Edge number results for piecewise-Linear knots

Piecewise Linear–Linear Latent Growth Mixture Models With Unknown Knots

Latent growth curve models with piecewise functions are flexible and useful analytic models for investigating individual behaviors that exhibit distinct phases of development in observed variables. As an extension of this framework, this study considers a piecewise linear–linear latent growth mixture model (LGMM) for describing segmented change of individual behavior over time where the data co...

Edge-Preserving Piecewise Linear Image Smoothing Using Piecewise Constant Filters

Most image smoothing filters in the literature assume a piecewise constant model of smoothed output images. However, the piecewise constant model assumption can cause artifacts such as gradient reversals in applications such as image detail enhancement, HDR tone mapping, etc. In these applications, a piecewise linear model assumption is more preferred. In this paper, we propose a simple yet ver...

Exact Results on the Number of Restricted Edge Colorings for Some Families of Linear Hypergraphs

For k-uniform hypergraphs F and H and an integer r ≥ 2, let cr,F (H) denote the number of r-colorings of the set of hyperedges of H with no monochromatic copy of F and let cr,F (n) = maxH∈Hn cr,F (H), where the maximum is over the family Hn of all k-uniform hypergraphs on n vertices. Moreover, let ex(n, F ) be the usual extremal function, i.e., the maximum number of hyperedges of an n-vertex k-...

Edge 2-rainbow domination number and annihilation number in trees

A edge 2-rainbow dominating function (E2RDF) of a graph G is a ‎function f from the edge set E(G) to the set of all subsets‎ ‎of the set {1,2} such that for any edge.......................

Piecewise Constant Controlled Linear Fuzzy Systems