For the Sylvester continued fraction expansions of real numbers,FAN et al.(2007)proved that,for almost all real numbers,the nth partial quotient grows exponentially with respect to the product of the first n-1 partial...For the Sylvester continued fraction expansions of real numbers,FAN et al.(2007)proved that,for almost all real numbers,the nth partial quotient grows exponentially with respect to the product of the first n-1 partial quotients.In this paper,we establish the Hausdorff dimension of the exceptional set where the growth rate is a general function.展开更多
该文在有界光滑域Ω■R^(n)(n≥3)上研究了一个带奇异灵敏度的两组分非局部模型,该模型是三组分的Jones-Brantingham-Chayes趋向性模型的一个简化模型,后者被用于模拟在警察威慑下犯罪活动的时空动态.该文在较大趋化敏感系数范围内证明...该文在有界光滑域Ω■R^(n)(n≥3)上研究了一个带奇异灵敏度的两组分非局部模型,该模型是三组分的Jones-Brantingham-Chayes趋向性模型的一个简化模型,后者被用于模拟在警察威慑下犯罪活动的时空动态.该文在较大趋化敏感系数范围内证明了相应初边值问题拥有全局经典解.值得指出的是,相较于无警察威慑效应的Short et al趋向性犯罪模型的相关结果,警察威慑扩大了确保解全局存在的趋化敏感系数范围,在某种意义下这也表明了警察威慑效应对模型解性质具有正则化效应.注意,先前数值结果(Jones,Brantingham and Chayes.Math Models Methods Appl Sci,2010)表明警察威慑有益于镇压犯罪热点的形成,因此该文的研究结果也是相应数值结果的一个理论支持.展开更多
基金Supported by Projects from Chongqing Municipal Science and Technology Commission(CSTB2022NSCQ-MSX0445)。
文摘For the Sylvester continued fraction expansions of real numbers,FAN et al.(2007)proved that,for almost all real numbers,the nth partial quotient grows exponentially with respect to the product of the first n-1 partial quotients.In this paper,we establish the Hausdorff dimension of the exceptional set where the growth rate is a general function.
文摘该文在有界光滑域Ω■R^(n)(n≥3)上研究了一个带奇异灵敏度的两组分非局部模型,该模型是三组分的Jones-Brantingham-Chayes趋向性模型的一个简化模型,后者被用于模拟在警察威慑下犯罪活动的时空动态.该文在较大趋化敏感系数范围内证明了相应初边值问题拥有全局经典解.值得指出的是,相较于无警察威慑效应的Short et al趋向性犯罪模型的相关结果,警察威慑扩大了确保解全局存在的趋化敏感系数范围,在某种意义下这也表明了警察威慑效应对模型解性质具有正则化效应.注意,先前数值结果(Jones,Brantingham and Chayes.Math Models Methods Appl Sci,2010)表明警察威慑有益于镇压犯罪热点的形成,因此该文的研究结果也是相应数值结果的一个理论支持.
