LEVEL SETS AND EQUIVALENCES OF MORAN-TYPE SETS

In the paper, we consider Moran-type sets E;given by sequences {a;};and{n;};. we prove that E;may be decompose into the disjoint union of level sets. Moreover,we define three type of equivalence between two dimension functions associated to two Morantype sets, respectively, and we classify Moran-type sets by these equivalent relations.

Calculation Model of Equivalent Strength for Induced Crack Based on Double-K Fracture Theory and Its Optimizing Setting in RCC Arch Dam

By means of fracture testing on roller-compacted concrete （RCC） three-point bending beams with two different specimen sizes, the P-CMOD complete curve for RCC was gained. Furthermore, by applying double-K fracture theory, KiniⅠC,KunⅠC, as well as the critical effective crack length and the critical crack tip opening displacement, were evaluated. Based on the double-K fracture parameters above, the calculation model of equivalent strength for induced crack was established, thus the calculation method on its initiation, stable propagation and unstable fracture was ascertained. Moreover, the finite element simulation analysis of stress field in ShaPai arch dam and the on-site observational splaying points of induced crack at different altitudes validated the reliability of the model. Finally, crack inducer′s optimal setting in RCC arch dam was studied. It improves the design level of induced crack in RCC arch dam and satisfies the necessity of engineering practice.

Equivalent elastic compliance tensor for rock mass with multiple persistent joint sets:Exact derivation via modified crack tensor

Discontinuities constitute an integral part of rock mass and inherently affect its anisotropic deformation behavior.This work focuses on the equivalent elastic deformation of rock mass with multiple persistent joint sets.A new method based on the space geometric and mechanical properties of the modified crack tensor is proposed,providing an analytical solution for the equivalent elastic compliance tensor of rock mass.A series of experiments validate the capability of the compliance tensor to accurately represent the deformation of rock mass with multiple persistent joint sets,based on conditions set by the basic hypothesis.The spatially varying rules of the equivalent elastic parameters of rock mass with a single joint set are analyzed to reveal the universal law of the stratified rock mass.

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.

Martingales and Super-Martingales Relative to a Convex Set of Equivalent Measures

In the paper, the martingales and super-martingales relative to a convex set of equivalent measures are systematically studied. The notion of local regular super-martingale relative to a convex set of equivalent measures is introduced and the necessary and sufficient conditions of the local regularity of it in the discrete case are founded. The description of all local regular super-martingales relative to a convex set of equivalent measures is presented. The notion of the complete set of equivalent measures is introduced. We prove that every bounded in some sense super-martingale relative to the complete set of equivalent measures is local regular. A new definition of the fair price of contingent claim in an incomplete market is given and the formula for the fair price of Standard Option of European type is found. The proved Theorems are the generalization of the famous Doob decomposition for super-martingale onto the case of super-martingales relative to a convex set of equivalent measures.

IMPROVED ACCURACY AND ROUGHNESS MEASURES FOR ROUGH SETS

Accuracy and roughness, proposed by Pawlak(1982), might draw a conclusion inconsistent with our intuition in some cases. This letter analyzes the limitations in these measures and proposes improved accuracy and roughness measures based on information theory.

Set-Valued Non-Linear Random Implicit Quasivariational Inclusions

In this paper, we propose iterative algorithms for set valued nonlinear random implicit quasivariational inclusions. We define the related random implicit proximal operator equations and establish an equivalence between them. Finally, we prove the existence and convergence of random iterative sequences generated by random iterative algorithms.

抽取等价类算法在基于Rough Sets的数据挖掘中的应用

主要讨论抽取等价类算法在基于粗集R(ough Sets)的数据挖掘中的应用.

基于不确定性的跳阶序贯三支决策模型

序贯三支决策模型作为一种能够有效处理不确定性信息的数据挖掘方法,采用了渐进的思维进行决策。然而,边界域可能存在部分不确定性较大的等价类,即便添加属性也无法准确划分,导致决策的分类精度降低,同时延迟代价较高。因此,通过条件概率来刻画等价类的不确定性,基于阴影集理论筛选不确定性较大的等价类,并对其采取跳阶延迟处理的方法,提出了基于不确定性的跳阶序贯三支决策模型。实验结果表明,所提模型与经典序贯三支决策模型相比,在分类性能上具有更好的有效性。

柴储微电网虚拟惯量和阻尼系数可行域分析方法

采用虚拟同步发电机(virtual synchronous generator,VSG)技术的储能系统能够有效提升高比例新能源接入的独立柴储微电网的惯量及频率稳定性。首先推导基于VSG的柴储微电网简化频率分析模型;在此基础上,提出一种储能VSG虚拟惯量与阻尼系数的可行域分析和设计方法。该方法计及VSG最大输出功率与能量约束,保证系统满足频率最低点等基本频率稳定指标约束,并有针对性地考虑阻尼比或VSG等效功率平滑时间等定制化动态性能需求。此外,针对柴储微电网在扰动初期出现的功率振荡现象,建立计及线路阻抗的稳定性机理分析模型,并提出基于虚拟阻抗的振荡抑制策略。最后,搭建了1台50kV·A柴油发电机和1台50kV·A虚拟同步机构成的仿真和实验平台,验证所提方法的有效性。

基于遗传神经网络的舰船磁场等效源重构方法

针对传统等效源模型的磁场预测精度和稳定性易受等效源参数设置(数量和位置)影响的问题,本文提出了利用遗传神经网络重构等效源的舰船磁场预测算法。以传统的等效源理论为基础,利用人工神经网络的非线性学习能力和遗传算法的自适应寻优功能,通过多次网络训练,得到一个隐性的等效源模型;设计了数值仿真试验和船模试验,把包含场点和源点信息的系数向量作为神经网络的输入,把近场平面的磁场测量值作为输出,代入隐性等效源模型。结果表明:该方法的磁场预测精度优于传统等效源模型,对船模磁场垂向分量的预测误差小于5%,具有工程应用价值。

Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets

This paper investigates the Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets D=(r_1D)∪(r_2D+(1+r_1-r_2-r_3)/2)∪(r_3D+1+r_3) and E=(r_1E)∪(r_2E+1-r_2- r_3)∪(r_3E+1-r_3),and proves that D and E are Lipschitz equivalent if and only if there are positive integers m and n such that r_1~m=r_3~n.

