The Direct and Inverse Spectral Problems for some Banded Matrices

2000 Mathematics Subject Classification: 15A29.

A fast two-grid and finite section method for a class of integral equations on the real line with application to an acoustic scattering problem in the half-plane

We consider the numerical treatment of second kind integral equations on the real line of the form ∅(s) = ∫_(-∞)^(+∞)▒〖κ(s-t)z(t)ϕ(t)dt,s=R〗 (abbreviated ϕ= ψ+K_z ϕ) in which K ϵ L_1 (R), z ϵ L_∞ (R) and ψ ϵ BC(R), the space of bounded continuous functions on R, are assumed known and ϕ ϵ BC(R) is to be determined. We first derive sharp error estimates for the finite section approximation (reducing the range of integration to [-A, A]) via bounds on (1-K_z )^(-1)as an operator on spaces of weighted continuous functions. Numerical solution by a simple discrete collocation method on a uniform grid on R is then analysed: in the case when z is compactly supported this leads to a coefficient matrix which allows a rapid matrix-vector multiply via the FFT. To utilise this possibility we propose a modified two-grid iteration, a feature of which is that the coarse grid matrix is approximated by a banded matrix, and analyse convergence and computational cost. In cases where z is not compactly supported a combined finite section and two-grid algorithm can be applied and we extend the analysis to this case. As an application we consider acoustic scattering in the half-plane with a Robin or impedance boundary condition which we formulate as a boundary integral equation of the class studied. Our final result is that if z (related to the boundary impedance in the application) takes values in an appropriate compact subset Q of the complex plane, then the difference between ϕ(s)and its finite section approximation computed numerically using the iterative scheme proposed is ≤C_1 [kh log⁡〖(1⁄kh)+(1-Θ)^((-1)⁄2) (kA)^((-1)⁄2) 〗 ] in the interval [-ΘA,ΘA](Θ<1) for kh sufficiently small, where k is the wavenumber and h the grid spacing. Moreover this numerical approximation can be computed in ≤C_2 N log⁡N operations, where N = 2A/h is the number of degrees of freedom. The values of the constants C1 and C2 depend only on the set Q and not on the wavenumber k or the support of z.

A Refinement of some Overrelaxation Algorithms for Solving a System of Linear Equations

In this paper we propose a refinement of some successive overrelaxation methods based on the reverse Gauss–Seidel method for solving a system of linear equations Ax = b by the decomposition A = Tm − Em − Fm, where Tm is a banded matrix of bandwidth 2m + 1. We study the convergence of the methods and give software implementation of algorithms in Mathematica package with numerical examples. ACM Computing Classification System (1998): G.1.3.

A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation

The method of lines is a standard method for advancing the solution of partial differential equations (PDEs) in time. In one sense, the method applies equally well to space-fractional PDEs as it does to integer-order PDEs. However, there is a significant challenge when solving space-fractional PDEs in this way, owing to the non-local nature of the fractional derivatives. Each equation in the resulting semi-discrete system involves contributions from every spatial node in the domain. This has important consequences for the efficiency of the numerical solver, especially when the system is large. First, the Jacobian matrix of the system is dense, and hence methods that avoid the need to form and factorise this matrix are preferred. Second, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. In this paper, we show how an effective preconditioner is essential for improving the efficiency of the method of lines for solving a quite general two-sided, nonlinear space-fractional diffusion equation. A key contribution is to show, how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Equalisation of time variant multipath channels using amplitude banded LMS algorithms

For the purpose of equalisation of rapidly time variant multipath channels, we derive a novel adaptive algorithm, the amplitude banded LMS (ABLMS); which implements a nonlinear adaptation based on a coefficient matrix. Then we develop the: ABLMS algorithm as the adaptation procedure for a linear transversal equaliser (LTE) and a decision feedback equaliser (DFE) where a parallel adaptation scheme is deployed. Computer simulations demonstrate that with a small increase of computational complexity, the ABLMS based parallel equalisers provide a significant improvement related to the conventional LMS DFE and the LMS LTE in the case of a second order Markov communication channel model.

