Almost perfect sequences based on cyclic difference sets

The perfect sequences are so ideal that all out-of-phase autocorrelation coefficients are zero, and if the sequences are used as the coding modulating signal for the phase-modulated radar, there will be no interference of side lobes theoretically. However, it has been proved that there are no binary perfect sequences of period 4 〈 n ≤ 12100. Hence, the almost perfect sequences with all out-of-phase autocorrelation coefficients as zero except one are of great practice in engineering. Currently, the cyclic difference set is one of most effective tools to analyze the binary sequences with perfect periodic autocorrelation function. In this article, two characteristic formulas corresponding to the autocorrelation and symmetric structure of almost perfect sequences are calculated respectively. All almost perfect sequences with period n, which is a multiple of 4, can be figured out by the two formulas. Several almost perfect sequences with different periods have been hunted by the program based on the two formulas and then applied to the simulation program and practical application for ionospheric sounding.

Fuzzy Difference Equations in Diagnoses of Glaucoma from Retinal Images Using Deep Learning

The intuitive fuzzy set has found important application in decision-making and machine learning.To enrich and utilize the intuitive fuzzy set,this study designed and developed a deep neural network-based glaucoma eye detection using fuzzy difference equations in the domain where the retinal images converge.Retinal image detections are categorized as normal eye recognition,suspected glaucomatous eye recognition,and glaucomatous eye recognition.Fuzzy degrees associated with weighted values are calculated to determine the level of concentration between the fuzzy partition and the retinal images.The proposed model was used to diagnose glaucoma using retinal images and involved utilizing the Convolutional Neural Network(CNN)and deep learning to identify the fuzzy weighted regularization between images.This methodology was used to clarify the input images and make them adequate for the process of glaucoma detection.The objective of this study was to propose a novel approach to the early diagnosis of glaucoma using the Fuzzy Expert System(FES)and Fuzzy differential equation(FDE).The intensities of the different regions in the images and their respective peak levels were determined.Once the peak regions were identified,the recurrence relationships among those peaks were then measured.Image partitioning was done due to varying degrees of similar and dissimilar concentrations in the image.Similar and dissimilar concentration levels and spatial frequency generated a threshold image from the combined fuzzy matrix and FDE.This distinguished between a normal and abnormal eye condition,thus detecting patients with glaucomatous eyes.

Difference Sets of Null Density Subsets of N

Let , and for any , . If is positive, then B is considered as a large set with . Its difference set has both high density and rich structure. The set with is also relatively large and it is a long standing conjecture that like sets with positive upper density they have arithmetic progression of arbitrary length. Here we show their difference set may not be substantial;for any there exists such that and .

RITT-WU'S CHARACTERISTIC SET METHOD FOR ORDINARY DIFFERENCE POLYNOMIAL SYSTEMS WITH ARBITRARY ORDERING

In this paper, a Ritt-Wu＇s characteristic set method for ordinary difference systems is proposed, which is valid for any admissible ordering. New definition for irreducible chains and new zero decomposition algorithms are also proposed.

Study on covering rough sets with topological methods

The authors study the covering rough sets by topological methods. They combine the covering rough sets and topological spaces by means of defining some new types of spaces called covering rough topological (CRT) spaces based on neighbourhoods or complementary neighbourhoods. As the separation axioms play a fundamental role in general topology, they introduce all these axioms into covering rough set theories and thoroughly study the equivalent conditions for every separation axiom in several CRT spaces. They also investigate the relationships between the separation axioms in these special spaces and reveal these relationships through diagrams in different CRT spaces.

OPTIMIZATION OF THE METHOD OF SELECTING THE TOOTH NUMBER SERIES IN A SET OF CHANGE GEARS Part Ⅱ The Rules for Permuting the DBL’s of the First Order and Their Intercalated Sets

The problem in practice of determining the proper combination of Zi in a set of changegears may be abstracted to the problem of finding the proper combination and permutation ofthe elements ai,i+1 of the set A1 to give maximum M-d. Some results to find optimal combina-tions of the elements of the set A1 have been reported in part I. In this part, some rules forpermuting these elements are introduced. By means of these rules, three kinds of intercalated setsof A1 have been found, namely: （1） Sets with an even left wing, （2） Sets with coincidence of bothwings, and （3） Sets with circulated elements.

