Parabolic Capacity and Soft Measures for Nonlinear Equations

We first introduce, using a functional approach, the notion of capacity related to the parabolic p-Laplace operator. Then we prove a decomposition theorem for measures (in space and time) that do not charge the sets of null capacity. We apply this result to prove existence and uniqueness of renormalized solutions for nonlinear parabolic initial boundary-value problems with such measures as right-hand side.     

Bubble dispersion patterns in bubbly-flow released from a porous plug into a gas-stirred ladle

Bubbles released from a porous plug into a gas-stirred ladle present different bubbly dispersion patterns that can be studied by CFD means. Recent modeling (Alexiadis et al.) has, in fact, led to numerical results in accord with experimental data. However, due to the high number of equations involved, it is not easy to understand the physical reasons of the transitions between these patterns. In the present paper, attention was focused on the role of fragmentation and coalescence and the pattern-transition modeled by means of intersection points between these functions.     

X-ray damage characterization in BaLiF3,KMgF3 and LiCaAlF6 complex fluorides

Two-inch sized KMgF₃,BaLiF₃ and LiCaAlF₆ (LiCAF) single crystals were grown by the Czochralski method under a CF₄ atmosphere. X-ray irradiation was used to carry out a comparative study of induced optical absorption phenomena and colour centre creation in the ultra-violet and visible spectral regions. The integral of the induced absorption spectra is significantly lower in LiCAF with respect to the other studied materials. It is found that the amplitude of the F-absorption band is suppressed more than a factor of 3 by Mg-doping. For Mg-doped crystals, the optimum doping concentration is about 0.2 mol% of Mg²⁺.     

Principal components and spatial patterns of rain over Northern Italy, in relation to wind and geopotential fields

Summary A statistical study of precipitation over the Po Valley and the Alps during four winters, based on the application of a principal component (p.c.) method, exhibited a good correlation between the first three rotated eigenvectors of the cross-product matrix (between time series of data recorded at 70 stations) and three typical atmospheric circulation schemes over Northern Italy. The study is here continued, by relating these results to meteorological fields evaluated over a region wider than the area previously considered. Our attention mainly concentrated on the fields of time trend of geopotential height at 850 hPa over Europe, between latitude 34.5 and 51 degrees North and longitudes 0 and 21 degrees East. This was suggested by some peculiar relationships shown by the statistical distributions of geopotential height and wind direction and speed with respect to the first three p.c.’s. These relationships made us think of the possibility to use those trends as predictors of precipitation fields. Our analysis puts into evidence that three spatial patterns of geopotential, height time trend can be safely associated to the first three p.c.’s and, as a consequence, to the three precipitation modes corresponding to the spatial distributions of the eigenvectors, previously identified by us. They can therefore be considered meaningful precursors of precipitation field patterns over Northern Italy and Alpine regions.

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Riassunto Uno studio statistico della precipitazione sulla pianura padana e sulle Alpi durante quattro inverni, basato sull’applicazione del metodo delle componenti principali (c.p.), ha mostrato una buona correlazione fra i primi tre autovettori rotati della matrice dei prodotti incrociati (fra le serie temporali dei dati registrati in 70 stazioni) e tre tipici schemi di circolazione atmosferica sull’Italia del Nord. Lo studio viene qui prosequito, mettendo in relazione tali risultati con campi meteorologici valutati su una zona piú ampia di quella precedentemente considerata. La nostra attenzione si è prevalentemente concentrata sui campi di tendenza temporale dell’altezza di geopotenziale a 850 hPa sull’Europa, a latitudini comprese tra 34.5 e 51 gradi Nord e longitudini fra 0 e 21 gradi Est. Ciò è stato suggerito da alcune relazioni peculiari mostrate dalle distribuzioni statistiche di altezza di geopotenziale e di direzione ed intensità del vento rispetto alle prime tre c.p., che ci hanno fatto pensare alla possibilità di usare tali tendenze come predittori del campo di precipitazione. La nostra analisi ha messo in evidenza il fatto che tre distribuzioni spaziali di tendenza temporale del campo di altezza di geopotenziale possono essere con sicurezza associate alle prime tre c.p. e., quindi, ai tre modi di precipitazione corrispondenti alle distribuzioni spaziali degli autovettori precedentemente da noi identificati. Essi possono pertanto essere considerati significativi precursori del campo di precipitazione sull’Italia del Nord e sulle regioni alpine.

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Резюме Статистическое исследование выпадения осадков над долиной реки По и Альпами в течение четырех зим, основанное на применении метода главных компонент, обнаруживает хорошую корреляцию между первыми тремя вращающимися собственными векторами матрицы векторного произведения (между временными последовательностями данных, зарегистрированных на 70 станциях) и тремя схемами типичной атмосферной циркуляции над Северной Италией. В этой работе продолжены исследования. Полученные результаты связывайотся с метеорологическими полями, вычисленными над областью, которая шире ранее рассмотренной области. Главное внимание мы обращаем на поля временного хода для геопотенциальной высоты при 850гПа над Европой, между 34.5^щ и 51^щ северной широты и между 0^щ и 21^щ восточной долготы. Это следует из специальных соотношений, полученных с помощью статистических распределений геопотенциальной высоты и направления и скорости ветра относительно первых трех главных компонент. Эти соотношения позволяют нам использовать исследованные тенденции, как предсказатели полей вьшадения осадков. Нам анализ подтверждает, что три пространственным распределения временного хода для геопотенциальной высоты могут быть связаны с первыми тремя главными компонентами и, как следствие, с тремя моделями выцадения осадков, которые соответствуют пространственным распределениям собственных векторов, ранее идентифицированных в работе [Ш]. Следовательно, они могут рассматриватяся как предвестники для распределений полей осадков над Северной Италией и над Альпами.

