Search results for "Square-free polynomial"
showing 4 items of 4 documents
Identities of *-superalgebras and almost polynomial growth
2015
We study the growth of the codimensions of a *-superalgebra over a field of characteristic zero. We classify the ideals of identities of finite dimensional algebras whose corresponding codimensions are of almost polynomial growth. It turns out that these are the ideals of identities of two algebras with distinct involutions and gradings. Along the way, we also classify the finite dimensional simple *-superalgebras over an algebraically closed field of characteristic zero.
Polynomial Fuzzy Models for Nonlinear Control: A Taylor Series Approach
2009
Classical Takagi-Sugeno (T-S) fuzzy models are formed by convex combinations of linear consequent local models. Such fuzzy models can be obtained from nonlinear first-principle equations by the well-known sector-nonlinearity modeling technique. This paper extends the sector-nonlinearity approach to the polynomial case. This way, generalized polynomial fuzzy models are obtained. The new class of models is polynomial, both in the membership functions and in the consequent models. Importantly, T-S models become a particular case of the proposed technique. Recent possibilities for stability analysis and controller synthesis are also discussed. A set of examples shows that polynomial modeling is…
A Leibniz variety with almost polynomial growth
2005
Abstract Let F be a field of characteristic zero. In this paper we study the variety of Leibniz algebras V ˜ 1 defined by the identity y 1 ( y 2 y 3 ) ( y 4 y 5 ) ≡ 0 . We give a complete description of the space of multilinear identities in the language of Young diagrams through the representation theory of the symmetric group. As an outcome we show that the variety V ˜ 1 has almost polynomial growth, i.e., the sequence of codimensions of V ˜ 1 cannot be bounded by any polynomial function but any proper subvariety of V ˜ 1 as polynomial growth.
Zeroes of real polynomials on C(K) spaces
2007
AbstractFor a compact Hausdorff topological space K, we show that the function space C(K) must satisfy the following dichotomy: (i) either it admits a positive definite continuous 2-homogeneous real-valued polynomial, (ii) or every continuous 2-homogeneous real-valued polynomial vanishes in a non-separable closed linear subspace. Moreover, if K does not have the Countable Chain Condition, then every continuous polynomial, not necessarily homogeneous and with arbitrary degree, has constant value in an isometric copy of c0(Γ), for some uncountable Γ.