NUMERICAL RESIDUAL ELIMINATION METHOD OF FINITE DIFFERENTIAL EQUATIONS

In this paper, a new elimination of finite differential equations has been discussed. It applies the numerical direct iteration to obtain the residual equations, in which the number of unknowns has been reduced greatly. The solution process is simple and efficient, and the solution is exact

Residual curvature migration velocity analysis for angle domain common imaging gathers

Pre-stack depth migration velocity analysis is one of the keys to influencing the imaging quality of pre-stack migration.In this paper we cover a residual curvature velocity analysis method on angle-domain common image gathers（ADCIGs） which can depict the relationship between incident angle and migration depth at imaging points and update the migration velocity.Differing from offset-domain common image gathers（ODCIGs）,ADCIGs are not disturbed by the multi-path problem which contributes to imaging artifacts,thus influencing the velocity analysis.On the basis of horizontal layers,we derive the residual depth equation and also propose a velocity analysis workflow for velocity scanning.The tests to synthetic and field data prove the velocity analysis methods adopted in this paper are robust and valid.

Research on the optimal dynamical systems of three-dimensional Navier-Stokes equations based on weighted residual

In this paper, the theory of constructing optimal dynamical systems based on weighted residual presented by Wu & Sha is applied to three-dimensional Navier-Stokes equations, and the optimal dynamical system modeling equations are derived. Then the multiscale global optimization method based on coarse graining analysis is presented, by which a set of approximate global optimal bases is directly obtained from Navier-Stokes equations and the construction of optimal dynamical systems is realized. The optimal bases show good properties, such as showing the physical properties of complex flows and the turbulent vortex structures, being intrinsic to real physical problem and dynamical systems, and having scaling symmetry in mathematics, etc.. In conclusion, using fewer terms of optimal bases will approach the exact solutions of Navier-Stokes equations, and the dynamical systems based on them show the most optimal behavior.

A computational model of the human glucose-insulin regulatory system

Objective：A computational model of insulin secretion and glucose metabolism for assisting the diagnosis of diabetes mellitus in clinical research is introduced.The proposed method for the estimation of parameters for a system of ordinary differential equations（ODEs）that represent the time course of plasma glucose and insulin concentrations during glucose tolerance test（GTT）in physiological studies is presented.The aim of this study was to explore how to interpret those laboratory glucose and insulin data as well as enhance the Ackerman mathematical model.Methods：Parameters estimation for a system of ODEs was performed by minimizing the sum of squared residuals（SSR）function,which quantifies the difference between theoretical model predictions and GTT＇s experimental observations.Our proposed perturbation search and multiple-shooting methods were applied during the estimating process.Results：Based on the Ackerman＇s published data,we estimated the key parameters by applying R-based iterative computer programs.As a result,the theoretically simulated curves perfectly matched the experimental data points.Our model showed that the estimated parameters,computed frequency and period values,were proven a good indicator of diabetes.Conclusion：The present paper introduces a computational algorithm to biomedical problems,particularly to endocrinology and metabolism fields,which involves two coupled differential equations with four parameters describing the glucose-insulin regulatory system that Ackerman proposed earlier.The enhanced approach may provide clinicians in endocrinology and metabolism field insight into the transition nature of human metabolic mechanism from normal to impaired glucose tolerance.

Verifiable Secret Sharing Scheme Based on Certain Projective Transformation

The main purpose of verifiable secret sharing scheme is to solve the honesty problem of participants. In this paper, the concept of nonzero k-submatrix and theresidual vector of system of hyperplane intersecting line equations is proposed. Based on certain projective transformations in projective space, a verifiable (t, n)-threshold secret sharing scheme is designed by using the structure of solutions of linear equations and the difficulty of solving discrete logarithm problems. The results show that this scheme can verify the correctness of the subkey provided by each participant before the reconstruction of the master key, and can effectively identify the fraudster. The fraudster can only cheat by guessing and the probability of success is only 1/p. The design of the scheme is exquisite and the calculation complexity is small. Each participant only needs to hold a subkey, which is convenient for management and use. The analysis shows that the scheme in this paper meets the security requirements and rules of secret sharing, and it is a computationally secure and effective scheme with good practical value.

Research on fault diagnosis for MMC-HVDC Systems

Introduction:With the development of flexible HVDC technology,the fault diagnosis of MMC-HVDC becomes a new research direction.Based on the fault diagnosis theory,this paper proposes a robust fault diagnosis method to study the fault diagnosis problem of MMC-HVDC systems.Methods:By optimizing the gain matrix in the fault observer,fault detection with good sensitivity and robustness to disturbance is achieved.In the MMC-HVDC system,because of the inherently uncertain system and the presence of various random disturbances,the study of robust fault diagnosis method is particularly important.Results:Simulation studies during various AC faults have been carried out based on a 61-level MMC-HVDC mathematical model.The results validate the feasibility and effectiveness of the proposed fault diagnosis method.Conclusions:So this fault diagnosis method can be further applied to the actual project,to quickly achieve system fault diagnosis and accurately complete fault identification.