The Recognition of Double Euler Trails in Series-Parallel Networks

Given a series-parallel network (network, for short)N, its dual networkN′ is given by interchanging the series connection and the parallel connection of networkN. We usually use a series-parallel graph to represent a network. LetG[N] andG[N′] be graph representations ofNandN′, respectively. A sequence of edgese₁, e₂,…,e_kis said to form a common trail on (G[N], G[N′]) if it is a trail on bothG[N] andG[N′]. If a common trail covers all of the edges inG[N] andG[N′], it is called adouble Euler trail.However, there are many different graph representations for a network. We say that a networkNhas a double Euler trail (DET) if there is a common Euler trail for someG[N] and someG[N′]. Finding a DET in a network is essential for optimizing the layout area of a complementary CMOS functional cell. Maziasz and Hayes (IEEE Trans. Computer-Aided Design9(1990), 708–719) gave a linear time algorithm for solving the layout problem in fixedG[N] andG[N′] and an exponential algorithm for finding the optimal cover in a network without fixing graph representations. In this paper, we study properties of subnetworks of a DET network. According to these properties, we propose an algorithm that automatically generates the rules for composition of trail cover classes. On the basis of these rules, a linear time algorithm for recognizing DET networks is presented. Furthermore, we also give a necessary and sufficient condition for the existence of a double Euler circuit in a network.     

The behavior of cracked cross-ply composite laminates under shear loading

An interlaminar-shear-stress analysis developed earlier by Tsai et al. (1990, Micro-cracking-Induced Damage in Composites) for a [φ_m/θ_n], bi-directional composite laminate is used to solve the case of a cross-ply [0_m/90_n]_x laminate with the 90° layer only or both layers cracked under pure shear loading. Strains, forces and laminate shear modulus reduction due to matrix cracking were obtained. Experimental results for shear modulus as a function of crack densities were obtained by a simple shear test and they agree very well with the theoretical prediction.     

Tip-induced local anodic oxidation on p-GaAs surface with non-contact atomic force microscopy

Nano-sized oxide structures resulted from localized electrochemical oxidation induced by a negatively biased atomic force microscopy (AFM) tip operated with the non-contact mode were fabricated on p-GaAs(1 0 0) surface. The geometrical characteristics of the oxide patterns and their dependences on various fabrication parameters, e.g., the anodization time, the biased voltages, the tip scanning rates, as well as the formation mechanism and relevant growth kinetics are investigated. Results indicate that the height of the protruded oxide dots grow exponentially as a function of time in the initial stage of oxidation and soon reaches a maximum height depending linearly with the anodized voltages, in according with the behaviors predicted by space charge limited local oxidation mechanism. In addition, selective micro-Auger analysis of the anodized region reveals the formation of Ga(As)O_x, indicating the prominent role played by the field-induced nanometer-size water meniscus in producing the nanometer-scale oxide dots and bumps on p-GaAs(1 0 0) surface.     

Improved coating method for uniform polymer layer in infrared hollow fiber

An improved coating method was proposed in order to form a uniform polymer layer in the fabrication of cyclic olefin polymer-coated silver (COP/Ag) hollow fiber. A COP solution was flowed in a closed loop, in which the silver-coated tube was used as a part of the loop. Owing to the constant flowing speed of the COP solution and the airtight flowing environment, a COP layer was uniformly formed. The hollow fibers attain high performance and deliver multi-wavelength laser light from the infrared to the visible simultaneously. The method was successfully applied to the fabrication of practical hollow fibers with 2 m length for the near and mid-infrared lasers.     

Mesoporous nanotube aggregates obtained from hydrothermally treating TiO2 with NaOH

Nanotube aggregates with high porosity were prepared from hydrothermal treatment of TiO₂ particles in NaOH at 130 °C, followed by HCl rinsing to different pH values. Pore structure of the aggregates, which were mainly mesoporous, was characterized by analyzing the N₂ sorption isotherm with different methods including the t-plot and density function theory. The surface area, pore volume and mean pore size of the aggregates increased with the rinsing acidity to reach a maximum (e.g. 400 m²/g in surface area) at pH 1.6 and then decreased with further increase of the acidity. The crystalline phase and composition of the aggregates were, as well, significantly affected by the acidity of the post-treatment rinsing. Large-surface area aggregates were of loosely-attached nanotubes, composed of both anatase TiO₂ and H₂Ti₂O₅·H₂O, obtained under a mildly acidic rinsing condition, while basic or highly acidic conditions resulted in the formation of closely coagulated dense structures consisting of different crystalline phases.     

Preparation and characterization of rigid poly(vinyl chloride)/MMT nanocomposites. II. XRD,morphological and mechanical characteristics

A Haake torque rheometer equipped with an internal mixer is used to study the influence of the amount of sodium montmorillonite (Na⁺‐MMT) and organically modified MMT (O‐MMT) on X‐ray diffraction (XRD), morphology, and mechanical characteristics of rigid poly (vinyl chloride) (PVC)/Na⁺‐MMT and PVC/O‐MMT nanocomposites, respectively. Results of XRD and transmission electron microscopy (TEM) indicate that MMT is partially encapsulated and intercalated in the rigid PVC/Na⁺‐MMT nanocomposites. However, results of XRD and TEM show MMT is partially intercalated and exfoliated in the rigid PVC/O‐MMT nanocomposites. Tensile strength, yield strength, and elongation at break of the rigid PVC/MMT nanocomposites were improved simultaneously with adding 1–3 wt % Na⁺‐MMT or O‐MMT with respect to that of pristine PVC. However, the addition of Na⁺‐MMT or O‐MMT should be kept as not more than 3 wt % to optimize the mechanical properties and the processing stability of the rigid PVC/MMT nanocomposites. SEM micrographs of the fractured surfaces of the rigid PVC/Na⁺‐MMT and PVC/O‐MMT nanocomposites both before and after tensile tests were also illustrated and compared. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2145–2154, 2006     

Synthesis of selenium-containing polyphenolic acid esters and evaluation of their effects on antioxidation and 5-lipoxygenase inhibition

Six novel selenium-containing polyphenolic acid esters were synthesized and evaluated as antioxidants and 5-lipoxygenase inhibitors. Synthesis of the title compounds involved the Mitsunobu reaction of polyphenolic acids with 2-phenylselenoethanol. Compounds and were found to be very effective antioxidants and 5-lipoxygenase inhibitors with activity comparable to or better than caffeic acid (3,4-dihydroxycinnamic acid) phenethyl ester (CAPE).     

Effects of electrolytes used in roughening gold substrates by oxidation–reduction cycles on surface-enhanced Raman scattering

In this work, the effects of electrolytes used in roughening gold substrates by electrochemical methods on surface-enhanced Raman scattering (SERS) were first investigated. First, gold substrates were roughened by triangular-wave oxidation–reduction cycles (ORC) in aqueous solutions containing different kinds of 0.1 M electrolytes. Then Rhodamine 6G (R6G) was used as Raman probe to examine this effect of electrolytes used on the SERS observed. The result indicates that the highest intensity of SERS of R6G was obtained on the roughened Au substrate prepared in 0.1 M NaCl, which was less used in the literature. Meanwhile, it was also found that the rougher surface morphology observed, which is contributive to the higher SERS obtained, is corresponding to the smaller cathodic peak area shown in the cyclic voltammograms for roughening the Au substrate.