Riemannian Gaussian distributions on the space of positive-definite quaternion matrices

Recently, Riemannian Gaussian distributions were defined on spaces of positive-definite real and complex matrices. The present paper extends this definition to the space of positive-definite quaternion matrices. In order to do so, it develops the Riemannian geometry of the space of positive-definite quaternion matrices, which is shown to be a Riemannian symmetric space of non-positive curvature. The paper gives original formulae for the Riemannian metric of this space, its geodesics, and distance function. Then, it develops the theory of Riemannian Gaussian distributions, including the exact expression of their probability density, their sampling algorithm and statistical inference.Comment: 8 pages, submitted to GSI 201

Guidelines for the establishment of a search and rescue service

The main reason for embarking on this topic is the urgent necessity for establishing a Search and Rescue Service in the Kingdom of Saudi Arabia. Many disasters have been caused by a minor accident such as electrical spark , or a match stick, hesitation in taking actions to avoid collisions, which result in loss of lives and property. To minimize such losses one must have a responsive Search and Rescue Service, which unfortunately is not properly established in the Kingdom. The area is congested with traffic without any search and rescue coverage by the Kingdom or even neighbouring countries, which should be available in all coastal states to render such services. This is part of the coastal states international obligation as stated in :- 1) The International Convention for the Safety of Life at Sea, 1974 (SOLAS \u2774), Regulation 15 - Chapter V. 2) The UN Convention on the High Seas, 1958 - Article 12(2). 3) The UN Convention on the Law of the Sea, 1978\u27 (UNCLOS III). Article 98 (2) refers to: Duty to render assistance. As I have discovered, carrying out research in this field was hard but my educational background and speciality as a technical person (Marine Engineer) have assisted greatly whilst conducting such a task. However, because of the importance and necessity of this topic for the Kingdom which oversees two strategic maritime zones (the Red Sea and the Arabian Gulf) each as important as the other, and since the Kingdom is the leading country in the region in many aspects, she must obviously and automatically play the leading role and take the necessary steps to establish such a valuable and active service in the field of Search and Rescue . She should take into consideration her ability to conduct such a service after careful study and well established research nationally, regionally, and internationally. Therefore this study has chiefly been derived from information provided by states which have had considerable experience in the field of Search and Rescue, e.g. Federal Republic of Germany, Sweden, United Kingdom, United States, and Canada. The study and research was not limited to reading their publications. Field visits were made to most of them mainly: United States of America, the Federal Republic of Germany, as well as the host country of the World Maritime University - Sweden. Even though the Kingdom of Saudi Arabia has the means to establish a Search and Rescue Service with the latest techniques available, my study was based on providing practical and economical Search and Rescue coverage of the area

Decompounding on compact Lie groups

Noncommutative harmonic analysis is used to solve a nonparametric estimation problem stated in terms of compound Poisson processes on compact Lie groups. This problem of decompounding is a generalization of a similar classical problem. The proposed solution is based on a char- acteristic function method. The treated problem is important to recent models of the physical inverse problem of multiple scattering.Comment: 26 pages, 3 figures, 25 reference

A review of social cohesion initiatives and challenges with a focus on Jordan and education

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Spectral studies of some hydroxy-derivatives of anthraquinones

The u.v., visible, and i.r. spectra of several hydroxy-anthraquinones are discussed and the bands are assigned. These bands are compared with those of anthracene and anthraquinone. The band at 207 nm. is assigned to a n-sigma* transition; the bands at 252, 272, and 326 nm. are assigned by measuring spectra in solvents of various polarities. The stability constant for the 12-dihydroxyanthraquinone-ethanol complex is obtained

Explicit Solution of the Time Domain Volume Integral Equation Using a Stable Predictor-Corrector Scheme

An explicit marching-on-in-time (MOT) scheme for solving the time domain volume integral equation is presented. The proposed method achieves its stability by employing, at each time step, a corrector scheme, which updates/corrects fields computed by the explicit predictor scheme. The proposedmethod is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit MOT schemes. Numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements

Leadership style, organisational culture and disputes in public construction

The increasing occurrence of construction disputes has compounded the fragmentation, complexity and adversarial nature of the construction industry. Disputes are associated with high cost, delays, low quality and even the destruction of important relationships among project parties that have taken long years to build and disputes have become ‘the rule rather than the exception’. Despite considerable attempts in literature towards dispute minimization in construction projects, very few studies have addressed the roots behind the occurrence of disputes. Leadership and organisational culture are key influential factors in the construction industry. Effective project leaders should, not only achieve the goals and objectives of the organisations they lead, but also, minimize conflicts and disputes. Also by instilling strong organisational culture, construction organisations can control dispute to minimum levels. Therefore, this study aims to draw research attention toward the core of disputes by providing theoretical insight and empirical investigation concerning the roots of this problem. A framework is presented to minimize disputes in public organisations of construction. The mixed methodology adopted includes a survey conducted to investigate the current practice and semi-structured interviews to explore best practice that combined to form a foundation for the framework that assess leaders and organisations to minimize construction disputes. The findings revealed that among the most significant dispute causes are: delay by the contractor, lack of team spirit, slow contractor response, poor communication, unrealistic tendering, inadequate contractor selection, unforeseen site conditions and inadequate site supervision. Significant correlations were noted between transformational leadership and the most significant dispute causes. Also significant association was indicated between clan culture and disputes. Emerging from the study is that transformational leadership and clan culture appear to be the most suitable leadership style and organisational culture, respectively, in public construction organisations (owner organisations) that help minimize disputes with contractors