FINITE ELEMENT APPROXIMATION OF A NONLINEAR STEADY-STATE HEAT CONDUCTION PROBLEM

1. Introduction Anciellt Chinese mathematicians have done many fund~al discoveries, even thoughmad of them are now usually called by western names, e.g., the Pascal triangle, the HornerIcheme, the Gaussian elimination, see [231. In the modern era3 Chinese mathematiciare have.jalso got many priorities. For instance, the fast Proof Of convergence of the finite element methodfor a linear elliptic boundary vajue problem was done in the pioneering work [61 by K. Feng in1965 (for the English tra…     

On the existence of solutions of nonlinear equations

Results on the existence of solutions are derived for asymptotically quasilinear, nonlinear operator equations. Applications are given to implicit nonlinear integral equations.

     

Ultrafast all-optical modulation on a silicon chip

We experimentally demonstrate ultrafast all-optical modulation using a micrometer-sized silicon photonic integrated device. The device transmission is strongly modulated by photoexcited carriers generated by low-energy pump pulses. A p-i-n junction is integrated on the structure to permit control of the generated carrier lifetimes. When the junction is reverse biased, carriers are extracted from the device in a time as short as 50 ps, permitting greater than 5 Gbit/s modulation of optical signals on a silicon chip.     

Learning beginning algebra in a computer-intensive environment

We present a design research on learning beginning algebra in an environment where spreadsheets were available at all times but the decision about using them or not, and how, in any particular situation was left to the students. Students’ activity is analyzed in Kieran’s framework of generational, transformational and global/meta-level activity, and compared to the designers’ intentions. We do this by focusing on the activity of one student in four sessions spread over several months and discussing the activity of 51 additional students in view of the analysis of the focus student. We show that the environment enables a number of different entries into algebra and as such supports students in becoming autonomous learners of algebra, and in making the shift from arithmetic to algebra via generational and global/meta-level activity before dealing with the more technical transformational activities.     

Recording 2-D Nutation NQR Spectra by Random Sampling Method

The method of random sampling was introduced for the first time in the nutation nuclear quadrupole resonance (NQR) spectroscopy where the nutation spectra show characteristic singularities in the form of shoulders. The analytic formulae for complex two-dimensional (2-D) nutation NQR spectra (I = 3/2) were obtained and the condition for resolving the spectral singularities for small values of an asymmetry parameter η was determined. Our results show that the method of random sampling of a nutation interferogram allows significant reduction of time required to perform a 2-D nutation experiment and does not worsen the spectral resolution.     

Synthesis,crystal structure and magnetic properties of a new tri‐nuclear iron (II,III) complex,a precursor for the preparation of superparamagnetic Fe3O4 nanoparticles applicable in the removal of Cd2+

This study reports the structural and spectroscopic characterization of a novel metal organic compound formulated as [Fe (bpy)₃] [Fe (dipic)₂]₂.7H₂O ( 1 ) (dipic = pyridine‐2,6‐dicarboxylate and bpy = 2,2^′‐bipyridine). 1 was investigated by elemental analysis, FT‐IR spectroscopy, powder X‐ray diffraction and single crystal X‐ray diffraction (SC‐XRD), which revealed a triclinic structure of expected composition. Thermal degradation of 1 was also investigated. Complex 1 was used as a precursor to prepare superparamagnetic nanoparticles of Fe₃O₄ by thermal analysis. The obtained Fe₃O₄ was characterized by Fourier transformed infrared spectroscopy (FT‐IR), powder X‐ray diffraction (XRD) and scanning electron microscopy (SEM). Fe₃O₄ nanoparticles were used as a nano‐adsorbent to remove Cd²⁺ from water at room temperature. The results showed that this nano‐adsorbent is effective in removing Cd²⁺ from contaminated water sources, and that the maximal effectivity of adsorption occurs at pH = 6. Magnetic measurements of complex 1 and Fe₃O₄ nanoparticles at room temperature revealed paramagnetic and superparamagnetic behavior, respectively.     

Optimization of o‐phtaldialdehyde/2‐mercaptoethanol postcolumn reaction for the hydrophilic interaction liquid chromatography determination of memantine utilizing a silica hydride stationary phase

A rapid procedure for the determination of memantine based on hydrophilic interaction chromatography with fluorescence detection was developed. Fluorescence detection after postcolumn derivatization with o‐phtaldialdehyde/2‐mercaptoethanol was performed at excitation and emission wavelengths of 345 and 450 nm, respectively. The postcolumn reaction conditions such as reaction temperature, derivatization reagent flow rate, and reagents concentration were studied due to steric hindrance of amino group of memantine. The derivatization reaction was applied for the hydrophilic interaction liquid chromatography method which was based on Cogent Silica‐C stationary phase with a mobile phase consisting of a mixture of 10 mmol/L citric acid and 10 mmol/L o‐phosphoric acid (pH 6.0) with acetonitrile using an isocratic composition of 2:8 v/v. The benefit of the reported approach consists in a simple sample pretreatment and a quick and sensitive hydrophilic interaction chromatography method. The developed method was validated in terms of linearity, accuracy, precision, and selectivity according to the International Conference on Harmonisation guidelines. The developed method was successfully applied for the analysis of commercial memantine tablets.     

A ferrocenyl‐substituted pseudo­titanocene complex

The title compound, (η⁵‐cyclo­penta­dienyl)[(1,2,3,4,5‐η)‐4‐ferro­cenyl‐1,2,5,6‐tetrakis­(tri­methyl­silyl)­cyclo­hexa‐2,4‐dien‐1‐yl]­titanium(II), [TiFe(C₅H₅)₂(C₂₃H₄₂Si₄)] or [Ti{η⁵‐C₆H₂{Fe­(η⁵‐C₅H₄)(η⁵‐C₅H₅)}{Si(CH₃)₃}₄}(η⁵‐C₅H₅)], possesses two directly linked metallocene units that subtend an angle of 52.9 (1)° (defined by the least‐squares planes of the directly connected π‐ligands) associated with the steric requirements of the bulky tri­methyl­silyl substituents. The cyclo­hexa­dienyl ligand adopts an envelope conformation; the perpendicular distance of its η⁵‐plane to the Ti atom is 1.512 (1) Å.