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In this paper, we propose preconditioned Krylov-subspace iterative methods to perform efficient DC and transient simulations for large-scale linear circuits with an emphasis on power delivery circuits. We also prove that a circuit with inductors can be simplified from MNA to NA format, and the matrix becomes an s.p.d matrix. This property makes it suitable for the conjugate gradient with incomplete Cholesky decomposition as the preconditioner, which is faster than other direct and iterative methods. Extensive experimental results on large-scale industrial power grid circuits show that our method is over 200 times faster for DC analysis and around 10 times faster for transient simulation compared to SPICE3. Furthermore, our algorithm reduces over 75% of memory usage than SPICE3 while the accuracy is not compromised.

The newly developed marketing channel of electronic commerce (EC) is different from traditional channels and has been promoted by the government for a period of time. In EC, integrated information is not only provided to the enterprises involved but the procedures needed for trade are fewer, promoting environmentally friendly practices. It has, however, caused great variation in the business environment. The e‐invoice plays a vital role in keeping track of cash and business information, and its implementation will help to convert the whole supply chain to electronic form and lower overall operational costs. At present, e‐invoices are only used in certain situations such as for online shopping, for electronic purchases by suppliers, in value‐added networks, and so on. They are not applied in daily life or used by the public. However, a mobile e‐invoice system can be designed to connect the e‐invoice to the Web for the ordinary user. In this era of the mobile interactive Internet use, where individual computers interact with one another, this will help in the application of many kinds of network and real‐life services. © 2012 Wiley Periodicals, Inc.

The general approach to modeling binary data for the purpose of estimating the propagation of an internal solitary wave (ISW) is based on the maximum likelihood estimate (MLE) method. In cases where the number of observations in the data is small, any inferences made based on the asymptotic distribution of changes in the deviance may be unreliable for binary data (the model's lack of fit is described in terms of a quantity known as the deviance). The deviance for the binary data is given by D. Collett (2003). may be unreliable for binary data. Logistic regression shows that theP-values for the likelihood ratio test and the score test are both<0.05. However, the null hypothesis is not rejected in the Wald test. The seeming discrepancies inP-values obtained between the Wald test and the other two tests are a sign that the large-sample approximation is not stable. We find that the parameters and the odds ratio estimates obtained via conditional exact logistic regression are different from those obtained via unconditional asymptotic logistic regression. Using exact results is a good idea when the sample size is small and the approximateP-values are<0.10. Thus in this study exact analysis is more appropriate.

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