A deep neural network-based method for solving obstacle problems

In this paper, we propose a method based on deep neural networks to solve obstacle problems. By introducing penalty terms, we reformulate the obstacle problem as a minimization optimization problem and utilize a deep neural network to approximate its solution. The convergence analysis is established by decomposing the error into three parts: approximation error, statistical error and optimization error. The approximate error is bounded by the depth and width of the network, the statistical error is estimated by the number of samples, and the optimization error is reflected in the empirical loss term. Due to its unsupervised and meshless advantages, the proposed method has wide applicability. Numerical experiments illustrate the effectiveness and robustness of the proposed method and verify the theoretical proof.     

关于Jacobsthal数和Jacobsthal-Lucas数的r-循环矩阵的行列式和逆

和 是n阶r-循环矩阵, 其中 , 是Jacobsthal数, , 是Jacobsthal-Lucas数, 研究得出了 和 的关于Jacobsthal数和Jacobsthal-Lucas数的行列式的值. 同时, 计算出了矩阵 和 的逆.     

半透明介质中辐射传递方程的反演计算及数值模拟

本文介绍了一侧为半透明、另一侧为非透明界面时一维半透明介质的辐射强度计算式。采用辐射与导热复合换热模型计算半透明介质内温度场。利用已知的温度场求半透明介质的辐射强度一正问题计算。将此辐射强度代入辐射反问题计算模型，引入测量误差，采用Ｃｈａｈｉｎｅ方法及演半透明介质内温度场一反问题计算。数值模拟表明，本文所采用的辐射反演法具有较高的精度及稳定性。     

Properties of noninteger moments in a first passage time problem

We calculate the moments t ^q , whereq is not necessarily an integer, of the first passage time to trapping for a simple diffusion problem in one dimension. If a characteristic length of the system isL and t _q ~L (q) asL, then we show that there is a phase transition atq=q _c such that whenq<q _c ,(g)=0, and forq>q _c , (q) is a linear function ofq. These analytical results can be used to explain results for large moments for diffusion on a hierarchic structure. We also show how to calculate noninteger moments in terms of characteristic functions.     

基于改进NAS-RIF的三维显微图像盲复原

对二维NAS-RIF算法进行了改进,并将它用于三维显微图像复原,分别用模拟样本和真实生物样本进行了实验。针对原算法对噪声有放大作用,提出了基于中值滤波去噪的改进。在支持域的确定、最小点的搜索上进行改进,提高复原质量。改进了原算法仅适用于均匀背景的不足,扩大了应用范围。实验结果表明,该算法在三维显微图像盲复原中具有较好的效果。     

一种金属腔体中微波断层成像的最优分层非均一背景

针对基于金属腔体的微波断层成像系统,提出了一种最优分层非均一背景的设计方法.该方法使用一种新的微波断层成像积分算子评价方法和模拟退火法等最优化方法.首先,介绍了一种基于有限元法的微波断层成像积分算子计算方法.然后,提出一种新的微波断层成像积分算子度量,该度量可以综合评价整个积分算子奇异值谱,并通过一组仿真研究证明该度量与反演结果的误差具有相关性;该度量用一个数值综合评价一个积分算子,可以方便地应用于最优化算法中;利用模拟退火法选择圆形金属腔体中分层非均一背景的每一层介质的相对介电常数,从而获得一个最优分层非均一背景.最后,对尺寸小于半波长的圆柱目标和"凹"字形复杂目标进行仿真研究,仿真结果证明该最优分层非均一背景可以提高微波断层成像算法的收敛速度,提高反演结果的准确性.     

Double-Alekseev inverse scattering method in the stationary axi-symmetric vacuum gravitation field equations

We present a new improvement to the Alekseev inverse scattering method. This improved inverse scattering method is extended to a double form, followed by the generation of some new solutions of the double-complex Kinnersley equations. As the double-complex function method contains the Kramer-Neugebauer substitution and analytic continuation, a pair of real gravitation soliton solutions of the Einstein’s field equations can be obtained from a double N-soliton solution. In the case of the flat Minkowski space background solution, the general formulas of the new solutions are presented.      

Hansen Solubility Parameters in the Analysis of Solvent–Solvent Interactions by Inverse Gas Chromatography

The Flory–Huggins interaction parameters, for a solute with pure nonvolatile solvents and with binary mixtures of nonvolatile solvents were evaluated using Inverse Gas Chromatography (IGC) data at 403.15 K. The five solvents used have similar structure and nearly the same molar volume and their mixtures form regular solutions. The values were used to evaluate the Hansen solubility parameters (HSP) for the pure solvents and mixed solvent systems. The HSP are plotted as a function of composition of the polar solvent. The dispersion component, , and the polar component, , exhibited negative deviation whereas the hydrogen bonding component, , showed positive deviation in the four mixtures. However, the total solubility parameter was found to be almost linear with composition in the four binary systems. Further the total solubility parameter, , was used to calculate the molar excess heat of vaporization for the solvents (C78 + POH, C78 + PCN, C78 + TTF, and C78 + TMO) that was found to be negative for C78 (19,24-dioctadecyldotetracontane) + POH(18,23-dioctadecylhentetracontan-1-ol) and C78 + PCN(1-cyano-18,23-dioctadecylhentetracontane) systems and positive for C78 + TTF [19,24-bis(18,18,18-trifluorooctadecyl)-1,1,1,42,42,42-hexafluorodotetracontane), and C78 + TMO(17,22-bis-(16-methoxyhexadecyl)-1,38-dimethoxyoctatriacontane] and the other systems.     

弹性矩形板方程在非线性边界条件下整体解的存在唯一性

考虑了在非线性边界条件下的弹性矩形板方程.利用Galerkin方法,首先证明了该方程在非线性边界(a)及初值w⁰∈W,w¹∈W的条件下初边值问题存在唯一整体弱解w(t).其次证明了该方程在非线性边界(b)及初值w⁰∈W₁,w¹∈W₁的条件 关键词： 弹性矩形板方程 非线性边界条件 初边值问题 整体解