Asymptotic null controllability of nonlinear perturbed systems

In this paper, sufficient conditions are obtained for the asymptotic null controllability of the system $$\dot x(t) = g(t,x(t)) + B(t,x(t))u(t) + f(t,x(t),u(t)).$$ The results are obtained by using the Leray-Schauder fixed-point theorem.     

Coordination of cations in TiNb2O7 by Raman spectroscopy

The Raman spectrum of the compound TiNb₂O₇ prepared by a liquid mix technique was recorded at room temperature using the 530.98-nm line from a krypton-ion laser as exciter. The bands observed at 998 and 884 cm^?1 are assigned to the edge-shared and corner-shared NbO₆ octahedra, respectively. The relative intensities of these two bands are consistent with the structure of TiNb₂O₇ worked out by earlier investigators using X-ray and neutron diffraction. The strong band observed at 647 cm^?1 is assigned to the vibration of the TiO₆ octahedra. The octahedral coordination for both cations based on the results of the Raman spectrum measurements is in essential agreement with the available structural data for the compound TiNb₂O₇. The weak band observed at 840 cm^?1 is suggestive of the presence of NbO₄ tetrahedra in small concentrations in TiNb₂O₇.     

Synthesis,crystal structure and reactivity of trans-diaquo N,N′-ethylenebis-(3-methoxysalicylideneiminato)chromium(III)

A new chromium(III) Schiff base complex, [Cr(3-methoxysalen)(H₂O)₂]ClO₄, where salen=N,N-ethylenebis- (salicylideneimine), has been synthesized and characterized by spectroscopic techniques. Single crystal X-ray data reveals that the complex assumes a trans-diaquo structure with formulation [Cr(C₁₈H₂₂N₂O₆)]ClO₄ but, unlike in Cr (salen)(H₂O)₂ ⁺, the two trans-water molecules are equidistant from Cr^III. The effect of the substituent on the phenyl ring in respect of redox reactivity has been investigated. The kinetics of the oxidation of [Cr(Schiff base)- (H₂O)₂]ClO₄, where Schiff base=salen, (1) and 3-OMe-salen, (2) by PhOI has been studied. The bimolecular rate constant for the formation of the O=Cr^v Schiff base in case of (2) was four times faster than that of (1). The introduction of the OMe group substituent on the phenyl ring influences not only the structure and crystal packing, but also the reactivity of the complex and the electronic environment around the metal ion.     

Raman spectra of titanium dioxide

First-order Raman spectra have been recorded at room temperature for the anatase and rutile phases of polycrystalline titanium dioxide using an argon ion laser as exciter. The high-temperature rutile phase was found to be stabilized at temperatures below 450°C. Anatase transforms to rutile phase at ～750°C. All the Raman active fundamentals predicted by group theory are observed.     

An Experimental Design Approach to Quantitative Expression for Quality Control of a Multicomponent Antidiabetic Formulation by the HILIC Method

A rapid and reproducible hydrophilic liquid chromatography (HILIC) process was established for concomitant determination of remogliflozin etabonate (RE), vildagliptin (VD), and metformin (MF) in a formulation. A face-centered central composite experimental design was employed to optimize and predict the chromatographic condition by statistically studying the surface response model and design space with desirability close to one. A HILIC column with a simple mobile phase of acetonitrile (65% v/v) and 20 mM phosphate buffer (35% v/v, pH 6, controlled with orthophosphoric acid) was used to separate RE, VD, and MF. RE, VD, and MF were separated in 3.6 min using an isocratic mode mobile phase flow at a flow rate of 1.4 mL at room temperature, and the analytes were examined by recording the absorption at 210 nm. The developed HILIC method was thoroughly validated for all parameters recommended by ICH, and linearity was observed in the ranges 20–150 µg/mL, 10–75 µg/mL, and 50–750 µg/mL for RE, VD, and MF, respectively, along with excellent regression coefficients (r² > 0.999). The calculated percentage relative deviation and relative error ascertained the precision and accuracy of the method. The selectivity and accuracy were further confirmed by the high percentage recovery of added standard drugs to the formulation using the standard addition technique. The robustness of the HILIC processes was confirmed by developing a half-normal probability plot and Pareto chart, as the slight variation of a single factor had no significant influence on the assay outcomes. Utilization of the optimized HILIC procedure for concurrent quantification of RE, VD, and MF in solid dosage forms showed accurate and reproducible results. Hence, the fast HILIC method can be regularly employed for the quality assurance of pharmaceutical preparations comprising RE, VD, and MF.     

In vitro dielectrophoresis of HEK cell migration for stimulating chronic wound epithelialization

This article describes a dielectrophoresis (DEP)-based simulation and experimental study of human epidermal keratinocyte (HEK) cells for wounded skin cell migration toward rapid epithelialization. MyDEP is a standalone software designed specifically to study dielectric particles and cell response to an alternating current (AC) electric field. This method demonstrated that negative dielectrophoresis (N_DEP) occurs in HEK cells at a wide frequency range in highly conductive medium. The finite element method was used to characterize particle trajectory based on DEP and drag force. The performance of the system was assessed using HEK cells in a highly conductive EpiLife suspending medium. The DEP experiment was performed by applying sinusoidal wave AC potential at the peak-to-peak voltage of 10 V in a tapered aluminum microelectrode array from 100 kHz to 1 MHz. We experimentally observed the occurrence of NDEP, which attracted HEK cells toward the local electric field minima in the region of interest. The DIPP-MotionV software was used to track cell migration in the prerecorded video via an automatic marker and estimate the average speed and acceleration of the cells. The results showed that HEK cell migration was accomplished approximately at 6.43 μm/s at 100 kHz with 10 V, and F_DEP caused the cells to migrate and align at the target position, which resulted in faster wound closures because of the application of an electric field frequency to HEK cells in random locations.     

Noise-induced chaotic-attractor escape route

Nonlinear Dynamics - In the present article, a combination of numerical and experimental studies is undertaken to comprehend the influence of noise on the responses of continuous-time dynamical...