Real Paley-Wiener theorems associated with the weinstein operator

In this paper we use real analysis techniques to establish a new real Paley-Wiener theorems for the Fourier-Bessel transform associated with the Weinstein operator. More precisely we characterize the C ^∞-functions whose image under the Fourier-Bessel transform are functions with compact support through an L ^p growth condition, p ∈ [1, +∞] and we give another version of the real Paley-Wiener theorem for L ²-functions.     

Comment: Towards a Complete Classification of Spherically Symmetric Lorentzian Manifolds According to Their Ricci Collineations

General expressions for the components of the Ricci collineation vector are derived and the related constraints are obtained. These constraints are then solved to obtain Ricci collineations and the related constraints on the Ricci tensor components for all spacetime manifolds (degenerate or non-degenerate, diagonal or non-diagonal) admitting symmetries larger than so(3) and already known results are recovered. A complete solution is achieved for the spacetime manifolds admitting so(3) as the maximal symmetry group with non-degenerate and non diagonal Ricci tensor components. It is interesting to point out that there appear cases with finite number of Ricci collineations although the Ricci tensor is degenerate and also the cases with infinitely many Ricci collineations even in the case of non-degenerate Ricci tensor. Interestingly, it is found that the spacetime manifolds with so(3) as maximal symmetry group may admit two extra proper Ricci collineations, although they do not admit a G ₅ as the maximal symmetry group. Examples are provided which show and clarify some comments made by Camci et al. [Camci, U., and Branes, A. (2002). Class. Quantum Grav. 19, 393–404]. Theorems are proved which correct the earlier claims made in [Carot, J., Nunez, L. A., and Percoco, U. (1997). Gen. Relativ. Gravit. 29, 1223–1237; Contreras, G., Núñez, L. A., and Percolo, U. (2000). Gen. Relativ. Gravit. 32, 285–294].     

On-column trace enrichment by sequential frontal and elution electrochromatography II. Enhancement of sensitivity by segmented capillaries with z-cell configuration--application to the detection of dilute samples of moderately polar and nonpolar pesticides

An on-column trace enrichment method for capillary electrochromatography of dilute samples is described. It involves the sequential use of frontal and elution electrochromatography on a segmented capillary column comprising of two contiguous segments each packed with a different sorbent. While the entering segment is for preconcentration by frontal electrochromatography the second segment is much longer and is meant for separation of the enriched analytes in the subsequent elution electrochromatography step. The preconcentration segment is usually packed with a sorbent that affords the highest affinity towards the solutes of interest while the separation segment is packed with a stationary phase that exhibits the highest selectivity and separation efficiency for the analytes. The detection is performed in the UV using a z-cell configuration for achieving an increased path length for detection. The effectiveness of this on-column trace enrichment is demonstrated on dilute samples of moderately polar solutes (e.g., carbamate insecticides) and nonpolar solutes (e.g., pyrethroid insecticides). Under optimal frontal and elution electrochromatography conditions. 817- and 1100-fold sensitivity increase are achieved for permethrin (a pyrethroid insecticide) and methiocarb (a carbamate insecticide), respectively, with a UV detector. The method is demonstrated with real water samples (e.g., tap and lake water samples) spiked with carbamate and pyrethroid insecticides. The limits of detection for the pesticides achieved in tap and lake waters reached 10(-8) to 10(-9) M.     

Analysis of tungsten-containing mixtures and some alloy steels by potentiometric titration methods

Reliable potentiometric titration methods are adopted for the analysis of tungsten mixtures analogous to some industrially important alloys such as low alloy tap steel, tungsten chisel, and high speed steels. Tungsten is separated as Hg₂WO₄ and unreacted Hg(I) is titrated with KBr. The techniques of oxidation with I₂ or reduction with KI and use of the selective arsenite reduction of Cr(VI) and/or Mn(IV) in the presence of V(V) or Fe(III) make it possible to determine alloy components without tedious separations. In all titrations the potential break is sharp enough for the precise establishment of the end point.     

