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.

A green and highly effective solvent-free protocol has been reported for the synthesis of N,N′-alkylidene bisamides via the reaction of arylaldehydes (1 eq.) with primary amides (2 eq.) in the presence of saccharin-N-sulfonic acid (SaSA) as a solid-acid catalyst. The mentioned compounds have been obtained in high yields and short reaction times.

In view of the lack o realism of an AWGN model for ambient noise arising in many practical channels in which multiuser detection techniques may be applied, natural questions arise concerning the applicability, robustness, and performance of multiuser detection techniques for non-Gaussian multiple-access channels. In this paper, we consider the multiple access mitigation problem in DS-CDMA chann...