A moment problem associated to rational Szegő functions

Leta ₁,...,a _p be distinct points in the finite complex plane ?, such that |a _j|>1,j=1,..., p and let \(b_j = 1/\bar \alpha _j ,\) j=1,..., p. Let μ₀, μ _π ^(j) , ν _π ^(j) j=1,..., p;n=1, 2,... be given complex numbers. We consider the following moment problem. Find a distribution ψ on [?π, π], with infinitely many points of increase, such that $$\begin{array}{l} \int_{ - \pi }^\pi {d\psi (\theta ) = \mu _0 ,} \\ \int_{ - \pi }^\pi {\frac{{d\psi (\theta )}}{{(e^{i\theta } - a_j )^n }} = \mu _n^{(j)} ,} \int_{ - \pi }^\pi {\frac{{d\psi (\theta )}}{{(e^{i\theta } - b_j )^n }} = v_n^{(j)} ,} j = 1,...,p;n = 1,2,.... \\ \end{array}$$ It will be shown that this problem has a unique solution if the moments generate a positive-definite Hermitian inner product on the linear space of rational functions with no poles in the extended complex plane ?^* outside {a ₁,...,a _p,b ₁,...,b _p}.     

Derivatives of 2-thiohydantoin as spectrophotometric analytical reagents

The synthesis, characteristics, properties and reaction with metallic ions of four pyridine derivatives of 2-thiohydantoin have been studied. 5-(2-Pyridyl)methylene-2-thiohydantoin, 5-(6-methyl-2-pyridyl) methylene-2-thiohydantoin, 5-(di-2-pyridyl)methylene-2-thiohydantoin and 5-[1-(2-pyridyl)-1-methyl] methylene-2-thiohydantoin have been synthesized. The substances exhibit three pK values in aqueous solution and with Ag(I), Au(III), Cu(II), Pd(II) and Zn(II) form complexes with high molar absorptivities.     

Evaluation of polymeric flocculants for oily water systems using a photometric dispersion analyzer

During oil production and treatment, oil-in-water (O/W) emulsions are formed. These dispersions require treatment prior to disposal. In order to improve oil/water separation processes through any physical process (decanting, flotation, centrifuging etc), the particle size of the dispersed phase should be increased. This may be obtained by a flocculation process, which consists in the agglomeration of several particles or drops using as flocculating agent hydrophilic high molecular weight macromolecules. Poly (ethylene-b-propylene oxide) and poly (vinyl alcohol) polymers have been evaluated as flocculating agents for oily water systems. Their performance is related to the particle size increase of the dispersed phase. In this work, a photometric dispersion analyzer (PDA) has been used to accomplish the oil drop agglomeration. Synthetic as well as produced water was used. Data are in good agreement with previous tests. Qualitative information related to aggregates or particle size distribution of the oily water systems can be obtained using PDA.     

Transition metal-mediated intramolecular [2+2+2] cycloisomerizations of cyclic triynes and enediynes

[reaction: see text] Nitrogen-containing 15-membered triacetylenic macrocycles known as 1,6,11-tris(arylsulfonyl)-1,6,11-triazacyclopentadeca-3,8,13-triynes (1) and enediynic macrocycles called 1,6,11-tris(arylsulfonyl)-1,6,11-triazacyclopentadeca-3-ene-8,13-diynes (4 and 5) were satisfactorily prepared. [2+2+2] cycloisomerization processes catalyzed by transition metals were tested in the above-mentioned macrocycles. Readily available and familiar cyclotrimerization precatalysts were examined for efficiency. Among them, the RhCl(CO)(PPh(3))(2) complex was found to catalyze the cycloisomerization reaction giving the desired cycloadducts in high yields.     

Simultaneous determination of chromium (III) and copper (II) by using derivative spectrophotometry with MEDTA

The application of derivative spectrophotometry to the simultaneous determination of chromium (III) and copper (II) with MEDTA is described. The procedure is suitable for concentrations of 0.40–2.60 mg ml^–1 of chromium (III) and 0.15–0.60 mg ml^–1 of copper (II). The main interferences, both anionic and cationic, are easily eliminated. The method was applied to different aqueous matrices. It was compared with an atomic absorption method and good results were obtained. Received: 12 June 1996 / Revised: 30 July 1996 / Accepted: 2 August 1996