A Perron iteration for the solution of a quadratic vector equation arising in Markovian Binary Trees

We propose a novel numerical method for solving a quadratic vector equation arising in Markovian Binary Trees. The numerical method consists in a fixed point iteration, expressed by means of the Perron vectors of a sequence of nonnegative matrices. A theoretical convergence analysis is performed. The proposed method outperforms the existing methods for close-to-critical problems

Shift techniques for Quasi-Birth and Death processes: canonical factorizations and matrix equations

We revisit the shift technique applied to Quasi-Birth and Death (QBD) processes (He, Meini, Rhee, SIAM J. Matrix Anal. Appl., 2001) by bringing the attention to the existence and properties of canonical factorizations. To this regard, we prove new results concerning the solutions of the quadratic matrix equations associated with the QBD. These results find applications to the solution of the Poisson equation for QBDs

On Functions of quasi Toeplitz matrices

Let $a(z)=\sum_{i\in\mathbb Z}a_iz^i$ be a complex valued continuous function, defined for $|z|=1$, such that $\sum_{i=-\infty}^{+\infty}|ia_i|<\infty$. Consider the semi-infinite Toeplitz matrix $T(a)=(t_{i,j})_{i,j\in\mathbb Z^+}$ associated with the symbol $a(z)$ such that $t_{i,j}=a_{j-i}$. A quasi-Toeplitz matrix associated with the continuous symbol $a(z)$ is a matrix of the form $A=T(a)+E$ where $E=(e_{i,j})$, $\sum_{i,j\in\mathbb Z^+}|e_{i,j}|<\infty$, and is called a CQT-matrix. Given a function $f(x)$ and a CQT matrix $M$, we provide conditions under which $f(M)$ is well defined and is a CQT matrix. Moreover, we introduce a parametrization of CQT matrices and algorithms for the computation of $f(M)$. We treat the case where $f(x)$ is assigned in terms of power series and the case where $f(x)$ is defined in terms of a Cauchy integral. This analysis is applied also to finite matrices which can be written as the sum of a Toeplitz matrix and of a low rank correction

Computing the Exponential of Large Block-Triangular Block-Toeplitz Matrices Encountered in Fluid Queues

The Erlangian approximation of Markovian fluid queues leads to the problem of computing the matrix exponential of a subgenerator having a block-triangular, block-Toeplitz structure. To this end, we propose some algorithms which exploit the Toeplitz structure and the properties of generators. Such algorithms allow to compute the exponential of very large matrices, which would otherwise be untreatable with standard methods. We also prove interesting decay properties of the exponential of a generator having a block-triangular, block-Toeplitz structure

General solution of the Poisson equation for Quasi-Birth-and-Death processes

We consider the Poisson equation $(I-P)\boldsymbol{u}=\boldsymbol{g}$, where $P$ is the transition matrix of a Quasi-Birth-and-Death (QBD) process with infinitely many levels, $\bm g$ is a given infinite dimensional vector and $\bm u$ is the unknown. Our main result is to provide the general solution of this equation. To this purpose we use the block tridiagonal and block Toeplitz structure of the matrix $P$ to obtain a set of matrix difference equations, which are solved by constructing suitable resolvent triples

HIV/AIDS, Crime and Security in Southern Africa

HIV/AIDS, crime, security and governance are linked issues in the region of Southern Africa. According to the Joint United Nations Programme on HIV/AIDS (UNAIDS) and World Health Organisation (WHO), sub-Saharan Africa is home to approximately 10 percent of the world’s population and 2/3 of this population is infected with HIV. Within sub- Saharan Africa, Southern Africa remains the world’s most affected region: globally, 32% of people with HIV live in this sub-region and 34% of AIDS deaths occur within this region as well. Infection rates in Southern Africa indicate that huge numbers of people will die over the next 10 years, thus affecting the basic functioning of society. The skills and human resources needed for an effective government will become scarce. The HIV/AIDS pandemic has become an issue no less destructive than warfare itself. It is recognised that ‘health’ is part of the fabric of what constitutes a country’s security, not only due to the impact a disease can pose to a state’s stability, but also to the state’s ability tomaintain internal stability and external security. This situation has called for the attention of the international community to assist Southern African governments, especially during conflict situations and humanitarian emergencies. In addition, selected sections of personal interviews with four South African experts on AIDS-related issues have been included in this manuscript in order to clarify some theoretical aspects

When the selfing process goes wrong: Social-biofeed-back, causal mechanisms, and pathological narcissism

In direct opposition to the dominant nativist perspective tracing back to Descartes, William James suggested that the sense of self is constructed through a never-ending process of reflexivity. In more recent years, empirical data from various psychological domains (notably developmental, clinical and social psychology) have further strengthened this constructivist perspective. Notably, Gergely and Watson\u2019s social biofeedback model has been proposed as a central mechanism in the development of emotional introspection, which itself constitutes a crucial step in the process leading to a mature sense of self. In accordance with the social bio-feedback model, it has been suggested that reiterated failures in biofeedback mechanisms predispose an individual to mental suffering. While borderline personality disorder and antisocial behavior have received the most attention, here I make a preliminary attempt to examine the impact of dysfunctional biofeedback on the pathogenesis of narcissism, suggesting that some central features of pathological narcissism may result from serious and reiterated disruptions in social biofeedback. This preliminary exploration aims to deepen our understanding of the origins of psychological suffering. In this sense, my effort could contribute to the construction of a causal model going beyond the purely categorical, atheoretical analysis of mental diseases typical of the diagnostic and statistical manuals

