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...     

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.     

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.     

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.     

Nonlinear interaction of optical beams in a Bose-Einstein condensate

The results of simulation of the interaction of optical beams with different frequencies in an inhomogeneous Bose-Einstein condensate are given. The potential well has a parabolic profile, and the nonlinearity belongs to a defocusing class. The total reflection of a signal wave induced by a pump beam at a negative inhomogeneity during the wave capture in the potential well is considered.     

Reaction of N-acetyldehydrophenylalanyl-S-proline with Ca(II) and Ni(II) ions and its role in asymmetric hydrogenation

N-Ac-Phe-S-Pro forms strong coordination complexes with the CO₂H group of the proline residue and weak coordination complexes through the -C(=O)-N groups with Ca(II) and Ni(II) ions in 95% aqueous methanol as indicated by the pK _a values, PMR spectroscopy, and paramagnetic broadening of the¹³C NMR signals in the nickel complex. Complex formation enhances the rigidity of the dehydrodipeptide conformation, leading to a strong increase in the optical yield upon hydrogenation over achiral catalysts.Institute of Food Substances, Russian Academy of Sciences, 117813 Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 7, pp. 1667–1670, July, 1992.     

Elasto-dipolar magnons—a new class of nonexchange spin-wave excitations

Interference of phonon and magnetic dipolar spin-spin interaction mechanisms in a finite magnet can result in a previously unexplored class of nonexchange spin waves.     

Morpholine-substituted soluble polyimides

The interaction of undescribed 1,3-diamino-4-morpholinebenzene with dianhydrides of various aromatic tetracarboxylic acids yields morpholine-substituted soluble polyimides. The thermal properties of these polymers are studied.