Synthesis of 3‐(2‐Aryloxazolidin‐3‐yl)tropanes.

Abstract

Pyridine derivatives with bridgesPyridine derivatives with bridges R 0460 Synthesis of 3-(2-Aryloxazolidin-3-yl)tropanes. -The title compounds (VI) are obtained by acid-catalyzed reaction of 2-hydroxyethylaminotropane (IV) with aromatic aldehydes (V). A spiro-nortropane (IX) containing an oxazolidine moiety is prepared by reaction of urethane (VII) with benzylaminoethanol. -(KOSTOCHKA, L. M.; LEZINA, V. P.; KOSTOCHKA, M. L.; Chem. Heterocycl.

Relaxed two-coloring of cubic graphs

“…In [5] the determination of α(0, 2) was raised. The wheel graph shows that α(0, 2) 4, while Kostochka [7] proved a lower bound of 3. The greedy coloring implies that α(k, 0) = k, for any k. We would be very much interested in the value of α(1, 1).…”

Synthesis, characterization, and antihyperglycemic activity of novel oxazolidine derivatives

“…It is now clear that aggressive control of hyperglycemia in patients with diabetes can prevent or delay the onset of complications such as retinopathy, nephropathy, and neuropathy (Kumar et al, 2007). We have found that oxazolidines and related oxazolidine are classes of heterocycles that are of considerable interest because of the diverse range of their biological properties, such as antihypertensive (Caroon et al, 1983), antidepressant (Pinder, 1985), antithyroid (Gardrat and Latxague, 1990), leishmanicidal (Sonika and Satyavan, 1990), antidiabetic (Heong et al, 2007), anti-HIV (Sharma et al, 2003), antiarrhythmic (Kostochka et al, 2003), antitumor (Vara Prasad et al, 2006), and anticonvulsant and antimicrobial (Kim et al, 2008). This background information led to the design of 3-benzyl-2-(4'-substituted phenyl)-4(5H)-(4''-nitrophenyl amino)-1, 3-oxazolidine derivatives (6a-e).…”

A Note on Large Rainbow Matchings in Edge-coloured Graphs

“…Kostochka, Pfender and Yancey [6] considered a similar problem with δ c (G) instead of properly edge-coloured graphs. They showed that if G is such that δ c (G) ≥ k and n > 17 4 k 2 , then G contains a rainbow matching of size k. Kostochka [5] then asked: can n be improved to a linear bound in k? In this paper, we show that n ≥ 4k − 4 is sufficient for k ≥ 4.…”