ON THE APPROXIMATELY SIMILARITY OF OPERATORS

1.IntroductionInwhatfollows,allofHilbertspacesappearedinthispaperareinfinite-dimensionalseparablecomplexHilbertspace.IfHisaHilbertspace,thenC(n)denotestheC*--algebraofallboundedlinearoperatorsonHandK(H)denotesthesetofcompactoperatorsonn.TwooperatorsSandTarecalledapproximatelyequivalentifthereisasequenc{Un}ofunitaryoperatorssuchthatlIU:SUn--Tll-0(n-- co).SimilarlytwooperatosSandTareapproximatelysimilarifthereisasequence{Vn}ofinvertibleoperatorswithsup(llVn11,11VJ'11)相似文献   

商标数据库存储模式及其检索算法研究

依据商标专家的先验知识和基于内容的图像检索技术，提出了一种新的商标库存储结构，并依据该存储结构设计了以三级检索算法为核心的实用商标登记注册管理系统，对于检索算法，一级检索采用人工确认，二级检索采用傅立叶描述子作为边缘特征向量，三级检索采用hu不变矩组作为矩特征向量，从而达到提高商标申请注册中的检索速度和查准率。     

An Experimental Study on the Preparation of Soft Rock Similar Materials Using Redispersible Latex Powder as a Modifier

The engineering geological problems of soft rock are common in large slope engineering and underground engineering surrounding rock. In order to study the change in mechanical properties of soft rock under the action of loading, excavation and rainfall, this paper carried out experimental research on similar materials of soft rock. The similar material of soft rock is prepared by using iron fine powder, barite powder and quartz sand as aggregate, gypsum as binder and redispersible latex powder as regulator. A single-factor influence test was designed with the content of redispersible latex powder as variation parameter. Analysis the influence of redispersible latex powder from the perspectives of physical and mechanical indexes, failure forms, stress–strain states and changes after water seepage. In addition, evaluate the feasibility of this similar material in geomechanical model test. Experimental results show that the density, compressive strength and Poisson’s ratio of similar materials can be improved to a certain extent by the redispersible latex powder with low dosage. However, the above indexes show a significant downward trend with the increase in dosage when the dosage exceeds 2%. The deformation modulus always shows a downward trend, and this trend becomes more significant especially when the dosage exceeds 2%. With the increase in the redispersible latex powder, the stress–strain curves of similar materials show obvious elastic and plastic stages. The failure mode gradually changes to X-shaped conjugate failure, which is common in soft rock, and the material changes from brittle failure to plastic failure. In addition, this type of similar material with gypsum as cementing agent will cause serious damage and loss of bearing capacity after seepage. These methods produce similar materials with low strength, low deformation modulus and plastic failure form, which can be used to simulate the stability of soft rock engineering caused by loading or excavation. At the same time, it also sheds lights on preparing similar materials of hard rock.     

STUDY ON THE PROPERTIES OF BLEND OF NATURAL RUBBER LATEX/METHYL METHACRYLATE GRAFTED RUBBER LATEX BY GAMMA RADIATION

Natural rubber latex(NRL)and methyl methacrylate(MMA)grafted rubber latex were blended in different ratios and irradiated at various absorbed doses by gamma rays from Co-60 source at room temperature.The tensile properties, swelling ratio and permanent set were measured.The maximum tensile strength and modulus at 500% elongation were obtained at an absorbed dose of 8 kGy.Modulus increases from 6.99 MPa to 9.87 MPa for an increase in proportion of MMA grafted rubber from 40% to 60% in the blend at similar absorbed dose.Elongation at break and swelling ratio decrease with increasing absorbed dose as well as the MMA grafted rubber content in the blends.The decreasing trend of permanent set is high up to 5 kGy absorbed dose,and beyond that dose,it becomes almost flat.     

一种基于三角形区域生长的图像篡改检测方法

针对现有的多数图像篡改检测算法中存在着的对旋转、缩放等篡改失效和计算量大等问题,利用三角形具有抗平移、旋转、尺度缩放的优越特性,提出了一种新的图像篡改检测算法.首先,利用Delaunay三角剖分算法对提取的Harris特征角点进行三角剖分,进行相似三角形的初始匹配.然后,以匹配的相似三角形顶点为种子点,建立三角形组,再进行一次相似三角形的匹配,实现对篡改区域的三角形生长.最后,利用区域面积阈值和数学形态学准确定位出篡改区域.实验结果表明,该算法与同类算法相比不仅能有效地对抗旋转、缩放,噪声等后期处理操作,而且对篡改区域有很好的检测和定位效果并具有计算复杂度低的特点.     

First and second moments for self‐similar couplings and Wasserstein distances

We study aspects of the Wasserstein distance in the context of self‐similar measures. Computing this distance between two measures involves minimising certain moment integrals over the space of couplings, which are measures on the product space with the original measures as prescribed marginals. We focus our attention on self‐similar measures associated to equicontractive iterated function systems consisting of two maps on the unit interval and satisfying the open set condition. We are particularly interested in understanding the restricted family of self‐similar couplings and our main achievement is the explicit computation of the 1st and 2nd moment integrals for such couplings. We show that this family is enough to yield an explicit formula for the 1st Wasserstein distance and provide non‐trivial upper and lower bounds for the 2nd Wasserstein distance for these self‐similar measures.     

随机次自相似集的表示

本文引进了随机次自相似集与随机推移集的概念,讨论了随机次自相似集的结构,并证明了任一随机集是随机次自相似集的充分必要条件是：该随机集可以表为某一个随机推移集的某个像集。     

相似非线性算子的谱相等

引进非线性算子相似的定义,证明了相似的非线性算子的谱相等。     

Fractional Brownian Heavy Traffic Approximations of Multiclass Feedforward Queueing Networks

We consider multiclass feedforward queueing networks under first in first out and priority service disciplines driven by long-range dependent arrival and service time processes. We show that in critical loading the normalized workload, queue length and sojourn time processes can converge to a multi-dimensional reflected fractional Brownian motion. This weak heavy traffic approximation is deduced from a deterministic pathwise approximation of the network behavior close to constant critical load in terms of the solution of a Skorokhod problem. Since we model the doubly infinite time interval, our results directly cover the stationary case.AMS subject classification: primary 90B15, secondary 60K25, 68M20     

On the approximation to solutions of operator equations by the least squares method

We consider the equation Au = f, where A is a linear operator with compact inverse A ^–1 in a separable Hilbert space . For the approximate solution u _n of this equation by the least squares method in a coordinate system {e _k } _k that is an orthonormal basis of eigenvectors of a self-adjoint operator B similar to A ( (B) = (A)), we give a priori estimates for the asymptotic behavior of the expressions r _n = u _n – u and R _n = Au _n – f as n . A relationship between the order of smallness of these expressions and the degree of smoothness of u with respect to the operator B is established.__________Translated from Funktsional nyi Analiz i Ego Prilozheniya, Vol. 39, No. 1, pp. 85–90, 2005Original Russian Text Copyright © by M. L. GorbachukSupported by CRDF and Ukrainian Government Joint Grant UM1-2567-OD03.Translated by V. M. Volosov