Mössbauer study of Brazilian soapstone

Steatite mineral rocks, soapstone, have been studied by X-ray diffraction, optical microscopic analysis (modal analysis), electron probe micro analysis and Mössbauer spectroscopy for characterization, mineral percentages and chemical composition. Mössbauer spectra show both, magnetic interactions corresponding to magnetite and doublets corresponding to talc. chlorite, dolomite and tremolite. The temperature dependence of the quadrupole splitting in dolomite has been explained in terms of crystal field interaction.     

Phase diagram of the ANNNI model in the Hamiltonian limit

The Hamiltonian limit of the ANNNI model in (1+1) dimensions is studied by using the Quantum Statistical Monte Carlo method. Even if recent results suggest that Monte Carlo calculations may prove unreliable in the study of this system, the phase diagram of the quantum version of the model was successfully obtained. In particular, the clusive transitions between the disordered, the floating incommensurate and the degenerate 2, 2 are determined by analysing the correlation length behaviour in finite lattices.Partially supported by CONICET Argentina     

A grothendieck factorization theorem on 2-convex schatten spaces

We prove that for every bounded linear operatorT:C ^2p →H(1≤p<∞,H is a Hilbert space,C ^{2 p} p is the Schatten space) there exists a continuous linear formf onC ^p such thatf≥0, ‖f‖(C _C ^p)*=1 and $$\forall x \in C^{2p} , \left\| {T(x)} \right\| \leqslant 2\sqrt 2 \left\| T \right\|< f\frac{{x * x + xx*}}{2} > 1/2$$ . Forp=∞ this non-commutative analogue of Grothendieck’s theorem was first proved by G. Pisier. In the above statement the Schatten spaceC ^2p can be replaced byE _E ² whereE ⁽²⁾ is the 2-convexification of the symmetric sequence spaceE, andf is a continuous linear form onC _E. The statement can also be extended toL _E{(su2)}(M, τ) whereM is a Von Neumann algebra,τ a trace onM, E a symmetric function space.     

The bestL 2-approximation by finite sums of functions with separable variables

Summary We consider the problem of the best approximation of a given functionh L ² (X × Y) by sums _k=1 ⁿ f _k f _k, with a prescribed numbern of products of arbitrary functionsf _k L ² (X) andg _k L ² (Y). As a co-product we develop a new proof of the Hilbert—Schmidt decomposition theorem for functions lying inL ² (X × Y).