The <i>general purpose of the research</i>—systematical clarifying and explicating the too vague proper philosophical concepts of space, void, matter, motion, inertia, for making a logical harmony between...The <i>general purpose of the research</i>—systematical clarifying and explicating the too vague proper philosophical concepts of space, void, matter, motion, inertia, for making a logical harmony between them and the corresponding notions of proper physics. The <i>special purpose of the research</i>—invention (construction) of a <i>formal inference of the well-known Newton’s first law of mechanics</i> within a logically formalized axiomatic epistemology system from a set of precisely defined presumptions. For realizing this aim <i>the following work has been done</i>: a two-valued algebraic system of metaphysics as formal axiology has been applied to philosophical epistemology and philosophy of nature;a formal axiomatic theory called Sigma has been applied to physics for realizing the above-indicated special purpose of the research. Thus, constructing a discrete mathematical model of relationship between universal epistemology and philosophy of physics has been done. <i>Research results</i>: The main hitherto not published significantly new nontrivial scientific result of applied investigations presented in this article is a <i>formal inference of the well-known Newton’s first law of mechanics</i> within the formal axiomatic epistemology system Sigma from conjunction of the <i>formal-axiological analog</i> of the proper-law-of-mechanics (which <i>analog</i> is the <i>formal-axiological law</i> of two-valued algebra of metaphysics) and the assumption of a-priori-ness of knowledge. For obtaining this main research result, a set of accessory nontrivial novelties has been used, for instance;a precise algorithmic definition is given for the notion “<i>law of metaphysics</i>” in the algebraic system of metaphysics as formal axiology;a <i>formal-axiological equivalence</i> in the algebraic system is defined precisely. Precise tabular definitions are given for relevant evaluation-functions determined by evaluation-arguments, for example;“movement of (what, whom) <i>x</i>”;“speed of <i>x</i>”;“vecto展开更多
Due to the simplicity and flexibility of the power law process,it is widely used to model the failures of repairable systems.Although statistical inference on the parameters of the power law process has been well deve...Due to the simplicity and flexibility of the power law process,it is widely used to model the failures of repairable systems.Although statistical inference on the parameters of the power law process has been well developed,numerous studies largely depend on complete failure data.A few methods on incomplete data are reported to process such data,but they are limited to their specific cases,especially to that where missing data occur at the early stage of the failures.No framework to handle generic scenarios is available.To overcome this problem,from the point of view of order statistics,the statistical inference of the power law process with incomplete data is established in this paper.The theoretical derivation is carried out and the case studies demonstrate and verify the proposed method.Order statistics offer an alternative to the statistical inference of the power law process with incomplete data as they can reformulate current studies on the left censored failure data and interval censored data in a unified framework.The results show that the proposed method has more flexibility and more applicability.展开更多
对S-粗集给出改进,把函数这个分析工具引入到S-粗集中,提出函数S-粗集(function singularrough sets)。函数单向S-粗集(function one direction singular rough sets)是函数S-粗集的基本形式之一,它是以R-函数等价类[u]定义的;ui∈[u]...对S-粗集给出改进,把函数这个分析工具引入到S-粗集中,提出函数S-粗集(function singularrough sets)。函数单向S-粗集(function one direction singular rough sets)是函数S-粗集的基本形式之一,它是以R-函数等价类[u]定义的;ui∈[u]是一个函数,函数是一个规律。函数单向S-粗集具有单向动态特性与规律特征:利用函数单向S-粗集的规律特征,给出F-规律推理与F-规律推理的规律挖掘概念,提出F-规律推理的规律挖掘定理,F-规律推理的规律挖掘原理与F-规律推理的规律挖掘应用。F-规律推理的规律挖掘是寻找系统中未知规律研究的一个新的研究方向。展开更多
文摘The <i>general purpose of the research</i>—systematical clarifying and explicating the too vague proper philosophical concepts of space, void, matter, motion, inertia, for making a logical harmony between them and the corresponding notions of proper physics. The <i>special purpose of the research</i>—invention (construction) of a <i>formal inference of the well-known Newton’s first law of mechanics</i> within a logically formalized axiomatic epistemology system from a set of precisely defined presumptions. For realizing this aim <i>the following work has been done</i>: a two-valued algebraic system of metaphysics as formal axiology has been applied to philosophical epistemology and philosophy of nature;a formal axiomatic theory called Sigma has been applied to physics for realizing the above-indicated special purpose of the research. Thus, constructing a discrete mathematical model of relationship between universal epistemology and philosophy of physics has been done. <i>Research results</i>: The main hitherto not published significantly new nontrivial scientific result of applied investigations presented in this article is a <i>formal inference of the well-known Newton’s first law of mechanics</i> within the formal axiomatic epistemology system Sigma from conjunction of the <i>formal-axiological analog</i> of the proper-law-of-mechanics (which <i>analog</i> is the <i>formal-axiological law</i> of two-valued algebra of metaphysics) and the assumption of a-priori-ness of knowledge. For obtaining this main research result, a set of accessory nontrivial novelties has been used, for instance;a precise algorithmic definition is given for the notion “<i>law of metaphysics</i>” in the algebraic system of metaphysics as formal axiology;a <i>formal-axiological equivalence</i> in the algebraic system is defined precisely. Precise tabular definitions are given for relevant evaluation-functions determined by evaluation-arguments, for example;“movement of (what, whom) <i>x</i>”;“speed of <i>x</i>”;“vecto
基金supported by the National Natural Science Foundation of China(51775090)。
文摘Due to the simplicity and flexibility of the power law process,it is widely used to model the failures of repairable systems.Although statistical inference on the parameters of the power law process has been well developed,numerous studies largely depend on complete failure data.A few methods on incomplete data are reported to process such data,but they are limited to their specific cases,especially to that where missing data occur at the early stage of the failures.No framework to handle generic scenarios is available.To overcome this problem,from the point of view of order statistics,the statistical inference of the power law process with incomplete data is established in this paper.The theoretical derivation is carried out and the case studies demonstrate and verify the proposed method.Order statistics offer an alternative to the statistical inference of the power law process with incomplete data as they can reformulate current studies on the left censored failure data and interval censored data in a unified framework.The results show that the proposed method has more flexibility and more applicability.
文摘对S-粗集给出改进,把函数这个分析工具引入到S-粗集中,提出函数S-粗集(function singularrough sets)。函数单向S-粗集(function one direction singular rough sets)是函数S-粗集的基本形式之一,它是以R-函数等价类[u]定义的;ui∈[u]是一个函数,函数是一个规律。函数单向S-粗集具有单向动态特性与规律特征:利用函数单向S-粗集的规律特征,给出F-规律推理与F-规律推理的规律挖掘概念,提出F-规律推理的规律挖掘定理,F-规律推理的规律挖掘原理与F-规律推理的规律挖掘应用。F-规律推理的规律挖掘是寻找系统中未知规律研究的一个新的研究方向。
