On the JWKB solution of the uniformly lengthening pendulum via change of independent variable in the Bessel’s equation

Common recipe for the lengthening pendulum (LP) involves some change of variables to give a relationship with the Bessel’s equation. In this work, conventional semiclassical JWKB solution (named after Jeffreys, Wentzel, Kramers and Brillouin) of the LP is being obtained by first transforming the related Bessel’s equation into the normal form ‘via the suggested change of independent variable’. JWKB approximation of the first-order Bessel functions (ν=1) of both types along with their zeros are being obtained analytically with a very good accuracy as a result of the appropriately chosen associated initial values and they are extended to the neighbouring orders (ν=0 and 2) by the recursion relations. The required initial values are also being studied and a quantization rule regarding the experimental LP parameters is being determined. Although common numerical methods given in the literature require adiabatic LP systems where the lengthening rate is slow, JWKB solution presented here can safely be used for higher lengthening rates and a criterion for its validity is determined by the JWKB applicability criterion given in the literature. As a result, the semiclassical JWKB method which is normally used for the quantum mechanical and optical waveguide systems is applied to the classical LP system successfully.     

Diazo Strategy for the Synthesis of Pyridazines: Pivotal Impact of the Configuration of the Diazo Precursor on the Process

Phosphazenes of vinyldiazocarbonyl compounds having cis stereochemistry of the functional groups on the vinyl bond readily produce pyridazines by a diaza‐Wittig process, whereas their counterparts with trans configuration remain intact under similar reaction conditions. Upon UV irradiation trans‐phosphazenes furnish pyridazines through a tandem trans‐to‐cis isomerization followed by intramolecular cyclization. At elevated temperatures trans‐(triphenyl)phosphazenes dissociate to give the initial vinyldiazo compounds, which produce pyrazoles in high yields. The first theoretical study on the mechanism of the diaza‐Wittig process by DFT calculations at the M06‐2X/6‐31G(d) level of theory suggest that for the cis‐phosphazenes a rapid tandem [2+2] cycloaddition/cycloelimination process with low energy barriers is preferred over trans isomers.     

A convenient synthesis of functionalized 1H-pyrimidine-2-thiones

The furan-2,3-dione 1 and the thiosemicarbazones 2 combine with loss of carbon dioxide and water yielding the 1-methylenaminopyrimidine-2-thione derivatives 3 in moderate yields (30–60%). Their molecular skeleton is confirmed with aid of an X-ray structure determination of 3c . Hydrolysis of 3 leads to the 1-aminopyrimidine-2-thione 5 .     

Synthesis of some new imidazo[1,2-a]pyrimidin-5(1H)-ones as potential antineoplastic agents

Some substituted imidazo[1,2-a]pyrimidin-5(1H)-ones have been synthesized via the reaction of 2-aminoimidazole sulfate with some β-keto esters, diethyl ethoxymethylenemalonate and ethyl ethoxymethylenecyanoacetate. Several compounds were screened for their in vitro antineoplastic and anti-HIV activity but were inactive.     

Potenzen und gruppentheoretische Eigenschaften

Ohne Zusammenfassung     

Nebenprodukt bei der Herstellung von 4-Hydroxy-3-phenylcumarin

The synthesis of 4-hydroxy-3-phenylcoumarin (3a) from phenol (1) and diethylphenylmalonate (2) yields the isocoumarin derivative4 as a by-product (1–2%). If3a is heated with2 or diphenylcarbonate (6) at 300°C the coumarino-isocoumarin4 is formed in 83% and 85% yield, respectively.     

Synthesis of 4-hydroxy-2(1H)-pyridones from azomethines and substituted dialkylmalonates

Summary The reaction of azomethines4 with substituted dialkyl malonates5 leads to the formation of 3-substituted 4-hydroxy-2(1H)-pyridones6 in moderate yields. The azomethines4 are preparedvia arylaminopropionitriles3 or in the conventional way by acid catalyzed condensation of ketones1 with anilines2. Chlorination of pyridones6 with sulfuryl chloride leads to compounds8–10.

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Synthese von 4-Hydroxy-2(1H)-pyridonen aus Azomethinen und substituierten Dialkylmalonaten

Zusammenfassung Umsetzung der Azomethine4 mit den substituierten Dialkylmalonaten5 ergibt die in 3-Stellung substituierten 4-Hydroxy-2(1H)-pyridone6 in mäßigen Ausbeuten. Die Azomethine4 werden entweder über dieStrecker-Verbindungen3 oder konventionell über durch Säuren katalysierte Kondensation der Ketone1 mit den Aminen2 hergestellt. Chlorierung der Pyridone6 mit Sulfurylchlorid führt zu den Verbindungen8–10.

     

Preparation of thioamide building blocks via microwave-promoted three-component kindler reactions

A microwave-enhanced variation of the Kindler thioamide synthesis is introduced. Taking advantage of the sealed vessel capabilities of a dedicated single-mode microwave reacto,r a diverse selection of 13 aldehyde and 12 amine precursors was utilized in the construction of a representative 34-member library of substituted thioamides. The three-component condensations of aldehydes, amines, and elemental sulfur were carried out using 1-methyl-2-pyrrolidone (NMP) as solvent employing microwave flash heating at 110-180 degrees C for 2-20 min. A simple workup protocol allows the isolation of synthetically valuable primary, secondary, and tertiary thioamide building blocks in 83% average yield and >90% purity.     

Tunable carbon-carbon and carbon-sulfur cross-coupling of boronic acids with 3,4-dihydropyrimidine-2-thiones

Direct microwave-assisted Pd(0)-catalyzed/Cu(I)-mediated carbon-carbon cross-coupling of 3,4-dihydropyrimidine-2-thiones and boronic acids under Liebeskind-Srogl conditions leads to 2-aryl-1,4-dihydropyrimidines in moderate to high yield. In contrast, Cu(II)-mediated reaction of the same substrates leads to carbon-sulfur cross-coupling. [reaction: see text]