Aurifeuillian factorizations and the period of the Bell numbers modulo a prime

We show that the minimum period modulo of the Bell exponential integers is for all primes and several larger . Our proof of this result requires the prime factorization of these periods. For some primes the factoring is aided by an algebraic formula called an Aurifeuillian factorization. We explain how the coefficients of the factors in these formulas may be computed.

     

The effect of interface deformation due to gravity on line tension measurement by the capillary rise in a conical tube

Much research has been done on line tension measurement and interpretation, and attempts have also been made to measure line tension with simple, cheap and reliable methods that do not require excessive sophistication. Of particular interest is the method of determining line tensions of solid–liquid–vapor systems from the capillary rise in a conical tube. This simple and relatively inexpensive method gives line tension values comparable to those reported in the literature obtained via highly sophisticated instruments or techniques such as the well known axisymmetric drop shape analysis technique. The absolute value of line tension obtained using the conical tube method and assuming a spherical liquid–vapor interface is larger but of the same order of magnitude (1 μJ m⁻¹) as that reported in the literature. A theoretical analysis presented herein shows that by including the deformation of the liquid–vapor interface due to gravity in the conical capillary analysis, the line tension value inferred from the experimental data is reduced by approximately 50% and compares better with values in the literature obtained using other sophisticated methods. Thus a relatively simple, cheap, accurate and reliable method of line tension measurement has been advanced.     

Catalytic oxidation of thiols to disulfides using iodine and CeCl3·7H2O in graphite

A very simple procedure for the efficient oxidation of thiols to disulfides catalyzed by I₂/CeCl₃·7H₂O in graphite and ethyl acetate as the solvent, in an open system at room temperature is described. The reaction proceeds cleanly under mild conditions and was performed with aromatic, aliphatic, and heterocyclic thiols.     

Emulsifier-free emulsion copolymerization of styrene and butyl acrylate. I. Kinetic studies in the absence of surfactant

Soapless emulsion copolymerization of styrene (S) and n-butyl acrylate (BuA) has been investigated using two types of initiator and different comonomer feed mixtures. When using K₂S₂O₈ as initiator, the particle size and size distribution of the final latexes (500 nm and 1.003, respectively) is not significantly affected by the comonomer feed composition, whereas the molecular weight and surface characteristics were found to sharply change at high butyl acrylate content. Based on the most probable particle nucleation mechanism and type of chain termination in the monomer swollen particles, a tentative explanation of these results has been proposed. Replacing persulfate by a carboxylic initiator (4-4′-azobiscyanopentanoic acid) results in the formation of stable particles as α observed with the persulfate, provided the aqueous phase pH is fixed in between 6 and 7. Results on the initiator residue location as a function of the conversion point out that the particle flocculation mechanism is strongly significant in the preparation of such latexes.     

Stereoselective synthesis of 3-substituted 2-aminocyclopentanecarboxylic acid derivatives and their incorporation into short 12-helical beta-peptides that fold in water

A stereoselective synthetic route is reported for the introduction of side chains at the 3-position of trans-2-aminocyclopentanecarboxylic acid (ACPC). Ring opening of the aziridine 2-benzyloxymethyl-6-azabicyclo[3.1.0]hexane with selected nucleophiles occurs in a regioselective manner and provides ACPC precursors with functional groups at the 3-position, trans to the 2-amino group. Oligomers composed of the 3-substituted ACPC residues maintain the 12-helical conformation displayed by the nonsubstituted analogues, as shown by their similar circular dichroism signatures. The added diversity of the new residues provides good dispersion of NMR signals, allowing the assignment of nearly all the NOE signals of a selected hexamer in aqueous solution. The NOEs between protons on nonadjacent residues are characteristic of the 12-helix. 3-Substituted ACPC residues allow one to arrange specific functional groups in a geometrically defined fashion, which should facilitate the design of beta-peptides for biological applications.     

