Hopf–Galois Extensions with Central Invariants and Their Geometric Properties

We set up a general framework to study representation theory of certain algebras whichusually appear in the study of restricted Lie algebras or various quantum objects at roots of unity.The object of the study is a Hopf–Galois extension with central invariants. It turns out that theseextensions possess some geometric properties which are close to those of principal bundles andFrobenius manifolds. We define Hopf–Galois extensions of not necessarily affine schemes andprove that the classification problem of such extensions leads to a stack.     

Photoelectron spectroscopy of negative ions solvated in clusters

We have measured the photoelectron spectra of Cl^?, Br^? and I^? complexed with water molecule and of I^?·(CO₂) _n clusters wheren=1?7. The significance of these measurements to the understanding of solvation phenomena is discussed.     

Effect of surface tension on the free outflow of a wetting fluid from a horizontal tube

The flow structure for which the Kármán hypothesis is valid is explored experimentally and theoretically. It is established that there exists not a point but a region of finite size, adjacent to the upper generator of the tube and including the moving line of contact between the phase interface and the wall, in which the fluid is stationary relative to the line of contact, i.e., in which the no-slip condition is not satisfied. The dimensions of the region depend on the surface tension. The action of this stagnant zone on the flow is fully explained by the effect of the surface tension in experiments [1]. It is established that depending on the ratio of the tube diameter to the dimension of the stagnant zone two flow regimes are possible: in sufficiently wide tubes, an inertial regime for which Kármán's hypothesis holds and the no-slip condition is not satisfied, and, in sufficiently narrow tubes, a creep regime in which the no-slip condition continues to apply. The values of the determining dimensionless parameter corresponding to the change of regime and the cessation of flow are calculated. They are similar to the experimental values.deceasedTranslated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 85–93, March–April, 1988.     

The Synthesis of New Organoselenium Heterocyclic Compounds: 2‐aryl‐4‐phenyl‐5,6,7,8‐tetrahydro‐4H‐selenochromenes

We have explored the reactions of 2‐(3‐oxo‐1‐aryl‐3‐phenylpropyl)cyclohexanone ( 1–3 ) with hydrogen selenide in situ in conditions of acid catalysis, and synthesized new 2‐aryl‐4‐phenyl‐5,6,7,8‐tetrahydro‐4H‐selenochromenes ( 4–6 ).     

Synthesis, structure, and spectroscopic characterization of [H(8-n)Rh22(CO)35](n-) (n = 4, 5) and [H2Rh13(CO)24{Cu(MeCN)}2](-) clusters: assessment of CV and DPV as techniques to circumstantiate the presence of elusive hydride atoms

The previously ill-characterized [H(x)Rh(22)(CO)(35)](4-/5-) carbonyl cluster has been obtained as a byproduct of the synthesis of [H(3)Rh(13)(CO)(24)](2-) and effectively separated by metathesis of their sodium salts with [NEt(4)]Cl. Although the yields are modest and never exceed 10-15% (based on Rh), this procedure affords spectroscopically pure [H(3)Rh(22)(CO)(35)](5-) anion. Formation of the latter in mixture with other Rh clusters was also observed by electrospray ionization-mass spectrometry (ESI-MS) in the oxidation of [H(2)Rh(13)(CO)(24)](3-) with Cu(2+) salts. The recovery of further amounts of [H(3)Rh(22)(CO)(35)](5-) was hampered by too similar solubility of the salts composing the mixture. Conversely, the reaction in CH(3)CN of [H(2)Rh(13)(CO)(24)](3-) with [Cu(MeCN)(4)](+)[BF(4)](-) leads to the [H(2)Rh(13)(CO)(24){Cu(MeCN)}(2)](-) bimetallic cluster. The X-ray crystal structures of [H(4)Rh(22)(CO)(35)](4-), [H(3)Rh(22)(CO)(35)](5-), and [H(2)Rh(13)(CO)(24){Cu(MeCN)}(2)](-) are reported. From a formal point of view, the metal frame of the former two species can be derived by interpenetration along two orthogonal axes of two moieties displaying the structure of the latter. The availability of [H(8-n)Rh(22)(CO)(35)](n-) salts prompted their detailed chemical, spectroscopic, and electrochemical characterization. The presence of hydride atoms has been directly proved both by ESI-MS and (1)H NMR. Moreover, both [H(4)Rh(22)(CO)(35)](4-) and [H(3)Rh(22)(CO)(35)](5-) undergo distinctive electrochemically reversible redox changes. This allows to assess electrochemical studies as indisputable though circumstantial evidence of the presence of (1)H NMR-silent hydride atoms in isostructural anions of different charge.     

Comprehensive core-level study of the effects of isomerism, halogenation, and methylation on the tautomeric equilibrium of cytosine

Core-level X-ray photoemission and near-edge X-ray absorption fine structure spectra of 5-methylcytosine, 5-fluorocytosine, and isocytosine are presented and discussed with the aid of high-level ab initio calculations. The effects of the methylation, halogenation, and isomerization on the relative stabilities of cytosine tautomers are clearly identified spectroscopically. The hydroxy-oxo tautomeric forms of these molecules have been identified, and their quantitative populations at the experimental temperature are calculated and compared with the experimental results and with previous calculations. The calculated values of Gibbs free energy and Boltzmann population ratios are in good agreement with the experimental results characterizing tautomer equilibrium.     

An easily accessible Re-based catalyst for the selective conversion of methanol: evidence for an unprecedented active site structure through combined operando techniques

Heterogeneous Re/SiO(2) catalysts prepared using a one pot sol-gel synthesis were found to display high activity in the direct, selective methanol conversion to methylal, which is correlated to an unprecedented rhenium oxide structure.     

Flow Structure of Swirling Turbulent Propane Flames

Flow structure of premixed propane–air swirling jet flames at various combustion regimes was studied experimentally by stereo PIV, CH* chemiluminescence imaging, and pressure probe. For the non-swirling conditions, a nonlinear feedback mechanism of the flame front interaction with ring-like vortices, developing in the jet shear layer, was found to play important role in the stabilisation of the premixed lifted flame. For the studied swirl rates (S = 0.41, 0.7, and 1.0) the determined domain of stable combustion can be divided into three main groups of flame types: attached flames, quasi-tubular flames, and lifted flames. These regimes were studied in details for the case of S = 1.0, and the difference in the flow structure of the vortex breakdown is described. For the quasi-tubular flames an increase of flow precessing above the recirculation zone was observed when increased the stoichiometric coefficient from 0.7 to 1.4. This precessing motion was supposed to be responsible for the observed increase of acoustic noise generation and could drive the transition from the quasi-tubular to the lifted flame regime.     

Rational design of an inhibitor of dethiobiotin synthetase; interaction of 6-hydroxypyrimindin-4(3H)-one with the adenine base binding site

Modelling of the H-bonding interactions involved in the binding of the adenine base component of ATP to E. coli dethiobiotin synthetase (DTBS) suggested that 6-hydroxypyrimidin-4(3H)-one (6-HP4) should selectively bind to this site in the enzyme. Kinetic studies show that 6-HP4 is a competitive inhibitor of DTBS and x-ray crystallography shows that 6-HP4 binds specifically in the purine base binding site of the enzyme.