Optical cavity has long been critical for a variety of applications ranging from precise measurement to spectral analysis.A number of theories and methods have been successful in describing the optical response of a s...Optical cavity has long been critical for a variety of applications ranging from precise measurement to spectral analysis.A number of theories and methods have been successful in describing the optical response of a stratified optical cavity,while the inverse problem,especially the inverse design of a displacement sensitive cavity,remains a significant challenge due to the cost of computation and comprehensive performance requirements.This paper reports a novel inverse design methodology combining the characteristic matrix method,mixed-discrete variables optimization algorithm,and Monte Carlo method-based tolerance analysis.The material characteristics are indexed to enable the mixed-discrete variables optimization,which yields considerable speed and efficiency improvements.This method allows arbitrary response adjustment with technical feasibility and gives a glimpse into the analytical characterization of the optical response.Two entirely different light-displacement responses,including an asymmetric sawtooth-like response and a highly symmetric response,are dug out and experimentally achieved,which fully confirms the validity of the method.The compact Fabry-Perot cavities have a good balance between performance and feasibility,making them promising candidates for displacement transducers.More importantly,the proposed inverse design paves the way for a universal design of optical cavities,or even nanophotonic devices.展开更多
Mathematics homework is an important part of mathematics teaching. The new curriculum reform has not made specific measures for mathematics homework. At present, teachers dont know how to design layered homework in ho...Mathematics homework is an important part of mathematics teaching. The new curriculum reform has not made specific measures for mathematics homework. At present, teachers dont know how to design layered homework in homework arrangement. Mathematics is a logical subject, and most students have resistance to mathematics learning. Some researchers use the experimental method to study the design of elementary school mathematics stratified homework, taking the students in parallel classes as the research objects, and designing the mathematics homework to meet the students learning needs according to the students learning characteristics. Based on this, this paper studies the optimal design strategy of hierarchical exercises of senior mathematics in primary schools for reference.展开更多
In recent years there has been an increasing interest in developing spatial statistical models for data sets that are seemingly spatially independent.This lack of spatial structure makes it difficult,if not impossible...In recent years there has been an increasing interest in developing spatial statistical models for data sets that are seemingly spatially independent.This lack of spatial structure makes it difficult,if not impossible to use optimal predictors such as ordinary kriging for modeling the spatial variability in the data.In many instances,the data still contain a wealth of information that could be used to gain flexibility and precision in estimation.In this paper we propose using a combination of regression analysis to describe the large-scale spatial variability in a set of survey data and a tree-based stratification design to enhance the estimation process of the small-scale spatial variability.With this approach,sample units（i.e.,pixel of a satellite image） are classified with respect to predictions of error attributes into homogeneous classes,and the classes are then used as strata in the stratified analysis.Independent variables used as a basis of stratification included terrain data and satellite imagery.A decision rule was used to identify a tree size that minimized the error in estimating the variance of the mean response and prediction uncertainties at new spatial locations.This approach was applied to a set of n=937 forested plots from a state-wide inventory conducted in 2006 in the Mexican State of Jalisco.The final models accounted for 62% to 82% of the variability observed in canopy closure（%）,basal area（m2·ha-1）,cubic volumes（m3·ha-1） and biomass（t·ha-1） on the sample plots.The spatial models provided unbiased estimates and when averaged over all sample units in the population,estimates of forest structure were very close to those obtained using classical estimates based on the sampling strategy used in the state-wide inventory.The spatial models also provided unbiased estimates of model variances leading to confidence and prediction coverage rates close to the 0.95 nominal rate.展开更多
基金We are grateful for financial supports from National Natural Science Foundation of China(62004166)Natural Science Foundation of Ningbo(202003N4062)+2 种基金National Postdoctoral Program for Innovative Talents(BX20200279)Natural Science Basic Research Program of Shaanxi Province(2020JQ-199)Fundamental Research Funds for the Central Universities(31020190QD027).
文摘Optical cavity has long been critical for a variety of applications ranging from precise measurement to spectral analysis.A number of theories and methods have been successful in describing the optical response of a stratified optical cavity,while the inverse problem,especially the inverse design of a displacement sensitive cavity,remains a significant challenge due to the cost of computation and comprehensive performance requirements.This paper reports a novel inverse design methodology combining the characteristic matrix method,mixed-discrete variables optimization algorithm,and Monte Carlo method-based tolerance analysis.The material characteristics are indexed to enable the mixed-discrete variables optimization,which yields considerable speed and efficiency improvements.This method allows arbitrary response adjustment with technical feasibility and gives a glimpse into the analytical characterization of the optical response.Two entirely different light-displacement responses,including an asymmetric sawtooth-like response and a highly symmetric response,are dug out and experimentally achieved,which fully confirms the validity of the method.The compact Fabry-Perot cavities have a good balance between performance and feasibility,making them promising candidates for displacement transducers.More importantly,the proposed inverse design paves the way for a universal design of optical cavities,or even nanophotonic devices.
文摘Mathematics homework is an important part of mathematics teaching. The new curriculum reform has not made specific measures for mathematics homework. At present, teachers dont know how to design layered homework in homework arrangement. Mathematics is a logical subject, and most students have resistance to mathematics learning. Some researchers use the experimental method to study the design of elementary school mathematics stratified homework, taking the students in parallel classes as the research objects, and designing the mathematics homework to meet the students learning needs according to the students learning characteristics. Based on this, this paper studies the optimal design strategy of hierarchical exercises of senior mathematics in primary schools for reference.
文摘In recent years there has been an increasing interest in developing spatial statistical models for data sets that are seemingly spatially independent.This lack of spatial structure makes it difficult,if not impossible to use optimal predictors such as ordinary kriging for modeling the spatial variability in the data.In many instances,the data still contain a wealth of information that could be used to gain flexibility and precision in estimation.In this paper we propose using a combination of regression analysis to describe the large-scale spatial variability in a set of survey data and a tree-based stratification design to enhance the estimation process of the small-scale spatial variability.With this approach,sample units（i.e.,pixel of a satellite image） are classified with respect to predictions of error attributes into homogeneous classes,and the classes are then used as strata in the stratified analysis.Independent variables used as a basis of stratification included terrain data and satellite imagery.A decision rule was used to identify a tree size that minimized the error in estimating the variance of the mean response and prediction uncertainties at new spatial locations.This approach was applied to a set of n=937 forested plots from a state-wide inventory conducted in 2006 in the Mexican State of Jalisco.The final models accounted for 62% to 82% of the variability observed in canopy closure（%）,basal area（m2·ha-1）,cubic volumes（m3·ha-1） and biomass（t·ha-1） on the sample plots.The spatial models provided unbiased estimates and when averaged over all sample units in the population,estimates of forest structure were very close to those obtained using classical estimates based on the sampling strategy used in the state-wide inventory.The spatial models also provided unbiased estimates of model variances leading to confidence and prediction coverage rates close to the 0.95 nominal rate.
