Dispersion polymerization of styrene: Effect of surfactant

The influence of poly(vinyl alcohol) (PVA), a steric stabilizer, and sodium dodecyl sulfate (SDS), an electrostatic stabilizer, on the stability of styrene dispersion polymerized systems was studied. It was shown that in stabilization by PVA there was pronounced bridging of the submicron emulsion particles to 10-μ dispersion particles and that the emulsion particles could not be washed off. In SDS stabilization, on the other hand, the emulsion formed was easily washed off because bridging with SDS does not occur. The surface tension of the aqueous phase measured during polymerization showed different characteristics for stable and unstable systems.     

Proton NMR studies of reduced porphyrin compounds

Detailed ¹H NMR studies of ms tetraphenylchlorins (H₂TPC), new amino- and hydroxypyrroline substituted ms tetraphenylchlorins and ms tetraphenylisobacteriochlorins (H₂TPisoB) are presented and discussed. The results obtained are consistent with the general aspects of the ring current models as applied to the parent porphyrins. According to proton chemical shifts a gradual reduction in the magnitude of the ring current is observed in the order ms tetraphenylporphyrin (H₂TPP) > H₂TPC> ms tetraphenylbacteriochlorin (H₂TPB) > H₂TPisoB. The ¹H NMR spectra show chemical non-equivalence of the pyrroline ring protons due to adjacent substituents, and effects of steric constraints on the aminoalkyl substituents due to the close vicinity to the meso phenyl rings. The non-equivalence of the methylene protons of the pyrroline ring produces geminal coupling between the two methylene protons and vicinal coupling with the adjacent pyrroline proton, more pronounced in H₂TPC? OH and in . Restricted configuration of the methylene groups in the ethyl groups of H₂TPC? C(H)(CH₃)N(CH₂CH₃)₂ produces observable geminal coupling between the methylene protons. ¹H NMR reveals the difference between two types of meso phenyls in the chlorins, and three types of meso phenyls in isobacteriochlorins, as reflected in the chemical shifts of the o-phenyl protons.     

New theta constant identities

The residue theorem is employed to obtain new identities amongpthe powers of theta constants with rational characteristics. The technique is then used to derive some known identities of Ramanujan. Dedicated to John Thompson for his many original contributions to mathematics Research by HMF partially sponsored by the Edmund Landau Center for Research in Mathematical Analysis, supported by the Minerva Foundation (Germany).     

On a Roelcke-precompact Polish group that cannot act transitively on a complete metric space

We study when a continuous isometric action of a Polish group on a complete metric space is, or can be, transitive. Our main results consist of showing that for certain Polish groups, namely Aut* (μ) and Homeo+ [0, 1], such an action can never be transitive (unless the space acted upon is a singleton).We also point out that in all known examples, this pathology coincides with the pathology of Polish groups that are not closed permutation groups and yet have discrete uniform distance, asking whether there is a relation. We conclude with a general characterisation/classification of transitive continuous isometric actions of a Roelcke-precompact Polish group on a complete metric space. In particular, the morphism from a Roelcke-precompact Polish group to its Bohr compactification is surjective.     

Cusp forms for congruence subgroups of and theta functions

In this paper we use theta functions with rational characteristic to construct cusp forms for congruence subgroups of .The action of the quotient group on these forms is conjugate to the linear action of on . We show that these forms are higher-dimensional analogues of the Fricke functions.

     

Reactions along the astrophysical s-process path and prospects for neutron radiotherapy with the Liquid-Lithium Target (LiLiT) at the Soreq Applied Research Accelerator Facility (SARAF)

The European Physical Journal A - An empirical formula is proposed for the two-proton decay half-lives. This study is an extension of the empirical formula reported recently by us for calculating...     

Effect of inititiator on the molecular weight distribution in dispersion polymerization of styrene

Dispersion polymerization of styrene in the particle size range of 10 μ with lauroyl peroxide as initiator results in a double-peak molecular weight (MW) distribution. The high-MW fraction was due to emulsion polymerization. The same phenomenon also exists in AIBN and benzoyl peroxide initiation, although it is less obvious. The kinetics of the reaction for dispersion polymerization was dependent on the concentration of the dispersing agent and the nature of the initiator.     

Applying the concept of partially ordered sets on the ranking of near-shore sediments by a battery of tests

When a ranking of some objects (chemicals, geographical sites, river sections, etc.) by a multicriteria analysis is of concern, then it is often difficult to find a common scale among the criteria, and therefore even the simple sorting process is performed by applying additional constraints, just to get a ranking index. However such additional constraints, often arising from normative considerations, are controversially discussed. The theory of partially ordered sets and its graphical representation (Hasse diagrams) does not need such additional information just to sort the objects. Here, the approach of using partially ordered sets is described by applying it to a battery of tests, developed by Dutka et al. In our analysis we found the following: (1) The dimension analysis of partially ordered sets suggests that, at least in the case of the 55 analyzed samples and the evaluation by the scores, developed by Dutka et al., there is a considerable redundancy with respect to ranking. The visualization of the sediment sites can be performed within a two-dimensional grid. (2) Information, obtained from the structure of the Hasse diagram: For example six classes of sediment sites have high priority, and each class exhibits a different pattern of results. (3) Loss of information, when an aggregation of test results is used in order to guarantee complete comparability among all objects. A relation between information drawn from the graphic and the uncertainty of ranking after using an aggregation is given. (4) The sensitivity analysis identifies one test as most important, namely the test for Fecal Coliforms/Escherichia coli. This means that the ranking of samples is heavily influenced by the results of this specific test.     

On the Curve X(9)

Computations using theta functions with characteristic show that the modular curve X(9) is the complete intersection of two cubics. The holomorphic differentials and Weierstrass gap sequence are also computed.