Some inequalities involving the Fox’s H-function

In this paper we establish certain inequalities for the Fox’s H-function with the help of certain known inequalities for the generalized hypergeometric function.     

Sensitive determination of hydrazine using poly(phenolphthalein), Au nanoparticles and multiwalled carbon nanotubes modified glassy carbon electrode

This study reports a detailed analysis of an electrode material containing poly(phenolphthalein), carbon nanotubes and gold nanoparticles which shows superior catalytic effect towards to hydrazine oxidation in Britton–Robinson buffer (pH 10.0). Glassy carbon electrode was modified by electropolymerization of phenolphthalein (PP) monomer (poly(PP)/GCE) and the multiwalled carbon nanotubes (MWCNTs) was dropped on the surface. This modified surface was electrodeposited with gold nanoparticles (AuNPs/CNT/poly(PP)/GCE). The fabricated electrode was analysed the determination of hydrazine using cyclic voltammetry, linear sweep voltammetry and amperometry. The peak potential of hydrazine oxidation on bare GCE, poly(PP)/GCE, CNT/GCE, CNT/poly(PP)/GCE, and AuNPs/CNT/poly(PP)/GCE were observed at 596 mV, 342 mV, 320 mV, 313 mV, and 27 mV, respectively. A shift in the overpotential to more negative direction and an enhancement in the peak current indicated that the AuNPs/CNT/poly(PP)/GC electrode presented an efficient electrocatalytic activity toward oxidation of hydrazine. Modified electrodes were characterized with High-resolution transmission electron microscopy (HRTEM), scanning electron microscopy (SEM), X-ray photoelectron spectroscopy (XPS) and electrochemical impedance spectroscopy (EIS). Amperometric current responses in the low hydrazine concentration range of 0.25–13 µM at the AuNPs/CNT/poly(PP)/GCE. The limit of detection (LOD) value was obtained to be 0.083 µM. A modified electrode was applied to naturel samples for hydrazine determination.     

Asymptotic Normality of the Whittle Estimator in Linear Regression Models with Long Memory Errors

This paper establishes the asymptotic normality of the Whittle estimator of the unknown dependence parameters in a linear regression model with long memory moving average errors. The design variables are taken to be deterministic or random. In the latter case they are assumed to have a moving average representation that includes both short and long memory. In all cases, it is observed that the rate of consistency of the regression parameter estimator has an effect on the asymptotic normality of the Whittle estimator.     

Rose Oxides: A Facile Chemo and Chemo‐Enzymatic Approach

Nonracemic rose oxides were synthesized from racemic or nonracemic monoterpene alcohol citronellol by a novel chemo and chemo‐enzymatic route. After the key step of bromomethoxylation of citronellol, the intermediate was dehydrobrominated by a base, followed by an acid catalyzed demethoxylation along with cyclization to furnish rose oxides in high yield. The racemic dehydrobrominated precursor was also kinetically resolved using various lipases to produce nonracemic rose oxides.     

A validated high‐performance thin‐layer chromatography method for the identification and simultaneous quantification of six markers from Platanus orientalis and their cytotoxic profiles against skin cancer cell lines

Betulinic acid ( 1 ), betulinic acid‐3‐acetate ( 2 ), 3‐acetylbetulinaldehyde ( 3 ), oleanolic acid‐3‐acetate ( 4 ), 3‐β‐hydroxy‐28,19‐β‐olenolide ( 5 ), and β‐sitosterol ( 6 ) were isolated from Platanus orientalis and a high‐performance thin‐layer chromatography method was developed for their simultaneous quantification. The markers were first derivatized on the chromatogram with ceric ammonium sulfate and then high‐performance thin‐layer chromatography densitometry was carried out. Chromatographic separation of these markers was carried out on silica gel 60 plates using a ternary solvent system n‐hexane/toluene/acetone (6:3.5:1 v/v/v) as a mobile phase. For marker 1 , a deuterium (D₂) lamp and wavelength of 420 nm was used. A tungsten (W) lamp was used for markers 2 and 3 at 550 nm and for 4 – 6 at 500 nm. The method was validated for accuracy, precision, LOD, and LOQ. All calibration curves showed a good linear relationship (r > 0.9919). The precision evaluated by an intra‐ and interday study showed RSDs < 2.51% and accuracy validation recovery between 95.54 and 99.33% with RSDs < 1.55%. The successful application of the validated method showed 1 as the most abundant component (4.63%) and 5 (0.017%) the least. The markers displayed a significant cytotoxic effect against human keratinocyte, mouse melanoma, and human skin epithelial carcinoma cancer cells by using a 3‐(4,5‐dimethylthiazol‐2‐yl)‐2,5‐diphenyltetrazolium bromide assay.     

Testing the tail index in autoregressive models

We propose a class of nonparametric tests on the Pareto tail index of the innovation distribution in the linear autoregressive model. The simulation study illustrates a good performance of the tests. Such tests have various applications in a study of flood flows, rainflow data, behavior of solids, atmospheric ozone layer and reliability analysis, in communication engineering, in stock markets and insurance. Research of J. Jurečková and J. Picek was partly supported by Czech Republic Grant 201/05/2340, by the Research Project LC06024 and by the NSF grant DMS 0071619. Research of H. L. Koul was partly supported by the NSF grants DMS 0071619 and 0704130.     

Testing a sub-hypothesis in linear regression models with long memory covariates and errors

This paper considers the problem of testing a sub-hypothesis in homoscedastic linear regression models when the covariate and error processes form independent long memory moving averages. The asymptotic null distribution of the likelihood ratio type test based on Whittle quadratic forms is shown to be a chi-square distribution. Additionally, the estimators of the slope parameters obtained by minimizing the Whittle dispersion is seen to be n ^1/2-consistent for all values of the long memory parameters of the design and error processes. Research of the first author was partly supported by the NSF DMS Grant 0701430. Research of the second author was partly supported by the bilateral France-Lithuania scientific project Gilibert and the Lithuanian State Science and Studies Foundation grant T-15/07.     

Non-resonant microwave absorption studies of superconducting MgB2 and MgB2 + MgO

Non-resonant microwave absorption (NRMA) studies of superconducting MgB₂ and a sample containing ∼10% by weight of MgO in MgB₂ are reported. The NRMA results indicate near absence of intergranular weak links in the pure MgB₂ sample. A linear temperature dependence of the lower critical field H _c1 is observed indicating a non-s wave superconductivity. However, the phase reversal of the NRMA signal which could suggest d wave symmetry is also not observed. In the MgB₂ + MgO sample, much larger low field dependent absorption is observed indicating the presence of intergranular weak links. The hysteretic behavior of NRMA is compared and contrasted in the two samples. In the pure MgB₂ sample, a large hysteresis is observed between the forward and the reverse scans of the magnetic field indicating strong pinning of flux lines. This hysteresis saturates a few degrees below T _c while in the MgB₂ + MgO sample, a much slower increase of hysteresis with decreasing temperature is observed, a signature of weaker pinning.