Explicit solutions to some nonlinear physical models by a two-step ansatz

Explicit solutions are derived for some nonlinear physical model equations by using a delicate way of two-step ansatz method.

A two-step approach to investigate the effect of rating curve uncertainty in the Elbe decision support system

For river basin management, the reliability of the rating curves mainly depends on the accuracy and time period of the observed discharge and water level data. In the Elbe decision support system (DSS), the rating curves are combined with the HEC-6 model to investigate the effects of river engineering measures on the Elbe River system. In such situations, the uncertainty originating from the HEC-6 model is of significant importance for the reliability of the rating curves and the corresponding DSS results. This paper proposes a two-step approach to analyze the uncertainty in the rating curves and propagate it into the Elbe DSS: analytic method and Latin Hypercube simulation. Via this approach the uncertainty and sensitivity of model outputs to input parameters are successfully investigated. The results show that the proposed approach is very efficient in investigating the effect of uncertainty and can play an important role in improving decision-making under uncertainty.

A two-step rectification algorithm for airborne linear images with POS data

Rectification for airborne linear images is an indispensable preprocessing step. This paper presents in detail a two-step rectification algorithm. The first step is to establish the model of direct georeference position using the data provided by the Po- sitioning and Orientation System (POS) and obtain the mathematical relationships between the image points and ground reference points. The second step is to apply polynomial distortion model and Bilinear Interpolation to get the final precise rectified images. In this step, a reference image is required and some ground control points (GCPs) are selected. Experiments showed that the final rectified images are satisfactory, and that our two-step rectification algorithm is very effective.

Effect of inlet temperature and equivalence ratio on HCCI engine performance fuelled with ethanol:Numerical investigation

A numerical model is presented to investigate the performance of homogeneous charge compression ignition(HCCI) engines fueled with ethanol. Two approaches are studied. On one hand, two-step reaction mechanisms with Arrhenius reaction rates are implemented in combustion chemistry modeling. On the other hand, a reduced mechanism containing important reactions of ethanol involving heat release rate and reaction rates compatible with experimental data is employed. Since controls of combustion phenomenon and ignition timing are the main issues of these engines, the effects of inlet temperature and equivalence ratio as the controlling factors on the operating parameters such as ignition timing, burn duration, in-cylinder temperature and pressure of HCCI engines are explored. The results show that the maximum predicted pressures for thermodynamic model are about 71.3×10~5 Pa and 79.79×10~5 Pa, and for chemical kinetic model, they are about 71.48×10~5 Pa and 78.123×10~5 Pa, fairly comparable with corresponding experimental values of 72×10~5 Pa and 78.7×10~5 Pa. It is observed that increasing the initial temperature advances the ignition timing, decreases the burn duration and increases the peak temperature and pressure. Moreover, the maximum temperature and pressure are associated with richer mixtures.

A two-step method for estimating high-dimensional Gaussian graphical models

The problem of estimating high-dimensional Gaussian graphical models has gained much attention in recent years. Most existing methods can be considered as one-step approaches, being either regression-based or likelihood-based. In this paper, we propose a two-step method for estimating the high-dimensional Gaussian graphical model. Specifically, the first step serves as a screening step, in which many entries of the concentration matrix are identified as zeros and thus removed from further consideration. Then in the second step, we focus on the remaining entries of the concentration matrix and perform selection and estimation for nonzero entries of the concentration matrix. Since the dimension of the parameter space is effectively reduced by the screening step,the estimation accuracy of the estimated concentration matrix can be potentially improved. We show that the proposed method enjoys desirable asymptotic properties. Numerical comparisons of the proposed method with several existing methods indicate that the proposed method works well. We also apply the proposed method to a breast cancer microarray data set and obtain some biologically meaningful results.

General Convergence Analysis for Three-step Projection Methods and Applications to Variational Problems

First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let H be a real Hilbert space and K be a nonempty closed convex subset of H. For arbitrarily chosen initial points x0, y0, z0 ∈ K, compute sequences xn, yn, zn such thatT ： K→ H is a nonlinear mapping onto K. At last three-step models are applied to some variational inequality problems.

Statistical Inferences in a Partially Linear Model with Autoregressive Errors

In this paper,we consider the statistical inferences in a partially linear model when the model error follows an autoregressive process.A two-step procedure is proposed for estimating the unknown parameters by taking into account of the special structure in error.Since the asymptotic matrix of the estimator for the parametric part has a complex structure,an empirical likelihood function is also developed.We derive the asymptotic properties of the related statistics under mild conditions.Some simulations,as well as a real data example,are conducted to illustrate the finite sample performance.

ESTIMATION ON SEMIVARYING COEFFICIENT MODELS WITH DIFFERENT DEGREES OF SMOOTHNESS

Semivarying coefficient models are frequently used in statistical models.In this paper,under the condition that the coefficient functions possess different degrees of smoothness,a two-stepmethod is proposed.In the case,one-step method for the smoother coefficient functions cannot beoptimal.This drawback can be repaired by using the two-step estimation procedure.The asymptoticmean-squared error for the two-step procedure is obtained and is shown to achieve the optimal rate ofconvergence.A few simulation studies are conducted to evaluate the proposed estimation methods.

Study for Prognosis and Survival Rate of Ovarian Cancer

In this paper, we analyze ovarian cancer cases from six hospitals in China, screen the prognostic factors and predict the survival rate. The data has the feature that all the covariates are categorical. We use three methods to estimate the survival rate–the traditional Cox regression, the two-step Cox regression and a method based on conditional inference tree. By comparison, we know that they are all effective and can predict the survival curve reasonably. The analysis results show that the survival rate is determined by a combination of risk factors, where clinical stage is the most important prognosis factor.

Generalized Cointegrated Time Series: Representation and Estimation

Cointegration analysis is often of special interest in the analysis of nonstationary vector valued time series, especially for the vector with higher order integrated components. In this paper we present the representation theorem for a generalized cointegrated system, and formulate the generalized error correction model(GECM). We also provide the modified EG two step procedure to estimate the parameters in a GECM. The paper extends some important results of cointegration into the analysis of generalized cointegration, and is of great importance in the analysis of nonstationary time series.