One-pot, three-component condensation of 2-hydroxybenzaldehyde derivatives, primary amines with alkyl isocyanides to N-alkyl-2-(2-hydroxyphenyl)-2-imino-acetamides

One-pot, three-component condensation of 2-hydroxybenzaldehyde derivatives, primary amines with alkyl isocyanides is reported. N-alkyl-2-(2-hydroxyphenyl)-2-iminoacetamide derivatives are generated presumably via the preliminary formation of N, N′-disubstituted benzo[b]furan-2,3-diamines and subsequent oxidation with molecular oxygen.      

A facile synthesis of chromeno[3,4-c]spiropyrrolidine-oxindoles via 1,3-dipolar cycloadditions

A facile one-pot synthesis of chromene bearing novel spiropyrrolidine-oxindoles has been accomplished by the [3+‏2]-cycloaddition reaction of 3-acetyl-2H-chromen-2-ones with azomethine ylides derived in situ from isatin or N-methyl isatin with sarcosine.     

One-pot synthesis of 1,2-disubstituted pyrrolo[2,3-b]quinoxalines via palladium-catalyzed heteroannulation in water

The reaction of N-alkyl-3-chloroquinoxaline-2-amines with 1-alkynes, catalyzed by Pd-Cu, in the presence of sodium lauryl sulfate as the surfactant in water, leads to the one-pot formation of 1,2-disubstituted pyrrolo[2,3-b]quinoxalines in good-to-high yields.     

Zero divisors and units with small supports in group algebras of torsion-free groups

Kaplansky’s zero divisor conjecture (unit conjecture, respectively) states that for a torsion-free group G and a field 𝔽, the group ring 𝔽[G] has no zero divisors (has no units with supports of size greater than 1). In this paper, we study possible zero divisors and units in 𝔽[G] whose supports have size 3. For any field 𝔽 and all torsion-free groups G, we prove that if αβ = 0 for some non-zero α,β∈𝔽[G] such that |supp(α)| = 3, then |supp(β)|≥10. If 𝔽 = 𝔽₂ is the field with 2 elements, the latter result can be improved so that |supp(β)|≥20. This improves a result in Schweitzer [J. Group Theory, 16 (2013), no. 5, 667–693]. Concerning the unit conjecture, we prove that if αβ = 1 for some α,β∈𝔽[G] such that |supp(α)| = 3, then |supp(β)|≥9. The latter improves a part of a result in Dykema et al. [Exp. Math., 24 (2015), 326–338] to arbitrary fields.     

A Straightforward Method for the Synthesis of Functionalized Trisubstituted Alkenes through Na2S/Al2O3 Catalyzed Knoevenagel Condensation

Na₂S/Al₂O₃ catalyzed the Knoevenagel condensation between an aldehyde and an active methylene compound to yield various trisubstituted alkenes.     

Quasiconvexity and uniqueness of stationary points in the multi-dimensional calculus of variations

Let be a bounded starshaped domain. In this note we consider critical points of the functional

where of class satisfies the natural growth

for some and 0$">, is suitably rank-one convex and in addition is strictly quasiconvex at . We establish uniqueness results under the extra assumption that is stationary at with respect to variations of the domain. These statements should be compared to the uniqueness result of Knops & Stuart (1984) in the smooth case and recent counterexamples to regularity produced by Müller & Sverák (2003).

     

Thermodynamics of the solvent extraction of thorium and europium nitrates by neutral phosphorylated ligands

Solvent extraction of tetravalent thorium and trivalent europium ions from nitrate media into dichloromethane solution of triphenylphosphine oxide (TPPO) has been studied. The extractant was shown to be more efficient for europium than for thorium. A conventional log-log analysis reveals that the extraction of both metal nitrates takes place via the formation of the species with 1 : 2 metal to ligand ratio. Thermodynamic parameters i.e., ΔG°, ΔH° and ΔS° of the extraction process using 1,2-dichloroethane as diluent have been calculated based on the influence of the temperature on extraction equilibria in the range 293-313 K. While the extraction of europium is controlled by enthalpy changes, the extraction of thorium is an endothermic process and is driven by entropy changes. A comparison of these data with those obtained for the extraction of europium and thorium nitrates by two other related phosphorylated ligands, tri-n-octylphosphine oxide (TOPO) and diphenyl-N,N-dimethylcarbamoylmethylphosphine oxide (DФDMCMPO), indicates that DФDMCMPO coordinates presumably as a chelating ligand. This revised version was published online in July 2006 with corrections to the Cover Date.     

Ultraviolet lasing in cholesteric liquid crystals

We report the observation of stimulated emission and mirrorless lasing in pure cholesteric liquid crystals. The lasing action is attributed to the combination of the fluorescence and the distributed feedback that are due to the inherent periodic structure of the liquid crystal. If the reflection band matches the intrinsic emission of the cholesteric liquid crystal, the crystal becomes a natural laser material, which will self-lase, without any optical elements or the addition of dyes, under picosecond excitation at 355 nm. Samples have been made to lase at different wavelengths in the near UV by shifting of the edge of the reflection band in the range of 385-405 nm. Typical linewidths observed are of the order of 0.5 nm.     

Synthesis of 5-amino-1,3,4-thiadiazoles containing dithiocarbamate groups

Synthesis of alkyl ((5-[alkylamino]-1,3,4-thiadiazol-2-yl)methyl)carbamodithioates via the reaction of glycine-based dithiocarbamates with thiosemicarbazides in the presence of POCl₃ in ethanol is disclosed. The main advantages of this method including the use of ethanol as solvent, no need to column chromatography for purification and high to excellent yields of products are noteworthy.