Behaviour and Design of Aluminium Alloy Structural Elements

Aluminium alloys are nonlinear metallic materials with continuous stress-strain curves that are not well represented by the simplified elastic, perfectly plastic material model used in most existing design specifications. The aims of this study are to develop a more efficient design method for aluminium alloy structures by rationally exploiting strain hardening. The key components of this study include laboratory testing, numerical modelling and development of design guidance for aluminium alloy structures. As part of the present study, the experimental programme included tests on 11 stub columns, 40 simply supported beams, 46 continuous beams and corresponding tensile coupon tests. Numerical investigations of aluminium alloy simply supported beams and continuous beams were also conducted. The validated finite element models were used for extensive parametric studies, generating 96 results for beams under three-point bending, 96 under four-point bending and 210 for continuous beams. The experiments and numerical simulations have shown the following key features of the inelastic behaviour of aluminium alloy structural elements: (1) the significance of strain hardening, indicated by the ultimate stress over the yield stress, could be up to 50%; (2) non-slender section capacities could be generally up to 40% higher than the yield limits in compression, and 50% greater than the plastic moments in bending; (3) the experimental and numerical ultimate loads of continuous beams on non-slender sections go beyond the calculated loads corresponding to the occurrence of the first hinge by more than 10%. Previous experimental data on aluminium alloy stub columns and simply supported beams were also collected. These collected test data were used together with the newly generated experimental and numerical results obtained from this study, totalling about 900 data, to assess the design predictions of the American, Australian/New Zealand and European specifications. On average, the existing design methods under-estimated the capacity of aluminium alloy stub columns by around 15%~22%, simply supported beams by around 18%~40% and continuous beams by around 27% ~ 50%. Existing section classification limits in Eurocode 9 (2007) were also assessed, and while they were found to be safe, some improved limits were proposed. The combined experimental and numerical results were used to develop and calibrate a new design method, termed the continuous strength method (CSM). Two key components of the CSM – a base curve and a bi-linear material model for aluminium alloys have been proposed in this study. Global plastic analysis allowing for moment redistribution has also been adopted in the CSM. Unlike current practices, the CSM has the merits of adopting the continuous treatment for the cross-section deformation response, rationally exploiting the available capacity beyond the yield limit and reasonably allowing for redistributing the internal forces. The capacity predictions of aluminium alloy structural members have been improved by more than 30% using the CSM. Reliability analyses have also been performed to assess the reliability level of different design methods according to the American Institute of Steel Construction (2010) and European Standard EN1990 (2002) approaches. The CSM has been shown to be safe, efficient and consistent for aluminium alloy structural members.Open Acces

Tinjauan Kembali Pengaruh Tingkat Adopsi IFRS terhadap Persistensi Laba Perusahaan

Globalization causes the financial and investment flows between companies and countries to increase. To facilitate interaction between companies between countries, it is felt necessary for each country to use the same financial statement standards in order to facilitate all relevant parties to be able to compare cross-country reporting. IFRS is an international financial reporting standard that can be adopted by companies in various countries, but not all countries adopt these standards. This study aims to re-analyze how the influence of the level of IFRS adoption on financial quality reports as measured by the persistence of company earnings, especially those listed on the ASEAN-5 Stock Exchange. The novelty of the research lies in the research method using a Dynamic Panel Data, which has considered the effect over time. The results of this study are expected to be used as important input for policy makers in addressing the impact of IFRS adoption on the quality of corporate financial reports. &nbsp;Globalisasi menyebabkan arus keuangan dan investasi antar perusahaan dan antar negara semakin meningkat. Untuk memudahkan interaksi antar perusahaan antar negara tersebut maka dirasakan perlu bagi masing-masing negara untuk menggunakan standar laporan keuangan yang sama agar memudahkan semua pihak terkait untuk dapat membandingkan pelaporan lintas negara. IFRS merupakan standar pelaporan keuangan internasional yang dapat diadopsi oleh perusahaan di berbagai negara, namun belum semua negara mengadopsi standar tersebut. Penelitian ini bertujuan untuk menganalisis kembali bagaimana pengaruh tingkat adopsi IFRS terhadap kualitas laporan keuangan yang diukur dengan persistensi laba perusahaan khususnya yang terdaftar di Bursa Efek negara ASEAN-5. Kebaruan penelitian ini terletak pada metode penelitian dengan menggunakan Data Panel Dinamis, yang sudah mempertimbangkan efek antar waktu. Hasil penelitian ini diharapkan dapat dimanfaatkan sebagai masukan penting bagi para pembuat kebijakan di berbagai negara dalam mensikapi dampak adopsi IFRS terhadap kualitas laporan keuangan perusahaan. &nbsp