In the 19th century, Cantor created the infinite cardinal number theory based on the “1-1 correspondence” principle. The continuum hypothesis is proposed under this theoretical framework. In 1900, Hilbert made it th...In the 19th century, Cantor created the infinite cardinal number theory based on the “1-1 correspondence” principle. The continuum hypothesis is proposed under this theoretical framework. In 1900, Hilbert made it the first problem in his famous speech on mathematical problems, which shows the importance of this question. We know that the infinitesimal problem triggered the second mathematical crisis in the 17-18th centuries. The Infinity problem is no less important than the infinitesimal problem. In the 21st century, Sergeyev introduced the Grossone method from the principle of “whole is greater than part”, and created another ruler for measuring infinite sets. The discussion in this paper shows that, compared with the cardinal number method, the Grossone method enables infinity calculation to achieve a leap from qualitative calculation to quantitative calculation. According to Grossone theory, there is neither the largest infinity and infinitesimal, nor the smallest infinity and infinitesimal. Hilbert’s first problem was caused by the immaturity of the infinity theory.展开更多
Concluding the conformity of XBRL(eXtensible Business Reporting Language)instance documents law to the Benford's law yields different results before and after a company's financial distress.A new idea of apply...Concluding the conformity of XBRL(eXtensible Business Reporting Language)instance documents law to the Benford's law yields different results before and after a company's financial distress.A new idea of applying the machine learning technique to redefine the way conventional auditors work is therefore proposed since the unacceptable conformity implies a large likelihood of a fraudulent document.Fuzzy support vector machines models are developed to implement such an idea.The dependent variable is a fuzzy variable quantifying the conformity of an XBRL instance document to the Benford's law;whereas,independent variables are financial ratios.The interval factor method is introduced to express the fuzziness in input data.It is found the range of a fuzzy support vector machines model is controlled by maximum and minimum dependent and independent variables.Therefore,defining any member function to describe the fuzziness in input data is unnecessary.The results of this study indicate that the price-to-book ratio versus equity ratio is suitable to classify the priority of auditing XBRL instance documents with the less than 30%misclassification rate.In conclusion,the machine learning technique may be used to redefine the way conventional auditors work.This study provides the main evidence of applying a future project of training smart auditors.展开更多
To study the Very Fast Transient Over-voltage (VFTO) distribution in transformer windings in gas insulated substation (GIS), a systematic methodology based on S-parameters is presented for establishing high-frequency ...To study the Very Fast Transient Over-voltage (VFTO) distribution in transformer windings in gas insulated substation (GIS), a systematic methodology based on S-parameters is presented for establishing high-frequency model of transformer windings. Firstly, voltage transfer functions are derived from S-parameters which are calculated or measured from transformer windings. Secondly, voltage transfer functions are fitted with rational functions by the vector fitting method and then the rational transfer functions are order-reduced by optimal Pade-approximation algorithm. Lastly, the resultant voltage transfer functions are synthesized by network technology. Computational results are consistent with simulation results of Electromagnetic Transient Program (EMTP) and confirm the feasibility and validity of proposed methodology.展开更多
针对变压器故障诊断中油溶气体技术的改良三比值法存在故障区域边界值判断模糊的问题,在分析改良三比值法的基础上,以欧式距离来表征隶属每种故障概率大小的形式,建立了不同故障下的基本信任分配函数(BBA)诊断模型进行变压器故障诊断,...针对变压器故障诊断中油溶气体技术的改良三比值法存在故障区域边界值判断模糊的问题,在分析改良三比值法的基础上,以欧式距离来表征隶属每种故障概率大小的形式,建立了不同故障下的基本信任分配函数(BBA)诊断模型进行变压器故障诊断,并采用D-S合成规则对不同故障的BBA进行融合,实现了对多BBA模型函数重新构造以及归一表述的功能。利用该模型对长春某500 k VA变电站的变压器故障进行实例计算,并通过改良三比值法和模糊算法进行对比分析。结果表明:该诊断模型能准确、有效地对变压器的多种常见故障进行诊断;用计算隶属故障概率的形式弥补了改良三比值法边界值计算模糊的缺陷,使故障的判别更加趋于真实准确,为电力变压器故障诊断提供了一种有效的方法。展开更多
A concrete numerical example of Z6-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 having at least 24 limit cycles and the configurations of compound eyes are given by using the bifurcati...A concrete numerical example of Z6-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 having at least 24 limit cycles and the configurations of compound eyes are given by using the bifurcation theory of planar dynamical systems and the method of detection functions. There is reason to conjecture that the Hilbert number H(2k + 1) ? (2k + I)2 - 1 for the perturbed Hamiltonian systems.展开更多
文摘In the 19th century, Cantor created the infinite cardinal number theory based on the “1-1 correspondence” principle. The continuum hypothesis is proposed under this theoretical framework. In 1900, Hilbert made it the first problem in his famous speech on mathematical problems, which shows the importance of this question. We know that the infinitesimal problem triggered the second mathematical crisis in the 17-18th centuries. The Infinity problem is no less important than the infinitesimal problem. In the 21st century, Sergeyev introduced the Grossone method from the principle of “whole is greater than part”, and created another ruler for measuring infinite sets. The discussion in this paper shows that, compared with the cardinal number method, the Grossone method enables infinity calculation to achieve a leap from qualitative calculation to quantitative calculation. According to Grossone theory, there is neither the largest infinity and infinitesimal, nor the smallest infinity and infinitesimal. Hilbert’s first problem was caused by the immaturity of the infinity theory.
