We consider a class of modified quasilinear Schrodinger equations-△u+k/2u△u^(2)=λα(x)u^(-α)+b(x)u^(β) in Ω with u(x)=0 on■Ω,where Ω■R^(N)is a bounded domain with a regular boundary,N≥3,a and b are bounded ...We consider a class of modified quasilinear Schrodinger equations-△u+k/2u△u^(2)=λα(x)u^(-α)+b(x)u^(β) in Ω with u(x)=0 on■Ω,where Ω■R^(N)is a bounded domain with a regular boundary,N≥3,a and b are bounded mensurable functions,0<α<1<β<2*-1 and k,λ≥0 are two parameters.We establish the global existence and multiplicity results of positive solutions in H^(1)_(0)(Ω)∩L^(∞)(Ω)for appropriate classes of parameters k andλand coefficients a(x)and b(x).展开更多
We study a double phase Dirichlet problem with a reaction that has a parametric singular term. Using the Nehari manifold method, we show that for all small values of the parameter, the problem has at least two positiv...We study a double phase Dirichlet problem with a reaction that has a parametric singular term. Using the Nehari manifold method, we show that for all small values of the parameter, the problem has at least two positive, energy minimizing solutions.展开更多
In this paper, we establish the existence of at least four distinct solutions to an elliptic problem with singular cylindrical potential, a concave term, and critical Caffarelli-Kohn-Nirenberg exponent, by using the N...In this paper, we establish the existence of at least four distinct solutions to an elliptic problem with singular cylindrical potential, a concave term, and critical Caffarelli-Kohn-Nirenberg exponent, by using the Nehari manifold and mountain pass theorem.展开更多
针对中长期电力负荷序列噪声含量高、难以直接提取序列周期规律从而影响预测精度的问题,提出了一种基于完全自适应噪声集合经验模态分解(complete ensemble empirical mode decomposition with adaptive noise,CEEMDAN)和奇异谱分析(sin...针对中长期电力负荷序列噪声含量高、难以直接提取序列周期规律从而影响预测精度的问题,提出了一种基于完全自适应噪声集合经验模态分解(complete ensemble empirical mode decomposition with adaptive noise,CEEMDAN)和奇异谱分析(singular spectrum analysis,SSA)双重分解的双向长短时记忆网络(bidirectional long and short time memory,BiLSTM)预测模型。首先,采用CEEMDAN对历史负荷进行分解,以得到若干个周期规律更为清晰的子序列;再利用多尺度熵(multiscale entropy,MSE)计算所有子序列的复杂程度,根据不同时间尺度上的样本熵值将相似的子序列重构聚合;然后,利用SSA去噪的功能,对高度复杂的新序列进行二次分解,去除序列中的噪声并提取更为主要的规律,从而进一步提高中长序列预测精度;再将得到的最终一组子序列输入BiLSTM进行预测;最后,考虑到天气、节假日等外部因素对电力负荷的影响,提出了一种误差修正技术。选取了巴拿马某地区的用电负荷进行实验,实验结果表明,经过双重分解可以将均方根误差降低87.4%;预测未来一年的负荷序列时,采用的BiLSTM模型将拟合系数最高提高2.5%;所提出的误差修正技术可将均方根误差降低9.7%。展开更多
When calculating electromagnetic scattering using method of moments （MoM）, integral of the singular term has a significant influence on the results. This paper transforms the singular surface integral to the contour...When calculating electromagnetic scattering using method of moments （MoM）, integral of the singular term has a significant influence on the results. This paper transforms the singular surface integral to the contour integral. The integrand is expanded to Taylor series and the integral results in a closed form. The cut-off error is analyzed to show that the series converges fast and only about 2 terms can agree wel with the accurate result. The comparison of the perfect electric conductive （PEC） sphere＇s bi-static radar cross section （RCS） using MoM and the accurate method validates the feasibility in manipulating the singularity. The error due to the facet size and the cut-off terms of the series are analyzed in examples.展开更多
空调负荷的精准预测对建筑空调系统优化控制具有重要意义。为提高空调负荷预测精度,提出了一种基于奇异谱分析(SSA,Singular Spectrum Analysis)的卷积神经网络(CNN,Convolutional Neural Network)和双向长短时记忆网络(BiLSTM,Bidirect...空调负荷的精准预测对建筑空调系统优化控制具有重要意义。为提高空调负荷预测精度,提出了一种基于奇异谱分析(SSA,Singular Spectrum Analysis)的卷积神经网络(CNN,Convolutional Neural Network)和双向长短时记忆网络(BiLSTM,Bidirectional Long Short Term Memory)短期空调负荷预测模型。使用皮尔森相关系数选取与空调负荷高相关性特征。针对空调负荷的波动性和随机性,采用SSA将空调负荷分解为多个分量,同时将各个分量带入CNN-BiLSTM模型进行预测,该模型利用了CNN的特征提取和BiLSTM的双向学习能力,并将各个分量预测结果进行重构。通过不同建筑类型的空调数据对该模型进行验证分析,发现所提出模型在预测办公建筑空调负荷中RMSE、MAPE和MAE为19.47RT、14.72RT和2.33%,在预测商业建筑空调负荷中RMSE、MAPE和MAE为82.5RT、34.21RT和0.87%。结果表明,所提出的模型具有普适性且精度较高,可进行推广应用。展开更多
