In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit ...In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit disk in R^(2):By delicate and relatively complicated computation of radial solutions to the above equation and the asymptotic expansion of solutions near the boundary of B_(1),the uniqueness of positive solutions is obtained.The results of this paper extend the uniqueness result for the semilinear equation with critical exponential growth in CHEN et al.(2022)to the case that includes a Henon term.展开更多
The conventional Kibble–Zurek mechanism,describing driven dynamics across critical points based on the adiabatic-impulse scenario(AIS),has attracted broad attention.However,the driven dynamics at the tricritical poin...The conventional Kibble–Zurek mechanism,describing driven dynamics across critical points based on the adiabatic-impulse scenario(AIS),has attracted broad attention.However,the driven dynamics at the tricritical point with two independent relevant directions have not been adequately studied.Here,we employ the time-dependent variational principle to study the driven critical dynamics at a one-dimensional supersymmetric Ising tricritical point.For the relevant direction along the Ising critical line,the AIS apparently breaks down.Nevertheless,we find that the critical dynamics can still be described by finite-time scaling in which the driving rate has a dimension of r_(μ)=z+1/v_(μ)with z and v_(μ)being the dynamic exponent and correlation length exponent in this direction,respectively.For driven dynamics along another direction,the driving rate has a dimension of r_(p)=z+1/v_(p)with v_(p)being another correlation length exponent.Our work brings a new fundamental perspective into nonequilibrium critical dynamics near the tricritical point,which could be realized in programmable quantum processors in Rydberg atomic systems.展开更多
为了克服开放街道地图数据的空间异质性特征对其在数据匹配、更新等方面应用所造成的影响,提出一种基于指标相关性的指标权重确定算法(Criteria Importan ce Through Inter-criteria Correlation,简称CRITIC)的开放街道地图面实体匹配...为了克服开放街道地图数据的空间异质性特征对其在数据匹配、更新等方面应用所造成的影响,提出一种基于指标相关性的指标权重确定算法(Criteria Importan ce Through Inter-criteria Correlation,简称CRITIC)的开放街道地图面实体匹配方法。该方法充分考虑开放街道地图数据的空间异质性,在开放街道地图中面实体与其他数据进行匹配时,引入CRITIC算法计算开放街道地图数据中每个面要素几何相似因子的权重,避免了对匹配数据集中的所有面实体采用相同的相似因子权重,减少了人为定权方法所带来的主观性及局限性,提高了开放街道地图面实体与其他数据集的匹配精度。实验结果表明,该方法有效地克服了开放街道地图数据的空间异质性特点对匹配精度的影响,提升了开放街道地图中面实体与其他面实体数据的匹配精度,匹配的准确率、召回率和F1分数分别达到97.56%、98.04%和97.80%,均优于对比方法。展开更多
为了更合理地评价复杂多样的电价套餐,促进电价套餐适应我国电力市场的发展,在考虑电力市场多方需求的背景下,提出一种基于直觉模糊层次分析法(Intuitionistic Fuzzy Analytic Hierarchy Process,IFAHP)、指标相关法(Criteria Importanc...为了更合理地评价复杂多样的电价套餐,促进电价套餐适应我国电力市场的发展,在考虑电力市场多方需求的背景下,提出一种基于直觉模糊层次分析法(Intuitionistic Fuzzy Analytic Hierarchy Process,IFAHP)、指标相关法(Criteria Importance Though Intercrieria Correlation,CRITIC)和改进逼近理想解排序法(Technique for Order Preference by Similarity to an Ideal Solution,TOPSIS)的电价套餐评价方法。首先,从市场角度确定套餐评价指标;然后,分别采用IFAHP赋权法和CRITIC客观赋权法给各项指标赋予主观权重和客观权重,并利用纳什均衡确定各项指标的综合权重;最后,基于灰色关联度分析(Grey Relational Analysis,GRA)改进TOPSIS,使用GRA-欧氏距离测度对套餐做出评价。算例结果表明,该方法能够准确、科学地完成电价套餐评价。展开更多
得益于日趋完善的状态监测系统,抽水蓄能电站记录了海量机组运行信息,为开展抽蓄机组劣化趋势评估提供了可靠的数据保障。为此,提出了一种基于Optuna-CatBoost和CRITIC(Criteria Importance though Intercrieria Correlation)评价法的...得益于日趋完善的状态监测系统,抽水蓄能电站记录了海量机组运行信息,为开展抽蓄机组劣化趋势评估提供了可靠的数据保障。为此,提出了一种基于Optuna-CatBoost和CRITIC(Criteria Importance though Intercrieria Correlation)评价法的水电机组劣化评估方法。首先利用最大互信息系数(Maximal Information Coefficient)筛选出机组关键工况系数;然后利用Optuna对CatBoost进行参数寻优,建立Optuna-CatBoost水电机组劣化趋势评估模型;最后基于CRITIC评价法对各通道劣化序列客观赋权,生成机组整机劣化序列。试验结果表明,所提模型的精度优于其他对比模型,能很好地反映机组整机劣化趋势。展开更多
基金Supported by the Natural Science Foundation of China(12571122,12061010)。
文摘In this paper,we study the uniqueness of positive solutions to the following semilinear equations{-Δu=λ|x|^(α)ue^(u^(2)),in B_(1),u=0,onδB_(1)ueu2;in B_(1);u=0;on@B_(1);whereλ>0,α>-2;B_(1)denotes the unit disk in R^(2):By delicate and relatively complicated computation of radial solutions to the above equation and the asymptotic expansion of solutions near the boundary of B_(1),the uniqueness of positive solutions is obtained.The results of this paper extend the uniqueness result for the semilinear equation with critical exponential growth in CHEN et al.(2022)to the case that includes a Henon term.
