for example, if i want to say that my system is stable on the basis of X theorem or X lemma (which is proven or stated by others) is it valid?
or if i want to include lemma,proposition or corollary,definition or theorem i have to make my own?i have already gone through a several papers n thesis,alas i dont understand that they used their own lemmas or cited from others..cause most of them have not put any references.
thanx in advance
any help will be appreciated
If a theorem is adopted from another source -- it is always referenced. Sometimes, the authors completely reproduce a theorem for better reading. How you organize your analysis is up to you. Sometimes, a theorem, a proof of which becomes large, is divided into lemma(s) and a theorem. The proof then refers to the results of lemma(s). Corollary is usually used to make a statement close to the theorem. For example, a stronger result comes from a stronger condition and the proof does not require major adjustment -- it is not necessary to state another theorem.
If that's your own, you need to prove it; if it is form other references, you need to cite them.
Stability results are well-known in the Control Systems community. Maybe you should explain better the results you are trying to present
Although obligatory Wiki, but very useful :)
http://en.wikipedia.org/wiki/Theorem#Terminology
Sure it is valid! You can even use an already proved statement inside your own proof, as a specific step. That is elegant. Sometimes reproducing a whole demonstration from somebody is useful for the context, and sometimes it is not. Usually, people reproduce only the statement, without the demonstration, which is enough. What you cannot do is to take some existent result without referencing. Plus, there's usually a proper space in a paper for reproducing existent results. This is done before you present your own results. About definitions, although you can reproduce them from others, my personal opinion is that they should be described in textual form, specially if you have your own "ton" of definitions.
It is important to cite correctly another results even in case that are included in your new results
In order to prove your results, you might require some analytical relations which are already proven or you may be proving with existing literature. In this regard, you have to use propositions, lemmas and theorems.
The attached short and nice note describes difference between definition, theorem, lemma, corollary, proposition, conjecture, claim, axiom, identity and paradox. All the technical terms in one note, credit to Prof. D Richeson.
- Badges
- Science topic
- Similar topics
- Engineering
- Control Theory
- Control Systems
- Control Systems Engineering