Predictability and stopping on lattices of sets

Summary As a first step in the development of a general theory of set-indexed martingales, we define predictability on a general space with respect to a filtration indexed by a lattice of sets. We prove a characterization of the predictable -algebra in terms of adapted and left-continuous processes without any form of topology for the index set. We then define a stopping set and show that it is a natural generalization of the stopping time; in particular, the predictable -algebra can be characterized by various stochastic intervals generated by stopping sets.Research supported by a grant from the Natural Sciences and Engineering Research Council of CanadaResearch partially done while the second author was visiting the University of Ottawa. He wishes to thank the Department of Mathematics for its hospitality     

Studies on the Non-Isothermal Decomposition of H3PMo12O40·xH2O and H4PVMo11O40·yH2O

This paper reports a comparative study of the non-isothermal decompositions of the heteropolyacids HPM and HPVM, with structures consisting of Keggin units (KUs). Non-isothermal analysis at low heating rates demonstrated the existence of 4 crystal hydrate species, depending on the temperature. The stability domains of the anhydrous forms of HPM and HPVM were found to be 150–380°C, respectively. Processing of the TG curves obtained at different heating rates by the Ozawa method revealed that the decomposition of anhydrous HPM takes place according to a unitary mechanism, whilst for anhydrous HPVM two mechanisms are observed. Thus, the first part of the constitution water is lost simultaneously with the departure of vanadium from the KU as VO²⁺, while the second part is lost at higher temperatures as in the case HPM. This revised version was published online in August 2006 with corrections to the Cover Date.     

The effect of series resistance on capacitance-voltage characteristics of Schottky barrier diodes

The capacitance-voltage (C-V) and current-voltage (I-V) characteristics of the Ti/p-Si Schottky barrier diodes (SBDs) have been investigated taking into account the effect of the interface states and series resistance of the device. The forward C-V measurements have been carried out in the range frequency of 0.3-2 MHz (at six different frequencies). It is seen that the forward C-V plots exhibit anomalous peaks in the presence of a series resistance. It has been experimentally determined that the peak positions in the C-V plot shift towards lower voltages and the peak value of the capacitance decreases with increasing frequency. In addition to, the effect of series resistance on the capacitance is found appreciable at higher frequencies due to the capacitance decreases with increasing frequency.     

Synthesis of novel rhodium‐xylyl linked N‐heterocyclic carbene complexes as hydrosilylation catalysts

Reaction of ortho‐xylylbis(N‐2,4,6‐trimethylbenzylimidazolinium); xylylbis(N‐butylimidazolinium) and para‐xylylbis(N‐2,4,6‐trimethylbenzylimidazolinium); xylylbis(N‐butylimidazolinium) salts with KOBu^t and [RhCl(COD)]₂ yields ortho‐ and para‐xylylbis{(N‐alkylimidazolidin‐2‐ylidene)chloro(η⁴‐1,5‐cyclooctadiene) rho dium(I)} complexes (2a–d). All compounds synthesized were characterized by elemental analysis and NMR spectroscopy, and the molecular structures of the 2a and 2d were determined by X‐ray crystallography. Triethylsilane reacts with acetophenone derivatives in the presence of catalytic amount of the new rhodium(I)–carbene complexes (2a–d), to give the corresponding silylethers in good yields (83–99%). Copyright © 2008 John Wiley & Sons, Ltd.     

Manufacturer’s mixed pallet design problem

We study a problem faced by a major beverage producer. The company produces and distributes several brands to various customers from its regional distributors. For some of these brands, most customers do not have enough demand to justify full pallet shipments. Therefore, the company decided to design a number of mixed or “rainbow” pallets so that its customers can order these unpopular brands without deviating too much from what they initially need. We formally state the company’s problem as determining the contents of a pre-determined number of mixed pallets so as to minimize the total inventory holding and backlogging costs of its customers over a finite horizon. We first show that the problem is NP-hard. We then formulate the problem as a mixed integer linear program, and incorporate valid inequalities to strengthen the formulation. Finally, we use company data to conduct a computational study to investigate the efficiency of the formulation and the impact of mixed pallets on customers’ total costs.     

Chaoticity analysis of the current through pure, hydrogenated and hydrophobically modified PEG-Si thin films under varying relative humidity

Polyethylene Glycol has an irregular current characteristic under constant voltage and slowly varying relative humidity. The current through a thin film of Gamma-isocyanatopropyltriethoxysilane added Polyethylene glycol (PEG-Si), its hydrogenated and hydrophobically modified forms, as a function of increasing relative humidity at equal time steps is analyzed for chaoticity. We suggest that the irregular behavior of current through PEG-Si thin films as a function of increasing relative humidity could best be analyzed for chaoticity using both time series analysis and detrended uctuation analysis; the relative humidity is kept as a slowly varying parameter. The presence of more then one regime is suggested by the calculation of the maximal Lyapunov exponents. Furthermore, the maximal Lyapunov exponent in each of the regimes was positive, thus confirming the presence of low dimensional chaos. DFA also confirms the presence of at least two different regimes, in agreement with the behavior of the maximal Lyapunov exponent in the time series analysis. We also suggest that the irregular behavior of the current through PEG-Si can be reduced by hydrogenating and hydrophobically modifying PEG-Si and the improvement in stability can be confirmed by our study.      

Investigation of radiosterilization feasibility of sulfamethoxazole by ESR spectroscopy

In the present study, the spectroscopic features of the radiolytic intermediates that were produced in gamma-irradiated (5, 10, 25 and 50?kGy) sulfamethoxazole (SMX) have been investigated by electron spin resonance (ESR) spectroscopy and the radiation sterilization feasibility of SMX by ionizing radiation was examined. Gamma-irradiated SMX exhibited a complex ESR spectrum consisting of 13 resonance lines where spectral parameters for the central resonance line were found to be g?=?2.0062 and ΔH_pp?=?0.6?mT. The radiation yield of SMX was calculated to be relatively low (G?=?0.1) by ESR spectroscopy and no meaningful difference was observed in the comparison of unirradiated and 50?kGy gamma irradiated SMX by the Fourier transform infrared (FT-IR) technique, confirming that SMX is a radioresistive material. Although SMX could not be accepted to be a good dosimetric material, the identification of irradiated SMX from the unirradiated sample was possible even for the low absorbed radiation doses and for a relatively long time (three months) after the irradiation process. Decay activation energy of the radical species, which is mostly responsible for the central intense resonance line, is calculated to be 45.15?kJ/mol by using the signal intensity decay data derived from annealing studies. Four radical species with different spectroscopic properties were accepted to be responsible for the ESR spectra of gamma-irradiated SMX, by simulation calculations. It is concluded that SMX and SMX-containing drugs can be sterilized by gamma radiation and ESR spectroscopy is an appropriate technique for the characterization of these induced radical intermediates during the gamma irradiation process of SMX. Toxicology tests should also be done for its safe usage.     

Graybody radiation phenomena in a fractional manner

In this paper, the graybody radiation phenomena has been handled with the help of fractional calculus. Fractional definition of graybody spectrum has been written in terms of Mittag‐Leffler function. The obtained data from fractional calculus approximation for nearly 2.87 × 10⁷ K have been compared with literature values and standard blackbody radiation.