We use the AI proof planning techniques of recursion analysis and rippling as tools to analyze so called inductionless induction proof techniques. Recursion analysis chooses induction schemas and variables and rippling controls rewriting in explicit induction proofs. They provide a basis for explaining the success and failure of inductionless induction both in deduction of critical pairs and in...

In the eld of inductive theorem proving syntactical diierences between the induction hypothesis and induction conclusion are used in order to guide the proof BvHS91, Hut90, Hut]. This method of guiding induction proofs is called rippling / coloring terms and there is considerable evidence of its success on practical examples. For equality reasoning we use these annotated terms to represent synt...

Here we report a new method combining strain and defect engineering for the periodic modulation of graphene nanoscale rippling. First, gold nanoparticles 16 nm in diameter were synthesized by seed-mediated, wet-chemical approach, thiol-terminated polyethylene glycol (mPEG-SH) molecules grafted onto their surface. High-density monolayers PEGylated successfully prepared on Si substrates Langmuir-...

In the eld of inductive theorem proving syntactical diierences between the induction hypothesis and induction conclusion are used in order to guide the proof BvHS91, Hut90, Hut]. This method of guiding induction proofs is called rippling / coloring terms and there is considerable evidence of its success on practical examples. For equality reasoning we use these annotated terms to represent synt...

Myxobacteria colonies during their aggregation phase propagate complex waves over their surface. These waves are fundamentally different from the analogous phenomenon in diffusion-reaction systems or in populations of Dictyostelium discoideum where colliding waves annhilate. Myxobacterial waves appear to pass through one another, analogous to solitons. Moreover, individual bacteria oscillate ba...