在偏序集上引入并考察了滤子极大理想的概念,证明了相应的存在性定理。引入并考察了伪极大元和伪既约元的概念,利用图表的形式对连续格中各种类型的既约元和素元之间的关系进行了归纳总结,完善了文献《Continuous Lattices and Domains...在偏序集上引入并考察了滤子极大理想的概念,证明了相应的存在性定理。引入并考察了伪极大元和伪既约元的概念,利用图表的形式对连续格中各种类型的既约元和素元之间的关系进行了归纳总结,完善了文献《Continuous Lattices and Domains》(作者:G.Gierz,et al)中的一个图表的相关内容,填补了在分配的连续格情形该图表的一个未知内容,部分地回答了该文献中的一个问题。展开更多
This compendium review focuses on the spatial distribution of sensitivity to localized absorption changes in optically diffuse media,particularly for measurements relevant to near-infrared spectroscopy.The three tempo...This compendium review focuses on the spatial distribution of sensitivity to localized absorption changes in optically diffuse media,particularly for measurements relevant to near-infrared spectroscopy.The three temporal domains,continuous wave,frequency domain,and time domain,each obtain different optical data types whose changes may be related to effective homogeneous changes in the absorption coefficient.Sensitivity is the relationship between a localized perturbation and the recovered effective homogeneous absorption change.Therefore,spatial sensitivity maps representing the perturbation location can be generated for the numerous optical data types in the three temporal domains.The review first presents a history of the past 30 years of work investigating this sensitivity in optically diffuse media.These works are experimental and theoretical,presenting one-,two-,and three-dimensional sensitivity maps for different Near-Infrared Spectroscopy methods,domains,and data types.Following this history,we present a compendium of sensitivity maps organized by temporal domain and then data type.This compendium provides a valuable tool to compare the spatial sensitivity of various measurement methods and parameters in one document.Methods for one to generate these maps are provided in Appendix A,including the code.This historical review and comprehensive sensitivity map compendium provides a single source researchers may use to visualize,investigate,compare,and generate sensitivity to localized absorption change maps.展开更多
In this paper we study the properties of the set consisting of all fixed points of a Scott continuous self-map between domains. All the results give an answer to an open problem posed by Lawson and Mislove in 1990.
推广连续D om a in的权的概念到连续偏序集上,探讨连续偏序集的权、相应内蕴拓扑的权、定向完备化的权以及Sm yth幂D om a in的权间的关系。得到了几个等权定理:(1)连续偏序集的权与其上Scott拓扑、L aw son拓扑的权相等;(2)连续偏序集...推广连续D om a in的权的概念到连续偏序集上,探讨连续偏序集的权、相应内蕴拓扑的权、定向完备化的权以及Sm yth幂D om a in的权间的关系。得到了几个等权定理:(1)连续偏序集的权与其上Scott拓扑、L aw son拓扑的权相等;(2)连续偏序集的权与其定向完备化的权相等;(3)无穷连续D om a in的权与其Sm yth幂D om a in的权相等;(4)有限D om a in的权小于或等于它的Sm yth幂D om a in的权。展开更多
Spatial modeling of ore grades is frequently impacted by the local variation in geological domains such as lithological characteristics,rock types,and geological formations.Disregarding this information may lead to bi...Spatial modeling of ore grades is frequently impacted by the local variation in geological domains such as lithological characteristics,rock types,and geological formations.Disregarding this information may lead to biased results in the final ore grade block model,subsequently impacting the downstream processes in a mining chain project.In the current practice of ore body evaluation,which is known as stochastic cascade/hierarchical geostatistical modeling,the geological domain is first characterized,and then,within the geological model,the ore grades of interest are evaluated.This practice may be unrealistic in the case when the variability in ore grade across the boundary is gradual,following a smooth transition.To reproduce such characteristics,the cross dependence that exists between the ore grade and geological formations is considered in the conventional joint simulation between continuous and categorical variables.However,when using this approach,only one ore variable is considered,and its relationship with other ore grades that may be available at the sample location is ignored.In this study,an alternative approach to jointly model two cross-correlated ore grades and one categorical variable(i.e.,geological domains)with soft contact relationships that exist among the geological domains is proposed.The statistical and geostatistical tools are provided for variogram inference,Gibbs sampling,and conditional cosimulation.The algorithm is also tested by applying it to a Cu deposit,where the geological formations are managed by the local and spatial distribution of two cross-correlated ore grades,Cu and Au,throughout the deposit.The results show that the proposed algorithm outperforms other geostatistical techniques in terms of global and local reproduction of statistical parameters.展开更多
