Here, we determine formulae, for the numbers of representations of a positive integer by certain sextenary quadratic forms whose coefficients are 1, 2, 3 and 6.
Binary signed digit representation （BSD-R） of an integer is widely used in computer arithmetic, cryptography and digital signal processing. This paper studies what the exact number of optimal BSD-R of an integer is ...Binary signed digit representation （BSD-R） of an integer is widely used in computer arithmetic, cryptography and digital signal processing. This paper studies what the exact number of optimal BSD-R of an integer is and how to generate them entirely. We also show which kinds of integers have the maximum number of optimal BSD-Rs.展开更多
In this paper, firstly using different method and technique we derive the cor-responding integral representation formulas of （0, q）（q 〉 0） differential forms for the twotypes of the bounded domains in complex sub...In this paper, firstly using different method and technique we derive the cor-responding integral representation formulas of （0, q）（q 〉 0） differential forms for the twotypes of the bounded domains in complex submanifolds with codimension-m. Secondly weobtain the unified integral representation formulas of （0, q）（q 〉 0） differential forms for thegeneral bounded domain in complex submanifold with codimension-m, which include Hatzi-afratis formula, i.e. Koppelman type integral formula for the bounded domain with smoothboundary in analytic varieties. In particular, when m -- 0, we obtain the unified integralrepresentation formulas of （0, q）（q 〉 0） differential forms for general bounded domain in Cn,which are the generalization and the embodiment of Koppelman-Leray formula.展开更多
In this paper, we first introduce a concept of companion vector, and studythe Jordan canonical forms of quaternion matrices by using the methods of complex representation and companion vector, not only give out a prac...In this paper, we first introduce a concept of companion vector, and studythe Jordan canonical forms of quaternion matrices by using the methods of complex representation and companion vector, not only give out a practical algorithm for Jordancanonical form J of a quaternion matrix A, but also provide a practical algorithm forcorresponding nonsingular matrix P with P- 1 AP = J.展开更多
已有关于系统惯性时空分布(spatial-temporal distribution of system inertia,SDSI)的研究大多聚焦于惯量估计,而对其概念的表征并不统一,也缺乏对其性质的深入剖析与相关概念的系统梳理与辨析。该文试图探索大扰动下系统惯性时空分布...已有关于系统惯性时空分布(spatial-temporal distribution of system inertia,SDSI)的研究大多聚焦于惯量估计,而对其概念的表征并不统一,也缺乏对其性质的深入剖析与相关概念的系统梳理与辨析。该文试图探索大扰动下系统惯性时空分布特性的表征形式。基于频率动态过程分析剖析了惯性时空分布特性,提出系统节点惯量概念并给出该参量的性质描述参量,基于惯性物理机理提出了这些参量的量化分析方法并推导了相关系数的差分计算公式。仿真算例验证了对系统惯性时空分布特性所做的分析与判断,利用所提出的表征形式可全面而规范地表征系统惯性时空分布特征。研究可为电力系统惯性时空分布特性表征体系的构建提供参考。展开更多
In order to solve fuzzy mathematical programming with soft constraints,the initial models must first be converted into crisp models.Membership functions are employed to describe the fuzzy right-hand side parameters ne...In order to solve fuzzy mathematical programming with soft constraints,the initial models must first be converted into crisp models.Membership functions are employed to describe the fuzzy right-hand side parameters needed to achieve this conversion.In some cases,echelon form membership functions(EFMFs)are required to depict the actual fuzzy situation.However,due to their discrete properties,fuzzy programming problems with such membership functions cannot be modeled by traditional methods.Motivated by these challenges,this paper introduces a novel absolute value representation modeling approach to formulate fuzzy programming using EFMFs.This approach can translate a discrete model to a continuous one which can then be easily solved.Finally,by means of a numerical example,the effectiveness of our new approach is demonstrated.展开更多
文摘Here, we determine formulae, for the numbers of representations of a positive integer by certain sextenary quadratic forms whose coefficients are 1, 2, 3 and 6.
基金Supported by Chinese National Basic Research Program(2007CB807902)
文摘Binary signed digit representation （BSD-R） of an integer is widely used in computer arithmetic, cryptography and digital signal processing. This paper studies what the exact number of optimal BSD-R of an integer is and how to generate them entirely. We also show which kinds of integers have the maximum number of optimal BSD-Rs.
文摘In this paper, firstly using different method and technique we derive the cor-responding integral representation formulas of （0, q）（q 〉 0） differential forms for the twotypes of the bounded domains in complex submanifolds with codimension-m. Secondly weobtain the unified integral representation formulas of （0, q）（q 〉 0） differential forms for thegeneral bounded domain in complex submanifold with codimension-m, which include Hatzi-afratis formula, i.e. Koppelman type integral formula for the bounded domain with smoothboundary in analytic varieties. In particular, when m -- 0, we obtain the unified integralrepresentation formulas of （0, q）（q 〉 0） differential forms for general bounded domain in Cn,which are the generalization and the embodiment of Koppelman-Leray formula.
基金Supported by the National Natural Science Foudnation of China and Shanghai Priority Academic Discipline Foundation,Shanghai,China.
文摘In this paper, we first introduce a concept of companion vector, and studythe Jordan canonical forms of quaternion matrices by using the methods of complex representation and companion vector, not only give out a practical algorithm for Jordancanonical form J of a quaternion matrix A, but also provide a practical algorithm forcorresponding nonsingular matrix P with P- 1 AP = J.
文摘已有关于系统惯性时空分布(spatial-temporal distribution of system inertia,SDSI)的研究大多聚焦于惯量估计,而对其概念的表征并不统一,也缺乏对其性质的深入剖析与相关概念的系统梳理与辨析。该文试图探索大扰动下系统惯性时空分布特性的表征形式。基于频率动态过程分析剖析了惯性时空分布特性,提出系统节点惯量概念并给出该参量的性质描述参量,基于惯性物理机理提出了这些参量的量化分析方法并推导了相关系数的差分计算公式。仿真算例验证了对系统惯性时空分布特性所做的分析与判断,利用所提出的表征形式可全面而规范地表征系统惯性时空分布特征。研究可为电力系统惯性时空分布特性表征体系的构建提供参考。
文摘In order to solve fuzzy mathematical programming with soft constraints,the initial models must first be converted into crisp models.Membership functions are employed to describe the fuzzy right-hand side parameters needed to achieve this conversion.In some cases,echelon form membership functions(EFMFs)are required to depict the actual fuzzy situation.However,due to their discrete properties,fuzzy programming problems with such membership functions cannot be modeled by traditional methods.Motivated by these challenges,this paper introduces a novel absolute value representation modeling approach to formulate fuzzy programming using EFMFs.This approach can translate a discrete model to a continuous one which can then be easily solved.Finally,by means of a numerical example,the effectiveness of our new approach is demonstrated.
