Search results for "Applied Mathematics"

Planar maps whose second iterate has a unique fixed point

2007

Let a>0, F: R^2 -> R^2 be a differentiable (not necessarily C^1) map and Spec(F) be the set of (complex) eigenvalues of the derivative F'(p) when p varies in R^2. (a) If Spec(F) is disjoint of the interval [1,1+a[, then Fix(F) has at most one element, where Fix(F) denotes the set of fixed points of F. (b) If Spec(F) is disjoint of the real line R, then Fix(F^2) has at most one element. (c) If F is a C^1 map and, for all p belonging to R^2, the derivative F'(p) is neither a homothety nor has simple real eigenvalues, then Fix(F^2) has at most one element, provided that Spec(F) is disjoint of either (c1) the union of the number 0 with the intervals ]-\infty, -1] and [1,\infty[, or (c2) t…

The Spectrum of Analytic Mappings of Bounded Type

2000

Abstract A Banach space E is said to be (symmetrically) regular if every continuous (symmetric) linear mapping from E to E ′ is weakly compact. For a complex Banach space E and a complex Banach algebra F , let H b ( E ,  F ) denote the algebra of holomorphic mappings from E to F which are bounded on bounded sets. We endow H b ( E ,  F ) with the usual Frechet topology. M ( H b ( E ,  F ),  F ) denotes the set of all non-null continuous homomorphisms from H b ( E ,  F ) to F . A subset of G EF on which the extension of Zalduendo is multiplicative is presented and it is shown that, in general, the sets G EF and M ( H b ( E ,  F ),  F ) do not coincide. We prove that if E is symmetrically regu…

Simple and semisimple Lie algebras and codimension growth

1999

On complete set of solutions for polynomial matrix equations

1990

Abstract In this paper we introduce the concept of co-solution of a polynomial matrix equation which permits us to obtain necessary and sufficient conditions so that a set of solutions be a complete set.

Approximate fixed points of set-valued mapping in b-metric space

2016

We establish existence results related to approximate fixed point property of special types of set-valued contraction mappings, in the setting of b-metric spaces. As consequences of the main theorem, we give some fixed point results which generalize and extend various fixed point theorems in the existing literature. A simple example illustrates the new theory. Finally, we apply our results to establishing the existence of solution for some differential and integral problems.

On the subset sum problem for finite fields

2021

Abstract Let G be the additive group of a finite field. J. Li and D. Wan determined the exact number of solutions of the subset sum problem over G, by giving an explicit formula for the number of subsets of G of prescribed size whose elements sum up to a given element of G. They also determined a closed-form expression for the case where the subsets are required to contain only nonzero elements. In this paper we give an alternative proof of the two formulas. Our argument is purely combinatorial, as in the original proof by Li and Wan, but follows a different and somehow more “natural” approach. We also indicate some new connections with coding theory and combinatorial designs.

Common Fixed points for multivalued generalized contractions on partial metric spaces

2013

We establish some common fixed point results for multivalued mappings satisfying generalized contractive conditions on a complete partial metric space. The presented theorems extend some known results to partial metric spaces. We motivate our results by some given examples and an application for finding the solution of a functional equation arising in dynamic programming.

Point counting on Picard curves in large characteristic

2005

We present an algorithm for computing the cardinality of the Jacobian of a random Picard curve over a finite field. If the underlying field is a prime field Fp, the algorithm has complexity O(p).

On the connectedness of the attainability set for lattice dynamical systems

2012

We prove the Kneser property (i.e. the connectedness and compactness of the attainability set at any time) for lattice dynamical systems in which we do not know whether the property of uniqueness of the Cauchy problem holds or not. Using this property, we can check that the global attractor of the multivalued semiflow generated by such system is connected.

On the number of constituents of products of characters

2022

It has been conjectured that if the number of distinct irreducible constituents of the product of two faithful irreducible characters of a finite p-group, for p ≥ 5, is bigger than (p + 1)/2, then it is at least p. We give a counterexample to this conjecture.