Direct Computation of Operational Matrices for Polynomial Bases

Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.

Piezoaeroelastic Modeling and Analysis of a Generator Wing with Continuous and Segmented Electrodes

Unmanned air vehicles (UAVs) and micro air vehicles (MAVs) constitute unique application platforms for vibration-based energy harvesting. Generating usable electrical energy during their mission has the important practical value of providing an additional energy source to run small electronic components. Electrical energy can be harvested from aeroelastic vibrations of lifting surfaces of UAVs and MAVs as they tend to have relatively flexible wings compared to their larger counterparts. In this work, an electromechanically coupled finite element model is combined with an unsteady aerodynamic model to develop a piezoaeroelastic model for airflow excitation of cantilevered plates representing wing-like structures. The electrical power output and the displacement of the wing tip are investigated for several airflow speeds and two different electrode configurations (continuous and segmented). Cancelation of electrical output occurs for typical coupled bending-torsion aeroelastic modes of a cantilevered generator wing when continuous electrodes are used. Torsional motions of the coupled modes become relatively significant when segmented electrodes are used, improving the broadband performance and altering the flutter speed. Although the focus is placed on the electrical power that can be harvested for a given airflow speed, shunt damping effect of piezoelectric power generation is also investigated for both electrode configurations.

Orthodontic-surgical treatment of Class III malocclusion with extraction of an impacted canine and multi-segmented maxillary surgery

Establishment of a treatment plan is based on efficacy and easy application by the clinician, and acceptance by the patient. Treatment of adult patients with Class III malocclusion might require orthognathic surgery, especially when the deformity is severe, with a significant impact on facial esthetics. Impacted teeth can remarkably influence treatment planning, which should be precise and concise to allow a reasonably short treatment time with low biologic cost. We report here the case of a 20-year-old man who had a skeletal Class III malocclusion and impaction of the maxillary right canine, leading to remarkable deviation of the maxillary midline; this was his chief complaint. Because of the severely deviated position of the impacted canine, treatment included extraction of the maxillary right canine and left first premolar for midline correction followed by leveling, alignment, correction of compensatory tooth positioning, and orthognathic surgery to correct the skeletal Class III malocclusion because of the severe maxillary deficiency. This treatment approach allowed correction of the maxillary dental midline discrepancy to the midsagittal plane and establishment of good occlusion and optimal esthetics. (Am J Orthod Dentofacial Orthop 2010;137:840-9)

Generating Segmented Quality Meshes from Images

Techniques devoted to generating triangular meshes from intensity images either take as input a segmented image or generate a mesh without distinguishing individual structures contained in the image. These facts may cause difficulties in using such techniques in some applications, such as numerical simulations. In this work we reformulate a previously developed technique for mesh generation from intensity images called Imesh. This reformulation makes Imesh more versatile due to an unified framework that allows an easy change of refinement metric, rendering it effective for constructing meshes for applications with varied requirements, such as numerical simulation and image modeling. Furthermore, a deeper study about the point insertion problem and the development of geometrical criterion for segmentation is also reported in this paper. Meshes with theoretical guarantee of quality can also be obtained for each individual image structure as a post-processing step, a characteristic not usually found in other methods. The tests demonstrate the flexibility and the effectiveness of the approach.

Foliations and polynomial diffeomorphisms of R(3)

Let Y = (f, g, h): R(3) -> R(3) be a C(2) map and let Spec(Y) denote the set of eigenvalues of the derivative DY(p), when p varies in R(3). We begin proving that if, for some epsilon > 0, Spec(Y) boolean AND (-epsilon, epsilon) = empty set, then the foliation F(k), with k is an element of {f, g, h}, made up by the level surfaces {k = constant}, consists just of planes. As a consequence, we prove a bijectivity result related to the three-dimensional case of Jelonek`s Jacobian Conjecture for polynomial maps of R(n).

Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 3

In this paper, we classify all the global phase portraits of the quadratic polynomial vector fields having a rational first integral of degree 3. (C) 2008 Elsevier Ltd. All rights reserved.

The univalent polynomial of Suffridge as a summability kernel

A positive summability trigonometric kernel {K(n)(theta)}(infinity)(n=1) is generated through a sequence of univalent polynomials constructed by Suffridge. We prove that the convolution {K(n) * f} approximates every continuous 2 pi-periodic function f with the rate omega(f, 1/n), where omega(f, delta) denotes the modulus of continuity, and this provides a new proof of the classical Jackson`s theorem. Despite that it turns out that K(n)(theta) coincide with positive cosine polynomials generated by Fejer, our proof differs from others known in the literature.

Generating segmented meshes from textured color images

This paper presents a new framework for generating triangular meshes from textured color images. The proposed framework combines a texture classification technique, called W-operator, with Imesh, a method originally conceived to generate simplicial meshes from gray scale images. An extension of W-operators to handle textured color images is proposed, which employs a combination of RGB and HSV channels and Sequential Floating Forward Search guided by mean conditional entropy criterion to extract features from the training data. The W-operator is built into the local error estimation used by Imesh to choose the mesh vertices. Furthermore, the W-operator also enables to assign a label to the triangles during the mesh construction, thus allowing to obtain a segmented mesh at the end of the process. The presented results show that the combination of W-operators with Imesh gives rise to a texture classification-based triangle mesh generation framework that outperforms pixel based methods. Crown Copyright (C) 2009 Published by Elsevier Inc. All rights reserved.

