Tridiagonal canonical matrices of bilinear or sesquilinear forms and of pairs of symmetric, skew-symmetric, or Hermitian forms

Tridiagonal canonical forms of square matrices under congruence or *congruence, pairs of symmetric or skew-symmetric matrices under congruence, and pairs of Hermitian matrices under *congruence are given over an algebraically closed field of characteristic different from 2. (C) 2008 Elsevier Inc. All rights reserved.

QRT: A Qr-based tridiagonalization algorithm for nonsymmetric matrices

The stable similarity reduction of a nonsymmetric square matrix to tridiagonal form has been a long-standing problem in numerical linear algebra. The biorthogonal Lanczos process is in principle a candidate method for this task, but in practice it is confined to sparse matrices and is restarted periodically because roundoff errors affect its three-term recurrence scheme and degrade the biorthogonality after a few steps. This adds to its vulnerability to serious breakdowns or near-breakdowns, the handling of which involves recovery strategies such as the look-ahead technique, which needs a careful implementation to produce a block-tridiagonal form with unpredictable block sizes. Other candidate methods, geared generally towards full matrices, rely on elementary similarity transformations that are prone to numerical instabilities. Such concomitant difficulties have hampered finding a satisfactory solution to the problem for either sparse or full matrices. This study focuses primarily on full matrices. After outlining earlier tridiagonalization algorithms from within a general framework, we present a new elimination technique combining orthogonal similarity transformations that are stable. We also discuss heuristics to circumvent breakdowns. Applications of this study include eigenvalue calculation and the approximation of matrix functions.

Algoritmo paralelo para determinação de autovalores de matrizes hermitianas

Dissertação (mestrado)–Universidade de Brasília, Universidade UnB de Planaltina, Programa de Pós-Graduação em Ciência de Materiais, 2015.

Tridiagonal Reproducing Kernels and Subnormality

We consider analytic reproducing kernel Hilbert spaces H with orthonormal bases of the form {(a(n) + b(n)z)z(n) : n >= 0}. If b(n) = 0 for all n, then H is a diagonal space and multiplication by z, M-z, is a weighted shift. Our focus is on providing extensive classes of examples for which M-z is a bounded subnormal operator on a tridiagonal space H where b(n) not equal 0. The Aronszajn sum of H and (1 - z)H where H is either the Hardy space or the Bergman space on the disk are two such examples.

Promoting the use of cycling as an environmentally and socially sustainable form of transport.

Solar Cities Congress 2008 “Energising Sustainable Communities – Options for Our Future” THEME 3: Climate Change. Impact on Society and Culture. Sub Theme: planning and implementing holistic strategies for sustainable transport Abstract Promoting the use of cycling as an environmentally and socially sustainable form of transport. We need to reduce carbon emissions. We need to reduce fuel consumption. We need to reduce pollution. We need to reduce traffic congestion. As obesity levels and associated health problems in the developed nations continue to increase we need to adopt a healthier lifestyle. Few if any would argue with these statements. In fact many would consider these problems to be amongst the most urgent that our society faces. What if we had a vehicle that uses no fossil fuel to power it, creates no pollution, takes up far less space on the roads and promotes an active, healthy lifestyle. What if this machine would have energy efficiency levels 50 times greater than the car? This is a solution that is here, now and ready to go and many of us already own one. It is the humble bicycle. Although bicycle sales in Australia now outnumber car sales, bicycle use as a form of transport (as opposed to recreation) only constitutes around 3% to 4% of all trips. So, why are bicycles the forgotten form of transport if they promise to deliver the benefits that I have just outlined? This paper examines the underlying reasons for the relatively low use of bicycles as a means of transport. It identifies the areas of greatest potential for encouraging the use of the world’s most efficient form of transport. Tim Williams - May 2007

Estimating total cross sections from neutron-nucleus collisions using a simple functional form

Total cross sections for neutron scattering from nuclei, with energies ranging from 10 to 600 MeV and from many nuclei spanning the mass range 6Li to 238U, have been analyzed using a simple, three-parameter, functional form. The calculated cross sections are compared with results obtained by using microscopic (g-folding) optical potentials as well as with experimental data. The functional form reproduces those total cross sections very well. When allowance is made for Ramsauer-like effects in the scattering, the parameters of the functional form required vary smoothly with energy and target mass. They too can be represented by functions of energy and mass.

Consonance in urban form : morphogenetic analysis of architectural elements within urban forms

"By understanding how places have evolved, we are better able to guide development and change in the urban fabric and avoid the incongruity created by so much of the modern environment" (MacCormac, R (1996), An anatomy of London, Built Environment, Dec 1996 This paper proposes a theory on the relevance of mapping the evolutionary aspects of historical urban form in order to develop a measure of evaluating architectural elements within urban forms, through to deriving parameters for new buildings. By adopting Conzen's identification of the tripartite division of urban form; the consonance inurban form of a particular palce resides in the elements and measurable values tha makeup the fine grain aggregates of urban form. The paper will demonstrate throughthe case study of Brisbane in Australia, a method of conveying these essential components that constitute a cities continuity of form and active usage. By presenting the past as a repository of urban form characteristics, it is argued that concise architectural responses that stem from such knowledge should result in an engaged urban landscape. The essential proposition is that urban morphology is a missing constituent in the process of urban design, and that the approach of the geographical discipline to the study of urban morphology holds the key to providing the evidence of urban growth characteristics, and this methodology suggests possibilities for an architectural approach that can comprehensively determine qualitative aspects of urban buildings. The relevance of this research lies in a potential to breach the limitations of current urban analysis whilst continuing the evolving currency of urban morphology as an integral practice in the design of our cities.

Structuring free-form tagging in online news

Tagging has become one of the key activities in next generation websites which allow users selecting short labels to annotate, manage, and share multimedia information such as photos, videos and bookmarks. Tagging does not require users any prior training before participating in the annotation activities as they can freely choose any terms which best represent the semantic of contents without worrying about any formal structure or ontology. However, the practice of free-form tagging can lead to several problems, such as synonymy, polysemy and ambiguity, which potentially increase the complexity of managing the tags and retrieving information. To solve these problems, this research aims to construct a lightweight indexing scheme to structure tags by identifying and disambiguating the meaning of terms and construct a knowledge base or dictionary. News has been chosen as the primary domain of application to demonstrate the benefits of using structured tags for managing the rapidly changing and dynamic nature of news information. One of the main outcomes of this work is an automatically constructed vocabulary that defines the meaning of each named entity tag, which can be extracted from a news article (including person, location and organisation), based on experts suggestions from major search engines and the knowledge from public database such as Wikipedia. To demonstrate the potential applications of the vocabulary, we have used it to provide more functionalities in an online news website, including topic-based news reading, intuitive tagging, clipping and sharing of interesting news, as well as news filtering or searching based on named entity tags. The evaluation results on the impact of disambiguating tags have shown that the vocabulary can help to significantly improve news searching performance. The preliminary results from our user study have demonstrated that users can benefit from the additional functionalities on the news websites as they are able to retrieve more relevant news, clip and share news with friends and families effectively.

Closed-form design equations for decoupling networks of small arrays

Small element spacing in compact arrays results in strong mutual coupling between the array elements. A decoupling network consisting of reactive cross-coupling elements can alleviate problems associated with the coupling. Closed-form design equations for the decoupling networks of symmetrical arrays with two or three elements are presented.