Design and synthesis of a C2-symmetric self-complementary hydrogen-bonding cleft molecule based on the bicyclo[3.3.1]nonane and 4-oxo-5-azaindole framework. formation of channels and inclusion complexes in the solid state

The synthesis of a C2-symmetric cleft molecule 2 based on the fused framework between bicyclo[3.3.1]nonane and 4-oxo-5-azaindole, incorporating a self-complementary hydrogen-bonding motif, in both racemic and enantiomerically pure forms is reported. This cleft molecule is reminiscent of analogues of Tr?ger's base though with different cleft dimensions and tilt angles. The framework of 2 provides a building block for the construction of self-assembled hydrogen-bonded supramolecular structures. The solid-state structure of 2 is highly influenced by the limited solubility of (+/-)-2 and (-)-2. The solvents interact with the potential hydrogen-bonding motifs of (+/-)-2 and (-)-2, forming different three-dimensional structures as revealed by X-ray diffraction analysis. In the solid state (+/-)-(2)2 x 5DMF forms hydrogen-bonded pleated band structures that build up three-dimensional pens between adjacent bands in which two molecules of DMF are trapped. In contrast, the aggregate obtained from (-)-2, (-)-2 x 2AcOH, showed infinite bands of complex constitution.     

The relaxed Newton method derivative: Its dynamics and non-linear properties

The dynamic behaviour of the one-dimensional family of maps f(x)=_c2[(a−1)x+_c1]^{−λ/(α−1)}$f\left(x\right)=c_2{[(a-1)x+c_1]}^{-\lambda /(\alpha -1)}$ is examined, for representative values of the control parameters a,_c1$a,c_1$, _c2$c_2$ and λ$\lambda$. The maps under consideration are of special interest, since they are solutions of the relaxed Newton method derivative being equal to a constant a$a$. The maps f(x)$f\left(x\right)$ are also proved to be solutions of a non-linear differential equation with outstanding applications in the field of power electronics. The recurrent form of these maps, after excessive iterations, shows, in an _xn$x_n$ versus λ$\lambda$ plot, an initial exponential decay followed by a bifurcation. The value of λ$\lambda$ at which this bifurcation takes place depends on the values of the parameters a,_c1$a,c_1$ and _c2$c_2$. This corresponds to a switch to an oscillatory behaviour with amplitudes of f(x)$f\left(x\right)$ undergoing a period doubling. For values of a$a$ higher than 1 and at higher values of λ$\lambda$ a reverse bifurcation occurs. The corresponding branches converge and a bleb is formed for values of the parameter _c1$c_1$ between 1 and 1.20. This behaviour is confirmed by calculating the corresponding Lyapunov exponents.     

Pareto set approximation by the method of adjustable weights and successive lexicographic goal programming

A nonlinear multiobjective optimization problem is considered. Two methods are proposed to generate solutions with an approximately uniform distribution in a Pareto set. The first method is supposed to find the solutions as minimizers of weighted sums of objective functions where the weights are properly selected using a branch and bound type algorithm. The second method is based on lexicographic goal programming. The proposed methods are compared with several metaheuristic methods using two and three-criteria tests and applied problems.