A Finite Difference Method for Space Fractional Differential Equations with Variable Diffusivity Coefficient

Anomalous diffusion is a phenomenon that cannot be modeled accurately by second-order diffusion equations,but is better described by fractional diffusion models.The nonlocal nature of the fractional diffusion operators makes substantially more difficult the mathemati-cal analysis of these models and the establishment of suitable numerical schemes.This paper proposes and analyzes the first finite difference method for solving variable-coefficient one-dimensional(steady state)fractional differential equations(DEs)with two-sided fractional derivatives(FDs).The proposed scheme combines first-order forward and backward Euler methods for approximating the left-sided FD when the right-sided FD is approximated by two consecutive applications of the first-order backward Euler method.Our scheme reduces to the standard second-order central difference in the absence of FDs.The existence and uniqueness of the numerical solution are proved,and truncation errors of order h are demonstrated(h denotes the maximum space step size).The numerical tests illustrate the global 0(h)accu-racy,except for nonsmooth cases which,as expected,have deteriorated convergence rates.

Chinese Value VS American Value in Friendship

This article compares and contrasts Chinese value and American value in friendship from many aspects and concludes in their cultural difference.

QRS waves detection algorithm based on positive-negative adaptive threshold method

In order to accurately detect the occasional negative R waves in electrocardiography （ECG） signals, the positive-negative adaptive threshold method is adopted to determine the positive R waves and the negative R waves, according to difference characteristics of ECG signals. The Q and S waves can then be accurately positioned based on the basic characteristics of QRS waves. Finally, the algorithm simulation is made based on the signals from MIT-BIH database with MATLAB. The ex- perimental results show that the algorithm can improve the detection accuracy rate to 99. 91% and o- vercome the problem of larger computation load for wavelet transform and other methods, so the al- gorithm is suitable for real-time detection.

Second-Order Finite Difference/Spectral Element Formulation for Solving the Fractional Advection-Diffusion Equation

The main aim of this paper is to analyze the numerical method based upon the spectral element technique for the numerical solution of the fractional advection-diffusion equa-tion.The time variable has been discretized by a second-order finite difference procedure.The stability and the convergence of the semi-discrete formula have been proven.Then,the spatial variable of the main PDEs is approximated by the spectral element method.The convergence order of the fully discrete scheme is studied.The basis functions of the spectral element method are based upon a class of Legendre polynomials.The numerical experiments confirm the theoretical results.

Wind speed retrieval using GNSS-R technique with geographic partitioning

In this paper,the efect of geographical location on Cyclone Global Navigation Satellite System(CYGNSS)observables is demonstrated for the frst time.It is found that the observables corresponding to the same wind speed vary with geographic location regularly.Although latitude and longitude information is included in the conventional method,it cannot efectively reduce the errors caused by geographic diferences due to the non-monotonic changes of observables with respect to latitude and longitude.Thus,an improved method for Global Navigation Satellite System Refectometry(GNSS-R)wind speed retrieval that takes geographical diferences into account is proposed.The sea surface is divided into diferent areas for independent wind speed retrieval,and the training set is resampled by considering high wind speed.To balance between the retrieval accuracies of high and low wind speeds,the results with the random training samples and the resampling samples are fused.Compared with the conventional method,in the range of 0–20 m/s,the improved method reduces the Root Mean Square Error(RMSE)of retrieved wind speeds from 1.52 to 1.34 m/s,and enhances the correlation coefcient from 0.86 to 0.90;while in the range of 20–30 m/s,the RMSE decreases from 8.07 to 4.06 m/s,and the correlation coefcient increases from 0.04 to 0.45.Interestingly,the SNR observations are moderately correlated with marine gravities,showing correlation coefcients of 0.5–0.6,which may provide a useful reference for marine gravity retrieval using GNSS-R in the future.

Complete Convergence and Complete Moment Convergence for Martingale Diference Sequence

In the paper,we investigate the complete convergence and complete moment convergence for the maximal partial sum of martingale diference sequence.Especially,we get the Baum–Katz-type Theorem and Hsu–Robbins-type Theorem for martingale diference sequence.As an application,a strong law of large numbers for martingale diference sequence is obtained.

ON DISCRETE SEQUENTIAL FRACTIONAL BOUNDARY VALUE PROBLEM WITH FRACTIONAL BOUNDARY CONDITIONS

In this paper we consider a discrete fractional boundary value problem(FBVP for short). We provide a delicate analysis for the property of Green’s function. Our analysis motivates the study of discrete fractional boundary value problems with fractional boundary conditions. As an application, we give conditions under which such problems admit at least one positive solution. Our results extend the results presented in [4].

Influence of diferent starting time of urokinase therapy after acute myocardial infarction on eficacy of thrombolysis

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A HYBRID EXPLICIT-IMPLICIT SCHEME FOR THE TIME-DEPENDENT WIGNER EQUATION

This paper designs a hybrid scheme based on finite difference methods and a spectral method for the time-dependent Wigner equation,and gives the error analysis for the full discret ization of its initial value problem.An explicit-implicit time-splitting scheme is used for time integration and the second-order upwind finite difference scheme is used to dis-cretize the advection term.The consistence error and the stability of the full discretization are analyzed.A Fourier spectral method is used to approximate the pseudo-differential operator term and the corresponding error is studied in detail.The final convergence result shows clearly how the regularity of the solution affects the convergence order of the pro-posed scheme.N umerical results are presented for confirming the sharpness of the analysis.The scattering effects of a Gaussian wave packet tunneling through a Gaussian potential barrier are investigated.The evolution of the density function shows that a larger portion of the wave is reflected when the height and the width of the barrier increase.Mathematics subject classification:65M06,65M70.