Ergodic theory and the Strong Law of Large Numbers on Riesz spaces

In [W.-C. Kuo, C.C.A. Labuschagne, B.A. Watson, Discrete-time stochastic processes on Riesz spaces, Indag. Math. (N.S.) 15 (3) (2004) 435-451], we introduced the concepts of conditional expectations, martingales and stopping times on Riesz spaces. Here we formulate and prove order theoretic analogues of the Birkhoff, Hopf and Wiener ergodic theorems and the Strong Law of Large Numbers on Riesz spaces (vector lattices).     

牛顿第二定律实验中的误差分析

本文是通过对加速度的实验值和理论值进行比较和分析，给出误差的合理范围。     

Almost-sure path properties of fractional Brownian sheet

The almost sure sample function behavior of the vector-valued fractional Brownian sheet is investigated. In particular, the global and the local moduli of continuity of the sample functions are studied. These results give precise information about the continuity and the oscillation behavior of the sample functions.     

Study of migration of active components of phosphorescent oxygen sensors for food packaging applications

A study of migration of the active components of oxygen sensors into food is presented. Six types of sensors, based on different oxygen sensitive dyes (two metalloporphyrins and one ruthenium dye), polymers (polystyrene and polysulfone) and support materials, were exposed to a number of standard ‘food simulants’ recommended by FDA/EU guidelines and then assayed for migration or sensor components and changes in oxygen calibration. Both metalloporphyrin sensor dyes leached only in olive oil and in 95% ethanol (used as a positive control), at maximum levels of 19.22 μg/dm² for PtOEPK and 113.96 μg/dm² for PtTFPP. The RuDPP dye showed maximum leaching in 95% ethanol (25.19 μg/dm²) while also migrating in an acidic aqueous simulant. Planar supports such as polyester tended to enhance the stability of the sensor. Migration of the styrene monomer from the polystyrene encapsulation medium was concluded to be low enough to be insignificant. Migration of sensor components was shown to correlate with the changes in sensor response to oxygen. Based on these results, sensor combinations were ranked on the basis of their resistance to leaching and their general stability, safety and suitability for use on a large scale in packaged foods and related food applications was proven.     

Solid-phase microextraction for qualitative and quantitative determination of migrated degradation products of antioxidants in an organic aqueous solution

Low molecular weight aromatic substances may migrate out from plastic packaging to their contents, especially if they consist of organic aqueous solutions or oils. It is, therefore, extremely important to be able to identify and quantify any migrated substances in such solutions, even at very low concentrations. We have in this work investigated and evaluated the use of solid-phase microextraction for the specific task of extraction from an organic aqueous solution such as a simulated pharmaceutical solution consisting of 10 vol.% ethanol in water. The goal was furthermore to investigate the possibility of simultaneously identifying and quantifying the substances in spite of differences in their chemical structures. Methods were developed and evaluated for extraction both with direct sampling and with headspace sampling. Difficulties appeared due to the ethanol in the solution and the minute amounts of substances present. We have shown that a simultaneous quantification of migrated low molecular weight degradation products of antioxidants using only one fibre is possible if the extraction method and temperature are adjusted in relation to the concentration levels of the analytes. Comparions were made with solid-phase extraction.     

A law of the iterated logarithm for processes with independent increments

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Molecular orbital study for Na, Mg, and Al adsorption on the Si (111) surface

We investigated the interactions between the Si(111) surface and the Na, Mg, and Al atoms using cluster model calculations. Calculations were performed at levels of complete-active-space self-consistent-field (CASSCF) and multi-reference singly and doubly excited configuration interaction (MRSDCI) calculations using the model core potential method. Our calculations revealed that the most favorable sites of Na, Mg, and Al adsorption on Si(111) are on top (T₁), bridge (B₂), and 3-fold filled (T₄) sites, respectively. The nature of chemical bonds between these metal atoms and the dangling bonds of the surface Si atoms are found to be essentially covalent.     

A rapid HPIC method for the quantitative determination of tetramethylammonium chloride in some aqueous solutions used as food simulants

Summary The present paper reports a rapid HPIC method for the determination of tetramethylammonium chloride in aqueous matrices which are used as food simulants in migration tests. These simulants were: bidistilled water, an aqueous solution of 3% acetic acid, an aqueous solution of 15% ethyl alcohol, a mixed aqueous solution of 3% acetic acid and 15% ethyl alcohol. The method, as developed, has been applied to the determination of unreacted tetramethylammonium chloride residues which are able to migrate from finished epoxy resins which are used as food packaging materials.Research partially supported by National Research Council of Italy, Special Project RAISA, sub-project 4, Paper N^o 695.