Hölder Continuity and Injectivity of Optimal Maps

Consider transportation of one distribution of mass onto another, chosen to optimize the total expected cost, where cost per unit mass transported from x to y is given by a smooth function c(x, y). If the source density f ⁺(x) is bounded away from zero and infinity in an open region ${U' \subset \mathbf{R}^n}$ , and the target density f ^?(y) is bounded away from zero and infinity on its support ${\overline{V} \subset \mathbf{R}^n}$ , which is strongly c-convex with respect to U′, and the transportation cost c satisfies the ${\mathbf{A3}_{\rm w}}$ condition of Trudinger and Wang (Ann Sc Norm Super Pisa Cl Sci 5, 8(1):143–174, 2009), we deduce the local Hölder continuity and injectivity of the optimal map inside U′ (so that the associated potential u belongs to ${C^{1,\alpha}_{loc}(U')}$ ). Here the exponent α > 0 depends only on the dimension and the bounds on the densities, but not on c. Our result provides a crucial step in the low/interior regularity setting: in a sequel (Figalli et al., J Eur Math Soc (JEMS), 1131–1166, 2013), we use it to establish regularity of optimal maps with respect to the Riemannian distance squared on arbitrary products of spheres. Three key tools are introduced in the present paper. Namely, we first find a transformation that under ${\mathbf{A3}_{\rm w}}$ makes c-convex functions level-set convex (as was also obtained independently from us by Liu (Calc Var Partial Diff Eq 34:435–451, 2009)). We then derive new Alexandrov type estimates for the level-set convex c-convex functions, and a topological lemma showing that optimal maps do not mix the interior with the boundary. This topological lemma, which does not require ${\mathbf{A3}_{\rm w}}$ , is needed by Figalli and Loeper (Calc Var Partial Diff Eq 35:537–550, 2009) to conclude the continuity of optimal maps in two dimensions. In higher dimensions, if the densities f ^± are Hölder continuous, our result permits continuous differentiability of the map inside U′ (in fact, ${C^{2,\alpha}_{loc}}$ regularity of the associated potential) to be deduced from the work of Liu et al. (Comm Partial Diff Eq 35(1):165–184, 2010).     

DNA Binding Studies and Cytotoxicity of a Dinuclear Pt(II) Diazapyrenium-Based Metallo-supramolecular Rectangular Box

The interaction with native DNA of a 2,7-diazapyrenium-based ligand 1 and its Pt(II) rectangular metallacycle 2 is explored through circular and linear dichroism and fluorescence spectroscopies. The metal-free ligand 1 binds through intercalation, with a binding constant of approximately 5×10(5) M(-1) , whereas the metallacycle 2 binds and bends the DNA with a binding constant of 7×10(6) M(-1) . PCR assays show that metallo-supramolecular box 2 interferes with DNA transactions in vitro whereas the intercalator 1 does not. The metallacycle is active against four human cancer cell lines, with IC(50) values ranging between 3.1 and 19.2?μM and shows similar levels of efficacy, but a different spectrum of activity, to cisplatin.     

Analysis of some reaction pathways active during cyclopentadiene pyrolysis

The cyclopentadienyl radical (cC(5)H(5)) is among the most stable radical species that can be generated during the combustion and pyrolysis of hydrocarbons and it is generally agreed that its contribution to the gas phase reactivity is significant. In this study the kinetics of one key cC(5)H(5) reaction channel, namely the reaction between cC(5)H(5) and cyclopentadiene (cC(5)H(6)), was investigated using ab initio calculations and RRKM/Master Equation theory. It was found that most of the excited C(5)H(5)_C(5)H(6) adducts formed by the addition of cC(5)H(5) to cC(5)H(6) decompose back to reactants and that the major reaction products are, in order of importance, indene, vinylfulvene (a most probable styrene precursor), phenylbutadiene, and benzene. The preferred reaction pathway of the C(5)H(5)_C(5)H(6) adduct is started by the migration of the tertiary hydrogen of the C(5)H(5) ring to a vicinal carbon and followed by the β-opening of the C(5)H(6) ring, which is the rate determining step. Successive molecular rearrangements lead to decomposition to the four possible products. The kinetic constants for the four reaction channels, calculated at atmospheric pressure and interpolated in cm(3) mol(-1) s(-1) between 900 and 2000 K, are k(indene) = 10(25.197)T(-3.935)?exp(-11630/T(K)), k(vinylfulvene) = 10(65.077)T(-14.20)?exp(-37567/T(K)), k(benzene) = 10(29.172)T(-4.515)?exp(-20570/T(K)), and k(phenylbutadiene) = 10(16.743)T(-1.407)?exp(-11804/T(K)). The predictive capability of the reaction set so determined was tested through the simulations of recent cC(5)H(6) pyrolysis and combustion experiments using a detailed kinetic mechanism. A quantitative agreement with experimental data was obtained by assuming that vinylfulvene converts rapidly to stryrene, increasing its reaction channel by a factor of 2, and assuming that phenylbutadiene rapidly decomposes with equal probability to styrene and benzene.     

Dye solar cells efficiency maps: a parametric study

In this work we present a numerical simulation of a dye solar cell efficiency using a drift-diffusion model for the complete cell. The physical parameters such as the active layer thickness, the electron mobility and the dye spectrum are varied systematically in a range of values individuated experimentally, in order to obtain efficiency maps that reveal interesting features in this kind of devices.     

