Jordan derivations of full matrix algebras

Let A be a unital associative ring and M be a 2-torsion free A-bimodule. Using an elementary and constructive method we show that every Jordan derivation from M_n(A) into M_n(M) is a derivation.     

Amenability properties of the centres of group algebras

Let G be a locally compact group, and ZL¹(G) be the centre of its group algebra. We show that when G is compact ZL¹(G) is not amenable when G is either non-abelian and connected, or is a product of infinitely many finite non-abelian groups. We also, study, for some non-compact groups G, some conditions which imply amenability and hyper-Tauberian property, for ZL¹(G).     

Local boundedness of monotone bifunctions

We consider bifunctions ${F : C\times C\rightarrow \mathbb{R}}$ where C is an arbitrary subset of a Banach space. We show that under weak assumptions, monotone bifunctions are locally bounded in the interior of their domain. As an immediate corollary, we obtain the corresponding property for monotone operators. Also, we show that in contrast to maximal monotone operators, monotone bifunctions (maximal or not maximal) can also be locally bounded at the boundary of their domain; in fact, this is always the case whenever C is a locally polyhedral subset of ${\mathbb{R}^{n}}$ and F(x, ·) is quasiconvex and lower semicontinuous.     

A Simple Method for Melatonin Determination in the Presence of High Levels of Tryptophan using an Unmodified Carbon Paste Electrode and Square Wave Anodic Stripping Voltammetry

Electrochemical determination of melatonin in the presence of tryptophan is a challenge because of the coincidence of voltammetric signals of these compounds when executing a voltammetric technique. The new method for selective determination of melatonin based on the square wave anodic stripping voltammetry determination of an electroactive product of melatonin was suggested here. This product is produced by previously applied positive pre-potential to a carbon paste electrode, immersed in the test solution. By this means, the electrochemical signal of melatonin was separated effectively from that of tryptophan, making it possible to determine melatonin in the presence of a high concentration of tryptophan. The effect of important parameters on electrode performance was studied and optimized. The optimum response was obtained at pH=2 and utilizing the pre-potential magnitude of +0.8 V, applied for 10 s. A linear relationship was found between peak current intensity and melatonin concentrations over the range of 5.00×10⁻⁷ to 8.00×10⁻⁵ mol L⁻¹. A detection limit of 8.30×10⁻⁸ mol L⁻¹ was calculated for the method (S/N=3). The selectivity of the method was considerably high, because of the independence of melatonin signal to the presence of higher amounts of some potentially interfering agents such as ascorbic acid, tryptophane glucose, etc. As an analytical application, the proposed sensor was used for the determination of melatonin in pharmaceutical and food samples.     

Growth of KCl crystal by Czochralski method and influence of nanodiamond impurity on its hardness and optical properties

KCl alkali halide crystal with different nanodiamond impurity was grown by Czochralski method. X‐Ray diffraction of the outcome samples reveals that they are still single crystal. Also crystal hardness observation reveals that the hardness of KCl single crystal has been increased by adding different percentage of nanodiamond impurity. In addition, the study of FTIR spectrums of the pure and doped crystals represents that the KCl optical properties has not changed.