A stabilization process applied to a hidden variables method for evaluating the uncertainties on foundation impedances and their effect on vibrations induced by railways in a building

The paper is devoted to stochastic foundation impedance modeling for buildings submitted to vibrations. The hidden-variables method used in seismic engineering is revisited, due to a larger frequency range used in vibration prediction. Indeed, in this new context, instability of the solution and non-physical nature of mass and stiffness random matrices have been observed. The hidden variable method has been therefore implemented by enforcing explicitly the stability of the solution and the positiveness of mass and stiffness matrices. The effects of numerical parameters used throughout the process are shown and the improved hidden-variables method has been used for predicting the level of vibrations inside a building induced by railway sources. We present here steps of stabilization process, and then discuss on an example of application.     

Synthesis and photochemistry of a two-position Ru(terpy)(phen)(L)2+ scorpionate complex

A dissymmetric 1,10-phenanthroline chelate (N-phen-S) bearing two polyether chains terminated by two monodentate ligands of the benzonitrile (N) and dialkylesulfoxide (S) types was synthesized, characterized, and coordinated to ruthenium. The corresponding Ru(terpy)(N-phen-S)2+ complexes (terpy = 4'-(3,5-ditertiobutylphenyl)-2,2';6',2' '-terpyridine) were fully characterized as being two coordination isomers of the scorpionate type with one of the two tails occupying the sixth position on the coordination sphere. Photoexpulsion of the coordinated tail led to opening of the ruthena-macrocycle and subsequent rearrangement of the bidentate chelate. This rearrangement consisted of a 90 degrees rotation of the phenanthroline around the ruthenium atom. Selective irradiation of one isomer in a mixture of the two was undertaken using band-pass filters; this resulted in an enrichment of the nonirradiated isomer in the mixture. Thermal back-coordination of the tail was investigated in the dark. It took place quantitatively from the corresponding ruthenium chloride complex by trapping of the anion with silver salts.     

Exploring bovine pancreatic trypsin inhibitor phase transitions

This paper presents an investigation of the phase diagram of BPTI (bovine pancreatic trypsin inhibitor)/350 mM KSCN at pH 4.9 by direct observation and numerical simulations. We report optical microscopy and light and X-ray scattering experiments coupled with theoretical data analysis using numerical tools. The phase diagram is thoroughly determined, as a function of temperature. Two polymorphs are observed by video microscopy and their solubility measured. In this phase diagram, the liquid-liquid phase separation (LLPS) is metastable with respect to the solid-liquid phase separation. Above the T(L-L) boundary curve, solutions are composed of a mixture of BPTI monomers and decamers. Attractive interactions are stronger between decamers than between monomers. Below the T(L-L) boundary curve, the dense phase is highly concentrated in protein and composed of BPTI decamers alone. Thus, the driving force for liquid-liquid or liquid-solid phase separation is the attraction between decamers at low pH. The structure factors of the dense phases are characteristic of repulsive dense phases because of a hard sphere repulsion core, meaning that in the dense phase proteins are actually in contact (interparticle distance of 53 A). In agreement with the Oswald rule of stages, LLPS occurs prior to and impedes the solid nucleation.     

Cohomology of regular differential forms for affine curves

Let C be a complex affine reduced curve, and denote by H¹(C) its first truncated cohomology group, i.e. the quotient of all regular differential 1-forms 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:

     

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).