Fast Moving Window Algorithm for QR and Cholesky Decompositions

This paper proposes a fast moving window algorithm for QR and Cholesky decompositions by simultaneously applying data updating and downdating. The developed procedure is based on inner products and entails a similar downdating to that of the Chambers’ approach. For adding and deleting one row of data from the original matrix, a detailed analysis shows that the proposed algorithm outperforms existing ones in terms or computational efficiency, if the number of columns exceeds 7. For a large number of columns, the proposed algorithm is numerically superior compared to the traditional sequential technique.

Multi-mode approximations to wave scattering by an uneven bed

Approximations to the scattering of linear surface gravity waves on water of varying quiescent depth are Investigated by means of a variational approach. Previous authors have used wave modes associated with the constant depth case to approximate the velocity potential, leading to a system of coupled differential equations. Here it is shown that a transformation of the dependent variables results in a much simplified differential equation system which in turn leads to a new multi-mode 'mild-slope' approximation. Further, the effect of adding a bed mode is examined and clarified. A systematic analytic method is presented for evaluating inner products that arise and numerical experiments for two-dimensional scattering are used to examine the performance of the new approximations.

Dichotomous Hamiltonians with unbounded entries and solutions of Riccati equations

An operator Riccati equation from systems theory is considered in the case that all entries of the associated Hamiltonian are unbounded. Using a certain dichotomy property of the Hamiltonian and its symmetry with respect to two different indefinite inner products, we prove the existence of nonnegative and nonpositive solutions of the Riccati equation. Moreover, conditions for the boundedness and uniqueness of these solutions are established.

Stochastic Arithmetic Theory and Experiments

Stochastic arithmetic has been developed as a model for exact computing with imprecise data. Stochastic arithmetic provides confidence intervals for the numerical results and can be implemented in any existing numerical software by redefining types of the variables and overloading the operators on them. Here some properties of stochastic arithmetic are further investigated and applied to the computation of inner products and the solution to linear systems. Several numerical experiments are performed showing the efficiency of the proposed approach.

Semi-Symmetric Algebras: General Constructions. Part II

2000 Mathematics Subject Classification: 15A69, 15A78.

The sweet aroma of success: Modification of products for new markets in the case of TORQ by Di Bella Coffee

In 2002, Phillip Di Bella’s childhood passion for coffee and keen entrepreneurial spirit led him to establish a small coffee roasting warehouse in in the inner suburbs of Brisbane (Di Bella, 2012). With a keen sense of direction and passion for his coffee products and providing unparalleled customer service, Di Bella Coffee quickly grew to become a key player in the coffee roasting scene. This passion for the ultimate coffee experience is evident in the firm’s logo ‘Di Bella Coffee Inspires Passion’. Phillip Di Bella stated that ‘the common denominator of this company is about inspiration and passion. We are not a coffee company, we are a people company. You know, are we inspiring you from the moment you walk in the door to the moment you leave. If you are not feeling inspired then we haven’t done our job properly as a company’. Fundamentally, providing the ultimate coffee experience, as detailed in the following case is one in which focuses on the coffee consumption experience, not the coffee itself. Over that last 10 years Di Bella Coffee has constantly strived for the ultimate coffee, while expanding business operations into the booming Asian coffee market, establishing headquarters in Shanghai in 2010. In 2011, Di Bella Coffee commenced their second international venture with the launch of operations in India (Di Bella Coffee, 2012); followed shortly by the creation of a new category of coffee, set to revolutionise to coffee industry. The fusion of two traditional forms of coffee; espresso coffee and instant coffee, to create a third category- espresso instant, led to the development of TORQ by Di Bella.

Impaired retinal angiogenesis in diabetes: role of advanced glycation end products and galectin-3

