Factors in the Single-Step Bulk Process Preparation of a Triple Janus Emulsion

Some factors in the preparation of triple Janus emulsions in a single-step bulk process were investigated using optical microscopy. The emulsions consisted of water, O.097 weight fraction, a commercial surfactant, Tween 80, 0.03 weight fraction, a vegetable oil (VO), 0.18 weight fraction, and a silicone oil (SO), 0.72 weight fraction. A surprising connection was found between the state of the compounds prior to mixing and the final morphology as well as stability of the emulsion. Separately adding the compounds or with the surfactant dissolved in the vegetable oil, prior to mixing, did not result in a Janus emulsion. Instead, simpler emulsions with limited stability were attained even with prolonged mixing. Storing the compounds together without mixing for two days followed by mixing resulted in a Janus emulsion in which the (VO + SO)/W/VO drops were more sparsely populated with Janus drops, and emulsion stability was limited. Finally, preparing the emulsion from the aqueous surfactant solution and the two oils gave a (VO + SO)/W/VO/SO emulsion with the W drops heavily populated by Janus drops and with improved stability.      

Intersection Local Times as Generalized White Noise Functionals

For any dimension we present the expansions of Brownian motion self-intersection local times in terms of multiple Wiener integrals. Suitably subtracted, they exist in the sense of generalized white noise functionals; their kernel functions are given in closed (and remarkably simple) form.     

Synthesis and reactions of methylbenzo[c]quinolizinium salts

Six isomers of the methylbenzo[c]quinolizinium salt 3 including four new monomethyl derivatives were synthesized by thermal-intramolecular quaternization of the cis-methyl-substituted 2-[2-(2-chlorophenyl)-vinyl]pyridines 4 or by the irradiation of trans- 4 with selected wavelengths (290 < λ < 340 nm and λ > 400 nm) in acetonitrile. Among the regioisomeric monomethyl derivatives 3 , the 1-, 3-, and 6-methyl derivatives 3b, 3d , and 3g reacted with p-methoxybenzaldehyde in the presence of bis(l-piperidino)-(p-methoxyphenyl)-methane 7 to yield trans-(p-methoxystyryl)benzo[c]quinolizinium salts 6 . The reactivity of 3 and methylbenzo[a]quinolizinium salts 1 was discussed on the basis of their π-electron energy.     

Generalized Brownian functionals and stochastic integrals

The purpose of this paper is two-fold; i) a new class of generalized Brownian functionals, in fact generalized linear functionals, is introduced and ii) generalized stochastic integrals based on creation operators are discussed. These topics are in line with the causal calculus of Brownian functionals.Communicated by H. H. Kuo     

Hida Replies:

A Reply to the Comment by Yang and Hyman.     

A noise of new type and its application

The purpose of this paper is to introduce a new noise depending on the space parameter and the construction of a space of generalized functional of the new noise. One of the significant applications is to give a concrete answer to the jump finding problem raised in [10] where the first step to the approach has been made. It is noted that the new noise, denoted by P??(u), is quite different from the time derivative ?(t) of a Poisson process P(t).