Continuous selections and convergence of best Lp –approximations in subspaces of spline functions

The chief purpose of this paper is to study the problem of existence of continuous selections for the metric projection and of convergence of best L_p–approximations in subspaces of polynomial spline functions defined on a real compact interval I. Nürnberger-Sommer [8] have shown that there exists a continuous selection s if and only if the numberof knots k is less than or equal to the order m of the splines. Using their construction of s the author [12] has proved that the sequence of best L_p–approximations of f converges to s(f) as ρ→∞ for every continuous function f. The main results of this paper say that also in the case when k>m there exists always a continuous selection s (it is even pointwise-Lipschitz-continuous and quasi-linear) provided that the approximation problem is restricted to certain subsets I_epsilon; of I. In addition it is shown that anologously as for k≤m the sequence of best L_papproximations of f converges to s(f) for every continuous function f on Iε     

Combining [Arene–Ru] with Azocarboxamide to Generate a Complex with Cytotoxic Properties

Azocarboxamide (azcH) has been combined for the first time with [Ru–Cym] to generate metal complexes with N,N‐ and N,O‐coordination mode, [(Cym)Ru(azc)Cl] and [(Cym)Ru(azcH)Cl]⁺[PF₆]^?. Geometric and electronic structures of the complexes are reported along with their in vitro activities against different tumour cell lines and preliminary results on solution chemistry. Compound [(Cym)Ru(azc)Cl] exhibited remarkable cytotoxic properties. It was cell‐type specific and had comparable IC₅₀ values towards both cancer cells and their drug‐resistant subline. A tenfold increase in the sensitivity towards [(Cym)Ru(azc)Cl] was noted for the tumour cells with depleted intracellular glutathione (GSH) level, suggesting the essential role of GSH in cell response to this compound.     

ScIII‐Doped Zeolites as New Heterogeneous Catalysts: Mukaiyama Aldol Reaction

Sc^III‐doped solids based on zeolite materials have been investigated for the first time as catalysts in organic synthesis. Sc^III–USY zeolite proved to be a novel and very efficient heterogeneous catalyst for the Mukaiyama aldol reaction. This easy‐to‐prepare catalyst exhibited wide scope and compatibility with functional groups and is very simple to use, easy to remove (by simple filtration), and is recyclable (up to three times without loss of activity).     

A Geometric Framework for Stochastic Shape Analysis

We introduce a stochastic model of diffeomorphisms, whose action on a variety of data types descends to stochastic evolution of shapes, images and landmarks. The stochasticity is introduced in the vector field which transports the data in the large deformation diffeomorphic metric mapping framework for shape analysis and image registration. The stochasticity thereby models errors or uncertainties of the flow in following the prescribed deformation velocity. The approach is illustrated in the example of finite-dimensional landmark manifolds, whose stochastic evolution is studied both via the Fokker–Planck equation and by numerical simulations. We derive two approaches for inferring parameters of the stochastic model from landmark configurations observed at discrete time points. The first of the two approaches matches moments of the Fokker–Planck equation to sample moments of the data, while the second approach employs an expectation-maximization based algorithm using a Monte Carlo bridge sampling scheme to optimise the data likelihood. We derive and numerically test the ability of the two approaches to infer the spatial correlation length of the underlying noise.

     

Laser drilling of stainless steel with nanosecond double-pulse

Nanosecond double-pulse laser drilling is reported in this paper. The double-pulse herein represents two closely conjoint pulses with 21 ns pulse duration and about 52 ns interpulse separation, which are acquired by temporal pulse shaping. Percussion drilling with such double-pulse is performed in stainless steel samples with different laser fluences, sample's thickness, repetition rates and ambient pressures. The experimental results show that the drilling rates of double-pulse drilling are more than one order of magnitude higher than that of conventional single-pulse drilling in air. Differences in the processing results between single-pulse and double-pulse with various processing parameters are investigated. In addition the ablation mechanisms of the double-pulse drilling are discussed.     

Algebraic construction of a Nambu bracket for the two-dimensional vorticity equation

So far fluid mechanical Nambu brackets have mainly been given on an intuitive basis. Alternatively an algorithmic construction of such a bracket for the two-dimensional vorticity equation is presented here. Starting from the Lie-Poisson form and its algebraic properties it is shown how the Nambu representation can be explicitly constructed as the continuum limit from the structure preserving Zeitlin discretization.