APPROXIMATION OPERATORS AND SELFSIMILARITY OVER P-ADIC FIELD

Fourier analysis on local fields has been developed since M. H. Taiblesoa, Some of its theory and technique are much similar to the classical ones while some are not and even have not appropriately mathematical toolS to deal with. Recently we find there are a few but interesting applications to fractals ,especial to self-similar functions of the p-adic analysis and such a setting seems to be natural. This note also includes a concept of a derivative and approximation operators.     

Scaling in the bombay stock exchange index

In this paper we study Bombay stock exchange (BSE) index financial time series for fractal and multifractal behaviour. We show that BSE index time series is monofractal and can be represented by a fractional Brownian motion.     

Local field enhancements on gold and silver nanostructures for aperture near field spectroscopy

Optical properties of silver and gold semi-continuous films near the percolation threshold are investigated by scanning near field optical microscopy (SNOM) operating in the collection/transmission mode. The electromagnetic enhanced fields, due to plasmon-polariton localizations, are observed and the intensity distribution is shown to present high intensity variations that increase with the wavelength. The local fields are also demonstrated to be polarization dependent. The intensity distribution is investigated as function of the incident wavelength both for gold and silver films. The calculated probability distribution function (PDF) exhibits an exponential decay for large enhancement factors and is proved to be wavelength dependent.     

Fractal aggregates induced by liposome-liposome interaction in the presence of Ca2+

We present a study of the fractal dimension of clusters of large unilamellar vesicles (LUVs) formed by egg yolk phosphatidylcholine (EYPC), dimyristoylphosphocholine (DMPC) and dipalmitoylphosphocholine (DPPC) induced by Ca²⁺ . Fractal dimensions were calculated by application of two methods, measuring the angular dependency of the light scattered by the clusters and following the evolution of the cluster size. In all cases, the fractal dimensions fell in the range from 2.1 to 1.8, corresponding to two regimes: diffusion-limited cluster aggregation (DLCA) and reaction-limited cluster aggregation (RLCA). Whereas DMPC clusters showed a typical transition from the RLCA to the DLCA aggregation, EYPC exhibited an unusual behaviour, since the aggregation was limited for a higher concentration than the critical aggregation concentration. The behaviour of DPPC was intermediate, with a transition from the RLCA to the DLCA regimes with cluster sizes depending on Ca²⁺ concentration. Studies on the reversibility of the aggregates show that EYPC and DPPC clusters can be re-dispersed by dilution with water. DMPC does not present reversibility. Reversibility is evidence of the existence of secondary minima in the DLVO potential between two liposomes. To predict these secondary minima, a correction of the DLVO model was necessary taking into account a repulsive force of hydration.     

Analysis on Fractal Objects

Irregular objects are often modeled by fractals sets. In order to formulate partial differential equations on these nowhere differentiable sets the development of a “new analysis” is necessary. With the help of the model case of the Sierpinski gasket the definition of energy forms and Laplacians on self-similar finitely ramified fractals is explained. Moreover, some results for certain classes of non-self-similar fractals are presented. 2000 Math. Subj. Class.: Primary 28A80, 35J15; Secondary 31C25, 35P05     

Algorithm for determining pure pointedness of self-affine tilings

Overlap coincidence in a self-affine tiling in Rd is equivalent to pure point dynamical spectrum of the tiling dynamical system. We interpret the overlap coincidence in the setting of substitution Delone set in Rd and find an efficient algorithm to check the pure point dynamical spectrum. This algorithm is easy to implement into a computer program. We give the program and apply it to several examples. In the course of the proof of the algorithm, we show a variant of the conjecture of Urbański (Solomyak (2006) [40]) on the Hausdorff dimension of the boundaries of fractal tiles.     

一类融合逼近和插值的曲线细分

采用生成多项式为主的方法对一类融合逼近和插值三重细分格式的支撑区间、多项式生成、连续性、多项式再生及分形性质进行了分析,给出并证明了极限曲线C^k连续的充分条件.通过对融合型细分规则中参数变量的适当选择来实现对极限曲线的形状调整,从而衍生出具有良好性质的新格式,并将这类新格式与现有格式进行比较.数值实例表明这类新格式生成的极限曲线具有较好的保形性.     

First order phase change detection using planar waveguide Bragg grating refractometer

Solid-to-liquid and gas-to-liquid phase changes in water and ordered-to-isotropic phase changes in a nematic liquid crystal are detected with an optical sensor. A planar Bragg grating defined purely by refractive index modulation is covered with a water or liquid crystal overcladding and the temperature is controlled to trigger phase changes. Measurement of the Bragg wavelength allows changes of effective refractive index to be detected and discontinuities in behaviour caused by phase transitions can be clearly identified.     

Radiative lifetimes of the NaRb C(3)1Σ+ state: experiment and theory

Radiative lifetimes for 2≤v^′≤44 rovibronic C¹Σ⁺ state levels of NaRb and quenching collision cross-sections with Rb atoms have been directly measured in a thermal cell by detecting time resolved laser induced fluorescence after pulsed excitation. Many body multipartitioning theory was applied to calculate C¹Σ⁺-X¹Σ⁺ and C¹Σ⁺-A¹Σ⁺ transition dipole moments. The relevant ab initio matrix elements were converted to the C¹Σ⁺ state radiative lifetimes. The strong spin-orbit A¹Σ⁺∼ b³Π coupling effect on the total C → A transition probabilities and lifetimes of the C¹Σ⁺ state is discussed. The measured radiative lifetimes show a decrease from 61 to 34 ns as the v^′ values increase, the results being in good agreement with calculations. The averaged collisional quenching cross-section value σ=(3±1)×10^-14 cm² was determined for NaRb (C¹Σ⁺) + Rb collisions from the Stern-Volmer plots.