Generalized fractional integral operators on variable exponent Morrey spaces of an integral form

Acta Mathematica Hungarica - We establish the boundedness of generalized fractional integral operators $$I_{\rho}$$ on variable exponent Morrey spaces of an integral form...     

Reproducing Kernels for Iterated Parabolic Operators on the Upper Half Space with Application to Polyharmonic Bergman Spaces

We consider parabolic operators of fractional order and their iterates on the upper half space of the euclidean space. We deal with Hilbert spaces of solutions of those parabolic equations. We shall show, in this note, the existence of reproducing kernels and give a formula by using their fundamental solutions. As an application, we also discuss the polyharmonic Bergman spaces and give their reproducing kernels by using the Poisson kernel on the upper half space.     

Flexible Alkylene Bridges as a Tool To Engineer Crystal Distyrylbenzene Structures Enabling Highly Fluorescent Monomeric Emission

To design ultrabright fluorescent solid dyes, a crystal engineering strategy that enables monomeric emission by blocking intermolecular electronic interactions is required. We introduced propylene moieties to distyrylbenzene (DSB) as bridges between the phenyl rings either side of its C=C bonds. The bridged DSB derivatives formed compact crystals that emit colors similar to those of the same molecules in dilute solution, with high quantum yields. The introduction of flexible seven-membered rings to the DSB core produced moderate distortion and steric hindrance in the DSB π-plane. However, owing to this strategy, it was possible to control the molecular arrangement with almost no decrease in the crystal density, and intermolecular electronic interactions were suppressed. The bridged DSB crystal structure differs from other DSB derivative structures; thus, bridging affords access to novel crystalline systems. This design strategy has important implications in many fields and is more effective than the conventional photofunctional molecular crystal design strategies.     

Trudinger's inequality for Riesz potentials of functions in Musielak–Orlicz spaces

In this paper we are concerned with Trudinger's inequality for Riesz potentials of functions in Musielak–Orlicz spaces.     

Fast multipole method for three-dimensional systems with periodic boundary condition in two directions

We derived a new expression for the electrostatic interaction of three-dimensional charge-neutral systems with two-dimensional periodic boundary conditions (slab geometry) using a fast multipole method (FMM). Contributions from all the image cells are expressed as a sum of real and reciprocal space terms, and a self-interaction term. The reciprocal space contribution consists of two parts: zero and nonzero terms of the absolute value of the reciprocal lattice vector. To test the new expressions, electrostatic interactions were calculated for a randomly placed charge distribution in a cubic box and liquid water produced by molecular dynamics calculation. The accuracy could be controlled by the degree of expansion of the FMM. In the present expression, the computational complexity of the electrostatic interaction of N-particle systems is order N, which is superior to that of the conventional two-dimensional periodic Ewald method for a slab geometry and the particle mesh Ewald method with a large empty space at an interface of the unit cell. © 2020 Wiley Periodicals, Inc.     

Effects of sub-millimeter-bubble injection on transition to turbulence in natural convection boundary layer along a vertical plate in water

Temperature and velocity measurements are performed to clarify the effects of sub-millimeter-bubble injection on the transition to turbulence in the natural convection boundary layer along a vertical plate in water. In particular, we focus on the relationship between the bubble injection position L and the transition to turbulence in the natural convection boundary layer. The bubble injection positions used in our experiments are L = 1.6 and 3.6 mm. Bubble injection at L = 1.6 mm delays the transition to turbulence in the natural convection boundary layer, while that at L = 3.6 mm accelerates the transition to turbulence in the boundary layer. In the case of L = 1.6 mm, the appearance region of the liquid velocity fluctuation in the bubble-induced upward flow in the upstream unheated section is restricted to near the wall, although the peak of the liquid velocity fluctuation is high. In contrast, in the case of L = 3.6 mm, the relatively large liquid velocity fluctuation is distributed widely over the laminar boundary layer width. These results suggest that the effect of the liquid velocity fluctuation on the laminar boundary layer is quite different between L = 1.6 and 3.6 mm. It is therefore expected that the transition to turbulence in the natural convection boundary layer for the case with bubble injection is dependent on the magnitude and appearance region of the liquid velocity fluctuation in the bubble-induced upward flow in the upstream unheated section.