An application of lattice basis reduction to polynomial identities for algebraic structures

The authors` recent classification of trilinear operations includes, among other cases, a fourth family of operations with parameter q epsilon Q boolean OR {infinity}, and weakly commutative and weakly anticommutative operations. These operations satisfy polynomial identities in degree 3 and further identities in degree 5. For each operation, using the row canonical form of the expansion matrix E to find the identities in degree 5 gives extremely complicated results. We use lattice basis reduction to simplify these identities: we compute the Hermite normal form H of E(t), obtain a basis of the nullspace lattice from the last rows of a matrix U for which UE(t) = H, and then use the LLL algorithm to reduce the basis. (C) 2008 Elsevier Inc. All rights reserved.

A NOTE ON FREE GROUPS IN THE RING OF FRACTIONS OF SKEW POLYNOMIAL RINGS

Let L be a function field over the rationals and let D denote the skew field of fractions of L[t; sigma], the skew polynomial ring in t, over L, with automorphism sigma. We prove that the multiplicative group D(x) of D contains a free noncyclic subgroup.

Polynomial identities for the ternary cyclic sum

We simplify the results of Bremner and Hentzel [J. Algebra 231 (2000) 387-405] on polynomial identities of degree 9 in two variables satisfied by the ternary cyclic sum [a, b, c] abc + bca + cab in every totally associative ternary algebra. We also obtain new identities of degree 9 in three variables which do not follow from the identities in two variables. Our results depend on (i) the LLL algorithm for lattice basis reduction, and (ii) linearization operators in the group algebra of the symmetric group which permit efficient computation of the representation matrices for a non-linear identity. Our computational methods can be applied to polynomial identities for other algebraic structures.

POLYNOMIAL AND GROUP IDENTITIES IN ALTERNATIVE LOOP ALGEBRAS

We investigate polynomial identities on an alternative loop algebra and group identities on its (Moufang) unit loop. An alternative loop ring always satisfies a polynomial identity, whereas whether or not a unit loop satisfies a group identity depends on factors such as characteristic and centrality of certain kinds of idempotents.

POLYNOMIAL IDENTITIES OF FINITE DIMENSIONAL SIMPLE ALGEBRAS

Let F be an algebraically closed field and let A and B be arbitrary finite dimensional simple algebras over F. We prove that A and B are isomorphic if and only if they satisfy the same identities.

Classificação de sistemas meteorológicos e comparação da precipitação estimada pelo radar e medida pela rede telemétrica na bacia hidrográfica do alto Tietê

Foram analisadas características da precipitação estimada a partir de 145.194 campos de refletividade, de um total de 827 dias entre 1998 e 2003, obtidos do Radar Meteorológico de São Paulo (RSP). Os eventos foram classificados de acordo com intensidades de precipitação; em Convectivos (EC) e Estratiformes (EE). Quanto à morfologia, cinco tipos de sistemas foram identificados; Convecção Isolada (CI), Brisa Marítima (BM), Linhas de Instabilidade (LI), Bandas Dispersas (BD) e Frentes Frias (FF). Eventos convectivos dominam na primavera e verão e estratiformes no outono e inverno. A CI e a BM tiveram maiores picos de atuação entre outubro e março enquanto as FF de abril a setembro. BD atuam durante todo o ano e as LI só não foram observadas nos meses de junho e julho. Uma comparação pontual entre a precipitação medida pela telemetria e estimada com o radar foi realizada e, mostrou haver, na maioria dos casos, um viés positivo do RSP, para acumulações de 10, 30 e 60 minutos. Com o objetivo de integrar as estimativas de precipitação do radar com as medidas da rede telemétrica, por meio de uma análise objetiva estatística, foram obtidas dos campos de precipitação do radar as estruturas das correlações espaciais em função da distância para acumulações de chuva de 15, 30, 60 e 120 minutos para os cinco tipos de sistemas precipitantes que foram caracterizados. As curvas das correlações espaciais médias de todos os eventos de precipitação de cada sistema foram ajustadas por funções polinomiais de sexta ordem. Os resultados indicam diferenças significativas na estrutura espacial das correlações entre os sistemas precipitantes.

A new genus and a new species of Clausiidae (Crustacea, Copepoda) parasitic on Dipolydora armata (Polychaeta, Spionidae) in Brazil

A new genus and species of parasitic copepod (Clausiidae), Spionicola mystaceus, associated with the polychaete Dipolydora armata (Spionidae) is described and figured. The new copepod has an elongate body, 5-segmented antennule, 2-segmented rami on legs 1 and 2, 2 spines representing leg 3, no leg 4, leg 5 well developed and reduced armature elements on feeding limbs. The host is a mollusk-shell borer, collected off São Sebastião Island, State of São Paulo, Brazil.