A highly efficient procedure for the preparation of N,N'-alkylidenebisamides in the presence of BF3.SiO2 as a catalyst is described. N,N'-alkylidenebisamides have been prepared via one-pot three-component condensation reaction of various aldehydes and amides. All of the reactions proceeded in high yields and in moderately short reaction times.

In this article, the notion of $n-$derivation is introduced for all integers $ngeq 2$. Although all derivations are $n-$derivations,  in general these notions are not equivalent. Some properties of ordinary derivations are  investigated for $n-$derivations. Also, we show that under certain mild condition  $n-$derivations are derivations.

We investigate the long-term behavior of solutions of the difference equation[ x_{n+1}=x_{n}x_{n-3}-1 ,, n=0 ,, 1 ,, ldots ,, ]noindent where the initial conditions $x_{-3} ,, x_{-2} ,, x_{-1} ,, x_{0}$ are real numbers.  In particular, we look at the periodicity and asymptotic periodicity of solutions, as well as the existence of unbounded solutions.