Almost Connected Orders

One of the standard axioms for semiorders states that no three-point chain is incomparable to a fourth point. We refer to asymmetric relations satisfying this axiom as almost connected orders or ac-orders. It turns out that any relation lying between two weak orders, one of which covers the other for inclusion, is an ac-order (albeit of a special kind). Every ac-order is bracketed in a natural way by two weak orders, one the maximum in the set of weak orders included in the ac-order, and the other minimal, but not necessarily the minimum, in the set of weak orders that include the ac-order. The family of ac-orders on a finite set with at least five elements is not well graded (in the sense of Doignon and Falmagne, 1997). However, such a family is both upgradable and downgradable, as every nonempty ac-order contains a pair whose deletion defines an ac-order on the same set, and for every ac-order which is not a chain, there is a pair whose addition gives an ac-order.     

On finding the K best cuts in a network

We show that the O(K · n⁴) algorithm of Hamacher (1982) for finding the K best cut-sets fails because it may produce cuts rather than cut-sets. With the convention that two cuts $\text{(X,}\text{X}\text{)}$ and $\text{(Y,}\text{Y}\text{)}$ are different whenever X ≠ Y the K best cut problem can be solved in O(K · n⁴).     

A universal constant for the convergence of Newton's method and an application to the classical homotopy method

We give a new theorem concerning the convergence of Newton's method to compute an approximate zero of a system of equations. In this result, the constanth ₀=0.162434... appears, which plays a fundamental role in the localization of good initial points for the Newton iteration. We apply it to the determination of an appropriate discretization of the time interval in the classical homotopy method.     

IsoméRisation avant la perte d'eau des ions aldéhydes et cétones protonés en spectrométrie de masse

Isomerization of Protonated Aldehyde and Ketone Ions in the Mass-Spectrography Before the Loss of Water In mass spectrometry, protonated aldehyde and ketone ions isomerize before the loss of a molecule of water. In order to specify this process, the spectra of deuterium labelled protonated aldehydes and ketones have been compared to the spectra of the corresponding isomer ions.     

Pyrolysis of poly-α-acetoxystyrene,a polymer derived from polystyrene and poly(vinyl acetate)

The pyrolysis of poly-α-acetoxystyrene was investigated by using two methods thermogravimetry, and a reactor working under dynamic conditions coupled with a chromatograph.Thermogravimetry was used firstly with a constant heating rate and secondly under isothermal conditions. Two different degradation steps for the polymer were found, the first between 140 and 200°C and the second above 220°C. The kinetics of the overall pyrolysis were studied for the first thermal degradation step. The degradation order is zero when the weight loss is less than 10%, and unity when the weight loss is between 10 and 32%. The activation energy is about 40 kcal/mole for either order. The results obtained by using dynamic and isothermal thermogravimetry are in good agreement.Volatile products were identified and analysed by using a reactor working under dynamic conditions coupled with a chromatograph. The decomposition is similar to that of poly(vinyl acetate) and different to that of known substituted polystyrenes. Acetic acid was the main component of the volatile products (90–95%), the others being the monomer and acetophenone.     

The Helmholtz equation with impedance in a half-space

In this Note we obtain existence and uniqueness results for the Helmholtz equation in the half-space ${\mathbb{R}}_{+}^3$ with an impedance or Robin boundary condition. Basically, we follow the procedure we have already used in the bi-dimensional case (the half-plane). Thus, we compute the associated Green's function with the help of a double Fourier transform and we analyze its far field in order to obtain radiation conditions that allow us to prove the uniqueness of an outgoing solution. Again, these radiation conditions are somewhat unusual due to the appearance of a surface wave guided by the boundary. An integral representation of the solution is presented by means of the Green's function and the boundary data. To cite this article: M. Durán et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Monoid of self-equivalences and free loop spaces

Let be a simply-connected closed oriented -dimensional manifold. We prove that for any field of coefficients there exists a natural homomorphism of commutative graded algebras where is the loop algebra defined by Chas and Sullivan. As usual denotes the monoid of self-equivalences homotopic to the identity, and the space of based loops. When is of characteristic zero, yields isomorphisms where denotes the Hodge decomposition on .

     

Reconstruction of physics objects at the Circular Electron Positron Collider with Arbor

After the Higgs discovery, precise measurements of the Higgs properties and the electroweak observables become vital for the experimental particle physics. A powerful Higgs/Z factory, the Circular Electron Positron Collider (CEPC) is proposed. The Particle Flow oriented detector design is proposed to the CEPC and a Particle Flow algorithm, Arbor is optimized accordingly. We summarize the physics object reconstruction performance of the Particle Flow oriented detector design with Arbor algorithm and conclude that this combination fulfills the physics requirement of CEPC.     

M?ssbauer spectroscopy: analysis and predictions for Li-ion batteries

Due to their high storage capacity Sn-based materials are of considerable interest as negative electrode for Li-ion batteries. However the strong volume change occurring during the alloy formation strongly limits the electrochemical performances (cycle and time life). Analysis by M?ssbauer spectroscopy using model compounds (Sn, Sn-Li and transition metal-Sn alloys) shows that the volume expansion is related to the structural change from a Sn based network to a Li based network. Two types of materials are proposed here to overcome this problem: tin dispersion in an electrochemically inactive oxide matrix with buffer role to absorb volume changes or tin alloying with an inactive transition metal to minimize the volume expansion. The use of M?ssbauer spectroscopy (in situ operando mode) allows a dynamic approach which is essential to understand the fundamental causes of ageing on cycling and to define then the key issues to be solved for material’s application.