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.     

Effect of electrolyte type on the electrokinetic behavior of sulfonated polystyrene model colloids

Sulfonated polystyrene latex particles were prepared by a two-stage shot-growth emulsion polymerization process in the absence of emulsifier. Sodium styrene sulfonate (NaSS) was used as an ionic co-monomer to produce a series of latex particles with the same particle size but with different surface charge densities. The electrophoretic mobility of this functionalized model colloid was studied in the presence of various types of inorganic electrolytes. The _e curves of these latexes exhibit a pronounced maximum at high electrolyte concentrations: 5·10^–2 M for 11 electrolytes and 10^–2 M for 21 and 12 electrolytes. When a 31 electrolyte (LaCl₃) was used, the electrophoretic mobility changed to positive values at high concentration due to the specific adsorption of lanthanum species. The experimental results for the electrokinetic characterization of these sulfonated polystyrene model colloids suggest that the surface of the particles is covered by a layer of oligomers or polymer chains which shift the shear plane toward the bulk solution, increasing the anomalous surface conductance of the polystyrene microsphere-electrolyte solution interface.     

Optimal allocation of replicas in parallel tempering simulations

We have studied the efficiency of parallel tempering simulations for a variety of systems including a coarse-grained protein, an atomistic model polypeptide, and the Lennard-Jones fluid. A scheme is proposed for the optimal allocation of temperatures in these simulations. The method is compared to the existing empirical approaches used for this purpose. Accuracy associated with the computed thermodynamic quantities such as specific heat is also computed and their dependence on the trial-exchange acceptance rate is reported.