Extended Darboux function in a Weyl hypersurface

In this paper, by means of the prolonged differentiation, we introduce a pair of operators D andD ^* which enable us to extend the Darboux functions associated with a surface to the case of hypersurface in a Weyl space and discuss a few properties of these functions.     

Control and exponential stabilization for the equation of an axially moving viscoelastic strip

The aim through this work is to suppress the transverse vibrations of an axially moving viscoelastic strip. A controller mechanism (dynamic actuator) is attached at the right boundary to control the undesirable vibrations. The moving strip is modeled as a moving beam pulled at a constant speed through 2 eyelets. The left eyelet is fixed in the sense that there is no transverse displacement (see Figure 1 ). The mathematical model of this system consists of an integro‐partial differential equation describing the dynamic of the strip and an integro‐differential equation describing the dynamic of the actuator. The multiplier method is used to design a boundary control law ensuring an exponential stabilization result.     

High Performance Liquid Chromatography for the Determination of Metoclopramide in Pharmaceutical Preparations Using Pre‐column Derivatization with Fluorescamine

A simple, rapid and sensitive high performance liquid chromatography (HPLC) method was developed for the determination of metoclopramide in pharmaceutical preparation. The method is based on the derivatization of metoclopramide with fluorescamine. The separation was achieved on a C₁₈ column using methanol‐water (70:30, V/V) mobile phase. Fluorescence detector was used at the excitation and emission of 403 and 485 nm, respectively. The method was validated for linearity, limit of detection, limit of quantification, precision, accuracy, recovery, robustness and system suitability. The assay was linear over the concentration range of 100–2000 ng/mL. The mean recovery was 100.37%. The proposed method was successfully applied to the assay of metoclopramide in tablet preparation. The preparation was also analyzed with an official method and statistical comparison by t‐ and F‐tests revealed that there was no significant difference between the results of the two methods with respect to mean values and standard deviations at the 95% confidence level.     

A sensitive and rapid determination of ranitidine in human plasma by HPLC with fluorescence detection and its application for a pharmacokinetic study

A novel precolumn derivatization reversed-phase high-performance liquid chromatography method with fluorescence detection is described for the determination of ranitidine in human plasma. The method was based on the reaction of ranitidine with 4-fluoro-7-nitrobenzo-2-oxa-1,3-diazole forming yellow colored fluorescent product. The separation was achieved on a C(18) column using methanol-water (60:40, v/v) mobile phase. Fluorescence detection was used at the excitation and emission of 458 and 521 nm, respectively. Lisinopril was utilized as an internal standard. The flow rate was 1.2 mL/min. Ranitidine and lisinopril appeared at 3.24 and 2.25 min, respectively. The method was validated for system suitability, precision, accuracy, linearity, limit of detection, limit of quantification, recovery and robustness. Intra- and inter-day precisions of the assays were in the range of 0.01-0.44%. The assay was linear over the concentration range of 50-2000 ng/mL. The mean recovery was determined to be 96.40 ± 0.02%. This method was successfully applied to a pharmacokinetic study after oral administration of a dose (150 mg) of ranitidine.     

Stability and Unconditional Uniqueness of Solutions for Energy Critical Wave Equations in High Dimensions

In this paper we establish a complete local theory for the energy-critical nonlinear wave equation (NLW) in high dimensions ? × ? ^d with d ≥ 6. We prove the stability of solutions under the weak condition that the perturbation of the linear flow is small in certain space-time norms. As a by-product of our stability analysis, we also prove local well-posedness of solutions for which we only assume the smallness of the linear evolution. These results provide essential technical tools that can be applied towards obtaining the extension to high dimensions of the analysis of Kenig and Merle [17 Kenig , C.E. , Merle , F. ( 2008 ). Global well-posedness, scattering and blow-up for the energy critical focusing non-linear wave equation . Acta Math. 201 : 147 – 212 .[Crossref], [Web of Science ®] , [Google Scholar]] of the dynamics of the focusing (NLW) below the energy threshold. By employing refined paraproduct estimates we also prove unconditional uniqueness of solutions for d ≥ 6 in the natural energy class. This extends an earlier result by Planchon [26 Planchon , F. ( 2003 ). On uniqueness for semilinear wave equations . Math. Z. 244 : 587 – 599 .[Web of Science ®] , [Google Scholar]].     

Negative energy blowup results for the focusing Hartree hierarchy via identities of virial and localized virial type

Abstract

We establish virial and localized virial identities for solutions to the Hartree hierarchy, an infinite system of partial differential equations which arises in mathematical modeling of many body quantum systems. As an application, we use arguments originally developed in the study of the nonlinear Schrödinger equation (see work of Zakharov, Glassey, and Ogawa–Tsutsumi) to show that certain classes of negative energy solutions must blowup in finite time. The most delicate case of this analysis is the proof of negative energy blowup without the assumption of finite variance; in this case, we make use of the localized virial estimates, combined with the quantum de Finetti theorem of Hudson and Moody and several algebraic identities adapted to our particular setting. Application of a carefully chosen truncation lemma then allows for the additional terms produced in the localization argument to be controlled.     

Stabilization of a viscoelastic Timoshenko beam

A viscoelastic Timoshenko beam is investigated. We prove an exponential decay of solutions for a large class of kernels with weaker conditions than the existing ones in the literature. This will allow the use of other types of viscoelastic material for Timoshenko type beams than the usually used ones.     

Well–posedness for an Abstract Semilinear Integro–differential Fractional Problem

We consider an abstract second order semilinear integrodifferential equation involving fractional time derivatives of order between 1 and 2. Well–posedness is established under appropriate conditions on the initial data and the nonlinearity which is itself a fractional integral. These conditions will determine the exact underlying space where to look for solutions.