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Academic literature on the topic 'Multilinear polynomial'

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Published: 4 June 2021

Last updated: 15 February 2022

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Journal articles on the topic "Multilinear polynomial"

1

Šiljak, Dragoslav D., and Matija D. Šiljak. "Nonnegativity of uncertain polynomials." Mathematical Problems in Engineering 4, no. 2 (1998): 135–63. http://dx.doi.org/10.1155/s1024123x98000763.

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The purpose of this paper is to derive tests for robust nonnegativity of scalar and matrix polynomials, which are algebraic, recursive, and can be completed in finite number of steps. Polytopic families of polynomials are considered with various characterizations of parameter uncertainty including affine, multilinear, and polynomic structures. The zero exclusion condition for polynomial positivity is also proposed for general parameter dependencies. By reformulating the robust stability problem of complex polynomials as positivity of real polynomials, we obtain new sufficient conditions for robust stability involving multilinear structures, which can be tested using only real arithmetic. The obtained results are applied to robust matrix factorization, strict positive realness, and absolute stability of multivariable systems involving parameter dependent transfer function matrices.

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Ghosal, Purnata, and B. V. Raghavendra Rao. "On Proving Parameterized Size Lower Bounds for Multilinear Algebraic Models." Fundamenta Informaticae 177, no. 1 (December 18, 2020): 69–93. http://dx.doi.org/10.3233/fi-2020-1980.

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We consider the problem of obtaining parameterized lower bounds for the size of arithmetic circuits computing polynomials with the degree of the polynomial as the parameter. We consider the following special classes of multilinear algebraic branching programs: 1) Read Once Oblivious Branching Programs (ROABPs), 2) Strict interval branching programs, 3) Sum of read once formulas with restricted ordering. We obtain parameterized lower bounds (i.e., nΩ(t(k)) lower bound for some function t of k) on the size of the above models computing a multilinear polynomial that can be computed by a depth four circuit of size g(k)nO(1) for some computable function g. Further, we obtain a parameterized separation between ROABPs and read-2 ABPs. This is obtained by constructing a degree k polynomial that can be computed by a read-2 ABP of small size such that the rank of the partial derivative matrix under any partition of the variables is large.

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GORDIENKO, ALEXEY, and GEOFFREY JANSSENS. "ℤSn-MODULES AND POLYNOMIAL IDENTITIES WITH INTEGER COEFFICIENTS." International Journal of Algebra and Computation 23, no. 08 (December 2013): 1925–43. http://dx.doi.org/10.1142/s0218196713500513.

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We show that, like in the case of algebras over fields, the study of multilinear polynomial identities of unitary rings can be reduced to the study of proper polynomial identities. In particular, the factors of series of ℤSn-submodules in the ℤSn-modules of multilinear polynomial functions can be derived by the analog of Young's (or Pieri's) rule from the factors of series in the corresponding ℤSn-modules of proper polynomial functions. As an application, we calculate the codimensions and a basis of multilinear polynomial identities of unitary rings of upper triangular 2 × 2 matrices and infinitely generated Grassmann algebras over unitary rings. In addition, we calculate the factors of series of ℤSn-submodules for these algebras. Also we establish relations between codimensions of rings and codimensions of algebras and show that the analog of Amitsur's conjecture holds in all torsion-free rings, and all torsion-free rings with 1 satisfy the analog of Regev's conjecture.

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Latyshev, V. N. "Combinatorial generators of the multilinear polynomial identities." Journal of Mathematical Sciences 149, no. 2 (February 2008): 1107–12. http://dx.doi.org/10.1007/s10958-008-0049-5.

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Giambruno, Antonio, and Mikhail Zaicev. "Codimension growth of central polynomials of Lie algebras." Forum Mathematicum 32, no. 1 (January 1, 2020): 201–6. http://dx.doi.org/10.1515/forum-2019-0130.

