Because of this, a solution of (1) gives rise to a linear representation of the braid group Bn on V⊗n for every n. In [D], Drinfel’d raised the question of finding set-theoretical solutions of the YangBaxter equation. Specifically, we consider a set S and an invertible map R : S×S → S×S. We think of the Yang-Baxter equation (1) as an equality of maps from S×S×S to S×S×S. As in the linear case, ...

Let lK be a commutative field and (P, +) be a uniquely 2-divisible group (not necessarily abelian). We characterize all functions T: IK -+ P such that the Cauchy difference T(s+ t) T(t) T(s) depends only on the product st for all s, t E ~{. Further, we apply this result to describe solutions of the functional equation F(s + t) = K(st) 0 H(s) 0 G(t), where the unknown functions F, K, H, G map th...

In this note we consider two S-unit equations for which we will exhibit many solutions. Our first problem concerns solutions to the equation a + b = c where a, b, and c are coprime integers such that all prime factors of abc lie in a given set S of s primes. In [8] J.-H. Evertse showed that this S-unit equation has at most exp(4s+ 6) solutions. On the other hand, in [6] P. Erdős, C. Stewart, an...

A complex of Cu(II) with 1-(6-HydroxyNaphthalen-2-yl) Butane-1,3-Dione (HNBD) was synthesized and characterized by elemental analysis, IR, UV and DTA-TG-DTG techniques.    IR spectra as well as UV-visible absorption measurements indicated that Cu(II) ion was coordinated to the HNBD ligand. The TG-DTA-DTG curves showed that thermal decomposition o...

An investigation of the drying of spherical food particles was performed, using peas as the model material. In the development of a mathematical model for drying curves, moisture diffusion was modelled using Fick’s second law for mass transfer. The resulting partial differential equation was solved using a forward-time central-space finite difference approximation, with the assumption of variab...