On the recognition problem of quasi-homogeneous locally nilpotent derivations in dimension three

We give a criterion to decide if a given w-homogeneous derivation on A?k[X₁,X₂,X₃] is locally nilpotent. We deduce an algorithm which decides if a k-subalgebra of A, which is finitely generated by w-homogeneous elements, is the kernel of some locally nilpotent derivation.     

Large effect of polydispersity on defect concentrations in colloidal crystals

We compute the equilibrium concentration of stacking faults and point defects in polydisperse hard-sphere crystals. We find that, while the concentration of stacking faults remains similar to that of monodisperse hard-sphere crystals, the concentration of vacancies decreases by about a factor of 2. Most strikingly, the concentration of interstitials in the maximally polydisperse crystal may be some six orders of magnitude larger than in a monodisperse crystal. We show that this dramatic increase in interstitial concentration is due to the increased probability of finding small particles and that the small-particle tail of the particle size distribution is crucial for the interstitial concentration in a colloidal crystal.     

The effect of (natural) polyols on the initial colour of heavy metal- and zinc-free poly(vinyl chloride)

The propensity of (natural) polyols dispersed in heavy metal- and zinc-free PVC sheets to improve the initial colour, e.g. the colour during the first minutes of exposure to high processing temperatures (short-term stability), has been investigated. It is shown using W(Lab) values that the initial colour improves upon addition of polyols containing primary hydroxyl groups. The polyols act as HCl scavengers, presumably via an acid-catalysed S_N2 substitution of the primary hydroxyl groups by chloride ions. In contrast, polyols with only secondary or tertiary hydroxyl groups accelerate the thermal degradation of PVC. Notwithstanding, the efficacy of the (natural) polyols containing primary hydroxyl groups will be reduced if the polyol is susceptible to competitive acid-catalysed intramolecular cyclodehydration reactions under the processing conditions. This is substantiated by a comparison of the behaviour of mannitol and 3,4-di-O-methyl-d-mannitol. The methylated derivative, which is less prone to undergo intramolecular cyclodehydration, improves the initial colour of heavy metal- and zinc-free PVC sheets more significantly than mannitol itself.     

Oxidative addition of the ethane C-C bond to Pd. An ab initio benchmark and DFT validation study

We have computed a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the ethane C-C bond to the palladium atom and have used this to evaluate the performance of 24 popular density functionals, covering LDA, GGA, meta-GGA, and hybrid density functionals, for describing this reaction. The ab initio benchmark is obtained by exploring the PES using a hierarchical series of ab initio methods [HF, MP2, CCSD, CCSD(T)] in combination with a hierarchical series of five Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account either through a relativistic effective core potential for palladium or through a full four-component all-electron approach. Our best estimate of kinetic and thermodynamic parameters is -10.8 (-11.3) kcal/mol for the formation of the reactant complex, 19.4 (17.1) kcal/mol for the activation energy relative to the separate reactants, and -4.5 (-6.8) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). Our work highlights the importance of sufficient higher angular momentum polarization functions for correctly describing metal-d-electron correlation. Best overall agreement with our ab initio benchmark is obtained by functionals from all three categories, GGA, meta-GGA, and hybrid DFT, with mean absolute errors of 1.5 to 2.5 kcal/mol and errors in activation energies ranging from -0.2 to -3.2 kcal/mol. Interestingly, the well-known BLYP functional compares very reasonably with a slight underestimation of the overall barrier by -0.9 kcal/mol. For comparison, with B3LYP we arrive at an overestimation of the overall barrier by 5.8 kcal/mol. On the other hand, B3LYP performs excellently for the central barrier (i.e., relative to the reactant complex) which it underestimates by only -0.1 kcal/mol.     

The photochemistry of benzotricyclo[3.1.0.02,6]Hex-3-ene1

Irradiation of $\text{1}$ in methanoi with λ 254 nm yields $\text{3}$ and $\text{4}$ as the main primary products which result from the excited singlet state hy initial cyclopropane bond homolysis, but no primary photosolvolysis products.     

Novel Monte Carlo scheme for systems with short-ranged interactions

We propose a Monte Carlo (MC) sampling algorithm to simulate systems of particles interacting via very short-ranged discontinuous potentials. Such models are often used to describe protein solutions or colloidal suspensions. Most normal MC algorithms fail for such systems because, at low temperatures, they tend to get trapped in local potential-energy local minima due to the short range of the pair potential. To circumvent this problem, we have devised a scheme that changes the construction of trial moves in such a way that the potential-energy difference between initial and final states drops out of the acceptance rule for the Monte Carlo trial moves. This approach allows us to simulate systems with short-ranged attraction under conditions that were unreachable up to now.     

