Hindered rotation around the N(sp2)-C(sp3) single bond in 2,4,6-trimethyl-N-alkylpyridinium cations:H DNMR analysist

Pairwise chemical shift nonequivalence of the 2,6-methyl and 3,5-protons in ¹H NMR spectra, as well as of the 2,6-methyl, 2,6-ring and 3,5-ring carbons in ¹³C NMR spectra, was observed for N-alkyl-2,4,6-trimethylpyridinium salts 2. Dynamic NMR spectroscopy demonstrates appreciably higher activation free energies ΔG^# for rotation around the N(sp²)-C(sp³ bond than ΔG# for the analogously substituted mesityl derivatives, in agreement with the shorter N-C bond distance than for the C-C bond.     

Molecular topology. IV. Regressive vertex degrees (new graph invariants) and derived topological indices

New local graph invariants, “regressive vertex degrees” (which are slightly augmented vertex degrees) are introduced on the basis of decreasing contributions of more remote vertexes to the classical vertex degrees. Several such invariants are proposed (BR, ER, SR) where t (either t = 1 or t = 2) is an operator expressing the attenuation with increasing topological distance, according to formula (1) or (2). With the aid of these new local invariants, new topological indices (global graph invariants), Y (namely BY, EY or SY) are introduced and exemplified. Their ability to express the branching and to order alkanes is investigated. An appendix gives some recursive relationships for computing these indices.     

Removal of <Superscript>60</Superscript>Co<Superscript>2+</Superscript> and <Superscript>137</Superscript>Cs<Superscript>+</Superscript> ions from low radioactive solutions using <Emphasis Type="Italic">Azolla caroliniana</Emphasis> willd. water fern

This study concerns the removal of the ¹³⁷Cs⁺ and ⁶⁰Co²⁺ β+γ-radioactive ions in Azolla caroliniana Willd. water fern. The living fern and two different types of biosorbent prepared from Azolla caroliniana were tested to remove the above-mentioned radioactive ions from dilute solutions, in the absence and in the presence of the ionic competition. Effective ¹³⁷Cs⁺ and ⁶⁰Co²⁺ ions removal from low radioactive wastewaters was demonstrated. The time dependent K _d (t) values were calculated from the absorption data. These results indicate that removal process achieved equilibrium in about 120 min and that it involves two steps: rapid and slow absorption; the active process (metabolic bioaccumulation on the living fern) was responsible for above one half of the total removal process. A thin layer radiochromatography study leads to the conclusion that the biochemical components in which ¹³⁷Cs⁺ and ⁶⁰Co²⁺ place themselves are of a polysaccharide and lipoid fractions.     

Discrete Radon transforms and applications to ergodic theory

We prove L ^p boundedness of certain non-translation-invariant discrete maximal Radon transforms and discrete singular Radon transforms. We also prove maximal, pointwise, and L ^p ergodic theorems for certain families of non-commuting operators.     

On the index of fractions with square-free denominators in arithmetic progressions

We prove asymptotic formulas for the first and second moments of the index of fractions with square-free denominators of order Q streaming in a given arithmetic progression as Q→∞. A. Zaharescu was supported by NSF grant number DMS-0456615. This research was also partially supported by the CERES Program 4-147/2004 of the Romanian Ministry of Education and Research.     

The ligand effect in Ti‐mediated living radical styrene polymerizations initiated by epoxide radical ring opening. 2. Scorpionate and half‐sandwich LTiCl3 complexes

The ligand effect and the reaction conditions for the living radical polymerization of styrene initiated by epoxide radical ring opening was investigated in a series of piano‐stool, Ti(IV) scorpionate and, half‐sandwich metallocenes (LTiCl₃; L = Tp, Cp*, Ind and Cp, where Tp = hydrotris(pyrazol‐1‐ylborato), Cp* = pentamethylcyclopentadienyl, Ind = indenyl and Cp = cyclopentadienyl). The polymerization is mediated by the reversible termination of the growing chains with Ti(III) species derived from Zn reduction of parent Ti(IV) derivatives. A poor performance was observed for TpTiCl₃ because of probable over‐reduction. The strong electron donating effect of Cp* accounts for a strong C? Ti chain end bond and consequently, a living‐like process is observed only at T > 110 °C. However, both Ind and Cp ligands provide a linear dependence of M_n on conversion and narrow polydispersity over a wide range of experimental conditions. Investigation of the effect of temperature and reagent ratios generates an optimum for epoxide/CpTiCl₃/Zn = 1/2/4 at 70–90 °C. On the basis of a combination of steric and electronic properties, the ligands rank as Cp ≥ Ind ? Cp* ? Tp. This trend is different from coordination polymerization, and in conjunction with our previous results on Cp₂TiCl₂, further supports a radical mechanism. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 6039–6047, 2005     

Association phenomena of the ferrocenylsiloxane polyamide in solution

A ferrocenyl‐siloxane polyamide, poly{1,1′‐ferrocene‐diamide‐[1,3‐bis(propylene)tetramethyldisiloxane]}, FAS, prepared by polycondensation in solution (methylene chloride) of 1,1′‐di(chlorocarbonyl)ferrocene with 1,3‐bis(aminopropyl)tetramethyldisiloxane has been dissolved in various concentrations in the range 0–1.5 g/dL in dimethylformamide. The solutions were investigated by tensiometry, viscometry, and UV–vis spectrophotometry at different temperatures. The results suggested the association occurrence, depending on the two parameters (concentration and temperature). The aggregates formation and their sizes were emphasized by dynamic light scattering and scanning electron microscopy. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 5845–5852, 2009     

Living ring‐opening polymerization of ϵ‐caprolactone with Ti alkoxides derived from the Cp2TiCl‐catalyzed SET reduction of aldehydes

A series of substituted benzaldehydes were investigated as initiators for the living ring‐opening polymerization (LROP) of ε‐caprolactone (CL) mediated by titanium alkoxides obtained from the Cp₂TiCl‐catalyzed single electron transfer (SET) reduction of the carbonyl group following the in situ reduction of Cp₂TiCl₂ with Zn. The aldehyde initiation was demonstrated (NMR) by the presence of the initiator derived fragment on the polycaprolactone (PCL) chain end. The effect of the nature of the aldehyde functionality (R‐Ph‐CHO, R = H, Cl, PhCH₂O, NMe₂, CH₃O, NO₂, and CHO), reagent ratios ([CL]/[aldehyde] = 50/1 to 400/1, [aldehyde]/[Cp₂TiCl₂] = 1/1 to 1/4, and [Cp₂TiCl₂]/[Zn] = 1/0.5 to 1/2), and temperature (T = 75–120 °C) was investigated over a wide range of values to reveal a living polymerization in all cases with an optimum observed at 90 °C with typical stoichiometric ratios of [CL]/[aldehyde]/[Cp₂TiCl₂]/[Zn] = 100/1/1/2. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2869–2877, 2008     

Formulas for Kronecker invariants using a representation theoretical approach

Using a representation theoretical modular approach we present some explicit formulas for the Kronecker invariants of a matrix pencil and we also give a short proof for the Demmel–Edelman codimension formula of a pencil.