The Minimal Solutions of Boolean Matrix-equation A~k=J

ＬｅｔＢ ={0 ,1 }ｂｅｔｈｅｕｓｕａｌｂｉｎａｒｙＢｏｏｌｅａｎａｌｇｅｂｒａ .ＴｈｅｍａｔｒｉｃｅｓｏｖｅｒＢａｒｅｃａｌｌｅｄＢｏｏｌｅａｎｍａｔｒｉｃｅｓ.Ａｎｎ×ｎＢｏｏｌｅａｎｍａｔｒｉｘＡｉｓｃａｌｌｅｄａｐｒｉｍｉｔｉｖｅｍａｔｒｉｘｉｆｔｈｅｒｅｅｘｉｓｔｓａｐｏｓｉｔｉｖｅｉｎｔｅｇｅｒｋｓｕｃｈｔｈａｔＡｋ=Ｊ (ｗｈｅｒｅＪｉｓｔｈｅｕｎｉｖｅｒｓａｌｍａｔｒｉｘ) .ＴｈｅｌｅａｓｔｓｕｃｈｋｉｓｃａｌｌｅｄｔｈｅｅｘｐｏｎｅｎｔｏｆＡ ,ｄｅｎｏｔｅｄｂｙγ(Ａ) .　Ｉｎ ｐｒｏｊ…     

多目标优化问题的完全标量化

本文首先利用松弛变量和广义Tchebycheff范数的推广形式提出一类新的标量化优化问题.进一步,通过调整几种参数范围获得一般多目标优化问题弱有效解、有效解和真有效解的一些完全标量化刻画.此外,本文提出例子对主要结果进行说明,利用相应的标量化方法判定给定的多目标优化问题的可行解是否是弱有效解、有效解和真有效解.     

弹性力学问题的局部Petrov—Galerkin方法

提出了弹性力学平面问题的局部Petrov-Galerkin方法,这是一种真正的无网格方法。这种方法采和移动最小二乘近似函数作为试函数,并且采用移动最小二乘近似函数的权函数作为加权残值法加权函数;同时这种方法只包含中心在所考虑点处的规则局部区域上以及局部边界上的积分,所得系统矩阵是一个带状稀疏矩阵,该方法可以容易推广到求解非线性问题以及非均匀介质的力学问题。还计算了两个弹性力学平面问题的例子,给出了位移和能量的索波列夫模及其相对误差。所得计算结果证明：该方法是一种具有收敛快、精度高、简便有效的通用方法;在工程中具有广阔的应用前景。     

反中心对称矩阵反问题解存在的条件

讨论了反中心对称矩阵反问题及其最佳逼近。研究了矩阵反问题有解的充分和必要条件,利用这类矩阵的结构和特征性质得到了矩阵反问题解的通式;证明了最佳逼近问题存在唯一解,并给出了求最佳逼近解的算法和数值算例。     

一类矩阵方程的对称次反对称解及其最佳逼近

利用矩阵的广义奇异值分解 ,得到了矩阵方程 ATXA =B有对称次反对称解的充分必要条件及其通解的表达式 ,并且给出了在矩阵方程的解集合中与给定矩阵的最佳逼近解的表达式 .     

对称正交对称矩阵逆特征值问题

Let P∈ Rn×n such that PT = P, P-1 = PT.A∈Rn×n is termed symmetric orthogonal symmetric matrix ifAT = A, (PA)T = PA.We denote the set of all n × n symmetric orthogonal symmetric matrices byThis paper discuss the following two problems:Problem I. Given X ∈ Rn×m, A = diag(λ1,λ 2, ... ,λ m). Find A SRnxnP such thatAX =XAProblem II. Given A ∈ Rnδn. Find A SE such thatwhere SE is the solution set of Problem I, ||·|| is the Frobenius norm. In this paper, the sufficient and necessary conditions under which SE is nonempty are obtained. The general form of SE has been given. The expression of the solution A* of Problem II is presented. We have proved that some results of Reference [3] are the special cases of this paper.     

概率度量空间中的一类非线性算子方程的可解性

利用泛函在概率度量空间中引入半序,并利用此半序的方法研究了概率度量空间中的非线性算子方程Lx=Ax的可解性问题,得到了几个新的定理,同时推广了若干重要定理。     

Reduction principle for a certain class of kernel-type operators

The classical Hardy–Littlewood inequality asserts that the integral of a product of two functions is always majorized by that of their non-increasing rearrangements. One of the pivotal applications of this result is the fact that the boundedness of an integral operator acting near zero is equivalent to the boundedness of the same operator restricted to the cone of positive non-increasing functions. It is well known that an analogous inequality for integration away from zero is not true. We will show in this paper that, nevertheless, the equivalence of the two inequalities is still preserved for certain rather general class of kernel-type operators under a mild restriction and regardless of the measure of the underlying integration domain.     

Weighted mixed‐norm inequalities through extrapolation

We prove that operators satistying weighted inequalities with radial weights are bounded in mixed‐norm spaces of radial‐angular type, even with a weight in the radial part. This is achieved by using the usual extrapolation methods, adapted to the radial setting. All the versions of the extrapolation theorem can be adapted to this setting, and in particular we get results in variable Lebesgue spaces and also for multilinear operators. Furthermore, quantitative estimates are obtained with this approach, but their sharpness remains an open question.     

NanoSIMS image enhancement by reducing random noise using low-rank method

NanoSIMS images are usually affected by random noises because of various types of sources, which degrade the quality of ion images and increase the uncertainty of the geochemical interpretations. Here, we applied the weighted nuclear norm minimization (WNNM) method to reduce the random noise in the NanoSIMS image. The low-rank property of the image is fully considered to suppress random noise while retaining reliable details of weak signals. Numerical experiments on four different kinds of NanoSIMS ion images show that the denoising ability of the WNNM method is superior to that of the median filter, no matter the size of the filtering windows used (eg, 3 × 3, 5 × 5, and 7 × 7). The WNNM method can reduce random noise while preserving the most critical details in the original NanoSIMS observations, which can significantly enhance reliability when distinguishing critical boundaries and structures.