Here the authors are interested in the zero set of Sobolev functions and functions of bounded variation with negative power of integrability. The main result is a general Hausdorff dimension estimate on the size of ze...Here the authors are interested in the zero set of Sobolev functions and functions of bounded variation with negative power of integrability. The main result is a general Hausdorff dimension estimate on the size of zero set. The research is motivated by the model on van der waal force driven thin film, which is a singular elliptic equation. After obtaining some basic regularity result, the authors get an estimate on the size of singular set; such set corresponds to the thin film rupture set in the thin film model.展开更多
Considering the Julia set J（Tλ） of the Yang-Lee zeros of the Potts model on the diamond hierarchical Lattice on the complex plane, the authors proved that HDJ（Tλ） 〉 1 and discussed the continuity of J（Tλ） in...Considering the Julia set J（Tλ） of the Yang-Lee zeros of the Potts model on the diamond hierarchical Lattice on the complex plane, the authors proved that HDJ（Tλ） 〉 1 and discussed the continuity of J（Tλ） in Hausdorff topology for λ∈R.展开更多
开放集文字识别(Open-set text recognition,OSTR)是一项新任务,旨在解决开放环境下文字识别应用中的语言模型偏差及新字符识别与拒识问题.最近的OSTR方法通过将上下文信息与视觉信息分离来解决语言模型偏差问题.然而,这些方法往往忽视...开放集文字识别(Open-set text recognition,OSTR)是一项新任务,旨在解决开放环境下文字识别应用中的语言模型偏差及新字符识别与拒识问题.最近的OSTR方法通过将上下文信息与视觉信息分离来解决语言模型偏差问题.然而,这些方法往往忽视了字符视觉细节的重要性.考虑到上下文信息的偏差,局部细节信息在区分视觉上接近的字符时变得更加重要.本文提出一种基于自适应字符部件表示的开放集文字识别框架,构建基于文字局部结构相似度量的开放集文字识别方法,通过对不同字符部件进行显式建模来改进对局部细节特征的建模能力.与基于字根(Radical)的方法不同,所提出的框架采用数据驱动的部件设计,具有语言无关的特性和跨语言泛化识别的能力.此外,还提出一种局部性约束正则项来使模型训练更加稳定.大量的对比实验表明,本文方法在开放集、传统闭集文字识别任务上均具有良好的性能.展开更多
In this paper, a Ritt-Wu＇s characteristic set method for ordinary difference systems is proposed, which is valid for any admissible ordering. New definition for irreducible chains and new zero decomposition algorithm...In this paper, a Ritt-Wu＇s characteristic set method for ordinary difference systems is proposed, which is valid for any admissible ordering. New definition for irreducible chains and new zero decomposition algorithms are also proposed.展开更多
By viewing spacetime as a transfinite Turing computer, the present work is aimed at a generalization and geometrical-topological reinterpretation of a relatively old conjecture that the wormholes of general relativity...By viewing spacetime as a transfinite Turing computer, the present work is aimed at a generalization and geometrical-topological reinterpretation of a relatively old conjecture that the wormholes of general relativity are behind the physics and mathematics of quantum entanglement theory. To do this we base ourselves on the comprehensive set theoretical and topological machinery of the Cantorian-fractal E-infinity spacetime theory. Going all the way in this direction we even go beyond a quantum gravity theory to a precise set theoretical understanding of what a quantum particle, a quantum wave and quantum spacetime are. As a consequence of all these results and insights we can reason that the local Casimir pressure is the difference between the zero set quantum particle topological pressure and the empty set quantum wave topological pressure which acts as a wormhole “connecting” two different quantum particles with varying degrees of entanglement corresponding to varying degrees of emptiness of the empty set (wormhole). Our final result generalizes the recent conceptual equation of Susskind and Maldacena ER = EPR to become ZMG = ER = EPR where ZMG stands for zero measure Rindler-KAM geometry (of spacetime). These results were only possible because of the ultimate simplicity of our exact model based on Mauldin-Williams random Cantor sets and the corresponding exact Hardy’s quantum entanglement probability P(H) = where is the Hausdorff dimension of the topologically zero dimensional random Cantor thin set, i.e. a zero measure set and . On the other hand the positive measure spatial separation between the zero sets is a fat Cantor empty set possessing a Hausdorff dimension equal while its Menger-Urysohn topological dimension is a negative value equal minus one. This is the mathematical quintessence of a wormhole paralleling multiple connectivity in classical topology. It is both physically there because of the positive measure and not there because of the negative topological dimension.展开更多
针对当前近零碳园区综合评价指标体系缺失的问题,首先,构建了包含7项一级指标和20项二级指标的评价体系,并明确了指标内涵及计算方法;其次,通过主客观结合的集值迭代–批判法(Set value iteration,SVI;Criteria importance through inte...针对当前近零碳园区综合评价指标体系缺失的问题,首先,构建了包含7项一级指标和20项二级指标的评价体系,并明确了指标内涵及计算方法;其次,通过主客观结合的集值迭代–批判法(Set value iteration,SVI;Criteria importance through intercrieria correlation,CRITIC)确定指标主客观权重,根据矩阵论基本理论计算各指标组合权重,从而避免了单一赋权的片面性;然后,分别研究定性和定量指标的模糊综合计算方式,构建了综合评价模型;最后,以某近零碳园区运行数据为例进行了验证。验证结果表明,所提方法能较为全面地对近零碳排放园区建设情况进行科学评价。展开更多
文摘Here the authors are interested in the zero set of Sobolev functions and functions of bounded variation with negative power of integrability. The main result is a general Hausdorff dimension estimate on the size of zero set. The research is motivated by the model on van der waal force driven thin film, which is a singular elliptic equation. After obtaining some basic regularity result, the authors get an estimate on the size of singular set; such set corresponds to the thin film rupture set in the thin film model.
