A minimax theorem for vector-valued functions,part 2

We deal with the minimax problem relative to a vector-valued functionf: X ₀×Y ₀ »V, where a partial ordering in the topological vector spaceV is induced by a closed and convex coneC. In Ref. 1, under suitable hypotheses, we proved that $$Max\bigcup\limits_{s\varepsilon X_0 } {Min_w f(s,Y_0 )} \subset Min\bigcup\limits_{t\varepsilon Y_0 } {Maxf(X_0 ,t) + C;}$$ the exact meaning of the symbols is given in Section 2. In this work, we prove that, under a reasonable setting of hypotheses, the previous inclusion holds and also we have that $$Min_w \bigcup\limits_{t\varepsilon Y_0 } {Max} f(X_0 ,t) \subset Max\bigcup\limits_{s\varepsilon X_0 } {Min_w } f(s,Y_0 ) - C.$$      

Thermal stability and related thermodynamic properties of N-ethylthiourea

The enthalpy and entropy of sublimation of N-ethylthiourea were obtained from the temperature dependence of its vapour pressure measured by both the torsion–effusion and the Knudsen effusion method in the temperature range 360–380 K. The compound undergoes no solid-to-solid phase transition or decomposition below 380 K. The pressure against reciprocal temperature resulted in lg(p, kPa) = (13.40 ± 0.27) − (6067 ± 102) /T(K). The molar sublimation enthalpy and entropy at the mid interval temperature were Δ_subH_m(370 K) = (116.1 ± 2.0) kJ mol⁻¹ and Δ_subS_m(370 K) = (218.0 ± 5.2) J mol⁻¹ K⁻¹, respectively. The same quantities derived at 298.15 K were (118.8 ± 2.1) kJ mol⁻¹ and (226.1 ± 5.5) J mol⁻¹ K⁻¹, respectively.     

Transpositions de doubles liaisons de terpènes bicycliques catalysées par des bases

The displacements of double bonds and dehydrogenation by basic catalysts are examined by analogy with the preceding studies on p-menthenes and p-menthadienes [1] with bicyclic terpenes: α- and β-pinenes, sabinene and 3-carene.     

A force-field study of the conformational characteristics of the iduronate ring

Methods of molecular mechanics were applied to investigate the conformation of the (methyl 2-O-sulfate-4-methyl-α-L-idopyranose) uronic acid (DMIS), in order to correlate the peculiar vicinal proton coupling constants observed in polysaccharides containing the iduronate ring to the conformational characteristics of this sugar ring. We found three conformers with comparable energies, namely the two chair forms ¹C₄ and ⁴C₁ and the skew-boat form ²S₀(L); the latter is separated from each chair form by a barrier of about 9 kcal/mol. Along the pseudorotational path three additional minima (³S₁, ¹S₃, and ¹S₅) were found, yet at least 4 kcal/mol higher than ²S₀. The results obtained for the relative energies of the three conformers and the conformation of the side groups were affected by the inclusion of the electrostatic term and, in particular, by the charge assigned to the ionic groups of DMIS. However, the conformational properties of the idopyranosidic ring in DMIS (and in related compounds) should still be interpreted in terms of equilibrium among these three conformers only.     

How Electronic Excitation Can be Used to Inhibit Some Mechanisms Associated to Substituent Effects

Despite the fact that transferability and chemistry go hand in hand, transferability studies in electronically excited states (EESs) are normally omitted, although these states are becoming extremely important in modern processes and applications. In this work, it is shown that this kind of studies can be used to understand how substituent effects can be modified in EESs. Thus, for example, the analysis of the carbonyl oxygen transferability in different HCO‐R molecules allowed us to find that the excitation can be used to break the π conjugation associated to the resonance substituent effect. Moreover, as a direct consequence, the oxygen transferability is enhanced in the first electronically excited state.     

