Remarks on power structures

Chris Brink, in his paper,Power Structures, describes the construction ofgeneralized quotient algebras. IfA is any algebra, the corresponding generalized quotient algebraA/R is defined for every value-preserving relation . As we will see in the present paper, in order to make the corresponding operations on the setA/R well-defined, it is not enough forR to be value-preserving. The only redundancy in the definition of the usual quotient algebra is symmetry.Presented by G. Grätzer.     

On norm dependent positive definite functions

In the first part of the paper we prove a decomposition theorem for positive definite functions (Theorem 2.3) generalizing a result of de Leeuw and Glicksberg. Using this theorem, we then show (Theorem 3.1) that certain norm dependent positive definite functions are automatically continuous at every point different from zero.     

On lower bounds for theL 2-Wasserstein metric in a Hilbert space

We provide two families of lower bounds for theL ²-Wasserstein metric in separable Hilbert spaces which depend on the basis chosen for the space. Then we focus on one of these families and we provide a necessary and sufficient condition for the supremum in it to be attained. In the finite dimensional case, we identify the basis which provides the most accurate lower bound in the family.Research partially supported by the Spanish DGICYT under grants PB91-0306-02-00, 01 and 02.     

Continuous additive functions and difference equations of infinite order

Пустьq∈(1, 2) иL=(q?1)^?1. Дляz∈[0,L] обозначимδ(z) функцию, для которойδ(z)=1, еслиz≧1/q иδ(z)=0, еслиz<1/q. Пустьy(z) определяется из урав ненияz= =δ(z)q ^?1+y(z)q ^?1, и регулярное представление \(\mathop \Sigma \limits_{n = 1}^\infty \varepsilon _n \left( x \right)q^{ - n} \) аргументах определя ется из следующих соотношен ий: $$x = x_0 , \varepsilon _n \left( x \right) = \delta \left( {x_n } \right), x_{n + 1} = y\left( {x_n } \right).$$ ФункцияF: [0,L]→C называе тся аддитивной, если о на представляется в вид е $$F\left( x \right) = \mathop \Sigma \limits_{n = 1}^\infty \varepsilon _n \left( x \right)a_n ,$$ где ε ¦a _n ¦<∞. «Бесконеч ное» представление 1=εl _i q ^?1 числа 1 определяется с ледующим образом: еслие _n (1)=1 для б есконечно многихп, т оl _n =ε _n (1) (n=1, 2, ...); если ? максим альный индекс, для которогоε _s (1)=1, то $$l_{ks + 1} = \left\{ \begin{gathered} \varepsilon _i \left( 1 \right) \left( {k = 0, 1, 2, ...; i = 1, ..., s - 1} \right) \hfill \\ 0 \left( {i = 0; k = 1, 2, ...} \right). \hfill \\ \end{gathered} \right.$$ В более ранней работе, опубликованной в это м журнале, авторы доказали, что а ддитивная функция является неп рерывной на отрезке [0,L] тогда и только тогда, когда ра венство $$a_n = \mathop \Sigma \limits_{i = 1}^\infty l_i a_{n + 1} $$ выполняется для всехn∈N. В настоящей работе ра ссматриваются непре рывные функции для которых в ыполняются дополнительные усло вия видаa _n =O(q ^??n ) (0a _n ≧0. Анализируются их свя зи с корнями функцииG(z)=1 +ε l _i z ⁱ . Доказы вается, что непрерывн ая аддитивная функция и ли вляется линейной, или нигде не дифференцир уема на отрезке [0,L].     

Possible Loss and Recovery of Gibbsianness¶During the Stochastic Evolution of Gibbs Measures

We consider Ising-spin systems starting from an initial Gibbs measure ν and evolving under a spin-flip dynamics towards a reversible Gibbs measure μ≠ν. Both ν and μ are assumed to have a translation-invariant finite-range interaction. We study the Gibbsian character of the measure νS(t) at time t and show the following: (1) For all ν and μ, νS(t) is Gibbs for small t. (2) If both ν and μ have a high or infinite temperature, then νS(t) is Gibbs for all t > 0. (3) If ν has a low non-zero temperature and a zero magnetic field and μ has a high or infinite temperature, then νS(t) is Gibbs for small t and non-Gibbs for large t. (4) If ν has a low non-zero temperature and a non-zero magnetic field and μ has a high or infinite temperature, then νS(t) is Gibbs for small t, non-Gibbs for intermediate t, and Gibbs for large t. The regime where μ has a low or zero temperature and t is not small remains open. This regime presumably allows for many different scenarios. Received: 26 April 2001 / Accepted: 10 October 2001     