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AbstractLet L be a finite-dimensional simple Lie algebra over an algebraically closed field of characteristic zero and let I be the T-ideal of polynomial identities of the adjoint representation of L. We prove that the number of multilinear central polynomials in n variables, linearly independent modulo I, grows exponentially like {(\dim L)^{n}}.

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CHEN, SHENSHI, YAQING CHEN, and QUANHAI YANG. "TOWARD RANDOMIZED TESTING OF q-MONOMIALS IN MULTIVARIATE POLYNOMIALS." Discrete Mathematics, Algorithms and Applications 06, no. 02 (March 19, 2014): 1450016. http://dx.doi.org/10.1142/s1793830914500165.

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Given any fixed integer q ≥ 2, a q-monomial is of the format [Formula: see text] such that 1 ≤ sj ≤ q - 1, 1 ≤ j ≤ t. q-monomials are natural generalizations of multilinear monomials. Recent research on testing multilinear monomials and q-monomials for prime q in multivariate polynomials relies on the property that Zq is a field when q ≥ 2 is prime. When q > 2 is not prime, it remains open whether the problem of testing q-monomials can be solved in some compatible complexity. In this paper, we present a randomized O*(7.15k) algorithm for testing q-monomials of degree k that are found in a multivariate polynomial that is represented by a tree-like circuit with a polynomial size, thus giving a positive, affirming answer to the above question. Our algorithm works regardless of the primality of q and improves upon the time complexity of the previously known algorithm for testing q-monomials for prime q > 7.

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Belaada, Abdelaziz, Khalil Saadi, and Abdelmoumen Tiaiba. "On the Composition Ideals of Schatten Class Type Mappings." Journal of Mathematics 2016 (2016): 1–5. http://dx.doi.org/10.1155/2016/3492934.

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We study the composition ideals of multilinear and polynomial mappings generated by Schatten classes. We give some coincidence theorems for Cohen strongly 2-summing multilinear operators and factorization results like that given by Lindenstrauss-Pełczński for Hilbert Schmidt linear operators.

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Chillara, Suryajith. "On Computing Multilinear Polynomials Using Multi- r -ic Depth Four Circuits." ACM Transactions on Computation Theory 13, no. 3 (September 30, 2021): 1–21. http://dx.doi.org/10.1145/3460952.

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In this article, we are interested in understanding the complexity of computing multilinear polynomials using depth four circuits in which the polynomial computed at every node has a bound on the individual degree of r ≥ 1 with respect to all its variables (referred to as multi- r -ic circuits). The goal of this study is to make progress towards proving superpolynomial lower bounds for general depth four circuits computing multilinear polynomials, by proving better bounds as the value of r increases. Recently, Kayal, Saha and Tavenas (Theory of Computing, 2018) showed that any depth four arithmetic circuit of bounded individual degree r computing an explicit multilinear polynomial on n O (1) variables and degree d must have size at least ( n / r 1.1 ) Ω(√ d / r ) . This bound, however, deteriorates as the value of r increases. It is a natural question to ask if we can prove a bound that does not deteriorate as the value of r increases, or a bound that holds for a larger regime of r . In this article, we prove a lower bound that does not deteriorate with increasing values of r , albeit for a specific instance of d = d ( n ) but for a wider range of r . Formally, for all large enough integers n and a small constant η, we show that there exists an explicit polynomial on n O (1) variables and degree Θ (log 2 n ) such that any depth four circuit of bounded individual degree r ≤ n η must have size at least exp(Ω(log 2 n )). This improvement is obtained by suitably adapting the complexity measure of Kayal et al. (Theory of Computing, 2018). This adaptation of the measure is inspired by the complexity measure used by Kayal et al. (SIAM J. Computing, 2017).

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Pınar Eroglu, Münevver, and Nurcan Argaç. "On Identities with Composition of Generalized Derivations." Canadian Mathematical Bulletin 60, no. 4 (December 1, 2017): 721–35. http://dx.doi.org/10.4153/cmb-2016-072-4.

