Numerical calculation of domains of analyticity for perturbation theories in the presence of small divisors

We study numerically the complex domains of validity for KAM theory in generalized standard mappings. We compare methods based on Padé approximants and methods based on the study of periodic orbits.     

A multineuron interaction model for neural networks

A multineuron interaction model (RS model) with an energy function given by the product of the squared distances in phase space between the state of the net and the stored patterns is studied in detail within a mean-field approach. Two limits are considered: when the patterns and antipatterns are stored (as in the Hopfield model), PAS case, and when only the patterns are taken into account, OPS case. TheT=0 solutions for the proper memories are exactly obtained for all finite values of, as a consequence of the energy function: whenever one of the overlaps is exactly one the corresponding equations decouple and no configuration average is required. Special interest is focused on the OPS situation, which presents a peculiar phase space topology. On the other hand, the PAS configuration recovers the Hopfield model in the appropriate limit, while keeping associative memory abilities far beyond the critical values of other models when the full Hamiltonian is considered.     

On blocking sets in symmetric BIBD's with λ⩾2

Blocking sets in symmetric BIBD's with 2 are defined and bounds for their sizes are found. Thus, some results known in projective planes are generalized to symmetric BIBD's.     

MPT versus: A manifestly covariant presentation of motion reversal and particle-antiparticle exchange

We show that particle-antiparticle exchange and covariant motion reversal are two physically different aspects of the same mathematical transformation, either in the prequantal relativistic equation of motion of a charged point particle, in the general scheme of second quantization, or in the spinning wave equations of Dirac and of Petiau-Duffin-Kemmer. While, classically, charge reversal and rest mass reversal are equivalent operations, in the wave mechanical case mass reversal must be supplemented by exchange of the two adjoint equations, implying .Denoting by M the rest mass reversal, P the parity reversal, T the Racah time reversal, and Z the exchange, the connection with the usual scheme of charge conjugation, parity reversal, and Wigner motion reversal, is with, of course,     

The luminescence of Pr3+ in BaY4Si5O17

The cell constants of four new monoclinic compounds BaR₄X₅O₁₇ (R = Y, Gd; X = Si, Ge) are given. The luminescence of various RE activators in the silicates is reported. Pr³⁺-activated BaY₄Si₅O₁₇ shows efficient ultraviolet 5d → 4f emission and weak 4f → 4f emission (mainly red luminescence from the ¹D₂ level). The 5d → 4f emission is ascribed to Pr³⁺ on Y sites, the 4f → 4f emission to Pr³⁺ on Ba sites. Energy transfer from Pr³⁺ to Gd³⁺ has been observed. Gd³⁺ plays an intermediate role in the energy transfer from Pr³⁺ to Sm³⁺ and to Dy³⁺ in BaGd₄Si₅O₁₇. Upon activation with Tb³⁺ the silicates show characteristic green Tb³⁺ luminescence with a quantum efficiency of 75% for ultraviolet excitation.