Search results for "Partition"
showing 10 items of 411 documents
Enumerating the Walecki-Type Hamiltonian Cycle Systems
2017
Let Kv be the complete graph on v vertices. A Hamiltonian cycle system of odd order v (briefly HCS(v)) is a set of Hamiltonian cycles of Kv whose edges partition the edge set of Kv. By means of a slight modification of the famous HCS(4n+1) of Walecki, we obtain 2n pairwise distinct HCS(4n+1) and we enumerate them up to isomorphism proving that this is equivalent to count the number of binary bracelets of length n, i.e. the orbits of Dn, the dihedral group of order 2n, acting on binary n-tuples.
Weak regularity of functions and sets in Asplund spaces
2006
Abstract In this paper, we study a new concept of weak regularity of functions and sets in Asplund spaces. We show that this notion includes prox-regular functions, functions whose subdifferential is weakly submonotone and amenable functions in infinite dimension. We establish also that weak regularity is equivalent to Mordukhovich regularity in finite dimension. Finally, we give characterizations of the weak regularity of epi-Lipschitzian sets in terms of their local representations.
Graded algebras with polynomial growth of their codimensions
2015
Abstract Let A be an algebra over a field of characteristic 0 and assume A is graded by a finite group G . We study combinatorial and asymptotic properties of the G -graded polynomial identities of A provided A is of polynomial growth of the sequence of its graded codimensions. Roughly speaking this means that the ideal of graded identities is “very large”. We relate the polynomial growth of the codimensions to the module structure of the multilinear elements in the relatively free G -graded algebra in the variety generated by A . We describe the irreducible modules that can appear in the decomposition, we show that their multiplicities are eventually constant depending on the shape obtaine…
The Phagocyte Lattice of Dyck Words
2006
We introduce a new lattice structure on Dyck words. We exhibit efficient algorithms to compute meets and joins of Dyck words.
The pianigiani-yorke measure for topological markov chains
1997
We prove the existence of a Pianigiani-Yorke measure for a Markovian factor of a topological Markov chain. This measure induces a Gibbs measure in the limit set. The proof uses the contraction properties of the Ruelle-Perron-Frobenius operator.
Composition operators on uniform algebras, essential norms, and hyperbolically bounded sets
2006
Let A be a uniform algebra, and let o be a self-map of the spectrum M A of A that induces a composition operator C o on A. The object of this paper is to relate the notion of "hyperbolic boundedness" introduced by the authors in 2004 to the essential spectrum of C o . It is shown that the essential spectral radius of C o , is strictly less than 1 if and only if the image of M A under some iterate o n of o is hyperbolically bounded. The set of composition operators is partitioned into "hyperbolic vicinities" that are clopen with respect to the essential operator norm. This partition is related to the analogous partition with respect to the uniform operator norm.
Conjugate unstable manifolds and their underlying geometrized Markov partitions
2000
Abstract Conjugate unstable manifolds of saturated hyperbolic sets of Smale diffeomorphisms are characterized in terms of the combinatorics of their geometrized Markov partitions. As a consequence, the relationship between the local and the global point of view is also made explicit.
On the continuity of discrete maximal operators in Sobolev spaces
2014
We investigate the continuity of discrete maximal operators in Sobolev space W 1;p (R n ). A counterexample is given as well as it is shown that the continuity follows under certain sucient assumptions. Especially, our research verifies that for the continuity in Sobolev spaces the role of the partition of the unity used in the construction of the maximal operator is very delicate.
Data Compression Using Wavelet and Local Cosine Transforms
2015
The chapter describes an algorithm that compresses two-dimensional data arrays, which are piece-wise smooth in one direction and have oscillating events in the other direction. Seismic, hyper-spectral and fingerprints data, for example, have such a mixed structure. The transform part of the compression process is an algorithm that combines wavelet and local cosine transform (LCT). The quantization and the entropy coding parts of the compression are taken from the SPIHT codec. To efficiently apply the SPIHT codec to a mixed coefficients array, reordering of the LCT coefficients takes place. On the data arrays, which have the mixed structure, this algorithm outperforms other algorithms that a…
Identity dynamics and social partitions : the case of identity "racial" Blacks in France
2011
Our research work investigates - from a psycho-social point of view - the «racial» identity of the black population in France, notably in their relation with the white population, so as to point up the identity dynamics that exist between the various groups. The theoretical framework is related to social grouping and one of its developments, i.e. the concept of social partitioning. Such conception is based on the existence of several types of inter-category relations (partitioning) that allow apprehending the nature of individuals’ identity positioning within the framework of an inter-group relation and make it dynamic through the notion of co-construction. Our methodology is based mainly o…