1 Introduction Let A be a collection of n pairwise disjoint simple closed curves on an orientable closed surface F of genus n ≥2. We say that A is a complete system of F if the surface obtained by cutting F along A i...1 Introduction Let A be a collection of n pairwise disjoint simple closed curves on an orientable closed surface F of genus n ≥2. We say that A is a complete system of F if the surface obtained by cutting F along A is a 2n-punctured sphere. Let A1, A2 be two non-empty subsets of A. We say that (A1,A2) is a partition of A if A1 ∩A2 = (?) and A1 ∪A2 = A. Let (A1, A2) be a partition of A on F, and C a simple closed curve on F. We say that C is separating with respect to (A1, A2) if it is disjoint from A and it cuts F into two pieces F1,F2 with A1(?) F1,A2 (?) F2.展开更多
Let {A, B} be a complete system of the closed orientable surface F of genus 2. A simple closed curve C on F is separating with respect to （A, B） if it is disjoint from A U B and it cuts F into two once-punctured tor...Let {A, B} be a complete system of the closed orientable surface F of genus 2. A simple closed curve C on F is separating with respect to （A, B） if it is disjoint from A U B and it cuts F into two once-punctured tori X, Y with A belong X, B belong Y. Let γ be a simple closed curve on F which is disjoint from A ∪ B and intersects C essentially in two points. In this paper, we show that up to isotopy, {hγ^n（C） ： n ∈ Z} is the set containing all the simple closed curves on F which is separating with respect to （A, B）, where hγ is the Dehn twist along γ on F. This also shows how two simple closed curves on F which are separating with respect to （A, B） are related. The result can be applied to yield all Haken spheres of a Heegaard splitting V∪F W which are weakly equivalent to a given Heken sphere of the splitting.展开更多
In the process of ultrafine particle classification,the separation curve,which reflects the characteristics of separating process,is frequently influenced by the characteristics of separation flow field and operating ...In the process of ultrafine particle classification,the separation curve,which reflects the characteristics of separating process,is frequently influenced by the characteristics of separation flow field and operating parameters,etc.This paper introduces the concept of system deviation and deduces the calculating method of the separation curves.Meanwhile,it analyses the influences of classification flow field's specific properties and some operating parameters on the separation curves.The results show that,in the process of ultrafine particle classification,the local vortex in the separation field improves the separation efficiency to a certain degree,but the accuracy will decrease;the coacervation action of particles will seriously influence the classification accuracy.展开更多
基金Supported in part by a grant (10171024) of NSFC a grant of the outstanding Youth fellowship of Hei Long Jiang Province.
文摘1 Introduction Let A be a collection of n pairwise disjoint simple closed curves on an orientable closed surface F of genus n ≥2. We say that A is a complete system of F if the surface obtained by cutting F along A is a 2n-punctured sphere. Let A1, A2 be two non-empty subsets of A. We say that (A1,A2) is a partition of A if A1 ∩A2 = (?) and A1 ∪A2 = A. Let (A1, A2) be a partition of A on F, and C a simple closed curve on F. We say that C is separating with respect to (A1, A2) if it is disjoint from A and it cuts F into two pieces F1,F2 with A1(?) F1,A2 (?) F2.
基金The NSF (10171024,10471020) of Chinaa grant of the outstanding Youth fellowship of Hei Long Jiang Province and the Science Foundation (20060106) for Yong Teachers of Northeast Normal University.
文摘Let {A, B} be a complete system of the closed orientable surface F of genus 2. A simple closed curve C on F is separating with respect to （A, B） if it is disjoint from A U B and it cuts F into two once-punctured tori X, Y with A belong X, B belong Y. Let γ be a simple closed curve on F which is disjoint from A ∪ B and intersects C essentially in two points. In this paper, we show that up to isotopy, {hγ^n（C） ： n ∈ Z} is the set containing all the simple closed curves on F which is separating with respect to （A, B）, where hγ is the Dehn twist along γ on F. This also shows how two simple closed curves on F which are separating with respect to （A, B） are related. The result can be applied to yield all Haken spheres of a Heegaard splitting V∪F W which are weakly equivalent to a given Heken sphere of the splitting.
文摘In the process of ultrafine particle classification,the separation curve,which reflects the characteristics of separating process,is frequently influenced by the characteristics of separation flow field and operating parameters,etc.This paper introduces the concept of system deviation and deduces the calculating method of the separation curves.Meanwhile,it analyses the influences of classification flow field's specific properties and some operating parameters on the separation curves.The results show that,in the process of ultrafine particle classification,the local vortex in the separation field improves the separation efficiency to a certain degree,but the accuracy will decrease;the coacervation action of particles will seriously influence the classification accuracy.