基金supported by the National Natural Science Foundation of China(Grant Nos.12222515,12075324 for S.Yin,and 12347107,1257-4160 for Y.F.Jiang)the National Key R&D Program of China(Grant No.2022YFA1402703 for Y.F.Jiang)+1 种基金the Science and Technology Projects in Guangdong Province(Grant No.2021QN02X561 for S.Yin)the Science and Technology Projects in Guangzhou City(Grant No.2025A04J5408 for S.Yin)。
文摘The conventional Kibble–Zurek mechanism,describing driven dynamics across critical points based on the adiabatic-impulse scenario(AIS),has attracted broad attention.However,the driven dynamics at the tricritical point with two independent relevant directions have not been adequately studied.Here,we employ the time-dependent variational principle to study the driven critical dynamics at a one-dimensional supersymmetric Ising tricritical point.For the relevant direction along the Ising critical line,the AIS apparently breaks down.Nevertheless,we find that the critical dynamics can still be described by finite-time scaling in which the driving rate has a dimension of r_(μ)=z+1/v_(μ)with z and v_(μ)being the dynamic exponent and correlation length exponent in this direction,respectively.For driven dynamics along another direction,the driving rate has a dimension of r_(p)=z+1/v_(p)with v_(p)being another correlation length exponent.Our work brings a new fundamental perspective into nonequilibrium critical dynamics near the tricritical point,which could be realized in programmable quantum processors in Rydberg atomic systems.
文摘为了克服开放街道地图数据的空间异质性特征对其在数据匹配、更新等方面应用所造成的影响,提出一种基于指标相关性的指标权重确定算法(Criteria Importan ce Through Inter-criteria Correlation,简称CRITIC)的开放街道地图面实体匹配方法。该方法充分考虑开放街道地图数据的空间异质性,在开放街道地图中面实体与其他数据进行匹配时,引入CRITIC算法计算开放街道地图数据中每个面要素几何相似因子的权重,避免了对匹配数据集中的所有面实体采用相同的相似因子权重,减少了人为定权方法所带来的主观性及局限性,提高了开放街道地图面实体与其他数据集的匹配精度。实验结果表明,该方法有效地克服了开放街道地图数据的空间异质性特点对匹配精度的影响,提升了开放街道地图中面实体与其他面实体数据的匹配精度,匹配的准确率、召回率和F1分数分别达到97.56%、98.04%和97.80%,均优于对比方法。
文摘为了更合理地评价复杂多样的电价套餐,促进电价套餐适应我国电力市场的发展,在考虑电力市场多方需求的背景下,提出一种基于直觉模糊层次分析法(Intuitionistic Fuzzy Analytic Hierarchy Process,IFAHP)、指标相关法(Criteria Importance Though Intercrieria Correlation,CRITIC)和改进逼近理想解排序法(Technique for Order Preference by Similarity to an Ideal Solution,TOPSIS)的电价套餐评价方法。首先,从市场角度确定套餐评价指标;然后,分别采用IFAHP赋权法和CRITIC客观赋权法给各项指标赋予主观权重和客观权重,并利用纳什均衡确定各项指标的综合权重;最后,基于灰色关联度分析(Grey Relational Analysis,GRA)改进TOPSIS,使用GRA-欧氏距离测度对套餐做出评价。算例结果表明,该方法能够准确、科学地完成电价套餐评价。
文摘得益于日趋完善的状态监测系统,抽水蓄能电站记录了海量机组运行信息,为开展抽蓄机组劣化趋势评估提供了可靠的数据保障。为此,提出了一种基于Optuna-CatBoost和CRITIC(Criteria Importance though Intercrieria Correlation)评价法的水电机组劣化评估方法。首先利用最大互信息系数(Maximal Information Coefficient)筛选出机组关键工况系数;然后利用Optuna对CatBoost进行参数寻优,建立Optuna-CatBoost水电机组劣化趋势评估模型;最后基于CRITIC评价法对各通道劣化序列客观赋权,生成机组整机劣化序列。试验结果表明,所提模型的精度优于其他对比模型,能很好地反映机组整机劣化趋势。
