构造相应于有限维非退化可解李代数的顶点代数

设g是带有非退化不变对称双线性型的有限维可解李代数，该文首先应用g的仿射李代数g的表示理论，构造出一类水平为l的限制g-模Vg（l，0）．然后应用顶点算子的局部理论在hom（Vg（l，0），Vg（l，0）（（x）））中找到一类顶点代数Lvg（l，0）．建立了LVg（l，0）到Vg（l，0）的映射，最后证明了这类映射是顶点代数同构．     

Characters of Fundamental Representations of Quantum Affine Algebras

We give closed formulae for the q-characters of the fundamental representations of the quantum loop algebra of a classical Lie algebra, in terms of a family of partitions satisfying some simple properties. We also give the multiplicities of the eigenvalues of the imaginary subalgebra in terms of these partitions.     

铝合金等离子体淹没氮离子注入层的摩擦学性能研究

用等离子体淹没离子注入技术对ＬＹ１２和ＬＤ１０铝合金表面进行氮离子注入。用俄歇电子能谱分析离子注入层中氮的浓度分布，在此基础上进行了摩擦磨损试验。用扫描电观察和分析磨损表面特征。研究表明：氮离子注入铝合金形成细小，弥散的硬质ＡｌＮ析出相，铝合金表层的显微硬度增加，摩擦系数降低；耐磨性随着注入剂量和电压的增加而提高。磨损机制主要为粘着磨损，随离子注入剂量的增加，粘着磨损趋行减轻。     

Complete Caps in with Both N and q Odd

In this work, an inductive method to construct complete caps in affine spaces is provided. Using this tool, for odd and q odd, complete caps smaller than all already known ones are obtained.     

添加剂与铝合金的相互作用研究 Ⅰ.静态反应膜及油润滑下的摩擦学性能

静态下分别于２５℃，９０℃及１８０℃下进行硫化异丁烯（ＳＯ）、亚磷酸二正丁酯（ＤＢＰ）、ＳＯ＋ＤＢＰ的混合物（质量比２０∶１）、二烷基二硫代磷酸锌（ＺＤＤＰ）及十二酸（ＬＡ）５种添加剂均以质量分数为２％的比例添加到液体石蜡（ＬＰ）中与铝合金进行油浸试验．用动－静摩擦系数精密测定仪评价了在铝合金表面上所形成的静态反应膜的摩擦磨损行为，并考察了上述添加剂在ＬＰ中对铝合金－钢摩擦副的润滑作用．结果表明：静态反应膜的摩擦磨损行为与添加剂的化学活性密切相关，其中ＤＢＰ最易与铝合金发生反应，故其反应膜具有最低的摩擦系数和最长的耐磨寿命；ＺＤＤＰ在１８０℃下的静态反应膜具有较低的摩擦系数和较长的耐磨寿命；ＳＯ、ＳＯ与ＤＢＰ的混合物及ＬＡ的静态反应膜则不具有减摩抗磨性能，预示这些添加剂在ＬＰ中不与铝合金发生较强的化学作用．含上述添加剂的ＬＰ润滑下的摩擦磨损试验显示，ＤＢＰ与ＺＤＤＰ具有较好的摩擦学性能．这表明添加剂在铝合金表面静态反应膜的摩擦磨损试验结果与其在常规润滑下的具有较好的相关性．     

EXACT LINEARIZATION BASED MULTIPLE-SUBSPACE ITERATIVE RESOLUTION TO AFFINE NONLINEAR CONTROL SYSTEM

To the optimal control problem of affine nonlinear system, based on differential geometry theory, feedback precise linearization was used. Then starting from the simulative relationship between computational structural mechanics and optimal control, multiple-substructure method was inducted to solve the optimal control problem which was linearized. And finally the solution to the original nonlinear system was found. Compared with the classical linearizational method of Taylor expansion, this one diminishes the abuse of error expansion with the enlargement of used region.     

广义仿射李代数上的非交换Poisson代数结构

非交换的Poisson代数同时具有(未必交换的)结合代数和李代数两种代数结构,且结合代数和李代数之间满足所谓的Leibniz法则.本文确定了一般广义仿射李代数上所有的Poisson代数结构.     

Strong immersion is a well-quasi-ordering for semicomplete digraphs

We prove that the strong immersion order is a well-quasi-ordering on the class of semicomplete digraphs, thereby strengthening a result of Chudnovsky and Seymour (2011, J. Comb. Theory, Series B, 101, 47–53) that this holds for the class of tournaments.     

A Partial First-Order Affine-Scaling Method

We present a partial first-order affine-scaling method for solving smooth optimization with linear inequality constraints. At each iteration, the algorithm considers a subset of the constraints to reduce the complexity. We prove the global convergence of the algorithm for general smooth objective functions, and show it converges at sublinear rate when the objective function is quadratic. Numerical experiments indicate that our algorithm is efficient.     

Complex affine distributions

Geometry of affine immersions is the study of hypersurfaces that are invariant under affine transformations. As with the hypersurface theory on the Euclidean space, an affine immersion can induce a torsion-free affine connection and a (pseudo)-Riemannian metric on the hypersurface. Moreover, an affine immersion can induce a statistical manifold, which plays a central role in information geometry. Recently, a statistical manifold with a complex structure is actively studied since it connects information geometry and Kähler geometry. However, a holomorphic complex affine immersion cannot induce such a statistical manifold with a Kähler structure. In this paper, we introduce complex affine distributions, which are non-integrable generalizations of complex affine immersions. We then present the fundamental theorem for a complex affine distribution, and show that a complex affine distribution can induce a statistical manifold with a Kähler structure.