Model Analysis of Equivalence Classes in UML Events Relations

Unified Modeling Language (UML) has become a de facto standard for design, specification and modeling of object oriented software systems. UML structures being graphical in nature lack defining semantics of the systems and are prone to causing errors. Formal methods are proved to be a powerful tool for requirement analysis, design and specification of software systems. Hence, linking UML with formal approaches will enhance modeling power of software systems. In this paper, an approach is developed by integrating UML and Z notation focusing on equivalence relation of the state diagrams. The Z is used because it is based on the first order predicate logic having rigorous computer tool support. The reflexivity, symmetry and transitivity properties, being important at design level, are identified and described. It is believed that this approach will be effective and useful at both academics and industrial level. The need, reasoning and benefits of the integrated approach are discussed. The resultant formal models are analyzed and validated using Z/Eves tool.

The application of fuzzy equivalence relation based on the quotient space in cluster analysis

A fuzzy clustering analysis model based on the quotient space is proposed. Firstly, the conversion from coarse to fine granularity and the hierarchical structure are used to reduce the multidimensional samples. Secondly, the fuzzy compatibility relation matrix of the model is converted into fuzzy equivalence relation matrix. Finally, the diagram of clustering genealogy is generated according to the fuzzy equivalence relation matrix, which enables the dynamic selection of different thresholds to effectively solve the problem of cluster analysis of the samples with multi-dimensional attributes.

Analysis of secondary makeup characteristics of drill collar joint and prediction of downhole equivalent impact torque of Well SDTK1

Based on the three-dimensional elastic-plastic finite element analysis of the 8"(203.2 mm)drill collar joint,this paper studies the mechanical characteristics of the pin and box of NC56 drill collar joints under complex load conditions,as well as the downhole secondary makeup features,and calculates the downhole equivalent impact torque with the relative offset at the shoulder of internal and external threads.On the basis of verifying the correctness of the calculation results by using measured results in Well GT1,the prediction model of the downhole equivalent impact torque is formed and applied in the first extra-deep well with a depth over 10000 m in China(Well SDTK1).The results indicate that under complex loads,the stress distribution in drill collar joints is uneven,with relatively higher von Mises stress at the shoulder and the threads close to the shoulder.For 203.2 mm drill collar joints pre-tightened according to the make-up torque recommended by American Petroleum Institute standards,when the downhole equivalent impact torque exceeds 65 kN·m,the preload balance of the joint is disrupted,leading to secondary make-up of the joint.As the downhole equivalent impact torque increases,the relative offset at the shoulder of internal and external threads increases.The calculation results reveal that there exists significant downhole impact torque in Well SDTK1 with complex loading environment.It is necessary to use double shoulder collar joints to improve the impact torque resistance of the joint or optimize the operating parameters to reduce the downhole impact torque,and effectively prevent drilling tool failure.

The Equivalence between Orthogonal Iterations and Alternating Least Squares

This note explores the relations between two different methods. The first one is the Alternating Least Squares (ALS) method for calculating a rank-k approximation of a real m×n matrix, A. This method has important applications in nonnegative matrix factorizations, in matrix completion problems, and in tensor approximations. The second method is called Orthogonal Iterations. Other names of this method are Subspace Iterations, Simultaneous Iterations, and block-Power method. Given a real symmetric matrix, G, this method computes k dominant eigenvectors of G. To see the relation between these methods we assume that G = AT A. It is shown that in this case the two methods generate the same sequence of subspaces, and the same sequence of low-rank approximations. This equivalence provides new insight into the convergence properties of both methods.

Einstein’s Dark Energy via Similarity Equivalence, ‘tHooft Dimensional Regularization and Lie Symmetry Groups