     

Convex polytopes whose projection bodies and difference sets are polars

In a paper by the author and B. Weissbach it was proved that the projection body and the difference set of ad-simplex (d≥2) are polars. Obviously, ford=2 a convex domain has this property if and only if its difference set is bounded by a so-called Radon curve. A natural question emerges about further classes of convex bodies inR ^d (d≥3) inducing the mentioned polarity. The aim of this paper is to show that a convexd-polytope (d≥3) is a simplex if and only if its projection body and its difference set are polars.     

Enantioselective synthesis of preclavulone A and its methyl ester

A highly enantioselective synthesis of the (8S,12S)-enantiomer of preclavulone A and its methyl ester is described featuring the Julia protocol for installing the (Z)-double bond in the lower chain. This procedure is suitable for the preparation of labeled preclavulone analogues for biosynthetic studies on marine clavulones.     

Experimental high-gain quantum-injected optical parametric amplification and multiphoton phase-covariant cloning

We investigate multiphoton states generated by high-gain optical parametric amplification of a single injected photon—polarization encoded as a qubit. The experimental configuration exploits the optimal phase-covariant cloning. The output state of the apparatus is found to exhibit the quantum superposition property of mesoscopic multiphoton assemblies involving about 300 photons. This work represents an experimental advance toward the test of several fundamental quantum processes in mesoscopic or macroscopic frameworks.     

Ion chromatography characterization of polysaccharides in ancient wall paintings

Specific programming of automated HPLC systems allows total on-line qualification, validation and stability monitoring using the concept of deferred standards. Setting up such a process for routine analyses in an automated HPLC system requires specific autosampler programming as well as specific monitoring software. With an autosampler, a double injection procedure is programmed, the first introducing the sample, and the second, a few minutes deferred, the deferred control standard. Two additional compounds are therefore added to the sample before and during the chromatographic process: the intemal standard for sample quantification and the deferred standard for system control. Specific methodologies are described of how to obtain classical quantitative analysis information as well as system qualification validation stability information. Experiments were performed to develop specified methodologies to monitor the quality of quantitative analysis during the life of the column by using the deferred standard concept to probe the effects of column ageing on separation characteristics.     

1,2-Oxopalladation versus pi-allyl palladium route. A regioconvergent approach to a key intermediate for cyclopentanoids synthesis. New insights into the Pd(II)-catalyzed lactonization reaction

Regioconvergent synthesis of the key lactone 1 from an equimolar mixture of the two olefins 4 and 5 was achieved by unique Pd(II) chemistry. The synthetic versatility of lactone 1 has been demonstrated in the synthesis of iridoids and of the endo-Corey lactone 2, which is a key intermediate for the F(2)-isoprostane synthesis. Upon exposure of the sodium salts of 4 and 5 to a catalytic amount of Pd(OAc)(2) under oxygen, in the presence of AcOH, an isomeric lactone 12 was obtained in addition to the title compound 1. The Pd(II) lactonization was optimized by fine-tuning all the factors participating in the catalytic cycle: solvent, oxidant, co-oxidant, and Pd(II) source. The Hosokawa's heterobimetallic couple emerged as the catalyst of choice. With a Cu(II)-Pd(II) couple, the redox process was transferred to copper, and the formal oxidation state of palladium remained constant during the reaction. By virtue of this new methodology, lactone 1 was obtained in a rewarding 60% yield, along with isomeric lactone 12 in 30% yield. A detailed mechanistic study was carried out in order to elucidate the formation of lactones 1 and 12. Lactone 1 was formed from either olefin 8 or olefin 10; on the other hand, lactone 12 was formed exclusively from olefin 10. An intramolecular 1,2-acyloxypalladiation was invoked for the transformation of 8 into 1, whereas the pi-allyl complexes 13 and 11 were involved in the transformation of olefin 10 into 12 and 1, respectively.     

Magnetic resonance study on lamellar phases of ammonium perfluorooctanoate

The aggregation properties of ammonium perfluorooctanoate (NH₄-PFO) in concentrated aqueous phases have been investigated by magnetic resonance techniques and have been compared with the aggregation properties in dilute solutions. Magnetic resonance methods indicated that NH₄-PFO—water systems with surfactant concentrations below 45% (w/w) behaved as isotropic purely micellar solutions in the temperature range 285–340 K. For higher concentrations the system exhibited a rather complex structure, having both isotropic and anisotropic components. The nematic nature of the anisotropic fraction was demonstrated by ¹⁹F NMR studies. The ¹⁹F NMR and EPR of nitroxides (TempTMA⁺, 5- and 16-DXSA) inserted as paramagnetic probes into the concentrated NH₄-PFO—water systems allowed us to establish that the lamellar phase could be mechanically oriented between quartz slides. The EPR investigation also gave details concerning the dynamics of both the oriented and non-oriented structures.