Matemática e Estatística | Artigos em revistas internacionais / Papers in international journals
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- Abundance of elliptic dynamics on conservative three-flowsPublication . Bessa, Mário; Duarte, PedroWe consider a compact three-dimensional boundaryless Riemannian manifold M and the set of divergence-free (or zero divergence) vector fields without singularities, then we prove that this set has a C 1-residual (dense G_δ) such that any vector field inside it is Anosov or else its elliptical orbits are dense in the manifold M. This is the flow-setting counterpart of Newhouse's Theorem 1.3 (S. Newhouse, Quasi-elliptic periodic points in conservative dynamical systems, Am. J. Math. 99 (1977), pp. 1061–1087). Our result follows from two theorems, the first one says that if Λ is a hyperbolic invariant set for some class C^1 zero divergence vector field X on M, then either X is Anosov, or else Λ has empty interior. The second one says that, if X is not Anosov, then for any open set U ⊆ M there exists Y arbitrarily close to X such that Y t has an elliptical closed orbit through U.
- Acid phosphatase, some genetic polymorphism and obesity risk factors in adult womenPublication . Carolino, E.; Oliveira, T.; Silva, A. P.; Carvalho, R; Bicho, M.Recent works point out to a relation between some genetic factors and the predisposition for obesity. We believe, therefore, to be relevant to conduct this kind of study in the Portuguese population. In the present work the following genetic factors are considered: Haptoglobin phenotype, the Acid Phosphatasehenotype and two blood group systems, the MN System and the Lewis System. In addition, it was also considered one demographic factor, age, and one enzymatic activity, the Acid Phosphatase Activity. Haptoglobin (Hp) is a hemoglobin-binding protein of the immune system expressed by a genetic polymorphism with three major phenotypes. This protein is associated in some works with susceptibility for common pathological situations, such as some disorders related with obesity. The Acid phosphatase, more precisely the Acid phosphatase locus 1 (ACP1), is a highly polymorphic enzyme that has an important role in flavoenzyme activity and in the control of insulin receptor activity. High ACP1 activity was positively associated with high glycemic levels and with high body mass index (BMI) values. The MN blood system is a blood group system with three phenotypes each one showing different associations with some diseases, including some related with obesity. Finally, the Lewis System was focused on a single locus with two antigens, Le a and Le b. Confirming this characteristic as a genetic marker of obesity may contribute to the explanation of individual differences in the prevalence of obesity. The group under study involves 85 Portuguese adult women with complete data for all variables, taken from a data base with 714 subjects from the Genetic Laboratory, Centre of Endocrinology and Metabolism of University of Lisbon. The aim of the study is to explore and examine the relationship between the weight categories and the explanatory variables, with emphasis on risk for obesity. Therefore, an ordinal regression model was tried, considering as the regressor variables the Haptoglobin phenotype, Acid phosphatase (ACP1) phenotype, MN blood group system, Lewis system, the enzymatic activity of ACP1, age and some association effects between these factors. Some significant main effects were found at a 5% significance level: the phenotypeLe(a-b+) of Lewis System (p-value=0,021) and age (p-value=0,002). The phenotype Le(a-b+) of Lewis System is associated with a decreased risk for obesity (odds ratio 0,139; CI95%(0,016; 0,754)); age (as expected) is associated with an increased risk for obesity (odds ratio 1,11; CI95%(1,038; 1,190))
- An elegant 3-basis for inverse semigroupsPublication . Araújo, João; Kinyon, MichaelAbstract It is well known that in every inverse semigroup the binary operation and the unary operation of inversion satisfy the following three identities: x = (xx′)x, (xx′)(y′y) = (y′y)(xx′), (xy)z = x(yz′′). The goal of this note is to prove the converse, that is, we prove that an algebra of type ⟨2, 1⟩ satisfying these three identities is an inverse semigroup and the unary operation coincides with the usual inversion on such semigroups.
- An elementary proof that every singular matrix is a product of idempotent matricesPublication . Araújo, João; Mitchell, James D.In this note we give an elementary proof of a theorem first proved by J. A. Erdos [3]. This theorem, which is the main result of [3], states that every noninvertible n ⇥ n matrix is a finite product of matrices M with the property that M2 = M. (These are known as idempotent matrices. Noninvertible matrices are also called singular matrices.) An alternative formulation of this result reads: every noninvertible linear mapping of a finite dimensional vector space is a finite product of idempotent linear mappings ↵, linear mappings that satisfy ↵2 = ↵. This result was motivated by a result of J. M. Howie asserting that each selfmapping ↵ of a nonempty finite set X with image size at most |X|−1 (which occurs precisely when ↵ is noninvertible) is a product of idempotent mappings. We shall see that Erdos’s theorem is a consequence of Howie’s result. Together the papers [3] and [4] are cited in over one hundred articles, dealing with subjects including universal algebra, ring theory, topology, and combinatorics. Since its publication, various proofs of the result in [3] have appeared. For example, a semigroup theoretic proof appears in [1, pp. 121-131] and linear operator theory is used to prove the theorem in [2]. Here we give a new proof using a basic combinatorial argument. Unlike the previous proofs our argument involves only elementary results from linear algebra and one basic result concerning permutations. On the way to proving the main result of this note we provide a short proof of Howie’s result. Throughout this paper X signifies an arbitrary nonempty finite set. If ↵ : A ! X, where A is a subset of X, then A is the domain of ↵; we denote this set by dom(↵). Naturally, the set ↵(A) is called the image of ↵ and is denoted by im(↵). Recall that a mapping ↵ is injective (or one-to-one) if ↵(x) 6= ↵(y) for all x and y in dom(↵) with x 6= y. Let TX denote the set of all mappings from X to X with domain X. We note that this set is closed under composition of mappings and that this composition is associative. We now define one of the most important notions we require in the proofs in this note. For a mapping ↵ : dom(↵) ! X we say that ↵ is a restriction of an element " of TX if " and ↵ agree on the domain of ↵. In other words, "(x) = ↵(x) for all x in dom(↵). For x and y in X we denote the transposition that fixes every point of X other than x or y and that maps x to y, and vice versa, by (x y).
