Trigonometric polynomials with many real zeros

This is a contribution to the theory of “incomplete trigonometric polynomials”T _n , but mainly for the case when their zeros are not concentrated at just one point, but are distributed in some intervalI whose length is not too large. We begin with the simple theorem that if ∥T _n ∥ ≤ 1 and ifT _n has ≥θn, 0<θ< 2, zeros at 0, thenT _n (t) must be small on the interval |t|<2 arcsin (θ/2). There are similar but more complicated and more difficult to prove results whenT _n has ≥θn zeros onI. These results have the following application: IfT _n →f a.e., and if ∥T _n >∥_∞<-1, thenf vanishes on a set of the circleT whose measure is controlled by lim sup (N _n /n), whereN _n is the number of zeros ofT _n onT. In turn, this has further applications to series of polynomials, to norms of Lagrange operators, and to Hardy classes.     

Optical waveguide sensors in analytical chemistry: today’s instrumentation, applications and trends for future development

Current concepts for chemical and biochemical sensing based on detection with optical waveguides are reviewed. The goals are to provide a framework for classifying such sensors and to assist a designer in selecting the most suitable detection techniques and waveguide arrangements. Sensor designs are categorized on the basis of the five parameters that completely describe a light wave: its amplitude, wavelength, phase, polarization state and time-dependent waveform. In the fabrication of a successful sensor, the physical or chemical property of the determined species and the particular light wave parameter to detect it should be selected with care since they jointly dictate the sensitivity, stability, selectivity and accuracy of the eventual measurement. The principle of operation, the nature or the detected optical signal, instrumental requirements for practical applications, and associated problems are analyzed for each category of sensors. Two sorts of sensors are considered: those based on direct spectroscopic detection of the analyte, and those in which the analyte is determined indirectly through use of an analyte-sensitive reagent. Key areas of recent study, useful practical applications, and trends in future development of optical waveguide chemical and biochemical sensors are considered.     

Validated ion-exclusion chromatographic method for citrate and acetate in medical fluids

In this paper we describe the development and validation of a solid-phase extraction procedure, followed by ion-exclusion chromatographic determination of citrate and acetate in medical fluids. The medical fluids contained trace levels of non-polar compounds, which were not of interest for the purposes of assay requirements, but due to their strong affinity towards the ion-exclusion chromatography column necessitated a 180-min long runtime to elute. The developed SPE procedure, based on trapping the hydrophobic compounds, on a reversed-phase material, while allowing analytes of interest elute off unretained, shortened the runtime to 35 min. The procedure is simple since it has only two steps, conditioning of the SPE cartridge with acetonitrile and treating the sample. The SPE procedure followed by ion-exclusion chromatographic determination was successfully validated per the International Conference on Harmonization (ICH) guidelines in terms of specificity, accuracy as recovery versus untreated sample, precision, range, linearity of response, ruggedness, stability of treated samples, and robustness. The validation data showed that the method is specific, accurate, precise, rugged, and robust. The validated method has been routinely used in the manufacturing environment.     

Pyrazolines — Derivatives of 2-nitrochalcone

By the reaction of 2-nitrochalcone with hydrazine hydrate, 5-(2-nitrophenyl)-3-phenyl-1H-2-pyrazoline (I) and the hydrazone of 3-(5-(2-nitrophenyl)-3-phenyl-2-pyrazolin-1-yl)-3-(2-nitrophenyl)propiophenol (II) have been prepared. The acylation of both compounds I and II leads to N-acyl derivatives of the first. The acylating ability of formamide and N,N-dimethylformamide was observed in reactions with pyrazoline I. An x-ray structural study was carried out on compound II.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 360–366, March, 1993.     

Structure of the product of the reaction of 6-dehydroeldelidine with sodium in liquid ammonia

Institute of the Chemistry of Plant Substances, Uzbek SSR Academy of Sciences, Tashkent. Abu Ali ibn Sina [Avicenna] Tashkent State Medical Institute, Dushanbe. Translated from Khimiya Prirodnykh Soedinenii, No. 2, pp. 279–281, March–April, 1990.     

Ecdysteroids of a culture of tissues and cells ofAjuga turkestanica

The possibility has been studied of obtaining ecdysteroids — ecdysterone and turkesterone — with the aid of a culture of the tissues and cells of the plantAjuga turkestanica. Conditions have been selected under which the yield of ecdysteroids in the culture of tissues and cells is comparable with amounts of the same substances in the organs of the whole plant.Institute of the Chemistry of Plant Substances, Academy of Sciences of the Uzbek SSR, Tashkent. Translated from Khimiya Prirodnykh Soedinenii, No. 1, pp. 51–52, January–February, 1990.     

Mass spectrometric study of mixed fluorinated rare earth element β-diketonates with triphenylphosphine oxide

A series of new adducts of fluorinated REE -diketonates with triphenylphosphine oxide was synthesized. The paths of their fragmentation under electron impact were investigated. It was shown that in contrast to the complex with 1,1,1,2,2,3,3-heptafluoro-7,7-dimethyloctane-4,6-dione, the complexes of europium with 1-trifluoromethoxy-1,1-difluoro-5,5-dimethylhexane-2,4-dione and 1, 1,1-trifluoro-5,5-dimethylhexane-2,4-dione form dimeric associates in the gaseous phase. The reasons for this difference in the behavior of the complexes and the possible structure of one of the dimers are discussed.Translated from Teoreticheskaya i Eksperimental'naya Khimiya, Vol. 26, No. 2, March–April, 1990.     

The reaction of thiocaprylic acid with methyl thiocyanate

Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 9, pp. 2154–2155, September, 1989.