Free Boolean algebras over unions of two well orderings

Given a partially ordered set P there exists the most general Boolean algebra which contains P as a generating set, called the free Boolean algebra over P. We study free Boolean algebras over posets of the form P=P₀∪P₁, where P₀, P₁ are well orderings. We call them nearly ordinal algebras.Answering a question of Maurice Pouzet, we show that for every uncountable cardinal κ there are κ² pairwise non-isomorphic nearly ordinal algebras of cardinality κ.Topologically, free Boolean algebras over posets correspond to compact 0-dimensional distributive lattices. In this context, we classify all closed sublattices of the product (ω₁+1)×(ω₁+1), showing that there are only ℵ₁ many types. In contrast with the last result, we show that there are ℵ₁² topological types of closed subsets of the Tikhonov plank (ω₁+1)×(ω+1).     

Gaussian Weighted Trajectory Method. IV. No Rainbow Effect in Practice

高斯加权轨迹法(GWMT)是无规随机相态近似下的经典S矩阵理论(CSMT)的实际应用. CSMT曾经是1970年代初期发展起来的第一个和最简单的半经典分子碰撞理论. 虽然GWMT非常接近于纯粹的经典描述,但GWMT在一定程度上包含了对被研究的碰撞过程中不同自由度的量子化. 尽管CSMT会得出发散的末态分布,这与弹性散射理论中的的彩虹效应有关,但GWTM却从来不会导致这种数学灾难. 本文为这一现象提供了解释.     

On the Two Closely Related Phases of [Ru(C5Me5)(η6-1,3-(Me2NCH2)2C6H4)](BF4) and the Reversible Solid–Solid Order–Disorder Phase Transition

Abstract  

Crystals of the complex [Ru(C₅Me₅)(η⁶-1,3-(Me₂NCH₂)₂C₆H₄)](BF₄) have been examined over the temperature range 150–300 K via X-ray diffraction measurements. This study shows that the Ru complex is a two-phase system in this T-range and the solid–solid transition is reversible. At 150 K, phase II (P2₁/c, Z′ = 4) is ordered and non-merohedrally twinned, a = 16.4396 (9) ?, b = 17.3226 (4) ?, c = 32.1874 (11) ?, β = 91.375 (2)°. At 295 K, phase I (Pbca, Z′ = 1) is disordered, a = 8.5071 (3) ?, b = 17.1567 (3) ?, c = 32.8250 (8) ?. The relationship between the two phases is obvious because the packing remains similar in the two phases. The greatest structural changes between the two phases are found in the rows of adjacent cations [Ru(C₅Me₅)(η⁶-1,3-(Me₂NCH₂)₂C₆H₄)]⁺ packed along the a direction. These rows are ordered in phase II but are disordered in phase I. The phase transition is first order. Significant changes in thermal motion for the cations are considered as being the driving force for the occurrence of this phase transition.     

Minimal invariant varieties and first integrals for algebraic foliations

Let X be an irreducible algebraic variety over ℂ, endowed with an algebraic foliation . In this paper, we introduce the notion of minimal invariant variety V( , Y) with respect to ( , Y), where Y is a subvariety of X. If Y = {x} is a smooth point where the foliation is regular, its minimal invariant variety is simply the Zariski closure of the leaf passing through x. First we prove that for very generic x, the varieties V( , x) have the same dimension p. Second we generalize a result due to X. Gomez- Mont (see [G-M]). More precisely, we prove the existence of a dominant rational map F : X → Z, where Z has dimension (n − p), such that for very generic x, the Zariski closure of F⁻¹(F(x)) is one and only one minimal invariant variety of a point. We end up with an example illustrating both results.     

Selective Preparation of a Heteroleptic Cyclometallated Ruthenium Complex Capable of Undergoing Photosubstitution of a Bidentate Ligand

Cyclometallated ruthenium complexes typically exhibit red-shifted absorption bands and lower photolability compared to their polypyridyl analogues. They also have lower symmetry, which sometimes makes their synthesis challenging. In this work, the coordination of four N,S bidentate ligands, 3-(methylthio)propylamine (mtpa), 2-(methylthio)ethylamine (mtea), 2-(methylthio)ethyl-2-pyridine (mtep), and 2-(methylthio)methylpyridine (mtmp), to the cyclometallated precursor [Ru(bpy)(phpy)(CH₃CN)₂]⁺ (bpy=2,2′-bipyridine, Hphpy=2-phenylpyridine) has been investigated, furnishing the corresponding heteroleptic complexes [Ru(bpy)(phpy)(N,S)]PF₆ ([ 2 ]PF₆–[ 5 ]PF₆, respectively). The stereoselectivity of the synthesis strongly depended on the size of the ring formed by the Ru-coordinated N,S ligand, with [ 2 ]PF₆ and [ 4 ]PF₆ being formed stereoselectively, but [ 3 ]PF₆ and [ 5 ]PF₆ being obtained as mixtures of inseparable isomers. The exact stereochemistry of the air-stable complex [ 4 ]PF₆ was established by a combination of DFT, 2D NMR, and single-crystal X-ray crystallographic studies. Finally, [ 4 ]PF₆ was found to be photosubstitutionally active under irradiation with green light in acetonitrile, which makes it the first cyclometallated ruthenium complex capable of undergoing selective photosubstitution of a bidentate ligand.     

