The Module Structure Theorem for Sobolev Spaces on Open Manifolds

We prove a general embedding theorem for Sobolev spaces on open manifolds of bounded geometry and infer from this the module structure theorem. Thereafter we apply this to weighted Sobolev spaces.     

Structural and electrical properties of crystalline (1−x)Ta2O5−xTiO2 thin films fabricated by metalorganic decomposition

Polycrystalline (1−x)Ta₂O₅−xTiO₂ thin films were formed on Si by metalorganic decomposition (MOD) and annealed at various temperatures. As-deposited films were in the amorphous state and were completely transformed to crystalline after annealing above 600 °C. During crystallization, a thin interfacial SiO₂ layer was formed at the (1−x)Ta₂O₅−xTiO₂/Si interface. Thin films with 0.92Ta₂O₅–0.08TiO₂ composition exhibited superior insulating properties. The measured dielectric constant and dissipation factor at 1 MHz were 9 and 0.015, respectively, for films annealed at 900 °C. The interface trap density was 2.5×10¹¹ cm⁻² eV⁻¹, and flatband voltage was −0.38 V. A charge storage density of 22.8 fC/μm² was obtained at an applied electric field of 3 MV/cm. The leakage current density was lower than 4×10⁻⁹ A/cm² up to an applied electric field of 6 MV/cm.     

Structure induced by irradiation of femtosecond laser pulse in dyed polymeric materials

We investigated the structures induced by an irradiation of a near‐infrared (NIR) femtosecond laser pulse in dye‐doped polymeric materials {poly(methyl methacrylate) (PMMA), thermoplastic epoxy resin (Epoxy), and a block copolymer of methyl methacrylate and ethyl acrylate‐butyl acrylate [p(MMA/EA‐BA) block copolymer]}. Dyes used were classified into two types—type 1 with absorption at 400 nm and type 2 with no absorption at 400 nm. The 400‐nm wavelength corresponds to the two‐photon absorption region by the irradiated NIR laser pulse at 800 nm. Type 1 dye‐doped PMMA and p(MMA/EA‐BA) block copolymer showed a peculiar dye additive effect for the structures induced by the line irradiation of a NIR femtosecond laser pulse. On the contrary, dye‐doped Epoxy did not exhibit a dye additive effect. The different results among PMMA, p(MMA/EA‐BA) block copolymer, and Epoxy matrix polymers are supposed to be related to the difference of electron‐acceptor properties. The mechanism of this type 1 dye‐additive‐effect phenomenon for PMMA and p(MMA/EA‐BA) block copolymer is discussed on the basis of two‐photon absorption of type 1 dye at 400 nm by the irradiation of a femtosecond laser pulse with 800 nm wavelength and the dissipation of the absorbed energy to the polymer matrix among various transition processes. Dyes with a low‐fluorescence quantum yield favored the formation of thicker grating structures. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2800–2806, 2002     

Unique edge structure and stability of fabricated dimer islands on Si(001)

The edge structure and stability of monolayer-high islands fabricated on Si(001) surfaces by scanning tunneling microscopy have been analyzed theoretically. In contrast to the edges of similar islands grown by depositing Si, the properties of edges of fabricated islands are determined by the length of the trench of dimers that are removed to create the island. We demonstrate the possibility of controlling the edge structure, and thus the stability, through a selective process of atom removal.     

F－L模型的状态方程与退禁闭相变图象

用温度场论方法计算了Ｆ－Ｌ模型在有限温度和密度下的状态方程，分析了压强对净重子数密度的等温线．结果表明，在平均场近似下，Ｆ－Ｌ模型所给出的退禁闭相变为一级相变．     

Short-range order and F ion diffusion inside the Pb1 − xAlxF2 + x solid solution Part II: Al NMR investigation and proposal of clustering process

A ²⁷Al nuclear magnetic resonance (NMR) investigation at room temperature of the Pb_{1 − x}Al_xF_{2 + x} (0 ≤ x ≤ 0.12) solid solution and of the ordered Pb₉Al₂F₂₄ phase is carried out. Two different types of aluminium ions are identified and their ratio is determined as a function of x. A clustering process based on the formation of column clusters, more and more extended when x increases, is proposed on the basis of results issued from the ¹⁹F (Part I) and ²⁷Al NMR investigations.     

Uniform random number generation

In typical stochastic simulations, randomness is produced by generating a sequence of independent uniform variates (usually real-valued between 0 and 1, or integer-valued in some interval) and transforming them in an appropriate way. In this paper, we examine practical ways of generating (deterministic approximations to) such uniform variates on a computer. We compare them in terms of ease of implementation, efficiency, theoretical support, and statistical robustness. We look in particular at several classes of generators, such as linear congruential, multiple recursive, digital multistep, Tausworthe, lagged-Fibonacci, generalized feedback shift register, matrix, linear congruential over fields of formal series, and combined generators, and show how all of them can be analyzed in terms of their lattice structure. We also mention other classes of generators, like non-linear generators, discuss other kinds of theoretical and empirical statistical tests, and give a bibliographic survey of recent papers on the subject.     

Circularly polarized light-induced electrogyration in the Au nanoparticles on the ITO

We have found that the gold nanoparticles on the ITO substrates might be considered promising materials for circularly polarized light-induced linear electrogyration (EG). The maximal achieved value of the EG susceptibility described by third-order axial tensor caused by probe circularly polarized light at a wavelength of 1060 nm was equal to about 13 deg/mm at pulsed electric field strength 30.0 V/cm with a duration of about 1 ms. We have revealed that the maximal EG coefficient is achieved for the samples possessing maximal resistivity. The investigated composites possess long-lived EG grating which decreases by not more than 12% after 120 min of laser treatment. Applying a non-circular pump light leads to the diminishing of the observed EG.