The dynamical behaviors of the novel four-dimensional memristor self-oscillated system with periodic excitation are discussed. With the change of amplitude and angular frequency of external periodic excitation, the proposed system can generate various dynamics including chaotic, periodic and bursting oscillations. Using the numerical simulation method, the phase trajectory and time series are employed to verify the behavior of the considered system.

In this paper, we propose a meshless method for option pricing which uses the radial basis quasi-interpolation method to solve the Black-Scholes equation. The quasi-interpolation operator is used to force the first and second derivatives of stock prices in spatial direction and the forward difference method is used in time direction. Its convergence of order $o (Δt+ h^{\frac{2}{3}})$ in $l_∞$−norm is also derived in the paper. The advantage of this method is that it can fit the scattered data well, which makes it be a good approximation method for the option prices that fluctuate randomly. The feasibility of the proposed method is verified by numerical examples of uniform points and scattered points. The results show that this method has a good fitting effect on option prices.

Though image denoising has experienced rapid development, there remain problems to be solved such as preserving the edge and meaningful details in image denoising. In this paper, we focus on this hot issue. Considering the parameter in original method is a constant, we introduce a new adaptive parameter selection based on EPLL (Expected Patch Log Likelihood) by the use of image gradient and the local variance, which varies with different regions of the image. What’s more, for solving staircase effect which common in anisotropic diffusion models, we add a gradient fidelity term to release it. The experiment shows that our proposed method proves the effectiveness not only in vision but also on quantitative evaluation.

Stock price prediction has always been the focus of investors' attention in the stock market. In recent years, deep learning technology has been widely used in this field. In the era of big data, feature selection is a necessary part of data preprocessing. Feature selection is a data dimensionality reduction technology, and its main purpose is to select the relevant features that are most beneficial to the algorithm from the original data, reduce the dimensionality of the data and the difficulty of learning tasks, and improve the efficiency of the model. This paper has performed analysis of input feature selection with three feature selection methods: Multiple linear regression analysis, Correlation matrix heatmap, Feature importance. Plus the original features set, four different input features sets were provided for predicting stock price of ten China's new energy leading stocks with LSTM. From the conducted experiments, it is found that after using the feature selection method, the prediction results of all ten stocks are performed better than the prediction results under the original features.

In this paper, we aim to construct an explicit finite difference scheme for solving the two-dimensional sine–Gordon equation. By using Taylor expansion, we prove that the local truncation error of the scheme is of $o(h^2+\tau^2)$ with grid size $h$ and time step $\tau.$ Numerical results are reported to test the theoretical analysis.

This paper uses the finite difference method to numerically solve the space fractional nonlinear Schrodinger equation. First, we give some properties of the fractional Laplacian $Δ_h^\alpha.$ Then we construct a numerical scheme which satisfies the mass conservation law without proof and the scheme’s order is $o(\tau^2+h^2)$ in the discrete $L^\infty$ norm. Moreover, The scheme conserves the mass conservation and is unconditionally stable about the initial values. Finally, this article gives a numerical example to verify the relevant properties of the scheme.

This article presents a mathematical model to study the impact of electro kinetic variable viscosity on peristaltic transfer of Jeffrey fluid. We have considered the non-Newtonian Jeffrey fluid model with the use of linear momentum. Poisson-Boltzmann equations are simplified by using Debye-Hückel linearization approximation. The closed form analytical solutions are presented by using long wavelength and low Reynolds number assumptions. The expressions for pressure rise and pressure gradient are determined by using perturbation method. The influence of various parameters like Jeffrey fluid parameter, Electroosmotic parameter, Electroosmotic velocity and Viscosity parameter on the flow characteristics are discussed through graphs. It is revealed that with an increase in the Viscosity parameter there is decrease in the pumping, free pumping, enhances in the augmented pumping region and the axial pressure gradient decreases with increasing Viscosity.

The business process model and service interaction model represent the behaviour model on business view and system view respectively. The automatic transformation from the business process model to the service interaction model can effectively narrow the gap between the business view and the system view. Thus, in this paper, a model transformation approach that can transform the business process model described by extended Petri net into service interaction model in system view is proposed. This approach by extending the UML sequence diagram meta model represents service interaction model, and by using model-driven development designs the transformation from extended Petri net to service interaction model. Especially, each situation of the behaviour transition linked to the different types of places in extended Petri net model are detailed analyzed. According with the these situation, the transformation rules from each situation to different types of message in the service interaction model are designed. In order to carry out the automatic executing of the formalization transformation, the transformation rules are described by the ATL model transformation language, and the ATL codes are implemented by Eclipse platform. Finally, the executing result of the model transformation plug is demonstrated by the Travel Agency system. The experimental results show that the approach in this paper can realize the automatic transformation from business process model to service interaction model, and improve the efficiency of software development.

The ionosphere has an impact on the radio system, therefore, the determination of the ionospheric state is significant. The total electron content (TEC), as an important ionospheric parameter, can characterize the state of the ionosphere. This paper introduces a new ionospheric disturbed index N13 by correcting the existing index N27, and also proposes the theory foundation for determination the ionospheric state using cross validation method. The N13 is defined as the normalized relative variation of the ionospheric TEC, in which the TEC background value is the sliding median of 27 days. Analyzing the N13 calculated from the TEC data at Taipei station from January 2002 to July 2014, the results show that the two indexes N13 and N27 generally have the same statistical characters against with season and local time, however, they are always different at one time. Based on the probability density function of N13，an optimization model is also constructed to determine the ionospheric disturb proportion by cross validation method. It is found that the proportion is about 25%, when the ionospheric disturbed index range is $N_{13}<−1$ or $N_{13}>1.$