Zeros of Jacobi polynomials Pn( α, β)$ P_{n}^{(\alpha ,\beta)} $, − 2 < α, β < − 1

The sequence of Jacobi polynomials \(\{P_{n}^{(\alpha ,\beta )}\}_{n = 0}^{\infty }\) is orthogonal on (??1,1) with respect to the weight function (1 ? x)^α(1 + x)^β provided α > ??1,β > ??1. When the parameters α and β lie in the narrow range ??2 < α, β < ??1, the sequence of Jacobi polynomials \(\{P_{n}^{(\alpha ,\beta )}\}_{n = 0}^{\infty }\) is quasi-orthogonal of order 2 with respect to the weight function (1 ? x)^α+?1(1 + x)^β+?1 and each polynomial of degree n,n ≥?2, in such a Jacobi sequence has n real zeros. We show that any sequence of Jacobi polynomials \(\{P_{n}^{(\alpha ,\beta )}\}_{n = 0}^{\infty }\) with ??2 < α, β < ??1, cannot be orthogonal with respect to any positive measure by proving that the zeros of Pn??1(α,β) do not interlace with the zeros of Pn(α,β) for any \(n \in \mathbb {N},\)n ≥?2, and any α,β lying in the range ??2 < α, β < ??1. We also investigate interlacing properties satisfied by the zeros of equal degree Jacobi polynomials Pn(α,β),Pn(α,β+?1) and Pn(α+?1,β+?1) where ??2 < α, β < ??1. Upper and lower bounds for the extreme zeros of quasi-orthogonal order 2 Jacobi polynomials Pn(α,β) with ??2 < α, β < ??1 are derived.     

P-31 Solid State Nuclear Magnetic Resonance Investigations on Cyclophosphazenes

Abstract

The present study deals with solid state NMR investigations on cyclophosphazeaes wah the following substituents: -NH₂, -OMe, -F, -Cl, -Br, at which the substituent atoms are elements of the 2^nd period (N, O, and F) or elements of the 7^th main group (F, Cl, and Br). The NMR spectra were obtained by a BRUKER MSL 300 spectrometer using a resonance frequenacy of 121.496 MHz. With each compound a static powder spectrum, a hgh speed MAS spectrum, and several side band spectra were recorded.     

A new non-enzymatic tracer for time-resolved fluoroimmunoassay of triazine herbicides

Summary The synthesis, characterization and application of a new kind of conjugate as tracer for use in time-resolved fluoroimmunoassay of triazine herbicides is described. Bovine serum albumin (BSA) served as carrier molecule, to which a triazine herbicide derivative and the Eu(III)-chelate W8044-Eu were subsequently coupled. The conjugate was characterized after each synthesis step by matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS). The total composition was 1 BSA : 5.2 (±0.7) haptens : 5.1 (±0.4) fluorophores as calculated from the MALDI-MS data. The conjugate was successfully applied in competitive fluoroimmunoassays with sequential or simultaneous incubation of herbicide and tracer. With the sequential assay, the lowest detection limit was 0.1 g/l for terbutryn. Results of assays performed with microtiter strips were compared with those obtained with commercial micro affinity columns.     

An Experimental and Mechanistic Investigation of the Complexities Arising During Inhibition of the Briggs?Rauscher Reaction by Antioxidants

A method to determine the relative antioxidant capacity of radical scavengers based on the inhibition of the oscillations of the Briggs? Rauscher (BR) oscillating reaction was previously reported. A semiquantitative mechanistic interpretation of the inhibitory effects required two steps to obtain simulated inhibition times in very good agreement with the experimental ones. The first step is inhibitory, involving H‐atom transfer from antioxidant to the HOO^. radical; the second step is a first‐order degradation of the antioxidant to unspecified products. Since the degradation may be due to oxidation and/or iodination of the antioxidant, we studied the kinetics of the subsystems IO (H⁺)+antioxidant and I₂(H⁺)+antioxidant. We used 2,5‐ and 2,6‐dihydroxybenzoic acids, caffeic acid (=3‐(3,4‐dihydroxyphenyl)prop‐2‐enoic acid), ferulic acid (=3‐(4‐hydroxy‐3‐methoxyphenyl)prop‐2‐enoic acid), pyrocatechol (=benzene‐1,2‐diol), and hydroquinone (=benzene‐1,4‐diol) as antioxidants. Spectra in the wavelength range 500–250 nm were repeated at given time intervals to follow the peaks of the iodine and oxidation products, which were mainly quinones. For the iodination of the above diphenols (=benzenediol derivatives) the substitution and/or addition reactions with I₂ or HOI were found to be relatively slow compared to oxidation by IO . Approximate rate constants for oxidation were obtained on the basis of a reasonable kinetic model by using a suitable numerical integration program. Although these complexities can arise also in the completely inhibited BR oscillator, we believe that the inhibitory effects are due to the HOO^. scavenging action by diphenols or by quinones since HOO^. radicals are also potential reducing agents. We propose two steps that could maintain a small reservoir of diphenol, while both quinone and diphenol deplete HOO^. radicals. In short, the complexities do not affect the method for monitoring the relative activity of antioxidants based on the BR oscillating reaction. The effects of temperature on the inverse of the oscillatory time in the BR‐uninhibited system, on the inverse of inhibition times, and on the time length of the resumed oscillations for four antioxidants were also investigated. Apparent average activation energies were obtained.     

