拓撲向量格 的英文怎麼說
中文拼音 [tàpūxiàngliánggé]
拓撲向量格
英文
topological vector lattice-
We use a size changeable adjacent field to describe the topological structure of 3d unorganized points in our algorithm. it can offer essential dynamic information for tessellation and points " normal
演算法採用可以控制大小的鄰域作為空間散亂數據點的拓撲關系的幾何描述，為網格劃分和點的法向量的幾何描述提供了必要的動態幾何信息。The primary studies in this paper are the following : ( 1 ) we define a generalized alexandroff topology on an l - fuzzy quasi ordered set which is a generalization of the alexandroff topology on an ordinary quasi ordered set, prove that the generalized alexandroff topology on an l - quasi ordered set ( x, e ) can be obtained by the join of a family of the alexandroff topologies on it, a topology on any topological space can be represented as a generalized alexandroff topology on some l - quasi ordered set, and the generalized alexandroff topologies on l - fuzzy quasi ordered sets are generalizations of the generalized alexandroff topologies on generalized ultrametric spaces which are defined by j. j. m. m. rutten etc. ( 2 ) by introducing the concepts of the join of l - fuzzy set on an l - fuzzy partial ordered set with respect to the l - fuzzy partial order and l - fuzzy directed set on an l - fuzzy quasi ordered set ( with respect to the l - fuzzy quasi order ), we define l - fuzzy directed - complete l - fuzzy partial ordered set ( or briefly, l - fuzzy dcpo or l - fuzzy domain ) and l - fuzzy scott continuous mapping, prove that they are respectively generalizations of ordinary dcpo and scott continuous mapping, when l is a completely distributive lattice with order - reversing involution, the category l - fdom of l - fuzzy domains and l - fuzzy scott continuous mappings is isomorphic to a special kind of the category of v - domains and scott continuous mappings, that is, the category l - dcqum of directed - complete l - quasi ultrametric spaces and scott continuous mappings, and when l is a completely distributive lattice in which 1 is a molecule, l - fuzzy domains and l - fuzzy scott continuous mappings are consistent to directed lim inf complete categories and lim inf co ntinuous mappings in [ 59 ]
本文主要工作是： （ 1 ）在l - fuzzy擬序集上定義廣義alexandroff拓撲，證明了它是通常擬序集上alexandroff拓撲的推廣，一個l - fuzzy擬序集（ x ， e ）上的廣義alexandroff拓撲可以由其上一族alexandroff拓撲取並得到，任意一個拓撲空間的拓撲都可以表示為某個l - fuzzy擬序集上的廣義alexandroff拓撲，以及l - fuzzy擬序集上的廣義alexandroff拓撲是j . j . m . m . rutten等定義的廣義超度量空間上廣義alexandroff拓撲的推廣。 （ 2 ）通過引入l - fuzzy偏序集上的l - fuzzy集關于l - fuzzy偏序的並以及l - fuzzy擬序集上（關于l - fuzzy擬序）的l - fuzzy定向集等概念，定義了l - fuzzy定向完備的l - fuzzy偏序集（簡稱l - fuzzydcpo ，又叫l - fuzzydomain ）和l - fuzzyscott連續映射，證明了它們分別是通常的dcpo和scott連續映射的推廣，當l是帶有逆序對合對應的完全分配格時，以l - fuzzydomain為對象， l - fuzzyscott連續映射為態射的范疇l - fdom同構於一類特殊的v - domain范疇，即以定向完備的l -值擬超度量空間為對象， scott連續映射為態射的范疇l - dcqum ，以及當l是1為分子的完全分配格時， l - fuzzydomain和l - fuzzyscott連續映射一致於k . wagner在[ 59 ]中定義的定向liminf完備的-范疇和liminf連續映射。To completely avoid producing elements jointed at their corner nodes and checkerboard patterns, which frequently occur when the topology optimization of plane continuum is studied, the theory of topology analysis of plane continuum in topology optimization process and the simple algorithm for programming are studied. according to algebraic topology theory, the boundary of elements and plane continuum are operated as a one - dimensional complex. by use of the adjacency vector in graph theory, the structural topology is described and the topological operation is achieved on a computer. by above, the structural topological feature in the evolutionary process is gained. these methods are effcient and reliable. under topology constraints, according to the results of stress analysis, by deleting elements and moving nodes at the boundary, more satisfactory results can be gained by using a few numbers of elements and iterations. to demonstrate the efficiency of these methods, solutions including some well - known classical problems are presented
避免目前平面連續體結構拓撲優化過程中經常出現的單元鉸接以及「棋盤格」等現象，研究了連續體結構拓撲優化過程的拓撲分析方法，以及在計算機上實現的簡便演算法.根據代數拓撲理論，單元及連續體的邊界作為1 -復形進行運算.利用圖論中的鄰接向量概念，在計算機上實現了結構的拓撲描述及拓撲運算，得到了結構在拓撲演化過程中的拓撲特性，方法簡單、可靠.在一定的拓撲約束下，根據應力分析結果，採用刪除單元、單元退化、移動節點等方法，可以用較少單元得到更為滿意的結果，提高計算效率.為演示方法的有效性，給出幾個包括常見經典問題的解答
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