China’s economy is expected to remain stable throughout 2025.According to projections by the Center for Forecasting Science of the Academy of Mathematics and Systems Science under the Chinese Academy of Sciences,Chin...China’s economy is expected to remain stable throughout 2025.According to projections by the Center for Forecasting Science of the Academy of Mathematics and Systems Science under the Chinese Academy of Sciences,China’s GDP(gross domestic product)growth should settle at around 4.8 percent this year and will likely hit 5 percent if the government’s stimulus package is effectively implemented.I personally believe that the Chinese economy will maintain growth of about 4.6 percent in 2025 with robust performance in the first and fourth quarters and slower economic activity in the second and third quarters.展开更多
A proper conflict-free k-coloring of a graph is a proper k-coloring in which each nonisolated vertex has a color that appears ex-actly once in its open neighborhood.A graph is PCF k-colorable if it admits a proper con...A proper conflict-free k-coloring of a graph is a proper k-coloring in which each nonisolated vertex has a color that appears ex-actly once in its open neighborhood.A graph is PCF k-colorable if it admits a proper conflict-free k-coloring.The PCF chromatic number of a graph G,denoted by χ_(pcf)(G),is the minimum k such that G is PCF k-colorable.Caro et al conjectured that for a connected graph G with maximum degreeΔ≥3,χ_(pcf)(G)≤Δ+1.One case in this conjecture,a connected graph with maximum degree 3 is PCF 4-colorable,can be derived from the result of Liu and Yu.Jiménez et al stated that the upper bound of PCF chromatic number of a graph G is max{5,x(G)}without a proof.In this paper,we give new proofs of the two results above and derive that for a connected graph G with maximum degreeΔ≥3,its complete subdivision is PCF(Δ+1)-colorable.展开更多
A novel gappy technology, gappy autoencoder with proper orthogonal decomposition(Gappy POD-AE), is proposed for reconstructing physical fields from sparse data. High-dimensional data are reduced via proper orthogonal ...A novel gappy technology, gappy autoencoder with proper orthogonal decomposition(Gappy POD-AE), is proposed for reconstructing physical fields from sparse data. High-dimensional data are reduced via proper orthogonal decomposition(POD),and low-dimensional data are used to train an autoencoder(AE). By integrating the POD operator with the decoder, a nonlinear solution form is established and incorporated into a new maximum-a-posteriori(MAP)-based objective for online reconstruction.The numerical results on the two-dimensional(2D) Bhatnagar-Gross-Krook-Boltzmann(BGK-Boltzmann) equation, wave equation, shallow-water equation, and satellite data show that Gappy POD-AE achieves higher accuracy than gappy proper orthogonal decomposition(Gappy POD), especially for the data with slowly decaying singular values,and is more efficient in training than gappy autoencoder(Gappy AE). The MAP-based formulation and new gappy procedure further enhance the reconstruction accuracy.展开更多
The influence of the distribution of nano-pores on the mechanical properties evaluation of porous low-k films by surface acoustic waves （SAW） is studied. A theoretical SAW propagation model is set up to characterize...The influence of the distribution of nano-pores on the mechanical properties evaluation of porous low-k films by surface acoustic waves （SAW） is studied. A theoretical SAW propagation model is set up to characterize the periodic porous dielectrics by transversely isotropic symmetry. The theoretical deductions of SAW propagating in the low-k film/Si substrate layered structure are given in detail. The dispersive characteristics of SAW in differ- ent propagation directions and the effects of the Young＇s moduli E, E′ and shear modulus G′ of the films on these dispersive curves are found. Computational results show that E′ and G′ cannot be measured along the propagation direction that is perpendicular to the nano-pores＇ direction.展开更多
Improved delay detached eddy simulation is performed to explore the flow features and aero-optical effects of turrets with different bottom cylinder height at a freestream Mach number Ma=0.7.Analysis of both the time-...Improved delay detached eddy simulation is performed to explore the flow features and aero-optical effects of turrets with different bottom cylinder height at a freestream Mach number Ma=0.7.Analysis of both the time-averaged and instantaneous flow features demonstrate that the shock motion causes the oscillation of separated shear layer.In flow analysis,two unsteady shock-wake-correlated modes are discerned:the asymmetric shifting mode and the symmetric breathing mode.With the increase of cylinder height,the relative energy of shock gradually increases,which goes from 26%to 59%.The proper orthogonal decomposition analysis yields the single frequency peak for the two dominant modes.The frequency peaks of shifting mode are generally at StD<0.23,while the frequency peaks of breathing mode are generally at StD>0.26.The dynamic mode decomposition analysis gives range of frequency peak.The frequency peaks of shifting mode are in the range of StD=0.11-0.23,and the frequency peaks of breathing mode are in range of StD=0.26-0.41.Optical distortion analysis indicates that the distortion calculated in five cases is linked to the breathing mode.When the beam passes through the turbulent wake,it exhibits the high-frequency and high-amplitude characteristics.展开更多
文摘China’s economy is expected to remain stable throughout 2025.According to projections by the Center for Forecasting Science of the Academy of Mathematics and Systems Science under the Chinese Academy of Sciences,China’s GDP(gross domestic product)growth should settle at around 4.8 percent this year and will likely hit 5 percent if the government’s stimulus package is effectively implemented.I personally believe that the Chinese economy will maintain growth of about 4.6 percent in 2025 with robust performance in the first and fourth quarters and slower economic activity in the second and third quarters.
