Function spaces over GO-spaces: Part I

We describe the structure of spaces of continuous step functions over GO-spaces. We establish a relation between the Dedekind completion of a GO-space L and properties of the space of continuous functions from L to 2 with finitely many steps. We use the established relation to prove that a countably compact GO-space L has Lindelöf Cp(L) iff the Dedekind remainder of L is Lindelöf and every compact subspace of L is metrizable. Or equivalently, a countably compact GO-space L has Lindelöf Cp(L) iff every compact subspace of L is metrizable and a Gδ-set in L. Other results are obtained.     

Synthesis and characterization of poly(arylene ether)s containing 6‐(4‐hydroxyphenyl)pyridazin‐3(2H)‐one or 6‐(4‐hydroxyphenyl)pyridazine moieties

A series of novel soluble pyridazinone‐ or pyridazine‐containing poly(arylene ether)s were prepared by a polycondensation reaction. The pyridazinone monomer, 6‐(4‐hydroxyphenyl)pyridazin‐3(2H)‐one ( 1 ), was synthesized from the corresponding acetophenone and glyoxylic acid in a simple one‐pot reaction. The pyridazinone monomer was successfully copolymerized with bisphenol A (BPA) or 1,2‐dihydro‐4‐(4‐hydroxyphenyl)phthalazin‐1(2H)‐one (DHPZ) and bis(4‐fluorophenyl)sulfone to form high‐molecular‐weight polymers. The copolymers had inherent viscosities of 0.5–0.9 dL/g. The glass‐transition temperatures (T_g's) of the copolymers synthesized with BPA increased with increasing content of the pyridazinone monomer. The T_g's of the copolymers synthesized from DHPZ with different pyridazinone contents were similar to those of the two homopolymers. The homopolymers showed T_g's from 202 to 291 °C by differential scanning calorimetry. The 5% weight loss temperatures in nitrogen measured by thermogravimetric analysis were in the range of 411–500 °C. 4‐(6‐Chloropyridazin‐3‐yl)phenol ( 2 ) was synthesized from 1 via a simple one‐pot reaction. 2 was copolymerized with 4,4′‐isopropylidenediphenol and bis(4‐fluorophenyl)sulfone to form high‐T_g polymers. The copolymers with less than 80 mol % pyridazinone or chloropyridazine monomers were soluble in chlorinated solvents such as chloroform. The copolymers with higher pyridazinone contents and homopolymers were not soluble in chlorinated solvents but were still soluble in dipolar aprotic solvents such as N‐methylpyrrolidinone. The soluble polymers could be cast into flexible films from solution. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3328–3335, 2006     

Synthesis and characterization of polyimides derived from (3‐amino‐2,4,6‐trimethylphenyl)‐(3′‐aminophenyl)methanone and aromatic dianhydrides

A series of new polyimides were prepared via the polycondensation of (3‐amino‐2,4,6‐trimethylphenyl)‐(3′‐aminophenyl)methanone and aromatic dianhydrides, that is, 3,3′,4,4′‐biphenyltetracarboxylic dianhydride (BPDA), 4,4′‐oxydiphthalic anhydride, 3,3′,4,4′‐benzophenone tetracarboxylic dianhydride, and 2,2′‐bis(3,4‐dicarboxyphenyl) hexafluoropropane dianhydride. The structures of the polyimides were characterized by Fourier transform infrared and NMR measurements. The properties were evaluated by solubility tests, ultraviolet–visible analysis, differential scanning calorimetry, and thermogravimetric analysis. The two different meta‐position‐located amino groups with respect to the carbonyl bridge in the diamine monomer provided it with an unsymmetrical structure. This led to a restriction on the close packing of the resulting polymer chains and reduced interchain interactions, which contributed to the solubility increase. All the polyimides except that derived from BPDA had good solubility in strong aprotic solvents, such as N‐methyl‐2‐pyrrolidinone, N,N′‐dimethylacetamide, N,N‐dimethylformamide, and dimethyl sulfone, and in common organic solvents, such as cyclohexanone and chloroform. In addition, these polyimides exhibited high glass‐transition values and excellent thermal properties, with an initial thermal decomposition temperature above 470 °C and glass‐transition temperatures in the range of 280–320 °C. The polyimide films also exhibited good transparency in the visible‐light region, with transmittance higher than 80% at 450 nm and a cutoff wavelength lower than 370 nm. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1291–1298, 2006     

Metal-Assisted Oxidative Cyclization of Arylamidrazones I. Synthesis of 3-Acetyl-1,4-dihydro-1-phenyl-1,2,4-benzotriazine

In the presence of RuCl₃, N-phenylamidrazone underwent oxidative cyclization into 1,4-dihydro-1-phenyl-1,2,4-benzotriazine, the structure of which is established by spectral and X-ray diffraction data.     

