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.     

Analysis of deprenyl metabolites in some body compartments of rats using GC-MSD

Summary Deprenyl metabolites were analyzed in various organs of rats after chronic oral treatment. The investigation was carried out by gas chromatography combined with MSD after derivatization of the metabolites. When (−)-deprenyl (selegiline) was administered to rats higher ratios of methamphetamine to amphetamine were found in the kidney, and the heart at 1 and 5 h after treatment, than after (+)-deprenyl administration. Both deprenyl and its demethylated metabolite were also detected; however, their level was generally lower than that of either methamphetamine or amphetamine. Coadministration of verapamil with selegiline did not essentially alter the major metabolic pathway of deprenyl metabolism.     

Occurrence and behavior of system peaks in RP HPLC with solely aqueous mobile phases

System peaks are important but often also disturbing phenomena occurring in separation systems. Behavior of system peaks was studied in reversed phase high performance liquid chromatography (RP HPLC) systems consisting of an RP Amide C16 column and aqueous solutions of organic acids with alkaline metal hydroxides as mobile phases. Binary mobile phases, composed of benzoic acid and lithium hydroxide (LiOH) or cesium hydroxide (CsOH), yielded two system peaks. The first peak was stationary and the second one moved with dilution of the mobile phase or with changes of the alkaline metal hydroxide concentration. The latter changes affected dissociation of the benzoic acid present in the mobile phase and thereby its retention. The presumption that the first system peak is not influenced by the type of alkaline metal cation and that it is related to the non‐adsorbed component of the mobile phase was confirmed by a cyclic procedure. Three‐component mobile phases composed of benzoic acid, tropic acid, and a hydroxide gave rise to three system peaks as expected. The first peak was again stationary and the two others shifted depending on the concentration variation of both acids. Resonance causing a zigzag peak, well described in capillary zone electrophoresis (CZE), was observed if 1‐pentanol was injected into a chromatographic system with one‐component mobile phase.     

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).