Representation dimension of m-replicated algebras

Let A be a finite-dimensional hereditary algebra over an algebraically closed field and A ^(m) be the m-replicated algebra of A. We prove that the representation dimension of A ^(m) is at most 3, and that the dominant dimension of A ^(m) is at least m.     

应用似然函数比以及Fourier变换计算置信度的解析方法

新粒子寻找的实验结果要通过计算置信度来解释,置信度的定义或是基于新粒子与本底并存的假设,或是基于唯有本底存在的假设.通常的计算方法是产生大量的toy Monte Carlo实验,这些实验按照某种定义的估计值的大小以顺序排列,然后将真正观测到的实验的估计值与之相比较,从而得到置信度.本文则介绍一种新的计算方法,通过定义似然函数比为实验的估计值,并应用Fourier变换,用解析的方法计算出置信度,与toy Monte Carlo方法相比,解析方法可极大地提高计算的速度和精度.     

Mixed symmetry states and isospin excitation in <Emphasis Type="Italic">N</Emphasis> = <Emphasis Type="Italic">Z</Emphasis> nucleus <Superscript>52</Superscript>Fe

The interacting boson model with isospin (IBM-3) was applied to study the band structure and electromagnetic transition properties of the low-lying states in the even-even N = Z nucleus ⁵²Fe. The isospin excitation states with T = 0, 1 and 2 were identified, and compared with the available data. The study shows that the 2₃⁺ state is the lowest mixed symmetry state in ⁵²Fe. The excitation energy of the second 0₂⁺ state with T = 0 in nucleus ⁵²Fe was identified. The model calculations with the data show a reasonably good agreement. Supported by the National Natural Science Foundation of China (Grant Nos. 10765001 and 10547003), the Natural Science Foundation of Inner Mongolian Autonomous Region of China (Grant No. 200607010111), and the Scientific Research Fund of Inner Mongolian Education Bureau (Grant Nos. NJZY07155 and NJZY07153)     

MgO-ZrO2共沉淀体系的结构表征及单层分散现象

用共沉淀法制备了一系列MgO-ZrO₂复合氧化物, 用XRD、XPS、BET、DTA、EXAFS和TEM等进行了表征. 结果表明, 500 ℃与600 ℃下焙烧得到的MgO-ZrO₂复合氧化物, 在ZrO₂高含量一端, MgO倾向于固溶到ZrO₂中, 最大固溶量可达到1:1(摩尔比)；固溶达到饱和后, MgO开始在固溶体表面分散, 并析出单独的MgO晶粒；在MgO高含量端, 少量的ZrO₂以分散态存在于MgO的表面, 并使其表面性质发生较明显的变化. 这些结果表明, 在共沉淀法制备的MgO-ZrO₂样品中, 在一定相对含量范围内, 会出现一种组分在另一种组分或由两种组分形成的固溶体上的单层分散现象.     

The transition matrix between PBW basis and semicanonical basis of U+(sl_n(C))

We prove that the transition matrix between a special Poincaré-Birkhoff-Witt(PBW)basis and the semicanonical basis of U+(sln(C))is upper triangular and unipotent under any order which is compatible with the partial order deg.     

Syntheses and X‐Ray crystal structures of aminated 4,4'‐Bi‐1,2,4‐triazole salts

3‐Amino‐4,4'‐bi‐1,2,4‐triazole hydrochlorate and 3,3'‐diamino‐4,4'‐bi‐1,2,4‐triazole ditosylate were obtained with the reduction of 3,3',5,5'‐tetraazide‐4,4'‐bi‐1,2,4‐triazole (TABT) by (Ph)₃P/H₂O and the followed salt forming reaction with concentrated HCl and aqueous TsOH, respectively. Their structures were characterized with elemental analyses, IR, MS, ¹H and ¹³C NMR spectra. The single crystals were cultivated and determined with X‐ray diffraction, test results reveal that H⁺ combines with electron‐rich N atom in triazole ring to form ionic salts, two N,N‐linked triazoles are almost perpendicular to each other due to lower steric hindrance. The aromatic π…π stacking interactions and hydrogen bonds between molecules are observed. These two novel salts and their derivatives may be applied in coordination chemistry, medicinal chemistry and energetic materials.     

IBFM模型U(6/4)超对称SO(6)极限的能谱统计

用相互作用玻色子费米子模型(IBFM)计算了奇A核U(6/4)超对称SO(6)极限的理论能谱，对不确定核的最近邻能级间距分布和能谱刚性度进行了研究，并对影响能谱统计特征的因素进行了讨论. 结果表明，有限的玻色子数N的大小显著地影响能谱统计. 当N接近于真实核的玻色子数时，子群SOBF(5)的作用强度和自旋对能谱统计起重要作用. 然而，当N趋于无穷大时，能谱统计总是趋于Poisson分布.     

The transition matrix between PBW basis and semicanonical basis of U +(\mathfrak{s}\mathfrak{l}_n (ℂ))

We prove that the transition matrix between a special Poincaré-Birkhoff-Witt(PBW)basis and the semicanonical basis of U+(sln(C))is upper triangular and unipotent under any order which is compatible with the partial order deg.