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AbstractLet R be a prime ring with extended centroid C, Q maximal right ring of quotients of R, RC central closure of R such that dim C(RC) > , ƒ (X1, . . . , Xn) a multilinear polynomial over C that is not central-valued on R, and f (R) the set of all evaluations of the multilinear polynomial f (X1 , . . . , Xn) in R. Suppose that G is a nonzero generalized derivation of R such that G2(u)u ∈ C for all u ∈ ƒ(R).

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Filippis, Vincenzo De, Onofrio Mario Di Vincenzo, and Ching-Yueh Pan. "Quadratic Central Differential Identities on a Multilinear Polynomial." Communications in Algebra 36, no. 10 (October 13, 2008): 3671–81. http://dx.doi.org/10.1080/00927870802157962.

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Dissertations / Theses on the topic "Multilinear polynomial"

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Almutairi, Najat Bandar. "ON MULTILINEAR POLYNOMIALS EVALUATED ON QUATERNION ALGEBRA." Kent State University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=kent1454279474.

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Moura, Fernanda Ribeiro de. "Ideais algebricos de aplicações multilineares e polinômios homogêneos." Universidade Federal de Uberlândia, 2014. https://repositorio.ufu.br/handle/123456789/16812.

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The main purpose of this dissertation is the study of ideals of multilinear mappings and homogeneous polynomials between linear spaces. By an ideal we mean a class that is stable under the composition with linear operators. First we study multilinear mappings and spaces of multilinear mappings. We also show how to obtain, from a given multilinear mapping, other multilinear mappings with degrees of multilinearity greater than, equal to or smaller than the degree of the original multilinear mapping. Next we study homogeneous polynomials and spaces of homogeneous polynomials, and we also show how to obtain, from a given n-homogeneous polynomial, other polynomials with degrees of homogeneity greater than, equal to or smaller than the degree of the original polynomial. Next we study ideals of multilinear mappings, or multi-ideals, and ideals of homogeneous polynomial, or polynomial ideals, giving several examples and presenting methods to generated multi-ideals and polynomial ideals from a given operator ideal. Finally we dene and give several examples of coherent multi-ideals and coherent polynomial ideals.
O principal objetivo desta dissertação e estudar os ideais de aplicações multilineares e polinômios homogêneos entre espaços vetoriais. Por um ideal entendemos uma classe de aplicações que e estavel atraves da composição com operadores lineares. Primeiramente estudamos as aplicações multilineares e os espaços de aplicações multilineares. Mostramos tambem como obter, a partir de uma aplicação multilinear dada, outras aplicações com graus de multilinearidade maiores, iguais ou menores que o da aplicação original. Em seguida estudamos os polinômios homogêneos e os espacos de polinômios homogêneos, e mostramos que, a partir de um polinômio n-homogêneo, tambem podemos construir novos polinômios homogêneos com graus de homogeneidade maiores, iguais ou menores que n. Posteriormente estudamos os ideais de aplicações multilineares, ou multi-ideais, e os ideais de polinômios homogêneos, exibindo varios exemplos e apresentando metodos para se obter um multi-ideais, ou ideais de polinômios, a partir de ideais de operadores lineares dados. Por m, denimos e exibimos varios exemplos de multi-ideais coerentes e de ideais coerentes de polinômios.
Mestre em Matemática

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Sarantopoulos, I. C. "Polynomials and multilinear mappings in Banach spaces." Thesis, Brunel University, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.376057.

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Ronchim, Victor dos Santos. "Extensões de polinômios e de funções analíticas em espaços de Banach." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-05122017-101547/.

