Tetra-2,3-pyrazinoporphyrazines with externally appended pyridine rings. 3. A new highly electron-deficient octacationic macrocycle: tetrakis-2,3-[5,6-di{2-(N-methyl)pyridiniumyl}pyrazino]porphyrazine, [(2-Mepy)8TPyzPzH(2)]8+

A new octacationic macrocycle, tetrakis-2,3-[5,6-di{2-(N-methyl)pyridiniumyl}pyrazino]porphyrazine, was obtained in its hydrated form as the water-soluble iodide salt. This compound, abbreviated as [(2-Mepy)(8)TPyzPzH(2)](I(8)).8H(2)O (2-Mepy = 2(N-methyl)pyridiniumyl moiety), was obtained by demetalation of the corresponding Mg(II) complex, [(2-Mepy)(8)TPyzPzMg(H(2)O)](I(8)).5H(2)O, which in turn was prepared from its corresponding neutral hydrated species tetrakis-2,3-[5,6-di(2-pyridyl)pyrazino]porphyrazinato(monoaquo)magnesium(II), [Py(8)TPyzPzMg(H(2)O)].4H(2)O, by reaction with CH(3)I in N,N-dimethylformamide. The quaternization reactions by using CH(3)I or methyl p-toluenesulfonate were also conducted on the monomeric precursor 2,3-dicyano-5,6-di(2-pyridyl)-1,4-pyrazine, [(CN)(2)Py(2)Pyz], with formation of the monoquaternized ion [(CN)(2)Py(2-Mepy)Pyz](+) neutralized by iodide and p-toluenesulfonate anions. Single-crystal X-ray work allowed elucidation of the structure of the two salt-like species. The diquaternized ion [(CN)(2)(2-Mepy)(2)Pyz](2+) could also be obtained as a p-toluenesulfonate salt, but attempts at direct macrocyclization of this dicationic species were unsuccessful. The iodide salt [(2-Mepy)(8)TPyzPzH(2)](I(8)).8H(2)O is water-soluble, with different solubilities depending on the range of pH explored. It was established that the macrocycle [(2-Mepy)(8)TPyzPzH(2)](8+) undergoes facile deprotonation and behaves as a strong acid. Aggregation phenomena are observed for both the octacation [(2-Mepy)(8)TPyzPzH(2)](8+) and its corresponding centrally deprotonated species [(2-Mepy)(8)TPyzPz](6+). Nevertheless, both cationic moieties exist in their monomeric form under specific experimental conditions. UV-visible monitored titrations with NaOH provide information about the type of protonation/deprotonation equilibria which are complicated by the occurrence of aggregation phenomena.     

Micro‐Raman spectroscopic study of artificially aged natural and dyed wool

The objective of this study was to evaluate the use of micro‐Raman spectroscopy as a non‐invasive vibrational spectroscopic technique applied to the examination of wool samples, which may be applied to textile materials of cultural heritage interest. In this work, a selection of wool materials were primarily investigated in their unaged states through the utility of a natural wool reference together with selected samples dyed with different natural colorants, namely woad, weld and madder. The identification of the main modes of vibration of the wool fibre keratin was assessed in all the samples, which aided the determination of the changes within the protein structure, in particular, through the cysteine and peptide cross‐linkages brought about by the addition of the dyes that can produce effects similar to degradation. The dye too was assessed importantly to enable its identification through its characteristic scattering or fluorescence emissions on a woollen matrix, as well as to ascertain whether a uniform covering across the surface of the wool was achieved or not. Regarding the artificial degradation of the samples it was possible to observe numerous modifications within the molecular structure of the wool, in particular, within the amide I, C H bending, amide III and S‐S stretchings along with the physical photo‐yellowing of fibres given by the presence of lipids dispersed across the surface of the wool. The effects of ageing on the dyed samples were also investigated, indicating that many of the bands relative to the colorants were still present, yet so too were numerous vibrations from the wool that also indicated a certain level of stress and degradation to the underlying wool. Copyright © 2008 John Wiley & Sons, Ltd.     

Fungal colonization on stoneworks. Interaction fungi-powdered stone samples

The microbial activity plays an important role in the biodegradative processes implied in stonework decay. In natural environments it is not possible to separate the damage produced by microorganisms from damage caused by physical and chemical agents. In vitro assays carried out with microbes isolated from weathered stones are required in order to understand the biological mechanisms involved in stone deterioration. We have described, as commented in the text, how fungal colonization observed on scaglia may be the result of the fine grain size of rock, whereas inhibition of growth on marble may depend on the surface characteristics of calcite grains after grinding. The extent of microbial growth clearly depends on the quantity of cations released in solution. However, fungal growth may, in turn, induce a decrease in pH, thus promoting mineral chemical attack. These observation points to selective action of fungal species in promoting weathering well evidenced by the presence of different extents of cations released in suspension from the same sample. Detailed studies are in progress in order to go into this question.     

