On a certain two-sided symmetric condition in magnetic field analysis and computations

A special two-sided condition for the incremental magnetic reluctivity is introduced which guarantees the unique existence of both the weak and the approximate solutions of the nonlinear stationary magnetic field distributed on a region composed of different media, as well as a certain estimate of the error between the two solutions. The condition, being discussed from the physical as well as the mathematical point of view, can be easily verified and is fulfilled for various magnetic reluctivity models used in electrotechnical practice.     

Some classes of non general type codimension two subvarieties inP n

We classify smooth subvarieties of codimension twoX⊂P ⁿ , 4≤n≤5, which are arithmetically Cohen-Macaulay and of non general type. By the way we exhibit some classes of non extendable subvarieties. Then we give new proofs of the classification of scrolls inP ⁴; finally we consider smooth surfaces of non general type inP ⁴ arising from rank three vector bundles.

---

Sunto Classifichiamo le sottovarietà lisce di codimensione dueX⊂P ⁿ , 4≤n≤5, aritmeticamente Cohen-Macaulay e non di tipo generale. Nel contempo descriviamo alcune classi di sottovarietà non estendibili. Diamo poi due nuove dimostrazioni della classificazione degli scrolls inP ⁴; infine consideriamo superfici lisce inP ⁴, non di tipo generale, associate a fibrati di rango tre.

     

Chiral phase transition and Anderson localization in the instanton liquid model for QCD

We study the spectrum and eigenmodes of the QCD Dirac operator in a gauge background given by an instanton liquid model (ILM) at temperatures around the chiral phase transition. Generically we find the Dirac eigenvectors become more localized as the temperature is increased. At the chiral phase transition, both the low lying eigenmodes and the spectrum of the QCD Dirac operator undergo a transition to localization similar to the one observed in a disordered conductor. This suggests that Anderson localization is the fundamental mechanism driving the chiral phase transition. We also find an additional temperature dependent mobility edge (separating delocalized from localized eigenstates) in the bulk of the spectrum which moves toward lower eigenvalues as the temperature is increased. In both regions, the origin and the bulk, the transition to localization exhibits features of a 3D Anderson transition including multifractal eigenstates and spectral properties that are well described by critical statistics. Similar results are obtained in both the quenched and the unquenched case though the critical temperature in the unquenched case is lower. Finally we argue that our findings are not in principle restricted to the ILM approximation and may also be found in lattice simulations.     

Effect of Ga doping on magneto-transport properties in colossal magnetoresistive La0.7Ca0.3Mn1−xGaxO3 (0<x<0.1)

Samples of La_0.7Ca_0.3Mn_1−xGa_xO₃ with x=0, 0.025, 0.05 and 0.10 were prepared by standard solid-state reaction. They were first characterized chemically, including the microstructure. The magnetic properties and various transport properties, i.e. the electrical resistivity, magnetoresistivity (for a field below 8 T), thermoelectric power and thermal conductivity measured each time on the same sample, are reported. The markedly different behaviour of the x=0.1 sample from those with a smaller Ga content, is discussed. The dilution of the Mn³⁺/Mn⁴⁺ interactions with Ga doping considerably reduces the ferromagnetic double exchange interaction within the manganese lattice leading to a decrease of the Curie temperature. The polaron binding energy varies from 224 to 243 meV with increased Ga doping.     

Mechanosynthesis of YIG and GdIG: A Structural and Mössbauer Study

We have investigated the mechanosynthesis of gadolinium and yttrium iron garnets by high-energy ball-milling of α-Fe₂O₃ and Gd₂O₃ or α-Fe₂O₃ and Y₂O₃, respectively, followed by short thermal annealings conducted at moderate temperatures. The samples were characterized by X-ray diffraction and Mössbauer spectroscopy, in order to determine the influence of the milling time and annealing conditions on the final products. For as-milled samples of each rare-earth system, the results revealed the formation of perovskite phases, in relative amounts that depend on the milling time. The formation of garnet phases was observed in as-annealed samples treated at 1000°C for 2 h or 1100°C for 3 h, i.e., at very modest annealing requirements when compared with ordinary solid-state-reaction processes performed without previous high-energy milling. Also, the occurrence was verified of a milling time for which the relative amount of garnet phases formed by annealing was maximized. This time depends on the rare-earth composing the garnet phase and on the annealing temperature.     

Symmetric Hilbert spaces arising from species of structures

Symmetric Hilbert spaces such as the bosonic and the fermionic Fock spaces over some lsquo;one particle space’ are formed by certain symmetrization procedures performed on the full Fock space. We investigate alternative ways of symmetrization by building on Joyal's notion of a combinatorial species. Any such species F gives rise to an endofunctor of the category of Hilbert spaces with contractions mapping a Hilbert space to a symmetric Hilbert space with the same symmetry as the species F. A general framework for annihilation and creation operators on these spaces is developed, and compared to the generalised Brownian motions of R. Speicher and M. Bożejko. As a corollary we find that the commutation relation with admits a realization on a symmetric Hilbert space whenever f has a power series with infinite radius of convergence and positive coefficients. Received: 7 April 2000; in final form: 28 November 2000 / Published online: 19 October 2001     

Studies on the chemical constituents of the South China Sea sponge Phacellia fusca

Three pyrrololactam alkaloids have been isolated from the marine sponge Phacellia fusca Schmidt collected from the South China Sea, and their structures were determined as 1–3 , on the grounds of spectral data. This is the first report of these compounds from this sponge. The structure of 1 was confirmed by X-ray analysis.