Self‐Assembly of Calix[6]arene–Diazapyrenium Pseudorotaxanes: Interplay of Molecular Recognition and Ion‐Pairing Effects

The calix[6]arene wheel CX forms pseudorotaxane species with the diazapyrenium‐based axle 1? 2PF₆ in CH₂Cl₂ solution. The macrocyclic component is a heteroditopic receptor, which can complex the electron‐acceptor moiety of the axle inside its cavity and the counterions with the ureidic groups on the upper rim. The self‐assembled supramolecular species is a complex structure, which involves three components—the wheel, the axle and its counterions—that can mutually interact and affect. The stoichiometry of the resulting supramolecular complex depends on the nature and concentration of the counterions. Namely, it is observed that in dilute solution and with low‐coordinating anions the axle takes two wheels, whereas with highly coordinating anions or in concentrated solutions the complex has a 1:1 stoichiometry.     

Bifurcation and chaos near sliding homoclinics

We study the chaotic behaviour of a time dependent perturbation of a discontinuous differential equation whose unperturbed part has a sliding homoclinic orbit that is a solution homoclinic to a hyperbolic fixed point with a part belonging to a discontinuity surface. We assume the time dependent perturbation satisfies a kind of recurrence condition which is satisfied by almost periodic perturbations. Following a functional analytic approach we construct a Melnikov-like function M(α) in such a way that if M(α) has a simple zero at some point, then the system has solutions that behave chaotically. Applications of this result to quasi-periodic systems are also given.     

An example of chaotic behaviour in presence of a sliding homoclinic orbit

We present an example on the chaotic behaviour of a 3-dimensional quasiperiodically perturbed discontinuous differential equation whose unperturbed part has a homoclinic orbit that is a solution homoclinic to a hyperbolic fixed point with a part belonging to a discontinuity plane. Melnikov type analysis is applied.     

Validation of a method for extraction of polycyclic aromatic hydrocarbons from sewage sludge and analysis by GC-MS

In the present study, the solid–liquid extraction with low temperature purification was validated for the determination of 16 polycyclic aromatic hydrocarbons from sewage sludge by gas chromatography-mass spectrometry. Recoveries ranged 70–114% for naphthalene, acenaphthylene, acenaphthene, fluorene, phenanthrene, anthracene, fluoranthene, pyrene, benzo[a]anthracene and chrysene, while the compounds benzo[b]fluoranthene, benzo[k]fluoranthene, benzo[a]pyrene, indeno[1,2,3-cd]pyrene, dibenzo[a,h]anthracene and benzo[g,h,i]perylene showed recoveries of between 40 and 70%. The relative standard deviation was less than 13% for all of the compounds. Negative matrix effect was observed on the 10 compounds with less retention time in the chromatographic analysis and positive matrix effect noticed on the others. The limits of quantification were from 2 to 20 μg kg^?1, about 30 times less than the maximum residue limit allowed in sludge by the European Union. The validated method produced quantification of 11 PAHs in one sludge sample at concentrations ranging 20–2000 μg kg^?1.     

On the Chaotic Behaviour of Discontinuous Systems

We follow a functional analytic approach to study the problem of chaotic behaviour in time-perturbed discontinuous systems whose unperturbed part has a piecewise C ¹ homoclinic solution that crosses transversally the discontinuity manifold. We show that if a certain Melnikov function has a simple zero at some point, then the system has solutions that behave chaotically. Application of this result to quasi periodic systems are also given.     

Periodic solutions of a periodically forced and undamped beam resting on weakly elastic bearings

We study the problem of existence of periodic solutions to a partial differential equation modelling the behavior of an undamped beam subject to an external periodic force. We assume that the ordinary differential equation associated to the first two modes of vibration of the beam has a symmetric homoclinic solution. By using methods borrowed by dynamical systems theory we prove that, if the period is non resonant with the (infinitely many) internal periods of the PDE, the equation has a weak periodic solution of the same period as the external force. In particular we obtain continua of periodic solutions for the undamped beam in absence of external forces. This result may be considered as an infinite dimensional analogue of a result obtained in [16] concerning accumulation of periodic solutions to homoclinic orbits in finite dimensional reversible systems. Matteo Franca: Partially supported by G.N.A.M.P.A. – INdAM (Italy).     

Preparation of potentially bioactive aza and thiaza polycyclic compounds containing a bridgehead nitrogen atom. Synthesis of pyrrolo[1,2,3-de]-1,4-benzothiazine derivatives

The synthesis of some pyrrolo[1,2,3-de]-1,4-benzothiazine derivatives by using a modified Bischler type cyclization of N-(2,2-diethoxyethyl)-2H-1,4-benzothiazines as a crucial step is described. The alternative approach based on Friedel-Crafts alkylation of the N-(2-chloroethyl)-2H-1,4-benzothiazines is shown to be impractical due to the low yield obtained.     

Chiroptical properties of cyclic amines

Chiroptical properties of several 2 or 3 monosubstituted azetidines, pyrrolidines and piperidines as free bases and N-[2-pyridyl N-oxide] derivatives has been examined. The absolute configuration can be unambiguously established, independently on the nature of the substituent and the size of the ring, only for 2-substituted N-[2-pyridyl N-oxide]amine derivatives. This behaviour is explained in terms of limited rotational freedom in these compounds.     

Global center manifolds in singular systems

The problem of existence of aglobal center manifold for a system of O.D.E. like (*) $$\left\{ {\begin{array}{*{20}c} {\dot x = A(y)x + F(x,y)} \\ {\dot y = G(x,y), (x,y) \in \mathbb{R}^n \times \mathbb{R}^m ,} \\ \end{array} } \right.$$ is considered. We give conditions onA(y), F(x, y), G(x, y) in order that a functionH: ? ^m →? ⁿ , with the same smoothness asA(y), F(x, y), G(x, y), exists and is such that the manifoldC={(x,y)∈? ⁿ ×? ^m ∣x=H(y),y∈? ^m } is an invariant manifold for (*), and there exists ρ>0 such that any solution of (*) satisfying sup _t∈?∣x(t)∣ <ρ must belong toC. This is why we callC global center manifold. Applications are given to the problem of existence of heteroclinic orbits in singular systems.