A constructive proof of the phase-type characterization theorem
نویسندگان
چکیده
The paper presents a new proof of O’Cinneide’s characterization theorem [7]. It is much simpler than the original one and constructive in the sense that we not only show the existence of a phase type representation, but present a procedure which creates a phase type representation. We prove that the procedure succeeds when the conditions of the characterization theorem hold.
منابع مشابه
The Basic Theorem and its Consequences
Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...
متن کاملA new proof for the Banach-Zarecki theorem: A light on integrability and continuity
To demonstrate more visibly the close relation between thecontinuity and integrability, a new proof for the Banach-Zareckitheorem is presented on the basis of the Radon-Nikodym theoremwhich emphasizes on measure-type properties of the Lebesgueintegral. The Banach-Zarecki theorem says that a real-valuedfunction $F$ is absolutely continuous on a finite closed intervalif and only if it is continuo...
متن کاملOn Tychonoff's type theorem via grills
Let ${X_{alpha}:alphainLambda}$ be a collection of topological spaces, and $mathcal {G}_{alpha}$ be a grill on $X_{alpha}$ for each $alphainLambda$. We consider Tychonoffrq{}s type Theorem for $X=prod_{alphainLambda}X_{alpha}$ via the above grills and a natural grill on $X$ related to these grills, and present a simple proof to this theorem. This immediately yields the classical theorem...
متن کاملCommon xed point theorem for w-distance with new integral type contraction
Boujari [5] proved a fixed point theorem with an old version of the integraltype contraction , his proof is incorrect. In this paper, a new generalizationof integral type contraction is introduced. Moreover, a fixed point theorem isobtained.
متن کاملA Proof-Theoretical Investigation of Zantema's Problem
We present a concrete example of how one can extract constructive content from a non{constructive proof. The proof investigated is a termination proof of the string{rewriting system 1100 ! 000111. This rewriting system is self{embedding, so the standard termination techniques which rely on Kruskal's Tree Theorem cannot be applied directly. Dershowitz and Hoot 3] have given a classical terminati...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1502.00521 شماره
صفحات -
تاریخ انتشار 2015