Directed polymers in Hartree-Fock approximation

A replica trick is used to map the problem of directed polymers into a quantum mechanics problem ofn-body bound states. This bound-state problem is then treated using a self-consistent method of Hartree-Fock. Ford=2, the exact result of the DP exponents is reproduced; and for complex DP, the ground-state energyE _n n² is found, confirming previous numerical results.     

Discrete symmetry groups of vertex models in statistical mechanics

We analyze discrete symmetry groups of vertex models in lattice statistical mechanics represented as groups of birational transformations. They can be seen as generated by involutions corresponding respectively to two kinds of transformations onq×q matrices: the inversion of theq×q matrix and an (involutive) permutation of the entries of the matrix. We show that the analysis of the factorizations of the iterations of these transformations is a precious tool in the study of lattice models in statistical mechanics. This approach enables one to analyze two-dimensionalq ⁴-state vertex models as simply as three-dimensional vertex models, or higher-dimensional vertex models. Various examples of birational symmetries of vertex models are analyzed. A particular emphasis is devoted to a three-dimensional vertex model, the 64-state cubic vertex model, which exhibits a polynomial growth of the complexity of the calculations. A subcase of this general model is seen to yield integrable recursion relations. We also concentrate on a specific two-dimensional vertex model to see how the generic exponential growth of the calculations reduces to a polynomial growth when the model becomes Yang-Baxter integrable. It is also underlined that a polynomial growth of the complexity of these iterations can occur even for transformations yielding algebraic surfaces, or higher-dimensional algebraic varieties.     

“无中生有”计的一个博弈模型

“无中生有”计系《三十六计》中的第七计,本首先给出此计的一个博弈模型,然后由此研究破此计的一个算法。     

一类多步矩阵对策上的计策问题

以有序树为工具,研究了可以描述连环计,诱敌深入等多步矩阵对策上的一类计策模型.在不考虑信息环境的封闭对策系统中,及局中人对每一步矩阵对策的赢得矩阵,两个局中人的策略集合以及局中人的理性等的了解都是局中人的共同知识的假定下,提出了局中人的最优计策链及将计就计等概念,研究了局中人中计和识破计策的固有概率,讨论了局中人在什么情况下最好主动用计,在什么情况下最好从动用计以及求解最优计策等问题.     

稀疏正则化最小类散度半监督分类机

基于稀疏表示理论提出一种稀疏正则化最小类散度半监督分类机(SRMCV), 且对于模式分类问题, SRMCV通过引入稀疏Laplacian正则化项和类内散度信息以实现预测空间函数在全局稀疏表示结构下平滑变化, 同时通过类内数据散度结构进一步优化决策函数的判别方向, 此方法能解决现有SSL方法对模型参数敏感和在噪声学习环境下缺乏鲁棒性等问题, 其有效性已在实际数据集上通过实验验证.     

DDTC-Na-based colorimetric chemosensor for the sensing of cyanide in water

Sodium diethyldithiocarbamate (DDTC-Na) was demonstrated to be a new colorimetric cyanide chemosensor by utilizing an indirect trick. First, some copper ions were added to the colorless aqueous solution of DDTC-Na. Then, the resultant brown solution was studied upon the addition of different anions, including Cl⁻, I⁻, IO₃⁻, SO₄²⁻, NO₂⁻, Br⁻, H₂PO₄⁻, F⁻, SCN⁻, HSO₄⁻, ClO₄⁻ and CN⁻. It was observed by naked eyes that the brown solution changed to colorless immediately after the addition of the trace cyanide, but there were no changes towards other anions, making DDTC-Na a good selective cyanide chemosensor in pure water. Supported by the National Natural Science Foundation of China (Grant Nos. 20674059 & 20402011)     

连续对策上的计策问题

限定一个连续对策不是平凡地无意义（例如对某个局中人绝对有利等），我们提出了连续对策上的计策的基本概念。最后得到结论，如果局中人1使用经典对策，那么他的赢得期望必不是赢得函数的最大值。如果局中人1使用计策成功（即使得局中人2中计），那么局中人1必取得赢得函数的最大值，局中人2也有对偶的结果。     

三步矩阵对策上的无中生有计及其实例

基于一个历史实例及假定:①三步矩阵对策中赢得矩阵都不变,②每步都是局中人1先行动,③对于每步对策,局中人2观测不到对手究竟使用了何策略;但局中人1可以观测到对手所用的策略,建立了三步矩阵对策上的无中生有计(《三十六计》中的第七计)的对策模型.研究了当局中人2中计,半识破和完全识破对手的无中生有计时的赢得和所用的策略的情况.并用上述实例对模型作了说明.     

矩阵计策的支撑解系

令[aij]n×n是二人零和对策的支付矩阵.局中人1可用其"计策"得到最大支付a＝max{aij|1≤i≤n,1≤j≤n},然而,一个开放问题是如何找到全体计策解,本文首先引进计策解系的一种特殊类型--支撑解系.然后研究支撑解系的特征、性质、代数结构.最后给出寻找全体基本支撑解系的一个算法.