Radiation pressure over dielectric and metallic nanocylinders on surfaces: polarization dependence and plasmon resonance conditions

Multiple scattering calculations of the electromagnetic force and the potential energy exerted by an evanescent field on a nanometric cylinder over a dielectric interface, as well as by a propagating Gaussian beam, are carried out. These calculations constitute a model that describes the gradient, scattering, and absorption components of the force in an elongated particle. The attractive or repulsive nature of the force is strongly dependent on the polarization of the incident field for a metallic particle, whereas a dielectric particle is only weakly attracted to high-intensity regions. Excitation of plasmon resonance in a metallic particle enhances both the scattering and the absorption components of the force, whereas it diminishes the gradient-force component.     

Infrared picosecond absorption spectroscopy of microcrystalline silicon: separation between carrier recombination in crystalline and amorphous fractions

We have studied ultra-fast carrier dynamics of photo-excited carriers in hydrogenated microcrystalline silicon prepared by a very high frequency glow-discharge technique. We report on direct observation of two types of dynamics using selective photo-excitation in picosecond pump and probe measurements. One type of the observed dynamics has been found to be independent of the sample preparation, while the other reflects the relative weights of crystalline and amorphous fractions. We propose a simple rate-equation model that describes the carrier dynamics in microcrystalline silicon in terms of the composition of those in Si microcrystallites and in the a-Si:H tissue which surrounds the microcrystallites. The model without any fitting parameters reproduces the experimental data very well when the dynamics are scaled with relative volume fractions as obtained from Raman spectra. Received: 23 November 2000 / Accepted: 17 March 2001 / Published online: 23 May 2001     

Magnetic Study of Doped Ba Ferrites Prepared by Citrate Method

The M-type barium ferrite is doped with either Co²⁺-Ti⁴⁺ or Co²⁺-Zr⁴⁺ pairs to reduce its intrinsically high uniaxial magnetic anisotropy in order to make fine particles for magnetic recording. The magnetic parameters were investigated by magnetic measurements and the Mössbauer spectroscopy. Compounds (BaF) obtained from BaCo _x (Ti,Zr) _x Fe_12-2x O₁₉ with 0x1.0 have been prepared by the modified citrate method with the initial ratio of Ba:Fe equal to 1:10.8. The substitution of Co - Ti or Co - Zr for Fe³⁺ ions affects mainly the positions 2a and 4f ₂. Ba ferrite with the substitution x 0.8 is promising for perpendicular recording media applications.     

Time-Resolved Fluorescence Spectroscopy Study on the Photophysical Behavior of Quantum Dots

Room-temperature time-resolved luminescence measurements on single CdSe/ZnS quantum dots (QDs) are presented. Fluorescence emission spectra were recorded over periods of up to 30 minutes with a time resolution as small as 6 ms. For QDs in ambient air, a clear 30–40 nm blue shift in the emission wavelength is observed, before the luminescence stops after about 2–3 minutes because of photobleaching. In a nitrogen atmosphere, the blue shift is absent while photobleaching occurs after much longer times (i.e., 10–15 minutes). These observations are explained by photoinduced oxidation. The CdSe surface is oxidized during illumination in the presence of oxygen. This effectively results in shrinkage of the CdSe core diameter by almost 1 nm and consequently in a blue shift. The faster fading of the luminescence in air suggests that photoinduced oxidation results in the formation of non-radiative recombination centers at the CdSe/CdSeO_x interface. In a nitrogen atmosphere, photoinduced oxidation is prevented by the absence of oxygen. Additionally, a higher initial light output for CdSe/ZnS QDs in air is observed. This can be explained by a fast reduction of the lifetime of the long-lived defect states of CdSe QDs by oxygen.