(+)-syn-Benzotriborneol: the first functionalised enantiopure C3-symmetric benzocyclotrimer

Copper(I) thiophencarboxylate readily and effectively cyclotrimerises protected 5-bromo-6-trimethylstannylborn-5-en-2-ols, leading to oxygen-functionalised benzocyclotrimers. The remarkably high syn to anti ratio is driven by relative displacement of the halide and metal on the alkene moiety and depends on the steric hindrance of the protecting group of the hydroxy function. The less hindered methyl derivative affords exclusively syn-benzocyclotrimer. The readily removable methoxymethyl derivative gives enantiopure syn-tribenzoborneol in high yields.     

Multiple functional group cooperation in phosphate diester cleavage promoted by Zn(II) complexes

Zn(II) complexes bearing multiple auxiliary organic groups greatly accelerate the cleavage of a phosphate diester.     

Procedure for retrieving the optical properties of a two-layered medium from time-resolved reflectance measurements

A procedure for retrieving the optical properties of a two-layered diffusive medium based on an exact analytical solution of the diffusion equation and on relative multidistance time-resolved reflectance measurements is presented. The method overcomes some limitations of previously developed procedures. Five parameters of the medium have been fitted: the absorption and the reduced scattering coefficients of both layers and the thickness of the first layer. The actual values of the parameters are correctly retrieved by the procedure. The inversion procedure does not require an initial guess for the unknown optical properties, but the starting value for the thickness of the first layer needs to be estimated with an error smaller than 50%.     

Secondary ion mass spectrometry and X-ray photoelectron spectroscopy investigation on chemical vapor deposited CeO(2-)ZrO(2)-TiO(2) thin films

Mixed CeO(2)-ZrO(2) systems have attracted widespread interest for their use in three-way catalyst (TWC) technology for automotive exhaust conversion to non-toxic products. In this work, CeO(2)-ZrO(2) thin films were deposited, via chemical vapor deposition, in order to obtain nanoscale materials with a high surface-to-volume ratio, with precise control of system properties. The addition of TiO(2) as buffer layer was also investigated. Cordierite was chosen as substrate, being the usual refractory material for catalytic mufflers. The multilayers were characterized by scanning electron microscopy, X-ray photoelectron spectroscopy (XPS) and secondary ion mass spectrometry (SIMS). In particular, the combination of SIMS and XPS allowed us to investigate both surface and in-depth chemical composition, studying also film-intermixing phenomena induced by annealing processes.     

Global theory for thermodynamic behaviour of a continuous medium

Summary A global theory for the thermodynamic behaviour of a material is introduced on the based of the Systems Theory. Hence the hypotheses for which a local formulation is deducible are specified.

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Riassunto Partendo da una teoria globale del comportamento termodinamico di un materiale, espresso in termini della Teoria dei Sistemi, si precisano le ipotesi per le quali è possibile pervenire ad una formulazione locale.

     

Direct transition between a singlet Mott insulator and a superconductor

We argue that a normal Fermi liquid and a singlet, spin-gapped Mott insulator cannot be continuously connected, and that some intermediate phase must intrude between them. By explicitly working out a case study where the singlet insulator is stabilized by orbital degeneracy and an inverted Hund's rule coupling, mimicking a Jahn-Teller effect, we find that the intermediate phase is a superconductor.     

Derivatives of Wronskians with applications to families of special Weierstrass points

Let be a flat proper family of smooth connected projective curves parametrized by some smooth scheme of finite type over . On every such a family, suitable derivatives along the fibers" (in the sense of Lax) of the relative wronskian, as defined by Laksov and Thorup, are constructed. They are sections of suitable jets extensions of the -th tensor power of the relative canonical bundle of the family itself.

The geometrical meaning of such sections is discussed: the zero schemes of the -th derivative () of a relative wronskian correspond to families of Weierstrass Points (WP's) having weight at least .

The locus in , the coarse moduli space of smooth projective curves of genus , of curves possessing a WP of weight at least , is denoted by . The fact that has the expected dimension for all was implicitly known in the literature. The main result of this paper hence consists in showing that has the expected dimension for all . As an application we compute the codimension Chow (-)class of for all , the main ingredient being the definition of the -th derivative of a relative wronskian, which is the crucial tool which the paper is built on. In the concluding remarks we show how this result may be used to get relations among some codimension Chow (-)classes in (), corresponding to varieties of curves having a point with a suitable prescribed Weierstrass Gap Sequence, relating to previous work of Lax.

     

Effective method to compute vibrationally resolved optical spectra of large molecules at finite temperature in the gas phase and in solution

The authors present a new method for the computation of vibrationally resolved optical spectra of large molecules, including the Duschinsky rotation of the normal modes and the effect of thermal excitation. The method automatically selects the relevant vibronic contributions to the spectrum, independently of their frequency, and it is able to provide fully converged spectra with moderate computational times, both in vacuo and in solution. By describing the electronic states in the frame of the density functional theory and its time-dependent extension, they computed the room temperature absorption spectra of coumarin C153 and trans-stilbene in cyclohexane and the phosphorescence spectrum of porphyrazine in gas phase, showing that the method is fast and efficient. The comparison with experiment for trans-stilbene and coumarin C153 is very satisfactory, confirming the progress made toward a reliable method for the computation and interpretation for the optical spectra of large molecules.     

New approaches to multi-objective optimization

A natural way to deal with multiple, partially conflicting objectives is turning all the objectives but one into budget constraints. Many classical optimization problems, such as maximum spanning tree and forest, shortest path, maximum weight (perfect) matching, maximum weight independent set (basis) in a matroid or in the intersection of two matroids, become NP-hard even with one budget constraint. Still, for most of these problems efficient deterministic and randomized approximation schemes are known. Not much is known however about the case of two or more budgets: filling this gap, at least partially, is the main goal of this paper. In more detail, we obtain the following main results: Using iterative rounding for the first time in multi-objective optimization, we obtain multi-criteria PTASs (which slightly violate the budget constraints) for spanning tree, matroid basis, and bipartite matching with \(k=O(1)\) budget constraints. We present a simple mechanism to transform multi-criteria approximation schemes into pure approximation schemes for problems whose feasible solutions define an independence system. This gives improved algorithms for several problems. In particular, this mechanism can be applied to the above bipartite matching algorithm, hence obtaining a pure PTAS. We show that points in low-dimensional faces of any matroid polytope are almost integral, an interesting result on its own. This gives a deterministic approximation scheme for \(k\) -budgeted matroid independent set. We present a deterministic approximation scheme for \(k\) -budgeted matching (in general graphs), where \(k=O(1)\) . Interestingly, to show that our procedure works, we rely on a non-constructive result by Stromquist and Woodall, which is based on the Ham Sandwich Theorem.