239000002131 composite material Substances 0.000 title abstract description 6.SXTZYIWTRUTYCY-UHFFFAOYSA-N Rabeprazole Chemical compound COCCCOC1=CC=NC(CS(=O)C=2N=C3C=CC=C3N=2)=C1C SXTZYIWTRUTYCY-UHFFFAOYSA-N 0.000 title claims abstract 8.238000002360 preparation method Methods 0.000 title claims abstract description 22.229960004157 rabeprazole Drugs 0.000 title claims abstract description 32.Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.) Filing date Publication date Priority claimed from KR10-2017-0172473 external-priority Application filed by 한국유나이티드제약 주식회사, 사단법인 유나이티드사이언스알앤디센터 filed Critical 한국유나이티드제약 주식회사 Priority to US16/768,805 priority Critical patent/US20210177765A1/en Priority to RU2020118467A priority patent/RU2753697C1/en Priority to CN201880079811.1A priority patent/CN111479559A/en Priority to JP2020552648A priority patent/JP7017647B2/en Publication of WO2019117502A1 publication Critical patent/WO2019117502A1/en Priority to PH12020550806A priority patent/PH12020550806A1/en Links
Inventor 김병진 송희용 최연웅 김성엽 Original Assignee 한국유나이티드제약 주식회사 사단법인 유나이티드사이언스알앤디센터 Priority date (The priority date is an assumption and is not a legal conclusion. Google Patents WO2019117502A1 - Core tablet composite preparation comprising mosapride and rabeprazole Inversely: Theorem 2.WO2019117502A1 - Core tablet composite preparation comprising mosapride and rabeprazole The graph of a stacked d-polytope is a d -tree, that is, a chordal graph whose maximal cliques are of the same size \(d+1\). For example, the graph of a d-simplex is the complete graph on \(d+1\) vertices. We work in the d-dimensional extended Euclidean space \(\hat)\). 5 about edge-tangent polytopes, an object closely related to ball packings. The main and related results are proved in Sect. These constructions provide forbidden induced subgraphs for the tangency graphs of ball packings, which are helpful for the intuition, and some are useful in the proofs. 3, we construct ball packings for some graph joins. 2, we introduce the notions related to Apollonian ball packings and stacked polytopes. We prove in Corollary 4.1 and Theorem 4.3 that this only happens in dimension 3, when the ball packing contains Soddy’s hexlet, a special packing consisting of nine balls. On the other hand, the tangency graph of an Apollonian d-ball packing may not be the 1-skeleton of any stacked \((d+1)\)-polytope. (Main result) The 1-skeleton of a stacked 4-polytope is 3-ball packable if and only if it does not contain six 4-cliques sharing a 3-clique.įor even higher dimensions, we propose Conjecture 4.1 following the pattern of 2- and 3-dimensional ball packings.
4, gives a condition on stacked 4-polytopes to restore the relation in this direction: Theorem 1.1
On the one hand, the 1-skeleton of a stacked \((d+1)\)-polytope may not be realizable by the tangency relations of any Apollonian d-ball packing. However, this relation does not hold in higher dimensions. Namely, a graph can be realized by the tangency relations of an Apollonian disk packing if and only if it is the 1-skeleton of a stacked 3-polytope. There is a 1-to-1 correspondence between 2-dimensional Apollonian ball packings and 3-dimensional stacked polytopes. 2.3 and 2.4 respectively for formal descriptions. A stacked polytope is constructed from a simplex by repeatedly gluing new simplices onto facets. An Apollonian ball packing is constructed from a Descartes configuration (a collection of pairwise tangent balls) by repeatedly filling new balls into “holes”. In this paper we study the relation between Apollonian ball packings and stacked polytopes. However, little is known about the combinatorics of ball packings in higher dimensions. The combinatorics of disk packings (2-dimensional ball packings) is well understood thanks to the Koebe–Andreev–Thurston’s disk packing theorem, which asserts that every planar graph is disk packable. A graph is said to be ball packable if it can be realized by the tangency relations of a ball packing. A ball packing is a collection of balls with disjoint interiors.
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