基金Supported by the Youth Fund of Lanzhou Jiaotong University(1200061328)。
文摘A proper conflict-free k-coloring of a graph is a proper k-coloring in which each nonisolated vertex has a color that appears ex-actly once in its open neighborhood.A graph is PCF k-colorable if it admits a proper conflict-free k-coloring.The PCF chromatic number of a graph G,denoted by χ_(pcf)(G),is the minimum k such that G is PCF k-colorable.Caro et al conjectured that for a connected graph G with maximum degreeΔ≥3,χ_(pcf)(G)≤Δ+1.One case in this conjecture,a connected graph with maximum degree 3 is PCF 4-colorable,can be derived from the result of Liu and Yu.Jiménez et al stated that the upper bound of PCF chromatic number of a graph G is max{5,x(G)}without a proof.In this paper,we give new proofs of the two results above and derive that for a connected graph G with maximum degreeΔ≥3,its complete subdivision is PCF(Δ+1)-colorable.
基金supported by the National Natural Science Foundation of China(No.12472197)。
文摘A novel gappy technology, gappy autoencoder with proper orthogonal decomposition(Gappy POD-AE), is proposed for reconstructing physical fields from sparse data. High-dimensional data are reduced via proper orthogonal decomposition(POD),and low-dimensional data are used to train an autoencoder(AE). By integrating the POD operator with the decoder, a nonlinear solution form is established and incorporated into a new maximum-a-posteriori(MAP)-based objective for online reconstruction.The numerical results on the two-dimensional(2D) Bhatnagar-Gross-Krook-Boltzmann(BGK-Boltzmann) equation, wave equation, shallow-water equation, and satellite data show that Gappy POD-AE achieves higher accuracy than gappy proper orthogonal decomposition(Gappy POD), especially for the data with slowly decaying singular values,and is more efficient in training than gappy autoencoder(Gappy AE). The MAP-based formulation and new gappy procedure further enhance the reconstruction accuracy.
文摘The influence of the distribution of nano-pores on the mechanical properties evaluation of porous low-k films by surface acoustic waves （SAW） is studied. A theoretical SAW propagation model is set up to characterize the periodic porous dielectrics by transversely isotropic symmetry. The theoretical deductions of SAW propagating in the low-k film/Si substrate layered structure are given in detail. The dispersive characteristics of SAW in differ- ent propagation directions and the effects of the Young＇s moduli E, E′ and shear modulus G′ of the films on these dispersive curves are found. Computational results show that E′ and G′ cannot be measured along the propagation direction that is perpendicular to the nano-pores＇ direction.
基金funded by the National Key Lab Foundation,China(No.2020KLF030101)the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University,China(No.CX2025031)Shaanxi Innovative Research Team of Artificial Intelligence for Fluid Mechanics,China(No.2024RS-CXTD-16)。
文摘Improved delay detached eddy simulation is performed to explore the flow features and aero-optical effects of turrets with different bottom cylinder height at a freestream Mach number Ma=0.7.Analysis of both the time-averaged and instantaneous flow features demonstrate that the shock motion causes the oscillation of separated shear layer.In flow analysis,two unsteady shock-wake-correlated modes are discerned:the asymmetric shifting mode and the symmetric breathing mode.With the increase of cylinder height,the relative energy of shock gradually increases,which goes from 26%to 59%.The proper orthogonal decomposition analysis yields the single frequency peak for the two dominant modes.The frequency peaks of shifting mode are generally at StD<0.23,while the frequency peaks of breathing mode are generally at StD>0.26.The dynamic mode decomposition analysis gives range of frequency peak.The frequency peaks of shifting mode are in the range of StD=0.11-0.23,and the frequency peaks of breathing mode are in range of StD=0.26-0.41.Optical distortion analysis indicates that the distortion calculated in five cases is linked to the breathing mode.When the beam passes through the turbulent wake,it exhibits the high-frequency and high-amplitude characteristics.