Amplitude banded RLS approach to time variant channel equalization

This paper proposes a non-linear adaptive algorithm, the amplitude banded RLS (ABRLS) algorithm, as an adaptation procedure for time variant channel equalizers. In the ABRLS algorithm, a coefficient matrix is updated based on the amplitude level of the received sequence. To enhance the capability of tracking for the ABRLS algorithm, a parallel adaptation scheme is utilized which involves the structures of decision feedback equalizer (DFE). Computer simulations demonstrate that the novel ABRLS based equalizer provides a significant improvement relative to the conventional RLS DFE on a rapidly time variant communication channel.

Flow injection analysis (FIA) determination of lead by hydride generation in banded coral skeletons /

A flow injection hydride generation direct current plasma atomic emission spectrometric (FI-HG-DCP-AES) method was developed for the determination of lead at ng.ml-l level. Potassium ferricyanide (K3Fe(CN)6) was used along with sodium tetrahydroborate(III) (NaBH4) to produce plumbane (PbH4) in an acid medium. The design of a gas-liquid separator (hydride generator) was tested and the parameters of the flow injection system were optimized to achieve a good detection limit and sample throughput. The technique developed gave a detection limit of 0.7 ng.ml-l(3ob). The precision at 20 ng.ml"* level was 1.6 % RSD with 1 1 measurements (n=l 1). Volume of sample loop was 500 |J.l. A sample throughput of 120 h"^ was achieved. The transition elements, Fe(II), FeOH), Cd(n), Co(II), Mn(n), Ni(II) and Zn(n) do not interfere in this method but 1 mg,l'l Cu(II) will suppress 50 % of the signal from a sample containing 20 ng.ml'l Pb. This method was successfully applied to determine lead in a calcium carbonate (CaC03) matrix of banded coral skeletons from Si-Chang Island in Thailand.

Changes in cells's secretory organelles and extracellular matrix during endochondral ossification in the mandibular condyle of the growing rat

The mandibular condyle from 20-day-old rats was examined in the electron microscope with particular attention to intracellular secretory granules and extracellular matrix. Moreover, type II collagen was localized by an immunoperoxidase method. The condyle has been divided into five layers: (1) the most superficial, articular layer, (2) polymorphic cell layer, (3) flattened cell layer, (4) upper hypertrophic, and (5) lower hypertrophic cell layers. In the articular layer, the cells seldom divide, but in the polymorphic layer and upper part of the flattened cell layer, mitosis gives rise to new cells. In these layers, cells produce two types of secretory granules, usually in distinct stacks of the Golgi apparatus; type a, cylindrical granules, in which 300-nm-long threads are packed in bundles which appear lucent after formaldehyde fixation; and type b, spherical granules loaded with short, dotted filaments. The matrix is composed of thick banded lucent fibrils in a loose feltwork of short, dotted filaments. The cells arising from mitosis undergo endochondral differentiation, which begins in the lower part of the flattened cell layer and is completed in the upper hypertrophic cell layer; it is followed by gradual cell degeneration in the lower hypertrophic cell layer. The cells produce two main types of secretory granules: type b as above; and type c, ovoid granules containing 300-nm-long threads associated with short, dotted filaments. A possibly different secretory granule, type d, dense and cigar-shaped, is also produced. The matrix is composed of thin banded fibrils in a dense feltwork. In the matrix of the superficial layers, the lucency of the fibrils indicated that they were composed of collagen I, whereas the lucency of the cylindrical secretory granules suggested that they transported collagen I precursors to the matrix. Moreover, the use of ruthenium red indicated that the feltwork was composed of proteoglycan; the dotted filaments packed in spherical granules were similar to, and presumably the source of, the matrix feltwork. The superficial layers did not contain collagen II and were collectively referred to as perichondrium. In the deep layers, the ovoid secretory granules displayed collagen II antigenicity and were likely to transport precursors of this collagen to the matrix, where it appeared in the thin banded fibrils. That these granules also carried proteoglycan to the matrix was suggested by their content of short dotted filaments. Thus the deep layers contained collagen II and proteoglycan as in cartilage; they were collectively referred to as the hyaline cartilage region.

