Comment: “On the computation of molecular auxiliary functions<Emphasis Type="Italic">A</Emphasis><Subscript>n</Subscript>and<Emphasis Type="Italic">B</Emphasis><Subscript>n</Subscript>”

Guseinov, Mamedov, Kara and Orbay (Pramana - J. Phys. 56, 691 (2001)) propose methods for evaluating the molecular auxiliary functionsA _n(p) andB _n(pt) for the range 17 ≤n ≤ 60 and 25 ≤pt ≤ 60. However, their procedure forA _n(p) is not new, and that forB _n(pt) is less efficient for their target range than another well-known method. Their approach does have merit for smaller non-zero values ofpt. Two minor errors in table 1 of their paper are also identified.     

Absolute Continuity in Periodic Thin Tubes and Strongly Coupled Leaky Wires

Using a perturbative argument, we show that in any finite region containing the lowest transverse eigenmode, the spectrum of a periodically curved smooth Dirichlet tube in two or three dimensions is absolutely continuous provided the tube is sufficiently thin. In a similar way we demonstrate absolute continuity at the bottom of the spectrum for generalized Schrödinger operators with a sufficiently strongly attractive interaction supported by a periodic curve in R^d = 2, 3.     

用边界元法分析非均匀介质中的传输线

 从静电场边值问题的积分解出发,推导出用边界元法求解分区均匀介质填充传输线问题的矩阵表达式,给出传输线电容参数的计算公式,介绍用边界元法求解分区均匀介质填充传输线问题的基本原理和求解过程。对两类传输线的计算结果表明：用边界元法求解分区均匀介质填充传输线问题,不仅具有较高的计算精度,而且可以很方便地应用于各类复杂截面分区均匀介质填充传输线问题的工程设计与计算,边界元法是求解分区均匀介质填充传输线问题的一种有效方法。     

均匀核化过程中凝结核分维数研究

运用分子动力学模拟方法,对水蒸汽均匀核化凝结过程进行了研究.采用分形理论分维数统计中的小盒计数法,对二维条件下凝结核的分维数的变化规律进行了统计计算.模拟结果表明,水蒸汽均匀核化过程中所形成的凝结核表面的分维数并非一过程量,凝结核表面分维数并不随凝结核的长大而变化,当凝结核长大到一定程度后,其表面分维数将达到一恒定值.本文对初始温度为500℃,密度分别为100和200 kg/m3的过热水蒸气冷却到20℃的过程进行了模拟,水蒸汽在二维均匀核化过程中所形成的凝结核表面分维数为1.79.     

Singular value decomposition with normalized period for magnetocaridiography signal processing

In this paper, we have developed an algorithm based on singular value decomposition (SVD) for matrix. And the novel SVD algorithm with normalized period of cardiac cycles is presented. The results from real magnetocardiography (MCG) data processing show that the new algorithm is better than the standard one not only in suppressing noises, but also in providing high-fidelity MCG signals.     

On Computability of Decaying and Nondecaying States in Quantum Systems with Cantor Spectra

We study Hamiltonians with singular spectra of Cantor type with a constant ratio of dissection. The decay properties of the states in such systems depend on the nature of the dissection rate that can be characterized in terms of the algebraic number theory. We show that in spite of simplicity of the considered model the computational modeling of nondecaying states is in general impossible.     

PT-Symmetry, Canonical Decomposition, Perturbation Theory

Let H be any PT-symmetric Schrödinger operator of the type H=- ² +x ² +igW(x), where W is a real polynomial, odd under reflection of all coordinates, gR, acting on L ² ( R ^d ). The proof is outlined of the following statements: PH is self-adjoint and its eigenvalues coincide with the eigenvalues of (H*H). Moreover the eigenvalues of (H*H), known as the singular values of H, can be computed via perturbation theory by Borel summability.     

三维位势问题边界元法中几乎奇异积分的正则化

采用一种半解析正则化算法,计算了三维位势问题边界元法中近边界点的几乎强奇异和几乎超奇异面积分.该算法适用于三角形线性等参元.对高次单元将其细分为几个三节点三角形单元即可应用该算法.由于几乎奇异性,与内点邻近的单元上的积分,采用半解析正则化积分算法计算;而远处单元的积分仍保持常规高斯积分.对三维热传导算例,计算了近边界点的温度和热流.数值结果证明了该算法的有效性和精确性.     

结合傅里叶变换合成法设计均匀薄膜

基于傅里叶变换合成法的基本原理,合成了一个K9基底上的负滤光片,合成的渐变折射率薄膜具有期望光学特性,但实际制备难度很大,因此将其细分为足够多层离散折射率的均匀薄膜,由于实际薄膜材料种类有限,不能获得任意折射率膜层,鉴于两层高低折射率薄层可近似为一层中间折射率膜层的思想,将膜系转化成一个可实际制备的膜系结构:膜系采用ZrO2和SiO2两种膜料,膜层总数为183层,经单纯形调法优化后,膜层总厚度为7.09 μm,通带和截止带内平均透射比分别为97.56%和3.13%,其结果优于直接采用傅里叶方法合成的非均匀膜系,与期望透射比曲线吻合更好.说明通过这种思想设计任意光谱特性的膜系是可行的,也使傅里叶变换合成法设计的薄膜实际制备成为可能.