REPETITIVE CLUSTER-TILTED ALGEBRAS

Let H be a finite-dimensional hereditary algebra over an algebraically closed field k and C F m be the repetitive cluster category of H with m ≥ 1. We investigate the properties of cluster tilting objects in C F m and the structure of repetitive clustertilted algebras. Moreover, we generalize Theorem 4.2 in [12] (Buan A, Marsh R, Reiten I. Cluster-tilted algebra, Trans. Amer. Math. Soc., 359(1)(2007), 323-332.) to the situation of C F m , and prove that the tilting graph KCFm of C F m is connected.     

振动系统结构参数估计的Taylor变换法

引入了求解非线性微分方程的 Taylor变换法 ,将振动系统原分析模型变换为离散域内的代数方程组 ,建立了估计系统质量、阻尼和刚度矩阵的方程。该方法可以利用任意外载激励下的瞬态响应估计系统的结构参数 ,而不需要进行系统的模态试验 ,具有一定的工程应用价值。文中还研究了测试信号受噪声干扰时的参数估计方法 ,最后给出了 30 0 T转炉倾动机构的参数估计实例。     

Adjoint Functors and Representation Dimensions

We study the global dimensions of the coherent functors over two categories that are linked by a pair of adjoint functors. This idea is then exploited to compare the representation dimensions of two algebras. In particular, we show that if an Artin algebra is switched from the other, then they have the same representation dimension.     

Slice modules over minimal 2-fundamental algebras

We consider a class of algebras whose Auslander-Reiten quivers have starting components that are not generalized standard. For these components we introduce a generalization of a slice and show that only in finitely many cases (up to isomorphism) a slice module is a tilting module. The first named author was supported by the Polish Scientific Grant KBN No 1 P03A 018 27     

Structures and phase diagram for the system CaTiO3-La2/3TiO3

High-resolution neutron and synchrotron X-ray powder diffraction have been used to examine various compositions across the system (1−x)CaTiO₃−xLa_2/3TiO₃. The structures at room temperature were determined according to composition: in Pbnm for 0?x?0.5, Ibmm for 0.5<x<0.7, then I4/mcm for 0.7?x<0.9, and finally in Cmmm for x?0.9. Although the four structures are the same as those proposed previously in an X-ray diffraction study, the phase boundaries are somewhat different, in particular the Pbnm↔Ibmm phase boundary has been extended from x?0.4 to x>0.5 in the current study based on our high-resolution neutron diffraction data. From in situ measurements to identify structures above room temperature, an approximate composition-temperature phase diagram has been constructed, involving four temperature-induced phase transitions: Pbnm→I4/mcm, Ibmm→I4/mcm, I4/mcm→Pm3¯m and Cmmm→P4/mmm.     

Compression mechanisms of symmetric and Jahn-Teller distorted octahedra in double perovskites: A2CuWO6 (A=Sr, Ba), Sr2CoMoO6, and La2LiRuO6

Synchrotron X-ray powder diffraction was used to study the high pressure dependence of the lattice parameter and structural evolution of the monoclinic La₂LiRuO₆ and tetragonal Sr₂CoMoO₆, Sr₂CuWO₆, and Ba₂CuWO₆ double perovskite phases. The c lattice parameters of Sr₂CuWO₆ and Ba₂CuWO₆ decreased more rapidly than the a lattice parameters and Ba₂CuWO₆ exhibited a more anisotropic compression compared to Sr₂CuWO₆. Based on lower pressure refinements of Ba₂CuWO₆, the anisotropic compression is proposed to be due to the preferential compression of the Cu-O bonds containing cooperative Jahn-Teller distortions aligned parallel to the c-axis, which is in contrast to Sr₂CoMoO₆, where the change in the octahedral tilting and symmetric bond compression is the prevailing compression mechanism. The bulk moduli were obtained from a fit of the volume-pressure data using the second-order Murnaghan equation of state.     

Repetitive cluster-tilted algebras

Let H be a finite-dimensional hereditary algebra over an algebraically closed field k and C_Fm be the repetitive cluster category of H with m ≥ 1. We investigate the properties of cluster tilting objects in C_Fm and the structure of repetitive cluster-tilted algebras. Moreover, we generalize Theorem 4.2 in [12] (Buan A, Marsh R, Reiten I. Cluster-tilted algebra, Trans. Amer. Math. Soc., 359(1)(2007), 323-332.) to the situation of C_Fm, and prove that the tilting graph KC_Fm of C_Fm is connected.     

2-Calabi-Yau tilted代数的交换关系

本文研究了2-Calabi-Yau三角范畴上的2-Calabi-Yau tilted代数的almost complete tilting模.我们利用2-Calabi-Yau三角范畴上的交换关系给出了2-Calabi-Yau tilted代数的almost complete tilting模有两个(Bongartz)补的一系列充分必要条件.