‎‎we exhibit an explicit construction for the second cohomology group‎ ‎$h^2(l‎, ‎a)$ for a lie ring $l$ and a trivial $l$-module $a$‎. ‎we show how the elements of $h^2(l‎, ‎a)$ correspond one-to-one to the‎ ‎equivalence classes of central extensions of $l$ by $a$‎, ‎where $a$‎ ‎now is considered as an abelian lie ring‎. ‎for a finite lie‎ ‎ring $l$ we also show that $h^2(l‎, ‎c^*) cong m(l)$‎...

Two new stilbenoids, 9-(4'-hydroxy-3'-methoxyphenyl)-10-(hydroxymethyl)-11-methoxy-5,6,9,10-tetrahydrophenanthro[2,3-b]furan-3-ol and 2-(4''-hydroxybenzyl)-3-(3'-hydroxyphenethyl)-5-methoxy-cyclohexa-2,5-diene-1,4-dione, together with the three known stilbenoids were isolated from the tubers of Pleione bulbocodioides (Franch.) Rolfe. Their structures were elucidated by spectroscopic methods.

Donor-substituted 1,1,2,4,4-pentacyanobuta-1,3-dienes and a cyclohexa-2,5-diene-1,4-diylidene-expanded derivative were prepared by a [2 + 2] cycloaddition of tetracyanoethene (TCNE) or 7,7,8,8-tetracyanoquinodimethane (TCNQ) to anilino-substituted cyanoalkynes, followed by retro-electrocyclisation; they feature intense bathochromically-shifted intramolecular charge-transfer bands and undergo th...

The cationic Rh-SEGPHOS complex catalyzed an intermolecular [2 + 2 + 2] cycloaddition of enynes, possessing an ortho-substituted aryl group on their alkyne terminus, with acetylenedicarboxylates. Bicyclic cyclohexa-1,3-dienes with both central and axial chiralities were obtained in extremely highly diastereo- and enantioselective manner.

We present the first use of digital microfluidic techniques to perform on-chip solid phase extraction (SPE). The material used for SPE was a porous polymer monolith with 12-carbon functionality (C12 PPM) which was photopolymerized on-chip and used to desalt a peptide sample prior to nano-electrospray ionization mass spectrometric analysis (nano-ESI-MS). We anticipate this technique may be usefu...

we introduce the notion ofstrongly $alpha$-reversible rings which is a strong version of$alpha$-reversible rings, and investigate its properties. we firstgive an example to show that strongly reversible rings need not bestrongly $alpha$-reversible. we next argue about the strong$alpha$-reversibility of some kinds of extensions. a number ofproperties of this version are established. it is shown ...

in this paper, we introduce a class of rings which is a generalization of reversible rings. let r be a ring with identity. a ring r is called central reversible if for any a,b ∈ r, ab=0 implies ba belongs to the center of r. since every reversible ring is central reversible, we study sufficient conditions for central reversible rings to be reversible. we prove that some results of reversible ri...

in this paper we focus on a special class of commutative local‎ ‎rings called spap-rings and study the relationship between this‎ ‎class and other classes of rings‎. ‎we characterize the structure of‎ ‎modules and especially‎, ‎the prime submodules of free modules over‎ ‎an spap-ring and derive some basic properties‎. ‎then we answer the‎ ‎question of lam and reyes about strongly oka ideals fam...

The critical temperature in a superconducting ring changes periodically with the magnetic flux threading it, giving rise to the well-known Little-Parks magnetoresistance oscillations. Periodic changes of the critical current in a superconducting quantum interference device (SQUID), consisting of two Josephson junctions in a ring, lead to a different type of magnetoresistance oscillations utiliz...