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.

     

Multicomponent Diamond-Like Semiconductors Based on the InBV–CdS System: Bulk and Surface Properties

Semiconductors - According to developed methods, in the fields of the mutual solubility of initial binary compounds (InP, InSb, and CdS), solid solutions of the InP–CdS and InSb–CdS...     

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...     

Progressive NO2 Sensors with Rapid Alarm and Persistent Memory-Type Responses for Wide-Range Sensing Using Antimony Triselenide Nanoflakes

Antimony triselenide (Sb₂Se₃) nanoflake-based nitrogen dioxide (NO₂) sensors exhibit a progressive bifunctional gas-sensing performance, with a rapid alarm for hazardous highly concentrated gases, and an advanced memory-type function for low-concentration (<1 ppm) monitoring repeated under potentially fatal exposure. Rectangular and cuboid shaped Sb₂Se₃ nanoflakes, comprising van der Waals planes with large surface areas and covalent bond planes with small areas, can rapidly detect a wide range of NO₂ gas concentrations from 0.1 to 100 ppm. These Sb₂Se₃ nanoflakes are found to be suitable for physisorption-based gas sensing owing to their anisotropic quasi-2D crystal structure with extremely enlarged van der Waals planes, where they are humidity-insensitive and consequently exhibit an extremely stable baseline current. The Sb₂Se₃ nanoflake sensor exhibits a room-temperature/low-voltage operation, which is noticeable owing to its low energy consumption and rapid response even under a NO₂ gas flow of only 1 ppm. As a result, the Sb₂Se₃ nanoflake sensor is suitable for the development of a rapid alarm system. Furthermore, the persistent gas-sensing conductivity of the sensor with a slow decaying current can enable the development of a progressive memory-type sensor that retains the previous signal under irregular gas injection at low concentrations.     

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...     

Neutron Spectroscopy: The Initial Steps of Development in Our Country and Several Achievements

Crystallography Reports - Some questions related to the establishment, development, and prospects of physical studies using inelastic thermal-neutron scattering are briefly reviewed. The directions...     

Fractional derivative method for describing solitons on the surface of deep water

Theoretical and Mathematical Physics - The fractional derivative method is used to take wave dispersion into account in the wave equation when describing the propagation of gravitational soliton...     

Polycrystallinity in Gallium Arsenide Crystals Grown by the Czochralski Method

Crystallography Reports - The specific features of the formation of crystallites in gallium arsenide crystals grown by the Czochralski method have been investigated. The crystallites are found to...     

Biosynthesis of zinc oxide nanoparticles using Euphorbia milii leaf constituents: Characterization and improved photocatalytic degradation of methylene blue dye under natural sunlight

A facile biosynthesis route was followed to prepare zinc oxide nanoparticles (ZnO NPs) using Euphorbia milii (E. milii) leaf constituents. The SEM images exhibited presence of spherical ZnO NPs and the corresponding TEM images disclosed monodisperse nature of the ZnO NPs with diameter ranges between 12 and 20 nm. The Brunauer–Emmett–Teller (BET) analysis revealed that the ZnO NPs have specific surface area of 20.46 m²/g with pore diameter of 2 nm–10 nm and pore volume of 0.908 cm³/g. The EDAX spectrum exemplified the existence of Zn and O elements and non-appearance of impurities that confirmed pristine nature of the ZnO NPs. The XRD pattern indicated crystalline peaks corresponding to hexagonal wurtzite structured ZnO with an average crystallite size of 16.11 nm. The FTIR spectrum displayed strong absorption bands at 512 and 534 cm^?1 related to ZnO. The photocatalytic action of ZnO NPs exhibited noteworthy degradation of methylene blue dye under natural sunlight illumination. The maximum degradation efficiency achieved was 98.17% at an illumination period of 50 min. The reusability study proved considerable photostability of the ZnO NPs during photocatalytic experiments. These findings suggest that the E. milii leaf constituents can be utilized as suitable biological source to synthesis ZnO NPs for photocatalytic applications.     

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...