Dispersive Properties for Discrete Schr?dinger Equations

In this paper we prove dispersive estimates for the system formed by two coupled discrete Schr?dinger equations. We obtain estimates for the resolvent of the discrete operator and prove that it satisfies the limiting absorption principle. The decay of the solutions is proved by using classical and some new results on oscillatory integrals.     

Two-dimensional Meixner Random Vectors of Class ${mathcal{M}}_{L}$

The paper is divided into two parts. In the first part we lay down the foundation for defining the joint annihilation–preservation–creation decomposition of a finite family of not necessarily commutative random variables, and show that this decomposition is essentially unique. In the second part we show that any two, not necessarily commutative, random variables X and Y for which the vector space spanned by the identity and their annihilation, preservation, and creation operators equipped with the bracket given by the commutator forms a Lie algebra are equivalent up to an invertible linear transformation to two independent Meixner random variables with mixed preservation operators. In particular, if X and Y commute, then they are equivalent up to an invertible linear transformation to two independent classic Meixner random variables. To show this we start with a small technical condition called “non-degeneracy”.     

Determination of Non-Ionic Surfactants of the Alcohol Polyethoxylate Type by Means of High Temperature Gas Chromatography and Atomic Emission Detection

High temperature gas chromatography (HT-GC) coupled to atomic emission detection (AED) has been applied for the determination of alkyl chain distribution, mole average degree of ethoxylation and weight percent distribution of the corresponding homologues of alcohol ethoxylates without all the actual homologues being available as pure references. Based upon its constant elemental response, the HT-GC-AED system has been evaluated for its applicability to compound independent calibration within the homologous series of the alcohols and alcohol ethoxylates. Discrimination against high molecular weight components by gas chromatography requires conversion to the acetyl or trimethylsilyl derivatives. The latter includes introduction of the hetero atom silicon and thus allows monitoring of the silicon trace. Thus selectivity will be enhanced by excluding detection of compounds which do not react with the derivatization reagent. The method has been validated with the analysis of the technical product Brij 30, consisting of a mixture of alcohol ethoxylates with a vendor-specified mole average degree of ethoxylation of four. The experimental result yields a mole average degree of 4.0 ± 0.1 in the carbon, silicon and oxygen traces.     

Optimization of the response times of the feed kinematical linkages of the numerical control machine tools in order to minimize the path error

The main topic refers to enhancing the machining accuracy by minimizing the path error while machining through linear, circular or other interpolations on CNC machines for milling, boring and milling, grinding or turning. Currently the path error minimizing process while machining on CNC machine tools is a little explored, because of the absence of the dependence relations between the path error and the parameters of the kinematical axes taking part to the interpolation of the work piece contour. This work establishes and analyzes the relations of dependence between the path error and the response times of the kinematical axes that take part to the linear and circular interpolation. The theoretical results are experimentally verified by performing several machining operations through circular interpolation, where the moving speed along the contour and the response times of the kinematical axes are modified. The results of this research are intended for the machine tool designers and those who use such machines.     

High-Performance Thin-Layer Chromatographic Quantification of Some Essential Oils from Anethum graveolens Extracts

JPC – Journal of Planar Chromatography – Modern TLC - A high-performance thin-layer chromatography (HPTLC) method has been established for the analysis of α-phellandrene and...     

Formulation of Topical Dosage Forms Containing Synthetic and Natural Anti-Inflammatory Agents for the Treatment of Rheumatoid Arthritis

Topical anti-inflammatory and analgesic effect for the treatment of rheumatoid arthritis is of major interest because of their fewer side effects compared to oral therapy. The purpose of this study was to prepare different types of topical formulations (ointments and gels) containing synthetic and natural anti-inflammatory agents with different excipients (e.g.,: surfactants, gel-forming) for the treatment of rheumatoid arthritis. The combination of Non-Steroidal Anti-Inflammatory Drugs (NSAIDs), diclofenac sodium, a topical analgesic agent methyl salicylate, and a lyophilized extract of Calendula officinalis with antioxidant effect were used in our formulations. The aim was to select the appropriate excipients and dosage form for the formulation in order to enhance the diffusion of active substances and to certify the antioxidant, analgesic, and anti-inflammatory effects of these formulations. To characterize the physicochemical properties of the formulations, rheological studies, and texture profile analysis were carried out. Membrane diffusion and permeability studies were performed with Franz-diffusion method. The therapeutic properties of the formulations have been proven by an antioxidant assay and a randomized prospective study that was carried out on 115 patients with rheumatoid arthritis. The results showed that the treatment with the gel containing diclofenac sodium, methyl salicylate, and lyophilized Calendula officinalis as active ingredients, 2-propenoic acid homopolymer (Synthalen K) as gel-forming excipient, distilled water, triethanolamine, and glycerol had a beneficial analgesic and local anti-inflammatory effect.