确定等价电子杨盘基的等概率比对方法

给出了等价电子正则杨盘T^［λ］_ig的基本对称算子、完全对称算子概念,同时给出了这些对称算子作用于任一Slater函数_i所产生的根态、生成态概念.由正交归一化杨盘T^［λ］_ie的纵置换算子A^［λ］_ie的构造规则,给出了A^［λ］_ie中存在的对称算子和确定T^［λ］_ie的等概率比对方法,从而基本避免了牵涉到许多算子的极其复杂的代数,给出了求解N值较大的电子系统杨盘基问题的新方法. 关键词： 正则杨盘 对称算子 根态 等概率比对方法     

A Rational-Function Identity Related to the Murnaghan–Nakayama Formula for the Characters of S n

The Murnaghan–Nakayama formula for the characters of S _n is derived from Young's seminormal representation, by a direct combinatorial argument. The main idea is a rational function identity which when stated in a more general form involves Möbius functions of posets whose Hasse diagrams have a planar embedding. These ideas are also used to give an elementary exposition of the main properties of Young's seminormal representations.     

A path-transformation for random walks and the Robinson-Schensted correspondence

The author and Marc Yor recently introduced a path-transformation with the property that, for belonging to a certain class of random walks on , the transformed walk has the same law as the original walk conditioned never to exit the Weyl chamber . In this paper, we show that is closely related to the Robinson-Schensted algorithm, and use this connection to give a new proof of the above representation theorem. The new proof is valid for a larger class of random walks and yields additional information about the joint law of and . The corresponding results for the Brownian model are recovered by Donsker's theorem. These are connected with Hermitian Brownian motion and the Gaussian Unitary Ensemble of random matrix theory. The connection we make between the path-transformation and the Robinson-Schensted algorithm also provides a new formula and interpretation for the latter. This can be used to study properties of the Robinson-Schensted algorithm and, moreover, extends easily to a continuous setting.

     

On Young's Orthogonal Form and the Characters of the Alternating Group

A combinatorial method of determining the characters of the alternating group is presented. We use matrix representations, due to Thrall, that are closely related to Young's orthogonal form of representations of the symmetric group. The characters are computed directly from matrix entries of these representations and entries of the character table of the symmetric group.     

对取代苯Ph一X（X＝F，OH，NH_2）的价键理论研究

采用键表酉群方法对Ｃ６Ｈ５Ｆ、Ｃ６Ｈ５ＯＨ和Ｃ６Ｈ５ＮＨ２中的电子离域现象进行了计算和分析，讨论了取代苯的价键描述特性，并计算了取代基的π电子离域能．结果表明离子结构成分与离域能有直接关系，即离子成分越多，电子离域能越大．／６－３１Ｇ基组及“分子中的原子”方法将电荷密度分区积分得到各原子上的电荷集居数，并将此结果与取代苯的反应性能进行了比较。为在价键意义上分析和理解取代基对苯环电子结构及其反应性能的影响，本文对３个典型的取代苯Ｐｈ－Ｘ（Ｘ＝Ｆ，ＯＨ，ＮＨ２）进行了初步的价键计算和讨论．１计算方法及构型在键表酉群方法中［５］，体系的一个共振结构可用一个价键结构函数即键表ψ（ｋ）来描述，相应的体系总波函数Ψ可表示为Ｍ个正则键表的线性组合：式（１）便构成了键表相互作用（ＢＴＩ）计算方法［６］的基础．键表对体系的结构贡献定义为：原子轨道ｑ上的电荷集居数定义为：式中ｍｑ（ｋ）可取０、１或２，分别对应于键表ψ（ｋ）中原子轨道ｑ出现０、１或２次．为简比计算，我们将取代苯的σ骨架用ＨＦ分子轨道固定［７］，这样仅需考虑π电子及轨道．原子轨道积分及ＨＦ－ＳＣＦ计算采用Ｇａｕｓｓｉａｎ８０程序．联系人及第一作者：莫亦荣，男，２９     

线性规划无穷多最优解的讨论

利用线性规划单纯形表对线性规划原问题存在无穷多最优解和对偶问题存在无穷多最优解的情况进行了讨论,并分析了对偶问题存在无穷多最优解情况下的影子价格的方向性。最后以实例说明了各种情况。对初学者加深理解及决策者决策参考有一定帮助     

A quantummechanical derivation of the eigenvalues of the quadratic Casimir operator of the algebra SU(n) in Young tableau representation

The paper concerns the eigenvalues and eigenfunctions of the quadratic Casimir operator of the algebra $SU(n)$ in the Young tableau representation. Our starting point is a concrete physical problem in second quantized formalism. We use quantummechanical and group theoretical vehicles to determine the aimed quantities. The tableaux are organized according to their eigenvalue. We also investigate the modification rules.     

Limit shapes of bumping routes in the Robinson–Schensted correspondence

We prove a limit shape theorem describing the asymptotic shape of bumping routes when the Robinson–Schensted algorithm is applied to a finite sequence of independent, identically distributed random variables with the uniform distribution U[0,1] on the unit interval, followed by an insertion of a deterministic number α. The bumping route converges after scaling, in the limit as the length of the sequence tends to infinity, to an explicit, deterministic curve depending only on α. This extends our previous result on the asymptotic determinism of Robinson–Schensted insertion, and answers a question posed by Moore in 2006. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 48, 171–182, 2016     

线性规划的教学

作者给出了线性规划的一个更为一般的表现形式 ,明确定义了具有标准型形式的线性规划的等价变换 ,使得单纯形法的讲解更清晰简洁 ,便于学生掌握 ,且兼顾了数学形式美和逻辑美的学科特点 ;文中也体现了重视实例式教学的想法 .