Reductive amination of furfural was recently investigated
as a
straightforward method for the construction of biomass-based primary
amine (furfurylamine) and tertiary amine [tris(2-furanylmethyl)amine]
with, however, secondary amine [bis(2-furanylmethyl)amine]
as a problem due to a selectivity issue. In this research, we demonstrated
a highly selective and efficient strategy for the construction of bis(2-furanylmethyl)amine in 99% yield by Ir-catalyzed hydrogenative
homocoupling of biomass-based 2-furanacarbonitrile in one pot. The
Ir catalyst was prepared by immobilization of the [Cp*Ir(bpy)Cl]Cl
complex in a 2,2′-bipyridine-functionalized UiO-67. Both furfurylamine
and furfurylamine-derived secondary imine were successively detected
as intermediates. Detailed kinetic analysis suggested the secondary
imine hydrogenation as the rate-determining step instead of 2-furanacarbonitrile
hydrogenation. A variety of symmetry secondary amines (18 examples)
were selectively prepared in excellent to moderate yields from the
corresponding nitriles with the Ir catalyst. This research thus built
a bridge between a well-defined single-site catalyst with a metal–organic
framework as ligand/support and its homogeneous counterpart to understand
kinetic details in the biomass-based amine formation.
In this paper, we extend the original Normalized Least Mean Fourth (NLMF) and Normalized Least Mean Square (NLMS) adaptive filtering algorithms into Geometric Algebra (GA) space to enable them to process multidimensional signals. We redefine the cost functions and propose the GA based NLMF and NLMS algorithms (GA-NLMF & GA-NLMS). We take full advantage of the ability of GA to represent multidimensional signals in GA space. GA-NLMS minimizes the cost function of the normalized mean square of the error signal, and remain stable as the input signal of the filter increases. GA-NLMS has fast convergence rate but higher steady-state error. The GA-NLMF algorithm minimizes the cost function of the normalized mean fourth of the error signal. Simulation results show that our proposed GA-NLMS adaptive filtering algorithm outperforms original NLMS algorithm in terms of convergence rate and steady-state error, and GA-NLMF outperforms both NLMF and GA-NLMS algorithms. GA-NLMF has faster convergence rate and lower steady state error, which is proved in the experiments.
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