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Este trabalho tem como principal objetivo estudar extensões de aplicações multilineares, de polinômios homogêneos e de funções analíticas entre espaços de Banach. Desta maneira, nos baseamos em importantes trabalhos sobre o assunto. Inicialmente apresentamos o produto de Arens para álgebras de Banach, extensões de Aron-Berner e de Davie-Gamelin para aplicações multilineares e provamos que todas estas extensões coincidem. A partir destes resultados, apresentamos a extensão de polinômios homogêneos e o Teorema de Davie-Gamelin que afirma que, assim como no caso de aplicações multilineares, as extensões de polinômios preservam a norma e, como consequência deste teorema, apresentamos uma generalização do Teorema de Goldstine. Em seguida estudamos espaços de Banach regulares e simetricamente regulares, que são propriedades relacionadas com a unicidade de extensão e são definidas a partir do ideal de operadores lineares fracamente compactos K^w(E, F) . Finalmente apresentamos a extensão de uma função de H_b(E) para H_b(E\'\') e o resultado, de Ignacio Zalduendo, que caracteriza esta extensão em termos da continuidade fraca-estrela do operador diferencial de primeira ordem.
The main purpose of this work is to study extensions of multilinear mappings, homogeneous polynomials and analytic functions between Banach Spaces. In this way, we rely on important works on the subject. Firstly we present the Arens-product for Banach algebras, the Aron-Berner and Davie-Gamelin extensions for multilinear mappings and we prove that all these extensions are the same. From these results, we present an extension for homogeneous polynomials and the Davie-Gamelin theorem which asserts that, as in the case of multilinear mappings, the polynomial extension is norm-preserving and, as a consequence of this theorem, we present a generalization of the Goldstine theorem. After that we study regular and symmetrically regular Banach spaces which are properties related to the uniqueness of the extension and are defined in the setting of weakly compact linear operators K^w(E, F) . Lastly, we present the extension of a function of H_b(E) to one in H_b(E\'\') and the result, according to Ignacio Zalduendo, which characterizes this extension in terms of weak-star continuity of the first order differential operator.

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Torres, Ewerton Ribeiro. "Hiper-ideais de aplicações multilineares e polinômios homogêneos em espaços de Banach." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-05092016-143504/.

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Nesse trabalho introduzimos e desenvolvemos a teoria de hiper-ideais de aplicações multilineares contínuas e polinômios homogêneos contínuos entre espaços de Banach. A ideia central é refinar os conceitos de multi-ideais e de ideais de polinômios com o objetivo de explorar de forma mais aprofundada a natureza não-linear das aplicações envolvidas. Para isso tomamos a teoria de ideais de operadores lineares, aplicações multilineares e polinômios homogêneos, desenvolvida a partir dos trabalhos de Pietsch, tanto no caso linear como no caso multilinear, como referencial. Provamos resultados gerais para hiper-ideais, damos muitos exemplos ilustrativos, e desenvolvemos métodos para gerar hiper-ideais, tanto no caso multilinear como no caso polinomial.
In this work we introduce and develop the theory of hyper-ideals of multilinear mappings and homogeneous polynomials between Banach spaces. The main idea is to refine the concepts of multi-ideal and of ideal of polynomials with the purpose of exploring deeply the nonlinear nature of the underlying mappings. To do this we take the ideal theory of linear operators, multilinear mappings and homogeneous polynomials, developed from the works of Pietsch, both in the linear and nonlinear cases, as a reference. We prove general results for hyper-ideals, provide a number of illustrative examples, and develop methods to generate hyper-ideals of multilinear mappings, as well as of hyper-ideals of homogeneous polynomials.

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BERNARDINO, Adriano Thiago Lopes. "Contribuições à teoria multilinear de operadores absolutamente somantes." Universidade Federal de Pernambuco, 2016. https://repositorio.ufpe.br/handle/123456789/17977.

