Some Questions of Heinrich on Ultrapowers of Locally Convex Spaces

In this note we treat some open problems of Heinrich on ultrapowers of locally convex spaces. In section 1 we investigate the localization of bounded sets in the full ultrapower of a locally convex space, in particular the coincidence of the full and the bounded ultrapower, mainly concentrating in the case of (DF)-spaces. In section 2 we provide a partial answer to a question of Heinrich on commutativity of strict inductive limits and ultrapowers. In section 3 we analyze the relation between some natural candidates for the notion of superreflexivity in the setting of Fréchet spaces. We give an example of a Fréchet-Schwartz space which is not the projective limit of a sequence of superreflexive Banach spaces.     

Frequent hypercyclicity,chaos, and unconditional Schauder decompositions

We prove that if X is any complex separable infinite-dimensional Banach space with an unconditional Schauder decomposition, X supports an operator T which is chaotic and frequently hypercyclic. In contrast with the complex case, we observe that there are real Banach spaces with an unconditional basis which support no chaotic operator.     

Theoretical study on the structures and electronic spectra of TCNE2-.

Investigations into the charge-separated states and electron-transfer transitions in tetracyanoethylene (TCNE) complexes have recently generated much interest. In this work we present theoretical calculations showing that the most stable structure of the dianion TCNE2- has D2d symmetry in vacuum as well as in the solvents dichloromethane and acetonitrile. By means of the coupled cluster linear response, we compute the vertical electronic spectrum in both the gas phase and solution. The theoretical results are compared to the experimental data and good agreement is achieved.     

On the effect of a point mutation on the reactivity of CuZn superoxide dismutase: a theoretical study

In this paper, we investigate the effects of a point mutation on the enzymatic activity of copper-zinc superoxide dismutase, which we recently studied in detail by means of a theoretical-computational procedure. Comparison of the reactivity of the initial catalytic steps in this mutant (G93A mutation far from the active site) with our previous data, reveals the beautiful mechanical-dynamical architecture of the enzyme, altered by such an apparently irrelevant mutation. Finally, our results suggest a possible atomic-molecular-based explanation for the mutant-pathology correlation, in line with the most recent experimental data.     

Reactions of 6-hydrazino-, 6-hydroxylaminopurines and related derivatives

7H-Tetrazolo[5,1-i]purine was prepared by nitrosation of 6-hydrazinopurine and by reaction of 6-chloropurine with sodium azide; it was converted to adenine upon catalytic hydrogenation. 6-Hydroxylaminopurine was oxidized to 6-nitrosopurine with manganese dioxide, while alkaline treatment of the former gave 6,6′-azoxypurine. Nitrosation of 6-hydroxylaminopurine afforded 6-(N-nitroso)hydroxylaminopurine. Reaction of 6-chloropurine with 6-hydrazinopurine led to 6,6′-bisadenine; the corresponding ribosyl derivatives gave 6,6′-bisadenosine. Upon air oxidation, 6,6′-bisadenine was converted into 6,6′-azopurine. The related 6-thiosemicarbazino- and 6-(N-methyl)ureidopurine derivatives are also described. 6-N-(Nitroso)hydroxylaminopurine showed an inhibitory activity against several mouse tumors and leukemias.     

On-line double isotope dilution laser ablation inductively coupled plasma mass spectrometry for the quantitative analysis of solid materials

We report on the determination of trace elements in solid samples by the combination of on-line double isotope dilution and laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). The proposed method requires the sequential analysis of the sample and a certified natural abundance standard by on-line IDMS using the same isotopically-enriched spike solution. In this way, the mass fraction of the analyte in the sample can be directly referred to the certified standard so the previous characterization of the spike solution is not required. To validate the procedure, Sr, Rb and Pb were determined in certified reference materials with different matrices, including silicate glasses (SRM 610, 612 and 614) and powdered samples (PACS-2, SRM 2710a, SRM 1944, SRM 2702 and SRM 2780). The analysis of powdered samples was carried out both by the preparation of pressed pellets and by lithium borate fusion. Experimental results for the analysis of powdered samples were in agreement with the certified values for all materials. Relative standard deviations in the range of 6–21% for pressed pellets and 3–21% for fused solids were obtained from n = 3 independent measurements. Minimal sample preparation, data treatment and consumption of the isotopically-enriched isotopes are the main advantages of the method over previously reported approaches.     

Theoretical modeling of vibroelectronic quantum states in complex molecular systems: solvated carbon monoxide, a test case

In this paper we extend the perturbed matrix method by explicitly including the nuclear degrees of freedom, in order to treat quantum vibrational states in a perturbed molecule. In a previous paper we showed how to include, in a simple way, nuclear degrees of freedom for the calculation of molecular polarizability. In the present work we extend and generalize this approach to model vibroelectronic transitions, requiring a more sophisticated treatment.     

Synthesis,structural characterization and cytotoxic activity of organotin derivatives of indomethacin

The synthesis, characterization and cytotoxic properties in vitro of tri‐n‐butyltin 1‐(4‐chlorobenzoyl)‐5‐methoxy‐2‐methyl‐1H‐indole‐3‐acetate ( 1 ), tri‐phenyltin 1‐(4‐chlorobenzoyl)‐5‐methoxy‐2‐methyl‐1H‐indole‐3‐acetate ( 2 ), tetra‐n‐butyltin[bis‐1‐(4‐chlorobenzoyl)‐5‐methoxy‐2‐methyl‐1H‐indole‐3‐acetato]distannoxane ( 3 ) and di‐n‐butyltin bis‐1‐(4‐chlorobenzoyl)‐5‐methoxy‐2‐methyl‐1H‐indole‐3‐acetate ( 4 ) are described. These compounds have been characterized by ¹H, ¹³C and ¹¹⁹Sn NMR spectroscopy in solution and ¹¹⁹Sn NMR in the solid state, infrared spectroscopy, elemental analysis and X‐ray diffraction for compound 1 . The growth inhibition effects of compounds 1–4 against the lung adenocarcinoma cell line SK‐LU‐1 as well as the cervical cancer cell line HeLa were determined. Compounds 1 and 2 exhibit cytotoxic activity, whereas compounds 3 and 4 are inactive. Copyright © 2008 John Wiley & Sons, Ltd.     

Adaptive Martingale Approximations

H-systems are those orthonormal systems which allow computation of conditional expectations via a Fourier expansion. These systems provide natural approximations to continuous stochastic processes and we indicate how they could be used to perform lossy compression on a set of given signals. More specifically, we show how to construct, for a given random variable, an adaptive martingale approximation by means of generalized Haar functions. We also indicate how the construction can be extended to a given random vector. A generalized multiresolution analysis algorithm is also described and numerical examples are provided.