Topological Gysin Coherence for Algebraic Characteristic Classes of Singular Spaces

Brasselet, the second author and Yokura introduced Hodge-theoretic Hirzebruch-type characteristic classes $IT_{1, \ast}$, and conjectured that they are equal to the Goresky-MacPherson $L$-classes for pure-dimensional compact complex algebraic varieties. In this paper, we show that the framework of Gysin coherent characteristic classes of singular complex algebraic varieties developed by the first and third author in previous work applies to the characteristic classes $IT_{1, \ast}$. In doing so, we prove the ambient version of the above conjecture for a certain class of subvarieties in a Grassmannian, including all Schubert subvarieties. Since the homology of Schubert subvarieties injects into the homology of the ambient Grassmannian, this implies the conjecture for all Schubert varieties in a Grassmannian. We also study other algebraic characteristic classes such as Chern classes and Todd classes (or their variants for the intersection cohomology sheaves) within the framework of Gysin coherent characteristic classes

7,7-Dimethyl-4a-(3-methyl-2-buten­yl)-2-oxo-4a,5,6,7-tetra­hydro-2H-chromen-4-yl benzoate

An intra­molecular Claisen-like cyclization of ethyl 2-acet­oxy-4,4-dimethyl-1-(3-methyl­but-2-en­yl)cyclo­hex-2-enecarboxylate followed by dialkyl­ation yielded the bicyclic title compound, C23H26O4. In both of the fused six-membered rings exist fragments of four atoms which are planar, whereas the remaining two atoms deviate by up to 0.682 (3) Å on one side of the plane of the ring containing an O atom and by up to 0.415 (3) Å on opposite sides of the other ring. The dihedral anglebetween the planar fragments of the six-membered rings is 41.76 (10)

(3R,4R,5S)-4-Hydr­oxy-3-methyl-5-[(2S,3R)-3-methyl­pent-4-en-2-yl]-4,5-dihydro­furan-2(3H)-one

The relative configuration of the title compound, C11H18O3, which was synthesized using a catalytic asymmetric Gosteli–Claisen rearrangement, a diastereoselective reduction with K-Selectride and an Evans aldol addition, was corroborated by single-crystal X-ray diffraction analysis. The five-membered ring has an envelope conformation with a dihedral angle of 29.46 (16)° between the coplanar part and the flap (the hydr­oxy-bearing ring C atom). In the crystal, mol­ecules are connected via bifurcated O—H⋯(O,O) hydrogen bonds, generating [010] chains

(±)-syn-Isopropyl 4-(1,1,1,3,3,3-hexa­fluoro­propan-2-yl­oxy)-1-hydr­oxy-3-methyl-2-(prop-1-yn­yl)cyclo­pent-2-ene­carboxyl­ate

The title compound, C16H18F6O4, was obtained through an unprecedented one-pot reaction sequence involving a Gosteli–Claisen rearrangement and a cyclo­isomerization. The constitution and relative configuration were determined by single-crystal X-ray diffraction analysis. In the crystal, mol­ecules are connected via O—H ⋯ O hydrogen bonds

(2SR,3SR)-Isopropyl 3-{[dimeth­yl(phenyl)­sil­yl]meth­yl}-2-hy­droxy-2-vinyl­pent-4-enoate

The relative configuration of the title compound, C19H28O3Si, which was synthesized using a dienolate-[2,3]-Wittig rearrangement, was corroborated by single-crystal X-ray diffraction analysis. The Si—C bond distances are in the range 1.858 (2)–1.880 (2) Å and an intra­molecular O—H⋯O hydrogen bond helps to stabilize the mol­ecular conformation

A method to reconstruct flood scenarios using field interviews and hydrodynamic modelling: application to the 2017 Suleja and Tafa, Nigeria flood

Abstract The scarcity of model input and calibration data has limited efforts in reconstructing scenarios of past floods in many regions globally. Recently, the number of studies that use distributed post-flood observation data collected throughout flood-affected communities (e.g. face-to-face interviews) are increasing. However, a systematic method that applies such data for hydrodynamic modelling of past floods in locations without hydrological is lacking. In this study, we developed a method for reconstructing plausible scenarios of past flood events in data-scarce regions by applying flood observation data collected through field interviews to a hydrodynamic model (CAESAR-Lisflood). We tested the method using 300 spatially distributed flood depths and duration data collected using questionnaires on five river reaches after the 2017 flood event in Suleja and Tafa region, Nigeria. A stepwise process that aims to minimize the error between modelled and observed flood depth and duration at the locations of interviewed households was implemented. Results from the reconstructed flood depth scenario produced an error of ± 0.61 m for all observed and modelled locations and lie in the range of error produced by studies using comparable hydrodynamic models. The study demonstrates the potential of utilizing interview data for hydrodynamic modelling applications in data-scarce regions to support regional flood risk assessment. Furthermore, the method can provide flow depths and durations at houses without observations, which is useful input data for physical vulnerability assessment to complement disaster risk reduction efforts

(3R,4S,5S)-4-Hydr­oxy-3-methyl-5-[(2S,3R)-3-methyl­pent-4-en-2-yl]tetra­hydro­furan-2-one

The title compound, C11H18O3, was synthesized to prove the relative configuration of the corresponding acyclic C1—C8 stereopentade. It crystallizes with two mol­ecules in the asymmetric unit, which show only slight differences. The mol­ecules are linked via O—H⋯O hydrogen bonds, resulting in two crystallographically independent chains of mol­ecules propagating in the a-axis direction. The absolute configuration was known from the synthesis

{2,2-Bis[(4S)-4-tert-butyl-4,5-dihydro-1,3-oxazol-2-yl]propane}bis­(N,N-di­methyl­formamide)copper(II) bis­(hexa­fluoridoantimonate)

In the title compound, [Cu(C17H30N2O2)(C3H7NO)2][SbF6]2, which is a potential catalyst in the asymmetric Gosteli–Claisen rearrangement, the Cu atom adopts a distorted cis-CuN2O2 square-planar geometry arising from N,N′-bidentate coordin­ation by the chiral ligand and two O-bonded dimethyl­formamide mol­ecules. Two short C—H⋯O contacts occur within the ligand and two weak inter­molecular C—H⋯F bonds may help to establish the packing

Communication: Synthesis of a Novel Triphenyltin(IV) Derivative of 2- Mercaptonicotinic Acid with Potent Cytotoxicity in vitro

A novel triphenyltin(IV) derivative of 2-mercaptonicotinic acid (H2mna) of formula {[(C6H5)3Sn]2(mna).[(CH3)2CO]} (1) has been synthesized and characterized by elemental analysis and 1H, 13C-NMR, and FT-IR spectroscopic techniques. The crystal structure of complex (1) has been determined by single crystal X-ray diffraction analysis at 173(1) K. Compound (1) contains two triphenyltin moieties linked by a doubly de-protonated 2,mercaptonicotinic acid (H>2mna). It is an example of a pentacoordinated Ph3SnXY system with an axial-equatorial arrangement of the phenyl groups at Sn(1). Compound (1), exhibits potent, in vitro, cytotoxicity against sarcoma cancer cells (mesenchymal tissue) from the Wistar rat, polycyclic aromatic hydrocarbons (PAH, benzo[a]pyrene) carcinogenesis