Kinetic studies on the solvolysis and axial ligand substitutions of bis-triphenylphosphine(cyclohexane-1,2-dione-dioximato)ruthenium(II) in non-aqueous solvents

Kinetic studies of ligand substitutions of the six-coordinated Ru^II pseudo-macrocyclic complex [Ru(CHDH)₂- (PPh₃)₂] (CHDH=cyclohexanedione-dioximato) have been spectrophotometrically investigated in a variety of solvents and at 70, 80, 85 and 90°C. The reactions studied are of the form:[(PPh₃)Ru(CHDH)₂(PPh₃)] + L =[(PPh₃)Ru(CHDH)₂L] + PPH₃ where L is imidazole, pyridine, piperidine or thiophene or a solvent molecule (PhCl, PhMe, MeCN, DMSO or DMF). The solvolysis reactions with chlorobenzene and toluene proceed to an equilibrium position favoring the bis-triphenylphosphine complex. All other reactions proceed to completion. From a mechanistic point of view the reactions were found to proceed through the formation of a five coordinate intermediate that possesses little or no discriminating ability towards the incoming nucleophiles. The rate data were thus interpreted in terms of a dissociative (D) or dissociative interchange (Id) mechanism. Activation parameters H and S are reported. Preliminary studies on the solvatochromic behavior of [Ru(CHDH)₂(PPh₃)₂] and the corresponding mixed complexes are discussed.     

Applications involving the iodide ion-X determination of copper and analysis of cation mixtures and alloys

A rapid, accurate and highly selective method has been developed for estimation of copper, based on separating it as the slightly soluble copper(I) iodide, and potentiometric back-titration of unreacted iodide, in the filtrate, with mercury(II). By its aid binary, ternary and quaternary mixtures as well as a variety of copper alloys have been successfully analysed.     

Synthetic strategies and functional reactivity of versatile thiophene synthons

Abstract

Thiophenes are a highly important group of heterocycles and have been of great interest to researchers due to their various reactivities. Many synthetic strategies are used to generate functionalized thiophene derivatives. Several reactions are described, depending on the reactivity of the substituents attached to the thiophene nucleus toward different nucleophiles to yield the versatile thiophene products. Many diverse applications have been utilized for thiophenes from medicinal chemistry to material science.     

Extraction of tungsten and rhenium by basic or neutral extractants in xylene from mineral acidic media

Extraction of WO ₄ ^2– and ReO ₄ ^– by Adogen-381, tricaprylmethylammonium chloride, Hyamine 10-X, trioctylphosphine oxide or dibenzylsulphoxide in xylene from HNO₃, HCl or H₂SO₄ acid medium was investigated. Based on the separation factors obtained, the separation of ReO ₄ ^– from WO ₄ ^2– was elucidated. ReO ₄ ^– was separated from WO ₄ ^2– in high radiochemical purity: >99.9% by three successive extractions and strippings using Adogen-381 from HCl or HNO₃ acid medium.     

Back titration with mercuric ntrate in alkaline medium; potentiometric estimation of aluminium and manganese

Summary Mercuric nitrate has been successfully used for back titrating excess EDTA amounts than required for chelation with Al³⁺ or Mn²⁺ ions. This principle was the basis underlying the potentiometric determination of small amounts of both metals in the range of 10 g to 6 mg. End points are attended within 0.01 to 0.02 ml of titrant with fair accuracy and reasonable jumps ranging from 35 to 88 mv per 0.1 ml of titrant.     

Applications involving oxidation with KBrO3: III. Rapid potentiometric methods for vanadium alone or in mixtures

A rapid and reliable method is given for the determination of vanadium based on oxidation of the V(IV) with a known excess of bromate to V(V). The unreacted oxidant as well as V(V) are subsequently reduced with sulfurous acid to V(IV). The resulting Br^?1 was potentiometrically titrated with Hg(I) using silver amalgam as the indicator electrode. The method finds application to the analysis of some binary and ternary mixtures.