On local convexity of nonlinear mappings between Banach spaces

We find conditions for a smooth nonlinear map f: U → V between open subsets of Hilbert or Banach spaces to be locally convex in the sense that for some c and each positive ? < c the image f(B _?(x)) of each ?-ball B _?(x) ? U is convex. We give a lower bound on c via the second order Lipschitz constant Lip₂(f), the Lipschitz-open constant Lip_o(f) of f, and the 2-convexity number conv₂(X) of the Banach space X.     

Time dependent magnetically induced variations in optical transmission of magnetite nanoparticle aqueous suspension

We observe time dependent variations in the light intensity transmitted through an aqueous suspension of Fe₃O₄ nanoparticles caused by applied DC magnetic field. Two types of variations can be distinguished. Fast response takes less than 1ms while slow variations occur at the time interval fromseconds to hundreds of minutes. Possible mechanisms of these variations are discussed. Formation of chain-like structures consisted from iron oxide nanoparticles is responsible for the slow variations. It is also accompanied by a diffraction pattern when the magnetic field is orthogonal to the light beam. Fast variations are due to particle rotation and reorientation of the magnetic moment inside a nanoparticle.     

Stacked and continuous helical self-assemblies of guanosine monophosphates detected by vibrational circular dichroism

The aim of this study was to characterize self-assembled structures of guanosine derivatives in aqueous solutions by vibrational circular dichroism (VCD) and electronic circular dichroism (ECD). Three guanosine derivatives were studied [5'-guanosine monophosphate (GMP), diphosphate (GDP), and triphosphate (GTP)] using a broad range of concentrations and various metal/guanosine ratios. VCD was used for the first time in this field and showed itself to be a powerful method for obtaining specific structural information in solution. It can also help to determine the impact that the cations have, when added to the solution, on the versatile structures of guanine derivatives in terms of their association and disassociation. Based on the markedly different intensities and signs of the VCD signals observed for different concentrations of guanosine derivatives, we propose various structures based on guanine quartets for high guanosine concentrations and high K(+)/guanosine ratios (i.e., columnar helical organization of the quartets, which are rearranged into a continuous helix). We performed a degenerate coupled oscillator (DCO) calculation to interpret the VCD spectra obtained and how they vary during the assembly of guanosine derivatives. The calculations correctly predicted the VCD spectra and enabled us to identify the structures of the metal cation/guanosine monophosphate aggregates. ECD in the ultraviolet region was used as a diagnostic tool to characterize the studied systems and as a contact point between the previously defined structures of the guanine derivative assemblies and the molecular systems studied here. These studies revealed that the VCD technique is a powerful new method for determining the structures of optically active guanosine motifs.     

Simulation of vibrational spectra of SiO2 nanoclusters

The vibrational density of states of α-SiO₂ nanoclusters with different diameters has been calculated in terms of the shell model in the harmonic approximation. A decrease in the diameter of nanoparticles leads to an increase in the vibrational density of states in the low-frequency range of the spectrum, a shift of the spectrum in the high-frequency range, and the generation of gap vibrational modes. The interpretation of the observed features has been proposed.     

The Crystal Structure of Orthocetamol Solved by 3D Electron Diffraction

Orthocetamol is a regioisomer of the well‐known pain medication paracetamol and a promising analgesic and an anti‐arthritic medicament itself. However, orthocetamol cannot be grown as single crystals suitable for X‐ray diffraction, so its crystal structure has remained a mystery for more than a century. Here, we report the ab‐initio structure determination of orthocetamol obtained by 3D electron diffraction, combining a low‐dose acquisition method and a dedicated single‐electron detector for recording the diffracted intensities. The structure is monoclinic, with a pseudo‐tetragonal cell that favors multiple twinning on a scale of a few tens of nanometers. The successful application of 3D electron diffraction to orthocetamol introduces a new gold standard of total structure solution in all cases where X‐ray diffraction and electron‐microscope imaging methods fail.     

Intrinsic luminescence of rare-earth oxyorthosilicates

The spectra and decay kinetics of luminescence and the excitation and reflection spectra of the luminescence of orthosilicates A ₂SiO₅ (A = Y, Lu, Sc, Gd), both nominally pure and doped with cerium, are measured using time-resolved VUV spectroscopy in the ranges of energies ?ν = 1.5–16 eV and temperatures T = 8–3000 K. The band structure of the crystals is calculated in the local electron density approximation (LDA). The origin of the intrinsic luminescence in the crystals studied is established, and the assumption regarding the existence of self-trapped excitons and their structure is made.     

Surface Chemistry of Nanohybrids with Fumed Silica Functionalized by Polydimethylsiloxane/Dimethyl Carbonate Studied Using 1H, 13C,and 29Si Solid-State NMR Spectroscopy

The investigation of molecular interactions between a silica surface and organic/inorganic polymers is crucial for deeper understanding of the dominant mechanisms of surface functionalization. In this work, attachment of various depolymerized polydimethylsiloxanes (PDMS) of different chain lengths, affected by dimethyl carbonate (DMC), to silica nanoparticles pretreated at different temperatures has been studied using ²⁹Si, ¹H, and ¹³C solid-state NMR spectroscopy. The results show that grafting of different modifier blends onto a preheated silica surface depends strongly on the specific surface area (SSA) linked to the silica nanoparticle size distributions affecting all textural characteristics. The pretreatment at 400 °C results in a greater degree of the modification of (i) A-150 (SSA = 150 m²/g) by PDMS-10/DMC and PDMS-1000/DMC blends; (ii) A-200 by PDMS-10/DMC and PDMS-100/DMC blends; and (iii) A-300 by PDMS-100/DMC and PDMS-1000/DMC blends. The spectral features observed using solid-state NMR spectroscopy suggest that the main surface products of the reactions of various depolymerized PDMS with pretreated nanosilica particles are the (CH₃)₃SiO-[(CH₃)₂SiO-]_x fragments. The reactions occur with the siloxane bond breakage by DMC and replacing surface hydroxyls. Changes in the chemical shifts and line widths, as shown by solid-state NMR, provide novel information on the whole structure of functionalized nanosilica particles. This study highlights the major role of solid-state NMR spectroscopy for comprehensive characterization of functionalized solid surfaces.     

Virtual Screening in Search for a Chemical Probe for Angiotensin-Converting Enzyme 2 (ACE2)

We elaborate new models for ACE and ACE2 receptors with an excellent prediction power compared to previous models. We propose promising workflows for working with huge compound collections, thereby enabling us to discover optimized protocols for virtual screening management. The efficacy of elaborated roadmaps is demonstrated through the cost-effective molecular docking of 1.4 billion compounds. Savings of up to 10-fold in CPU time are demonstrated. These developments allowed us to evaluate ACE2/ACE selectivity in silico, which is a crucial checkpoint for developing chemical probes for ACE2.     

Spectroscopic investigation of the cathode region of an independent glow discharge in He

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 51, No. 2, pp. 203–207, August, 1989.