We give a new proof of a recent inequality for bicentric quadrilaterals that is an extension of the Euler-like inequality R ≥ √ 2r. A bicentric quadrilateral ABCD is a convex quadrilateral that has both an incircle and a circumcircle. In [6], Zhang Yun called these “double circle quadrilaterals” and proved that

One new pentacyclic triterpenoid, 3β-carboxylicfilic-4(23)-ene (1), and three known pentacyclic triterpenoids, adian-5-en-3α-ol (2), fernenol (3), and fern-7-en-3β-ol (4) were isolated from the petroleum ether phase of the ethanolic extract of Ainsliaea yunnanensis Franch. Their structures were established by spectroscopic methods including 1-D and 2-D NMR, and MS experiments. Compounds 1, 2, 3...

Based on molecular and morphological data of four specimens Pareas Wagler, 1830 collected from the type locality P. yunnanensis (Vogt, 1922), along with examination yunnanensis, we revalidate this poorly known, secretive species. Furthermore, based lines evidence also describe a new species Xishuangbanna Prefecture, Yunnan Province, China. Morphologically, closely resembles its sister nigriceps...

Six new 9,19-cycloartane triterpenes (1-6) were isolated from the aerial parts of Cimicifuga yunnanensis. The new chemical structures were determined by extensive analyses of 1D and 2D NMR spectroscopy. Compounds 1 and 2 are the first 9,19-cycloartane triterpenes characterized by CH₃-18 shifting from C-13 to C-12 in the Cimicifuga spp. The evaluation of inhibition activity against human HL-60, ...

The genus Cystacanthus was established by Anderson (1867: 457) and placed in tribe Ruellieae Dumortier (1829: 23) when published. In fact, it is closely related to Phlogacanthus Nees von Esenbeck (1832: 76, 99) and differs only in the corolla shape and indumentum. Thus, many authors merged Cystacanthus with Phlogacanthus (Benoist 1935, Imlay 1939, Brummit 1992, Mabberley 2008). But it was still...

In this paper, we study the existence of solution for a class variational inequality in whole $${\mathbb {R}}^N$$ where nonlinearity has critical growth $$N \ge 2.$$ By combining penalization scheme found del Pino and Felmer (Calc Var 4:121–137, 1996) with method due to Bensoussan Lions (Applications des inéquations variationelles en contrôle stochastique. Dunod, Paris, 1978), improve recent re...

Monographis queenslandicus n. sp. is described from Brisbane, Queensland, Australia. The genus Monographis may be divided into two groups based on the arrangement of sensilla on the 6th antennal article. Species with a crescent-shape arrangement are M. kraepelini, M. annandalei, M. baihualingensis, M. demangei and M. mirus; species with a triangular arrangement are M. tamoyensis, M. yunnanensis...