On the convergence of the inverses of Toeplitz matrices and its applications

Many issues in signal processing involve the inverses of Toeplitz matrices. One widely used technique is to replace Toeplitz matrices with their associated circulant matrices, based on the well-known fact that Toeplitz matrices asymptotically converge to their associated circulant matrices in the weak sense. This often leads to considerable simplification. However, it is well known that such a weak convergence cannot be strengthened into strong convergence. It is this fact that severely limits the usefulness of the close relation between Toeplitz matrices and circulant matrices. Observing that communication receiver design often needs to seek optimality in regard to a data sequence transmitted within finite duration, we define the finite-term strong convergence regarding two families of matrices. We present a condition under which the inverses of a Toeplitz matrix converges in the strong sense to a circulant matrix for finite-term quadratic forms. This builds a critical link in the application of the convergence theorems for the inverses of Toeplitz matrices since the weak convergence generally finds its usefulness in issues associated with minimum mean squared error and the finite-term strong convergence is useful in issues associated with the maximum-likelihood or maximum a posteriori principles.     

Comparison of total and faecal coliforms as faecal indicator in eutrophicated surface water.

The aim of this study was to evaluate the use of total coliforms (TC) and faecal coliforms (FC) using a membrane filtration method for precise monitoring of faecal pollution in Korean surface water. The samples were collected in Korea from both main rivers and their tributaries. Presumptive TC * FC were enumerated. The ratios of presumptive FC to TC were not constant, but varied widely, and TC were difficult to enumerate because of overgrowth by background colonies. For FC this was not the case. Seven hundred and three purified strains of presumptive TC * FC and their background colonies were biotyped using API 20E. Among 272 presumptive TC, non-faecal related species, Aeromonas hydrophila dominated (34.6%) and E. coli accounted for only 5.1%. In contrast, E. coli made up 89% of the 209 presumptive FC. Furthermore, of 164 background colonies on Endo Agar LES, 54.9% was A. hydrophila, while background colonies on m-FC Agar were few (58 strains), and despite their atypical colony appearance, most of them were biotyped as enteric bacteria. These results reveal that the detection of FC rather than TC using m-FC Agar is more appropriate for faecal pollution monitoring in eutrophicated surface water located in a temperate region.     

Corrected Sum Rule, Generalized Virial Identity and Elementary Excitation Spectrum of Bose–Einstein Condensates at Any Trapped Atom Number

Using a corrected sum rule and a generalized virial identity, we study the analytical expression for entire modes of the collective elementary excitation spectrum in a trapped Bose–Einstein condensate at any atom number. Explicit analytical formulas for the spectrum are obtained for the harmonic traps with both spherical symmetry and axial symmetry using the gaussian approximation for the N-body ground-state wave function of the condensate. These formulas give the simple dependence of all energy levels on the atom numbers, their interaction strength and trap geometry parameters.     

Microscale Patterning of Mesoscopic PZN-PT Single Crystal Films by Crystal ion Slicing and Laser-Induced Etching

Advances in the fabrication of solid-solution single crystal relaxor ferroelectrics have made it possible to produce highly efficient piezoelectric crystals, and have attracted renewed interest in the use of these crystals for a new generation of piezoelectric transducers, actuators and sensors. Of particular interest is their incorporation into micro-electromechanical systems (MEMS). In this paper we report on the laser-induced wet chemical etching of lead zinc niobate-lead titanate (PZN-PT) in hydrochloric acid (HCl). Argon-ion laser radiation at power levels up to 4 W is focused to a spot diameter of about 15μm and results in the chemical etching of grooves at patterning speeds up to 5μm/sec. Crystal ion slicing, an ion-implant-based film separation technique, is used in combination with laser etching to form 5 to 10μm-thick patterned and freestanding films for incorporation into micro-electromechanical devices.     

Valorisation of waste fractions from autohydrolysis of selected lignocellulosic materials

Non‐isothermal processing of lignocellulosic materials in aqueous media (autohydrolysis reaction) under mild conditions leads to solutions containing valuable chemicals (oligosaccharides, sugars and acetic acid) and other, undesired, compounds (belonging to the extractive and acid‐soluble lignin fractions) which have to be removed in further purification treatments. Liquors obtained by non‐isothermal autohydrolysis of Eucalyptus globulus wood and corncobs under a variety of operational conditions were extracted with ethyl acetate in order to remove non‐saccharide components, and the suitability of the fraction dissolved in the organic phase was assayed for possible utilisation as an antioxidant. The yield and antioxidant activity of ethyl acetate extracts (measured by the α,α‐diphenyl‐β‐picrylhydrazyl (DPPH) radical scavenging capacity) showed a strong dependence on the autohydrolysis conditions. The antioxidant activity of extracts obtained under selected operational conditions compared well with synthetic antioxidants. © 2003 Society of Chemical Industry     

