Approach regions for the square root of the Poisson kernel and boundary functions in certain Orlicz spaces

If the Poisson integral of the unit disc is replaced by its square root, it is known that normalized Poisson integrals of L ^p and weak L ^p boundary functions converge along approach regions wider than the ordinary nontangential cones, as proved by Rönning and the author, respectively. In this paper we characterize the approach regions for boundary functions in two general classes of Orlicz spaces. The first of these classes contains spaces L _Φ having the property L ^∞ ? L _Φ L ^p , 1 ? p > ∞. The second contains spaces L _Φ that resemble L ^p spaces.     

On property of the invariant of graphical representations of DNA sequences

In this article, we consider the influence of variation of DNA sequence on the leading eigenvalue of graphical representation of the biological sequences. The research interpret the rationality of the graphical representation method that compare different DNA sequences. And we show the result on two different models that presented before.      

Separation, purification and structure elucidation of a polysaccharide from root of Cudrania tricuspidata

A water-soluble polysaccharide (CPS-0) was obtained from the root of Cudrania tricuspidata (Carr.) Bur., by hot water extraction (70°C), deproteination using enzymolysis and Sevag method, precipitation with ethanol, and fractionation through DEAE-Sephadex A-50 chromatography. The purity of CPS-0 was determined by HPLC and the structure was elucidated by monosaccharide composition analysis, methylation analysis, GC, GC-MS, NMR spectral (¹H-NMR, ¹³C-NMR, HMQC), UV, IR, and elemental analysis. The CPS-0 was found to contain glucose residues only. The average repeating unit is a decasaccharide having a backbone consisting of 1,4-linked α-D-glucopyranosyl residues to which the side chain consisting of terminal and 1,4-linked α-D-glucopyranosyl residues was attached at position 6 of the branching residues. __________ Translated from Chemical Journal of Chinese Universities, 2007, 28(6): 1088–1091 [译自: 高等学校化学学报]     

On the complexity of computing the logarithm and square root functions on a complex domain

The problems of computing single-valued, analytic branches of the logarithm and square root functions on a bounded, simply connected domain S   are studied. If the boundary ∂S$\partial S$ of S   is a polynomial-time computable Jordan curve, the complexity of these problems can be characterized by counting classes #P$\#P$, MP (or MidBitP  ), and ⊕P$\oplus P$: The logarithm problem is polynomial-time solvable if and only if FP=#P$\mathit{FP}=\#P$. For the square root problem, it has been shown to have the upper bound P^MP$P^{\mathit{MP}}$ and lower bound P^⊕P$P^{\oplus P}$. That is, if P=MP$P=\mathit{MP}$ then the square root problem is polynomial-time solvable, and if P≠⊕P$P\ne \oplus P$ then the square root problem is not polynomial-time solvable.     

在役枞树型叶根原位相控阵超声检测技术*

本文是利用相控阵超声检测成像技术对枞树型叶根进行全覆盖检测系列文章的第二篇。根据检测工艺制作人工缺陷参考试块对叶根不同区域缺陷的检测覆盖和检测灵敏度进行验证研究,并与CIVA模拟缺陷信号结果进行对比。首先采用文章Ⅰ得出的全覆盖检测工艺进行相控阵超声检测实验,针对叶根检测空间受限设计了夹具对探头进行控制,保证了耦合与检测结果的重复性,实现叶根检测数据与检测位置的对应。检测结果表明：(1)叶根内、外弧缺陷相控阵检测数据成像与Civa仿真缺陷模拟检测结果基本一致,说明利用三维扫描尺寸建模和声学仿真模拟软件可有效解决不同规格枞树型叶根全覆盖检测工艺开发难题;(2)根据相控阵检测数据S视图和A视图,结合叶根截面外形结构图可有效判别叶根各截面第1齿根处的缺陷,实现了叶根相控阵全覆盖检测;(3)按照该相控阵组合检测工艺检测出的缺陷信号信噪比高,定位精准,能有效实现在役叶根原位检测。研究结果对相控阵超声技术在汽轮机叶根在役检测工程应用具有较大的参考价值。     

Improving the Accuracy of the Fast Inverse Square Root by Modifying Newton–Raphson Corrections

Direct computation of functions using low-complexity algorithms can be applied both for hardware constraints and in systems where storage capacity is a challenge for processing a large volume of data. We present improved algorithms for fast calculation of the inverse square root function for single-precision and double-precision floating-point numbers. Higher precision is also discussed. Our approach consists in minimizing maximal errors by finding optimal magic constants and modifying the Newton–Raphson coefficients. The obtained algorithms are much more accurate than the original fast inverse square root algorithm and have similar very low computational costs.     

金融时间序列中单位根的检验:在亚太地区主要股票市场中的应用(英文)

本文运用分数差分的方法研究了亚太地区主要股票市场的日股票价格.根据数据特征,我们运用了Robinson(1994)年提出的检验统计量的一种特殊形式对金融数据的单位根和不稳定性进行检验.结果证明,该地区股票价格长记忆行为各不相同但十分相似.     

On a class of iterative-difference equations

Solving the class of second order iterative-difference equations is a difficult problem, proposed as an open problem in Brillouët-Belluot [Aequationes Math. 61 (3) (2001), p. 304]. In this paper, we use three methods to approach such a class of equations, finding their affine solutions, proving the existence of their bounded continuous solutions and constructing their continuous and piecewise continuous solutions.     

A novel cubically convergent iterative method for computing complex roots of nonlinear equations

A fast and simple iterative method with cubic convergent is proposed for the determination of the real and complex roots of any function F(x) = 0. The idea is based upon passing a defined function G(x) tangent to F(x) at an arbitrary starting point. Choosing G(x) in the form of x^k or k^x, where k is obtained for the best correlation with the function F(x), gives an added freedom, which in contrast to all existing methods, accelerates the convergence. Also, this new method can find complex roots just by a real initial guess. This is in contrast to many other methods like the famous Newton method that needs complex initial guesses for finding complex roots. The proposed method is compared to some new and famous methods like Newton method and a modern solver that is fsolve command in MATLAB. The results show the effectiveness and robustness of this new method as compared to other methods.