The starting point of this article is represented by a recent work of Finch [2000]. Based on two asymptotic results concerning the Erdos function, he proposed some interesting equation concerning the moments of the Smarandache function. The aim of this note is give a bit modified proof and to show some computation results for one of the Finch equation. We will call the numbers obtained from com...

Redox reactions are the heart of function in biological systems. Using a deceptively simple toolbox, consisting largely of first row transition metals and the 20 canonical amino acids, nature has evolved proteins that contain cofactors with reduction potentials (E°′) between +1 V and −1 V. Chemists have long known that ligands to transition metals markedly alter E°′ of the metal, often in a sys...

The Golomb ruler problem has been proposed as a challenging constraint satisfaction problem. We consider a large number of diierent models of this problem, both binary and non-binary. The problem can be modelled using quaternary constraints, but in practice using a set of auxiliary variables and ternary constraints gives better results. A binary encoding of the problem gives a smaller search tr...

Noble metal nanoparticles have distinct optical properties arising from localized surface plasmon resonance (LSPR). It is wellestablished that a LSPR spectrum depends strongly on the size and shape of the nanoparticles as well as on the distance between the nanoparticles. The precise measurement of the interparticle distance-dependent LSPR spectrum has been the fundamental principle of many ana...

We investigate the distance vectors contained in individual Costas arrays and in pairs of Costas arrays, and prove some rigorous results in the case of the algebraically constructed arrays. Overall, it appears that the set with the property that every Costas array has a distance vector in this set, or that every pair of Costas arrays with a common vector have a common vector in this set, is in ...

Economic conditions are placing unprecedented pressures on universities and funding agencies. For young scholars, this translates into fewer postdoctoral and faculty lines. For highly experienced senior scholars, it emerges as fewer opportunities for new programs of research and collaborations, and this in turn limits the options available to senior scientists for training young scientists. Res...