Realizing the physical reality of ‘tHooft’s self similar and dimensionaly regularized fractal-like spacetime as well as being inspired by a note worthy anecdote involving the great mathematician of Alexandria, Pythagoras and the larger than life man of theoretical physics Einstein, we utilize some deep mathematical connections between equivalence classes of equivalence relations and E-infinity theory quotient space. We started from the basic principles of self similarity which came to prominence in science with the advent of the modern theory of nonlinear dynamical systems, deterministic chaos and fractals. This fundamental logico-mathematical thread related to partially ordered sets is then applied to show how the classical Newton’s kinetic energy E = 1/2mv2 leads to Einstein’s celebrated maximal energy equation E = mc2 and how in turn this can be dissected into the ordinary energy density E(O) = mc2/22 and the dark energy density E(D) = mc2(21/22) of the cosmos where m is the mass;v is the velocity and c is the speed of light. The important role of the exceptional Lie symmetry groups and ‘tHooft-Veltman-Wilson dimensional regularization in fractal spacetime played in the above is also highlighted. The author hopes that the unusual character of the analysis and presentation of the present work may be taken in a positive vein as seriously attempting to propose a different and new way of doing theoretical physics by treating number theory, set theory, group theory, experimental physics as well as conventional theoretical physics on the same footing and letting all these diverse tools lead us to the answer of fundamental questions without fear of being labelled in one way or another.

The Study of Semantic Functional Equivalence of Predicates in Xi Youji and Its English Version Journey to the West—From the Perspective of Transitivity Theory

Equivalence in translation was first put forward by Firth. It has been the nuclear topic of translation studies in western countries."Functional equivalence", Eugene Nida's key notion of translation theories, advocated the receptor-oriented translation standard. Through the contrastive study between Xi Youji and its English version Journey to the West, the content focuses on the translation of the verbal predicates and aims at studying the application of transitivity theory into Chinese-English translation and finding out the improved translations of Chinese and English examples of different processes. Due to limited article, this paper only discusses three of six processes in the concrete context and provides new translations for the questioned ones. Finally, the last part summarizes that the functional equivalence can be achieved when verbs referring to process of action share the same semantic attribute with the Chinese originals, so the English version of Xi Youji should be further perfected according to transitivity theory.

Novel Ring Compression Test Method to Determine the Stress-Strain Relations and Mechanical Properties of Metallic Materials

Although there are methods for testing the stress-strain relation and strength,which are the most fundamental and important properties of metallic materials,their application to small-volume materials and tube components is lim-ited.In this study,based on energy density equivalence,a new dimensionless elastoplastic load-displacement model for compressed metal rings with isotropy and constitutive power law is proposed to describe the relations among the geometric dimensions,Hollomon law parameters,load,and displacement.Furthermore,a novel test method was developed to determine the elastic modulus,stress-strain relation,yield and tensile strength via ring compression test.The universality and accuracy of the method were verified within a wide range of imaginary materials using finite element analysis(FEA),and the results show that the stress-strain curves obtained by this method are consistent with those inputted in the FEA program.Additionally,a series of ring compression tests were performed for seven metallic materials.It was found that the stress-strain curves and mechanical properties predicted by the method agreed with the uniaxial tensile results.With its low material consumption,the ring compression test has the potential to be as an alternative to traditional tensile test when direct tension method is limited.

高量测丢包率下基于共享模糊等价关系的配电网状态感知

配电网分布式新能源渗透率的不断增加,对实时监测的要求不断提高,大量量测数据在集中传输过程中常常出现延迟、丢包等现象导致配电网状态感知精度降低甚至不可观测。针对上述问题,提出基于共享模糊等价关系的状态感知方法。首先,将采集得到的多时间断面历史量测数据集作为源数据集,实时采集得到的高量测丢包率下的数据作为目标数据集。利用三角形隶属度函数分别将两组数据集写成模糊集的形式。然后采用一种向量间距离度量方法,分别计算得到两组模糊集的模糊等价关系矩阵。在此基础上,采用共享模糊等价关系的聚类方法,将知识从源数据集转移到目标数据集,减小两组数据集特征分布之间的差异。最后,利用深度神经网络对知识迁移后低维特征空间中高量测丢包率对应的数据进行标记,得到配电网实时状态。通过对IEEE标准算例和某实际地市公司配电网算例进行仿真测试,结果表明所提出的基于共享模糊等价关系的配电网状态估计方法能在高量测丢包率下获得准确的配电网实时运行状态,实现不同量测数据缺失程度下的配电网实时监测。

