Contractive mappings and existence of cycle times for a monotone and homogeneous function

Given a monotone and homogeneous self-mapping f$f$ of the n$n$-dimensional positive cone, a family of contractive mappings is used to define an equivalence relation in the index set, as well as a total order among the equivalence classes. Then, it is shown (i) that the cycle times are well-defined at each index belonging to the maximal and minimal classes, and (ii) that the cycle times of f$f$ exist at every index whenever a weak convexity condition is satisfied.     

Efficient solvability of Hamiltonians and limits on the power of some quantum computational models

One way to specify a model of quantum computing is to give a set of control Hamiltonians acting on a quantum state space whose initial state and final measurement are specified in terms of the Hamiltonians. We formalize such models and show that they can be simulated classically in a time polynomial in the dimension of the Lie algebra generated by the Hamiltonians and logarithmic in the dimension of the state space. This leads to a definition of Lie-algebraic "generalized mean-field Hamiltonians." We show that they are efficiently (exactly) solvable. Our results generalize the known weakness of fermionic linear optics computation and give conditions on control needed to exploit the full power of quantum computing.     

A radiation condition for uniqueness in a wave propagation problem for 2‐D open waveguides

We study the uniqueness of solutions of Helmholtz equation for a problem that concerns wave propagation in waveguides. The classical radiation condition does not apply to our problem because the inhomogeneity of the index of refraction extends to infinity in one direction. Also, because of the presence of a waveguide, some waves propagate in one direction with different propagation constants and without decaying in amplitude. We provide an explicit condition for uniqueness for rectilinear waveguides, which takes into account the physically significant components, corresponding to guided and non‐guided waves; this condition reduces to the classical Sommerfeld–Rellich condition in the relevant cases. By a careful asymptotic analysis we prove that the solution derived by Magnanini and Santosa (SIAM J. Appl. Math. 2001; 61 :1237–1252) for stratified media satisfies our radiation condition. Copyright © 2008 John Wiley & Sons, Ltd.     

Polysaccharides based hydrogels for biological applications

Polysaccharides based hydrogels show several peculiar properties which can be so reassumed: • Capability to absorb a great amount of water once immersed in biological fluids, assuming, consequently, a structure similar to extracellular matrix or biological tissue • Tissotropic property, i.e. possibility to be injected through a needle without lose of their rheological properties. These fundamental properties make them ideal materials for several biomedical applications, such as cellular scaffold, coatings for biomedical disposals, treatments for different diseases, controlled release of drugs, etc. Hyaluronane, Carboxymethyl cellulose and Alginic acid based 50% hydrogels (i.e. 50% of the carboxylate groups present in the macromolecule chain were involved in the cross-linking reaction) are synthesised. Their effectiveness in promoting cells adhesion and proliferation was verified. Furthermore the possibility of injecting and sterilising hydrogels permitted to test the effect of Hyal 50% in the osteoarthritis therapy. It was found that the in vivo effect of Hyal 50% in the treatment of surgically created chondral defect in the rabbit knee was positive. These materials can be both chemically and morphologically modified. In fact, the insertion of sulphate groups increase their hemocompatibility as demonstred by the increase of TT (time necessary to turn the fibrinogen to thrombin). Furthermore microporous hydrogels were obtained and tested as drug controlled release systems.     

Prediction of Sol Fraction and Average Molecular Weights after Gelation for Non‐Linear Free Radical Polymerizations Using a Kinetic Approach

Mass balance equations in terms of the moment generating function of the distribution of mole concentrations of polymer species for free radical copolymerizations of mono/divinyl monomers could be numerically solved after gel point using open source code ACDC, needed for extremely stiff two‐point boundary value problems. For the first time, it became possible to compare the error of earlier well‐known approximated estimation methods for the weight fraction of sol and average molecular weights to this accurate mathematical solution. It turns out that predictions by the pseudo‐kinetic method are reasonable only when equal reactivity of double bonds prevails, causing early gelation in the batch reactor. Otherwise the discrepancies between the exact and approximate solutions are quite important.

Comparison between predicted number‐average and weight‐average degrees of polymerization of sol in batch non‐linear free radical polymerizations of model system III.