On the large time behavior of the heat kernels of quasiperiodic differential operators

We prove an analog of the Berry-Esseen estimate for the heat kernel of second order elliptic differential operators with quasiperiodic coefficients. As an application of this result, we prove the L^p boundedness of the associated Riesz transform operators.     

Reverse inequalities

There are reverse inequalities for square functions of differences arising in ergodic theory and differentiation of functions. For example, it is shown that if A_n is the usual average in ergodic theory, and (n_k∶k=1,2,3,...) is an increasing lacunary sequence with no non-trivial common divisor, then one has for any p, 1<p<∞, there is a constant C_p such that for all f∃ L_p(X),

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

Sans résumé

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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.