Suppression of angiogenesis during diabetes is a recognized phenomenon but is less appreciated within the context of diabetic retinopathy. The current study has investigated regulation of retinal angiogenesis by diabetic serum and determined if advanced glycation end products (AGEs) could modulate this response, possibly via AGE-receptor interactions. A novel in vitro model of retinal angiogenesis was developed and the ability of diabetic sera to regulate this process was quantified. AGE-modified serum albumin was prepared according to a range of protocols, and these were also analyzed along with neutralization of the AGE receptors galectin-3 and RAGE. Retinal ischemia and neovascularization were also studied in a murine model of oxygen-induced proliferative retinopathy (OIR) in wild-type and galectin-3 knockout mice (gal3(-/-)) after perfusion of preformed AGEs. Serum from nondiabetic patients showed significantly more angiogenic potential than diabetic serum (P <0.0001) and within the diabetic group, poor glycemic control resulted in more AGEs but less angiogenic potential than tight control (P <0.01). AGE-modified albumin caused a dose-dependent inhibition of angiogenesis (P <0.001), and AGE receptor neutralization significantly reversed the AGE-mediated suppression of angiogenesis (P <0.01). AGE-treated wild-type mice showed a significant increase in inner retinal ischemia and a reduction in neovascularization compared with non-AGE controls (P <0.001). However, ablation of galectin-3 abolished the AGE-mediated increase in retinal ischemia and restored the neovascular response to that seen in controls. The data suggest a significant suppression of angiogenesis by the retinal microvasculature during diabetes and implicate AGEs and AGE-receptor interactions in its causation.

Three motAB stator gene products in Bdellovibrio bacteriovorus contribute to motility of a single flagellum during predatory and prey-independent growth

The predatory bacterium Bdellovibrio bacteriovorus uses flagellar motility to locate regions rich in Gram-negative prey bacteria, colliding and attaching to prey and then ceasing flagellar motility. Prey are then invaded to form a "bdelloplast" in a type IV pilus-dependent process, and prey contents are digested, allowing Bdellovibrio growth and septation. After septation, Bdellovibrio flagellar motility resumes inside the prey bdelloplast prior to its lysis and escape of Bdellovibrio progeny. Bdellovibrio can also grow slowly outside prey as long flagellate host-independent (HI) cells, cultured on peptone-rich media. The B. bacteriovorus HD100 genome encodes three pairs of MotAB flagellar motor proteins, each of which could potentially form an inner membrane ion channel, interact with the FliG flagellar rotor ring, and produce flagellar rotation. In 2004, Flannagan and coworkers (R. S. Flannagan, M. A. Valvano, and S. F. Koval, Microbiology 150:649-656, 2004) used antisense RNA and green fluorescent protein (GFP) expression to downregulate a single Bdellovibrio motA gene and reported slowed release from the bdelloplast and altered motility of the progeny. Here we inactivated each pair of motAB genes and found that each pair contributes to motility, both predatorily, inside the bdelloplast and during HI growth; however, each pair was dispensable, and deletion of no pair abolished motility totally. Driving-ion studies with phenamil, carbonyl cyanide m-chlorophenylhydrazone (CCCP), and different pH and sodium conditions indicated that all Mot pairs are proton driven, although the sequence similarities of each Mot pair suggests that some may originate from halophilic species. Thus, Bdellovibrio is a "dedicated motorist," retaining and expressing three pairs of mot genes.

Monotonicity and asymptotics of zeros of Sobolev type orthogonal polynomials: A general case

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Monotonicity of zeros of Laguerre-Sobolev-type orthogonal polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Monotonicity of zeros of Jacobi-Sobolev type orthogonal polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Monotonicity and asymptotics of zeros of Laguerre-Sobolev-type orthogonal polynomials of higher order derivatives

In this paper we analyze the location of the zeros of polynomials orthogonal with respect to the inner product where α >-1, N ≥ 0, and j ∈ N. In particular, we focus our attention on their interlacing properties with respect to the zeros of Laguerre polynomials as well as on the monotonicity of each individual zero in terms of the mass N. Finally, we give necessary and sufficient conditions in terms of N in order for the least zero of any Laguerre-Sobolev-type orthogonal polynomial to be negative. © 2011 American Mathematical Society.

Multivariate sobolev-type orthogonal polynomials

Multivariate orthogonal polynomials associated with a Sobolev-type inner product, that is, an inner product defined by adding to a measure the evaluation of the gradients in a fixed point, are studied. Orthogonal polynomials and kernel functions associated with this new inner product can be explicitly expressed in terms of those corresponding with the original measure. We apply our results to the particular case of the classical orthogonal polynomials on the unit ball, and we obtain the asymptotics of the kernel functions. © 2011 Universidad de Jaén.

Comportamento assintótico dos polinômios ortogonais de Sobolev-Jacobi e Sobolev-Laguerre

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)