Design of linear-phase IIR filters via impulse-response gramians

A new method for the design of a linear-phase infinite-impulse-response (IIR) filter is presented. It involves designing a finite-impulse-response (FIR) filter satisfying the given frequency response specifications and subsequently obtaining a significantly lower order IIR filter using model reduction based on impulse-response gramians. The general outline of the method and a brief overview of the existing linear-phase FIR filter design and model-reduction techniques are presented. The impulse-response gramian and the model-reduction algorithm used are presented. The method is illustrated by design examples and is compared with other methods for the design of linear-phase IIR filters using equalizers     

Improved results on frequency‐weighted balanced truncation and error bounds

In this paper, we present some new results on frequency‐weighted balanced truncation which is a significant improvement on Lin and Chiu's frequency‐weighted balanced truncation technique. The reduced‐order models, which are guaranteed to be stable in the case of double‐sided weighting, are obtained by direct truncation. Two sets of simple, elegant and easily calculatable a priori error bounds are also derived. Numerical examples and comparison with other well‐known techniques show the effectiveness of the proposed technique. Copyright © 2011 John Wiley & Sons, Ltd.     

Model reduction based on limited‐time interval impulse response Gramians

In this paper, three new Gramians are introduced namely ‐ limited‐time interval impulse response Gramians (LTIRG), generalized limited‐time Gramians (GLTG) and generalized limited‐time impulse response Gramians (GLTIRG). GLTG and GLTIRG are applicable to both unstable systems and also to systems which have eigenvalues of opposite polarities and equal magnitude. The concept of these Gramians is utilized to develop model reduction algorithms for linear time‐invariant continuous‐time single‐input single‐output (SISO) systems. In the cases of GLTIRG and GLTG based model reduction, the standard time‐limited Gramians are generalized to be applied to unstable systems by transforming the original system into a new system which requires the solution of two Riccati equations. Two numerical examples are included to illustrate the proposed methods. The results are also compared with standard techniques.     

Nonlinear Feedback Control for the Lorenz System

The Lorenz system is well known for its ability to produce chaotic motion and the control problem of this system has attracted much attention in recent years. In this paper, control of the Lorenz chaotic systems based on a nonlinear feedback technique is presented. The objective of control is two-fold: one is to drive the system to one of equilibrium points associated with uncontrolled chaotic motion and the other is to let one of the closed-loop system states track a given signal. The controllers designed here are based on exact linearization theory of nonlinear systems and can regulate the closed-loop system states globally to a given point. Finally, illustrative examples show the effectiveness of the proposed design method.     

Model reduction of singular systems

In this paper, model reduction for singular systems will be investigated. First, a previous model reduction algorithm is presented and proved to be not appropriate in practice. Detailed examination of this existing algorithm will show that the difficulty of model reduction for singular systems is to retain its impulsive nature. Thus, based on this kind of acute observation, we investigate impulsive controllability and impulsive observability and propose a new decomposition approach for singular systems. Then a new model reduction algorithm will be proposed on the basis of this new decomposition via the Nehari approximation technique. This new model reduction algorithm will retain the impulsive nature of the original singular system. Finally, one example will be presented to illustrate the effectiveness of the proposed model reduction algorithm.     

Doped oxides of cerium as inorganic colorants

The colour of inorganic colorants is based on metal ions such as cadmium, lead, chromium or cobalt, the majority of which are unfortunately potentially toxic. Thus, there is in a need to introduce alternative metal or metal oxides, which would be environmentally friendly and economically viable as a replacement for potentially toxic inorganic colorants. Rare earth-based colorants offer an additional opportunity for the development of optically pure colours. In this study, a replacement for potentially toxic colorants has been sought through the use of a rare earth metal ion, cerium. Appropriate doping of cerium oxides with molybdenum and iron gives an orange–red colorant. The conditions ideal for optimal colour have been standardised and the resultant colorant characterised through powder X-ray diffraction techniques, particle size measurement, etc. The colorants exhibit good hiding power and tinting strength.     

