Note on André's reflection principle

This note generalizes André's reflection principle to give a new combinatorial proof of a formula for the number of lattice paths lying within certain trapezoids.     

Lattice path combinatorics and asymptotics of multiplicities of weights in tensor powers

We give asymptotic formulas for the multiplicities of weights and irreducible summands in high-tensor powers V_λ^⊗N of an irreducible representation V_λ of a compact connected Lie group G. The weights are allowed to depend on N, and we obtain several regimes of pointwise asymptotics, ranging from a central limit region to a large deviations region. We use a complex steepest descent method that applies to general asymptotic counting problems for lattice paths with steps in a convex polytope.     

Brauer第24问题的推广

本文对Ｂｒａｕｅｒ第２４问题［１］作了推广．利用Ｄａｄｅ关于循环块的理论得到如下结果：设Ｇ是有限群，Ｐ是Ｇ的循环Ｓｙｌｏｗｐ子群．设｜Ｐ｜＝ｐａ，ａ为正整数．令Ｐｉ为Ｐ中唯一的ｐｉ阶子群，１ｉａ．则｜Ｃｌ（Ｇ）｜＝｜Ｃｌ（ＮＧ（Ｐｉ））｜的充分必要条件为ＰｉＧ．     

钙钛矿型La_((1 x)/2)Sr_((1-x)/2)Co_(1-x)Cu_xO_3催化CO氧化活性与表征

研究了钙钛矿型LaSrCoCu_xO_3催化剂对CO氧化反应的催化活性及其表面氧的催化作用．结果表明，x＝0．4的催化剂对CO氧化具有最高催化活性，常压及本实验条件下CO完全氧化的最低温度为168℃；催化剂均为氧缺陷化合物，吸附于表面晶格氧缺陷上的吸附氧是CO氧化反应的活性氧物种；并发现催化剂中存在有非常价态的C04 ，认为CO氧化反应是通过吸附氧调变Co3 和Co4 价态而进行．     

ANN原子参数法预报合金相晶型及晶格常数

运用人工神经网络方法，以二元合金组成元素的电子结构为基本特征，对二元合金相晶型作了区分，进一步对其晶格常数作了预报，结果令人满意。     

Collapse transition and asymptotic scaling behavior of lattice animals: Low-temperature expansion

A low-temperature expansion for the free energy density of lattice animals is derived. Analysis of the series yields a collapse transition temperature ofT _c - 0.54, in close agreement with previous estimates. It is demonstrated that _p,k, the number ofp-particle,p-bond animals, obeys the asymptotic scaling law log _p,k pg(k/p) + o(p). The low-temperature series and numerical data are used to estimate the scaling function.     

Extremality and the global Markov property II: The global markov property for non-FKG maximal Gibbs measures

We give a condition on a Gibbs measure for an attractive Markov specification, which assures extremality and the global Markov property. As an example of application we consider the class of attractive Markov specifications defined on a compact configuration space over a two-dimensional lattice by the interaction Hamiltonians (assumed to have a finite set of periodic ground configurations) satisfying Peierl's condition. We prove that each extremal Gibbs measure for such a specification, at sufficiently low temperature, has the global Markov property.On leave of absence from the Institute of Theoretical Physics, University of Wrocaw, Poland.     

Two-dimensional catena–polymer [[[bis (µ-aqua)(bis (µ-cpiap-K2O1:O2)sodium(I))] (µ-chlorido) bis(µ-cpiap-K5N1:O1:O2:O3,O3′)dicopper(II)]bis(µ-aqua)(aqua)bis(cpiap-K2O1,O2)copper(II)] hexa hydrate

The new title two-dimensional hetero-tetra nuclear Cu₃–Na coordination polymer {[NaCu₃Cl(cpiap)₂(H₂O)₃]_n·6nH₂O} (1) consists of crystallographically two-independent copper(II) centers, each bridged by a sodium cation through carboxylate-oxygen of the deprotonated H₃cpiap ligand (H₃cpiap = 2-(carboxyphenyl)iminoaceticpropanoic acid) to Cu^II (2) and Cu^II (2⁻) cations, and through water molecules to Cu^II (1) cation. Cu^II (2) and Cu^II (1) cations are bridged by carboxylate-oxygen atoms of the ligand in a syn-anti mode which, alternate regularly within the chain being bridged by a tetra coordinated sodium cation. Each Cu^II (2) and Cu^II (2⁻) cation in (1) is in an octahedral environment formed by four carboxylate-oxygens from two cpiap³⁻ ligands, one nitrogen atom and a bridging chloride atom. Cu^II (1) cation is in a square pyramidal environment formed by three water molecules and two carboxylate-oxygens from two cpiap³⁻ ligands. The ligand acts simultaneously as monodentate and tridentate toward Cu^II (1) and Cu^II (2) cations respectively. The lattice water molecules involved in OH···O hydrogen bonding are situated in the void spaces between layers. The zigzag chains, which run along the b-axes further construct three-dimensional metal-organic framework via hydrogen bonding and weak face-to-face π-π interactions. Weak CH···O interactions are also present.     

Al掺杂对尖晶石型Li[Mn(Al)]2O4结构的影响

采用共沉淀法按不同Al掺杂比例x[x=n(Al)∶n(Mn+Al)=0, 0.025, 0.050, 0.100, 0.150, 0.200]制得了Al(OH)3和Mn3O4混合物, 将其与LiNO3按一定比例混合, 在空气中于700 ℃烧结得Li[Mn(Al)]2O4样品. X射线衍射和Raman光谱结果表明, 在0≤x≤0.20范围内均得到了单相的尖晶石型样品, 随着x的增加, 晶胞参数减小, 晶格振动能量增加, Mn(Al)-O的结合增强, 结构稳定性增强.