Subset representations and eigenvalues of the universal intertwining matrix

We solve a combinatorial question concerning eigenvalues of the universal intertwining endomorphism of a subset representation.     

3维Maxwell方程局部1维多辛格式的能量恒等式

在理想导体边界条件下,对3维Maxwell方程的局部1维多辛Preissman格式的能量守恒性质进行研究.运用能量分析法推导了2个能量恒等式,这些恒等式说明了给出的格式在所定义的离散范数下是能量守恒和无条件稳定的,数值算例验证了结论的正确性.     

A simple three‐wave approximate Riemann solver for the Saint‐Venant‐Exner equations

Erosion and sediments transport processes have a great impact on industrial structures and on water quality. Despite its limitations, the Saint‐Venant‐Exner system is still (and for sure for some years) widely used in industrial codes to model the bedload sediment transport. In practice, its numerical resolution is mostly handled by a splitting technique that allows a weak coupling between hydraulic and morphodynamic distinct softwares but may suffer from important stability issues. In recent works, many authors proposed alternative methods based on a strong coupling that cure this problem but are not so trivial to implement in an industrial context. In this work, we then pursue 2 objectives. First, we propose a very simple scheme based on an approximate Riemann solver, respecting the strong coupling framework, and we demonstrate its stability and accuracy through a number of numerical test cases. However, second, we reinterpret our scheme as a splitting technique and we extend the purpose to propose what should be the minimal coupling that ensures the stability of the global numerical process in industrial codes, at least, when dealing with collocated finite volume method. The resulting splitting method is, up to our knowledge, the only one for which stability properties are fully demonstrated.     

Numerical Evaluation of a Two-Loop Diagram in the Cutoff Regularization

The sunset diagram of λφ4 theory is evaluated numerically in cutoff scheme and a nonzero finite term(in accordance with dimensional regularization (DR) result) is found in contrast to published calculations. This findingdramatically reduces the critical couplings for symmetry breaking in the two-loop effective potential discussed in ourprevious work.     

工业锅炉计算机控制技术

工业锅炉的计算机控制是近年来发展起来的一项新技术，根据山西焦煤集团屯兰矿SHL35型蒸汽锅炉的计算机控制系统改造，阐述了锅炉实行计算机控制的先进性，并对各种方案进行了对比分析。     

Efficient Collocation Schemes for Singular Boundary Value Problems

We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point.     

一类非线性Schr(o)dinger方程的守恒差分法与Fourier谱方法

考察了一类带导数项的非线性Schrodinger方程的周期边值问题，提出了一种守恒的差分格式，在空间方向上采用Fourier谱方法，证明了格式的稳定性和收敛性．数值试验得到了与理论分析一致的结果．     

可重构制造系统重组过程中设备选择模型的研究

根据生产任务选择加工设备进行制造资源重组是实现可重构制造系统的关键问题之一，由于设备的选择涉及到多种因素，既有定量指标，又有定性指标，传统的依靠人工经验的方法显得力不从心。本文首先结合实际情况，提出了一套设备选择评价体系，通过对模糊判断矩阵采用最小对数二乘法确定各评价因素的权重系数，针对定性指标和定量指标采用不同的方法确定其性能指标值，通过模糊积分对评判指标进行综合评判，最后进行了实例研究。所提出的方法有效地简化了决策过程，为可重构制造系统设备选择提供了一套行之有效的方法。     

一个门限RSA密码体制

传统的门限RSA密码体制由于都是在环Zψ（n )上进行的，而会遇到固有的困难；Zψ（n ）不是域且ψ（n）必须保密，提出了一个新的门限RSA密码体制，通过数学变换克服了以上的困难，并且对它的安全性进行了简要分析。