Moment-Based Multi-Resolution HWENO Scheme for Hyperbolic Conservation Laws

In this paper,a high-order moment-based multi-resolution Hermite weighted essentially non-oscillatory(HWENO)scheme is designed for hyperbolic conservation laws.The main idea of this scheme is derived from our previous work[J.Comput.Phys.,446(2021)110653],in which the integral averages of the function and its first order derivative are used to reconstruct both the function and its first order derivative values at the boundaries.However,in this paper,only the function values at the Gauss-Lobatto points in the one or two dimensional case need to be reconstructed by using the information of the zeroth and first order moments.In addition,an extra modification procedure is used to modify those first order moments in the troubledcells,which leads to an improvement of stability and an enhancement of resolution near discontinuities.To obtain the same order of accuracy,the size of the stencil required by this moment-based multi-resolution HWENO scheme is still the same as the general HWENO scheme and is more compact than the generalWENO scheme.Moreover,the linear weights are not unique and are independent of the node position,and the CFL number can still be 0.6whether for the one or two dimensional case,which has to be 0.2 in the two dimensional case for other HWENO schemes.Extensive numerical examples are given to demonstrate the stability and resolution of such moment-based multi-resolution HWENO scheme.

Particle Size Estimation Based on Edge Density

Given image sequences of closely packed particles, the underlying aim is to estimate diameters without explicit segmentation. In a way, this is similar to the task of counting objects without directly counting them. Such calculations may, for example, be useful）Cast estimation of particle size in different application areas. The topic is that of estimating average size （=average diameter） of packed particles, from formulas involving edge density, and the edges from moment-based thresholding are used. An average shape factor is involved in the calculations, obtained for some frames from crude partial segmentation. Measurement results from about 80frames have been analyzed.

Claim reserving for insurance contracts in line with the International Financial Reporting Standards 17:a new paid‑incurred chain approach to risk adjustments

This study considers the risk management of insurance policies in line with the implementation of the new International Financial Reporting Standards 17.It applies the paid-incurred chain method to model the future unpaid losses by combining the information channels of both the incurred claims and paid losses.We propose the recovery of the empirical distribution of the outstanding claims liabilities associated with a group of contracts via moment-based density approximation.We determine the risk measures and adjustments that are compliant with the new standard using the Monte–Carlo simulation method and approximated distributions.The historical data on the aggregate Ontario automobile insurance claims over a 15-year period are analyzed to examine the appropriateness and accuracy of our approach.

A dynamical neural network approach for distributionally robust chance-constrained Markov decision process

In this paper,we study the distributionally robust joint chance-constrained Markov decision process.Utilizing the logarithmic transformation technique,we derive its deterministic reformulation with bi-convex terms under the moment-based uncertainty set.To cope with the non-convexity and improve the robustness of the solution,we propose a dynamical neural network approach to solve the reformulated optimization problem.Numerical results on a machine replacement problem demonstrate the efficiency of the proposed dynamical neural network approach when compared with the sequential convex approximation approach.