Indium and tin oxide nanowires by vapor-liquid-solid growth technique

Regular three-dimensional (3-D) arrays of crystalline SnO₂-In₂O₃ nanowires were produced on m-sapphire using a gold catalyst-assisted vapor-liquid-solid growth process. The growth characteristics at multiple growth conditions were analyzed using scanning electron microscopy (SEM), transmission electron microscopy (TEM), selected area electron diffraction (SAED), x-ray photoemission spectroscopy (XPS), and Rutherford backscattering spectroscopy (RBS) to evaluate the functional dependence of nanowire structure and composition on growth parameters such as temperature and source composition. The results indicate that nanowires of mixed composition are not possible from the catalytic clusters; rather, a mixture of indium and tin oxide wires are formed in the range of conditions investigated here.     

Colored cool colorants based on rare earth metal ions

Colored pigments with high near infrared reflectance and not based on toxic metal ions like cadmium, lead and cobalt are being sought as cool colorants. Through appropriate doping two pigments Ce-Pr-Mo and Ce-Pr-Fe have been developed to offer a reddish brown and reddish orange color, respectively. These pigments have been characterized and found to be highly crystalline with an average size of 300 nm. A shift in band gap energy from 2.21 to 2.18 eV has been observed when Li₂CO₃ was used as a mineralizer. Scanning electron microscope-energy dispersive X-ray analysis (SEM-EDAX) measurement indicate a uniform grind shape and distribution of metal ion, with over 65% reflectance in the NIR region, these pigments can well serve as cool colorants.     

Mechanisms of 1D crystal growth in reactive vapor transport: indium nitride nanowires

Indium nitride (InN) nanowire synthesis using indium (In) vapor transport in a dissociated ammonia environment (reactive vapor transport) is studied in detail to understand the nucleation and growth mechanisms involved with the so-called "self-catalysis" schemes. The results show that the nucleation of InN crystal occurs first on the substrate. Later, In droplets are formed on top of the InN crystals because of selective wetting of In onto InN crystals. Further growth via liquid-phase epitaxy through In droplets leads the growth in one dimension (1D), resulting in the formation of InN nanowires. The details about the nucleation and growth aspects within these self-catalysis schemes are rationalized further by demonstrating the growth of heteroepitaxially oriented nanowire arrays on single-crystal substrates and "tree-like" morphologies on a variety of substrates. However, the direct nitridation of In droplets using dissociated ammonia results in the spontaneous nucleation and basal growth of nanowires directly from the In melt surface, which is quite different from the above-mentioned nucleation mechanism with the reactive vapor transport case. The InN nanowires exhibit a band gap of 0.8 eV, whereas the mixed phase of InN and In(2)O(3) nanowires exhibit a peak at approximately 1.9 eV in addition to that at 0.8 eV.     

Prioritizing Groundwater Monitoring in Data Sparse Regions using Atanassov Intuitionistic Fuzzy Sets (A-IFS)

Water quality index (WQI) is a single measure that is commonly used to prioritize water wells and manage groundwater resources. WQI is pragmatic as it combines several water quality parameters into a single index. However, the process of aggregation is imprecise and suffers from uncertainties in measurements and subjective specification of weights. The goal of this study is to demonstrate how Atanassov’s Intuitionistic Fuzzy Sets (A-IFS) can be used to aggregate water quality parameters into a composite index to rank and prioritize groundwater wells. The A-IFS weighted geometric mean (A-IFS-WGM) method and the A-IFS based Technique for Order of Preference by Similarity to Ideal Solution (A-IFS-TOPSIS) using Euclidean (A-IFS-TOPSIS-E) and Hamming (A-IFS-TOPSIS-H) are introduced and illustrated to prioritize and rank water supply wells in a fast growing yet poorly studied area in Guntur, Andhra Pradesh, India. The concept of A-IFS entropy is also presented to directly ascertain weights from the data. This objective selection of weights from the data eliminates the subjectivity and difficulties associated with assigning relative importance to different water quality parameters. The results of the study indicate that the weights obtained using the entropy methods are consistent with the geochemical characteristics of the regional aquifer. The A-IFS-WGM method is more sensitive to weights compared to the A-IFS-TOPSIS methods which are influenced to a larger extent by the membership and non-membership values (ratings). Special consideration must be placed on ascribing the hesitation margin of the decision maker and identifying the membership values for non-preference as the methods exhibit greater sensitivity to these factors. The developed methods provide pragmatic data-driven approaches to prioritize and rank groundwater wells within a monitoring network.