On optimizing edge connectivity of product graphs

This work studies the super edge connectivity and super restricted edge connectivity of direct product graphs, Cartesian product graphs, strong product graphs and lexicographic product graphs. As a result, sufficient conditions for optimizing the edge connectivity and restricted edge connectivity of these graphs are presented.     

On differential–algebraic equations in infinite dimensions

We consider a class of differential–algebraic equations (DAEs) with index zero in an infinite dimensional Hilbert space. We define a space of consistent initial values, which lead to classical continuously differential solutions for the associated DAE. Moreover, we show that for arbitrary initial values we obtain mild solutions for the associated problem. We discuss the asymptotic behaviour of solutions for both problems. In particular, we provide a characterisation for exponential stability and exponential dichotomies in terms of the spectrum of the associated operator pencil.     

强混响背景下悬浮目标的时反成像

提出了一种加权宽带全信号子空间时反成像方法,将扩展性目标建模为有限数量个、相互独立的点散射体构成,实现了时反成像在可疑目标区域的全信号子空间和整个宽带的累加。在实验室波导水池中,底部放置圆柱筒制造混响背景,共进行了两个实验,一是扩展性的悬浮目标位于圆柱筒附近,其回波与圆柱筒反射的混响不在同一个时间窗内,二是弱点目标回波与圆柱筒反射的混响重叠于同一个时间窗内,对所提出的方法进行强混响背景下弱悬浮目标的成像能力验证。结果表明,此方法对强混响背景下的弱悬浮目标的成像质量明显优于传统的时反成像方法。     

强阴离子交换柱分离-氢化物发生-原子荧光光谱法测定水中As(Ⅲ)和As(Ⅴ)

本文报道水中As(Ⅲ)和As(Ⅴ)的Supelco强阴离子交换(SAX)柱分离-氢化物发生-原子荧光光谱(HG-AFS)法检测的新方法.方法的检出限为0.0466 μg/L,相对标准偏差为0.89%～1.01%,加标回收率为95.10%～105.30%.该方法具有操作简单,分离效果好,测定精确度、准确度高等优点.将其应用于水样分析,可测定水中砷的不同价态.     

强碱性阴离子交换树脂分离富集土壤中的钼

研究了以强碱性阴离子交换树脂为固定相的离子交换色谱法分离富集土壤中钼,实现了钼与其他常见金属元素离子的选择性分离,富集在色谱柱上的钼以0.5mol.L^-1NH4NO3＋2mol.L^-1HNO3洗脱并用富氧火焰原子吸收光谱法进行测定,钼的回收率为99%—101.3%。     

Bergman polynomials on an archipelago: Estimates, zeros and shape reconstruction

Growth estimates of complex orthogonal polynomials with respect to the area measure supported by a disjoint union of planar Jordan domains (called, in short, an archipelago) are obtained by a combination of methods of potential theory and rational approximation theory. The study of the asymptotic behavior of the roots of these polynomials reveals a surprisingly rich geometry, which reflects three characteristics: the relative position of an island in the archipelago, the analytic continuation picture of the Schwarz function of every individual boundary and the singular points of the exterior Green function. By way of explicit example, fine asymptotics are obtained for the lemniscate archipelago |z^m−1|<r^m, 0<r<1, which consists of m islands. The asymptotic analysis of the Christoffel functions associated to the same orthogonal polynomials leads to a very accurate reconstruction algorithm of the shape of the archipelago, knowing only finitely many of its power moments. This work naturally complements a 1969 study by H. Widom of Szegő orthogonal polynomials on an archipelago and the more recent asymptotic analysis of Bergman orthogonal polynomials unveiled by the last two authors and their collaborators.     

条件泛函及其导数非参数估计的强一致收敛速度

研究了条件泛函及其导数的非参数估计,对随机与固定设计的条件泛函,分别利用核估计和非参数加权估计,在核函数及权函数满足一定条件下,证明了估计一致强收敛于待估函数的速度可达到最优。从而进一步推广和发展了Hrdle,etal.(1988)、Severini,etal.(1992)的许多结果。     

A Strong Maximum Principle for parabolic equations with the p-Laplacian

We prove the Strong Maximum Principle (SMP) under suitable assumptions for a class of quasilinear parabolic problems with the p  -Laplacian, p>1$p>1$, on bounded cylindrical domains of R^N+1${\mathbb{R}}^{N+1}$,

_∂tu−_Δpu−λ|u|^p−2u≥0,${\partial }_{t}u-{\mathrm{\Delta }}_{p}u-\lambda {|u|}^{p-2}u\ge 0,$

with nonnegative initial–boundary conditions and λ≤0$\lambda \le 0$, and we give some counterexamples to the SMP if some of our assumptions are violated. We show that the Hopf Maximum Principle holds for 1<p<2$1<p<2$, and give a counterexample to it for p>2$p>2$. Also the Weak Maximum Principle for λ≤_λ1$\lambda \le {\lambda }_1$ is established.     

On Best Approximations from RS-sets in Complex Banach Spaces

The concept of an RS-set in a complex Banach space is introduced and the problem of best approximation from an RS-set in a complex space is investigated. Results consisting of characterizations, uniqueness and strong uniqueness are established,     

He2 and HeH molecular ions in a strong magnetic field: The Lagrange-mesh approach

Accurate calculations for the ground state of the molecular ions He³⁺₂ and HeH²⁺ placed in a strong magnetic field B?10² a.u.$B?{10}^2\text{a.u.}$ (≈2.35×10¹¹ G$\approx 2.35\times {10}^{11}\text{G}$) using the Lagrange-mesh method are presented. The Born–Oppenheimer approximation of zero order (infinitely massive centers) and the parallel configuration (molecular axis parallel to the magnetic field) are considered. Total energies are found with 9–10 s.d. The obtained results show that the molecular ions He³⁺₂ and HeH²⁺ exist at B>100 a.u.$B>100\text{a.u.}$ and B>1000 a.u.$B>1000\text{a.u.}$, respectively, as predicted in Turbiner and López Vieyra (2007) [1] while a saddle point in the potential curve appears for the first time at B∼80 a.u.$B\sim 80\text{a.u.}$ and B∼740 a.u.$B\sim 740\text{a.u.}$, respectively.