Capability and limitation of max- and sum-type construction of Lyapunov functions for networks of iISS systems

This paper addresses the problem of verifying stability of networks whose subsystems admit dissipation inequalities of integral input-to-state stability (iISS). We focus on two ways of constructing a Lyapunov function satisfying a dissipation inequality of a given network. Their difference from one another is elucidated from the viewpoint of formulation, relation, fundamental limitation and capability. One is referred to as the max-type construction resulting in a Lipschitz continuous Lyapunov function. The other is the sum-type construction resulting in a continuously differentiable Lyapunov function. This paper presents geometrical conditions under which the Lyapunov construction is possible for a network comprising $n\ge 2$ subsystems. Although the sum-type construction for general $n>2$ has not yet been reduced to a readily computable condition, we obtain a simple condition of iISS small gain in the case of $n=2$. It is demonstrated that the max-type construction fails to offer a Lyapunov function if the network contains subsystems which are not input-to-state stable (ISS).     

磁控溅射法镀制氮化铝薄膜特性研究

氮化铝薄膜具有高折射率,良好的化学稳定性,耐磨摩、高电阻等特性在微电子器件和光学薄膜中有着广泛地应用.本文研究了反应式磁控溅射方法利用Ar/N2混合气体镀制氮化铝薄膜的工艺过程,实验表明在高真空和高泵浦速率条件下,放电电压直接依赖于反应气体珠浓度.薄膜的折射率,消光系数和薄膜硬度都依赖于氮气浓度的比例.通过工艺研究,找到了氮气在不同浓度下对氮化铝薄膜的折射率,消光系数以及薄膜硬度的影响,找出了镀制氮化镀制氮化铝薄膜的最佳工艺参数.在Ar/N2工作气体中氮气含量保持在40%条件下,用反应式磁控溅射方法,可以精确镀制出良好的氮化铝薄膜,其中折射率范围在2.25~2.4之间,消光系数为10-3,薄膜显微硬度大于20GPa.该薄膜可以广泛应用于微电子器件和光电器件上.     

A Conjecture on Wiener Indices in Combinatorial Chemistry

Drugs and other chemical compounds are often modeled as polygonal shapes, where each vertex represents an atom of the molecule, and covalent bonds between atoms are represented by edges between the corresponding vertices. This polygonal shape derived from a chemical compound is often called its molecular graph, and can be a path, a tree, or in general a graph. An indicator defined over this molecular graph, the Wiener index, has been shown to be strongly correlated to various chemical properties of the compound. The Wiener index conjecture for trees states that for any integer n (except for a finite set), one can find a tree with Wiener index n. This conjecture has been open for quite some time, and many authors have presented incremental progress on this problem. In this paper we present further progress towards proving this conjecture—through the design of efficient algorithms, we show that enumerating all possible trees to verify this conjecture (as done by all the previous approaches) is not necessary, but instead searching in a small special family of trees suffices, thus achieving the first polynomial (in n) time algorithm to verify the conjecture up to integer n. More precisely, we (i) present an infinite family of trees and prove various properties of these trees, (ii) show that a large number of integers, up to at least 10⁸ (compared with the previous best 10⁴) are representable as Wiener indices of trees in this succinct family, (iii) provide several efficient algorithms for computing trees with given Wiener indices, and (iv) implement our algorithms and experimentally show that their performance is asymptotically much better than their theoretical worst-case upper bound.     

Holographic digital Fourier microscopy for selective imaging of biological tissue

We present an application of digital Fourier holography for selective imaging of scatterers with different sizes in turbid media such as biological tissues. A combination of Fourier holography and high‐resolution digital recording, digital Fourier microscopy (DFM) permits crucial flexibility in applying filtering to highlight scatterers of interest in the tissue. The high‐resolution digital hologram is a result of the collation of Fourier holographic frames to form a large‐size composite hologram. It is expected that DFM has an improved signal‐to‐noise ratio as compared to conventional direct digital imaging, e.g., phase microscopy, as applied to imaging of small‐size objects. The demonstration of the Fourier filtering capacity of DFM using a biological phantom represents the main focus of this article. © 2005 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 14, 253–258, 2004; Published online inWiley InterScience (www.interscience.wiley.com). DOI 10.1002/ima.20031     

Ellipsoidal parameter or state estimation under model uncertainty

Ellipsoidal outer-bounding of the set of all feasible state vectors under model uncertainty is a natural extension of state estimation for deterministic models with unknown-but-bounded state perturbations and measurement noise. The technique described in this paper applies to linear discrete-time dynamic systems; it can also be applied to weakly non-linear systems if non-linearity is replaced by uncertainty. Many difficulties arise because of the non-convexity of feasible sets. Combined quadratic constraints on model uncertainty and additive disturbances are considered in order to simplify the analysis. Analytical optimal or suboptimal solutions of the basic problems involved in parameter or state estimation are presented, which are counterparts in this context of uncertain models to classical approximations of the sum and intersection of ellipsoids. The results obtained for combined quadratic constraints are extended to other types of model uncertainty.     

Direct Measurement of Fusion Enthalpy of LaAlO3 and Comparison of Energetics of Melt,Glass, and Amorphous Thin Films

Enthalpy of fusion and melting temperature of perovskite LaAlO₃ were measured using thermal analysis method as 124 ± 10 kJ/mol at 2134 ± 10°C, providing a value of 52 ± 4 J·(mol·K)^?1 for entropy of fusion. Crystallization enthalpy of amorphous LaAlO₃ thin films was found to change from ?24 to ?17 kJ/mol with decrease in film thickness from 100 to 20 nm. Differences in energetics of amorphous LaAlO₃ films and glass cannot be explained exclusively by surface energy contribution but must reflect differences in structure between films and glasses in this system.     

Geometry control of the junction between two fractal curves

The general objective of our work is to create a geometric modeller based on iterative processes. With this objective in mind, we have to provide tools that work with fractal objects in the same manner as with objects of classical topology. In this article we focus on the constructing of an intermediate curve between two other curves defined by different iterative construction processes. A similar problem often arises with subdivision surfaces, when the goal is to connect two surfaces with different subdivision masks. We start by dealing with curves, willing to later generalise our approach to surfaces. We formalise the problem with the Boundary Controlled Iterated Function System model. Then we deduct the conditions that guarantees continuity of the intermediate curve. These conditions determine the structure of subdivision matrices. By studying the eigenvalues of the subdivision operators, we characterise the differential behaviour at the connection points between the curves and the intermediate one. This behaviour depends on the nature of the initial curves and coefficients of the subdivision matrices. We also suggest a method to control the differential behaviour by adding intermediate control points.     

X-ray tomography as a diagnostic method of X-ray refractive optics

This article describes the application of high-resolution X-ray computed tomography to assess the critical parameters of refractive lenses for X-ray optics that determine the quality of compound optical systems. A microfocus Y. Cheetah X-ray system has been used for three-dimensional visualization of the surface and internal structure of refractive lenses made of high-purity aluminum with geometric apertures of 500 and 1500 μm. A Fein Focus X-ray tube with a focal spot size of less than 2 μm provides the resolution necessary for detecting critical-size microstructure defects in the material of the lens.