Abstract In this paper, by using the residue method of complex analysis, we obtain an explicit partial fraction decomposition for general rational function $\frac{x^{M}}{(x+1)^{\lambda}_{n}}$ x M ( + 1</...

In the present study, a comprehensive and systematic strategy was described to evaluate the performance of several three-way calibration methods on a bio-analytical problem. Parallel factor analysis (PARAFAC), alternating trilinear decomposition (ATLD), self-weighted alternating trilinear decomposition (SWATLD), alternating penalty trilinear decomposition (APTLD) and unfolded partial least squa...

A decomposition of a graph is a partition of the edge set. One can also look at partitions of the arc set but in this talk we restrict our attention to edges. If each part of the decomposition is a spanning subgraph then we call the decomposition a factorisation and the parts are called factors. Decompositions are especially interesting when the subgraphs induced by each part are pairwise isomo...

An H-decomposition of a graph G = (V,E) is a partition of E into subgraphs isomorphic to H. Given a fixed graph H, the H-decomposition problem is to determine whether an input graph G admits an H-decomposition. In 1980, Holyer conjectured that H-decomposition is NP-complete whenever H is connected and has three edges or more. Some partial results have been obtained since then. A complete proof ...

This paper sheds a new light on the split decomposition theory and T-theory from the viewpoint of convex analysis and polyhedral geometry. By regarding finite metrics as discrete concave functions, Bandelt-Dress’ split decomposition can be derived as a special case of more general decomposition of polyhedral/discrete concave functions introduced in this paper. It is shown that the combinatorics...

This paper sheds a new light on the split decomposition theory and T-theory from the viewpoint of convex analysis and polyhedral geometry. By regarding finite metrics as discrete concave function, Bandelt-Dress’ split decomposition can be derived as a special case of more general decomposition of polyhedral/discrete concave functions introduced in this paper. It is shown that the combinatorics ...