Convergence of Weighted Sums and Laws of Large Numbers in D([0,1]; E)

Convergence properties of weighted sums of functions in D([0, 1]; E) (E a Banach space) are investigated. We show that convergence in the Skorokhod J₁-topology of a sequence (x_n) in D([0, 1]; E) does not imply convergence of a sequence ( _n) of averages. Convergence in the J₁-topology of a sequence ( _n) of averages is shown, under the growth condition x_n ∞ = o(n), to be equivalent to the convergence of ( _n) in the uniform topology. Convergence of a sequence (x_n,) is shown to imply convergence of the sequence ( _n) of averages in the M₁ and M₂ topologies. The strong law of large numbers in D[0, 1] is considered and an example is constructed to show that different definitions of the strong law of large numbers are nonequivalent.     

Interaction between large and small signals in a resonant transmission line based on magnetostatic waves

The influence of a large signal on the characteristics of a small signal near the frequency of the former is experimentally studied for the case of their simultaneous propagation through a resonant transmission line based on backward volume magnetostatic waves. The effects observed are caused by the excitation of spin waves in a ferromagnetic film at different large-signal frequencies and by the back influence of excited spin-wave packets on the amplitude and phase characteristics of the small signal.     

Schemes of effective magnetic AND and XOR logic elements

Schemes and calculated characteristics of effective logic elements with two inputs for classical ground-state computations are reported. These elements have a high threshold (0.48) and perform a desired logical operation in a wide range of input signals.     

In‐situ synthesis of transparent and conductive carbon nanotube networks

A method for the production of transparent carbon nanotube networks (CNTNs) over transparent substrates was developed. In this method, CNTNs were grown directly in the target surface by applying the catalyst in specific zones of the substrate through lithographic techniques. The networks can be also transferred from the original substrate to other surfaces. The newly grown carbon nanotubes have a very high aspect ratio (>50000). Thus far, networks with an optical transmittance of 94% at 550 nm and a surface resistivity of 3.6 kΩ/sq have been produced. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

不等式约束优化问题的一个势函数

基于Carroll(1961)建立的罚函数，本文给出了不等式约束优化问题的一个势函数，并且讨论了该函数的性质．最后证明了在此基础上建立的对偶算法具有Q-线性收敛性．     

Realisation and metrological characterisation of thickness standards below 100 nm

High-accuracy film thickness measurements in the range below 100 nm can be made by various complex methods like spectral ellipsometry (SE), scanning force microscopy (SFM), grazing incidence X-ray reflectometry (GIXR), or X-ray fluorescence analysis (XRF). The measurement results achieved with these methods are based on different interactions between the film and the probe. A key question in nanotechnology is how to achieve consistent results on a level of uncertainty below one nanometre with different techniques.Two different types of thickness standards are realised. Metal film standards for X-ray techniques in the thickness range 10 to 50 nm are calibrated by GIXR with monochromatised synchrotron radiation of 8048 eV. The results obtained at four different facilities show excellent agreement. SiO₂ on Si standards for SE and SFM in the thickness range 6 to 1000 nm are calibrated by GIXR with monochromatised synchrotron radiation of 1841 eV and with a metrological SFM. Consistent results within the combined uncertainties are obtained with the two methods. Surfaces and interfaces of both types of standards are additionally investigated by transmission electron microscopy (TEM). PACS 61.10.Kw; 68.55.Jk; 06.20.Fn; 06.60.Mr; 07.79.Lh     

Mass spectral analysis and imaging of tissue by ToF-SIMS—The role of buckminsterfullerene, C60, primary ions

Recent developments in desorption/ionisation mass spectrometry techniques have made their application to biological analysis a realistic and successful proposition. Developments in primary ion source technology, mainly through the advent of polyatomic ion beams, have meant that the technique of secondary ion mass spectrometry (SIMS) can now access the depths of information required to allow biological imaging to be a viable option.Here the role of the primary ion C₆₀⁺ is assessed with regard to molecular imaging of lipids and pharmaceuticals within tissue sections. High secondary ion yields and low surface damage accumulation are demonstrated on both model and real biological samples, indicating the high secondary ion efficiency afforded to the analyst by this primary ion when compared to other cluster ion beams used in imaging. The newly developed 40 keV C₆₀⁺ ion source allows the beam to be focused such that high resolution imaging is demonstrated on a tissue sample, and the greater yields allow the molecular signal from the drug raclopride to be imaged within tissue section following in vivo dosing.The localisation shown for this drug alludes to issues regarding the chemical environment affecting the ionisation probability of the molecule; the importance of this effect is demonstrated with model systems and the possibility of using laser post-ionisation as a method for reducing this consequence of bio-sample complexity is demonstrated and discussed.     

On circle diffeomorphisms with discontinuous derivatives and quasi-invariance subgroups of Malliavin-Shavgulidze measures

This note is devoted to construction of the domain of the regular representation of Diff₊(S¹). We consider a subgroup of diffeomorphism group such that the Malliavin-Shavgulidze measure is quasi-invariant with respect to the left action of the subgroup. The measure appears to be quasi-invariant with respect to the left action of diffeomorphisms with discontinuous second derivative. We derive an expression for quasi-invariance density and obtain an additional PSL(2,R) symmetry breaking term.     

Vapour and plasma ignition thresholds for visible pulsed-laser ablation of metallic targets

The coupling of visible nanosecond laser pulses to metallic targets irradiated in vacuum is studied. The expressions of the vapour and plasma ignition times are obtained. Two cases for vapour breakdown in the plasma ignition process are considered. The first case is that 40 generations of new electrons are born in vapour generation time before plasma formation as assumed in the literature. The second case is that 10 generations of new electrons are born in vapour generation time. Molybdenum (Mo), niobium (Nb) and aluminium (Al) targets are considered for illustrations of our results. The expression of the plasma ignition time for the Al target is substantially different from that reported in the literature. The vapour and plasma ignition threshold laser intensities are calculated and compared with those reported in the literature. Reasons for disagreement are discussed. The plasma ignition threshold estimated in the second case is noted to be in good agreement with the reported experimental result.