Search results for "combinatoric"
showing 10 items of 1776 documents
Some properties of [tr(Q2p)]12p with application to linear minimax estimation
1990
Abstract A nondifferentiable minimization problem is considered which occurs in linear minimax estimation. This problem is solved by replacing the nondifferentiable maximal eigenvalue of a real nonnegative definite matrix Q with [tr( Q 2 p )] 1/2 p . It is shown that any descent algorithm with inexact step-length rule can be used to obtain linear minimax estimators for the parameter vector of a parameter-restricted linear model.
The structure of the state representation of shift invariant controllable and observable group codes
2000
AbstractIn this paper an investigation on the structure of the canonical trellis section of shift invariant, l-controllable and m-observable group codes is carried out. Necessary and sufficient conditions for a set of group homomorphisms in order that they represent the trellis section of this class of codes are established.
The Rotation χ-Lattice of Ternary Trees
2001
This paper generalizes to k-ary trees the well-known rotation transformation on binary trees. For brevity, only the ternary case is developped. The rotation on ternary trees is characterized using some codings of trees. Although the corresponding poset is not a lattice, we show that it is a χ-lattice in the sense of Leutola–Nieminen. Efficient algorithms are exhibited to compute meets and joins choosen in a particular way.
On the Bishop–Phelps–Bollobás theorem for multilinear mappings
2017
Abstract We study the Bishop–Phelps–Bollobas property and the Bishop–Phelps–Bollobas property for numerical radius. Our main aim is to extend some known results about norm or numerical radius attaining operators to multilinear and polynomial cases. We characterize the pair ( l 1 ( X ) , Y ) to have the BPBp for bilinear forms and prove that on L 1 ( μ ) the numerical radius and the norm of a multilinear mapping are the same. We also show that L 1 ( μ ) fails the BPBp-nu for multilinear mappings although L 1 ( μ ) satisfies it in the operator case for every measure μ.
On the ∗-cocharacter sequence of 3×3 matrices
2000
Abstract Let M 3 (F) be the algebra of 3×3 matrices with involution * over a field F of characteristic zero. We study the ∗ -polynomial identities of M 3 (F) , where ∗=t is the transpose involution, through the representation theory of the hyperoctahedral group B n . After decomposing the space of multilinear ∗ -polynomial identities of degree n under the B n -action, we determine which irreducible B n -modules appear with non-zero multiplicity. In symbols, we write the nth ∗ -cocharacter χ n (M 3 (F),*)=∑ r=0 n ∑ λ⊢r,h(λ)⩽6 μ⊢n−r,h(μ)⩽3 m λ,μ χ λ,μ , where λ and μ are partitions of r and n−r , respectively, χ λ,μ is the irreducible B n -character associated to the pair (λ,μ) and m λ,μ ⩾0 i…
Fixed points and completeness on partial metric spaces
2015
Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a selfmapping on a partial metric space that characterizes the partial metric 0-completeness. In this paper we prove a fixed point result for a new class of…
Ordinary and graded cocharacter of the Jordan algebra of 2x2 upper triangular matrices
2014
Abstract Let F be a field of characteristic zero and U J 2 ( F ) be the Jordan algebra of 2 × 2 upper triangular matrices over F . In this paper we give a complete description of the space of multilinear graded and ordinary identities in the language of Young diagrams through the representation theory of a Young subgroup of S n . For every Z 2 -grading of U J 2 ( F ) we compute the multiplicities in the graded cocharacter sequence and furthermore we compute the ordinary cocharacter.
Fine and Wilf's Theorem for Three periods and a Generalization of Sturmian Words
1999
AbstractWe extend the theorem of Fine and Wilf to words having three periods. We then define the set 3-PER of words of maximal length for which such result does not apply. We prove that the set 3-PER and the sequences of complexity 2n + 1, introduced by Arnoux and Rauzy to generalize Sturmian words, have the same set of factors.
A note on the packing of two copies of some trees into their third power
2003
Abstract It is proved in [1] that if a tree T of order n is not a star, then there exists an edge-disjoint placement of two copies of this tree into its fourth power. In this paper, we prove the packing of some trees into their third power.
Graphs of stable maps from closed surfaces to the projective plane
2018
Abstract We describe how to attach a weighted graph to each stable map from closed surfaces to projective plane and prove that any weighted graph with non negatively weighted vertices is the graph of some stable map from a closed surface to the projective plane.