The many faces of a character

We prove an identity between three infinite families of polynomials which are defined in terms of bosonic, fermionic, and one-dimensional configuration sums. In the limit where the polynomials become infinite series, they give different-looking expressions for the characters of the two integrable representations of the affine su(2) algebra at level one. We conjecture yet another fermionic sum representation for the polynomials which is constructed directly from the Bethe-ansatz solution of the Heisenberg spin chain.     

Zero cycles on conic fibrations and a conjecture of Bloch

Let X be a smooth projective surface over a number field k. Let (CH₀(X)) denote the Chow group of zero-cyles modulo rational equivalence on X. Let CH₀(X) be the subgroup of CH ₀(X) consisting of classes which vanish when going over to an arbitrary completion of k. Bloch put forward a conjecture asserting that this group is isomorphic to the Tate-Shafarevich group of a certain Galois module atttached to X. In this paper, we disprove this general conjecture. We produce a conic bundle X over an elliptic curve, for which the group (CH₀(X) is not zero, but the Galois-theoretic Tate-Shafarevich group vanishes.     

Topological hochschild homology of extensions of ?/p? by polynomials, and of ?[x]/(xn) and ?[x]/(xn?1)

Topological Hochschild homology is calculated for the rings /p[x]/(f(x)) (where p is prime and f(x) /p[x] any polynomial), [x]/(x ⁿ) and [x]/(x ⁿ–1). A spectral sequence argument is used for calculating the homology of the topological Hochschild homology spectrum, from which its stable homotopy structure can be read off since the spectrum is known for a priori reasons to be a restricted product of Eilenberg-MacLane spectra.     

Effect of aryl ligands on the chemical hardness of arylmercury cations

¹⁹F NMR spectroscopy was used to study the exchange reactions involving 4-fluorothiophenoxides, 4-nitrophenoxides, chlorides, and acetates of arylmercury and triphenylphosphinegold. The analysis of the data on equilibrium constants allows one to obtain information on the comparative chemical hardness of ArHg⁺ and Ph₃PAu⁺ cations. The increase in the electron-donating ability of aryl ligands enhances the chemical hardness of ArHg⁺ cations, their influence being best described by ⁰ constants of substituted phenyl groups.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 1255–1260, May, 1996.     

Order series of labelled posets

Order series of labelled posets are multi-analogues of the more familiar order polynomials; the corresponding multi-analogues of the related representation polynomials are calledE-series. These series can be used to describe the effect of composition of labelled posets on their order polynomials, whence their interest for us. We give a reciprocity theorem forE-series, and show that for an unlabelled poset the form of theE-series depends only upon the comparability graph of the poset. We also prove that theE-series of any labelled poset is a rational power series (in many indeterminates) and give an algorithm for computing it which runs in polynomial time when the poset is strictly labelled and of bounded width. Finally, we give an explicit product formula for theE-series of strictly labelled interval posets.This research was supported by the Natural Sciences and Engineering Research Council of Canada under operating grant #0105392.     

Aryl-bis(triorganylphosphine)nickel phenoxides

Compounds of general formulatrans-ArNi(PR₃)₂OAr' (R = Et, cyclohexyl; Ar = 2-MeC₆H₄, 2-FC₆H₄; Ar' = 4-FC₆H₄, 4-NO₂C₆H₄) were synthesized by the reaction of Ar'OK with cationic nickel complexes generated by treatment of ArNi(PR₃)₂Cl with TlBF₄. Syntheses of 4-fluorophenoxide complexes, ArNi(PR₃)₂OC₆H₄F-4, additionally give some quantities oftrans-[ArNi(PR₃)₂OC₆H₄F-4][HOC₆H₄F-4] adducts. Exchange reactions MeC₆H₄Ni(PEt₃)₂OC₆H₄F-4 + XC₆H₄OH 2-MeC₆H₄Ni(PEt₃)₂OC₆H₄X + 4-FC₆H₄OH were studied in THF. The equilibrium is shifted to the right as the acidity of ArOH increases. A linear relationship between lgK _eq and pK _a of XC₆H₄OH in DMSO was found. A conclusion concerning the strong polarization of the Ni-O bond was made on the basis of an analysis of the chemical shifts of fluorine atoms in 2-MeC₆H₄Ni(PEt₃)₂OC₆H₄F-4.Translated fromIvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2266–2271, November, 1995.     

19F and 1H NMR spectra of halocarbons

19F NMR chemical shifts and coupling constants are reported for 215 compounds. For 77 of these compounds, 1H NMR spectral data are also given. Long-range couplings, including 8J(F,F) and 5J(F,H), are reported. The complexity of halocarbon spectra owing to the presence of rotational isomers, asymmetric centers, long-range couplings, and chlorine isotope effects are illustrated, and the methods used for analyzing such complex spectra are briefly discussed.     

Full multinuclear resonance analysis of 4-amino-1,1,2,2,9,9,10,10-octafluoro[2.2]paracyclophane

The complete assignment of 19F, 1H and 13C NMR spectra for a monosubstituted octafluoro[2.2]paracyclophane derivative is described for the first time. The unambiguous assignments were achieved through the combination of 19F--1H HOESY, 1H COSY and 19F COSY techniques and then further confirmed employing a complementary approach using a Karplus-dependent 3JCF interaction. Interesting aspects of the coupling patterns for various JHH, JHF, JCF and JFF interactions are also discussed.     

Synthesis of 6α-methyl-16α,17α-cyclohexano-19-norprogesterone from a 19-methyl-6-desmethyl precursor

After prolonged refluxing of 19-tosyloxy-16α,17α-cyclohexanopregn-5-en-3β-ol-20-one (3) with NaI in 2-propanol, the initially formed 19-iodo derivative (4) undergoes supraface migration of the CH₂I group from the C(10) atom to the C(6) atom, probably through involvement of a homoallyl cation. The resulting 6β-iodomethyl-16α,17α-cyclohexano-19-norpregn-5(10)-en-3β-ol (5) was transformed in three steps into 6α-methyl-16α,17α-cyclohexano-19-norprogesterone (6α-methyl-19-nor-D′ ₆-pentarane,8). The transformation of compound5 into the target product8 also gave a side product, a pentarane with aromatic ringA (10), which was isolated and characterized by spectroscopic methods. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1688–1691, September, 1997.     

“化学在抗击新冠肺炎疫情中扮演的重要角色”专题教学

Considering COVID-19 epidemic prevention and control, education materials were excavated and refined, such as chemical disinfectants, typical drugs used in clinical treatment or trial and materials for preparation of medical protective equipment. We have carried out thematic teaching on "The important role of chemistry in the fight against COVID-19 epidemic", and integrated ideological and political education into the thematic teaching. Through thematic teaching, we can make students feel the charm of chemistry subject, stimulate students' interest in learning chemistry, fully mobilize students' learning enthusiasm and initiative, strengthen students' confidence and courage to overcome difficulties, cultivate the students' professional disciplines literacy and scientific literacy, activate students' love for the motherland, the people and the Communist Party of China.