Poly(ethylene glycol)--oligolactates with monodisperse hydrophobic blocks: preparation, characterization, and behavior in water

Methoxypoly(ethylene glycol)-b-oligo-L-lactate (mPEG-b-OLA) diblock oligomers with monodisperse OLA blocks were obtained by fractionation of polydisperse block oligomers using preparative HPLC. The fractionated oligomers were composed of an mPEG block with a molecular weight of 350, 550, or 750 and an OLA block with a degree of polymerization of 4, 6, 8, or 10. The diblock oligomers with a low PEG content were fully amorphous, with glass transition temperatures ranging from -60 to -20 degrees C, indicating that the blocks were miscible. Upon heating aqueous dispersions of the block oligomers, cloud points, depending on the PEG/OLA ratio of the block oligomer, were observed at temperatures above 40 degrees C. The monodispersity of the hydrophobic block enabled the amphiphilic molecules to form nanoparticles in water with a hydrodynamic radius of 130-300 nm, at concentrations above the critical aggregation concentration (0.4-1 mg/mL), whereas polydisperse mPEG-b-OLAs gave formation of large aggregates. Static light scattering measurements showed that the nanoparticles have a low density (0.6-25 mg/mL), indicating that the particles are highly hydrated. In agreement herewith, the (1)H NMR spectra of nanoparticles in D2O closely resembled spectra in a good solvent for both blocks (CDCl3). It is therefore suggested that the nanoparticles contain a hydrated core of mPEG-b-OLA block oligomers, stabilized by a thin outer PEG layer. The particles were stable for two weeks, except for the mPEG350 series and mPEG750-b-OLA4, indicating that both the PEG block size and the PEG weight fraction of the oligomers determine their stability. The evident self-emulsifying properties of mPEG-b-oligo-l-lactates with monodisperse hydrophobic blocks as demonstrated in this study, together with their expected biocompatibility and biodegradability, make these systems well suitable for pharmaceutical applications.     

Zeeman experiments on the 3Eu α 1A1g transition of platinum porphein in an n-alkane single crystal at 4.2

We report absorption spectra from the ground state to the photoexcited triplet state of platinum porphin (PtP) in single crystals of n-octane (C₈) and n-decane (C₁₀) at 4.2 K, with and without a magnetic field. For PtP in C₁₀ the same transition was studied in emission. From the experiments, values are derived of the spin-orbit coupling parameter Z, the crystal field splitting δ and the orbital angular momentum A for PtP in the two hosts: Z = 76 ± 2 cm^?1 (C₈, C₁₀), δ = 71 ± 1 cm^?1 (C₈), 55 ± 1 cm^?1 (C₁₀) and A = 1.6 ± 0.1 (C₈, C₁₀). For the ratio of the in-plane and the z-polarized electric dipole transition moments we obtain ¦Mx,y¦/¦Mz¦=76± 0.3 (C₈).     

ELLIPSOMETRY OF BLACK LIPID MEMBRANES OF EGG LECITHIN AND CHLOROPLAST EXTRACTS

Abstract— Ellipsometric angles and reflectivity of black lipid membranes containing either egg lecithin or chloroplast extracts were measured at a wavelength of 6328 Å. Evidence was found for positive uniaxial anisotropy in membranes of lecithin. If the thickness of those films is assumed to be 62 Å, the refractive index normal to the film surface is 1.471 ± 0.004, and the refractive index parallel to the film surface is 1.454 ± 0.003. The results for membranes of chloroplast extracts also indicate a positive anisotropy in the indices of absorption.     

Photochemistry of dienones—X: Photochemistry of (e)-β-ionone oxime ethyl ether

(E)-β-ionone oximc ethyl ether [(E, E)-4] upon direct irradiation with λ either254or 313 nm yields the geometrical isomer (E, Z)-4 and (Z)-retro-γ-ionone oxime ethyl ether (Z,E)-5 as the sole primary products, illustrating (E)-(Z) isomerization (φ₃₁₃ =0.49) and a 1, 5-hydrogen shift (φ313 =0.15) respectively. From studies with triplet photosensitizers and with ethyl iodide (to enhance the singlet-triplet intersystem crossing) it is concluded that these two products in the direct irradiation result only from the singlet excited state, and that the inter-system crossing quantum yield is relatively low. Upon prolonged irradiation of (E,E)-4 with λ 313 nm the eventual products are (Z,E)-5 and (Z,Z)-5, whereas with λ 254 nm they are (E,E)-5 and [(Z,E)-5 and/or (E,Z)-5]. Upon triplet photosensitization (E,E)-4 undergoes only (E)-(Z) isomerization, leading to a mixture of all the four geometrical isomers of4. From the dependence of the geometrical isomer distribution in the photostationary state on the triplet energy of the sensitizer the triplet energies of (E,E)-4, (E, Z)-4, (Z, E)-4, and (Z, Z)-4 have been determined to be ca 55, < 55,57, and 57 $\text{kcal}\text{mol}$ respectively.