The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is ob...The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is observed in several relaxation experiments on various dielectrics studies since late 19th Century. This relaxation law is also regarded as “universal-law” for dielectric relaxations;and is also termed as power law. This empirical Curie-von Schewidler relaxation law is then used to derive fractional differential equations describing constituent expression for capacitor. In this paper, we give simple mathematical treatment to derive the distribution of relaxation rates of this Curie-von Schweidler law, and show that the relaxation rate follows Zipf’s power law distribution. We also show the method developed here give Zipfian power law distribution for relaxing time constants. Then we will show however mathematically correct this may be, but physical interpretation from the obtained time constants distribution are contradictory to the Zipfian rate relaxation distribution. In this paper, we develop possible explanation that as to why Zipfian distribution of relaxation rates appears for Curie-von Schweidler Law, and relate this law to time variant rate of relaxation. In this paper, we derive appearance of fractional derivative while using Zipfian power law distribution that gives notion of scale dependent relaxation rate function for Curie-von Schweidler relaxation phenomena. This paper gives analytical approach to get insight of a non-Debye relaxation and gives a new treatment to especially much used empirical Curie-von Schweidler (universal) relaxation law.展开更多
事件抽取是自然语言处理(Natural Language Processing,NLP)领域的一个研究热点。现有的事件抽取模型大多基于小规模训练集,无法应用于大规模开放领域。针对大规模开放域事件抽取中事件表征困难的问题,提出了一种基于Zipf’s共生矩阵分...事件抽取是自然语言处理(Natural Language Processing,NLP)领域的一个研究热点。现有的事件抽取模型大多基于小规模训练集,无法应用于大规模开放领域。针对大规模开放域事件抽取中事件表征困难的问题,提出了一种基于Zipf’s共生矩阵分解的事件向量计算方法。首先,从开放语料中提取事件元组作为事件标签,并对事件元组进行抽象、剪枝和消歧。然后,利用Zipf’s共生矩阵表示事件的上下文分布,利用主成分分析(Principal Component Analysis,PCA)对共生矩阵进行分解,得到初始事件向量,并利用自编码器对初始事件向量进行非线性变换。采用最近邻检测和事件检测两种任务对事件向量的性能进行测试,结果表明,基于Zipf’s共生矩阵分解得到的事件向量能够对事件之间的相似性和相关性信息进行全局性表征,避免编码过细而造成语义偏移。展开更多
A set of techniques for well treatment aimed to enhance oil recovery are considered in the present study.These are based on the application of elastic waves of various types(dilation-wave,vibro-wave,or other acoustica...A set of techniques for well treatment aimed to enhance oil recovery are considered in the present study.These are based on the application of elastic waves of various types(dilation-wave,vibro-wave,or other acoustically induced effects).In such a context,a new technique is proposed to predict the effectiveness of the elastic-wave well treatment using the rank distribution according to Zipf’s law.It is revealed that,when the results of elastic wave well treatments are analyzed,groups of wells exploiting various geological deposits can differ in terms of their slope coefficients and free members.As the slope coefficient increases,the average increase in the well oil production rate(after the well treatment)becomes larger.An equation is obtained accordingly for estimating the slope coefficient in the Zipf’s equation from the frequency of the elastic wave.The obtained results demonstrate the applicability of the Zipf’s law in the analysis of the technological efficiency of elastic-wave well treatment methods.展开更多
文摘The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is observed in several relaxation experiments on various dielectrics studies since late 19th Century. This relaxation law is also regarded as “universal-law” for dielectric relaxations;and is also termed as power law. This empirical Curie-von Schewidler relaxation law is then used to derive fractional differential equations describing constituent expression for capacitor. In this paper, we give simple mathematical treatment to derive the distribution of relaxation rates of this Curie-von Schweidler law, and show that the relaxation rate follows Zipf’s power law distribution. We also show the method developed here give Zipfian power law distribution for relaxing time constants. Then we will show however mathematically correct this may be, but physical interpretation from the obtained time constants distribution are contradictory to the Zipfian rate relaxation distribution. In this paper, we develop possible explanation that as to why Zipfian distribution of relaxation rates appears for Curie-von Schweidler Law, and relate this law to time variant rate of relaxation. In this paper, we derive appearance of fractional derivative while using Zipfian power law distribution that gives notion of scale dependent relaxation rate function for Curie-von Schweidler relaxation phenomena. This paper gives analytical approach to get insight of a non-Debye relaxation and gives a new treatment to especially much used empirical Curie-von Schweidler (universal) relaxation law.
文摘事件抽取是自然语言处理(Natural Language Processing,NLP)领域的一个研究热点。现有的事件抽取模型大多基于小规模训练集,无法应用于大规模开放领域。针对大规模开放域事件抽取中事件表征困难的问题,提出了一种基于Zipf’s共生矩阵分解的事件向量计算方法。首先,从开放语料中提取事件元组作为事件标签,并对事件元组进行抽象、剪枝和消歧。然后,利用Zipf’s共生矩阵表示事件的上下文分布,利用主成分分析(Principal Component Analysis,PCA)对共生矩阵进行分解,得到初始事件向量,并利用自编码器对初始事件向量进行非线性变换。采用最近邻检测和事件检测两种任务对事件向量的性能进行测试,结果表明,基于Zipf’s共生矩阵分解得到的事件向量能够对事件之间的相似性和相关性信息进行全局性表征,避免编码过细而造成语义偏移。
基金supported by the Government of Perm Krai,Research Project No.C-26/628 dated 05/04/2021.
文摘A set of techniques for well treatment aimed to enhance oil recovery are considered in the present study.These are based on the application of elastic waves of various types(dilation-wave,vibro-wave,or other acoustically induced effects).In such a context,a new technique is proposed to predict the effectiveness of the elastic-wave well treatment using the rank distribution according to Zipf’s law.It is revealed that,when the results of elastic wave well treatments are analyzed,groups of wells exploiting various geological deposits can differ in terms of their slope coefficients and free members.As the slope coefficient increases,the average increase in the well oil production rate(after the well treatment)becomes larger.An equation is obtained accordingly for estimating the slope coefficient in the Zipf’s equation from the frequency of the elastic wave.The obtained results demonstrate the applicability of the Zipf’s law in the analysis of the technological efficiency of elastic-wave well treatment methods.