多因素波动影响下事件状态的联系数表示研究

为研究在因素波动影响下事件状态变化和不同状态出现的可能性,本文将语义划分与集对分析联系数的多级状态对应,建立因素波动影响下的事件状态联系数表示方法。制定了单因素波动情况下事件状态联系数的构建方法,以单位因素区间对因素平面进行离散,分别计算各离散区域的联系数,综合所有联系数形成事件状态联系数。根据数值逻辑的或关系和联系数运算法则耦合单因素事件状态联系数得到2因素事件状态联系数。多因素通过切片法降维至2因素才可使用上述方法。本文证明了离散求解与整体求解的等价性,使用各语义划分面积比例计算联系数较离散法更为方便。实例中使用整体求解法计算了2因素事件状态联系数。最后说明了本文方法面临的问题、原因和解决方法。

计及中等城市充电需求潜力与碳减排等效收益下的充电站规划策略

针对中等城市电动汽车充电设施过度分散、应用潜力未知等问题,构建动、静态充电需求结合的充电需求指标来分析不同区域的充电需求潜力.首先,基于区域充电需求潜力与充电站市场潜力、电动汽车用户出行数据等,提出中等城市充电需求承载力模型,结合马尔可夫链模型,构建充电需求潜力空间分布指数;其次,在考虑用户侧、充电站侧、电网侧成本与收益的基础上,构建区域充电站碳减排等效收益函数,通过免疫算法制定待选充电站选址定容方案;然后,采用熵权法改进的TOPSIS综合评价模型在保证电网接纳能力的基础上,确定相对最优规划方案;最后,选取中等城市湖北省宜昌市西陵区部分城区作为算例进行分析,通过IEEE33节点系统潮流计算检验规划结果的有效性和合理性,证明充电站能够在低碳减排方面带来高收益.

Lipschitz equivalence of self-similar sets with triangular pattern

In this paper, we discuss the Lipschitz equivalence of self-similar sets with triangular pattern. This is a generalization of {1, 3, 5}-{1, 4, 5} problem proposed by David and Semmes. It is proved that if two such self-similar sets are totally disconnected, then they are Lipschitz equivalent if and only if they have the same Hausdorff dimension.

Lipschitz equivalence of fractal sets in R

Let T（q, D） be a self-similar （fractal） set generated by {fi（x） = 1/q（（x ＋ di）}^Ni=1 where integer q 〉 1and D = {d1, d2 dN} C R. To show the Lipschitz equivalence of T（q, D） and a dust-iik-e T（q, C）, one general restriction is 79 C Q by Peres et al. [Israel] Math, 2000, 117： 353-379]. In this paper, we obtain several sufficient criterions for the Lipschitz equivalence of two self-similar sets by using dust-like graph-directed iterating function systems and combinatorial techniques. Several examples are given to illustrate our theory.

基于条件信息熵的决策表约简

Rough集理论是近年来发展起来的一种有效地处理不精确、不确定、含糊信息的数学理论方法 ,在机器学习、数据挖掘、智能数据分析、控制算法获取等领域取得了很大的成功 .研究者从不同的角度对这个理论进行研究 .本文将从信息论观点出发对 Rough集理论的基本概念和主要运算进行分析讨论 ,通过与 Rough集理论的代数观点进行比较分析 ,得到这两种观点下的一些等价性质和不同的特性 ,并基于条件信息熵提出决策表的约简算法 .

粗糙集概念与运算的布尔矩阵表示

建立了属性集与布尔矩阵以及逻辑方程组的解之间的关系;在此基础上给出了粗糙集理论中概念与运算的布尔矩阵表示;最后证明了属性约简在布尔矩阵和代数两种不同表示下是等价的。

不同粒度世界的描述法——商空间法

面对复杂对象 ,如何描述对象往往成为解决问题的基础 ,为此 ,该文提出了一种不同粒度世界的描述方法———商空间法 .在商空间法中用一个三元组 (X ,f,T)描述一个问题 ,在其论域上引入等价关系R ,对应于R的商集[X],然后将 [X]当作新的论域 ,对它进行分析、研究 ,从而将问题表述成不同的粒度世界 ,进而达到简化问题、解决问题的目的 .与粗糙集、决策树等方法相比较 ,商空间法具有更强的表达能力 ,它不仅可以定义多种不同的属性函数 ,而且可以描述论域中的元素、元素之间的相互关系 (即结构 )、运算等 .该文介绍粒度世界的描写、划分法、粒度确定以及不同粒度世界的关系 .最后给出了粒度世界的描述实例———互联网中的路由算法及称球游戏 。

信息表中不完备数据的填补方法

提出了一种基于粗糙集的不完备数据填补方法.本算法以突出信息表的决策规则为主要目的,选取重要断点为主要手段,以分类质量作为迭代约束条件.实验和数值实例表明,本算法不但不会产生冲突规则,而且能够进一步突出决策规则.