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.     

Stirling渐进公式的一个新的构造证明

本文用简易的分析工具，对ｎ！给出了一个精确等式，从而导出Ｓｔｉｒｌｉｎｇ渐近公式（２）的一个新的简短证明.     

Very high coercivities of top-layer diffusion Au/FePt thin films

The Au/FePt samples were prepared by depositing a gold cap layer at room temperature onto a fully ordered FePt layer, followed by an annealing at 800 °C for the purpose of interlayer diffusion. After the deposition of the gold layer and the high-temperature annealing, the gold atoms do not dissolve into the FePt Ll₀ lattice. Compared with the continuous FePt film, the TEM photos of the bilayer Au(60 nm)/FePt(60 nm) show a granular structure with FePt particles embedded in Au matrix. The coercivity of Au(60 nm)/FePt(60 nm) sample is 23.5 kOe, which is 85% larger than that of the FePt film without Au top layer. The enhancement in coercivity can be attributed to the formation of isolated structure of FePt ordered phase.     

Synthesis,and Antimycobacterial and Cytotoxic Evaluation of Certain Fluoroquinolone Derivatives

Certain 1‐ethyl‐ and 1‐aryl‐6‐fluoro‐1,4‐dihydroquinol‐4‐one derivatives were synthesized and evaluated for antimycobacterial and cytotoxic activities. Preliminary results indicated that, for 1‐aryl‐6‐fluoroquinolones, both 7‐(piperazin‐1‐yl)‐ and 7‐(4‐methylpiperazin‐1‐yl) derivatives, 9b and 11a , are able to completely inhibit the growth of M. tuberculosis at a concentration of 6.25 μg/ml, while the 7‐[4‐(2‐oxo‐2‐phenylethyl)piperazin‐1‐yl] derivative 13 exhibits only 31% growth inhibition at the same concentration. For 1‐ethyl‐6‐fluoroquinolones, both 7‐[4‐(2‐oxopropyl)piperazin‐1‐yl]‐ and 7‐[4‐(2‐oxo‐2‐phenylethyl)piperazin‐1‐yl]‐derivatives, 2a and 2b , respectively, show complete inhibition, while their 2‐iminoethyl and substituted phenyl counterparts 3a and 2c are less active. In addition, the 6,8‐difluoro derivative was a more‐favorable inhibitor than its 6‐fluoro counterpart ( 2b vs. 2d ). These results deserve full attention especially because 2a, 2b, 9b , and 11a are non‐cytotoxic at a concentration of 100 μM . Furthermore, compound 9b proved to be a potent anti‐TB agent with selective index (SI)>40 and an EC₉₀ value of 5.75 μg/ml.     

Enhancement of the imprinting effect in cholesterol-imprinted microporous silica

A sol-gel method has been used to fabricate a cholesterol MIP for application in polar solutions. In this study, (cholesteryl propylcarbamate)triethoxysilane and tetraethyl orthosilicate were used as the hydrophobic monomer and crosslinker, respectively. The MIP had a larger pore volume when formation of the polymer was catalyzed at a higher pH than when it was formed at lower pH values, with the pore diameters being 3.5 nm and 2 nm, respectively for materials formed at high and low pH values. Both of these pore volumes were greater than those found for the respective control polymers formed without template. However, only the polymers formed at low pH values showed an imprinting effect. Compared with other methods explored, the sol-gel procedure gave only a small amount of non-specific binding for both the MIP and NIP when synthesized at low pH values. The largest imprinting-induced promotion of binding (IPB) value of the MIP (13 650%) was obtained with [HCl] = 0.01 M in the sol-gel solution. The MIP showed high selectivity towards cholesterol in comparison with other steroid hormones, and also to a lesser extent recognized vitamin D3 in methanol solution containing 5 vol.% water.     

