Higher-Order Simple Lie Algebras

It is shown that the non-trivial cocycles on simple Lie algebras may be used to introduce antisymmetric multibrackets which lead to higher-order Lie algebras, the definition of which is given. Their generalised Jacobi identities turn out to be satisfied by the antisymmetric tensors (or higher-order “structure constants”) which characterise the Lie algebra cocycles. This analysis allows us to present a classification of the higher-order simple Lie algebras as well as a constructive procedure for them. Our results are synthesised by the introduction of a single, complete BRST operator associated with each simple algebra. Received: 3 June 1996 / Accepted: 8 November 1996     

Preperfect graphs

We say that a vertexx of a graph is predominant if there exists another vertexy ofG such that either every maximum clique ofG containingy containsx or every maximum stable set containingx containsy. A graph is then called preperfect if every induced subgraph has a predominant vertex. We show that preperfect graphs are perfect, and that several well-known classes of perfect graphs are preperfect. We also derive a new characterization of perfect graphs.     

Temperature dependence of the iron hyperfine field distribution in amorphous Fe-rich Fe-Zr alloys

The temperature dependence of the iron hyperfine field distribution is reported in melt-quenched amorphous Fe-Zr alloys. The most remarkable feature is the compositinal change in the shape of the average hyperfine field versus temperature curves. The unusual increase in the average hyperfine field below about 85 K is a characteristic feature of the RSG systems; however, no anomaly is observed in the width of the hyperfine field distribution as a function of temperature. The results cannot be properly explained in the framework of the existing spin glass models.     

Algebraic cycles and topology of real Enriques surfaces

For a real Enriques surface Y we prove that every homology class in H₁(Y (R), Z/2) can be represented by a real algebraic curve if and only if all connected components of Y(R) are orientable. Furthermore, we give a characterization of real Enriques surfaces which are Galois-Maximal and/or Z-Galois-Maximal and we determine the Brauer group of any real Enriques surface Y.     

Towards an universal classification of scale invariant processes

We consider fields which take random values over several decades. Starting from physical examples, we postulate that scale is not an absolute quantity. We then establish the equivalence between two existing approaches based on scale symmetry arguments as general as possible. This yields a classification of log-infinitely divisible laws, possibly universal. The physical significance of the parameters entering in the classification is discussed. Received: 7 November 1997 / Received in final form: 26 March 1998 / Accepted: 30 March 1998     

Mn-site doping induced CMR properties in calcium rich manganites Pr1‒xCaxMnO3(0.6 ≤ x ≤ 0.7)

Doping of Mn-site by chromium, cobalt and nickel has been investigated in the calcium rich manganites and . Whatever the nature of the doping element, a rapid disappearance of the charge ordered (CO) state is observed, decreasing as the doping rate increases. But the most important result concerns the Cr-doped compounds for which a re-entrant insulator to metal transition at 90-120 K is observed for x =0.10-0.12, in a zero magnetic field. The possibility to induce colossal magnetoresistance (CMR) properties for high (IV) contents ((IV)/) for x =0.07-0.12 is shown for the first time, the resistance ratios reaching at 30 K. This study also shows differently that the small size of the A-site cation (Pr, Ca) is not a redhibitory obstacle to the appearance of CMR properties in manganites, in contrast with previously established phase diagrams. Received: 18 June 1997 / Revised: 4 August 1997 / Accepted: 10 November 1997     

Collisions for the quantum Coulomb Hamiltonian

We study the propagation of phase space singularities for the time dependent Schrödinger equation with potential having Coulomb-type singularities in space dimension equal tothree. We prove that the singularities (frequency set) of the solution are reflected by a Coulomb center exactly as in the classical problem, i.e. the frequency set follows theregularized trajectories of Classical Mechanics after a collision.     

Unconventional antiferromagnetic correlations of the doped Haldane gapsystem Y 2 BaNi 1 - x Zn x O 5

We make a new proposal to describe the very low temperature susceptibility of the doped Haldane gap compound Y₂BaNi_1-xZn_xO₅. We propose a new mean field model relevant for this compound. The ground state of this mean field model is unconventional because antiferromagnetism coexists with random dimers. We present new susceptibility experiments at very low temperature. We obtain a Curie-Weiss susceptibility χ( T ) ∼ C /(Θ + T ) as expected for antiferromagnetic correlations but we do not obtain a direct signature of antiferromagnetic long range order. We explain how to obtain the “impurity” susceptibility ( T ) by subtracting the Haldane gap contribution to the total susceptibility. In the temperature range [1 K, 300 K] the experimental data are well fitted by T ( T ) = C _imp 1 + T _imp / T . In the temperature range [100 mK, 1 K] the experimental data are well fitted by T ( T ) = A ln( T / T _c ), where T _c increases with x. This fit suggests the existence of a finite Néel temperature which is however too small to be probed directly in our experiments. We also obtain a maximum in the temperature dependence of the ac-susceptibility ( T ) which suggests the existence of antiferromagnetic correlations at very low temperature. Received 17 July 2001     

Thickness dependence of the magnetic anisotropy of Fe layers separated by Al

Magnetic multilayers of ⁵⁷Fe with nominal thickness, T _nom, between 0.4 and 1.0 nm separated by 3.0 nm Al spacer layers were prepared by alternate deposition of the constituents in high vacuum. The samples were investigated at 4.2 K in external magnetic field. A fraction of Fe atoms corresponding to about 0.3 nm equivalent Fe-thickness was found to mix into the Al spacer. The extremely strong magnetic anisotropy observed for T _nom < 0.8 nm is attributed to Fe layers of approximately two atomic planes thick. The anisotropy decreases considerably after the building up of the third Fe atomic layer starts at T _nom = 0.8 nm, but full saturation was not achieved even for T _nom = 1 nm and 3 T magnetic field applied perpendicularly to the sample plane.