Nuclear Excitation by X-Ray Emission of Femtosecond Laser Plasma

The proposed model of laser plasma emission spectrum formation enables us to determine the absolute value of the laser pulse to plasma emitted radiation conversion factor, profile of the emission spectrum, and frequency distribution of the intensity and energy in the emitted spectra. This is of interest for laser plasma diagnostics and provides a means for direct calculation of the number of excited nuclei in dependent on the parameters of laser pulse. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mappings of Domains in Rn and Their Metric Tensors

We consider quasi-isometric mappings of domains in multidimensional Euclidean spaces. We establish that a mapping depends continuously in the sense of the topology of Sobolev classes on its metric tensor to within isometry of the space. In the space of metric tensors we take the topology determined by means of almost everywhere convergence. We show that if the metric tensor of a mapping is continuous then the length of the image of a rectifiable curve is determined by the same formula as in the case of mappings with continuous derivatives. (Continuity of the metric tensor of a mapping does not imply continuity of its derivatives.)     

On the isomorphism problem in the class of extensions of a free group by an infinite cyclic group

In the automorphism group of a rank 3 free group we find two nonconjugate automorphisms whose mapping tori are isomorphic groups.     

The fixed point property for multivalued nonexpansive mappings

We show some properties concerning geometrical constants of Banach spaces which imply the existence of fixed points for multivalued nonexpansive mappings and we study the relationship between these properties.     

X-ray metrology for advanced silicon processes

X-ray reflectivity (XRR), X-ray fluorescence (XRF) and small angle X-ray scattering (SAXS) techniques are used to the monitoring of Cu/porous low κ processes, which are developed for the next generation (≤65 nm) integrated circuits. Sensitivity of XRR and XRF is sufficient to detect drifts of the copper barrier layer, copper seed layer and Cu CMP (chemical-mechanical polishing) processes. Their metrology key parameters comply with production requirements. SAXS allows determining the pore structure of low κ films: average pore size and pore size distribution.     

X-ray photoelectron spectroscopy characterization of oxidated Si particles formed by pulsed ion-beam ablation

X-ray photoelectron spectroscopy (XPS) is used to probe oxidation states of Si species in particles deposited using a pulsed ion-beam evaporation method. The effects of He ambient gas, ion beam intensity and post-treatments on the oxides composition and oxygen content have been studied. It is found that presence of He ambient gas led to a profound oxidation of Si species as compared to that prepared in vacuum at the same ion-beam ablation energy, i.e. both increase of SiO₂ component and oxygen concentration in the oxides coverage. The deposition in He also resulted in an increase of oxygen concentration even under lower ablation intensity, but a higher Si suboxides concentration. It is revealed that the reaction between Si and O was controlled by the ion beam intensity (temperature of Si plasma) and the gas ambient (collision probability of Si and O species). The difference in structure of oxide layers for samples obtained under various conditions is discussed based on the results of XPS analyses.     

Generalized KKM Type Theorems in FC-Spaces with Applications (I)

The class KKM(X,Y) (resp., s-KKM(X,Y,Z)) of set-valued mappings with KKM (resp., s-KKM) property is introduced in FC-spaces without any convexity structure. Some generalized KKM (resp., s-KKM) type theorems are proved in FC-spaces under much weak assumptions. As applications, some new section theorems and coincidence theorems are established in FC-spaces. These theorems generalize many known results in literature. The further applications of these results will be given in a follow-up paper.     

Nanophotonics and nanometrology with planar X-ray waveguide-resonator

The mechanism of X-ray waveguide-resonance propagation or the radiation superstream model, which can become the ground of X-ray nanophotonics, is discussed briefly. Some attention is devoted to features consideration of the simplest devices characterized by the waveguide-resonance transportation of X-ray beams. The experimental data showing the user possibilities of a simplest waveguide-resonators application for diffractometry are presented. We discuss the main reasons to improve the metrological characteristics for total reflection X-ray fluorescence (TXRF) analytical method in case when the target exciting beam is formed by a waveguide-resonator. Some problems appearing during the waveguide-resonator application are formulated.     

向量变分不等式的严格可行性问题

本篇文章首先定义了向量变分不等式的严格可行点概念,其次在假设了映射是强(D)-伪单调的情况下,证明了向量变分不等式解集非空有界与其严格可行点存在的等价性问题,推广了在数量变分不等式上得到的相应结果．     

Extension of Isometries Between the Unit Spheres of Normed Space E and C（Ω）

In this paper, we study the extension of isometries between the unit spheres of normed space E and C（Ω）. We obtain that any surjective isometry between the unit spheres of normed space E and C（Ω） can be extended to be a linear isometry on the whole space E and give an affirmative answer to the corresponding Tingley＇s problem （where Ω be a compact metric space）.