Impedance and dielectric studies of ferroelectric SrBi2Nb2O9 ceramics

This paper reports the dielectric and impedance characteristics of ferroelectric SrBi₂Nb₂O₉ (SBN) ceramics in the 100 Hz-1 MHz frequency range at various temperatures (300-823 K). A strong low frequency dielectric dispersion (LFDD) associated with an impedance relaxation has been found to exist in these ceramics in the temperature range 573-823 K. The Z″ of the AC complex impedance showed two distinct slopes in the frequency range 100 Hz-1 MHz suggesting the existence of two dispersion mechanisms. This non-ideal behavior has been explained on the basis of the expression, Z*=R₀/(1+(iω/ω₁)^m+(iω/ω₂)ⁿ) [J. Phys. Chem. Solids 53 (1992) 1] where ω₁ and ω₂ characterize the lattice response and the charge carrier behavior, respectively. The exponents m and n were obtained from the curve fitting. The exponent n was found to exhibit a minimum at the Curie temperature, T_c (723 K) whereas the m was temperature independent.     

Non-Trivial t-Intersection in the Function Lattice

The function lattice, or generalized Boolean algebra, is the set of ℓ-tuples with the ith coordinate an integer between 0 and a bound n_i. Two ℓ-tuples t-intersect if they have at least t common nonzero coordinates. We prove a Hilton–Milner type theorem for systems of t-intersecting ℓ-tuples.Received September 29, 2004     

ΓD‐convergence for a class of quasilinear elliptic equations in thin structures

We study the asymptotic behaviour of the solution of a stationary quasilinear elliptic problem posed in a domain Ω^(ε) of asymptotically degenerating measure, i.e. meas Ω^(ε) → 0 as ε → 0, where ε is the parameter that characterizes the scale of the microstructure. We obtain the convergence of the solution and the homogenized model of the problem is constructed using the notion of convergence in domains of degenerating measure. Proofs are given using the method of local characteristics of the medium Ω^(ε) associated with our problem in a variational form. Copyright © 2005 John Wiley & Sons, Ltd.     

A direct independence proof of Buchholz's Hydra Game on finite labeled trees

We shall give a direct proof of the independence result of a Buchholz style-Hydra Game on labeled finite trees. We shall show that Takeuti-Arai's cut-elimination procedure of and of the iterated inductive definition systems can be directly expressed by the reduction rules of Buchholz's Hydra Game. As a direct corollary the independence result of the Hydra Game follows. Received: August 23, 1994 / Revised: July 24, 1995 and May 9, 1996     

Meeting infinitely many cells of a partition once

We investigate several versions of a cardinal characteristic defined by Frankiewicz. Vojtáš showed , and Blass showed . We show that all the versions coincide and that is greater than or equal to the splitting number. We prove the consistency of and of . Received: 2 October 1996 / Revised version: 22 May 1997     

Diffusing particles with electrostatic repulsion

Summary. We study a diffusion model of an interacting particles system with general drift and diffusion coefficients, and electrostatic inter-particles repulsion. More precisely, the finite particle system is shown to be well defined thanks to recent results on multivalued stochastic differential equations (see [2]), and then we consider the behaviour of this system when the number of particles goes to infinity (through the empirical measure process). In the particular case of affine drift and constant diffusion coefficient, we prove that a limiting measure-valued process exists and is the unique solution of a deterministic PDE. Our treatment of the convergence problem (as ) is partly similar to that of T. Chan [3] and L.C.G. Rogers - Z. Shi [5], except we consider here a more general case allowing collisions between particles, which leads to a second-order limiting PDE. Received: 5 August 1996 / In revised form: 17 October 1996     

A note on minimization problems and multistep methods

Summary. We use the qualitative properties of the solution flow of the gradient equation to compute a local minimum of a real-valued function . Under the regularity assumption of all equilibria we show a convergence result for bounded trajectories of a consistent, strictly stable linear multistep method applied to the gradient equation. Moreover, we compare the asymptotic features of the numerical and the exact solutions as done by Humphries, Stuart (1994) and Schropp (1995) for one-step methods. In the case of -stable formulae this leads to an efficient solver for stiff minimization problems. Received July 10, 1995 / Revised version received June 27, 1996     

Regularity of multiwavelets

The motivation for this paper is an interesting observation made by Plonka concerning the factorization of the matrix symbol associated with the refinement equation for B-splines with equally spaced multiple knots at integers and subsequent developments which relate this factorization to regularity of refinable vector fields over the real line. Our intention is to contribute to this train of ideas which is partially driven by the importance of refinable vector fields in the construction of multiwavelets. The use of subdivision methods will allow us to consider the problem almost entirely in the spatial domain and leads to exact characterizations of differentiability and Hölder regularity in arbitrary L _p spaces. We first study the close relationship between vector subdivision schemes and a generalized notion of scalar subdivision schemes based on bi-infinite matrices with certain periodicity properties. For the latter type of subdivision scheme we will derive criteria for convergence and Hölder regularity of the limit function, which mainly depend on the spectral radius of a bi-infinite matrix induced by the subdivision operator, and we will show that differentiability of the limit functions can be characterized by factorization properties of the subdivision operator. By switching back to vector subdivision we will transfer these results to refinable vectors fields and obtain characterizations of regularity by factorization and spectral radius properties of the symbol associated to the refinable vector field. Finally, we point out how multiwavelets can be generated from orthonormal refinable bi-infinite vector fields.     

Poincaré’s inequalities and Talagrand’s concentration phenomenon for the exponential distribution

Summary. We present a simple proof, based on modified logarithmic Sobolev inequalities, of Talagrand’s concentration inequality for the exponential distribution. We actually observe that every measure satisfying a Poincaré inequality shares the same concentration phenomenon. We also discuss exponential integrability under Poincaré inequalities and its consequence to sharp diameter upper bounds on spectral gaps. Received: 10 June 1996 / In revised form: 9 August 1996     

Maximal inner spaces and Hankel operators on the Bergman space

The paper deals with two closely related questions about the Bergman space of the unit disk. First, we investigate a special class of invariant subspaces of the Bergman space, namely, invariant subspaces induced by certain Hankel operators. We show that such spaces always have the co-dimension 1 or 2 property; and we determine exactly when such a space has the co-dimension 1 property. Second, we introduce the notion of inner spaces in the Bergman space and give several characterizations of when an inner space is maximal.Research supported by the National Science Foundation