New Characterizations of Operator-Valued Bases on Hilbert Spaces

In this paper we study operator valued bases on Hilbert spaces and similar to Schauder bases theory we introduce characterizations of this generalized bases in Hilbert spaces.We redefine the dual basis associated with a generalized basis and prove that the operators of a dual g-basis are continuous.Finally we consider the stability of g-bases under small perturbations.We generalize two results of KreinMilman-Rutman and Paley-Wiener [7] to the situation of g-basis.     

Identification of discriminatory variables in proteomics data analysis by clustering of variables

This article presents a data analysis method for biomarker discovery in proteomics data analysis. In factor analysis-based discriminate models, the latent variables (LV's) are calculated from the response data measured at all employed instrument channels. Since some channels are irrelevant and their responses do not possess useful information, the extracted LV's possess mixed information from both useful and irrelevant channels. In this work, clustering of variables (CLoVA) based on unsupervised pattern recognition is suggested as an efficient method to identify the most informative spectral region and then it is used to construct a more predictive multivariate classification model. In the suggested method, the instrument channels (m/z value) are clustered into different clusters via self-organization map. Subsequently, the spectral data of each cluster are separately used as the input variables of classification methods such as partial least square-discriminate analysis (PLS-DA) and extended canonical variate analysis (ECVA). The proposed method is evaluated by the analysis of two experimental data sets (ovarian and prostate cancer data set). It is found that our proposed method is able to detect cancerous from healthy samples with much higher sensitivity and selectivity than conventional PLS-DA and ECVA methods.     

A theoretical study on the interaction of [Al(H2O)6] and [Mg(H2O)6] cations with fullerene (C60), coronene and benzene π-systems

Density functional theory (DFT), Bader’s theory of atoms in molecules (AIM) and natural bond orbital (NBO) calculations have been used to understand the nature of the interaction between M(H₂O)₆ⁿ⁺ (M = Mg²⁺, Al³⁺) complexes and fullerene, coronene and benzene π-systems. The interaction energies were calculated for all the compounds and corrected for the basis set superposition error (BSSE). The results showed that the above π-systems have larger interaction energies with Al(H₂O)₆³⁺ than Mg(H₂O)₆²⁺. Also the AIM topological parameters for the bond critical points (BCPs) between the M(H₂O)₆ⁿ⁺ cations and the fullerene, coronene and benzene π-systems confirmed that {[Al(H₂O)₆]³⁺?fullerene} has a much stronger bonding interaction than the other systems. The calculated interaction energies correlate well with both the Wiberg bond indices and the global value of charge transfers from π-systems to cations evaluated through natural population analysis. The calculations suggest that the ionic potential of the central metal ion in the M(H₂O)₆ⁿ⁺ cation and the nature of π-system are two influential factors that affect the strength and the nature of the interaction.     

Self-assembly of insoluble porphyrins on Au(111) under aqueous electrochemical control

Self-assembled monolayers of a water-insoluble porphyrin, tetraphenyl porphyrin (TPP), in the presence of an aqueous electrolyte were characterized in situ with electrochemical scanning tunneling microscopy (EC-STM) at working electrode potentials of between 0.5 and -0.2 V. Isolated domains of TPP monolayers with differing orientation were observed on Au(111) in 0.1 M HClO(4) over this entire potential window. Individual TPP molecules could be resolved over a range of 700 mV, from open circuit potential (OCP) to near the hydrogen evolution potential. The unit cell is square, and the distance between neighboring molecules is about 1.4 ± 0.1 nm. High-resolution images allow the internal molecular structure to be discerned. No changes in the STM contrast of individual molecules were observed as the potential was changed. In a neutral electrolyte (0.1 M KClO(4), pH ~6), the potential range of stability of ordered structures is reduced. On HOPG, TPP forms ordered hexagonal structures with a lattice constant of about 2.6 nm in the double-layer potential region in 0.1 M HClO(4).     

The modifier action of NiO nanoparticles on the activity,structure, and stability of proteinase K

Monatshefte für Chemie - Chemical Monthly - In the present study, multi-spectroscopic methods were applied to investigate the effect of NiO nanoparticles on the structure, activity, and...     

Coarse graining makes it hard to see micro-macro entanglement

Observing quantum effects such as superpositions and entanglement in macroscopic systems requires not only a system that is well protected against environmental decoherence, but also sufficient measurement precision. Motivated by recent experiments, we study the effects of coarse graining in photon number measurements on the observability of micro-macro entanglement that is created by greatly amplifying one photon from an entangled pair. We compare the results obtained for a unitary quantum cloner, which generates micro-macro entanglement, and for a measure-and-prepare cloner, which produces a separable micro-macro state. We show that the distance between the probability distributions of results for the two cloners approaches zero for a fixed moderate amount of coarse graining. Proving the presence of micro-macro entanglement therefore becomes progressively harder as the system size increases.     

New mono and binuclear mercury(II) complexes of phosphorus ylides containing DMSO as ligand: Spectral and structural characterization

Reaction of phosphorus ylides Ph₃PCHC(O)C₆H₄NO₂ (Y′) and (p-tolyl)₃PCHC(O)C₆H₄Cl (Y″) with HgX₂ (X = Cl, Br and I) in equimolar ratios using methanol as solvent leads to binuclear products. The bridge-splitting reaction of binuclear complex [(Y″) · HgI₂]₂ by DMSO yields the mononuclear complex [(Y″) · HgI₂ · DMSO]. This bridge-splitting reaction can be also a method for the synthesis of mononuclear products. C-coordination of ylides and O-coordination of DMSO are demonstrated by single crystal X-ray analyses of binuclear complexes of [(Y′) · HgI₂]₂ and [(Y″) · HgI₂]₂ and mononuclear complex of [(Y″) · HgI₂ · DMSO]. Characterization of the obtained compounds was also performed by elemental analysis, IR, ¹H, ³¹P, and ¹³C NMR. Theoretical studies on Hg(II) complexes of Y′ show that the cis-like isomers are about 4–12 kcal/mol less stable than the trans-like structures and the relative energy of cis- and trans-like isomers significantly depends on the size of the bridging halide. These studies on mercury complexes of Y″ show that, formation of mononuclear complexes in DMSO solution in which DMSO acts as a ligand, energetically is more favorable than that of binuclear complexes.