Optical waveguide fabrication and integration with a micro-mirror inside photosensitive glass by femtosecond laser direct writing

Photosensitive glass is a potentially important material for micro-fluidic devices that can be integrated with micro-optical components for biochemical analysis. Here, we demonstrate the fabrication of optical waveguides inside glass by femtosecond laser direct writing. The influence of the laser parameters on the waveguide properties is investigated, and it is revealed that the waveguide mode can be well controlled. The single mode is achieved at a low writing energy, while the multimode is achieved with increasing energy. In spite of a longitudinally elongated elliptical shape of the cross-sectional profile, the far-field pattern of the single-mode waveguide shows an almost symmetric profile. The measured propagation loss and the coupling loss are evaluated to be ∼0.6 dB/cm and ∼1.6 dB at a wavelength of 632.8 nm, respectively, under the conditions of 1.0–2.0 μJ pulse energy and 200–500 μm/s scan speed. The increased optical loss is associated with a higher waveguide mode at higher writing energy. Furthermore, the integration of waveguides and a micromirror made of a hollow microplate inside the glass is demonstrated to bend the laser beam at an angle of 90° in a small chip. The bending loss is estimated to be smaller than 0.3 dB. PACS 42.62.-b; 42.82.Cr; 82.50.Pt; 42.79.Gn; 42.81.Qb     

One-dimensional stochastic Burgers equation driven by Lévy processes

In this paper, we proved the global existence and uniqueness of the strong, weak and mild solutions for one-dimensional Burgers equation perturbed by a Poisson form process, a Poisson form and Q-Wiener process with the Dirichlet bounded condition. We also proved the existence of the invariant measure of these models.     

A rule-based risk decision-making approach and its application in China's customs inspection decision

This paper addresses a kind of risk decision-making problem existing widely in public administration and business management, which is characterized by (1) occurrence probabilities of states of nature can be estimated by analysing historical observations, but historical observations of different objects are unhomogeneous, (2) the relation between observations and occurrence probabilities of states of nature are affected by some qualitative and quantitative indicators, (3) it is a real-time decision-making problem, that is, there are many decisions for different objects to be made in a limited time, (4) considering decision's execution, impact of resource constrains is an important issue in decision-making process. In this paper, we develop a rule-based approach to address the problem. In the proposed approach, a two-step clustering method is employed to classify objects into categories, and observations in each category can be approximately viewed as homogeneous. For objects in each category, occurrence probabilities of states of nature are estimated by logistic regression, and the decision rule is obtained through solving an optimization model, which is to minimize the total decision risks while satisfying resource constrains. Effect and efficacy of our approach are illustrated through its application to China's customs inspection decision.     

Copper diffusion in Ti-Si-N layers formed by inductively coupled plasma implantation

Ternary Ti-Si-N refractory barrier films of 15 nm thick was prepared by low frequency, high density, inductively coupled plasma implantation of N into Ti_xSi_y substrate. This leads to the formation of Ti-N and Si-N compounds in the ternary film. Diffusion of copper in the barrier layer after annealing treatment at various temperatures was investigated using time-of-flight secondary ion mass spectrometer (ToF-SIMS) depth profiling, X-ray diffractometer (XRD), field emission scanning electron microscopy (FESEM), energy dispersive X-ray (EDX) and sheet resistance measurement. The current study found that barrier failure did not occur until 650 °C annealing for 30 min. The failure occurs by the diffusion of copper into the Ti-Si-N film to form Cu-Ti and Cu-N compounds. FESEM surface morphology and EDX show that copper compounds were formed on the ridge areas of the Ti-Si-N film. The sheet resistance verifies the diffusion of Cu into the Ti-Si-N film; there is a sudden drop in the resistance with Cu compound formation. This finding provides a simple and effective method of monitoring Cu diffusion in TiN-based diffusion barriers.     

Spatiotemporal and Thermal Analysis of VCSEL for Short-range Gigabit Optical Links

High-speed Optoelectronic Modules using Vertical Cavity Surface Emitting Lasers (VCSEL) coupled to Multi Mode Fibers (MMF) are a performing and low-cost solution for 10 Gigabit Ethernet (10 GbE) in short-distance optical links. A complete model of the spatiotemporal behavior of multimode VCSELs, through static and dynamic response, noise, thermal effects, and its coupling to MMF has been investigated. Relative Intensity Noise shows modal dependence and can be affected by spatial filtering due to coupling and fiber propagation. Simulations permit to evaluate critical parameters, such as modulation formats, launching conditions, and operating temperature for global bandwidth and eye diagram optimization up to 10 Gb/s. Simulation results are compared to measurements on prototype optoelectronic modules.     

Optical and photoelectric properties of pure and cadmium-and lead-doped neodymium sesquisulfide thin films

A technique for preparing γ-Nd₂S₃ crystalline thin films through discrete vacuum thermal evaporation of a presynthesized bulk material is developed. The films deposited are doped with cadmium and lead. The reflectance and transmittance spectra of the films are measured in the photon energy range 0.2–3.0 eV at a temperature of 300 K. The frequency analysis of the absorption coefficient demonstrates that the γ-Nd₂S₃ films are characterized by an exponential absorption edge. The photoconductivity spectra and temperature dependences of the photoconductivity for the γ-Nd₂S₃ films doped with cadmium and lead are measured in the photon energy range 0.2–3.3 eV at temperatures varying from 115 to 380 K. The experimental data obtained are interpreted under the assumption that the acceptor levels formed by vacancies in the cation sublattice and compensated for by cadmium and lead donor dopants play a crucial role in the photoconduction. The ionization energy at the lead donor level is determined.