Despite of the wide use of the factor models, the issue of determining the number of factors has not been resolved in the statistics literature. An ad hoc approach is to set the number of factors to be the number of eigenvalues of the data correlation matrix that are larger than one, and subsequent statistical analysis proceeds assuming the resulting factor number is correct. In this work, we study the relation between the number of such eigenvalues and the number of factors, and provide the if and only if conditions under which the two numbers are equal. We show that the equality only relies on the properties of the loading matrix of the factor model. Guided by the newly discovered condition, we further reveal how the model error affects the estimation of the number of factors.
Passive daytime radiative cooling(PDRC)exhibits efficient cooling performance to reduce global fossil energy consumption and has attracted enormous interest.An efficient PDRC technology for achieving daytime subambient cooling is supposed to exhibit ultra-high solar reflectivity and infrared emissivity within atmospheric windows,among which ultra-high solar reflectivity is the principal property.In most PDRC technologies,spherical particles are selected as scatterers to achieve high solar reflectivity because the Mie scattering effect of spherical scatterers can provide a high scattering efficiency.However,the weak backward scattering of spherical scatterers remains a drawback.In this study,several nonspherical scatterers with strong backward scattering are introduced and researched systematically.The numerical analysis results indicate that pyramidal scatterers provide the strongest backward scattering and square/circular scatterers exhibit the highest scattering efficiency.Besides,by considering scattering efficiency and asymmetry factor comprehensively,a dimensionless evaluation parameter is proposed,which can be employed as a quantitative design criterion to achieve the optimal-object-oriented designing of superior scatterers.This work can provide an innovative strategy for designing efficient passive daytime radiative cooling materials.
Xinping ZHANGTairong KANGFuqiang WANGXiang LIHongliang YI
