A dynamical strategy for approximation methodsUne stratégie dynamique pour les méthodes d'approximation

The numerical result provided by an approximation method is affected by a global error, which consists of both a truncation error and a round-off error. Let us consider the converging sequence generated by successively dividing by two the step size used. If computations are performed until, in the convergence zone, the difference between two successive approximations is only due to round-off errors, then the global error on the result obtained is minimal. Furthermore its significant bits which are not affected by round-off errors are in common with the exact result, up to one. To cite this article: F. Jézéquel, C. R. Mecanique 334 (2006).     

Sound propagation above a porous road surface with extended reaction by boundary element method

Acoustic impedance of an absorbing interface is easily introduced in boundary element codes provided that a local reaction is assumed. But this assumption is not valid in the case of porous road surface. A two-domain approach was developed for the prediction of sound propagation above a porous layer that takes into account the sound propagation inside the porous material. The porous material is modeled by a homogeneous dissipative fluid medium. An alternative to this time consuming two-domain approach is proposed by using the grazing incidence approximate impedance in the traditional single-domain boundary element method (BEM). It can be checked that this value is numerically consistent with the surface impedance calculated at the interface from the pressure and surface velocity solutions of the two-domain approach. The single-domain BEM introducing this grazing incidence impedance is compared in terms of sound attenuation with analytical solutions and two-domain BEM. The comparison is also performed with the single-domain BEM using the normal incidence impedance, and reveals a much better accuracy for the prediction of sound propagation above a porous interface.     

Direct selected multireference configuration interaction calculations for large systems using localized orbitals

A selected multireference configuration interaction (CI) method and the corresponding code are presented. It is based on a procedure of localization that permits to obtain well localized occupied and virtual orbitals. Due to the local character of the electron correlation, using local orbitals allows one to neglect long range interactions. In a first step, three topological matrices are constructed, which determine whether two orbitals must be considered as interacting or not. Two of them concern the truncation of the determinant basis, one for occupied/virtual, the second one for dispersive interactions. The third one concerns the truncation of the list of two electron integrals. This approach permits a fine analysis of each kind of approximation and induces a huge reduction of the CI size and of the computational time. The procedure is tested on linear polyene aldehyde chains, dissociation potential energy curve, and reaction energy of a pesticide-Ca(2+) complex and finally on transition energies of a large iron system presenting a light-induced excited spin-state trapping effect.     

A note on random walk in random scenery

We consider a random walk in random scenery {Xn=η(S₀)+?+η(Sn),n∈N}, where a centered walk {Sn,n∈N} is independent of the scenery {η(x),x∈Zd}, consisting of symmetric i.i.d. with tail distribution P(η(x)>t)∼exp(−cαtα), with 1?α<d/2. We study the probability, when averaged over both randomness, that {Xn>ny} for y>0, and n large. In this note, we show that the large deviation estimate is of order exp(−ca(ny)), with a=α/(α+1).     

MoCu3TeO7Cl2·0.5H2O

Single crystals of molybdenum(VI) tricopper(II) tellurium(IV) hepta­oxide dichloride hemihydrate, MoCu₃TeO₇Cl₂·0.5H₂O, were synthesized via a transport reaction in sealed evacuated silica tubes. All atoms occupy general positions within the triclinic () unit cell. The building units are irregular CuO₄Cl and CuO₃Cl₂ square pyramids, distorted TeO₃₊₁E trigonal bipyramids (E is the lone pair of Te^IV) and irregular MoO₅ pyramids. The TeO₃₊₁E, CuO₄Cl and CuO₃Cl₂ polyhedra form (110) layers bridged by Mo atoms. The water mol­ecules are located in [100] channels.     

Asymmetric decarboxylative Claisen rearrangement reactions of sulfoximine-substituted allylic tosylacetic esters

Allylic acetate esters containing a variety of N-arylsulfonyl sulfoximines on the acetyl residue have been prepared and submitted to the decarboxylative Claisen rearrangement reaction. Rearranged products were isolated in generally good yields, and diastereoselectivities up to 82:18 have been obtained. The N-(2,4,6-triisopropylphenylsulfonyl)-S-phenyl sulfoximine moiety gave the best selectivity. The stereochemistry of the major isomer was established by X-ray crystallography. A model to explain the stereochemical course of the rearrangement is proposed.     

Calcium imaging in the ant <Emphasis Type="Italic">Camponotus fellah</Emphasis> reveals a conserved odour-similarity space in insects and mammals

Background  

Olfactory systems create representations of the chemical world in the animal brain. Recordings of odour-evoked activity in the primary olfactory centres of vertebrates and insects have suggested similar rules for odour processing, in particular through spatial organization of chemical information in their functional units, the glomeruli. Similarity between odour representations can be extracted from across-glomerulus patterns in a wide range of species, from insects to vertebrates, but comparison of odour similarity in such diverse taxa has not been addressed. In the present study, we asked how 11 aliphatic odorants previously tested in honeybees and rats are represented in the antennal lobe of the ant Camponotus fellah, a social insect that relies on olfaction for food search and social communication.     

Comparison of perturbative and variational treatments of molecular vibrations: application to the vibrational spectrum of HFCO up to 8000 cm(-1)

We calculated highly excited states of the HFCO molecule, comparing results from two methods. In the first method, Van Vleck perturbation theory is used to transform away all off-diagonal couplings except those between nearly degenerate states. This perturbative transformation leads to a matrix representation where eigenvalues are obtained with relatively small matrices. In the second method, variational eigenvalues are obtained by combining the Jacobi-Wilson approach with the block-Davidson scheme. The key ingredient here is a prediagonalized-perturbative scheme applied to a subspace of a curvilinear normal-mode basis set. Comparisons of the two methods provide a critical test of the less time-consuming perturbation theory. Two different coordinate sets are used to test the sensitivity of the results to coordinate choice. Perturbation theory also requires a polynomial fit to the potential. The implications of this restriction are investigated.     

Incorporation of a minimal nucleotide into DNA

Abasic sites are amongst the most frequent DNA lesions and result from spontaneous hydrolysis of the glycosidic bond or from the removal of damaged nucleobases. These depurination events can also occur on free deoxyribonucleoside triphosphates present in cells and lead to the formation of an abasic site triphosphate of which very little is known. Herein, we report the synthesis and biochemical characterization of the minimal triphosphate dФTP. Unexpectedly, dФTP is tolerated by various DNA polymerases and the incorporation efficiency obeys the A-rule. Single incorporation of dФMP units were also observed opposite abasic sites and the addition of prosthetic molecules mimicking base-pairs do not seem to favor the process.