Effects of Second-Order Sum-and Difference-Frequency Wave Forces on the Motion Response of a Tension-Leg Platform Considering the Set-down Motion

This paper presents a study on the motion response of a tension-leg platform(TLP) under first-and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave force is calculated using the full-field quadratic transfer function(QTF). The coupled effect of the horizontal motions, such as surge, sway and yaw motions, and the set-down motion are taken into consideration by the nonlinear restoring matrix. The time-domain analysis with 50-yr random sea state is performed. A comparison of the results of different case studies is made to assess the influence of second-order wave force on the motions of the platform. The analysis shows that the second-order wave force has a major impact on motions of the TLP. The second-order difference-frequency wave force has an obvious influence on the low-frequency motions of surge and sway, and also will induce a large set-down motion which is an important part of heave motion. Besides, the second-order sum-frequency force will induce a set of high-frequency motions of roll and pitch. However, little influence of second-order wave force is found on the yaw motion.

Trajectory Controllability of Nonlinear Integro-Differential System—An Analytical and a Numerical Estimations

A stronger concept of complete (exact) controllability which we call Trajectory Controllability is introduced in this paper. We study the Trajectory Controllability of an abstract nonlinear integro-differential system in the finite and infinite dimensional space setting. We will then discuss how approximations to these problems can be found computationally using finite difference methods and optimization. Examples will be presented in one, two and three dimensions.

A Construction of Relative Difference Set

In this paper, we give a construction of RDS in Galois ring by using some bent function, and obtain the equivalent relationship between RDS and a kind of bent function. At the same time, its existence is demonstrated.

On the Presentation of Social Class Difference in The Garden Party in terms of its Narrative Style and Settings Description

Katherine Mansfield was a predominant modernist writer who had written the well-known short story The Garden Party, which explicitly interprets the idea of social class difference between the upper class and the working class. This paper discusses its presentation of social class difference from two aspects, including the narrative style and the settings.

关于集合环的教学方法探讨

集合的运算性质是集合论课程的基础,通过引入集合环概念及其性质的讲授,帮助学生们理解集合代数运算的性质,促进对抽象代数结构的理解.在对称差运算满足结合律性质的证明过程中,启发学生们积极思考,从集合论的角度理解代数结构,锻炼学生们的抽象思维能力.

我国学前教育高质量发展的多组态路径——基于DPSIR框架的模糊集定性比较分析(fsQCA)

文章基于DPSIR框架设计评价指标体系对区域学前教育高质量发展水平进行评价,以熵权-TOPSIS计算指标权重和综合得分,结合模糊集定性比较分析(fsQCA)进行组态路径分析。研究发现:(1)我国学前教育高质量发展水平呈现由东向西递减的趋势,除东部外,中部与西部区域学前教育高质量发展水平均值均低于全国均值;(2)基于DPSIR框架的区域学前教育发展系统驱动学前教育高质量发展具有“多重并发”与非对称性的特点;(3)存在两条高水平组态路径与3条非高水平组态路径,多条组态路径殊途同归,且高水平组态与非高水平组态处于非对称状态;(4)东部、中部与西部组态路径存在一定差异,三大区域学前教育高质量发展均离不开状态因子与响应因子的支持。为此,要完善机制体制建设,为学前教育发展提供保障;因地制宜制定发展策略,以协同路径驱动学前教育高质量发展;聚焦区域重点,以重点发展引领区域学前教育高质量发展。

随机模拟半偏减法集对势的区域水资源承载力评价方法

为准确评价区域水资源承载力状态,探讨以联系数和集对势为理论基础构建评价模型,分析普通半偏减法集对势的整体结构及物理意义,为进一步挖掘联系数半偏减法集对势的不确定信息,建立了联系数差异度系数与半偏减法集对势差异度系数的关系,提出了半偏减法集对势差异度系数的三角模糊数随机模拟方法,建立了随机模拟半偏减法集对势差异度系数的区域水资源承载力评价方法。将评价方法应用于安徽省蚌埠市水资源承载力评价中,发现态势变化呈现由偏反势过渡到均势再到偏反势;评价等级值整体处于2~3级之间,说明蚌埠市整体水资源承载状态较差,但有好转趋势。评价模型应用结果与实际情况吻合,为保障区域水资源高质量发展提供了新的评价方法。