- An infinite dimensional umbral calculusPublication . Finkelshtein, Dmitri L.; Kondratiev, Yuri G.; Lytvynov, Eugene; Oliveira, Maria JoãoThe aim of this paper is to develop foundations of umbral calculus on the space $\mathcal D'$ of distributions on $\mathbb R^d$, which leads to a general theory of Sheffer polynomial sequences on $\mathcal D'$. We define a sequence of monic polynomials on $\mathcal D'$, a polynomial sequence of binomial type, and a Sheffer sequence. We present equivalent conditions for a sequence of monic polynomials on $\mathcal D'$ to be of binomial type or a Sheffer sequence, respectively. We also construct a lifting of a sequence of monic polynomials on $\mathbb R$ of binomial type to a polynomial sequence of binomial type on $\mathcal D'$, and a lifting of a Sheffer sequence on $\mathbb R$ to a Sheffer sequence on $\mathcal D'$. Examples of lifted polynomial sequences include the falling and rising factorials on $\mathcal D'$, Abel, Hermite, Charlier, and Laguerre polynomials on $\mathcal D'$. Some of these polynomials have already appeared in different branches of infinite dimensional (stochastic) analysis and played there a fundamental role.
- An uniqueness result for a class of wiener-space valued stochastic differential equationsPublication . Oliveira, Maria JoãoWe prove a generalization of Bismut-Itô-Kunita formula to infinite dimensions and derive an uniqueness result for Wiener space valued processes which holds for a special class of Bernstein processes.
- Analysis of a class of boundary value problems depending on left and right Caputo fractional derivativesPublication . Antunes, Pedro R. S.; Ferreira, Rui A. C.In this work we study boundary value problems associated to a nonlinear fractional ordinary differential equation involving left and right Caputo derivatives. We discuss the regularity of the solutions of such problems and, in particular, give precise necessary conditions so that the solutions are C1([0, 1]). Taking into account our analytical results, we address the numerical solution of those problems by the augmented-RBF method. Several examples illustrate the good performance of the numerical method.
- Analysis of residuals and adjustment in JRAPublication . Oliveira, Amilcar; Mexia, João Tiago; Oliveira, Teresa A.Joint Regression Analysis (JRA) is based in linear regression applied to yields, adjusting one linear regression per cultivar. The environmental indexes in JRA correspond to a non observable regressor which measures the productivity of the blocks in the field trials. Usually zig-zag algorithm is used in the adjustment. In this algorithm, minimizations for the regression coefficients alternate with those for the environmental indexes. The algorithm has performed very nicely but a general proof of convergence to the absolute minimum of the sum of squares of residues is still lucking. We now present a model for the residues that may be used to validate the adjustments carried out by the zig-zag algorithm.
- Analytic aspects of Poissonian white noise analysisPublication . Kondratiev, Yuri G.; Kuna, Tobias; Oliveira, Maria JoãoGeneral structures of Poissonian white noise analysis are presented.Simultaneously, the theory is developed on Poisson and Lebesgue- Poisson space. Both spaces have an own S-transform, well known in the Gaussian case. They give an extra connection between these two spaces via the Bargmann-Segal space. Test and generalized functions,different types of convolutions, and representations of creation and annihilation operators in the aforementioned spaces are considered.
- Application of BIBDR in health sciences using RPublication . Oliveira, Amilcar; Oliveira, Teresa A.The role of Experimental Design is very well known, considering applications to a broad range of areas, such as Agriculture, Biology, Medicine, Industry, Education, Economy, Engineering and Food Consumption Sciences. Motivated by the variety of problems faced in the several areas and simultaneously taking advantage of the emerging technological developments, new theoretical results, as well as new designs and structures, have been developed by researchers and practitioners accordingly to the needs. Experimental Design got a place among the most important statistical methodologies and, mainly because of allowing to separate variation sources, since the last century it has been strongly recommended for Health Sciences studies. In this area, particular attention has been devoted to Randomized Complete Block Designs and to Balanced Incomplete Block Designs (BIBD) - which allow testing simultaneously a number of treatments bigger than the block size. Thus, after a brief review of some particular BIBD properties and of BIBDR - Balanced Incomplete Blocks with Block Repetition, an applications to Health Sciences simulated data is illustrated, by exploring R software