预成像数字全息测量大物体三维形貌

为了扩大数字全息三维形貌测量的视场,提出了一种预成像的方法.物体先被成像镜头成一缩小的实像,再使用离轴菲涅耳数字全息对此实像进行全息记录.采用倾斜照明光的方法使两次数字全息的再现像之间产生相位差,通过相位去噪和去包裹处理从相位差中提取物体的三维形貌数据.实验证明,预成像方法使测量视场的大小得到了至少一个数量级的提高,采用离轴菲涅耳数字全息降低了测量系统对环境稳定性的要求.     

From recollement of triangulated categories to recollement of abelian categories

In this paper,we prove that if a triangulated category D admits a recollement relative to triangulated categories D' and D″,then the abelian category D/T admits a recollement relative to abelian categories D'/i(T) and D″/j(T) where T is a cluster tilting subcategory of D and satisfies i i (T)  T,j j (T) T.     

Crystal structure of Ln1/3NbO3 (Ln=Nd, Pr) and phase transition in Nd1/3NbO3

The crystal structure of the A-site deficient perovskite Ln_1/3NbO₃ (Ln=Nd, Pr) at room temperature has been determined, for the first time, as orthorhombic in space group Cmmm using high-resolution neutron powder diffraction. Pertinent features are the alternation of unoccupied layers of A-sites and layers partly occupied by Ln cations, as well as out-of-phase tilting of the NbO₆ octahedra around an axis perpendicular to the direction of the cation/vacancy ordering. The phase transition behaviour of Nd_1/3NbO₃ has also been studied in situ. This compound undergoes a continuous phase transition at around 650 °C to a tetragonal structure in space group P4/mmm due to the disappearance of the octahedral tilting. The analysis of spontaneous strains shows that this phase transition is tricritical in nature.     

Structure evolution and microwave dielectric response of (Ca0.5+xSr0.5−x)[(Al0.5Nb0.5)0.5Ti0.5]O3 solid solutions

The phase assemblage, crystal structure evolution and microwave dielectric response of (Ca_0.5+xSr_0.5−x)[(Al_0.5Nb_0.5)_0.5Ti_0.5]O₃ ceramics (abbreviated as CSANT hereafter) are investigated. Single perovskite solid solution is formed in the CSANT ceramics in Sr-rich composition range of x < −0.05, however, Ca₄Ti₃O₁₀-type layered perovskite phase begins to segregate after x = −0.05. The CSANT perovskites crystallized in Fm3m cubic symmetry in the composition range of x ≤ −0.2, however, as the Ca²⁺ content in A-site increased, the oxygen octahedral began to be anti-phase tilted at x = −0.1 and the crystal structure transited to P2₁/n pseudo-orthorhombic space group thereafter. The microwave dielectric response of the CSANT ceramics is elaborately discussed in terms of their crystallographic structure and chemical composition. When sintered at 1500 °C for 4 h, a dielectric constant ɛ_r of 52.5, a Qf product of 28000 GHz and a τ_f of +25.4 ppm/°C microwave dielectric ceramic can be obtained in the CSANT ceramics at x = 0.3.     

Cluster tilting for tilted algebras

We build a connection between iterated tilted algebras with trivial cluster tilting subcategories and tilted algebras of finite type.Moreover,all tilted algebras with cluster tilting subcategories are determined in terms of quivers.As a result,we draw the quivers of Auslander’s 1-Gorenstein algebras with global dimension 2 admitting trivial cluster tilting subcategories,which implies that such algebras are of finite type but not necessarily Nakayama.     

Complements to the Almost Complete Tilting A (m)-Modules

Let A be a finite dimensional hereditary algebra over an algebraically closed field and A ^(m) be the mth replicated algebra of A. We prove that if T is a faithful almost complete tilting A ^(m)-module with pd _{A ^(m)} T ≤ m, then T has exactly m + 1 indecomposable nonisomorphic complements with projective dimensions at most m. Moreover, we give an explicit distribution of the complements to T.     

Phase transition in the Ruddlesden-Popper layered perovskite Li2SrTa2O7

The crystal structure of the Ruddlesden-Popper layered perovskite Li₂SrTa₂O₇ has been characterized at various temperatures between −185 and 300 °C by several techniques: X-ray and neutron powder diffraction, single crystal diffraction, transmission electron microscopy and Raman spectroscopy. The low temperature structure has been confirmed to be orthorhombic Cmcm with a small octahedra antiphase tilting (ΦΦ0) (ΦΦ0) inside the perovskite blocks. With temperature, the tilting progressively vanishes leading around 230 °C to a tetragonal symmetry (S.G. I4/mmm). This reversible phase transition, followed by X-ray and neutron thermodiffraction and thermal Raman measurements, is considered as of second order. An attribution of the Raman bands based on normal mode analysis is proposed.     

Dn型路代数倾斜模与AR箭图边缘

代数表示理论是上个世纪七十年代初兴起的代数学的—个新的分支,而倾斜理论是研究代数表示理论的重要工具之一．本文主要对Dn型路代数倾斜模在其对应的AR-箭图上的结构特点进行研究．通过对Dn型路代数A的AR-箭图ΓA分析,证明了：Dn型路代数倾斜模T的—个必要条件是。〈T〉中至少有三个边缘点．     

Exceptional Sequences Determined by their Cartan Matrix

We investigate complete exceptional sequences E=(E ₁,¨,E _n ) in the derived category D ^b of finite-dimensional modules over a canonical algebra, equivalently in the derived category D ^b X of coherent sheaves on a weighted projective line, and the associated Cartan matrices C(E)=( [E _i ],[E _j ]). As a consequence of the transitivity of the braid group action on such sequences we show that a given Cartan matrix has at most finitely many realizations by an exceptional sequence E, up to an automorphism and a multi-translation (E ₁,¨,E _n )(E ₁[i ₁],¨,E _n [i _n ]) of D ^b . Moreover, we determine a bound on the number of such realizations. Our results imply that a derived canonical algebra A is determined by its Cartan matrix up to isomorphism if and only if the Hochschild cohomology of A vanishes in nonzero degree, a condition satisfied if A is representation-finite.     

Broué's abelian defect group conjecture for alternating groups

We establish Broué's abelian defect group conjecture for the alternating groups, using the Chuang-Rouquier theorem (proving this for the symmetric groups) and a descent result.