图的广义Randi\'{c} Estrada 指标的界

受图的Randi\'{c} Estrada 指标和广义 Randi\'{c} 能量的启发, 定义了图的广义 Randi\'{c} Estrada 指标. 利用代数方法和初等分析方法给出了n 阶简 单连通图和 r-正则图的广义Randi\'{c} Estrada指标的上下界, 推广了Bozkurt等人有关Randi\'{c} Estrada指标的结论.     

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In this paper, a new H\'{a}jek-R\'{e}nyi-type inequality for mean zero associated random variables is obtained, which generalizes and improves the result of Theorem 2.2 of \ncite{9}. In addition, a Brunk-Prokhorov-type strong law of large numbers is also given.     

厚尾相依序列的均值变点估计

本文研究了厚尾相依序列的均值变点估计. 证明了变点的CUSUM估计的一致性并得到了收敛速度.在方差无穷的情况下推广了H\'{a}jek--R\'{e}nyi不等式.     

Sz\''asz-Kantorovich-B\''{e}zier算子在$L_p[0, \infty)$上的逼近定理

本文利用Ditzian-Totik模得到了Sz\'{a}sz-Kantorovich-B\'{e}zier算子在$L_{p}[0,\infty)$空间逼近的正逆定理及等价定理.     

Hausdorff Dimension for Range and Graph of Multi-Parameter Operator Stable L\'{e}vy Processes

??The lower Hausdorff dimension results for the range and the graph of multi-parameter operator stable L\'{e}vy processes are established. The consequences are completely determined by the eigenvalues of its exponent matrix.     

三角B\''{e}zier曲面和四边B\''{e}zier曲面之间的相互转化

B\'{e}zier曲面有两种不同的形式:三角B\'{e}zier曲面和四边B\'{e}zier曲面,它们有着不同的基底和不同的几何拓扑结构, 但是它们也有很多共同的性质,因此三角B\'{e}zier曲面和四边B\'{e}zier曲面之间的相互转化就成为CAGD 里一个重要研究课题.在本文中, 我们用函数复合的方法实现两者之间的相互转化.被复合的两个函数, 一个用Polar形式表示,另一个用常见的Bernstein基形式表示.     

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??In this paper, we consider the optimal dividend problem in the spectrally positive L\'{e}vy model with regime switching. By an auxiliary optimal problem, the principle of dynamic programming and the fluctuation theory of L\'{e}vy processes, we show that optimal strategy is a modulated barrier strategy. The value function and the optimal dividend barrier are obtained by iteration.     

关于错排数与Bell数的一些循环公式

In this paper, a further investigation for the number of Derangements and Bell numbers is performed, and some new recursion formulae for the number of Derangements and Bell numbers are established by applying the generating function methods and Padé approximation techniques. Illustrative special cases of the main results are also presented.     

受迫Li\''{e}nard方程周期解的存在唯一性

本文利用整体反函数理论证明了受迫Li\'{e}nard方程$x'+f(x)x'+g(t,x)=e(t)$周期解的存在唯一性，推广和改进了现有的结果.     

论Poincar\''{e}型连续统及其某些基本性质

本文给出了Poincar\'{e}直觉主义连续统的一种超标准模型[PC],并证明了三条基本性质. [PC]是模型(PC)的深化和改进.作为其应用,文中还概述了子模型$\overline{R}$ (非Cantor型连续统)上的一种非标准微积分.     

关于商高数的Je\'{s}manowicz猜想

Let(a, b, c) be a primitive Pythagorean triple. Je′smanowicz conjectured in 1956 that for any positive integer n, the Diophantine equation(an)x+(bn)y=(cn)z has only the positive integer solution(x, y, z) =(2, 2, 2). Let p ≡ 3(mod 4) be a prime and s be some positive integer. In the paper, we show that the conjecture is true when(a, b, c) =(4p2s-1, 4p s, 4p2s+ 1) and certain divisibility conditions are satisfied.     

二部图形式的Erd\H{O}s-S\'{o}s猜想

二部图形式的Erd\H{O}s-S\''{o}s猜想     

含幺元的半格和群的Zappa-Sz\'{e}p积上的同余

Let P = E G be a Zappa-Szp product of a semilattice E with an identity and a group G. In this paper, we first introduce the concept of congruence pairs for P , and then prove that every congruence on P can be described by such a congruence pair. In fact the congruence lattice on P is lattice-isomorphic to the set of all congruence pairs for P . Finally,we characterize group congruences on P .     

On irreducible p,q‐representations of Lie algebras \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {G} (0,1)$\end{document} and \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {G} (0,0)$\end{document}

In this paper, the irreducible p, q‐representations of the Lie algebras $\mathcal {G}(0,1)$ and $\mathcal {G}(0,0)$ are discussed. We prove two theorems that classify certain irreducible p, q‐representations of these Lie algebras and construct their one variable models in terms of p, q‐derivative and dilation operators. As an application, we derive a p, q‐special function identity based on one such model.     

Global solution with \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$ \mathcal {C}^{k}$\end{document}‐estimates for \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\bar{\partial }$\end{document}‐equation on q‐convex intersections

We construct a global solution with $\mathcal {C}^{k}$‐estimates for the $\bar{\partial }$‐equation on q‐convex intersections.     

多线性Calder\'on-Zygmund算子的多权弱型估计

Let m be an integer and T be an m-linear Calderón-Zygmund operator, u, v1,..., vm be weights. In this paper, the authors give some sufficient conditions on the weights （u, vk） with 1 ≤ k ≤ m, such that T is bounded from Lp1（Rn, v1） × ··· × Lpm（Rn, vm） to Lp,∞（Rn, u）.