Eigenvalue Estimate for the Basic Laplacian on Manifolds with Foliated Boundary,Part II

On a compact Riemannian manifold N whose boundary is endowed with a Riemannian flow, we gave in El Chami et al. (Eigenvalue estimate for the basic Laplacian on manifolds with foliated boundary, 2015) a sharp lower bound for the first non-zero eigenvalue of the basic Laplacian acting on basic 1-forms. In this paper, we extend this result to the set of basic p-forms when \(p>1\). We then characterize the limiting case by showing that the manifold N is isometric to Open image in new window for some group \(\Gamma \) where \(B'\) denotes the unit closed ball. As a consequence, we describe the Riemannian product \({\mathbb {S}}^1\times {\mathbb {S}}^n\) as the boundary of a manifold.     

Area preserving analytic flows with dense orbits

The aim of this paper is to give sufficient conditions on area-preserving flows that guarantee the existence of dense orbits. We also answer a question by M.D. Hirsch [M.D. Hirsch, Dense recurrence in area-preserving flows on surfaces, Nonlinearity 12 (1999) 1545-1553]. The results of this work are a generalization of the ones in [M.D. Hirsch, Dense recurrence in area-preserving flows on surfaces, Nonlinearity 12 (1999) 1545-1553] and [H. Marzougui, Area preserving flows with a dense orbit, Nonlinearity 15 (2002) 1379-1384].     

Island formation in Ge films on GaAs(1 1 0)

The early stages of GaAs (1 1 0)/Ge heterojunction formation at room temperature have been investigated by Auger spectroscopy. Comparison between the experimental results and the predictions of simple deposition models indicates that the growth of the Ge film proceeds by island formation. A uniform overlayer starts to develop only in films thicker than 10 Å. Evidence is also found for As diffusion through the Ge film.     

Jump number of dags having Dilworth number 2

The jump number, denoted by σ, of a directed acyclic graph (dag) G, is the minimum number of arcs that have to be added to G such that the resulting graph is still acyclic and has a hamiltonian path.We study here the particular class of dags having an induced partial order of width 2, and give a characterization of such graphs with σ(G)=i. This yields immediately a polynomial algorithm to compute the jump number in this particular class.     

PREPARATION OF α-KETOPHOSPHONATES BY OXIDATION OF α-HYDROXYPHOSPHONATES WITH PYRIDINIUM CHLOROCHROMATE (PCC)

Various types of diethyl α-hydroxyphosphonates were converted efficiently to their corresponding diethyl α-ketophosphonates by pyridiinum chlorochromate (PCC) without cleavage of C(O)─P bond in the absence of solvent or in solution in high yields.     

Sol-Gel-based SPME and GC–MS for Trace Determination of Geosmin in Water and Apple Juice Samples

A headspace solid-phase microextraction (HS-SPME) method was developed for the trace determination of geosmin in water and apple juice samples. A poly(dimethylsiloxane) (PDMS) fiber was synthesized as coated fiber using sol-gel methodology. After performing the extraction in the headspace, the fiber was introduced directly into the injection port of a gas chromatography-mass spectrometry (GC–MS) using electron impact (EI) ionization mode. One-at-the-time optimization strategy was applied to investigate and optimize important extraction parameters such as extraction temperature and time, ionic strength, headspace volume, and desorption temperature and time. The analytical data exhibited an RSD of 2–15%, a linear calibration range of 1–1,000 ng L^?1, and a detection limit of 0.30 ng L^?1 using selected ion monitoring (SIM) mode. The proposed method was successfully applied to the extraction and determination of geosmin in the spiked real water and apple juice samples and a relative recovery of 95–102% were achieved. The developed method offers the advantage of being simple to use, with shorter analysis times, lower cost of equipment, very little matrix effect, and high relative recovery in comparison to conventional methods of analysis.     

A compilation of X- and gamma-ray sensitivities from isotopes produced by the (n, γ) reaction for utilization in instrumental neutron activation analysis

A comprehensive compilation of X- and γ-ray emitting isotopes produced by the (n, γ) reaction is reported in this paper for application to instrumental neutron activation analysis (INAA). The X- and γ-ray sensitivities are computed theoretically by a computer code. Interfering photons from isotopes of neighbouring elements are identified by the code and the percentage interference is computed. Additionally an advantage factor (X-ray: γ-ray sensitivity) is computed, which is a figure of merit for X-ray spectroscopy in INAA. Further, mathematical representation of background continua for typical matrices encountered in INAA allow the calculation of elemental detection limits for the X-ray and γ-ray photons.     

Voltammetric determination of thiocytosine based on its electrocatalytic oxidation on the surface of carbon-paste electrode modified with cobalt Schiff base complexes

The electrochemical oxidation of thiocytosine on the surface of carbon-paste electrode modified with Schiff base (salophen derivatives) complexes of cobalt is studied. The effect of the substituents in the structure of salophen on the catalytic property of the modified electrode is investigated by using cyclic and differential pulse voltammetry. Cobalt (II)-5-nitrosalophen, because of its electrophilic functional groups, leads to a considerable enhancement in the catalytic activity, sensitivity (peak current), and a marked increase in the anodic potential of the modified electrode. The differential pulse voltammetry is applied as a very sensitive method for the detection of thiocytosine. The linear dynamic range was between 1 × 10⁻³ to 4 × 10⁻⁶ M with a slope of 0.0168 μA/μM, and the detection limit was 1 × 10⁻⁶ M. The modified electrode is successfully applied for the voltammetric detection of thiocytosine in human synthetic serum sample and also pharmaceutical preparations. A linear range from 1 × 10⁻³ to 1 × 10⁻⁵ M with a slope of 0.0175 μA/μM is resulted for the standard addition of thiocytosine spiked to the buffered human serum, which is differing from the curve in buffer solution about 4%. The electrode has a very good reproducibility (relative standard deviation for the slope of the calibration curve is less than 3.5% based on six determinations in a month), high stability in its voltammetric response and low detection limit for thiocytosine, and high electrochemical sensitivity with respect to other biological thiols such as cysteine.