Search results for "Number"
showing 10 items of 3939 documents
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…
Matrix algebras with degenerate traces and trace identities
2022
In this paper we study matrix algebras with a degenerate trace in the framework of the theory of polynomial identities. The first part is devoted to the study of the algebra $D_n$ of $n \times n$ diagonal matrices. We prove that, in case of a degenerate trace, all its trace identities follow by the commutativity law and by pure trace identities. Moreover we relate the trace identities of $D_{n+1}$ endowed with a degenerate trace, to those of $D_n$ with the corresponding trace. This allows us to determine the generators of the trace T-ideal of $D_3$. In the second part we study commutative subalgebras of $M_k(F)$, denoted by $C_k$ of the type $F + J$ that can be endowed with the so-called st…
Superinvolutions on upper-triangular matrix algebras
2018
Let UTn(F) be the algebra of n×n upper-triangular matrices over an algebraically closed field F of characteristic zero. In [18], the authors described all abelian G-gradings on UTn(F) by showing that any G-grading on this algebra is an elementary grading. In this paper, we shall consider the algebra UTn(F) endowed with an elementary Z2-grading. In this way, it has a structure of superalgebra and our goal is to completely describe the superinvolutions which can be defined on it. To this end, we shall prove that the superinvolutions and the graded involutions (i.e., involutions preserving the grading) on UTn(F) are strictly related through the so-called superautomorphisms of this algebra. We …
Monads in double categories
2010
We extend the basic concepts of Street's formal theory of monads from the setting of 2-categories to that of double categories. In particular, we introduce the double category Mnd(C) of monads in a double category C and define what it means for a double category to admit the construction of free monads. Our main theorem shows that, under some mild conditions, a double category that is a framed bicategory admits the construction of free monads if its horizontal 2-category does. We apply this result to obtain double adjunctions which extend the adjunction between graphs and categories and the adjunction between polynomial endofunctors and polynomial monads.
Trace identities and almost polynomial growth
2021
In this paper we study algebras with trace and their trace polynomial identities over a field of characteristic 0. We consider two commutative matrix algebras: $D_2$, the algebra of $2\times 2$ diagonal matrices and $C_2$, the algebra of $2 \times 2$ matrices generated by $e_{11}+e_{22}$ and $e_{12}$. We describe all possible traces on these algebras and we study the corresponding trace codimensions. Moreover we characterize the varieties with trace of polynomial growth generated by a finite dimensional algebra. As a consequence, we see that the growth of a variety with trace is either polynomial or exponential.
Locally tame plane polynomial automorphisms
2010
Abstract For automorphisms of a polynomial ring in two variables over a domain R , we show that local tameness implies global tameness provided that every 2-generated locally free R -module of rank 1 is free. We give examples illustrating this property.
Varieties of special Jordan algebras of almost polynomial growth
2019
Abstract Let J be a special Jordan algebra and let c n ( J ) be its corresponding codimension sequence. The aim of this paper is to prove that in case J is finite dimensional, such a sequence is polynomially bounded if and only if the variety generated by J does not contain U J 2 , the special Jordan algebra of 2 × 2 upper triangular matrices. As an immediate consequence, we prove that U J 2 is the only finite dimensional special Jordan algebra that generates a variety of almost polynomial growth.
Supramolecular silver polyoxometalate architectures direct the growth of composite semiconducting nanostructures.
2009
Nanosilver on a string: Crystalline silver polyoxovanadate supramolecular architectures are employed as precursors for the synthesis of composite nanowires (see scheme). The nanostructures are composed of semiconducting vanadium oxide which forms wires with high aspect ratios, and are embedded with metallic silver nanoparticles. © 2009 Wiley-VCH Verlag GmbH & Co. KCaA.
Karyological data of three Hieracium (Asteraceae) from Sicily and South Italy
2021
Chromosome numbers are given for three endemic Hieracium taxa from Sicily and Campania (Southern Italy). All the examined taxa resulted triploid (2n = 3x = 27). The triploid chromosome set found in the population of H. pallidum from Rocche dell’Argimusco (Peloritani Mountains, NE-Sicily) differs from the previous counts (2n = 4x = 36) reported for the same species from its locus classicus (Mt. Etna).
An Innovative Friction Stir Welding Based Technique to Produce Dissimilar Light Alloys to Thermoplastic Matrix Composite Joints
2016
Abstract Aluminum sheets can be joined to composite materials with different techniques. Each of them has advantages and weak points over the others. In literature, new techniques and patents are continuously developed to overcome these difficulties. In the paper a new Friction Stir Welding based approach is proposed to mechanically join AA6082-T6 to self-reinforced polypropylene. The aluminum sheet is pre-holed along both the sides of the weld line. A pinless tool generates the heat and pressure needed to activate back-extrusion of the composite. Joints have been produced with varying hole diameter and pitch. The mechanical resistance of the joint has been evaluated and the different failu…