Certain asymptotic expansions for laguerre polynomials and Charlier polynomials

Here proposed are certain asympotic expansion formulas for L _n ^(∞-1) (λz) and C _n ^(∞) (λz) in which 0<w=0(λ) and C_n/(^w)(λz), z being a complex number. Also presented are certain estimates for the remainders (error bounds) of the asymptotic expansions within the regions D₁(-∞<R_ez<=1/2(ω/λ) and D₂(1/2(ω/λ)<=Re_z<∞), respectively. Supported by NSERC (Canada) and also by the National Natural Science Foundation of China.     

Synthesis and light emitting properties of polyacetylenes having pendent fluorene groups

Five novel fluorene‐containing polymers, poly[(9,9‐dimethylfluoren‐2‐yl)acetylene] ( PFA1 ), poly[(1‐pentyl‐2‐(9,9‐dimethylfluoren‐2‐yl)acetylene) ( PFA2 ), poly[1‐decyl‐2‐(9,9‐dimethylfluoren‐2‐yl)acetylene] ( PFA3 ), poly[1‐phenyl‐2‐(9,9‐dimethylfluoren‐2‐yl)acetylene] ( PFA4 ), and poly[1‐(3,4‐difluorophenyl)‐2‐(9,9‐dimethylfluoren‐2‐yl)acetylene] ( PFA5 ) were synthesized by the polymerization of the corresponding fluorene‐substituted acetylenic monomers ( M1–M5), using WCl₆, MoCl_5, and TaCl₅ as catalysts and n‐Bu₄Sn as a cocatalyst. The synthesized polymers were thermally stable and readily soluble in common organic solvents. The degradation temperatures for a 5% weight loss of the polymers were ∼352–503 °C under nitrogen. PFA1–PFA5 show emission peaks from 402 to 590 nm. Besides, their electroluminescent properties were studied in heterostructure light‐emitting diodes (LEDs), using PFA2–PFA5 as an emitting layer. The PFA5 device revealed an orange‐red emission peak at 602 nm with a maximum luminescence of 923 cd/m² at 8 V. A device with the ITO/PEDOT/ a mixture of PFA2 (98 wt %) and PFA5 (2 wt %)/Ca/Al showed near white emission. Its maximum luminance and current efficiency are 450 cd/m² at 15 V and 1.3 cd/A, respectively. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 519–531, 2006     

Highly substituted poly(2,3‐diphenyl‐1,4‐phenylenevinylene) derivatives having bulky phenyl and fluorenyl pendant groups: Synthesis,characterization, and electro‐optical properties

Two series of poly(2,3‐diphenyl‐1,4‐phenylenevinylene) (DP‐PPV) derivatives containing multiple bulky substituents were synthesized. In the first series, two different groups were incorporated on C‐5,6 positions of the phenylene moiety to increase steric hindrance and to obtain blue‐shifted emissions. In the second series, bulky fluorenyl groups with two hexyl chains on the C‐9 position were introduced on two phenyl pendants to increase the solubility as well as steric hindrance to prevent close packing of the main chain. Polymers with high molecular weights and fine‐tuned electro‐optical properties were obtained by controlling the feed ratio of different monomers during polymerization. The maximum photoluminescent emissions of the thin films are located between 384 and 541 nm. Cyclic voltammetric analysis reveals that the band gaps of these light‐emitting materials are in the range from 2.4 to 3.3 eV. A double‐layer EL device with the configuration of ITO/PEDOT/P4/Ca/Al emitted pure green light with CIE′1931 at (0.24, 0.5). Using copolymer P6 as the emissive layer, the maximum luminescence and current efficiency were both improved when compared with the homopolymer P4. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6738–6749, 2006     

Study of ferromagnetism–superconductivity interactions in Co/Nb multilayers

We investigate Co/Nb multilayers to explore the spontaneous π-phase shift between the superconducting (SC) layers, which is attributed for causing the non-monotonic change of the SC transition temperature (T_c) with the ferromagnetic (FM) layer thickness (t_FM) in several FM/SC multilayered systems. The issue of interfacial roughness is also explored by growing Co/Nb multilayers at various sputtering pressures. Transport measurements show a non-monotonic dependence of T_c on t_FM, and this dependence is insensitive to the structural variation present in the samples, as measured by X-ray scattering.