Preparation and Characterization of Compositions Based on PbO-MgO-Nb2O5 Using the Sol-Gel Method

Lead Magnesium Niobate, Pb(Mg_1/3Nb_2/3)O₃ (PMN), is an important relaxor ferroelectric material. A significant problem exists, however, in the preparation of this material: it is very difficult to prepare pure phase, without the presence of a pyrochlore impurity phase which degrades the dielectric properties. Depending on the processing conditions, the amount of pyrochlore phase varies.Considering the ternary diagram PbO-MgO-Nb₂O₅, different compositions have been prepared by a simple sol-gel method at room temperature using Pb(CH₃COO)₂, Mg(CH₃COO)₂, Nb(OC₂H₅)₅ as precursors. After the heat treatment, the samples obtained were analyzed by XRD and EPMA with the purpose of studying the compositions formed.From the analysis of these results, it seems to be that the appearance of pyrochlore can be related to the reactivity of the MgO and/or the presence of other phases of the binary system PbO-Nb₂O₅. An excess of Pb and Mg is necessary for compositions to be formed near the PMN. The control of the amount of these two elements is very important because an excess of MgO would lead to rich compositions in Mg as a secondary phase.     

Effect of pressure on the proton transfer rate from a photoacid to a solvent. 4. Photoacids in methanol

The pressure dependence of the excited-state proton dissociation rate constant of four photoacids, 2-naphthol-6,8-disulfonate (2N68DS), 10-hydroxycamptothecin (10-CPT), 5-cyano-2-naphthol (5CN2), and 5,8-dicyano-2-naphthol (DCN2), are studied in methanol. The results are compared with the results of the pressure dependence study we recently conducted for several photoacids in water, ethanol, and propanol. The pressure dependence is explained using an approximate stepwise two-coordinate proton transfer model. The increase in rate, as a function of pressure, manifests a strong dependence of proton tunneling on the distance which decreases with an increase of pressure between the two oxygen atoms involved in the process. The decrease in the proton transfer rate with increasing pressure reflects the dependence of the reaction on the solvent relaxation rate. We found that, for the relatively weak photoacids 2N68DS, 10-CPT, and 5CN2, the proton transfer rate constant increases by a factor of about 5-8 at a pressure of about 1.5 GPa. For a strong photoacid like DCN2, the rate increase was only by a factor of 2.     

Extension of smooth functions from finitely connected planar domains

Consider the Sobolev space W _∞ ^k (Ω) of functions with bounded kth derivatives defined in a planar domain. We study the problem of extendability of functions from W _∞ ^k (Ω) to the whole ℝ² with preservation of class, i.e., surjectivity of the restriction operator W _∞ ^k (ℝ²) → W _∞ ^k (Ω).     

On the Lipschitz classification of normed spaces, unit balls, and spheres

For every normed space , we note its closed unit ball and unit sphere by and , respectively. Let and be normed spaces such that is Lipschitz homeomorphic to , and is Lipschitz homeomorphic to .

We prove that the following are equivalent:

1. is Lipschitz homeomorphic to .

2. is Lipschitz homeomorphic to .

3. is Lipschitz homeomorphic to .

This result holds also in the uniform category, except (2 or 3) 1 which is known to be false.

     

Geometric structure of b 2,2-orbihedra and interpolation of operators

We compute the normals to faces of b _2,2-orbihedra and apply the results to Operator Interpolation Theory.     

The concert queueing game: strategic arrivals with waiting and tardiness costs

We consider the noncooperative choice of arrival times by individual users, who seek service at a first-come first-served queueing system that opens up at a given time. Each user wishes to obtain service as early as possible, while minimizing the expected wait in the queue. This problem was recently studied within a simplified fluid-scale model. Here, we address the unscaled stochastic system, assuming a finite (possibly random) number of homogeneous users, exponential service times, and linear cost functions. In this setting, we establish that there exists a unique Nash equilibrium, which is symmetric across users, and characterize the equilibrium arrival-time distribution of each user in terms of a corresponding set of differential equations. We further establish convergence of the Nash equilibrium solution to that of the associated fluid model as the number of users is increased. We finally consider the price of anarchy in our system and show that it exceeds 2, but converges to this value for a large population size.     

and interpolation between Banach lattices

We study the possibility of obtaining the -norm by an interpolation method starting from a couple of Banach lattice norms. We describe all couples of Banach lattice norms in such that the -norm is a strict interpolation norm between them. Further we consider the possibility of obtaining the -norm by any method which guarantees interpolation of not only linear operators (= bilinear forms on but also of all polylinear forms. Here we show that either one of the initial norms has to be proportional to the -norm, or both have to be weighted -norms.

     

Geometric structure of b2,2-orbihedra and interpolation of operators

We compute the normals to faces of b_2,2-orbihedra and apply the results to Operator Interpolation Theory.     

Linear preservers of isomorphic types of lattices of invariant operator ranges

We describe all linear self-mappings of the space of bounded linear operators in an infinite dimensional separable complex Hilbert space which preserve the isomorphism class of the lattice of invariant operator ranges.