Nonnegative Trigonometric Polynomials

An extremal problem for the coefficients of sine polynomials, which are nonnegative in [0,π] , posed and discussed by Rogosinski and Szegő is under consideration. An analog of the Fejér—Riesz representation of nonnegative general trigonometric and cosine polynomials is proved for nonnegative sine polynomials. Various extremal sine polynomials for the problem of Rogosinski and Szegő are obtained explicitly. Associated cosine polynomials k _n (θ) are constructed in such a way that { k _n (θ) } are summability kernels. Thus, the L _p , pointwise and almost everywhere convergence of the corresponding convolutions, is established. April 26, 2000. Date revised: December 28, 2000. Date accepted: February 8, 2001.     

Untersuchung der Phasengleichgewichtein den Systemen Cs2SeO4-CoSeO4-H2Ound Cs2SeO4-NiSeO4-H2O bei 25.0°C

Zusammenfassung.  Die Phasengleichgewichte in den Systemen Cs₂SeO₄-CoSeO₄-H₂O und Cs₂SeO₄-NiSeO₄-H₂O bei 25.0°C wurden untersucht. Dabei wurde die Entstehung zweier kongruent l?slicher Doppelsalze (Cs₂Co(SeO₄)₂ċ6H₂O und Cs₂Ni(SeO₄)₂ċ6H₂O) festgestellt, die mittels chemischer, thermogravimetrischer und r?ntgenographischer Methoden identifiziert wurden.

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Investigation of the Phase Equilibria in the Systems Cs₂SeO₄-CoSeO₄-H₂Oand Cs₂SeO₄-NiSeO₄-H₂O at 25.0°C

Summary.  Phase equilibria in the systems Cs₂SeO₄-CoSeO₄-H₂O and Cs₂SeO₄-NiSeO₄-H₂O at 25.0°C were studied. Two congruently soluble double salts (Cs₂Co(SeO₄)₂ċ6H₂O and Cs₂Ni(SeO₄)₂ċ 6H₂O) were found to be formed which were identified by chemical, thermogravimetrical, and X-ray phase analysis.

Received October 14, 1999. Accepted (revised) February 1, 2000     

Spin correlation in Pr IV and Tm IV free ions

The coefficients \(c_{k}\) (k = 2, 4, 6) that pertain to spin-correlated matrix elements of the tensor operator \({{\varvec{U}}}^{{\varvec{(k)}}}\) have been evaluated by means of the differences \({{\varvec{U}}}^{{\varvec{(k)}}}\) (intermediate) \(-\) \({{\varvec{U}}}^{{\varvec{(k)}}}\) (LS) and the reduced matrix elements of the operator \({{\varvec{V}}}^{{\varvec{(1k)}}}\) . Only spin-allowed transitions have been considered from each ground level to the excited energy levels within the \(4\hbox {f}^{2}\) and \(4\hbox {f}^{12}\) configurations of the free ions Pr (3+) and Tm (3+), respectively. The values of the coefficients \(c_{k}\) thus found correspond in most cases by sign and order of magnitude to those determined in other sources as corrections to lanthanide (3+) crystal-field parameters.     

Adverse Effects of Environmental Noise on Acoustic Voice Quality Measurements

An accurate analysis of voice quality is imperative when using acoustic measurements to diagnose vocal pathologies. It is known that noise has a significant effect on the reliability and validity of acoustic voice measurements, but the precise relationship has not been established. The purpose of this study was to investigate the influence of noise on the accuracy, reliability, and validity of acoustic voice quality measurements while balancing for gender, age, intersubject and intrasubject variability, microphones, computer hardware, analysis software, and type of noise. Level of noise was precisely controlled. The specific focus of interest was to determine the critical levels of noise that can invalidate voice quality measurements and to generate practical recommendations. Results suggest that the recommended, acceptable, and unacceptable levels of noise in the acoustic environment are above 42 dB, above 30 dB, and below 30 dB signal-to-noise ratio, respectively.     

Mechanochemical effects in U3O8

The effect of the mechanical treatment of U₃O₈ in a planetary ball mill in air or as a suspension in benzene solution of thyolilthreefluoroacetone (TTA) on the nature of the oxide and on the leaching of U and ²³⁴Th into diluted aqueous solutions of HCl, Na₂EDTA and NaCl has been studied. Transformation of U₃O₈ to UO₂, is much stronger expressed when the mechanoactivation is performed in air is established. The leaching behavior of U and Th depends significantly on the activation mode and on the leaching reagent nature. The role of mechanochemically enhanced UO₂-ThO₂ solid solution formation for the observed effects is discussed.     

Structural analysis and antitumor potential of novel 5,6-disubstituted-17a-homo-17-oxa-androstane derivatives

Starting from 3β-acetoxy-17a-homo-17-oxa-androst-5-en-16-one (1) and in the reaction with N-bromoacetamide (NBA) and perchloric acid, the 5α-bromo-6β-hydroxy (2), 5β,6β-epoxy (3) and 5α,6β-dibromo (4) derivatives were obtained. The structure of compounds 2–4, particularly stereochemistry at C5 and C6, is established by detailed NMR and X-ray analysis. The in vitro antiproliferative activity of newly synthesized compounds 2–4 against six human tumor cell lines was evaluated. All three compounds showed a significant toxicity toward hormone-independent breast adenocarcinoma MDA-MB-231 and cervical carcinoma cells HeLa, while dibromo derivative 4 was active toward five human cancer cell lines. These new 5,6-disubstituted-D-homolactone steroidal compounds have also displayed selectivity toward cancerous cell lines against inactivity found for noncancerous control cell line. This selectivity was not found for control compound, well-known chemotherapy drug cisplatin.