Mechanism of adhesion and detachment at the anterior end of Merizocotyle icopae (Monogenea : Monocotylidae) including ultrastructure of the anterior adhesive matrix

The anterior adhesive mechanism was studied for Merizocotyle icopae (Monogenea: Monocotylidae). Adult anterior apertures can open and close. In addition, duct endings terminating within the apertures are everted or retracted depending on the stage of attachment. Adhesive in adults is synthesized from all 3 secretory types (rod-shaped, small and large spheroidal bodies) found within anterior apertures. All exit together and undergo mixing to produce the adhesive matrix, a process that depletes duct contents. A greater number of ducts carrying rod-shaped bodies is depleted than ducts containing spheroidal bodies which changes the ratio of secretory types present on detachment. Detachment involves elongation of duct endings and secretion of additional matrix as the worm pulls away from the substrate. The change in secretory type ratio putatively modifies the properties of the secreted matrix enabling detachment. Only after detachment do ducts refill. During attachment, individual secretory bodies undergo morphological changes. The larval and adult adhesive matrix differs. Anterior adhesive in oncomiracidia does not show fibres with banding whereas banded fibres comprise a large part of adult adhesive. The data Suggest that this is the result of adult spheroidal secretions modifying the way in which the adult adhesive matrix forms.

Dynamic matrix control on wind-induced vibration of spatial latticed structures [Chinese title = 空间网壳结构风振抑制的动态矩阵预测控制分析]

Ameliorated strategies were put forward to improve the model predictive control in reducing the wind induced vibration of spatial latticed structures. The dynamic matrix control (DMC) predictive method was used and the reference trajectory which is called the decaying functions was suggested for the analysis of spatial latticed structure (SLS) under wind loads. The wind-induced vibration control model of SLS with improved DMC model predictive control was illustrated, then the different feedback strategies were investigated and a typical SLS was taken as example to investigate the reduction of wind-induced vibration. In addition, the robustness and reliability of DMC strategy were discussed by varying the model configurations.

Decision Matrix Compared with Partnering Principles

The ideas for this CRC research project are based directly on Sidwell, Kennedy and Chan (2002). That research examined a number of case studies to identify the characteristics of successful projects. The findings were used to construct a matrix of best practice project delivery strategies. The purpose of this literature review is to test the decision matrix against established theory and best practice in the subject of construction project management.

Report on the Development and Validation of the Best Practice Decision Matrix

The Co-operative Research Centre for Construction Innovation (CRC-CI) is funding a project known as Value Alignment Process for Project Delivery. The project consists of a study of best practice project delivery and the development of a suite of products, resources and services to guide project teams towards the best procurement approach for a specific project or group of projects. These resources will be focused on promoting the principles that underlie best practice project delivery rather than simply identifying an off-the-shelf procurement system. This project builds on earlier work by Sidwell, Kennedy and Chan (2002), on re-engineering the construction delivery process, which developed a procurement framework in the form of a Decision Matrix

Towards a rule-based matrix for evaluating distress mechanisms in bridges

The effective management of bridge stock involves making decisions as to when to repair, remedy, or do nothing, taking into account the financial and service life implications. Such decisions require a reliable diagnosis as to the cause of distress and an understanding of the likely future degradation. Such diagnoses are based on a combination of visual inspections, laboratory tests on samples and expert opinions. In addition, the choice of appropriate laboratory tests requires an understanding of the degradation mechanisms involved. Under these circumstances, the use of expert systems or evaluation tools developed from “realtime” case studies provides a promising solution in the absence of expert knowledge. This paper addresses the issues in bridge infrastructure management in Queensland, Australia. Bridges affected by alkali silica reaction and chloride induced corrosion have been investigated and the results presented using a mind mapping tool. The analysis highights that several levels of rules are required to assess the mechanism causing distress. The systematic development of a rule based approach is presented. An example of this application to a case study bridge has been used to demonstrate that preliminary results are satisfactory.