A new algorithm for fixed design regression and denoising

In this paper, we present a new algorithm to estimate a regression function in a fixed design regression model, by piecewise (standard and trigonometric) polynomials computed with an automatic choice of the knots of the subdivision and of the degrees of the polynomials on each sub-interval. First we give the theoretical background underlying the method: the theoretical performances of our penalized least-squares estimator are based on non-asymptotic evaluations of a mean-square type risk. Then we explain how the algorithm is built and possibly accelerated (to face the case when the number of observations is great), how the penalty term is chosen and why it contains some constants requiring an empirical calibration. Lastly, a comparison with some well-known or recent wavelet methods is made: this brings out that our algorithm behaves in a very competitive way in term of denoising and of compression.     

Photoinduced dissociative electron transfer (DET) interactions in methoxycalixarene–chloroalkane systems

Fluorescence quenching of methoxycalixarenes (MOCX) by chloroalkanes (CA) has been investigated in acetonitrile solutions. Observed quenching is attributed to photoinduced dissociative electron transfer (DET) interaction, which is supported by the characterization of the Cl⁻ ions and by the radical scavenging experiments. Comparing the Cl⁻ yields with different DET systems, it is inferred that both concerted and stepwise DET mechanisms operate simultaneously in MOCX–CA systems. A correlation of the quenching constants with the free-energy changes following a suitable DET theory supports the above inference.     

Ab initio study of sodium intercalation into metal oxides

Using the full-potential linearized augmented plane wave (FP-LAPW) method, we have studied the effect of chemistry on the average intercalation voltage (AIV) caused by the Na ions intercalating into transition metal oxides. The effect of transition metal was systematically studied by varying M=Co, Ni and Mn in NaMO₂ and fixing the α-NaFeO₂ layered structure. The effect of the guest atoms into the host material is discussed in terms of the structural and electronic properties. Comparatively to Li intercalation, a significant electron transfer towards transition metal was found. This observation suggests that the transition metal contribute to the AIV determination and confirms the common assumption that intercalated electron reduces M⁴⁺ to M³⁺.     

Analysis of transient wave scattering from an inclusion with an unilateral smoothly contact interface by BEM

Summary A 2D time-domain Boundary Element Method (BEM) is applied to solve the problem of transient scattering of plane waves by an inclusion with a unilateral smooth contact interface. The incident wave is assumed strong enough so that localized separations take place along the interface. The present problem is indeed a nonlinear boundary value problem since the mixed boundary conditions involve unknown intervals (separation and contact regions). In order to determine the unknown intervals, an iterative technique is developed. As an example, we consider the scattering of plane waves by the cross section of a circular cylinder embedded in an infinite solid. Numerical results for the near field solutions are presented. The distortion of the response waves and the variation of the interface states are discussed. The financial support by the China National Natural Science Foundation under Grant No. 19872001 and No. 59878004 is gratefully acknowledged. The second author is also grateful to the support of the National Science Fund for Distinguished Young Scholars under Grant No. 10025211.     

Fluctuation Theory for a Three-Dimensional Model of Maxwellian Molecules

Under suitable assumptions, a functional central limit theorem is obtained for a three-dimensional model of Maxwellian molecules. This model is related to a nonlinear Boltzmann-type equation. It will be proved that the family of the distributions induced by fluctuation processes converges weakly.     

Synthesis and characterization of poly(vinyl alcohol)‐graft‐[poly(D,L‐lactide)/poly(D,L‐lactide‐co‐glycolide)] hydrogels

Poly(D ,L ‐lactide) and poly(D ,L ‐lactide‐co‐glycolide) with various composition and with one methacrylate and one carboxylate end group were synthesized and grafted onto poly(vinyl alcohol) (PVA) via the carboxylate group. The graft copolymers were crosslinked via the methacrylate groups using a free radical initiator. The polymer networks were characterized by means of NMR and studied qualitatively by means of IR spectroscopy. The influence of the glycolide content in the polyester grafts and of the number of ester units in the grafts on thermal properties and swellability were studied as well. The high swellability in water is characteristic of all hydrogels. Differential scanning calorimetry (DSC) showed a single glass transition temperature that occurs in the range between 51 and 69 °C. Thermogravimetric analysis (TGA) of the networks showed the main loss in weight in the temperature range between 290 and 370 °C. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4536–4544, 2007