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Submitted by Irene Nascimento (irene.kessia@ufpe.br) on 2016-10-11T18:36:34Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Tese Adriano Thiago.pdf: 1085326 bytes, checksum: 498b2bcfd47961466edce3360e11a858 (MD5)
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Neste trabalho estudamos algumas extens˜oes do conceito de operadores multilineares absolutamente somantes, generalizamos alguns resultados conhecidos e respondemos parcialmente alguns problemas abertos. Para a classe das aplica¸c˜oes absolutamente (p; q; r)-somantes, obtemos alguns resultados de coincidˆencia e inclus˜ao e mostramos que o ideal de polinˆomios absolutamente (p; q; r)-somantes n˜ao ´e corente, de acordo com a no¸c˜ao de ideais coerentes devida a D. Carando, V. Dimant e S. Muro. Para contornar esta falha, introduzimos o conceito de aplica¸c˜oes m´ultiplo (p; q; r)-somantes e mostramos que, com essa nova abordagem, o ideal de polinˆomios m´ultiplo (p; q; r)- somantes ´e coerente e compat´ıvel com o ideal de operadores lineares absolutamente (p; q; r)-somantes.
In this work we investigate some extensions of the concept of absolutely summing operators, generalize some known results and provide partial answers to some open questions. For the class of absolutely (p; q; r)-summing mappings we obtain some inclusion and coincidence results and show that the ideal of absolutely (p; q; r)-summing polynomials is not coherent, according to the notion of coherent ideals due to D. Carando, V. Dimant and S. Muro. In order to bypass this deficiency, we introduce the concept of multiple (p; q; r)-summing multilinear and polynomial operators and show that, with this new approach, the ideal of multiple (p; q; r)-summing polynomials is coherent and compatible with the ideal of absolutely (p; q; r)-summing operators.

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Kuo, Po Ling. "Operadores de extensão de aplicações multilineares ou polinomios homogeneos." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307329.

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Orientador: Jorge Tulio Mujica Ascui
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Este trabalho está dedicado ao estudo dos operadores de Nicodemi, introduzidos em [7] a partir de uma idéia em [12]. Os operadores de Nicodemi levam aplicações multilineares (resp. polinômios homogêneos) de um espaço de Banach E em aplicações multilineares (resp. polinômios homogêneos) em um espaço de Banach F. O nosso primeiro objetivo é encontrar condições para que os operadores de Nicodemi preservem certos tipos de aplicações multilineares (resp. polinômios homogêneos). Em particular estudamos a preservação de aplicações multilineares simétricas, de tipo finito, nucleares, compactas ou fracamente compactas. O segundo objetivo é encontrar condições para que, se os espaços duais E¿ e F¿ são isomorfos, os espaços de aplicações multilineares (resp. polinômios homogêneos) em E e F sejam isomorfos também. Estudamos também o problema correspondente para os espaços de aplicações multilineares (resp. polinômios homogêneos) de um determinado tipo, como por exemplo, de tipo finito, nuclear, compacto ou fracamente compacto
Abstract: This work is devoted to studying the Nicodemi operators, introduced in [7], following an idea in [12]. The Nicodemi operators map multilinear mappings (resp. homogeneous polynomials) on a Banach spaces E into multilinear mappings (resp. homogeneous polynomials) on a Banach spaces F. Our first objective is to find conditions under which the Nicodemi operators preserve certain types of multilinear mappings (resp. homogeneous polynomials). In particular we examine the preservation of the multilinear mappings that are symmetric, of finite type, nuclear, compact or weakly compact. Our second objective is tofind conditions under which, whenever the dual spaces E¿ and F¿ are isomorphic, the spaces of multilinear mappings (resp. homogeneous polynomials) on E and F are isomorphic as well. We also examine the corresponding problem for the spaces of multilinear mappings (resp. homogeneous polynomials) of a certain type, for instance of finite, nuclear, compact or weakly compact type
Doutorado
Analise Funcional
Doutor em Matemática

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Reuss, Thomas. "The determinant method and applications." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:5b49acc6-bc16-45bf-972a-6dff1977db02.