运用差分特征列方法精确求解一类非线性有理差分方程

运用差分特征列方法来求解一组有理差分方程,即一类非线性差分方程。首先介绍了差分方程及特征列方法的理论知识,进而运用差分特征列方法对一类非线性差分方程组进行化简,通过有效化、判断一致性、可约分解等步骤,最终根据整序定理和零点分解定理得到这类非线性零点集。

动态差异度系数在淮北平原水资源承载力评价中的应用

为科学有效地评价区域水资源承载力,基于现有动态差异度系数的相关研究,充分挖掘评价样本与等级标准之间的不确定性信息,推导出随样本值变化而变化的差异度系数计算式,构建了基于动态差异度系数的四元联系数值法的区域水资源承载力定量评价方法。该方法在安徽省淮北平原的应用结果表明:2015—2019年安徽省淮北平原六市水资源承载状况均处于2级临界可载与3级临界超载之间,说明水资源承载状况较差;联系数值法得出的评价结果与级别特征值法、四元减法集对势基本相同,联系数值法较其他两种方法更客观,灵敏度更高;联系数值法可准确判断集对系统的发展趋势,为解决水资源、水环境等领域类似评价提供参考。

采用集约化开放集差异分布对齐策略的轴承故障诊断方法

针对当前迁移学习算法应用于轴承故障诊断领域时,目标域中可能存在未知故障类别进而导致识别准确率过低的问题,引入了开集域自适应方法。针对现有的开放集域自适应算法在进行分布对齐时,多注重跨域对齐,很少关注领域内部的分布情况,从而导致对未知类别识别率较低的问题,提出了一种采用集约化开放集差异分布对齐(IDAOD)策略的轴承故障诊断方法,集成了跨域散度对齐和域内分布异化方法。使用开放集最近邻类验证方法获取目标域伪标签,然后构造源域和目标域的总体散度矩阵,进行跨域的散度对齐。基于分布适配加权条件分布,进一步异化同领域内不同类别的空间分布。在结构风险最小化框架下,基于开放集差异理论构造的损失函数,引入正则化项,得到最优解和新的目标域伪标签。通过在Office-31数据集上进行试验,验证了IDAOD算法的可行性。分别在CWRU和JNU轴承数据集上进行故障诊断试验,所提方法对未知故障类别的识别率均高于其他对比开放集算法,验证了所提方法在轴承数据集上能有效提高目标样本含有未知样本时的准确率。

基于Level Set方法的西夏字轮廓提取

随着国内外对西夏研究的不断深入,收藏于世界各地的大批西夏古籍文献通过影印方式陆续出版。如何将这些西夏古籍文献进行数字化、文本化则有着极其重要的意义。首先利用平滑和细化算法对西夏影印文献进行了预处理,然后利用Level set方法对影印文献中的西夏字进行了轮廓提取。Level Set演化函数在空间方向上采用了四阶紧致差分逼近式离散,计算过程中加入了窄带算法及全局优化方法。实验表明,算法在不增加计算时间的基础上可以得到较精确的西夏字轮廓。

集合差系统的新构造

研究集合差系统新的构造方法.借助有限域上分圆类,给出集合差系统的两个直接构造;再利用克罗内克积建立集合差系统新的递归构造,并推广了已知构造.最后应用所得到的直接构造和递归构造给出了新的渐近最优的集合差系统.

基于Level Set方法的人脸轮廓提取

人脸轮廓提取在诸如安全检查、保安管理、交通电子监控、机器人研究等方面有着十分重要的应用价值。先利用图像背景差分法快速检测出人脸的初始矩形轮廓线,然后采用LevelSet方法对视频图像进行人脸轮廓提取,Level Set演化函数空间方向上采用四阶紧致差分逼近式离散,计算过程中加入了窄带算法和全局优化方法。数值实验结果表明,该算法在不增加计算时间的基础上,可以检测出模糊或离散的边界,并得到精确的人脸轮廓线。

R^(n)上Lebesgue微分定理的证明

通过分析下半连续函数的定义及其4种等价命题,建立对称差集的测度性质和球可数覆盖定理,证明了球极大函数的下半连续性、可测性及其分布函数的估计不等式,并利用球可数覆盖定理、Lebesgue积分的平移变换定理和Tonelli定理给出了R^(n)上Lebesgue微分定理的详细证明,改进和补充了已有文献的相应结果。