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This paper introduces a definition of reliability based on a process range. Thus, process failure is defined when the range of a process first reaches a given and unacceptable level. The Mean Time To Failure (MTTF) which is denned as the mean of the first time for a range to attain a given amplitude is then calculated for an asymmetric random walk process. The probability distribution of the range is then given and the process reliability over long periods of system operations are then calculated. Applications such as the control of wings movements, stock price and exchange rates volatility (defined in terms of reliability) are also used to motivate the usefulness of range processes in reliability studies. Finally, we point out that there is necessarily a relationship between the range reliability and the propensity of a series to become chaotic. 相似文献
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We consider the covariance matrix,G
mm
=q
2<(x,m);(y,m)>, of thed-dimensionalq-states Potts model, rewriting it in the random cluster representation of Fortuin and Kasteleyn. In any of theq ordered phases, we identify the eigenvalues of this matrix both in terms of representations of the unbroken symmetry group of the model and in terms of random cluster connectivities and covariances, thereby attributing algebraic significance to these stochastic geometric quantities. We also show that the correlation length corresponding to the decay rate of one of the eigenvalues is the same as the inverse decay rate of the diameter of finite clusers. For dimensiond=2, we show that this correlation length and the correlation length of the two-point function with free boundary conditions at the corresponding dual temperature are equal up to a factor of two. For systems with first-order transitions, this relation helps to resolve certain inconsistencies between recent exact and numerical work on correlation lengths at the self-dual point o. For systems with second order transitions, this relation implies the equality of the correlation length exponents from above and below threshold, as well as an amplitude ratio of two. In the course of proving the above results, we establish several properties of independent interest, including left continuity of the inverse correlation length with free boundary conditions and upper semicontinuity of the decay rate for finite clusters in all dimensions, and left continuity of the two-dimensional free boundary condition percolation probability at o. We also introduce DLR equations for the random cluster model and use them to establish ergodicity of the free measure. In order to prove these results, we introduce a new class of events which we call decoupling events and two inequalities for these events. The first is similar to the FKG inequality, but holds for events which are neither increasing nor decreasing; the second is similar to the van den Berg-Kesten inequality in standard percolation. Both inequalities hold for an arbitrary FKG measure. 相似文献
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Titania (TiO2) photocatalysts, each embedded with one of six metals (Ag, Ce, Co, Fe, Mg, and Mn), were prepared using a simplified ultrasonic process. The characteristics of the prepared metal-embedded TiO2 (metal–TiO2) were determined using transmission electron microscopy, energy-dispersive X-ray spectroscopy, X-ray diffraction spectroscopy, photoluminescence emission spectroscopy, UV–visible spectroscopy, and nitrogen adsorption–desorption. Except for Co–TiO2, the metal–TiO2 photocatalysts showed improved performance for the decomposition of gaseous benzene and toluene, which are two of the most problematic indoor air pollutants that can cause a variety of adverse health symptoms, under daylight lamp irradiation. Photocatalytic activity was greatest for the Mg–TiO2 sample, followed by, in order, the Ag–TiO2, Ce–TiO2, Fe–TiO2, Mn–TiO2, unmodified TiO2, and Co–TiO2 samples. Although Mg–TiO2 showed the least redshift in its light absorption and the highest electron–hole recombination rate among the metal–TiO2 photocatalysts, it yielded the highest photocatalytic activity, likely because of its increased adsorption capacity and anatase composition. The degradation of benzene and toluene over Mg–TiO2 improved as ultrasound treatment amplitude increased from 20 to 37 μm, then decreased gradually as amplitude was further increased to 49 μm. Degradation efficiency also improved as ultrasound operation time increased from 30 to 60 min, then decreased gradually as amplitude was further increased to 90 min. Overall, this process could be utilized to prepare metal–TiO2 photocatalysts with improved performance for the decomposition of gas phase pollutants under daylight lamp irradiation. 相似文献
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This paper addresses a previously unexplored regime of three-dimensional dissipative chaotic flows in which all but one of the nonlinearities are quadratic. The simplest such systems are determined, and their equilibria and stability are described. These systems often have one or more infinite lines of equilibrium points and sometimes have stable equilibria that coexist with the strange attractors, which are sometimes hidden. Furthermore, the coefficient of the single nonquadratic term provides a simple means for scaling the amplitude and frequency of the system. 相似文献
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Gold black coatings are deposited through a stencil shadow mask to produce infrared-absorbing patterns with sub-mm lateral dimensions. Such dimensions match the characteristic pitch of Long Wave Infrared (LWIR) array bolometers. Infrared spectral imaging with sub-micron spatial resolution reveals the spatial distribution of absorption across the pattern. 相似文献
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