A higher order boundary dement method （HOBEM） is implemented for wave-current action on structures. The freeterm coefficient and Cauchy principal value （ GPV） integrals are computed by direct methods. Numerical ex...A higher order boundary dement method （HOBEM） is implemented for wave-current action on structures. The freeterm coefficient and Cauchy principal value （ GPV） integrals are computed by direct methods. Numerical experiments are carried out to validate the computation of free-term coefficient and GPV integrals. The results show that the computation precision of free-term coefficient is very high for various bodies, even with edges and corners, and the convergence speed is fast for CPV integrals for different meshes. The comparison of the second order mean drift force due to wave-current action on a uniform cylinder is made with an analytic solution. It is found that good agreement exists between the present calculation and the analytic solutions. Finally, the numerical code is applied for computing wave-current action on Snorrc TLP.展开更多
The nonlinear viscoelastic wave equation ｜μt｜^pμtt-△μ-μutt＋∫^t0g（t-s）△μ（s）ds＋｜μ｜^pU=0,in a bounded domain with initial conditions and Dirichlet boundary conditions is consid- ered. We prove that, fo...The nonlinear viscoelastic wave equation ｜μt｜^pμtt-△μ-μutt＋∫^t0g（t-s）△μ（s）ds＋｜μ｜^pU=0,in a bounded domain with initial conditions and Dirichlet boundary conditions is consid- ered. We prove that, for a class of kernels 9 which is singular at zero, the exponential decay rate of the solution energy. The result is obtained by introducing an appropriate Lyapounov functional and using energy method similar to the work of Tatar in 2009. This work improves earlier results.展开更多
In this paper, we investigate the solvability of a class of semilinear elliptic equations which are perturbation of the problems involving critical Hardy-Sobolev exponent and Hardy singular terms. The existence of at ...In this paper, we investigate the solvability of a class of semilinear elliptic equations which are perturbation of the problems involving critical Hardy-Sobolev exponent and Hardy singular terms. The existence of at least a positive radial solution is established for a class of semilinear elliptic problems involving critical Hardy-Sobolev exponent and Hardy terms. The main tools are variational method, critical point theory and some analysis techniques.展开更多
基金supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq/Brazil) (Grant No.311562/2020-5)supported by National Natural Science Foundation of China (Grant Nos.11971436 and 12011530199)+1 种基金Natural Science Foundation of Zhejiang (Grant Nos.LZ22A010001 and LD19A010001)supported by Coordenacao de Aperfei coamento de Pessoal de Nível Superior (CAPES/Brazil) (Grant No.2788/2015-02)。
文摘We consider a class of modified quasilinear Schrodinger equations-△u+k/2u△u^(2)=λα(x)u^(-α)+b(x)u^(β) in Ω with u(x)=0 on■Ω,where Ω■R^(N)is a bounded domain with a regular boundary,N≥3,a and b are bounded mensurable functions,0<α<1<β<2*-1 and k,λ≥0 are two parameters.We establish the global existence and multiplicity results of positive solutions in H^(1)_(0)(Ω)∩L^(∞)(Ω)for appropriate classes of parameters k andλand coefficients a(x)and b(x).
基金supported by the NNSF of China (12071413, 12111530282)the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie grant agreement No. 823731 CONMECH。
文摘We study a double phase Dirichlet problem with a reaction that has a parametric singular term. Using the Nehari manifold method, we show that for all small values of the parameter, the problem has at least two positive, energy minimizing solutions.
文摘In this paper, we establish the existence of at least four distinct solutions to an elliptic problem with singular cylindrical potential, a concave term, and critical Caffarelli-Kohn-Nirenberg exponent, by using the Nehari manifold and mountain pass theorem.
