Computing the Hessenberg matrix associated with a self-similar measure

We introduce in this paper a method to calculate the Hessenberg matrix of a sum of measures from the Hessenberg matrices of the component measures. Our method extends the spectral techniques used by G. Mantica to calculate the Jacobi matrix associated with a sum of measures from the Jacobi matrices of each of the measures. We apply this method to approximate the Hessenberg matrix associated with a self-similar measure and compare it with the result obtained by a former method for self-similar measures which uses a fixed point theorem for moment matrices. Results are given for a series of classical examples of self-similar measures. Finally, we also apply the method introduced in this paper to some examples of sums of (not self-similar) measures obtaining the exact value of the sections of the Hessenberg matrix.

On a Five-Diagonal Jacobi Matrices and Orthogonal Polynomials on Rays in the Complex Plane

∗ Partially supported by Grant MM-428/94 of MESC.

Exploring isospectral spring-mass systems with firefly algorithm

This paper investigates in-line spring-mass systems (An), fixed at one end and free at the other, with n-degrees of freedom (d.f.). The objective is to find feasible in-line systems (B(n)) that are isospectral to a given system. The spring-mass systems, A(n) and B(n), are represented by Jacobi matrices. An error function is developed with the help of the Jacobi matrices A(n) and B(n). The problem of finding the isospectral systems is posed as an optimization problem with the aim of minimizing the error function. The approach for creating isospectral systems uses the fact that the trace of two isospectral Jacobi matrices A(n) and B(n) should be identical. A modification is made to the diagonal elements of the given Jacobi matrix (A(n)), to create the isospectral systems. The optimization problem is solved using the firefly algorithm augmented by a local search procedure. Numerical results are obtained and resulting isospectral systems are shown for 4 d.f. and 10 d.f. systems.

Universality of the Stochastic Airy Operator

We introduce a new method for studying universality of random matrices. Let T-n be the Jacobi matrix associated to the Dyson beta ensemble with uniformly convex polynomial potential. We show that after scaling, Tn converges to the stochastic Airy operator. In particular, the top edge of the Dyson beta ensemble and the corresponding eigenvectors are universal. As a byproduct, these ideas lead to conjectured operator limits for the entire family of soft edge distributions. (C) 2015 Wiley Periodicals, Inc.

Higher-order molecular properties and excitation energies in single-reference and multireference coupled-cluster theory

Coupled-cluster (CC) theory is one of the most successful approaches in high-accuracy quantum chemistry. The present thesis makes a number of contributions to the determination of molecular properties and excitation energies within the CC framework. The multireference CC (MRCC) method proposed by Mukherjee and coworkers (Mk-MRCC) has been benchmarked within the singles and doubles approximation (Mk-MRCCSD) for molecular equilibrium structures. It is demonstrated that Mk-MRCCSD yields reliable results for multireference cases where single-reference CC methods fail. At the same time, the present work also illustrates that Mk-MRCC still suffers from a number of theoretical problems and sometimes gives rise to results of unsatisfactory accuracy. To determine polarizability tensors and excitation spectra in the MRCC framework, the Mk-MRCC linear-response function has been derived together with the corresponding linear-response equations. Pilot applications show that Mk-MRCC linear-response theory suffers from a severe problem when applied to the calculation of dynamic properties and excitation energies: The Mk-MRCC sufficiency conditions give rise to a redundancy in the Mk-MRCC Jacobian matrix, which entails an artificial splitting of certain excited states. This finding has established a new paradigm in MRCC theory, namely that a convincing method should not only yield accurate energies, but ought to allow for the reliable calculation of dynamic properties as well. In the context of single-reference CC theory, an analytic expression for the dipole Hessian matrix, a third-order quantity relevant to infrared spectroscopy, has been derived and implemented within the CC singles and doubles approximation. The advantages of analytic derivatives over numerical differentiation schemes are demonstrated in some pilot applications.

Nonstandard Finite Difference Schemes with Application to Finance: Option Pricing

2000 Mathematics Subject Classification: 65M06, 65M12.

Higher order derivatives and norms of certain matrix functions

Tese de doutoramento, Matemática (Álgebra Lógica e Fundamentos), Universidade de Lisboa, Faculdade de Ciências, 2014

Formalismo de Hamilton-Jacobi à la Carathéodory. Parte 2: sistemas singulares

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

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

One of the key issues facing public asset owners is the decision of refurbishing aged built assets. This decision requires an assessment of the “remaining service life” of the key components in a building. The remaining service life is significantly dependent upon the existing condition of the asset and future degradation patterns considering durability and functional obsolescence. Recently developed methods on Residual Service Life modelling, require sophisticated data that are not readily available. Most of the data available are in the form of reports prior to undertaking major repairs or in the form of sessional audit reports. Valuable information from these available sources can serve as bench marks for estimating the reference service life. The authors have acquired similar informations from a public asset building in Melbourne. Using these informations, the residual service life of a case study building façade has been estimated in this paper based on state-of-the-art approaches. These estimations have been evaluated against expert opinion. Though the results are encouraging it is clear that the state-of-the-art methodologies can only provide meaningful estimates provided the level and quality of data are available. This investigation resulted in the development of a new framework for maintenance that integrates the condition assessment procedures and factors influencing residual service life