LEED investigation of mixed layers of carbon and sulfur on cobalt

The structure of mixed layers of carbon and sulfur on the Co(001) face was investigated by LEED as a function of composition. The results indicate that C and S atoms do not form seperate islands, but are present in the same domains on neighbor sites. Several models are discussed, on the basis of the Structure of the pure phases c(2×2)-S, p(2×2)-S and p(2×2)-C on Co(001), which are shown to be nearly the same as those reported for the Ni(001) face.     

Non-invasive and micro-destructive investigation of the <Emphasis Type="Italic">Domus Aurea</Emphasis> wall painting decorations

The paper reports on the exploitation of an educated multi-technique analytical approach based on a wide non invasive step followed by a focused micro-destructive step, aimed at the minimally invasive identification of the pigments decorating the ceiling of the Gilded Vault of the Domus Aurea in Rome. The combination of elemental analysis with molecular characterization provided by X-ray fluorescence and UV–vis spectroscopies, respectively, allowed for the in situ non-invasive identification of a remarkable number of pigments, namely Egyptian blue, green earth, cinnabar, red ochre and an anthraquinonic lake. The study was completed with the Raman analysis of two bulk samples, in particular, SERS measurements allowed for the speciation of the anthraquinonic pigment. Elemental mapping by scanning electron microscopy-energy dispersive spectrometer combined with micro-fluorimetry on cross-section gave an insight into both the distribution of different blend of pigments and on the nature of the inorganic support of the red dye.     

Nitroxide biradicals as thread units in paramagnetic cucurbituril-based rotaxanes

The first example of paramagnetic rotaxane containing cucurbit[6]urils has been reported and characterized both by ESR and NMR spectroscopy.     

Equations for the Missing Boundary Values in the Hamiltonian Formulation of Optimal Control Problems

Partial differential equations for the unknown final state and initial costate arising in the Hamiltonian formulation of regular optimal control problems with a quadratic final penalty are found. It is shown that the missing boundary conditions for Hamilton’s canonical ordinary differential equations satisfy a system of first-order quasilinear vector partial differential equations (PDEs), when the functional dependence of the H-optimal control in phase-space variables is explicitly known. Their solutions are computed in the context of nonlinear systems with ℝ ⁿ -valued states. No special restrictions are imposed on the form of the Lagrangian cost term. Having calculated the initial values of the costates, the optimal control can then be constructed from on-line integration of the corresponding 2n-dimensional Hamilton ordinary differential equations (ODEs). The off-line procedure requires finding two auxiliary n×n matrices that generalize those appearing in the solution of the differential Riccati equation (DRE) associated with the linear-quadratic regulator (LQR) problem. In all equations, the independent variables are the finite time-horizon duration T and the final-penalty matrix coefficient S, so their solutions give information on a whole two-parameter family of control problems, which can be used for design purposes. The mathematical treatment takes advantage from the symplectic structure of the Hamiltonian formalism, which allows one to reformulate Bellman’s conjectures concerning the “invariant-embedding” methodology for two-point boundary-value problems. Results for LQR problems are tested against solutions of the associated differential Riccati equation, and the attributes of the two approaches are illustrated and discussed. Also, nonlinear problems are numerically solved and compared against those obtained by using shooting techniques.     

Reproduction of exponential polynomials by multivariate non-stationary subdivision schemes with a general dilation matrix

We study scalar multivariate non-stationary subdivision schemes with a general integer dilation matrix. We characterize the capability of such schemes to reproduce exponential polynomials in terms of simple algebraic conditions on their symbols. These algebraic conditions provide a useful theoretical tool for checking the reproduction properties of existing schemes and for constructing new schemes with desired reproduction capabilities and other enhanced properties. We illustrate our results with several examples.     

Factorization of Hermite subdivision operators preserving exponentials and polynomials

In this paper we focus on Hermite subdivision operators that act on vector valued data interpreting their components as function values and associated consecutive derivatives. We are mainly interested in studying the exponential and polynomial preservation capability of such kind of operators, which can be expressed in terms of a generalization of the spectral condition property in the spaces generated by polynomials and exponential functions. The main tool for our investigation are convolution operators that annihilate the aforementioned spaces, which apparently is a general concept in the study of various types of subdivision operators. Based on these annihilators, we characterize the spectral condition in terms of factorization of the subdivision operator.     

Non-invasive identification of surface materials on marble artifacts with fiber optic mid-FTIR reflectance spectroscopy

Research work using a compact and portable fiber optic mid-infrared reflectance spectrometer has been carried out to study surface materials on marble, first on laboratory reference models and then on historical objects. The laboratory research has shown that the complex optical reflectance phenomena of layered samples can be interpreted in terms of the nature of the compounds present (sulfates, oxalates, phosphates, resins, waxes and proteins were studied) even with a very low signal overlapping with the strong carbonate reflectance. The portable instrument was used for in situ examination of the surface condition of two Italian marble works of art: the Deposizione dalla Croce by Benedetto Antelami in the Parma cathedral and the David by Michelangelo in the Galleria dell’Accademia in Firenze.