Operator Interpolation and Systems of Linear Equations and Inequalities in Euclidean Spaces

Ukrainian Mathematical Journal - We establish new criteria of compatibility for a linear system of equations (equivalent to the Kronecker–Capelli theorem) or inequalities (equivalent to the...     

Restricted testing conditions for the multilinear maximal operator

Restricted testing conditions were considered recently. For the maximal operator, Hytönen, Li and Sawyer [8] first obtained parental testing condition. Later, they [9] showed that it suffices to restrict testing to doubling cubes. Chen and Lacey [3] gave a similar restricted testing condition. In our paper, we discuss a version of the latter in the multilinear setting.

     

Analytic Functions in Local Shift-Invariant Spaces and Analytic Limits of Level Dependent Subdivision

Journal of Fourier Analysis and Applications - We develop a theory of Sobolev orthogonal polynomials on the Sierpiński gasket ( $$SG$$ ), which is a fractal set that can be viewed as a limit...     

Effect of External Factors on the Ferromagnetic Resonance Line Width in Exchange-Biased Structures

Physics of the Solid State - The external factors which influence the ferromagnetic resonance (FMR) line width in bilayer (ferromagnet/antiferromagnet) exchange-biased systems are studied. The...     

Portable single-sided NMR measurements at variable temperatures: Implementation of a thermo-controlled device and application to the heating of bread dough

A temperature control unit was implemented to vary the temperature of samples studied on a commercial Mobile Universal Surface Explorer nuclear magnetic resonance (MOUSE-NMR) apparatus. The device was miniaturized to fit the maximum MOUSE sampling depth (25 mm). It was constituted by a sample holder sandwiched between two heat exchangers placed below and above the sample. Air was chosen as the fluid to control the temperature at the bottom of the sample, at the interface between the NMR probe and the sample holder, in order to gain space. The upper surface of the sample was regulated by the circulation of water inside a second heat exchanger placed above the sample holder. The feasibility of using such a device was demonstrated first on pure water and then on several samples of bread dough with different water contents. For this, T1 relaxation times were measured at various temperatures and depths and were then compared with those acquired with a conventional compact closed-magnet spectrometer. Discussion of results was based on biochemical transformations in bread dough (starch gelatinization and gluten heat denaturation). It was demonstrated that, within a certain water level range, and because of the low magnetic field strength of the MOUSE, a linear relationship could be established between T1 relaxation times and the local temperature in the dough sample.     

Crystallographic Parameters of Special Grain Boundaries in Multicrystalline Silicon

Crystallography Reports - The orientation of grains and the special boundaries formed by them in multicrystalline silicon has been studied by electron backscattered diffraction. It is found that...     

Methods of Coherent X-Ray Diffraction Imaging

Crystallography Reports - Methods of coherent X-ray diffraction imaging of the spatial structure of noncrystalline objects and nanocrystals (nanostructures) are considered. Particular attention is...     

Optimization of the Ambulance Fleet Location and Relocation

Journal of Applied and Industrial Mathematics - We study the problem of optimal location of the ambulance fleet at the base stations. The objective is to minimize the average waiting time for...     

Dynamic mechanism of epileptic seizures generation and propagation after ischemic stroke

Nonlinear Dynamics - Epilepsy is the second largest neurological disease which seriously threatens human life and health. The one important reason of inducing epileptic seizures is ischemic stroke...