Cohomologie des formes différentielles régulières pour les courbes affines

Let C be an affine curve, and denote by H¹(C) its first troncated De Rham cohomology group, i.e. the quotient of regular differential 1-forms on C by exact 1-forms. First we introduce a nonnegative invariant μ′(C,x) that measures the complexity of the singularity of C at the point x, and we establish the following formula:

$\text{dim}\text{H}{}^1\text{(C)=}\text{dim}\text{H}{}_1\text{(C)+}\text{∑}\text{x∈C}\text{μ′(C,x),}$

where H₁(C) is the first singular homology group of C with complex coefficients. Second we consider a family of curves given by the fibres of a morphism $\text{f}\text{:X→}\text{C}$, where X is an affine reduced surface. We analyse the behaviour of the function y?dimH¹(f^?1(y)). More precisely we show that it is constant over a Zariski open set, and that it is lower semi-continuous is general. To cite this article: P. Bonnet, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

Dielectric and raman spectroscopic studies on the rotational isomerism of t-butyl formate

Static dielectric constants, refractive indices and densities have been measured for t-butyl formate and acetate in cyclohexane at increasing concentrations and at two temperatures, 20°C and 60°C. The ΔH value for the cis-trans equilibrium of t-butyl formate and the dipole moment of the trans conformation has been calculated from the dielectric measurements taking the ΔS value calculated from the sum-over-states for the cis and trans conformations and assuming the dipole moment of the cis conformation to be equal to 1.94 D as found for t-butyl acetate, which has the cis conformation only.The relative intensities of the Raman bands corresponding to specific vibrations modes of the cis and trans conformations of t-butyl formate are measured in cyclohexane and acetonitrile at various concentrations. The enthalpy difference ΔH is also measured in the liquid state and in acetonitrile by variation of the intensity ratio of the bands with temperature.All thermodynamic quantities obtained from dielectric or Raman intensity measurements are compared with each other and with the theoretical values. The solvation energy difference between cis and trans conformations in cyclohexane and acetonitrile as well as in the liquid state are also compared with theoretical values. The large deviation of solvation energy difference between the experimental value and Onsager's model value are well described by an additional term, which considers dipole-dipole interaction.     

Surface potential mapping of dispersed proteins

We describe a method for detecting proteins after transfer to PVDF membranes, based on the surface potential attributed to each protein. Proteins separated by classical two-dimensional polyacrylamide gel electrophoresis could be detected by scanning the membrane surface with a vibrating capacitor (also called a Kelvin probe) on the basis of differences between their surface potential and that of the membrane. Coupled to colloidal gold staining, the technique enables detection of proteins previously undetectable by classical staining methods. Plotting variations of the surface potential in two dimensions visualizes proteins which migrate close together. Finally, we demonstrate that the Kelvin probe detects proteins over a concentration range from micro to sub-nanogram with increased sensitivity at lower concentrations, and unlike other methods, appears to be similar for all proteins tested so far. The method described is fast, reliable, and it can be automated for high throughput.     

Sequence dependent rigidity of single stranded DNA

Single stranded DNA (ssDNA) equilibrium dynamics are investigated using a fluorophore/quencher-labeled hairpin structure which thermally fluctuates between open and closed states. Temporal correlations of the fluorescence fluctuations are used to determine the energy barrier to conformational change. We find that ssDNA distortion is purely entropic for poly(T) but requires an additional enthalpy of +0.5 kcal x mol(-1) x base(-1) for poly(A), consistent with the disruption of base stacking. Such sequence dependent dynamics challenge the classical model of ssDNA as a completely flexible coil.     

Radiative decay of lithium-like ions following charge exchange collisions of 60 keV O6+ ions with H2

The distribution of captured electrons in the 60 keV $\text{O}{}^{\mathrm{6+}}\text{+}\text{H}{}_2\text{→}\text{O}{}^{\mathrm{5+1}}\text{(nl) +}\text{H}{}_2{}^{\mathrm{+}}$ collision is studied by detection of the subsequent far UV radiation. Strong lines corresponding to the 4f → 3d → 2p cascade have been observed. Assuming that capture to the n = 4 manifold dominates at this energy, a relative population of the l sublevels which increases with l-value is obtained.