文摘针对中长期电力负荷序列噪声含量高、难以直接提取序列周期规律从而影响预测精度的问题,提出了一种基于完全自适应噪声集合经验模态分解(complete ensemble empirical mode decomposition with adaptive noise,CEEMDAN)和奇异谱分析(singular spectrum analysis,SSA)双重分解的双向长短时记忆网络(bidirectional long and short time memory,BiLSTM)预测模型。首先,采用CEEMDAN对历史负荷进行分解,以得到若干个周期规律更为清晰的子序列;再利用多尺度熵(multiscale entropy,MSE)计算所有子序列的复杂程度,根据不同时间尺度上的样本熵值将相似的子序列重构聚合;然后,利用SSA去噪的功能,对高度复杂的新序列进行二次分解,去除序列中的噪声并提取更为主要的规律,从而进一步提高中长序列预测精度;再将得到的最终一组子序列输入BiLSTM进行预测;最后,考虑到天气、节假日等外部因素对电力负荷的影响,提出了一种误差修正技术。选取了巴拿马某地区的用电负荷进行实验,实验结果表明,经过双重分解可以将均方根误差降低87.4%;预测未来一年的负荷序列时,采用的BiLSTM模型将拟合系数最高提高2.5%;所提出的误差修正技术可将均方根误差降低9.7%。
基金supported by the National Natural Science Foundationof China for the Youth(51307004)
文摘When calculating electromagnetic scattering using method of moments （MoM）, integral of the singular term has a significant influence on the results. This paper transforms the singular surface integral to the contour integral. The integrand is expanded to Taylor series and the integral results in a closed form. The cut-off error is analyzed to show that the series converges fast and only about 2 terms can agree wel with the accurate result. The comparison of the perfect electric conductive （PEC） sphere＇s bi-static radar cross section （RCS） using MoM and the accurate method validates the feasibility in manipulating the singularity. The error due to the facet size and the cut-off terms of the series are analyzed in examples.
文摘为了解决单个神经网络预测的局限性和时间序列的波动性,提出了一种奇异谱分析(singular spectrum analysis,SSA)和Stacking框架相结合的短期负荷预测方法。利用随机森林筛选出与历史负荷相关性强烈的特征因素,采用SSA为负荷数据降噪,简化模型计算过程;基于Stacking框架,结合长短期记忆(long and short-term memory,LSTM)-自注意力机制(self-attention mechanism,SA)、径向基(radial base functions,RBF)神经网络和线性回归方法集成新的组合模型,同时利用交叉验证方法避免模型过拟合;选取PJM和澳大利亚电力负荷数据集进行验证。仿真结果表明,与其他模型比较,所提模型预测精度高。
文摘空调负荷的精准预测对建筑空调系统优化控制具有重要意义。为提高空调负荷预测精度,提出了一种基于奇异谱分析(SSA,Singular Spectrum Analysis)的卷积神经网络(CNN,Convolutional Neural Network)和双向长短时记忆网络(BiLSTM,Bidirectional Long Short Term Memory)短期空调负荷预测模型。使用皮尔森相关系数选取与空调负荷高相关性特征。针对空调负荷的波动性和随机性,采用SSA将空调负荷分解为多个分量,同时将各个分量带入CNN-BiLSTM模型进行预测,该模型利用了CNN的特征提取和BiLSTM的双向学习能力,并将各个分量预测结果进行重构。通过不同建筑类型的空调数据对该模型进行验证分析,发现所提出模型在预测办公建筑空调负荷中RMSE、MAPE和MAE为19.47RT、14.72RT和2.33%,在预测商业建筑空调负荷中RMSE、MAPE和MAE为82.5RT、34.21RT和0.87%。结果表明,所提出的模型具有普适性且精度较高,可进行推广应用。
基金This researchis supported by Research Fund for Doctoral Programs of Higher Education (Grant No.20030141006) ,and a Program for Changjiang Scholars and Innovative Research Teams in Universities (Grant No.IRT0420)
文摘A higher order boundary dement method （HOBEM） is implemented for wave-current action on structures. The freeterm coefficient and Cauchy principal value （ GPV） integrals are computed by direct methods. Numerical experiments are carried out to validate the computation of free-term coefficient and GPV integrals. The results show that the computation precision of free-term coefficient is very high for various bodies, even with edges and corners, and the convergence speed is fast for CPV integrals for different meshes. The comparison of the second order mean drift force due to wave-current action on a uniform cylinder is made with an analytic solution. It is found that good agreement exists between the present calculation and the analytic solutions. Finally, the numerical code is applied for computing wave-current action on Snorrc TLP.
文摘The nonlinear viscoelastic wave equation ｜μt｜^pμtt-△μ-μutt＋∫^t0g（t-s）△μ（s）ds＋｜μ｜^pU=0,in a bounded domain with initial conditions and Dirichlet boundary conditions is consid- ered. We prove that, for a class of kernels 9 which is singular at zero, the exponential decay rate of the solution energy. The result is obtained by introducing an appropriate Lyapounov functional and using energy method similar to the work of Tatar in 2009. This work improves earlier results.
文摘In this paper, we investigate the solvability of a class of semilinear elliptic equations which are perturbation of the problems involving critical Hardy-Sobolev exponent and Hardy singular terms. The existence of at least a positive radial solution is established for a class of semilinear elliptic problems involving critical Hardy-Sobolev exponent and Hardy terms. The main tools are variational method, critical point theory and some analysis techniques.
