# Artigos - Matemática - IBILCE

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ItemArtigo Coherent pairs of measures of the second kind on the real line and Sobolev orthogonal polynomials. An application to a Jacobi case(2023-01-01) Marcato, G. A. ; Marcellán, F. ; Ranga, A. Sri ; Lun, Yen Chi ; Universidade Estadual Paulista (UNESP) ; Universidad Carlos III de MadridExibir mais The aim here is to consider the orthogonal polynomials (Formula presented.) with respect to an inner product of the type (Formula presented.), where (Formula presented.) and (Formula presented.) is a coherent pair of positive measures of the second kind on the real line (CPPM2K on the real line). Properties of (Formula presented.) and the connection formulas they satisfy with the orthogonal polynomials associated with the measure ν0 are analyzed. It is also shown that the zeros of (Formula presented.) are the eigenvalues of a matrix, which is a single line modification of the (Formula presented.) Jacobi matrix associated with the measure ν0. The paper also looks at a special example of a CPPM2K on the real line, where one of the measures is the Jacobi measure, and provides a much more detailed study of the properties of the orthogonal polynomials and the corresponding connection coefficients. In particular, the relation that these connection coefficients have with the Wilson polynomials is exposed.Exibir mais ItemArtigo Algebraic integers of pure sextic extensions(2022-01-01) de Andrade, Antonio Aparecido ; Facini, Linara Stéfani ; Esteves, Livea Cichito ; Universidade Estadual Paulista (UNESP)Exibir mais Let K = Q(θ), where (Formula Presented), be a pure sextic field with d ≠ 1 a square free integer. In this paper, we characterize completely whether {1, θ,…, θ5} is an integral basis of K or do not. When d ≢ ±1,±17,±10,−15,−11,−7,−3, 5, 13(mod 36) we prove that K has a power integral basis. Furthermore, for the other cases we present an integral basisExibir mais ItemArtigo Coherent pairs of moment functionals of the second kind and associated orthogonal polynomials and Sobolev orthogonal polynomials(2023-09-01) Hancco Suni, M. ; Marcato, G. A. ; Marcellán, F. ; Sri Ranga, A. ; Universidade Estadual Paulista (UNESP) ; Universidad Carlos III de MadridExibir mais Given a pair of quasi-definite moment functionals {v0,v1} we introduce the concept of coherence of the second kind in terms of an algebraic relation that the corresponding sequences of orthogonal polynomials satisfy. We characterize such moment functionals and give some illustrative examples taking into account they are semiclassical of class at most one. The relation between the corresponding monic Jacobi matrices is stated. For a pair of moment functionals satisfying the coherence property of the second kind, a Sobolev inner product is introduced. The connection formulas between the sequence of monic orthogonal polynomials associated with such a Sobolev inner product and the sequence of monic polynomials orthogonal with respect to the moment functional v0 are given.Exibir mais ItemArtigo Global Phase Portrait and Local Integrability of Holomorphic Systems(2023-03-01) Gouveia, Luiz F. S. ; da Silva, Paulo R. ; Rondón, Gabriel ; Universidade Estadual Paulista (UNESP)Exibir mais Planar holomorphic systems x˙ = u(x, y) , y˙ = v(x, y) are those that u= Re (f) and v= Im (f) for some holomorphic function f(z). They have important dynamical properties, highlighting, for example, the fact that they do not have limit cycles and that center-focus problem is trivial. In particular, the hypothesis that a polynomial system is holomorphic reduces the number of parameters of the system. Although a polynomial system of degree n depends on n2+ 3 n+ 2 parameters, a polynomial holomorphic depends only on 2 n+ 2 parameters. In this work, in addition to prove that holomorphic systems are locally integrable, we classify all the possible global phase portraits, on the Poincaré disk, of systems z˙ = f(z) and z˙ = 1 / f(z) , where f(z) is a polynomial of degree 2, 3 and 4 in the variable z∈ C. We also classify all the possible global phase portraits of Moebius systems z˙=Az+BCz+D, where A, B, C, D∈ C, AD- BC≠ 0.Exibir mais ItemArtigo From Solutions to Linear Ordinary Differential Equations to Vertex Operators(2023-03-01) Salehyan, Parham ; Universidade Estadual Paulista (UNESP)Exibir mais Using the canonical isomorphism between the exterior power of solutions to generic linear Ordinary Differential Equations of order r< ∞ and the polynomial ring with r indeterminates, we define and compute certain vertex operators whose expression for r= ∞ is precisely that occurring in the classical treatment of the boson-fermion correspondence.Exibir mais ItemArtigo On multivariate orthogonal polynomials and elementary symmetric functions(2023-01-01) Bracciali, Cleonice F. ; Piñar, Miguel A. ; Universidade Estadual Paulista (UNESP) ; Facultad de Ciencias. Universidad de GranadaExibir mais We study families of multivariate orthogonal polynomials with respect to the symmetric weight function in d variables Bγ(x)=∏i=1dω(xi)∏i - 1 , where ω(t) is an univariate weight function in t∈ (a, b) and x= (x1, x2, … , xd) with xi∈ (a, b). Applying the change of variables xi, i= 1 , 2 , … , d, into ur, r= 1 , 2 , … , d, where ur is the r-th elementary symmetric function, we obtain the domain region in terms of the discriminant of the polynomials having xi, i= 1 , 2 , … , d, as its zeros and in terms of the corresponding Sturm sequence. Choosing the univariate weight function as the Hermite, Laguerre, and Jacobi weight functions, we obtain the representation in