On subspace lattices II. Continuity of Lat

We study the continuity of the map Lat sending an ultraweakly closed operator algebra to its invariant subspace lattice. We provide an example showing that Lat is in general discontinuous and give sufficient conditions for the restricted continuity of this map. As consequences we obtain that Lat is continuous on the classes of von Neumann and Arveson algebras and give a general approximative criterion for reflexivity, which extends Arvesonâ??s theorem on the reflexivity of commutative subspace lattices.

Crystallization and phase transformation behaviour of electroless nickel-phosphorus deposits with low and medium phosphorus contents under continuous heating

Electroless nickel-phosphorus deposits with 5-8 wt% P and 3-5 wt% P were analysed for the effects of continuous heating on the crystallization kinetics and phase transformation behaviour of the deposits. The as-deposited coatings consist of a mixture of amorphous and microcrystalline nickel phases, featuring in their X-ray diffraction patterns. Continuous heating processes to 300C-800C at 20C/min were carried out on the deposits in a differential scanning calorimetric apparatus. The subsequent X-ray diffraction analyses show that the sequence of phase transformation process was: amorphous phase + microcrystalline nickel, f.c.c. nickel + Ni3P stable phases. Preferred orientation of nickel {200} plane developed in the deposits after the heating processes. Differential scanning calorimetry of the deposits indicates that the crystallization temperatures increased with decreasing phosphorus content, and increasing heating rate. Crystallization activation energies of the deposits (230 and 322 kJ/mol, respectively) were calculated using the peak temperatures of crystallization process, from the differential scanning calorimetric curves at the heating rates ranging from 5 to 50C/min. It was found that the deposit with lower phosphorus content has higher activation energy.

Correspondence between continuous-variable and discrete quantum systems of arbitrary dimensions

We establish a mapping between a continuous-variable (CV) quantum system and a discrete quantum system of arbitrary dimension. This opens up the general possibility to perform any quantum information task with a CV system as if it were a discrete system. The Einstein-Podolsky-Rosen state is mapped onto the maximally entangled state in any finite-dimensional Hilbert space and thus can be considered as a universal resource of entanglement. An explicit example of the map and a proposal for its experimental realization are discussed.