An algebraic proof of Bogomolov-Tian-Todorov theorem

We give a completely algebraic proof of the Bogomolov-Tian-Todorov theorem. More precisely, we shall prove that if X is a smooth projective variety with trivial canonical bundle defined over an algebraically closed field of characteristic 0, then the L-infinity algebra governing infinitesimal deformations of X is quasi-isomorphic to an abelian differential graded Lie algebra.Comment: 20 pages, amspro

Origin of Nepheline-normative High-K Ankaramites and the Evolution of Eastern Srednogorie Arc in SE Europe

Eastern Srednogorie is part of the Apuseni-Banat-Timok-Srednogorie magmatic belt in SE Europe, the main arc related to the Late Cretaceous subduction and closure of the Tethys Ocean between Africa and Europe. Extrusive and shallow intrusive magmatism in the Eastern Srednogorie is abundant and extremely diverse in composition, covering a wide range from ultramafic volcanic rocks to granites; this provides a unique opportunity to study processes of primitive melt formation and magma evolution in an arc environment. In contrast to other parts of the belt, relatively mafic lavas predominate here. Three magmatic regions are distinguished within Eastern Srednogorie from south to north: Strandzha, Yambol-Burgas and East Balkan. Systematic differences exist between these regions, notably the increased alkalinity of samples from the Yambol-Burgas region in the central part. All rocks display a clear subduction-like signature in their trace-element patterns, particularly the enrichment in large ion lithophile elements and light rare earth elements relative to high field strength elements. A distinct primitive nepheline-normative ankaramite magma type is recognized among the mafic volcanic rocks from the Yambol-Burgas region and melt inclusions entrapped in olivine and clinopyroxene from a cumulitic rock. Lower crustal clinopyroxene and amphibole cumulates carried to the surface as xenoliths in a mafic dike represent a possible source for the ankaramite. Modeling of the melting process suggests that low degrees of batch melting of a clinopyroxene-rich, amphibole-bearing source similar to the cumulate xenoliths at 1 GPa, temperatures of 1240-1300°C, oxidized conditions and a water content of 0·2 wt % reproduce accurately most of the observed major- and trace-element characteristics of the studied ankaramites. The elevated Rb, K2O, Th, Ba content and higher Pb isotope ratios of the predicted liquids compared with the ankaramites are explained by mixing of the ankaramite magma with lherzolite partial melts derived from the subduction-modified mantle wedge. Underplating of such mantle-derived magmas at the crust-mantle boundary in an extensional environment as a response to slab roll-back provides also the necessary heat to melt lower crustal cumulates. Fractional crystallization of mainly clinopyroxene plus olivine and Fe-Ti oxides in a deep (equivalent to 8 kbar pressure) magma chamber produced most of the observed range of shoshonitic basalts and basaltic andesites in Eastern Srednogorie. The more evolved intermediate varieties were probably formed by mixing and crystallization at lower temperatures in lower pressure magma chambers. Whole-rock Sr and Pb isotope compositions indicate variable degrees of admixing of basement rocks to generate the intermediate to acid Late Cretaceous magmas, but assimilation was minimal for magmas with less than 53 wt % SiO2. The proposed model for the evolution of the magmatism in Eastern Srednogorie involves initial formation of the calc-alkaline and high-K arc magmatism in the Strandzha and East Balkan regions, followed by roll-back induced intra-arc rifting and the formation of high-K, shoshonitic and ultra-high-K magmatism, including primitive ankaramites in the Yambol-Burgas regio

Cyclooxygenase-2 inhibitors. 1,5-diarylpyrrol-3-acetic esters with enhanced inhibitory activity toward cyclooxygenase-2 and improved cyclooxygenase-2/cyclooxygenase-1 selectivity.

he important role of cyclooxygenase-2 (COX-2) in the pathogenesis of inflammation and side effect limitations of current COX-2 inhibitor drugs illustrates a need for the design of new compounds based on alternative structural templates. We previously reported a set of substituted 1,5-diarylpyrrole derivatives, along with their inhibitory activity toward COX enzymes. Several compounds proved to be highly selective COX-2 inhibitors and their affinity data were rationalized through docking simulations. In this paper, we describe the synthesis of new 1,5-diarylpyrrole derivatives that were assayed for their in vitro inhibitory effects toward COX isozymes. Among them, the ethyl-2-methyl-5-[4-(methylsulfonyl)phenyl]-1-[3-fluorophenyl]-1H-pyrrol-3- acetate (1d), which was the most potent and COX-2 selective compound, also showed a very interesting in vivo anti-inflammatory and analgesic activity, laying the foundations for developing new lead compounds that could be effective agents in the armamentarium for the management of inflammation and pain