Preparation and biological evaluation of the new chlorin photosensitizer T3,4BCPC for detection and treatment of tumors

The new water-soluble photosensitizer 5,10,15,20-tetrakis[3,4-bis(carboxymethyleneoxy)phenyl]chlorin (T3,4BCPC) has been prepared, characterized and labeled with 99mTc radionuclide. The radiotracer was evaluated for tissue distribution in Wistar rats. Accumulation of administrated activities in the liver, kidney, bladder and large intestine at 4 h post-injection indicated that the labeled ligand was largely eliminated through the renal and partly through the hepatobiliary system. In vivo biodistribution studies of the labeled compound were carried out in rodent and murine tumor models in comparison with other tumor-seeking radiopharmaceuticals such as 99mTc(V)-dimercaptosuccinic acid (DMSA), 201thallous chloride (TlCl) and 99mTc-citrate using a gamma camera computer system. In N-nitrosomethylurea (NMU)-induced rat mammary tumors, the labeled ligand showed a five-fold tumor to muscle (T/M) ratio compared to 99mTc(V)-DMSA (3-fold) and 201TlCl (3-fold). In the case of C(3)H/J virus-induced spontaneous mammary tumors, the differences were not marked. However, in the transplanted rat C(6)-glioma, the T/M ratio of the labeled compound was appreciably higher (four-fold) than that noted with 99mTc(V)-DMSA (two-fold), 201TlCl (three-fold) and 99mTc-citrate (more than three-fold). These findings suggest that the radiolabeled T3,4BCPC may have potential for the detection of cancer. In order to ascertain the efficacy of the compound for photodynamic therapy applications, a preclinical PDT study was carried out in fibrosarcoma-bearing mice after injecting 5.0 mg/kg body weight of the T3,4BCPC. A laser dose of 20 mW for 60 s resulted in 80% destruction of tumors. These data suggest that this molecule could be useful for PDT of cancer. The labeled agent could also be useful in monitoring the progression/regression of tumors before, during, and after chemotherapy, radiation therapy or PDT.     

The mixed ionocovalent bonding in small insulating clusters

We report a selfconsistent tight binding calculation of the electronic and structural properties of small insulating clusters (up to 12 atoms): these include alkaline-earth oxides (MgO and CaO) and NaCl clusters. Interatomic distance contractions are found in most cases, as in small metallic clusters. In addition, new effects take place in some of the compounds; these are a reduction of the ionic charge and, for the first time, the prediction of a dimerization of the interatomic distances. The microscopic processes responsible for their occurence and size dependence are dicussed with analytical arguments. It is shown that for these small clusters the equilibrium configuration and the electronic structure are fixed by a competition between covalent and electrostatic interactions, especially in the oxides.     

Preparation of diastereomeric 5,8-methanobenzoxazino[2,1–6]- and [2,3–6]-1,3-benzoxazin-4-ones by reaction of norbornane/ene-condensed dihydro-1,3-oxazines with salicyl chloride

Norbornane and norbornene-condensed dihydro-1,3-oxazines 1–6 were converted with salicyl chloride to 5,8-methanobenzoxazino[2,1–6]- and -[2,3-b]-1,3-benzoxazin-4-ones 7–12. The addition takes place to the C ? N bond: after acylation, the intermediate is stabilized through cyclization to the aryl-substituted carbon by hydrogen chloride elimination. Diastereomers containing the oxazine rings in isomeric positions could be isolated in two cases. This is the first example of the isolation of diastereomers in such a salicyl chloride reaction. In contrast with earlier findings with reactions of related systems, no addition to the C ? C bond could be observed. The steric structures of the compounds were elucidated by ir, ¹H- and ¹³C-nmr spectroscopy.     

Temperature evolution of the umbrella structure in holmium iron garnet

Using neutron diffraction data, the thermal evolution of the magnetic structure of Ho₃Fe₅O₁₂ has been studied. Below the compensation temperature (T _comp=137 K), the umbrella structure parameters which fit the spontaneous ferrite magnetizations have been determined. AboveT _comp, the compound behaves as a Néel type ferrimagnet. Particular attentions have been given to the magnetic form factors of both iron sublattice on one hand and on the other hand to a rhombohedral distorsion fromI a3d toR below 30 K and in first approximation toR c forT>30 K.