A counterexample to a ‘‘theorem” on $L\sb{n}$ sets

A counterexample to the a-‘theorem’

We exhibit a renormalization group flow for a four-dimensional gauge theory along which the conformal central charge a increases. The flow connects the maximally superconformal point of an N = 2 gauge theory with gauge group SU(N+1) and Nf = 2N flavors in the ultraviolet, to a strongly-coupled superconformal point of the SU(N) gauge theory with Nf = 2N massless flavors in the infrared. Our exam...

A Counterexample to a Theorem of Chase

A Counterexample on a Theorem by Khojasteh, Goodarzi, and Razani

In the paper by Khojasteh et al. 2010 , the authors tried to generalize Branciari’s theorem, introducing the new integral type contraction mappings. In this note we give a counterexample on their main statement Theorem 2.9 . Also we give a comment explaining what the mistake in the proof is, and suggesting what conditions might be appropriate in generalizing fixed point results to cone spaces, ...

A counterexample to an integer analogue of Carath eodory's theorem

For n 6 we provide a counterexample to the conjecture that every integral vector of a n-dimensional integral polyhedral pointed cone C can be written as a nonnegative integral combination of at most n elements of the Hilbert basis of C. In fact, we show that in general at least b7=6 nc elements of the Hilbert basis are needed.

Classical counterexample to Bell ’ s theorem

We describe a strictly classical dice game, which emulates the main features of the EPR experiment, including violation of Bell’s inequalities. Therefore, the standard interpretation that Bell’s theorem provides necessary conditions for ‘local realism’ is disproved. PACS 03.65.Ud (Entanglement and quantum non locality)