Stability of the intersection of solution sets of semi-infinite systems

Many mathematical programming models arising in practice present a block structure in their constraint systems. Consequently, the feasibility of these problems depends on whether the intersection of the solution sets of each of those blocks is empty or not. The existence theorems allow to decide when the intersection of non-empty sets in the Euclidean space, which are the solution sets of systems of (possibly infinite) inequalities, is empty or not. In those situations where the data (i.e., the constraints) can be affected by some kind of perturbations, the problem consists of determining whether the relative position of the sets is preserved by sufficiently small perturbations or not. This paper focuses on the stability of the non-empty (empty) intersection of the solutions of some given systems, which can be seen as the images of set-valued mappings. We give sufficient conditions for the stability, and necessary ones as well; in particular we consider (semi-infinite) convex systems and also linear systems. In this last case we discuss the distance to ill-posedness.     

Relative acidities and structure analysis of cis and trans isomers of 1,5‐oxazaspiro[5.5] undecane derivatives by multinuclear magnetic resonance

The relative acidities of the cis and trans isomers of a series of 1,5‐oxazaspiro[5.5]undecane derivatives were determined by measuring ΔpK in acid‐base titrations followed by ¹ H NMR. Relative structural stabilities were determined by measuring substituent chemical shift and γ‐gauche effects in ¹³C, ¹⁵N, and ¹⁷O NMR. Crystallographic characterization of a model spiro[5.5]undecane is presented to support the basicity in solid state. Copyright © 2010 John Wiley & Sons, Ltd.     

Optical properties of multilayered Period-Doubling and Rudin-Shapiro porous silicon dielectric heterostructures

To investigate the optical properties in quasi-regular porous-silicon-based dielectric Period-Doubling and Rudin-Shapiro multilayer systems, we study here the reflection of light from these structures. The Period-Doubling and Rudin-Shapiro structures are fabricated in such a way that the optical thickness of each layer is one quarter of 600 and 640 nm respectively. We find that porous silicon Period-Doubling dielectric multilayers could demonstrate the optical properties similar to the classical periodic Febry–Perot interference filters with one or multiple resonant peaks, but with an advantage of having total optical thickness much lesser than the periodic structures. Additionally, light propagation in porous silicon Rudin-Shapiro structures is investigated for the first time, both theoretically and experimentally. The reflectance spectra of the structures exhibit photonic band gaps centered at predetermined wavelengths. In both cases, numerical simulation of light transmission is performed using transfer matrix method.     

Characterization of isomers of oleuropein aglycon in olive oils by rapid‐resolution liquid chromatography coupled to electrospray time‐of‐flight and ion trap tandem mass spectrometry

In this work, rapid‐resolution liquid chromatography (RRLC) coupled to electrospray ionization time‐of‐flight mass spectrometry (ESI‐TOF‐MS) and ion trap multiple mass spectrometry (IT‐MSⁿ) has been applied to separate and characterize eleven isomers of oleuropein aglycon in fourteen Spanish extra‐virgin olive oils. After the extra‐virgin olive oil sample had been dissolved in hexane and cleaned up by a diol‐bonded phase solid‐phase extraction (SPE) cartridge, the eluting extract was resolved in methanol and analyzed on an Angilent 1200 system with a 4.6 × 150 mm, 1.8 µm Zorbax Eclipse plus C18 column. Mass spectrometry was carried out on a Bruker Daltonics microTOF mass spectrometer and a Bruker Daltonics ion trap mass spectrometer. The characterization of isomers of oleuropein aglycon was based on accurate mass data and the isotope function of characteristic fragment ions in the studied compounds by TOF‐MS, and the fragment ions were further confirmed by IT‐MSⁿ. The fragmentation pathway of oleuropein aglycon was successfully elucidated and all possible transformations among isomers of oleuropein aglycon were suggested. Copyright © 2008 John Wiley & Sons, Ltd.     

Langmuir–Blodgett films of pyridinium-dicyanomethanide dyes mixtures with photobleachable absorption bands

We report on Langmuir-Blodgett (LB) films characterization of 4-[5-dicyanomethanido)thien-2-y1]-N-(n-hexadecyl)pyridinium (C₁₆H₃₃-PDCNT), and 1-(N-(n-hexadecy]-4-pyridinio)-2-[5-(dicyanomethanido)thien-2-yl]ethene (C₁₆H₃₃-PDCNTE); LB films of the pure compounds and of the mixtures of the two compounds were prepared at 291 K: UV-vis investigation revealed the presence of photobleachable absorption bands, the ones at about 530 nm and 640 nm were due to charge transfer transitions of the monomer of C16H33-PDCNT and C₁₆H₃₃-PDCNTE, respectively; the sharp, photobleachable ones shifted to shorter wavelengths were due to H-aggregates of the two compounds. By changing the molar ratios of the two compounds in the mixtures and in other cases by annealing the LB films, the absorption maxima of the sharp, photobleachable bands due to H-aggregates could be tuned in the range 415–467 nm. These LB films are thus very promising in view of optical data storage applications.