文摘在偏序集上引入并考察了滤子极大理想的概念,证明了相应的存在性定理。引入并考察了伪极大元和伪既约元的概念,利用图表的形式对连续格中各种类型的既约元和素元之间的关系进行了归纳总结,完善了文献《Continuous Lattices and Domains》(作者:G.Gierz,et al)中的一个图表的相关内容,填补了在分配的连续格情形该图表的一个未知内容,部分地回答了该文献中的一个问题。
文摘This compendium review focuses on the spatial distribution of sensitivity to localized absorption changes in optically diffuse media,particularly for measurements relevant to near-infrared spectroscopy.The three temporal domains,continuous wave,frequency domain,and time domain,each obtain different optical data types whose changes may be related to effective homogeneous changes in the absorption coefficient.Sensitivity is the relationship between a localized perturbation and the recovered effective homogeneous absorption change.Therefore,spatial sensitivity maps representing the perturbation location can be generated for the numerous optical data types in the three temporal domains.The review first presents a history of the past 30 years of work investigating this sensitivity in optically diffuse media.These works are experimental and theoretical,presenting one-,two-,and three-dimensional sensitivity maps for different Near-Infrared Spectroscopy methods,domains,and data types.Following this history,we present a compendium of sensitivity maps organized by temporal domain and then data type.This compendium provides a valuable tool to compare the spatial sensitivity of various measurement methods and parameters in one document.Methods for one to generate these maps are provided in Appendix A,including the code.This historical review and comprehensive sensitivity map compendium provides a single source researchers may use to visualize,investigate,compare,and generate sensitivity to localized absorption change maps.
基金the National Natural Science Foundation of China (Grant. No. 10071053) the SFEM of China and the Project of "Excellent Scholars Crossing Centuries" of the Education Ministry of China.
文摘In this paper we study the properties of the set consisting of all fixed points of a Scott continuous self-map between domains. All the results give an answer to an open problem posed by Lawson and Mislove in 1990.
文摘推广连续D om a in的权的概念到连续偏序集上,探讨连续偏序集的权、相应内蕴拓扑的权、定向完备化的权以及Sm yth幂D om a in的权间的关系。得到了几个等权定理:(1)连续偏序集的权与其上Scott拓扑、L aw son拓扑的权相等;(2)连续偏序集的权与其定向完备化的权相等;(3)无穷连续D om a in的权与其Sm yth幂D om a in的权相等;(4)有限D om a in的权小于或等于它的Sm yth幂D om a in的权。
基金The first author is thankful to Nazarbayev University for funding this work via“Faculty Development Competitive Research Grants for 2018-2020 under Contract No.090118FD5336 and 2021-2023 under Contract No.021220FD4951”This work is supported by Faculty Development Competitive Research Grants for 2018-2020 under Contract No.090118FD5336 and 2021-2023 under Contract No.021220FD4951.
文摘Spatial modeling of ore grades is frequently impacted by the local variation in geological domains such as lithological characteristics,rock types,and geological formations.Disregarding this information may lead to biased results in the final ore grade block model,subsequently impacting the downstream processes in a mining chain project.In the current practice of ore body evaluation,which is known as stochastic cascade/hierarchical geostatistical modeling,the geological domain is first characterized,and then,within the geological model,the ore grades of interest are evaluated.This practice may be unrealistic in the case when the variability in ore grade across the boundary is gradual,following a smooth transition.To reproduce such characteristics,the cross dependence that exists between the ore grade and geological formations is considered in the conventional joint simulation between continuous and categorical variables.However,when using this approach,only one ore variable is considered,and its relationship with other ore grades that may be available at the sample location is ignored.In this study,an alternative approach to jointly model two cross-correlated ore grades and one categorical variable(i.e.,geological domains)with soft contact relationships that exist among the geological domains is proposed.The statistical and geostatistical tools are provided for variogram inference,Gibbs sampling,and conditional cosimulation.The algorithm is also tested by applying it to a Cu deposit,where the geological formations are managed by the local and spatial distribution of two cross-correlated ore grades,Cu and Au,throughout the deposit.The results show that the proposed algorithm outperforms other geostatistical techniques in terms of global and local reproduction of statistical parameters.