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The thesis is structured into 5 chapters as follows: Chapter 1 is an introduction to the tools and methods we use most frequently. Chapter 2 Pairs of k-free Numbers, consecutive square-full Numbers. In this chapter, we refine the approximate determinant method by Heath-Brown. We present applications to asymptotic formulas for consecutive k-free integers, and more generally for k-free integers represented by r-tuples of linear forms. We also show how the method can be used to derive an upper bound for the number of consecutive square-full integers. Finally, we apply the method to make a statement about the size of the fundamental solution of Pell equations. Chapter 3 Power-Free Values of Polynomials. A conjecture by Erdös states that for any irreducible polynomial f of degree d≥3 with no fixed (d-1)-th power prime divisor, there are infinfinitely many primes p such that f(p) is (d-1)-free. We prove this conjecture and derive the corresponding asymptotic formulas. Chapter 4 Integer Points on Bilinear and Trilinear Equations. In the fourth chapter, we derive upper bounds for the number of integer solutions on bilinear or trilinear forms. Chapter 5 In the fifth chapter, we present a method to count the monomials that occur in the projective determinant method when the method is applied to cubic varieties.

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Maia, Mariana de Brito. "Um índice de somabilidade para operadores entre espaços de Banach." Universidade Federal da Paraíba, 2017. http://tede.biblioteca.ufpb.br:8080/handle/tede/9837.

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Nascimento, Lucas de Carvalho. "Um índice de somabilidade para pares de espaços de Banach." Universidade Federal da Paraíba, 2017. http://tede.biblioteca.ufpb.br:8080/handle/tede/9814.

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In this work, we study the notion of index of summability for pairs of Banach spaces. This index plays the role of a kind of “measure” of how the space of m-homogeneous polynomials from E to F (or the space of multilinear operators of E1×···×Em to F) are far from being the space of absolutely summing m-homogeneous polynomials (or with the space of multiple summing multilinear operators). In some cases the optimal index of summability is presented.
Neste trabalho, estudamos a noção de índice de somabilidade para pares de espaços de Banach. Esse índice desempenha o papel de um tipo de \medida" de como o espaço dos polinômios m-homogêneos de E em F (ou o espaço dos operadores multilineares de E Em em F) está longe de coincidir com o espaço dos polinômios m- homogêneos absolutamente somantes (ou com o espaço dos operadores multilineares multiplo somantes). Em alguns casos o índice ótimo de somabilidade e apresentado. Palavras-chave: Polinômios absolutamente somantes, operadores multilineares absolutamente somantes, espaços de Banach, índice de somabilidade.

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Books on the topic "Multilinear polynomial"

1

Galiffa, Daniel J. On the Higher-Order Sheffer Orthogonal Polynomial Sequences. New York, NY: Springer New York, 2013.

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Sarantopoulos, Ioannis C. Polynomials and multilinear mappings in Banach spaces. Uxbridge: Brunel University, 1986.

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Norman, Christopher. Finitely Generated Abelian Groups and Similarity of Matrices over a Field. London: Springer London, 2012.

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Random Matrices AMS Short Course. Modern aspects of random matrix theory: AMS Short Course, Random Matrices, January 6-7, 2013, San Diego, California. Edited by Vu, Van, 1970- editor of compilation. Providence, Rhode Island: American Mathematical Society, 2014.

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1962-, Sturmfels Bernd, ed. Introduction to tropical geometry. Providence, Rhode Island: American Mathematical Society, 2015.

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Bard, Gregory V. Sage for undergraduates. Providence, Rhode Island: American Mathematical Society, 2015.

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International Conference on p-Adic Functional Analysis (11th 2010 Université Blaise Pascal). Advances in non-Archimedean analysis: Eleventh International Conference on p-Adic Functional Analysis, July 5-9 2010, Université Blaise Pascal, Clermont-Ferrand, France. Edited by Araujo-Gomez Jesus 1965-, Diarra B. (Bertin) 1944-, and Escassut Alain. Providence, R.I: American Mathematical Society, 2011.

