We consider a Krull-Schmidt, Hom-finite, 2-Calabi Yau triangulated category with a basic rigid object T, and show a bijection between the set of isomorphism classes of basic rigid objects in the finite presented categ...We consider a Krull-Schmidt, Hom-finite, 2-Calabi Yau triangulated category with a basic rigid object T, and show a bijection between the set of isomorphism classes of basic rigid objects in the finite presented category pr T of T and the set of isomorphism classes of basic T-rigid pairs in the module category of the endomorphism algebra Endc（T）op. As a consequence, basic maximal objects in prT are one-to-one correspondence to basic support τ-tilting modules over Endc（T）op. This is a generalization of correspondences established by Adachi-Iyama-Reiten.展开更多
Let C be a triangulated category which has Auslander-Reiten triangles, and Ra functorially finite rigid subcategory of C. It is well known that there exist Auslander-Reiten sequences in rood R. In this paper, we give ...Let C be a triangulated category which has Auslander-Reiten triangles, and Ra functorially finite rigid subcategory of C. It is well known that there exist Auslander-Reiten sequences in rood R. In this paper, we give explicitly the relations between the Auslander-Reiten translations, sequences in mod R and the Auslander-Reiten functors, triangles in C, respectively. Furthermore, if T is a cluster-tilting subcategory of C and mod T- is a Frobenius category, we also get the Auslander-Reiten functor and the translation functor of mod T- corresponding to the ones in C. As a consequence, we get that if the quotient of a d-Calabi-Yau triangulated category modulo a cluster tilting subcategory is Probenius, then its stable category is （2d-1）-Calabi-Yau. This result was first proved by Keller and Reiten in the case d= 2, and then by Dugas in the general case, using different methods. 2010 Mathematics Subject Classification： 16G20, 16G70展开更多
A real-time animation technique for a kind of non-rigid objects, flexible and thin objects, is proposed, which can update with stability the state of n mass points of the mass-spring (MS) modei with time complexity of...A real-time animation technique for a kind of non-rigid objects, flexible and thin objects, is proposed, which can update with stability the state of n mass points of the mass-spring (MS) modei with time complexity of O (n ). The new implicit numerical integration technique of the authors, which is based on a simple approximation of the linear system, has great advantages over the existing implicit integration methods. Moreover, experiment shows that the new technique is highly efficient in animating a kind of non-rigid objects, and suitable for the draping module of the 3D garment CAD system.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11131001)supported by BIT Basic Scientific Research Grant(Grant No.3170012211408)
文摘We consider a Krull-Schmidt, Hom-finite, 2-Calabi Yau triangulated category with a basic rigid object T, and show a bijection between the set of isomorphism classes of basic rigid objects in the finite presented category pr T of T and the set of isomorphism classes of basic T-rigid pairs in the module category of the endomorphism algebra Endc（T）op. As a consequence, basic maximal objects in prT are one-to-one correspondence to basic support τ-tilting modules over Endc（T）op. This is a generalization of correspondences established by Adachi-Iyama-Reiten.
文摘Let C be a triangulated category which has Auslander-Reiten triangles, and Ra functorially finite rigid subcategory of C. It is well known that there exist Auslander-Reiten sequences in rood R. In this paper, we give explicitly the relations between the Auslander-Reiten translations, sequences in mod R and the Auslander-Reiten functors, triangles in C, respectively. Furthermore, if T is a cluster-tilting subcategory of C and mod T- is a Frobenius category, we also get the Auslander-Reiten functor and the translation functor of mod T- corresponding to the ones in C. As a consequence, we get that if the quotient of a d-Calabi-Yau triangulated category modulo a cluster tilting subcategory is Probenius, then its stable category is （2d-1）-Calabi-Yau. This result was first proved by Keller and Reiten in the case d= 2, and then by Dugas in the general case, using different methods. 2010 Mathematics Subject Classification： 16G20, 16G70
文摘A real-time animation technique for a kind of non-rigid objects, flexible and thin objects, is proposed, which can update with stability the state of n mass points of the mass-spring (MS) modei with time complexity of O (n ). The new implicit numerical integration technique of the authors, which is based on a simple approximation of the linear system, has great advantages over the existing implicit integration methods. Moreover, experiment shows that the new technique is highly efficient in animating a kind of non-rigid objects, and suitable for the draping module of the 3D garment CAD system.
