Fourier series and the conjugate function in the classes ϕ(L)

Обозначим через ? (L) кл асс всех ?-интегрируе мых 2π-периодических функ ций. При ограничении?(L)?L ¹ устанавливаются необходимые и достат очные условия, которым долж на удовлетворять?(t), что бы для каждой функцииf(x)ε ?(L) а) тригонометрически й ряд Фурье сходился в метрике ?, в) (С, а) средние ряда Фур ье сходились в метрик е ? для некоторого α > 0, с) сопряженная функци я \(\tilde f(x)\) также принадлежал а классу?(L).     

Zur Synthese sulfonierter Derivate von 2,3-Dimethylanilin und 3,4-Dimethylanilin

On the Synthesis of Sulfonated Derivatives of 2,3-Dimethylaniline and 3,4-Dimethylaniline Baking the hydrogensulfate salt of 2,3-dimethylaniline ( 1 ) or of 3,4-dimethylaniline ( 2 ) led to 4-amino-2,3-dimethylbenzenesulfonic acid ( 4 ) and 2-amino-4,5-dimethylbenzenesulfonic acid ( 5 ), respectively (Scheme 1). The sulfonic acid 5 was also obtained by treatment of 2 with sulfuric acid or by reaction of 2 with amidosulfuric acid. 3-Amino-4,5-dimethylbenzenesulfonic acid ( 3 ) and 5-Amino-2,3-dimethylbenzenesulfonic acid ( 6 ) were prepared by sulfonation of 1,2-dimethyl-3-nitrobenzene ( 9 ) to 3,4-dimethyl-5-nitrobenzenesulfonic acid ( 11 ) and of 1,2-dimethyl-4-nitrobenzene ( 10 ) to 2,3-dimethyl-5-nitrobenzenesulfonic acid ( 12 ), respectively, with subsequent Béchamp reduction (Scheme 1). Preparations of 2-amino-3,4-dimethylbenzenesulfonic acid ( 7 ) and of 6-amino-2,3-dimethylbenzenesulfonic acid ( 8 ) were achieved by the sulfur dioxide treatment of the diazonium chlorides derived from 3,4-dimethyl-2-nitroaniline ( 24 ) and from 2,3-dimethyl-6-nitroaniline ( 31 ) to 3,4-dimethyl-2-nitrobenzenesulfonyl chloride ( 29 ) and 2,3-dimethyl-6-nitrobenzenesulfonyl chloride ( 32 ), respectively, followed by hydrolysis to 3,4-dimethyl-2-nitrobenzenesulfonic acid ( 30 ) and 2,3-dimethyl-6-nitrobenzenesulfonic acid ( 33 ), and final reduction (Scheme 3). Compound 7 was also synthesized by reaction of 4-chloro-2,3-dimethylaniline ( 23 ) with amidosulfuric acid to 2-amino-5-chloro-3,4-dimethylbenzenesulfonic acid ( 20 ) and subsequent hydrogenolysis (Scheme 2). 4′-Bromo-2′, 3′-dimethyl-acetanilide ( 13 ) and 4′-chloro-2′, 3′-dimethyl-acetanilide ( 14 ) on treatment with oleum yielded 5-acetylamino-2-bromo-3,4-dimethylbenzenesulfonic acid ( 17 ) and 5-acetylamino-2-chloro-3,4-dimethylbenzenesulfonic acid ( 18 ), respectively. Their structures were proven by hydrolysis to 5-amino-2-bromo-3,4-dimethylbenzenesulfonic acid ( 21 ) and 5-amino-2-chloro-3,4-dimethylbenzenesulfonic acid ( 22 ), followed by reductive dehalogenation to 3 .     

Size-related vaporisation and ionisation of laser-induced glass particles in the inductively coupled plasma

Ongoing discussions about the origin of elemental fractionation occurring during LA-ICP-MS analysis show that this problem is still far from being well understood. It is becoming accepted that all three possible sources (ablation, transport, excitation) contribute to elemental fractionation. However, experimental data about the vaporisation size limit of different particles in the ICP, as produced in laser ablation, have not been available until now. This information should allow one to determine the signal contributing mass within the ICP and would further clarify demands on suitable laser ablation systems and gas atmospheres in terms of their particle size distribution.The results presented here show a vaporisation size limit of laser induced particles, which was found at particle sizes between 90 nm and 150 nm using an Elan 6000 ICP-MS. Due to the fact that the ICP-MS response was used as evaluation parameter, vaporisation and ionisation limits are not distinguishable.The upper limit was determined by successively removing the larger particles from the aerosol, which was created by ablation of a NIST 610 glass standard at a wavelength of 266 nm, using a recently developed particle separation device. Various particle fractions were separated from the aerosol entering the ICP. The decrease in signal intensity is not proportional to the decrease in volume, indicating that particles above 150 nm in diameter are not completely ionised in the ICP. Due to the limited removal range of the particle separation device, which cannot remove particles smaller than 150 nm, single hole ablations were used to determine the lower vaporisation limit. This is based on measurements showing that larger particles occur dominantly during the first 100 laser pulses only. After this period, the ratio of ICP-MS counts and total particle volume was found to be constant while most of the particles are smaller than 90 nm, indicating complete vaporisation and ionisation of these particles.To describe the influence of different plasma forward powers on the vaporisation limit, the range 1000–1600 W was studied. Results indicate that optimum vaporisation and ionisation occurs at 1300 W. However, an increase of the particle ionisation limit towards larger particles was not observed within the accuracy of this study using the full range of parameters available for optimisation on commonly used ICP-MS instruments.     