等差关系的个性阐释与序列技术的空间化解读——-勋伯格《钢琴组曲》(Op.25)新识

勋伯格的《钢琴组曲》(Op. 25)在序列原型设计上,以音高关系的“等差”为控制,特别突出差数为1和6的音程;在十二音方阵中,则以“等差”关系为本源,用分形将一维音高关系拓展至二维空间中;在作品创作中,更是以“等差”关系为其控制与转圜的枢纽,作大量的音级换序,展现出此类技法之个性化处理及观念化表达的各种可能。勋伯格的这部序列音乐作品不仅突破了传统音高逻辑方式,其中第二首又以织体形态体现加沃特舞曲的舞姿意象;不单从内容形式方面强化音乐的自洽性与逻辑性,更以有意味的谱式形态复沓昔日的哥特式审美,在展现表现主义的观念风格的同时,将美术与建筑中的空间观念纳入其序列音乐创作中。

用DUG三模型计算满射的个数和等价关系的个数

本文利用DUG三模型给出了有限集之间满射个数和有限集上等价关系个数的简洁计算公式.给出了更一般球盒分配问题的DUG三模型计算公式.

周边离焦框架眼镜与角膜塑形镜对儿童近视进展控制效果及视力相关生存质量的影响

目的:探讨周边离焦框架眼镜与角膜塑形镜(OK镜)对儿童近视进展控制效果及视力相关生存质量的影响。方法:前瞻性研究。选取2021-01/2022-01在湖州市中心医院眼科首次诊断为近视的患儿237例,根据不同矫正方式分为:周边离焦框架眼镜组105例105眼,OK镜组132例132眼(所有入组儿童眼部参数均选取右眼数据纳入统计)。使用中小学生视力相关生存质量量表对两组近视患儿进行随访调查,并记录首次就诊及随访1 a时儿童最佳矫正视力(BCVA)、等效球镜度数、眼轴(AL)数据。结果:戴镜1 a后,两组患儿等效球镜度数及AL均增长,但两组间比较均无差异(P>0.05)。周边离焦框架眼镜组患儿等效球镜度数变化量和AL变化量大于OK组(均P=0.001)。戴镜1 a后,两组患儿在中小学生视力相关生存质量量表问卷中,周边离焦框架眼镜组情感维度得分高于OK镜组(P<0.05)。OK镜组患儿情感维度得分变化量大于周边离焦框架眼镜组(P<0.05)。结论:OK镜控制儿童近视进展效果优于周边离焦框架眼镜。两种矫正方式均可显著提升近视患儿视力相关生存质量,OK镜在改善儿童视力相关生存质量量表情感维度上优于周边离焦框架眼镜。

Elastic wave insulation and propagation control based on the programmable curved-beam periodic structure

Curved-beams can be used to design modular multistable metamaterials(MMMs)with reprogrammable material properties,i.e.,programmable curved-beam periodic structure(PCBPS),which is promising for controlling the elastic wave propagation.The PCBPS is theoretically equivalent to a spring-oscillator system to investigate the mechanism of bandgap,analyze the wave propagation mechanisms,and further form its geometrical and physical criteria for tuning the elastic wave propagation.With the equivalent model,we calculate the analytical solutions of the dispersion relations to demonstrate its adjustability,and investigate the wave propagation characteristics through the PCBPS.To validate the equivalent system,the finite element method(FEM)is employed.It is revealed that the bandgaps of the PCBPS can be turned on-and-off and shifted by varying its physical and geometrical characteristics.The findings are highly promising for advancing the practical application of periodic structures in wave insulation and propagation control.

基于小冲杆试验评价钛合金的高温拉伸性能

基于能量密度等效理论,提出依据塑性弯曲阶段载荷-位移曲线,获取均匀连续、各向同性的钛合金圆片试样应力-应变曲线的小冲杆试验新方法;采用该方法预测得到不同名义屈服强度和硬化指数组合工况下假想材料的应力-应变数据,并与有限元预设曲线进行对比;基于小冲杆试验获得的TC4合金在室温、高温(400℃)下的载荷-位移曲线,采用上述方法获得该合金的真应力-真应变曲线,并与单轴拉伸真应力-应变曲线进行对比。结果表明:预测得到的假想材料应力-应变数据与有限元预设曲线之间的符合优度均高于0.96;预测获得的室温和400℃下TC4合金的真应力-真应变曲线与单轴拉伸曲线之间的符合优度均高于0.97,屈服强度和抗拉强度的最大相对误差分别为4.86%和4.63%,验证了该新方法的有效性。

基于模糊超群构建的Engel群及其性质研究

通过构造满足Engel递减条件的模糊超群(H,。)上最小的等价关系■^(*),使得模糊超群关于等价关系构建的商群(等价类的集合)H/■^(*)是一个Engel群,并通过等价关系的强正则性来刻画该Engel群,最后引入模糊超群的?-部分的概念,确定等价关系?是可传递的充要条件.

