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.

     

A low molecular weight hydrogel which exhibits electroosmotic flow and its use as a bioreactor and for electrochromatography of neutral species

A low molecular weight hydrogel which exhibits electroosmotic flow is described, and its use for separation and biocatalytic applications that require passage of a solvent stream through the gel is demonstrated.     

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.     

Coding for locality in reconstructing permutations

The problem of storing permutations in a distributed manner arises in several common scenarios, such as efficient updates of a large, encrypted, or compressed data set. This problem may be addressed in either a combinatorial or a coding approach. The former approach boils down to presenting large sets of permutations with locality, that is, any symbol of the permutation can be computed from a small set of other symbols. In the latter approach, a permutation may be coded in order to achieve locality. Both approaches must present low query complexity to allow the user to find an element efficiently. We discuss both approaches, and give a particular focus to the combinatorial one. In the combinatorial approach, we provide upper and lower bounds for the maximal size of a set of permutations with locality, and provide several simple constructions which attain the upper bound. In cases where the upper bound is not attained, we provide alternative constructions using a variety of tools, such as Reed-Solomon codes, permutation polynomials, and multi-permutations. In addition, several low-rate constructions of particular interest are discussed. In the coding approach we discuss an alternative representation of permutations, present a paradigm for supporting arbitrary powers of the stored permutation, and conclude with a proof of concept that permutations may be stored more efficiently than ordinary strings over the same alphabet.     

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.     

13C NMR studies of reduced porphyrin compounds. Aromatic delocalization pathways

¹³C NMR spectra of ms-tetraphenylchlorins, new aminoalkyl- and hydroxy-pyrroline substituted ms-tetra-phenylchlorins, and ms-tetraphenylisobacteriochlorins are presented and discussed. Significant changes in the chemical shifts of the α-pyrrole, α-pyrroline and meso skeletal carbons are found in chlorins and isobacteriochlorins in comparison to porphyrins. In contrast, the chemical shifts of the β-pyrrole carbons are almost unaffected by the structural modifications in chlorin and isobacteriochlorin. The chemical shifts of the α-pyrrole carbons in the various chlorins and isobacteriochlorins are strongly affected by the substitutents of the pyrroline ring, or by the introduction of an additional pyrroline ring in isobacteriochlorins. The results show that most of the electron density is concentrated in the unreduced part of the molecule, i.e. in the pyrrole rings and, especially, on the α-pyrrole carbons and is transferred or removed through the aromatic pathway by substituents on the pyrroline ring. These observations are supporting evidence that the α-pyrrole, α-pyrroline and meso-carbons are in the aromatic pathway and favour the proposal of a 16 atom dianion as the preferred delocalization pathway in chlorins and isobacteriochlorins.