On the Weak Invariance Principle for Stationary Sequences under Projective Criteria

In this paper, we study the central limit theorem and its weak invariance principle for sums of a stationary sequence of random variables, via a martingale decomposition. Our conditions involve the conditional expectation of sums of random variables with respect to the distant past. The results contribute to the clarification of the central limit question for stationary sequences. Magda Peligrad is supported in part by a Charles Phelps Taft research support grant at the Univeristy of Cincinnati and the NSA grant H98230-05-1-0066.     

Partial Least-Squares Study of the Effects of Organic Modifier and Physicochemical Properties on the Retention of Some Thiazoles

JPC – Journal of Planar Chromatography – Modern TLC - Reversed-phase (RP) HPTLC with aqueous ammonia-organic modifier (acetonitrile, dioxane, acetone) mobile phases has been used to...     

Structure–electrochemical properties correlations of some phenol derivatives investigated by electrochemical techniques

A series of 25 phenol derivative compounds having potential antioxidant capacity were studied by cyclic voltammetry and square-wave voltammetry, in order to estimate the electrochemical parameters of the redox process occurring at the graphite electrode. A correlation between the structure of phenol derivatives, the peak potential, the HOMO–LUMO gap and their antioxidant activity lead to a qualitative classification of the studied compounds as a function of the increase of their antioxidant capacity.     

Comparative Study of the Chemical Compositions and Antioxidant Activities of Fresh Juices from Romanian Cucurbitaceae Varieties

Cucurbitaceae is a family of health-promoting plants due to their compounds with beneficial effects. The aim of this study was to analyze, for the first time, the chemical composition, the antioxidant activity and the metal chelating properties of fruit juices obtained from four different species of the Cucurbitaceae family cultivated in Romania, namely Momordica charantia, Cucumis metuliferus, Benincasa hispida and Trichosanthes cucumerina. The samples of juice were analyzed by high-performance liquid chromatography (HPLC) and all the four species displayed high levels of the two triterpenes, oleanolic and ursolic acids, and also in phenolic compounds, including catechin, (−)-epicatechin and gallic acid. The juices demonstrated significant antioxidant activity against the free radical 2,2-diphenyl-1-picrylhydrazyl (ranging from 20 to 95%,), a good iron binding ability (ranging from 7.45 ± 0.28% to 86.95 ± 0.97%) and also promising antioxidant potential against the ABTS radical (ranging from 4.97 to 32.60 μETx/mL juice). Our findings raise interesting questions for further research on Cucurbitaceae fruit juices and, consequently, their very good antioxidant potential suggests these fruits should be further explored for their protective effect against oxidative damage. This is the first time the chemical composition and antioxidant activities of fruit juices from these four Romanian Cucurbitaceae varieties have been investigated.     

Robust fuzzy principal component analysis (FPCA). A comparative study concerning interaction of carbon-hydrogen bonds with molybdenum-oxo bonds

Principal component analysis (PCA) is a favorite tool in chemometrics for data compression and information extraction. PCA finds linear combinations of the original measurement variables that describe the significant variations in the data. However, it is well-known that PCA, as with any other multivariate statistical method, is sensitive to outliers, missing data, and poor linear correlation between variables due to poorly distributed variables. As a result data transformations have a large impact upon PCA. In this regard one of the most powerful approaches to improve PCA appears to be the fuzzification of the matrix data, thus diminishing the influence of outliers. In this paper we discuss a robust fuzzy PCA algorithm (FPCA). The new algorithm is illustrated on a data set concerning interaction of carbon-hydrogen bonds with transition metal-oxo bonds in molybdenum complexes. Considering, for example, a two component model, FPCA accounts for 97.20% of the total variance and PCA accounts only for 69.75%.     

Almost-Sure Results for a Class of Dependent Random Variables

The aim of this note is to establish almost-sure Marcinkiewicz-Zygmund type results for a class of random variables indexed by _d ⁺ —the positive d-dimensional lattice points—and having maximal coefficient of correlation strictly smaller than 1. The class of applications include filters of certain Gaussian sequences and Markov processes.     

Scanning tunneling microscopy and surface simulation of zinc-blende GaN(001) intrinsic 4x reconstruction: linear gallium tetramers?

Scanning tunneling microscopy images confirm electron diffraction studies that the zinc-blende GaN(001)-4x reconstruction consists of rows aligned along [110] with a spacing along [110] of 4a. Dual-bias imaging shows a 180 degree shift of the corrugation maximum position between the profiles of empty and occupied states, in agreement with surface simulations based on the 4 x 1 linear tetramer model of Neugebauer et al. [Phys. Rev. Lett. 80, 3097 (1998)]. Electronic structure calculations predict a surface band gap of 1.1 eV, close to the measured value of 1.14 eV and the previously predicted value (1.2 eV). Despite the successes of this model, high-resolution images reveal an unexpected 3x periodicity (not seen in diffraction) along the [110] row direction, indicating the need for a 4 x 3 model, and putting into question the existence of linear Ga tetramers.     

Spiroheterocyclic compounds: old stories with new outcomes

An efficient and straightforward method for the preparation of spirodiazine derivatives is reported which involves mild reaction conditions and easily accessible reactants. A new class of spiroazaheterocycles, spiro[pyrrolidine-pyrrolo[3,4-c]pyrroles], is obtained. A feasible explanation is given for the unexpected results obtained at high energy (high temperatures, MW and ultrasound irradiation).