How Fast can a Subharmonic Function Decay Along a Ray?

Much is known about the connection between the growth and decayof subharmonic functions. The results indicate that there isa general principle: asubharmonic function cannot decay ‘toofast’ relative to its growth.Three theorems are provedwhich, together with work previously published elsewhere, givea fairly complete account of how this principle works out fora subharmonic function having extremal decay along a ray. 1991Mathematics Subject Classification: 30D20, 31A05.     

Biosorption of beryllium from aqueous solutions onto modified chitosan resin: Equilibrium,kinetic and thermodynamic study

The goal of the present work is the recovery of beryllium ion from their solution by modified chitosan hydrogel. Chitosan was chemically cross-linked with glutaraldehyde to prevent its dissolution in aqueous acidic solutions. The obtained chitosan/glutaraldehyde adsorbent was reacted with chloroacetic acid to produce carboxymethyl chitosan (CMC), which was converted into sodium form by reaction with sodium hydroxide solution to increase its hydrophilic properties. The chemically synthesized chitosan adsorbent contains carboxylate group that expected to have a strong affinity to beryllium ions according to the hard-soft acid-base concept by Pearson because that beryllium ion is a hard acid and has smaller ionic radii. The synthesized adsorbent was characterized and its affinity towards beryllium ions was tested. The different experimental parameters including pH, beryllium concentration, agitation period and temperature were studied to optimize the biosorption process. The maximum biosorption values of beryllium species on the investigated biosorbent are 44.96 and 36.72?mg/g at pH 1 and 5, respectively. Kinetics and thermodynamic parameters of the biosorption process were evaluated from kinetic and biosorption experiments. The adsorbed beryllium species were eluted with a 3?M H₂SO₄ solution.     

Nematic nanotube gels

We report the creation of nematic nanotube gels containing large domains of isolated, oriented, half-micron-long, single-wall carbon nanotubes (SWNTs). We make them by homogeneously dispersing surfactant coated SWNTs at low concentration in an N-isopropyl acrylamide gel and then inducing a volume-compression transition. These gels exhibit hallmark properties of a nematic: birefrigence, anisotropy in optical absorption, and disclination defects. We also investigate the isotropic-to-nematic transition of these gels, and we describe the physical properties of their ensuing nematic state, including a novel buckling of sample walls. Finally, we provide a simple model to explain our observations.     

Search for isovector giant monopole resonances via the Pb(3He,tp) reaction

The (nat)Pb(3He,tp) reaction at E(3He) = 177 MeV was studied to identify 2Planck's over 2piomega isovector monopole strength in Bi isotopes. Monopole strength was found in the region -45相似文献