Michael additions of benzoins versus Michael-Stetter additions of aldehydes

Triethylamine catalyzed Michael additions of benzoins to chalcone can prevail over the expected Michael-Stetter additions when certain thiazolium ion conjugate bases - prepared $\text{in situ}$ from the pertinent thiazolium salts and triethylamine- are used as catalysts.     

Singular integral equations and boundary element method of cracks in thermally stressed planar solids

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Multiple solutions for three-point boundary value problem with nonlinear terms depending on the first order derivative

In this paper, we consider the following second-order three-point boundary value problem

Blow-Up for a Semi-linear Advection-Diffusion System with Energy Conservation

The authors study radial solutions to a model equation for the Navier-Stokes equations. It is shown that the model equation has self-similar singular solution if 5 ≤ n ≤ 9. It is also shown that the solution will blow up if the initial data is radial, large enough and n ≥5.     

求解垂直互补问题的参数牛顿法

给出了求解垂直互补问题的一种参数牛顿法,在较为温和的条件下证明了该方法的局部超线性收敛结果,并且给出了具体数值计算.     

Functoriality of automorphic L-functions through their zeros

Let E be a Galois extension of Q of degree , not necessarily solvable. In this paper we first prove that the L-function L(s,π) attached to an automorphic cuspidal representation π of GLm(EA) cannot be factored nontrivially into a product of L-functions over E. Next, we compare the n-level correlation of normalized nontrivial zeros of L(s,π1)···L(s,πk), where πj, j = 1,...,k, are automorphic cuspidal representations of GLmj(QA), with that of L(s,π). We prove a necessary condition for L(s,π) having a factoriz...     

Planar graphs with maximum degree 8 and without adjacent triangles are 9-totally-colorable

The Total Coloring Conjecture, in short, TCC, says that every simple graph is (Δ+2)-totally-colorable where Δ is the maximum degree of the graph. Even for planar graphs this conjecture has not been completely settled yet. However, every planar graph with Δ≥9 has been proved to be (Δ+1)-totally-colorable. In this paper, we prove that planar graphs with maximum degree 8 and without adjacent triangles are 9-totally-colorable.     

确定环形Markov链的Q-矩阵

给出了Markov链中任一状态集的逗留时间或击中时间的分布(混合指数分布),以及其分布的各阶微分与Q-矩阵之间的约束方程组.利用该约束关系及环形链结构的先验信息,采用Markov链反演方法证明了:对于有限状态环形Markov链,其Q-矩阵能由其中任意两个相邻状态的逗留时间和击中时间分布唯一决定,并给出了相应的算法.     

带加法白噪声的随机Boussinesq方程组的解的渐近行为

考虑速度和温度同时在加法白噪声扰动下的随机Boussinesq方程组的解的渐近特征.可以接轨道得到该随机方程组的唯一解,并可以验证该解生成随机动力系统,进而证明了该随机动力系统存在随机吸引子.