A discrete Hopf fibration of S15 over S8 with S7 (unit octonions) as fibers leads to a 16D Polytope P16 with 4320 vertices obtained from the convex hull of the 16D Barnes-Wall lattice Λ16. It is argued (conjectured) ...A discrete Hopf fibration of S15 over S8 with S7 (unit octonions) as fibers leads to a 16D Polytope P16 with 4320 vertices obtained from the convex hull of the 16D Barnes-Wall lattice Λ16. It is argued (conjectured) how a subsequent 2-1 mapping (projection) of P16 onto a 8D-hyperplane might furnish the 2160 vertices of the uniform 241 polytope in 8-dimensions, and such that one can capture the chain sequence of polytopes 241,231,221,211in D=8,7,6,5dimensions, leading, respectively, to the sequence of Coxeter groups E8,E7,E6,SO(10)which are putative GUT group candidates. An embedding of the E8⊕E8and E8⊕E8⊕E8lattice into the Barnes-Wall Λ16 and Leech Λ24 lattices, respectively, is explicitly shown. From the 16D lattice E8⊕E8one can generate two separate families of Elser-Sloane 4D quasicrystals (QC’s) with H4 (icosahedral) symmetry via the “cut-and-project” method from 8D to 4D in each separate E8 lattice. Therefore, one obtains in this fashion the Cartesian product of two Elser-Sloane QC’s Q×Qspanning an 8D space. Similarly, from the 24D lattice E8⊕E8⊕E8one can generate the Cartesian product of three Elser-Sloane 4D quasicrystals (QC’s) Q×Q×Qwith H4 symmetry and spanning a 12D space.展开更多
This paper presents a mathematical model for components/parts unification (CPU) policy. This model considers two components/parts that are functionally interchangeable but purchased from suppliers with different price...This paper presents a mathematical model for components/parts unification (CPU) policy. This model considers two components/parts that are functionally interchangeable but purchased from suppliers with different prices and quality characteristics. Because of the buyer's quality preference and suppliers' discount rates for bulky purchases, the model assists the procurement manager to determine how best to purchase the components/parts to meet its demand while minimizing the total acquisition costs.展开更多
Multi-sensor coordinate unification in dimensional metrology is used in order to get holistic, more accurate and reliable information about a workpiece based on several or multiple measurement values from ...Multi-sensor coordinate unification in dimensional metrology is used in order to get holistic, more accurate and reliable information about a workpiece based on several or multiple measurement values from one or more sensors. Because of the problem that standard ball is deficient as a standard artifact in the coordinate unification of high-precision composite measurement in two dimensions （2D） , a new method is proposed in this paper which uses angle gauge blocks as standard artifacts to achieve coordinate unification between the image sensor and the tactile probe. By comparing the standard ball with the angle gauge block as a standard artifact, theoretical analysis and experimental results are given to prove that it is more precise and more convenient to use angle gauge blocks as standard artifacts to achieve coordinate unification of high-precision composite measurement in two dimensions.展开更多
True color image city map is a sort of new-style map which combines the high resolution image and map symbols and shows both advantages in visualization. At the same time, the map unification and harmonization should ...True color image city map is a sort of new-style map which combines the high resolution image and map symbols and shows both advantages in visualization. At the same time, the map unification and harmonization should be taken into account dur-ing the design process, since some visual conflicts appear when map symbols overlaid on the true color image. The objective of this research is to explore the rules in the process of true color image city map design based on chromatic and aesthetic knowledge. At the end, taking the Image Atlas of Guangzhou as an example, image color adjustment, road network presentation, and symbol de-signing issues will be discussed in the application.展开更多
文摘A discrete Hopf fibration of S15 over S8 with S7 (unit octonions) as fibers leads to a 16D Polytope P16 with 4320 vertices obtained from the convex hull of the 16D Barnes-Wall lattice Λ16. It is argued (conjectured) how a subsequent 2-1 mapping (projection) of P16 onto a 8D-hyperplane might furnish the 2160 vertices of the uniform 241 polytope in 8-dimensions, and such that one can capture the chain sequence of polytopes 241,231,221,211in D=8,7,6,5dimensions, leading, respectively, to the sequence of Coxeter groups E8,E7,E6,SO(10)which are putative GUT group candidates. An embedding of the E8⊕E8and E8⊕E8⊕E8lattice into the Barnes-Wall Λ16 and Leech Λ24 lattices, respectively, is explicitly shown. From the 16D lattice E8⊕E8one can generate two separate families of Elser-Sloane 4D quasicrystals (QC’s) with H4 (icosahedral) symmetry via the “cut-and-project” method from 8D to 4D in each separate E8 lattice. Therefore, one obtains in this fashion the Cartesian product of two Elser-Sloane QC’s Q×Qspanning an 8D space. Similarly, from the 24D lattice E8⊕E8⊕E8one can generate the Cartesian product of three Elser-Sloane 4D quasicrystals (QC’s) Q×Q×Qwith H4 symmetry and spanning a 12D space.
文摘This paper presents a mathematical model for components/parts unification (CPU) policy. This model considers two components/parts that are functionally interchangeable but purchased from suppliers with different prices and quality characteristics. Because of the buyer's quality preference and suppliers' discount rates for bulky purchases, the model assists the procurement manager to determine how best to purchase the components/parts to meet its demand while minimizing the total acquisition costs.
基金National Key Scientific Instrument and Equipment Development Project(No.2013YQ170539)
文摘Multi-sensor coordinate unification in dimensional metrology is used in order to get holistic, more accurate and reliable information about a workpiece based on several or multiple measurement values from one or more sensors. Because of the problem that standard ball is deficient as a standard artifact in the coordinate unification of high-precision composite measurement in two dimensions （2D） , a new method is proposed in this paper which uses angle gauge blocks as standard artifacts to achieve coordinate unification between the image sensor and the tactile probe. By comparing the standard ball with the angle gauge block as a standard artifact, theoretical analysis and experimental results are given to prove that it is more precise and more convenient to use angle gauge blocks as standard artifacts to achieve coordinate unification of high-precision composite measurement in two dimensions.
文摘True color image city map is a sort of new-style map which combines the high resolution image and map symbols and shows both advantages in visualization. At the same time, the map unification and harmonization should be taken into account dur-ing the design process, since some visual conflicts appear when map symbols overlaid on the true color image. The objective of this research is to explore the rules in the process of true color image city map design based on chromatic and aesthetic knowledge. At the end, taking the Image Atlas of Guangzhou as an example, image color adjustment, road network presentation, and symbol de-signing issues will be discussed in the application.
