A simple proof for Imnang’s algorithms

A simple proof of Zariski's Lemma

‎Our aim in this very short note is to show that the proof of the‎ ‎following well-known fundamental lemma of Zariski follows from an‎ ‎argument similar to the proof of the fact that the rational field‎ ‎$mathbb{Q}$ is not a finitely generated $mathbb{Z}$-algebra.

A simple correctness proof for magic transformation

The paper presents a simple and concise proof of correctness of the magic transformation. We believe it may provide a useful example of formal reasoning about logic programs. The correctness property concerns the declarative semantics. The proof, however, refers to the operational semantics (LD-resolution) of the source programs. Its conciseness is due to applying a suitable proof method.

A Simple Combinatorial Proof of

A Simple Proof of The

We give elementary derivations of some classical summation formulae for bilateral (basic) hypergeometric series. In particular, we apply Gauß’ 2F1 summation and elementary series manipulations to give a simple proof of Dougall’s 2H2 summation. Similarly, we apply Rogers’ nonterminating 6φ5 summation and elementary series manipulations to give a simple proof of Bailey’s very-well-poised 6ψ6 summ...

A proof of convergence for Ant algorithms

A proof of convergence for Ant algorithms is developed. Ant algorithms were modeled as branching random processes: the branching random walk and branching Wiener process to derive rates of birth and death of ant paths. Substitution is then carried out in birth-death processes, which proves that a stable distribution is surely reached. This indicates that Ant algorithms converge with probability...