Preparation and characterization of multilayered structures with polyconjugated systems

Soluble poly(3-alkylthiophenes) can be conveniently tailored by the introduction of polar groups in the side chain with the aim of obtaining structures able to give multilayered films with the Langmuir Blodgett technique. The films, uniform in thickness, show orientation of the polyenic backbone in the dipping direction as detected by UV-visible measurements in polarised light. These materials can be conveniently used in electronic device preparation.     

Effective longitudinal shear moduli of periodic fibre-reinforced composites with functionally-graded fibre coatings

This paper presents a homogenization method for unidirectional periodic composite materials reinforced by circular fibres with functionally graded coating layers. The asymptotic homogenization method is adopted, and the relevant cell problem is addressed. Periodicity is enforced by resorting to the theory of Weierstrass elliptic functions. The equilibrium equation in the coating domain is solved in closed form by applying the theory of hypergeometric functions, for different choices of grading profiles. The effectiveness of the present analytical procedure is proved by convergence analysis and comparison with finite element solutions. The influence of microgeometry and grading parameters on the shear stress concentration at the coating/matrix interface is addressed, aimed at the composite optimization in regards to fatigue and debonding phenomena.     

Scattering amplitudes from multivariate polynomial division

We show that the evaluation of scattering amplitudes can be formulated as a problem of multivariate polynomial division, with the components of the integration-momenta as indeterminates. We present a recurrence relation which, independently of the number of loops, leads to the multi-particle pole decomposition of the integrands of the scattering amplitudes. The recursive algorithm is based on the weak Nullstellensatz theorem and on the division modulo the Gröbner basis associated to all possible multi-particle cuts. We apply it to dimensionally regulated one-loop amplitudes, recovering the well-known integrand-decomposition formula. Finally, we focus on the maximum-cut, defined as a system of on-shell conditions constraining the components of all the integration-momenta. By means of the Finiteness Theorem and of the Shape Lemma, we prove that the residue at the maximum-cut is parametrized by a number of coefficients equal to the number of solutions of the cut itself.     

CoAPO5 as a water oxidation catalyst and a light sensitizer

We report the first use of cobalt aluminophosphate (CoAPO5) as a water oxidation catalyst. A decrease in the overvoltage by about 0.2 V with respect to catalyst free FTO has been observed. Additionally, we show that CoAPO5, deposited on ITO or Pt, can also act as a photo-electro-catalyst, as it generates enhanced oxidation currents in the presence of light starting from a bias of +0.8 V vs. Ag/AgCl.     

Inductive Construction of the Loop Transform for Abelian Gauge Theories

We construct the loop transform in the case of Abelian gauge theories as a unitary operator given by the inductive limit of Fourier transforms on tori. We also show that its range, i.e. the space of kinematical states of the quantum loop representation, is the Hilbert space of square integrable complex valued functions on the group of hoops.     

A brill - noether theory for<Emphasis Type="Italic">κ</Emphasis>-gonal nodal curves

LetV(g, x, k, y) be the set of all pairs (X, F), whereX is an integral projective nodal curve withp _a(X)=g and card(Sing(X))=x andF is a rank 1 torsion free sheaf onX with deg(F)=k, card(Sing(F))=y andh ⁰(X, F)≥2. Here we study a general (X, F) εV(g, x, k, y) and in particular the Brill-Noether theory ofX and the scrollar invariants ofF.