Search results for "Discrete Mathematics"
showing 10 items of 1728 documents
On ergodic operator means in Banach spaces
2016
We consider a large class of operator means and prove that a number of ergodic theorems, as well as growth estimates known for particular cases, continue to hold in the general context under fairly mild regularity conditions. The methods developed in the paper not only yield a new approach based on a general point of view, but also lead to results that are new, even in the context of the classical Cesaro means.
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.
Rough Set Algebras as Description Domains
2009
Study of the so called knowledge ordering of rough sets was initiated by V.W. Marek and M. Truszczynski at the end of 90-ies. Under this ordering, the rough sets of a fixed approximation space form a domain in which every set ↓ is a Boolean algebra. In the paper, an additional operation inversion on rough set domains is introduced and an abstract axiomatic description of obtained algebras of rough set is given. It is shown that the resulting class of algebras is essentially different from those traditional in rough set theory: it is not definable, for instance, in the class of regular double Stone algebras, and conversely.
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).
Connected components in the space of composition operators onH∞ functions of many variables
2003
LetE be a complex Banach space with open unit ballBe. The structure of the space of composition operators on the Banach algebra H∞, of bounded analytic functions onBe with the uniform topology, is studied. We prove that the composition operators arising from mappings whose range lies strictly insideBe form a path connected component. WhenE is a Hilbert space or aCo(X)- space, the path connected components are shown to be the open balls of radius 2.
On fixed points of the Burrows-Wheeler transform
2017
The Burrows-Wheeler Transform is a well known transformation widely used in Data Compression: important competitive compression software, such as Bzip (cf. [1]) and Szip (cf. [2]) and some indexing software, like the FM-index (cf. [3]), are deeply based on the Burrows Wheeler Transform. The main advantage of using BWT for data compression consists in its feature of "clustering" together equal characters. In this paper we show the existence of fixed points of BWT, i.e., words on which BWT has no effect. We show a characterization of the permutations associated to BWT of fixed points and we give the explicit form of fixed points on a binary ordered alphabet a, b having at most four b's and th…
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.