A new class of long-tailed pausing time densities for the CTRW

We present some asymptotic results for the family of pausing time densities having the asymptotic (t) property(t) [t ln¹⁺(t/T)]^–1. In particular, we show that for this class of pausing time densities the mean-squared displacement r ²(t) is asymptotically proportional to ln(t/T), and the asymptotic distribution of the displacement has a negative exponential form.     

Properties of noninteger moments in a first passage time problem

We calculate the moments t ^q , whereq is not necessarily an integer, of the first passage time to trapping for a simple diffusion problem in one dimension. If a characteristic length of the system isL and t _q ~L (q) asL, then we show that there is a phase transition atq=q _c such that whenq<q _c ,(g)=0, and forq>q _c , (q) is a linear function ofq. These analytical results can be used to explain results for large moments for diffusion on a hierarchic structure. We also show how to calculate noninteger moments in terms of characteristic functions.     

Synthesis and characteristics of microspheres of polystyrene derivatives

Two sytrene derivatives formylstyrene and styrene sulfonylcholoride, were synthesized. Polymeric microspheres in diameters ranging from 0.1 to 2 μm were synthesized by polymerization of chlormoethylstyrene, formylstyrene, and styrene sulfonylcholoride in organic solvents, in the presence of appropriate surfactants. The kinetics of microsphere formation were studied. The molecular weight distribution of the products was determined by gel permeation chromatography. Conditions for binding various amino ligands to the microspheres were also established.     

Effect of solvents on the electrochemistry of olefins and aromatic molecules

Cyclic voltammetry and electrolysis studies were carried out in dimethyl sulfoxide, diglyme and liquid ammonia. The depolarizers were diethyl fumarate, ethyl cinnamate, stilbene and anthracene. The reduction reactions were carried out in the presence of organic halides, phenol, acids and water. The rates of the reactions were measured. The main solvent effect was noticed with water which reacts 100 times faster in diglyme than in liquid ammonia or DMSO. The results of electrolytic experiments with two reactants simultaneously were compared with those predicted from the kinetic data.     

Acrolein polymerization: Monodisperse,homo, and hybrido microspheres,synthesis, mechanism,and reactions

Monodisperse polyacrolien (PA) microspheres were obtained by a single step process via two mechanisms: (a) aqueous polymerization of acrolein under alkaline conditions and (b) aqueous radical polymerization of acrolein by irradiation with a cobalt source. The diameter of the former microspheres can be varied from 0.04 up to 8 μm. The monodispersity of the system is also discussed. The diameter of the latter microspheres can be varied up to 0.2 μm. Hybrido PA microspheres were formed by grafting PA microspheres of average diameter of 0.1 μm obtained by irradiation onto the surface of PA microspheres produced by the alkaline mechanism. The aldehyde content of the microspheres prepared by irradiation is much higher than those of the microspheres formed under alkaline conditions. The aldehyde groups were used for the covalent binding of ligands containing primary amino groups, such as proteins and drugs, in a single step under physiological pH.