Asymptotic Expansions of the Heat Kernel of the Laplacian for General Annular Bounded Domains with Robin Boundary Conditions：Further Results

The asymptotic expansions of the trace of the heat kernel θ(t)=∑^∞v=1^exp(-tλv) for small positive t,where {λv} are the eigenvalues of the negative Laplacian -△n=-∑^ni=1(D/Dx^1)^2 in R^2(n=2 or 3),are studied for a general annular bounded domain Ω with a smooth inner boundary DΩ1 and a smooth outer boundary DΩ2,where a finite number of piecewise smooth Robin boundary conditions(D/Dnj γh)Ф=0 on the components Гj(j= 1,...,m) of (DΩ1 and on the components Гj (j=k 1,…,m) of of DΩ2 are considered such that DΩl=U^kj=lГj and DΩ2= U^m=k 1Гj and where the coefficients γj(j=1,...,m) are piecewise smooth positive functions. Some applications of θ(t) for an ideal gas enclosed in the general annular bounded domain Ω are given. Further results are also obtained.     

截断平顶高斯光束M2因子的比较研究

使用熵束宽、渐近分析和环围功率法对截断平顶高斯光束的束腰宽度w、远场发散角θ0和M²因子作了比较研究.结果表明:按不同束宽定义得到的截断平顶高斯光束的w、θ0和M²因子不同,且与截断参量a/w0(a为光阑半宽度,w0为平顶高斯光束初始束腰宽度)有关.随a/w0的增加,三种方法计算得到的w、θ0和M²都分别趋于某常量.     

Asymptotic formulae for multivariate Kantorovich type generalized sampling series

In this paper an asymptotic formula of Voronovskaja type for a multivariate extension of the Kantorovich generalized sampling series is given. Moreover a quantitative version in terms of some moduli of smoothness is established. Finally some particular examples of kernels are discussed, as the Bochner-Riesz kernel and the multivariate splines.     

会算、会少算、也要会不算

高考对运算求解能力要求是:会根据法则、公式进行正确运算、变形和数据处理,能根据问题的条件寻找与设计合理、简捷的运算途径,能根据要求对数据进行估计和近似计算.     

On S-Shaped Bifurcation Curves for a Class of Perturbed Semilinear Equations

By making use of bifurcation analysis and continuation method, the authors discuss the exact number of positive solutions for a class of perturbed equations. The nonlinearities concerned are the so-called convex-concave functions and their behaviors may be asymptotic sublinear or asymptotic linear. Moreover, precise global bifurcation diagrams are obtained.     

关于组合交错和的渐近性

所谓的Rice’s方法是估计交错和Df_n=sum from k=0 to n(_k~n)(-1)~kf_k,其中,序列f_n能扩充为一个解析函数f(n).在算法分析的许多问题中,经常导出序列Df_n.在60年代,Knuth在分类交换基     

强平稳ρ-混合序列的精确渐近性

研究了强平稳ρ-混合序列部分和Sn=X1 X2 … Xn的精确渐近性:即当ε↘0时,概率级数∞∑n=1ψ(n)P(|Sn|≥εH(n))的极限行为和收敛速度,并揭示了函数ψ(n)与H(n)之间的关系.     

一类非线性奇摄动Robin问题解的渐近性态

利用渐近理论和微分不等式的方法,该文研究了一类非线性奇摄动Robin问题. 证明了其解的存在性,并得到了解的任意n 阶一致有效渐近展开式.     

重尾β混合随机变量序列的大偏差

设{X_n; n≥1}是重尾平稳非负随机变量序列, 研究其部分和 S_n=X₁+X₂+…+X_n的对数渐近性质. 对于适当的x, 在混合条件下, 给出了估计P(Sn>n^x)≈n^−αx+1, 其中α是特定的参数. 验证了Gantert提出的相关的猜想, 并且证明了所谓的上确界大偏差原理.