terms of the variables ur for the partial differential operators such that the respective Hermite, Laguerre, and Jacobi generalized multivariate orthogonal polynomials are the eigenfunctions. Finally, we present explicitly the partial differential operators for Hermite, Laguerre, and Jacobi generalized polynomials, for d= 2 and d= 3 variables.Exibir mais ItemArtigo Half-automorphism group of a class of Bol loops(2023-01-01) Souza de Barros, Dylene Agda ; Souza dos Anjos, Giliard ; Universidade Federal de Uberlândia (UFU) ; Universidade Estadual Paulista (UNESP)Exibir mais A Bol loop is a loop that satisfies the Bol identity (Formula presented.). If L is a loop and (Formula presented.) is a bijection such that (Formula presented.), for every x, (Formula presented.), then f is called a half-automorphism of L. In this paper, we describe the half-automorphism group of a class of Bol loops of order 4m.Exibir mais ItemArtigo SOME APPLICATIONS OF CAUCHY’S MEAN VALUE THEOREM(2020-01-01) Lozada-Cruz, German ; Universidade Estadual Paulista (UNESP)Exibir mais In this note we prove some applications of Cauchy’s mean value theorem.Exibir mais ItemArtigo Decomposable Tensors in Exterior Powers(Springer, 2016-01-01) Gatto, Letterio ; Salehyan, Parham ; Gatto, L ; Salehyan, P ; Politecn Torino ; Universidade Estadual Paulista (UNESP)Exibir mais ItemArtigo Vertex Operators via Generic LRS(Springer, 2016-01-01) Gatto, Letterio ; Salehyan, Parham ; Gatto, L ; Salehyan, P ; Politecn Torino ; Universidade Estadual Paulista (UNESP)Exibir mais ItemArtigo Schubert Derivations(Springer, 2016-01-01) Gatto, Letterio ; Salehyan, Parham ; Gatto, L ; Salehyan, P ; Politecn Torino ; Universidade Estadual Paulista (UNESP)Exibir mais ItemArtigo Hasse-Schmidt Derivations on Exterior AlgebrasExibir mais ItemEditorial Hasse-Schmidt Derivations on Grassmann Algebras With Applications to Vertex Operators IntroductionExibir mais ItemArtigo Generic Linear Recurrence SequencesExibir mais ItemEditorial Hasse-Schmidt Derivations on Grassmann Algebras With Applications to Vertex Operators PrologueExibir mais ItemArtigo Algebras and DerivationsExibir mais ItemEditorial Hasse-Schmidt Derivations on Grassmann Algebras With Applications to Vertex Operators PrefaceExibir mais ItemArtigo A TRANSMISSION PROBLEM FOR WAVES UNDER TIME-VARYING DELAY AND TIME-VARYING WEIGHTS(Int Press Boston, Inc, 2022-09-01) Nonato, Carlos A. S. ; Raposo, Carlos A. ; Bastos, Waldemar D. ; Universidade Federal da Bahia (UFBA) ; Universidade Estadual Paulista (UNESP)Exibir mais This manuscript focuses on in the transmission problem for one dimensional waves with time-varying weights on the frictional damping and time-varying delay. We prove global exis-tence of solutions using Kato's variable norm technique and we show the exponential stability by the energy method with the construction of a suitable Lyapunov functional.Exibir mais ItemArtigo BI-LIPSCHITZ AND DIFFERENTIABLE SUFFICIENCY OF WEIGHTED JETS(2022-01-01) Costa, João Carlos Ferreira ; Saia, Marcelo José ; Soares Junior, Carlos Humberto ; Universidade Estadual Paulista (UNESP) ; Universidade Federal de São Carlos (UFSCar) ; CCN-UFPIExibir mais In this work we study bi-Lipschitz and differential sufficiency in the set of weighted jets of map germs of weighted degree. Our main result improves the degree of sufficiency of jets in the classical jet space obtained by Takens and by Martins-Fávaro. Moreover, we give a condition for the bi-Lipschitz sufficiency in both the weighted and non-weighted cases. Bi-Lipschitz sufficiency was not considered in those previously cited works.Exibir mais ItemArtigo Formulations and exact solution approaches for a coupled bin-packing and lot-sizing problem with sequence-dependent setups(2022-01-01) Melega, Gislaine Mara ; de Araujo, Silvio Alexandre ; Jans, Raf ; Morabito, Reinaldo ; Universidade Federal de São Carlos (UFSCar) ; Universidade Estadual Paulista (UNESP) ; GERAD ; HEC Montréal and CIRRELTExibir mais We study bin-packing and lot-sizing decisions in an integrated way. Such a problem appears in several manufacturing settings where items first need to be cut and next assembled into final products. One of the main novelties of this research is the modeling of the complex setup operations in the cutting process, which is modeled using a bin-packing formulation. More specifically, we consider the operation regarding the insertion or removal of the knives in the cutting process. Since this operation depends on the number of items cut in the current cutting process and in the previous one, the number of insertions and removals is sequence-dependent. The setups in the lot-sizing problem related to the production of the final products are also sequence-dependent. To deal with such a problem, two compact formulations are proposed. The sequence-dependent setups in the bin-packing problem are modeled in two different ways: based on known constraints from the literature, and based on the idea of micro-periods and a phantom cutting process. Due to the dependency in the setups decisions, the resulting formulations are mixed-integer nonlinear mathematical models. In order to deal with the sequence-dependent cutting and production setups, different polynomial-sized sets of subtour elimination constraints are employed to the coupled problem. A computational study is conducted in order to analyze the impact of the proposed approaches to model sequence-dependent setups, as well as the different subtour elimination strategies to solve the coupled bin-packing and lot-sizing problem, via an automatic-Benders decomposition algorithm.Exibir mais