文摘Concluding the conformity of XBRL(eXtensible Business Reporting Language)instance documents law to the Benford's law yields different results before and after a company's financial distress.A new idea of applying the machine learning technique to redefine the way conventional auditors work is therefore proposed since the unacceptable conformity implies a large likelihood of a fraudulent document.Fuzzy support vector machines models are developed to implement such an idea.The dependent variable is a fuzzy variable quantifying the conformity of an XBRL instance document to the Benford's law;whereas,independent variables are financial ratios.The interval factor method is introduced to express the fuzziness in input data.It is found the range of a fuzzy support vector machines model is controlled by maximum and minimum dependent and independent variables.Therefore,defining any member function to describe the fuzziness in input data is unnecessary.The results of this study indicate that the price-to-book ratio versus equity ratio is suitable to classify the priority of auditing XBRL instance documents with the less than 30%misclassification rate.In conclusion,the machine learning technique may be used to redefine the way conventional auditors work.This study provides the main evidence of applying a future project of training smart auditors.
基金the I mportant National Science Foundation of Hebei Province (E2006001036)Science and Tech-nology Project of Hebei Province (072156167)
文摘To study the Very Fast Transient Over-voltage (VFTO) distribution in transformer windings in gas insulated substation (GIS), a systematic methodology based on S-parameters is presented for establishing high-frequency model of transformer windings. Firstly, voltage transfer functions are derived from S-parameters which are calculated or measured from transformer windings. Secondly, voltage transfer functions are fitted with rational functions by the vector fitting method and then the rational transfer functions are order-reduced by optimal Pade-approximation algorithm. Lastly, the resultant voltage transfer functions are synthesized by network technology. Computational results are consistent with simulation results of Electromagnetic Transient Program (EMTP) and confirm the feasibility and validity of proposed methodology.
文摘针对变压器故障诊断中油溶气体技术的改良三比值法存在故障区域边界值判断模糊的问题,在分析改良三比值法的基础上,以欧式距离来表征隶属每种故障概率大小的形式,建立了不同故障下的基本信任分配函数(BBA)诊断模型进行变压器故障诊断,并采用D-S合成规则对不同故障的BBA进行融合,实现了对多BBA模型函数重新构造以及归一表述的功能。利用该模型对长春某500 k VA变电站的变压器故障进行实例计算,并通过改良三比值法和模糊算法进行对比分析。结果表明:该诊断模型能准确、有效地对变压器的多种常见故障进行诊断;用计算隶属故障概率的形式弥补了改良三比值法边界值计算模糊的缺陷,使故障的判别更加趋于真实准确,为电力变压器故障诊断提供了一种有效的方法。
基金This work was supported by the Strategic Research (Grant No. 7000934) from the City University of Hong Kong.
文摘A concrete numerical example of Z6-equivariant planar perturbed Hamiltonian polynomial vector fields of degree 5 having at least 24 limit cycles and the configurations of compound eyes are given by using the bifurcation theory of planar dynamical systems and the method of detection functions. There is reason to conjecture that the Hilbert number H(2k + 1) ? (2k + I)2 - 1 for the perturbed Hamiltonian systems.