A First Approach to the cis‐trans‐cis‐Photocyclodimers of 1,2‐Naphthoquinone

On irradiation (λ=350 nm), 1,2‐naphthoquinone (=naphthalene‐1,2‐dione) monoacetals 1 are converted quantitatively to mixtures of the cis‐trans‐cis‐photocyclodimers 2 and 3 . Careful hydrolysis of each of the (parent) pentacyclic diacetals 2a and 3a affords the – rather unstable – compounds 4 and 5 , respectively.     

Potentiometric stripping analysis for zinc,cadmium. lead and copper in sea water

Analytical procedures for the determination of zinc(II), cadmium (II), lead(II) and copper(II) in sea water by potentiometric stripping analysis are described. The results are compared with those obtained by a combined solvent extraction-atomic absorption method both in the laboratory and on-board ship. The detection limits for zinc, cadmium, lead and copper are 0.03, 0.03, 0.01 and 0.02 μg l^-1, respectively, for a total analysis time of about 75 min. A very thin mercury film is useful in the determination of lead and copper.     

Recycling of process streams in ethanol production from softwoods based on enzymatic hydrolysis

In ethanol production from lignocellulose by enzymatic hydrolysis and fermentation, it is desirable to minimize addition of fresh-water and waste-water streams, which leads to an accumulation of substances in the process. This study shows that the amount of fresh water used and the amount of waste water thereby produced in the production of fuel ethanol from softwood, can be reduced to a large extent by recycling of either the stillage stream or part of the liquid stream from the fermenter. A reduction in fresh-water demand of more than 50%, from 3 kg/kg dry raw material to 1.5 kg/kg dry raw material was obtained without any negative effects on either hydrolysis or fermentation. A further decrease in the amount of fresh water, to one-fourth of what was used without recycling of process streams, resulted in a considerable decrease in the ethanol productivity and a slight decrease in the ethanol yield     

Die ersten Fluorotrithiatetraphosphaheptane

The First Fluoro-trithiatetraphospha-heptanes Fluorinated α- and β-tetraphosphorus-trisulfur molecules were prepared by the reaction of α- or β-P₄S₃X₂ (X = Cl, Br, I) with (n-butyl)₃SnF. The substitution reaction of the α-isomers yields under retention of the configuration at the phosphorus atoms α-P₄S₃XF and α-P₄S₃F₂. In the reaction of the β-isomers more products were observed, because the configuration of the phosphorus atom can be retained or inversed in the first step of the substitution which yields β-P₄S₃X_exoF_exo or β-P₄S₃X_exoF_endo. The mass relation of the products depends on the halogen ligand. In the second substitution β-P₄S₃(F_exo)₂ or β-P₄S₃F_exoF_endo are formed. β-P₄S₃(F_endo)₂ was not observed. By the reaction of β-P₄S₃I₂ with BiX₃ (X = Cl, Br, I) we also were able to prepare small amounts of β-P₄S₃X_endoX_exo-molecules (X = I, Cl, Br) with an inversed configuration at one phosphorus atom. The ³¹P- and ¹⁹F-NMR parameter of all compounds are discussed.     

Reaktionen von P4S3I2 mit bifunktionellen Liganden

Reactions of P₄S₃I₂ with Bifunctional Ligands Nitrogen, oxygen, selenium or carbon atoms were introduced as bridges into the P₄S₃ skeleton by the reaction of α- or β-P₄S₃I₂ with bifunctional ligands. Among compounds in the series α-P₄S₃-α-E, the oxide μ-P₄SO was made for the first time. High concentrations of α-P₄S₄Se, made by a new route, allowed observation of ⁷⁷Se satellites in its ³¹P NMR spectrum and hence the assignment of ³¹P chemical shifts. Polymeric species were more stable than these monomers, leading to low yields in both reactions. α- and β-isomers of P₄S₃I₂ reacted with diethyl malonate. While β-P₄S₃I₂ gave traces of β-P₄S₃(CR₂)(R = C₂H₅CO₂) and of β-P₄S₃(CHR₂)_exo(CHR₂)_endo, along with insoluble products, α-P₄S₃I₂ yielded α-P₄S₃(CR₂), which could be isolated. P₄S₂(CR₂), a new skeleton similar to that of P₄S₃, was formed on storage of CS₂ solutions of a-P₄S₃(CR₂) for two days. The ³¹P NMR data of the molecules are given.