基金supported by National Natural Science Foundation of China (10625107)Program for New Century Excellent Talents in University (04-0490)
文摘Considering the Julia set J（Tλ） of the Yang-Lee zeros of the Potts model on the diamond hierarchical Lattice on the complex plane, the authors proved that HDJ（Tλ） 〉 1 and discussed the continuity of J（Tλ） in Hausdorff topology for λ∈R.
文摘开放集文字识别(Open-set text recognition,OSTR)是一项新任务,旨在解决开放环境下文字识别应用中的语言模型偏差及新字符识别与拒识问题.最近的OSTR方法通过将上下文信息与视觉信息分离来解决语言模型偏差问题.然而,这些方法往往忽视了字符视觉细节的重要性.考虑到上下文信息的偏差,局部细节信息在区分视觉上接近的字符时变得更加重要.本文提出一种基于自适应字符部件表示的开放集文字识别框架,构建基于文字局部结构相似度量的开放集文字识别方法,通过对不同字符部件进行显式建模来改进对局部细节特征的建模能力.与基于字根(Radical)的方法不同,所提出的框架采用数据驱动的部件设计,具有语言无关的特性和跨语言泛化识别的能力.此外,还提出一种局部性约束正则项来使模型训练更加稳定.大量的对比实验表明,本文方法在开放集、传统闭集文字识别任务上均具有良好的性能.
文摘In this paper, a Ritt-Wu＇s characteristic set method for ordinary difference systems is proposed, which is valid for any admissible ordering. New definition for irreducible chains and new zero decomposition algorithms are also proposed.
文摘By viewing spacetime as a transfinite Turing computer, the present work is aimed at a generalization and geometrical-topological reinterpretation of a relatively old conjecture that the wormholes of general relativity are behind the physics and mathematics of quantum entanglement theory. To do this we base ourselves on the comprehensive set theoretical and topological machinery of the Cantorian-fractal E-infinity spacetime theory. Going all the way in this direction we even go beyond a quantum gravity theory to a precise set theoretical understanding of what a quantum particle, a quantum wave and quantum spacetime are. As a consequence of all these results and insights we can reason that the local Casimir pressure is the difference between the zero set quantum particle topological pressure and the empty set quantum wave topological pressure which acts as a wormhole “connecting” two different quantum particles with varying degrees of entanglement corresponding to varying degrees of emptiness of the empty set (wormhole). Our final result generalizes the recent conceptual equation of Susskind and Maldacena ER = EPR to become ZMG = ER = EPR where ZMG stands for zero measure Rindler-KAM geometry (of spacetime). These results were only possible because of the ultimate simplicity of our exact model based on Mauldin-Williams random Cantor sets and the corresponding exact Hardy’s quantum entanglement probability P(H) = where is the Hausdorff dimension of the topologically zero dimensional random Cantor thin set, i.e. a zero measure set and . On the other hand the positive measure spatial separation between the zero sets is a fat Cantor empty set possessing a Hausdorff dimension equal while its Menger-Urysohn topological dimension is a negative value equal minus one. This is the mathematical quintessence of a wormhole paralleling multiple connectivity in classical topology. It is both physically there because of the positive measure and not there because of the negative topological dimension.
文摘针对当前近零碳园区综合评价指标体系缺失的问题,首先,构建了包含7项一级指标和20项二级指标的评价体系,并明确了指标内涵及计算方法;其次,通过主客观结合的集值迭代–批判法(Set value iteration,SVI;Criteria importance through intercrieria correlation,CRITIC)确定指标主客观权重,根据矩阵论基本理论计算各指标组合权重,从而避免了单一赋权的片面性;然后,分别研究定性和定量指标的模糊综合计算方式,构建了综合评价模型;最后,以某近零碳园区运行数据为例进行了验证。验证结果表明,所提方法能较为全面地对近零碳排放园区建设情况进行科学评价。
