NMR Characterization of Lanthanide(3+) Complexes of Tetraazatetrakisphosphinato and Tetraazatetra­kisphosphonato Ligands

The three‐dimensional structures in aqueous solution of the entire series of the Ln³⁺ complexes [Ln(DOTP*‐Et)]^? (formed from the free ligand P,P′,P″,P′′′‐[1,4,7,10‐tetraazacyclododecane‐1,4,7,10‐tetrayltetrakis(methylene)]tetrakis[P‐ethylphosphinic acid] (H₄DOTP*‐Et) were studied by NMR techniques to rationalize the parameters governing the relaxivity of the Gd³⁺ complex and evaluate its potential as MRI contrast agent. From the ¹H‐ and ³¹P‐NMR lanthanide‐induced‐shift (LIS) values, especially of the [Yb(DOTP*‐Et)]^? complex, it was concluded that the [Ln(DOTP*‐Et)]^? complexes adopt in solution twisted square antiprismatic coordination geometries which change gradually their coordination‐cage structure along the lanthanide series. These complexes have no inner‐sphere‐H₂O coordination, and preferentially have the (R,R,R,R) configuration of the P‐atoms in the pendant arms. Self‐association was observed in aqueous solution for the tetraazatetrakisphosphonic acid ester complexes [Ln(DOTP*‐OEt)]^? (=[Ln(DOTP‐Et)]^?) and [Ln(DOTP*‐OBu)]^? (=[Ln(DOTP‐Bu)]^?) at and above 5 mM concentration, through analysis of ³¹P‐NMR, EPR, vapor‐pressure‐osmometry, and luminescence‐spectroscopic data. The presence of the cationic detergent cetylpyridinium chloride (CPC; but not of neutral surfactants) shifts the isomer equilibrium of [Eu(DOTP*‐OBu)]^? to the (S,S,S,S) form which selectively binds to the cationic micelle surface.     

An hyperbolic system of P.D.E. relevant in general relativity

Ricerche di Matematica - Assuming as starting point the validity of the Einstein-Rosen metric we study the hyperbolic system of P.D.E. to which the Einstein’s field equations can be reduced....     

A free boundary problem in the theory of electrically actuated microdevices

Electrostatically deflected elastic systems are increasingly used in technical applications. We study a typical situation as a free boundary problem and prove, under quite general hypotheses, the existence of a local branch of solutions. Hadamard’s variational formula is crucial in the proof, which is based on the implicit function theorem in Banach spaces.     

Invariant regions for the Nernst-Planck equations

We consider a coupling between the Nernst-Planck equations and the Navier-Stokes system; we study the stationary and the evolution problems. The crucial property turns out to be the existence of an invariant region. An asymptotic result in the case of Neumann boundary conditions is also given.     

Existence of weak solutions for the nonstationary problem of the Joule heating of a conductor

Summary An initial-boundary value problem for a system of two nonlinear partial differential equations is studied using the Faedo-Galerkin method. The problem describes the electric heating of a conducting body. The main result is a theorem of existence of weak solutions for an arbitrarily large interval of time.     

The plane stress problem of Ghizzetti in elasto-plasticity

The theory of variational inequalities is applied to some special problems of elastic-plastic deformation.     

On a problem of the theory of lubrication governed by a variational inequality

The hydrodynamic lubrication of a complete journal bearing of finite width is studied using the theory of variational inequalities: we deal mainly with existence, uniqueness and regularity of the solution.     

Existence results for a nonlinear elliptic system modelling a temperature dependent electrical resistor

Summary The electrical resistance in many substances varies greatly with the temperature which in turns depends on the Joule effect. This nonlinear effect is described under steady conditions by a system of nonlinear elliptic equations with a quadratic growth in the gradient. This work gives a theorem of existence for the related elliptic boundary value problem.     

Optimal control for the thermistor problem with a current limiting device

Email: cimatti{at}dm.unipi.it Received on September 26, 2005; Accepted on August 2, 2006 The problem of finding in the thermistor problem the optimaldifference of applied potential in order to minimize a suitablecost functional involving the temperature is studied. We findthe optimal system in the elementary case of constant electricconductivity. In addition, a theorem of existence of the optimalsolution is given in the general case of conductivities dependingon the temperature.