In this paper, we first establish a basic theorem on the zeros of general transcendental functions. Based on the basic theorem, we develop a decomposition technique to investigate the stability of some exponential polynomials, that is, to find conditions under which all zeros of the exponential polynomials have negative real parts. The technique combines the D-decomposition and τ -decomposition...

We provide an analogue of Gundy’s decomposition for L1-bounded non-commutative martingales. An important difference from the classical case is that for any L1-bounded non-commutative martingale, the decomposition consists of four martingales. This is strongly related with the row/column nature of non-commutative Hardy spaces of martingales. As applications, we obtain simpler proofs of the weak ...

The vertex set of the resonance graph of a hexagonal graph G consists of 1-factors of G, two 1-factors being adjacent whenever their symmetric difference forms the edge set of a hexagon of G. A decomposition theorem for the resonance graphs of catacondensed hexagonal graph is proved. The theorem intrinsically uses the Cartesian product of graphs. A canonical binary coding of 1-factors of cataco...

languages usually involves proving a decomposition theorem. Not only is such a proof tedious, un-inspiring, and error-prone, but also it is usually attempted many times during the design of a theory. With an eye towards automation, we develop an algorithm for checking the statement of the decomposition theorem. Our algorithm is expressed as a sound and complete term rewriting system with respec...

Dilworth s theorem states a duality relation between minimum chain decompositions of a directed acyclic graph and maximum antichains We generalize the theorem to apply when the chains of the decomposition are required to contain the chains of an initial decomposition We show that duality obtains precisely when an associated undirected graph is perfect We apply this result to a vehicle routing a...