Fixed points and functional equations connected with derivations on Banach algebras

Let 1≦m≦4 be a fixed integer and let f:X→Y be a mapping with X, Y two vector spaces. The functional equation (1.1) is said to be additive if m=1, quadratic if m=2, cubic if m=3 and quartic if m=4, respectively. For convenience, a solution of (1.1) will be called an m-mapping. Let $\mathcal{A}$ , $\mathcal{B}$ be two algebras. An m-mapping $f\colon \mathcal{A} \to \mathcal{B}$ will be called m-derivation if the equality f(xy)=x ^m f(y)+f(x)y ^m is fulfilled for all $x,y\in \mathcal{A}$ . In this paper, we use a fixed point method to prove the stability and hyperstability of m-derivations on Banach algebras.     

A novel pseudo-seven-component diastereoselective synthesis of λ-phosphanylidene bis(2,5-dioxotetrahydro-1H-pyrrole-3-carboxylates) via binucleophilic systems

The unusual 1:2 intermediate, generated by the addition of triphenylphosphine (TPP) to dialkyl acetylenedicarboxylates (DAAD) was trapped during the reaction of a Ph₃P/RN = C/DMAD binucleophilic system with TFA as an initial proton source in a pseudo-seven-component (7-CR) diastereoselective reaction to give λ⁵-phosphanylidene bis(2,5-dioxotetrahydro-1H-pyrrole-3-carboxylates) with three stereogenic centers and a phosphorane group in good yields.     

Synthesis of organosoluble polyamides with bulky triaryl imidazole pendent group

New unsymmetrical diamine monomer containing triaryl imidazole pendent group,4-[4-(4,5-diphenyl-1H-imidazol-2-yl)phenoxy] -1,3-benzenediamine,was synthesized via aromatic substitution reaction of 1-chloro-2,4-dinitrobenzene with 4-(4,5- diphenyl-1H-imidazol-2-yl)phenol,followed by palladium-catalyzed hydrazine reduction.This new monomer was further confirmed by FT-IR,~1H NMR and ~(13)C NMR.Novel polyamides having pendant triaryl imidazole group were prepared by the phosphorylation polycondensation of fou...     

Transformation of methane to synthesis gas over metal oxides without using catalyst

This article reviews a new developing method in the field of metal oxide reduction in chemical and metallurgical processes, which uses methane as a reducing agent. Commonly, coal is used as the reducing agent in the reduction of metal oxide and other inorganic materials; Metal producing factories are among the most intensive and concentrated source of greenhouse gases and other pollutants such as heavy metals, sulfur dioxide and fly ash. Thermodynamically, methane has a great reducing capability and can be activated to produce synthesis gas over a metal oxide as an oxygen donor. Metal oxide reduction and methane activation, two concurrent thermochemical processes, can be combined as an efficient and energy-saving process; nowadays this kind of technologies is of great importance. This new reduction process could improve energy efficiencies and significantly decrease greenhouse gas emission compared to the conventional process; furthermore, the produced gases are synthesis gas that is more valuable than methane. In this paper, thermodynamic studies and advantages of this promising method were discussed. The major aim of this article is to introduce methane as a best and environmentally friendly reducing agent at low temperature.     

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.     

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.     

Copper(II)-selective membrane electrode based on a recently synthesized naphthol-derivative Schiff’s base

A PVC membrane electrode for copper(II) ions based on a recently synthesized naphthol-derivative Schiff’s base as membrane carrier was prepared. The sensor exhibits a Nernstian response for Cu²⁺ ions over a wide concentration range (5.0 × 10^–6–5.0 × 10^–2 mol/L) with a detection limit of 3.1 × 10^–6 mol/L (0.2 μg/mL). It has a very short response time of about 5 s and can be used for ¶3 months without any divergence in potential. The proposed electrode revealed good selectivities over a wide variety of other cations including alkali, alkaline earth, transition and heavy metal ions and could be used in a pH range of 4.0–7.0. It was successfully applied to the direct determination and potentiometric titration of copper ion.     

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.