A generalisation of de la Vallée-Poussin procedure to multivariate approximations

Advances in Computational Mathematics - Persistence diagrams are one of the main tools in the field of Topological Data Analysis (TDA). They contain fruitful information about the shape of data....     

Elastic Dipole Mechanism of the Formation and Collapse of Fano Resonances at the Transmission of Transverse Phonons through Layered Magnetic Heterostructures

JETP Letters - At the resonant passage of a plane elastic shear wave through an acoustically continuous heterostructure consisting of magnetic and nonmagnetic layers in a symmetric nonmagnetic...     

Synthetic Humic Acids Solubilize Otherwise Insoluble Phosphates to Improve Soil Fertility

Artificial humic acids (A‐HA) made from biomass in a hydrothermal process turn otherwise highly insoluble phosphates (e.g. iron phosphate as a model) into highly available phosphorus, which contributes to the fertility of soils and the coupled plant growth. A detailed electron microscopy study revealed etching of the primary iron phosphate crystals by the ‐COOH and phenolic groups of humic acids, but also illustrated the importance of the redox properties of humic matter on the nanoscale. The combined effects result in the formation of then bioavailable phosphate nanoparticles stabilized by humic matter. Typical agricultural chemical tests indicate that the content of total P and directly plant‐available P improved largely. Comparative pot planting experiments before and after treatment of phosphates with A‐HA demonstrate significantly enhanced plant growth, as quantified in higher aboveground and belowground plant biomass.     

Excitation of surface waves near the boundary of nonlinear induced inhomogeneities

Trapping the inclined beam in a surface wave with a powerful reference beam at another frequency in defocusing media with cubic or cascade quadratic nonlinearity is investigated for the first time. The results from numerical simulations of the dynamics of flat and cylindrical surface wave formation are presented. Gaussian, Hyper-Gaussian, slit, and tube reference beams are considered.     

Low power, biologically benign NIR light triggers polymer disassembly

Near infrared (NIR) irradiation can penetrate up to 10 cm deep into tissues and be remotely applied with high spatial and temporal precision. Despite its potential for various medical and biological applications, there is a dearth of biomaterials that are responsive at this wavelength region. Herein we report a polymeric material that is able to disassemble in response to biologically benign levels of NIR irradiation upon two-photon absorption. The design relies on the photolysis of the multiple pendant 4-bromo7-hydroxycoumarin protecting groups to trigger a cascade of cyclization and rearrangement reactions leading to the degradation of the polymer backbone. The new material undergoes a 50% Mw loss after 25 sec of ultraviolet (UV) irradiation by single photon absorption and 21 min of NIR irradiation via two-photon absorption. Most importantly, even NIR irradiation at biologically benign laser power is sufficient to cause significant polymer disassembly. Furthermore, this material is well tolerated by cells both before and after degradation. These results demonstrate for the first time a NIR sensitive material with potential to be used for in vivo applications.     

Characterization Theorem for Best Polynomial Spline Approximation with Free Knots,Variable Degree and Fixed Tails

In this paper, we derive a necessary condition for a best approximation by piecewise polynomial functions of varying degree from one interval to another. Based on these results, we obtain a characterization theorem for the polynomial splines with fixed tails, that is the value of the spline is fixed in one or more knots (external or internal). We apply nonsmooth nonconvex analysis to obtain this result, which is also a necessary and sufficient condition for inf-stationarity in the sense of Demyanov–Rubinov. This paper is an extension of a paper where similar conditions were obtained for free tails splines. The main results of this paper are essential for the development of a Remez-type algorithm for free knot spline approximation.     

Unusual Fragmentation of β-Linked Peptides by ExD Tandem Mass Spectrometry

Ion-electron reaction based fragmentation methods (ExD) in tandem mass spectrometry (MS), such as electron capture dissociation (ECD) and electron transfer dissociation (ETD) represent a powerful tool for biological analysis. ExD methods have been used to differentiate the presence of the isoaspartate (isoAsp) from the aspartate (Asp) in peptides and proteins. IsoAsp is a β₃-type amino acid that has an additional methylene group in the backbone, forming a C_α–C_β bond within the polypeptide chain. Cleavage of this bond provides specific fragments that allow differentiation of the isomers. The presence of a C_α–C_β bond within the backbone is unique to β-amino acids, suggesting a similar application of ExD toward the analysis of peptides containing other β-type amino acids. In the current study, ECD and ETD analysis of several β-amino acid containing peptides was performed. It was found that N–C_β and C_α–C_β bond cleavages were rare, providing few c and z type fragments, which was attributed to the instability of the C_β radical. Instead, the electron capture resulted primarily in the formation of a and y fragments, representing an alternative fragmentation pathway, likely initiated by the electron capture at a backbone amide nitrogen protonation site within the β amino acid residues.     

Dependence of the properties of polycaproamide obtained in the presence of benzhydrazide on the symmetry type of the unit cell

The structure and properties of polycaproamide obtained in the presence of benzhydrazide have been studied. They are shown to depend on the duration of application of pressure in the mold. Under tensile deformation a transition from hexagonal to monoclinic polycaproamide takes place in the neck.Lugansk Machine-Building Institute. Institute of the Chemistry of High-Molecular Compounds, As UkrSSR, Kiev. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1125–1127, November–December, 1968.     

Reflection of light from an induced moving lattice

The reflection, refraction, and penetration of a signal optical pulse upon interaction with a pumping-induced moving lattice in media with cubic nonlinearity has been investigated. Numerical simulation is performed for different lattices and signal pulses.