等价数列的性质及应用

将集合论中的等价关系引入到数学分析中,给出了等价数列的概念及若干性质,并举例说明了等价数列在数学分析、线性代数和泛函分析中的应用.

Effect of Gravitational Formula Change on Gravitational Anomalies

The gravitational constant G is a basic quantity in physics, and, despite its relative imprecision, appears in many formulas, for example, also in the formulas of the Planck units. The “relative inaccuracy” lies in the fact that each measurement gives different values, depending on where and with which device the measurement is taken. Ultimately, the mean value was formed and agreed upon as the official value that is used in all calculations. In an effort to explore the reason for the inaccuracy of this quantity, some formulas were configured using G, so that the respective quantity assumed the value = 1. The gravitational constant thus modified was also used in the other Planck equations instead of the conventional G. It turned out that the new values were all equivalent to each other. It was also shown that the new values were all represented by powers of the speed of light. The G was therefore no longer needed. Just like the famous mass/energy equivalence E = m * c2, similar formulas emerged, e.g. mass/momentum = m * c, mass/velocity = m * c2 and so on. This article takes up the idea that emerges in the article by Weber [1], who describes the gravitational constant as a variable (Gvar) and gives some reasons for this. Further reasons are given in the present paper and are computed. For example, the Planck units are set iteratively with the help of the variable Gvar, so that the value of one unit equals 1 in each case. In this article, eleven Planck units are set iteratively using the variable Gvar, so that the value of one unit equals 1 in each case. If all other units are based on the Gvar determined in this way, a matrix of values is created that can be regarded both as conversion factors and as equivalence relationships. It is astonishing, but not surprising that the equivalence relation E = m * c2 is one of these results. All formulas for these equivalence relationships work with the vacuum speed of light c and a new constant K. G, both as a variable and as a constant, no longer appears in these formulae. The new thing about this theory is that the gravitational constant is no longer needed. And if it no longer exists, it can no longer cause any difficulties. The example of the Planck units shows this fact very clearly. This is a radical break with current views. It is also interesting to note that the “magic” number 137 can be calculated from the distances between the values of the matrix. In addition, a similar number can be calculated from the distances between the Planck units. This number is 131 and differs from 137 with 4.14 percent. This difference has certainly often led to confusion, for example, when measuring the Fine Structure Constant.

Green＇s Relations on Semigroups of Transformations Preserving Two Equivalence Relations

Let Tx be the full transformation semigroup on a set X. For a non-trivial equivalence F on X, letTF（X） = {f ∈ Tx ： arbieary （x, y） ∈ F, （f（x）,f（y）） ∈ F}.Then TF（X） is a subsemigroup of Tx. Let E be another equivalence on X and TFE（X） = TF（X） ∩ TE（X）. In this paper, under the assumption that the two equivalences F and E are comparable and E lohtain in F, we describe the regular elements and characterize Green＇s relations for the semigroup TFE（X）.

Contact Finite Determinacy of Relative Map Germs

The strong contact finite determinacy of relative map germs is studied by means of classical singularity theory. We first give the definition of a strong relative contact equivalence （or KS,T equivalence） and then prove two theorems which can be used to distinguish the contact finite determinacy of relative map germs, that is, f is finite determined relative to KS,T if and only if there exists a positive integer k, such that M^5（n）ε（S;n）p ∩→ TKs,T（f）.

Borel Equivalence Relations between l_1and l_p

In this paper, we show that, for each p 〉 1, there are continuum many Borel equivalence relations between Rω/l1 and Rω/p ordered by ≤B which are pairwise Borel incomparable.