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.     

Inorganic Sol-Gel Preparation of Medium Sized Microparticles of Li2TiO3 from TiCl4 as Tritium Breeding Material for Fusion Reactors

Microspheres of Li₂TiO₃ were fabricated by a classical, inorganic sol-gel process from commercially available TiCl₄. Elaborated process consists of the following main steps: (1) dissolving of TiCl₄ in concentrated aqueous HCl and addition of LiOH; (2) formation of sol emulsion in 2-ethylhexanol-1 containing the surfactant SPAN-80 (EH); (3) gelation of emulsion drops by extraction of water with partially dehydrated EH; (4) impregnation of gel to Li:Ti molar ratio MR = 2; (5) thermal treatment at 1200°C in order to receive chloride free product. This temperature can be significantly lowered (to 750°C) by dechlorination starting solution TiCl₄ by chemical treatment of the with nitric acid to form of nitrate-stabilized titania sols. Tritium release from sol-gel made Li₂TiO₃ microspheres were found very close to that observed for other traditional materials, however for the first sample process starts slightly earlier.     

Geometry and electronic structure of a heterometallic cluster Mo<Subscript>2</Subscript>Mg<Subscript>2</Subscript> in different oxidation states of Mo: a DFT study

Reduction of tetranuclear heterometallic complex Mo₂Mg₂ was simulated using the B3LYP and PBE density functional methods. The results of geometry calculations of the initial complex [Mo^VIO₂Mg(MeOH)₂(OMe)₄]₂ and a partially reduced Mo^V complex are in good agreement with experimental data. The reduced Mo^III complex is characterized by a decrease in the binding energy of aqua ligands. Structural rearrangement of the complex with release of a coordination position at the Mo atoms requires small energy expenditure. One can assume that the reduction of the polynuclear complex causes overcrowding of its coordination sphere, which favors formation of dinitrogen complexes. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 441–457, March, 2008.     

Difference schemes on uniform grids performed by general discrete operators

Our aim is to set the foundations of a discrete vectorial calculus on uniform n-dimensional grids, that can be easily reformulated on general irregular grids. As a key tool we first introduce the notion of tangent space to any grid node. Then we define the concepts of vector field, field of matrices and inner products on the space of grid functions and on the space of vector fields, mimicking the continuous setting. This allows us to obtain the discrete analogous of the basic first order differential operators, gradient and divergence, whose composition define the fundamental second order difference operator. As an application, we show that all difference schemes, with constant coefficients, for first and second order differential operators with constant coefficients can be seen as difference operators of the form for suitable choices of q, and  . In addition, we characterize special properties of the difference scheme, such as consistency, symmetry and positivity in terms of q, and  .     

Indirect boundary element method for unsteady linearized flow over prolate and oblate spheroids and hemispheroidal protuberances

The indirect boundary element method was used to study the hydrodynamics of oscillatory viscous flow over prolate and oblate spheroids, and over hemispheroidal bodies hinged to a plate. Analytic techniques, such as spheroidal coordinates, method of images, and series representations, were used to make the numerical methods more efficient. A novel method for computing the hydrodynamic torque was used, since for oscillatory flow the torque cannot be computed directly from the weightings. Instead, a Green's function for torque was derived to compute the torque indirectly from the weightings. For full spheroids, the method was checked by comparing the results to exact solutions at low and high frequencies, and to results computed using the singularity method. For hemispheroids hinged to a plate, the method for low frequencies was checked by comparing the results to previous results, and to exact solutions at high frequencies. Copyright © 2004 John Wiley & Sons, Ltd.     

Rate of Convergence of a Stochastic Particle System for the Smoluchowski Coagulation Equation

By continuing the probabilistic approach of Deaconu et al. (2001), we derive a stochastic particle approximation for the Smoluchowski coagulation equations. A convergence result for this model is obtained. Under quite stringent hypothesis we obtain a central limit theorem associated with our convergence. In spite of these restrictive technical assumptions, the rate of convergence result is interesting because it is the first obtained in this direction and seems to hold numerically under weaker hypothesis. This result answers a question closely connected to the Open Problem 16 formulated by Aldous (1999).     

Software Cold Test Simulation of Coupled Cavity Slow-Wave Structure in Millimeter Wave TWT

In this paper, the software cold-test simulation method to obtain RF dispersion, interaction impedance by MAFIA software is discussed considering effect of the conducting barrel in the millimeter-wave TWT. The dispersion simulation result is obtained more consistent with experiment data than the method that ignoring effect of the conducting barrel. By changing the structure parameter, high frequency characteristic will be affected. The change relationship of high frequency characteristic with structure parameter is obtained. The different calculation methods of the interaction impedance are discussed. These results are received and are consistent with experiment data.     

Kinetics and equilibrium of small metallic clusters: Ab initio confinement molecular dynamics study of 4

The ab initio molecular dynamics (AIMD) [1] is combined with the heuristic, successive confinement method of surveying a potential energy surface (PES) [2], thereby offering a framework for the simulation study of kinetics and equilibrium properties of metallic clusters. This approach is applied to the study of Au₄, a cluster possessing a simple but specific PES, which consists of very shallow and deep basins and due to this presents a challenge to the conventional AIMD methods. Among other things, the probabilities of the transitions between isomers have been found, and on this basis, both the time-dependent and equilibrium populations of the isomers have been calculated for the conditions typical of the NeNePo experiments [3] in the femtosecond pump-probe spectroscopy.     

Tail probabilities of the limiting null distributions of the Anderson–Stephens statistics

For the purpose of testing the spherical uniformity based on i.i.d. directional data (unit vectors) z_i, i=1,…,n, Anderson and Stephens (Biometrika 59 (1972) 613–621) proposed testing procedures based on the statistics S_max=max_u S(u) and S_min=min_u S(u), where u is a unit vector and nS(u) is the sum of squares of u′z_i's. In this paper, we also consider another test statistic S_range=S_max−S_min. We provide formulas for the P-values of S_max, S_min, S_range by approximating tail probabilities of the limiting null distributions by means of the tube method, an integral-geometric approach for evaluating tail probability of the maximum of a Gaussian random field. Monte Carlo simulations for examining the accuracy of the approximation and for the power comparison of the statistics are given.     

线性规划的符号跟踪算法

分析了只含一个约束条件的线性规划最优基变量的特征，将其运用到搜寻含m个约束条件的线性规划的最优基变量，从而提出了线性规划的符号跟踪算法，为线性规划求解提供了新途径。