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Galiffa, Daniel J. On the Higher-Order Sheffer Orthogonal Polynomial Sequences. Springer, 2013.

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Norman, Christopher. Finitely Generated Abelian Groups and Similarity of Matrices over a Field. Springer, 2012.

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Book chapters on the topic "Multilinear polynomial"

1

Ito, Kimihito, and Akihiro Yamamoto. "Polynomial-time MAT learning of multilinear logic programs." In Lecture Notes in Computer Science, 63–74. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/3-540-57369-0_28.

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2

Kwapień, Stanisław, and Wojbor A. Woyczyński. "Random Multilinear Forms in Independent Random Variables and Polynomial Chaos." In Random Series and Stochastic Integrals: Single and Multiple, 147–89. Boston, MA: Birkhäuser Boston, 1992. http://dx.doi.org/10.1007/978-1-4612-0425-1_7.

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3

Zhang, Liang Feng, and Reihaneh Safavi-Naini. "Private Outsourcing of Polynomial Evaluation and Matrix Multiplication Using Multilinear Maps." In Cryptology and Network Security, 329–48. Cham: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-02937-5_18.

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4

Matušů, Radek, and Bilal Şenol. "Application of Value Set Concept to Ellipsoidal Polynomial Families with Multilinear Uncertainty Structure." In Computational Statistics and Mathematical Modeling Methods in Intelligent Systems, 81–89. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-31362-3_9.

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5

Chen, Zhixiang, and Bin Fu. "Approximating Multilinear Monomial Coefficients and Maximum Multilinear Monomials in Multivariate Polynomials." In Combinatorial Optimization and Applications, 309–23. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-17458-2_26.

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6

Kraus, F. J., M. Mansour, and B. D. O. Anderson. "Robust Stability of Polynomials with Multilinear Parameter Dependence." In Robustness in Identification and Control, 263–80. Boston, MA: Springer US, 1989. http://dx.doi.org/10.1007/978-1-4615-9552-6_17.

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7

Filippis, Vincenzo De, Giovanni Scudo, and Feng Wei. "b-Generalized Skew Derivations on Multilinear Polynomials in Prime Rings." In Springer INdAM Series, 109–38. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-63111-6_7.

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8

Dhara, Basudeb. "Generalized Derivations with Nilpotent Values on Multilinear Polynomials in Prime Rings." In Algebra and its Applications, 307–19. Singapore: Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-1651-6_18.

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9

Emelyanov, Pavel, and Denis Ponomaryov. "On a Polytime Factorization Algorithm for Multilinear Polynomials over $$\mathbb {F}_2$$." In Developments in Language Theory, 164–76. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99639-4_11.

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"Upper bounds using multilinear polynomials." In The Student Mathematical Library, 127–36. Providence, Rhode Island: American Mathematical Society, 2018. http://dx.doi.org/10.1090/stml/086/21.

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Conference papers on the topic "Multilinear polynomial"

1

Anderson, Matthew, Dieter van Melkebeek, and Ilya Volkovich. "Derandomizing Polynomial Identity Testing for Multilinear Constant-Read Formulae." In 2011 IEEE Annual Conference on Computational Complexity (CCC). IEEE, 2011. http://dx.doi.org/10.1109/ccc.2011.18.

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2

Vaccari, David A. "Multivariate Polynomial Response Surface Analysis - Combining Advantages of Multilinear Regression and Artificial Neural Networks." In Modelling, Simulation and Identification. Calgary,AB,Canada: ACTAPRESS, 2018. http://dx.doi.org/10.2316/p.2018.857-021.

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3

Chen, Weining, and Ian R. Petersen. "An easily testable sufficient condition for the robust stability of multilinear uncertain polynomials." In 1997 European Control Conference (ECC). IEEE, 1997. http://dx.doi.org/10.23919/ecc.1997.7082723.

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