An end point estimate for maximal commutators

In this paper we prove that the maximal commutator of singular integral operator [b, T]^* satisfies the inequality:

Opérateur de Monge-Ampère et Tranchage des Courants Positifs Fermés

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Kähler structures on complex torus

Consider the complex torus T _C under the natural action of the compact real torus T. In this paper, we study T-invariant Kähler structures ω on T_C. For each ω, we consider the corresponding line bundleL on T _C. Namely, the Chern class ofL is [ω], and L is equipped with a connection ? whose curvature is ω. We construct a canonical T-invariant L ²-structure on the sections ofL,and let H _ω be the square-integrable holomorphic sections ofL.Then the Hilbert space H _ω is a unitary T-representation, and we study the multiplicity of the (l-dimensional) irreducible unitary T-representations in H_ω. We shall see that the multiplicity is controlled by the image of the moment map corresponding to the T-action preserving ω.     

A characterization of wavelets on general lattices

In the context of a general lattice Γ in Rⁿ and a strictly expanding map M which preserves the lattice, we characterize all the wavelet families. This result generalizes the characterization of Frazier, Garrigós, Wang, and Weis about the wavelet families with Γ = Zⁿ and M = 21. In the second part of the paper, we characterize all the MSF wavelets. Moreover, we give a constructive method for the support of the Fourier transform of an MSF wavelet and apply this method by giving examples with particular attention to the quincunx lattice.     

A numerical model of multimode fiber PON frequency response

Frequency response of passive optical network (PON) based on multimode fibers is investigated. The network comprises fibers, connectors and splitters/couplers. It is shown that due to mode filtering at splitters, the frequency response is different for different network nodes in otherwise symmetrical network.     

Measurement and modeling of the sooting propensity of binary fuel mixtures

The sooting behaviour of binary fuel mixtures was evaluated both experimentally and through computer simulations. The soot volume fraction in laminar diffusion flames of mixtures of ethylene/propane, methane/ethylene, methane/propane, methane/ethane, methane/butane, ethane/propane and ethane/ethylene fuels was measured using 2-dimensional line of sight attenuation. A synergistic effect was observed for the ethylene/propane, methane/ethylene, methane/ethane and ethane/ethylene mixtures. The synergistic effect translated into a higher soot concentration for a mixture fraction than could be yielded by the added contribution of both pure fuels. Such an effect was not observed for the methane/propane, methane/butane and ethane/propane mixtures. Through experiments in which the flame temperature was kept constant, it was determined that the synergistic effect in the methane/ethylene mixture is very temperature dependent whereas, that in the ethylene/propane mixture is not. This phenomenon was further studied through the modeling of the ethylene/propane mixture. Numerical simulations were carried out using two different soot models. The simulations confirmed the presence of a synergistic effect. It was found that the effect could be directly correlated to a synergistic effect in the concentration of n-C₄H₅ and n-C₄H₃, which could be traced back to an interaction between ethylene and methyl radical species. These results yield further insight into the pathways to soot formation and highlight the importance of further analyzing binary fuel mixtures as a means of understanding soot formation in practical devices using industrial fuels.     

Modeling the effects of cohesive energy for single particle on the material removal in chemical mechanical polishing at atomic scale

This paper proposes a novel mathematical model for chemical mechanical polishing (CMP) based on interface solid physical and chemical theory in addition to energy equilibrium knowledge. And the effects of oxidation concentration and particle size on the material removal in CMP are investigated. It is shown that the mechanical energy and removal cohesive energy couple with the particle size, and being a cause of the non-linear size-removal rate relation. Furthermore, it also shows a nonlinear dependence of removal rate on removal cohesive energy. The model predictions are in good qualitative agreement with the published experimental data. The current study provides an important starting point for delineating the micro-removal mechanism in the CMP process at atomic scale.     

三维实体造型技术在船舶与海洋工程专业实验教学中的应用

本文开发了一套适合于船舶与海洋工程专业实验教学的虚拟实验平台,分析了本专业教学计划中重要的教学实践环节——实验教学的重要性和目前发展状况。介绍了传统三维曲面和实体造型方法,并将NURBS曲面造型方法应用于某船体和海洋平台模型的结构仿真。实践表明,该系统可应用于船舶与海洋工程专业中实验环节的辅助教学。     

Pervaporation of benzene/cyclohexane mixtures using ion-exchange membrane containing copper ions

The sorption, diffusion, and pervaporation (PV) properties of benzene/cyclohexane (Bz/Cx) mixtures on cation-exchange membranes containing copper ions (Cu(II)) were investigated. The equilibrium sorption isotherms of pure vapors in the membranes and the partial solubility of binary solutions in the membranes were described using the UNIQUAC model. The τ_iM and τ_Mi values were 0.978 and 0.591 for Bz, and 0.922 and 0.475 for Cx. The transient regimes of vapor sorption were employed to calculate the concentration-dependent diffusion coefficients. Long’s model sufficiently explained the diffusivity of Bz and Cx in the membranes. The pre-exponential factors were 3×10⁻¹³ m²/s and the plasticization factors were 3.0 and 3.6 for Bz and Cx, respectively. Excellent agreement was found with the experimental results applying the solubility and diffusivity data to simulate the pervaporation performance (flux and selectivity) using the modified Maxwell–Stefan equation. The membrane containing Cu(II) demonstrates better facilitating capability for Bz transport than that with Na(I), mainly due to its preferential sorption property toward Bz. Replacing Na(I) with Cu(II) into a Neosepta membrane resulted in better separation efficiency and higher Bz flux throughout the entire Bz concentration range.     

Review of non-reactive and reactive wetting of liquids on surfaces

Wettability is a tendency for a liquid to spread on a solid substrate and is generally measured in terms of the angle (contact angle) between the tangent drawn at the triple point between the three phases (solid, liquid and vapour) and the substrate surface. A liquid spreading on a substrate with no reaction/absorption of the liquid by substrate material is known as non-reactive or inert wetting whereas the wetting process influenced by reaction between the spreading liquid and substrate material is known as reactive wetting. Young's equation gives the equilibrium contact angle in terms of interfacial tensions existing at the three-phase interface. The derivation of Young's equation is made under the assumptions of spreading of non-reactive liquid on an ideal (physically and chemically inert, smooth, homogeneous and rigid) solid, a condition that is rarely met in practical situations. Nevertheless Young's equation is the most fundamental starting point for understanding of the complex field of wetting. Reliable and reproducible measurements of contact angle from the experiments are important in order to analyze the wetting behaviour. Various methods have been developed over the years to evaluate wettability of a solid by a liquid. Among these, sessile drop and wetting balance techniques are versatile, popular and provide reliable data. Wetting is affected by large number of factors including liquid properties, substrate properties and system conditions. The effect of these factors on wettability is discussed. Thermodynamic treatment of wetting in inert systems is simple and based on free energy minimization where as that in reactive systems is quite complex. Surface energetics has to be considered while determining the driving force for spreading. Similar is the case of spreading kinetics. Inert systems follow definite flow pattern and in most cases a single function is sufficient to describe the whole kinetics. Theoretical models successfully describe the spreading in inert systems. However, it is difficult to determine the exact mechanism that controls the kinetics since reactive wetting is affected by a number of factors like interfacial reactions, diffusion of constituents, dissolution of the substrate, etc. The quantification of the effect of these interrelated factors on wettability would be useful to build a predictive model of wetting kinetics for reactive systems.