Individuation of characteristic parameters of “glass paste” of Meridional Etruria by the use of scientific methodologies

The individuation of parameters that characterize decorations in “glass paste” of Etruscan jewels in Meridional Etruria area, by the use of scientific methodologies, has the aim to collocate this typology of manufacts in a historical and geographical context and to improve the knowledge of the technology connected with their realization. The term “glass paste” is widely used in humanistic literature to describe different materials, all based on a “glass like” composition, but its definition is lacking or confusing if the term is not referred to a scientific meaning.The glass analysis is difficult owing to the complexity of the elements that compose the various classes of vitreous materials. For this reason the interpretation of the composition table containing the values of the numerous glass elements, induces the use of statistical methods for the elaboration of the results. The multivariate analysis can be a valid tool for an immediate lecture of the common characteristics of the different typologies of vitreous materials.In this work, the application of the Principal Component Analysis (PCA), has been applied for the elaboration of chemical composition data obtained by electronic microanalysis (SEM-EDS) on findings coming from Etruscan archaeological sites of Nepi and Cerveteri, and on pearls of a necklace from Castellani's Collection. Besides, an attempt has been made to compare the chemical elements found in the vitreous materials of the jewelry with the elements of sands from probable sites along the rivers present in the Etruscan sites by following the indications reported by historical fonts.The obtained results furnished information in various directions, either for the characterization of each historical sample analyzed or the validation of the applied statistical methodology for the composition data elaboration, besides it has been possible to contribute in the knowledge of the possible existence of glass production sites in the Meridional Etruria, more specifically for the realization of decoration in glass paste.     

Application of the Partial Least Square Technique to Identify Critical Variables in the Immunosorbent Manufacturing

The partial least square technique (PLS) was applied to the monoclonal antibody (Mab) CB.Hep-1 immunosorbent manufacturing to determine the influence of cyanate ester concentration, ligand concentration and target ligand density on Mab coupling efficiency, elution capacity, Hepatitis B surface antigen purity and ligand leakage (output variables). Results demonstrated that cyanate ester concentration, ligand concentration and density do not have an influence on output variables in assessed ranges. Conversely, the eluted antigen purity was significantly influenced by cyanate ester concentration and ligand concentration. In conclusion, the PLS application allows for the identification of critical variables and improvement of established chromatographic processes.     

Development and properties of a glass made from MSWI bottom ash

A uniform shiny black-coloured glass was obtained using bottom ash produced by a Portuguese municipal solid waste incinerator (MSWI). The bottom ash was the single batch material used in the formation of the glass, which was obtained by vitrification of the solid waste at 1400 °C for 2 h. Under these conditions, a homogeneous melt with an appropriate viscosity to be shaped was obtained, indicating the suitability of this waste material to be employed in the development of vitreous products. The characterization of the resulting glass was performed in order to assess its structural, physical, mechanical, thermal and chemical features. The glass had a density of 2.69 g cm⁻³, a hardness of 5.5 GPa, a fracture strength of 75 MPa, a thermal expansion coefficient of 9.5 × 10⁻⁶ °C⁻¹ and it exhibited a very good chemical stability. In summary, the MSWI bottom ash glass has good mechanical and chemical properties and may, therefore, be used in several applications, particularly as a construction material.     

Exploring Te–Te Bond Cleavage with Palladium(II): Synthesis,X‐ray Structural Characterization,and Optical Features of Tellurolate and Telluro‐Ether Complexes of Palladium(II)

The focus of this study was to explore reactions of (RTe)₂ with palladium(II) salts. These reactions led to Te–Te bond cleavage and the formation of three tellurolate‐bridged dinuclear complexes and a mononuclear telluro‐ether palladium(II) complex. The methodologies used yielded single source precursors for interesting materials. UV/vis spectroscopy results supported the measured optical bandgap for the complexes in the solid state. A study on the structure of all complexes in the solid state was carried out using single‐crystal X‐ray diffraction. Other analytical methodologies, such as elemental analysis and infrared spectroscopy, were also used for the characterization of the complexes.