Analysis of the ν9ν10 band system of allene

The infrared spectrum of allene has been recorded with high resolution (0.002-0.004 cm^?1) on a Fourier transform instrument in the region 730 to 1170 cm^?1 containing the perpendicular bands, ν₉ and ν₁₀. A total of 21 subbands with KΔK ranging from ?6 to +14 have been assigned in the ν₉ band, and 26 subbands with KΔK = ?10 to +15 have been assigned in the ν₁₀ band. The bands are affected by a combination of a J_z-Coriolis and a quartic anharmonic interaction between their upper states ν₉ and ν₁₀. In addition, several other more localized perturbations are found in the spectrum. The nature of the interactions responsible for these perturbations is discussed, and five of the strongest perturbations are quantitatively accounted for by constructing a Hamiltonian matrix which includes five different perturbing states and their Coriolis and anharmonic resonances with the ν₉ and ν₁₀ upper states. A set of spectroscopic constants for the ν₉ and ν₁₀ states and for some of the perturbing states is reported.     

1-Substituted morpholino ethenes—III: Carbocyclic and aliphatic heterocyclic compounds from 5-membered ring derivatives

[4+2] Cycloaddition reaction of 1-(cyclopenten-1-y1)-1-morpholino ethene with β-nitrostyrene leads to tetrahydroindan and tetrahydroindanone derivatives. A [4+2] adduct of interest is also obtained in the reaction of the same substrate with mesyl chloride. Reactivity of the same electrophiles with the morpholino enamine of cyclopentyl-methyl ketone is also examined. Some stereochemical aspects of the above mentioned reactions are discussed.     

Sur la stabilité du fibré de PicardOn the stability of the Picard bundle

We study the stability of the Picard bundle on the moduli space of stable vector bundles of fixed rank and determinant, over an irreducible, smooth, algebraic curve of genus g?2. To cite this article: V. Savin, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 885–888.     

ExperimentalJ/ψ hadronic production from 150 to 280 GeV/c

A detailed study ofJ/ψ hadronic production has been performed in a high statistics experiment (more than 1.5 10⁶ J/ψ observed in their dimuon decay mode). Data have been taken with incident π^±,K ^±,p ^±, on hydrogen and platinum targets, at 150, 200 and 280 GeV/c. We find from the observed nuclear dependance of the cross sections, that about 18% of theJ/ψ are produced diffractively. Using known structure functions of the quarks in the nucleon and in the pion, we derive estimations for the gluon structure functions.     

Differential impulse response of unipolar space-charge-limited current

Zusammenfassung Die Zeitabhängigkeit des Stromstossesi(t) wird berechnet, den eine kleine Ladung beeinflusst, wenn sie sich durch das elektrische FeldE(r) bewegt, das ein stationärer, raumladungsbegrenzter Strom in drei verschiedenen Medien und in Strukturen von ebener, zylindrischer und sphärischer Geometrie erzeugt. Die drei betrachteten Medien sind das Vakuum, und zwei Festkörper, in denen entweder die Beweglichkeit oder die Bahngeschwindigkeit der Ladungsträger von der Feldstärke unabhängig ist. Man findet, dass für die beiden Festkörperi(t) undE(r) zwei eng verwandte Funktionen sind, deren Zusammenhang beschrieben wird. Eine experimentelle Bestimmung der Feldverteilung nach diesem Verfahren erscheint knapp durchführbar und würde direkte Einsicht in den Vorgang des Stromflusses vermitteln.     

Surface structure of TiO2(011)-(2x1)

A combined experimental and first principles study of the (2x1)-reconstructed rutile TiO2(011) surface is presented. Our results provide evidence that the surface structure is described by a model that includes onefold coordinated (titanyl) oxygen atoms giving rise to double bonded Ti=O species. These species should play a special role in the enhanced photocatalytic activity of the TiO2(011) surface.     

Dynamical motifs: building blocks of complex dynamics in sparsely connected random networks

Spatiotemporal network dynamics is an emergent property of many complex systems that remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs-small subnetworks with periodic and chaotic dynamics. We simulate randomly connected neural networks and, with increasing density of connections, observe the transition from quiescence to periodic and chaotic dynamics. This transition is explained by the appearance of dynamical motifs in the structure of these networks. We also observe domination of periodic dynamics in simulations of spatially distributed networks with local connectivity and explain it by the absence of chaotic and the presence of periodic motifs in their structure.     

Fourier Multipliers and Integro-Differential Equations in Banach Spaces

Operator-valued Fourier multiplier theorems are used to establishmaximal regularity results for an integro-differential equationwith infinite delay in Banach spaces. Results are obtained undergeneral conditions for periodic solutions in the vector-valuedLebesgue and Besov spaces. The latter scale includes in particularthe Hölder spaces C, 0 < < 1 .     

Trotter-Kato product formula and fractional powers of self-adjoint generators

Let A and B be non-negative self-adjoint operators in a Hilbert space such that their densely defined form sum obeys dom(H^α)⊆dom(A^α)∩dom(B^α) for some α∈(1/2,1). It is proved that if, in addition, A and B satisfy dom(A^1/2)⊆dom(B^1/2), then the symmetric and non-symmetric Trotter-Kato product formula converges in the operator norm:

||(e−tB/2ne−tA/ne−tB/2n)n−e−tH||=O(n−(2α−1))||(e−tA/ne−tB/n)n−e−tH||=O(n−(2α−1))