1H-NMR-spektroskopische Analyse von 2-Chlor-1.3.2-dioxarsolan

The¹H-NMR-spectral data of 2-chloro-1.3.2-dioxarsolane are presented and discussed. The protons of the methylene groups form in concentrated solutions by rapide chlorine exchange anAAAA spin system. In dilute solutions the protons form anAABB spin system, which is changed to anAAAA system by addition of chlorine ions.The vicinal H–C–C–H-coupling constants indicate a twist-envelope conformation.

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Mit 1 Abbildung     

Windschiefe Kongruenzflächen konstanten Dralls

In this paper we study the curves of a surface ( _T -lines) which are base curves of ruled surfaces for which the parameter of distribution O has a constant value. Moreover we assume that the ruled surfaces belong to a given congruenceT of surface tangents of . Relations are established between the _T -lines and other curves of (asymptotic lines, lines of curvature, k _T -lines). The _T -lines are used to characterize the pseudospheres and the helicoids. The _T -lines of the surfaces of revolution are determined if the congruenceT consists of the tangents of the circles of latitude.

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Herrn WERNER BURAU zum 70.Geburtstag     

Sweet like chocolate

A new crystalline form of αβ‐d ‐lactose prepared by oven drying a concentrated aqueous solution of d ‐lactose is a lesson in the power of observation and the rigorous analysis of powder samples.     

Uranium,thorium and potassium occurrences in the vicinity of hot springs in the northern neotectonic belt in the Eastern Cape Province,South Africa

Gamma ray measurements were carried out along two parallel lines close to each of the hot springs using a RS 125 spectrometer to find the concentration (ppm) of U, Th, and K at Polile Tshisa, Aliwal North, and Badfontein hot springs. The RS 125 spectrometer is auto-stabilized on the naturally occurring U, Th, and K, and provides concentrations (ppm) of the radioelements. The results show that the concentration of thorium is higher, and is below the world average hazardous threshold of 7.4 ppm. Thorium is related to the occurrence of monazite seen at the scanning electron microscope. Higher ratios of U/K are indicative of an increase of uranium relative to potassium. Binary diagrams (Th–U, K–U, and K–Th) do not show a clear best fit except at Polile Tshisa hot spring where thorium shows a quasi positive correlation to potassium. In general, it can be concluded that the concentrations of these three radioelements are quite low, acceptable for groundwater, and could be hazardous to the health of humans and animals if exposed to long time radiations.     

The Diversity of a Polyclonal FluCell-SELEX Library Outperforms Individual Aptamers as Emerging Diagnostic Tools for the Identification of Carbapenem Resistant Pseudomonas aeruginosa

Textbook procedures require the use of individual aptamers enriched in SELEX libraries which are subsequently chemically synthesized after their biochemical characterization. Here we show that this reduction of the available sequence space of large libraries and thus the diversity of binding molecules reduces the labelling efficiency and fidelity of selected single aptamers towards different strains of the human pathogen Pseudomonas aeruginosa compared to a polyclonal aptamer library enriched by a whole-cell-SELEX involving fluorescent aptamers. The library outperformed single aptamers in reliable and specific targeting of different clinically relevant strains, allowed to inhibit virulence associated cellular functions and identification of bound cell surface targets by aptamer based affinity purification and mass spectrometry. The stunning ease of this FluCell-SELEX and the convincing performance of the P. aeruginosa specific library may pave the way towards generally new and efficient diagnostic techniques based on polyclonal aptamer libraries not only in clinical microbiology.     

Highly oriented crystalline Er:YAG and Er:YAP layers prepared by PLD and annealing

High quality, thick, highly oriented crystalline thin films of Yttrium Aluminum Garnet (Y₃Al₅O₁₂) and Yttrium Aluminum Perovskite (YAlO₃) doped with Erbium were prepared by pulsed laser deposition. Samples were created in vacuum or oxygen environment. Depositions were arranged at room temperature, or at high substrate temperatures ranging from 800 to 1100 °C. Amorphous layers were annealed by laser, or in oven (argon flow, temperatures in range from 1200 to 1400 °C). Fused silica and sapphire (0 0 0 1) were used as substrates. Properties of films were characterized by X-ray diffraction, atomic force microscopy, and by photoluminescence measurement. Size of crystalline grains was in the range 116-773 nm. Thickness of layers was up to 17 μm.