Minimax estimation of deterministic parameters in linear models with a random model matrix

We consider the problem of estimating an unknown deterministic parameter vector in a linear model with a random model matrix, with known second-order statistics. We first seek the linear estimator that minimizes the worst-case mean-squared error (MSE) across all parameter vectors whose (possibly weighted) norm is bounded above. We show that the minimax MSE estimator can be found by solving a semidefinite programming problem and develop necessary and sufficient optimality conditions on the minimax MSE estimator. Using these conditions, we derive closed-form expressions for the minimax MSE estimator in some special cases. We then demonstrate, through examples, that the minimax MSE estimator can improve the performance over both a Baysian approach and a least-squares method. We then consider the case in which the norm of the parameter vector is also bounded below. Since the minimax MSE approach cannot account for a nonzero lower bound, we consider, in this case, a minimax regret method in which we seek the estimator that minimizes the worst-case difference between the MSE attainable using a linear estimator that does not know the parameter vector, and the optimal MSE attained using a linear estimator that knows the parameter vector. For analytical tractability, we restrict our attention to the scalar case and develop a closed-form expression for the minimax regret estimator.     

Second harmonic generation from a ferroelectric film

We derive an expression for transmittivity (T_SHG) of second harmonic generation (SHG) signals from a ferroelectric (FE) film. Intensities of up and down fields in the medium are investigated in relation to T_SHG. The derivations are made based on undepletion of input fields and nonlinear wave equation derived from the Maxwell equations. We present two cases: film without mirrors and with partial mirrors. Expressions for the newly derived nonlinear susceptibility coefficients of SHG for real crystal symmetry [J. Opt. Soc. Am. B 19 (2002) 2007] are used to get more realistic results. Variations in T_SHG with respect to film thickness are illustrated.     

Evaluation and optimization of package processing and design through solder joint profile prediction

Solder joints are generated using a variety of methods to provide both mechanical and electrical connection for applications such as flip-chip, wafer level packaging, fine pitch, ball-grid array, and chip scale packages. Solder joint shape prediction has been incorporated as a key tool to aid in process development, wafer level and package level design and development, assembly, and reliability enhancement. This work demonstrates the application of an analytical model and the Surface Evolver software in analyzing a variety of solder processing methods and package types. Bump and joint shape prediction was conducted for the design of wafer level bumping, flip-chip assembly, and wafer level packaging. The results from the prediction methodologies are validated with experimentally measured geometries at each level of design.     

Synthesis of ZSM‐5 Films and Monoliths with Bimodal Micro/Mesoscopic Structures

A route to synthesize ZSM‐5 crystals with a bimodal micro/mesoscopic pore system has been developed in this study; the successful incorporation of the mesopores within the ZSM‐5 structure was performed using tetrapropylammonium hydroxide (TPAOH)‐impregnated mesoporous materials containing carbon nanotubes in the pores, which were encapsulated in the ZSM‐5 crystals during a solid rearrangement process within the framework. Such mesoporous ZSM‐5 zeolites can be readily obtained as powders, thin films, or monoliths.     

The First Template‐Free Growth of Crystalline Silicon Microtubes

A simple template‐free high‐temperature evaporation method was developed for the growth of crystalline Si microtubes for the first time. As‐grown Si microtubes were characterized using X‐ray diffraction, scanning electron microscopy, transmission electron microscopy, and room‐temperature photoluminescence. The lengths of the Si tubes can reach several hundreds of micrometers; some of them have lengths on the order of millimeters. Each tube has a uniform outer diameter along its entire length, and the typical outer diameter is ≈ 2–3 μm. Most of the tubes have a wall thickness of ≈ 400–500 nm, though a considerable number of them exhibit a very thin wall thickness of ≈ 50 nm. Room‐temperature photoluminescence measurement shows the as‐synthesized Si microtubes have two strong emission peaks centered at ≈ 589 nm and ≈ 617 nm and a weak emission peak centered at ≈ 455 nm. A possible mechanism for the formation of these Si tubes is proposed. We believe that the present discovery of the crystalline Si microtubes will promote further experimental studies on their physical properties and smart applications.