ON A NEW CLASS OF ANALYTIC FUNCTION DERIVED BY A FRACTIONAL DIFFERENTIAL OPERATOR

Making use of the fractional differential operator, we impose and study a new class of analytic functions in the unit disk （type fractional differential equation）. The main object of this paper is to investigate inclusion relations, coefficient bound for this class. Moreover, we discuss some geometric properties of the fractional differential operator.     

Turbulence production in flow over a wavy wall

Measurements of the spatial and time variation of two components of the velocity have been made over a sinusoidal solid wavy boundary with a height to length ratio of 2a/λ = 0.10 and with a dimensionless wave number of α⁺ = (2π/λ)(v/u ^?) = 0.02. For these conditions, both intermittent and time-mean flow reversals are observed near the troughs of the waves. Statistical quantities that are determined are the mean streamwise and normal velocities, the root-meansquare of the fluctuations of the streamwise and normal velocities, and the Reynolds shear stresses. Turbulence production is calculated from these measurements. The flow is characterized by an outer flow and by an inner flow extending to a distance of about α^?1 from the mean level of the surface. Turbulence production in the inner region is fundamentally different from flow over a flat surface in that it is mainly associated with a shear layer that separates from the back of the wave. Flow close to the surface is best described by an interaction between the shear layer and the wall, which produces a retarded zone and a boundary-layer with large wall shear stresses. Measurements of the outer flow compare favorably with measurements over a flat wall if velocities are made dimensionless by a friction velocity defined with a shear stress obtained by extrapolating measurements of the Reynolds stress to the mean levels of the surface (rather than from the drag on the wall).     

Modular fluorescent benzobis(imidazolium) salts: syntheses, photophysical analyses, and applications

A series of benzobis(imidazolium) (BBI) salts has been prepared and studied as a new class of versatile fluorescent materials. Using a high yielding, modular synthetic strategy, BBI salts with a range of functionality poised for investigating fundamental and applications-oriented characteristics, including emission wavelength tunability, solvatochromism, red-edge excitation, chemical stability, multiphoton excitation, and protein conjugation, were prepared in overall yields of 40-97%. Through structural variation, the BBIs exhibited lambda(em) ranging between 329 and 561 nm while displaying phi(f)s up to 0.91. In addition, the emission characteristics of these salts were found to exhibit strong solvent dependencies with Stokes shifts ranging from 4570 to 13 793 cm(-1), depending on the nature of the BBI core. Although red-edge effects for BBI salts with Br and BF4 counterions were found to be similar, unique characteristics were displayed by an analogue with MeSO4 anions. The stability of an amphiphilic BBI was quantified in aqueous solutions of varying pH, and >85% of the emission intensity was retained after 2 h at pH 3-9. Through multiphoton excitation experiments in aqueous solutions, a BBI salt was found to exhibit three-photon fluorescence action cross sections similar to serotonin. The application of BBI salts as fluorescent protein tags was demonstrated by conjugating bovine serum albumin to a maleimide-functionalized derivative.