electronic absorption band, and the energies of the ground and the first excited states of the anion. The difference of the anion excitation energies in the gas and condensed phases was rationalized by a calculation of the Jahn‐Teller distortion of the anion ground state. Contrary to expectations based on a single‐configuration model for the electronic states of 1 , it is found that the gap between the first two excited states is different in the singlet and the triplet manifold. This finding can be traced to the different importance of configuration interaction in the two multiplicity manifolds.     

Electron localizability indicators ELI–D and ELIA for highly correlated wavefunctions of homonuclear dimers. I. Li2, Be2, B2, and C2

Electron localizability indicators based on the parallel‐spin electron pair density (ELI–D) and the antiparallel‐spin electron pair density (ELIA) are studied for the correlated ground‐state wavefunctions of Li₂, Be₂, B₂, and C₂ diatomic molecules. Different basis sets and reference spaces are used for the multireference configuration interaction method following the complete active space calculations to investigate the local effect of electron correlation on the extent of electron localizability in position space determined by the two functionals. The results are complemented by calculations of effective bond order, vibrational frequency, and Laplacian of the electron density at the bond midpoint. It turns out that for Li₂, B₂, and C₂ the reliable topology of ELI–D is obtained only at the correlated level of theory. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Manufacturing of Volumetric Glass–Based Composites with Single‐ and Double‐QD Doping

Quantum dot (QD)‐based light‐emitting materials are gaining increased attention because of their easily tunable optical properties desired for various applications in biology, optoelectronics, and photonics. However, few methods can be used to manufacture volumetric materials doped with more than one type of QD other than QD‐polymer hybrids, and they often require complicated preparation processes and are prone to luminescence quenching by QD aggregation and separation from the matrix. Here, simultaneous doping of a volumetric glass‐based nanocomposite with two types of QDs is demonstrated for the first time in a single‐step process using the nanoparticle direct doping method. Glass rods doped with CdTe, CdSe/ZnS, or co‐doped with both QDs, are obtained. Photoluminescence and lifetime experiments confirm temperature‐dependent double emission with maxima at 596 and 720 nm with mean lifetimes up to 16 ns, as well as radiative energy transfer from the short wavelength–emitting QDs to the long wavelength–emitting QDs. This approach may enable the simple and cost‐efficient manufacturing of bulk materials that produce multicolor luminescence with cascade excitation pumping. Applications that could benefit from this include broadband optical fiber amplifiers, backlight systems in LCD screens, high‐power LEDs, or down‐converting solar concentrators used to increase the efficiency of solar panels.     

Inorganic ammonium salts as catalysts for direct aldol reactions in the presence of water

Inorganic ammonium salts catalyze the direct aldol reaction between unmodified ketones and aldehydes to furnish the corresponding β-hydroxy ketones in aqueous media. The reactions are highly chemoselective and operationally simple.     

Quantum chemistry in parallel with PQS

This article describes the capabilities and performance of the latest release (version 4.0) of the Parallel Quantum Solutions (PQS) ab initio program package. The program was first released in 1998 and evolved from the TEXAS program package developed by Pulay and coworkers in the late 1970s. PQS was designed from the start to run on Linux‐based clusters (which at the time were just becoming popular) with all major functionality being (a) fully parallel; and (b) capable of carrying out calculations on large—by ab initio standards—molecules, our initial aim being at least 100 atoms and 1000 basis functions with only modest memory requirements. With modern hardware and recent algorithmic developments, full accuracy, high‐level calculations (DFT, MP2, CI, and Coupled‐Cluster) can be performed on systems with up to several thousand basis functions on small (4‐32 node) Linux clusters. We have also developed a graphical user interface with a model builder, job input preparation, parallel job submission, and post‐job visualization and display. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009     

Application of tandem column solid phase extraction and flame atomic absorption spectrometry for the determination of inorganic and organically bound forms of iron in wine

A tandem column solid phase extraction (SPE) procedure has been devised to examine the fractionation of Fe in wine. Wine was filtered through a 0.45 μm filter and then, the filtrate was driven through an adsorbing Amberlite XAD-7HP column followed by a cation exchange Dowex 50W-x8-200 column. Three different Fe groupings are discriminated and assessed, including hydrophobic species of Fe bound to phenolic substances and related species (phenolic fraction), cationic species comprising simple Fe ions and labile Fe forms (cationic fraction), in addition to anionic and/or neutral Fe complexes with organic acids (residual fraction). The suitability of the procedure has been evaluated analyzing four bottled red wines. The results obtained were verified using another tandem column assemblage in which an adsorbing Amberlite XAD-16 column was exchanged by the Amberlite XAD-7HP column. The fractionation pattern ascertained for Fe in analyzed wines is discussed in reference to previously published works. In addition, a conditioning treatment and preparation of Amberlite XAD resins have been revised.