A principal component analysis of precipitation patterns over northern Italy

Summary A principal component analysis of rainfalls recorded during five winters (1981–1985) at about 70 stations in Northern Italy has been performed. The spatial distribution of the first four eigenvectors (whose principal components cumulatively account for about 81% of the total variance) is presented and discussed. A subsequent rotation of the first four principal components led to new spatial distributions which are are also described. Moreover, the rotation allowed associating the first three rotated principal components with atmospheric circulation patterns typically occurring in the area and belonging to a classification scheme of weather types on the Po Valley previously introduced by other authors on the base of a visual scanning of three years of daily maps.

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Riassunto è stata eseguita una analisi in componenti principali di dati di precipitazione raccolti durante cinque inverni (1981–1985) in circa 70 stazioni dell'Italia settentrionale. Vengono presentate e discusse le distribuzioni spaziali dei primi quattro autovettori, le cui componenti principali spiegano cumulativamente circa 81% della varianza totale. Una successiva rotazione delle prime quattro componenti principali ha condotto a nuove distribuzioni spaziali, che vengono anch'esse descritte. Inoltre la rotazione ha permesso di associare alle prime tre componenti principali ruotate dei modelli di circolazione atmosferica, tipicamente ricorrenti sull'area in questione e facenti parte di uno schema di classificazione dei tipi di tempo sulla Valle Padana introdotto precedentemente da altri autori sulla base di uno ?scanning? visuale di tre anni di mappe giornaliere.

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Резюме Проводится анализ главхых компонент количества вьавших осадков в течение пяти зим (1981–1985), зарегестрированных на 70 станциях в Северной Италии. Предлагается и обсуждается пространственное распределение первых четырех собственных векторов. Последующее вращение первых четырех главных компонент приводит к новым пространственным распределениям, которые также описываются и анализируются. Кроме того, указанное вращение позволяет связать первые три вращающиеся главные компоненты с диаграммами атмосферной цирркуляции, которая является типичной для этой области и пренадлежит к скхеме классификации погоды в долине По, введенной ранее друими авторами на основе визуального сканирования суточных карт в течение трех лет.

     

Metallacycles of porphyrins as building blocks in the construction of higher order assemblies through axial coordination of bridging ligands: solution- and solid-state characterization of molecular sandwiches and molecular wires

Treatment of the octahedral Ru(II)-dimethyl sulfoxide complexes trans-RuCl(2)(dmso-S)(4) (1), trans-RuCl(2)(dmso-O)(2)(CO)(2) (2), and trans-RuCl(2)(dmso)(3)(CO) (3) with a stoichiometric amount of 5,10-bis(4'-pyridyl)-15,20-diphenylporphyrin (4'-cis-DPyP) yields, after chromatographic purification, the novel 2+2 molecular squares of formula [trans,cis,cis-RuCl(2)(dmso-S)(2)(4'-cis-DPyP)](2) (4), [trans,cis,cis-RuCl(2)(CO)(2)(4'-cis-DPyP)](2) (5), and [trans,cis,cis-RuCl(2)(dmso-S)(CO)(4'-cis-DPyP)](2) (6), respectively. Compound 6 exists as an equimolar mixture of the isomeric metallacycles 6a and 6b, depending on whether the 4'-N(py) rings of 4'-cis-DPyP's are trans to CO or to dmso-S. Compounds 4-6 were fully characterized by NMR and IR spectroscopy and by FAB mass spectrometry. Treatment of 5 with excess zinc acetate in chloroform/methanol mixtures led to the isolation of the corresponding zinc adduct [trans,cis,cis-RuCl(2)(CO)(2)(Zn x 4'-cis-DPyP)](2) (5Zn). Treatment of 5Zn with 1 equiv of a trans ditopic N-donor ligand L (L = 4,4'-bipy, 5,15-bis(4'-pyridyl)-2,8,12,18-tetra-n-propyl-3,7,13,17-tetramethylporphyrin (4'-trans-DPyP-npm), or 5,15-bis(4'-pyridyl)-10,20-diphenylporphyrin (4'-trans-DPyP)) leads readily and selectively, according to (1)H NMR spectroscopy, to the quantitative assembling of 2:2 supramolecular adducts of stacked metallacycles of formula [(5Zn)(2)(mu-L)(2)] (7-9), which were thoroughly characterized in solution by NMR spectroscopy. NMR features indicate that, at ambient temperature, the equilibrium between 5Zn and L to yield [(5Zn)(2)(mu-L)(2)] has an intermediate to slow rate on the NMR time scale (relatively broad signals for L) and is totally shifted toward the 2:2 product (all or nothing process). Single-crystal X-ray investigations showed that, depending on the nature of the bridging ligand, in the solid state these sandwich structures can either be maintained or originate polymeric chains formulated as [(5Zn)(mu-L)](infinity). When L = 4'-trans-DPyP, both solution- and solid-state data indicate that [(5Zn)(2)(mu-4'-trans-DPyP)(2)] (9) is a discrete supramolecular assembly of two molecular squares of metalloporphyrins axially connected through other porphyrins. In this molecular box, the two bridging porphyrins are coplanar at a distance of about 11.4 A. When L = 4,4'-bipy, the corresponding adduct 7 has the anticipated sandwich-like discrete architecture [(5Zn)(2)(mu-4,4'-bipy)(2)] in solution, but it assumes a stair-like polymeric wire structure in the solid state. The polymer [(5Zn)(mu-4,4'-bipy)](infinity) is made by 5Zn squares bridged by 4,4'-bipy ligands which are axially coordinated alternatively on the two opposite sides of each square. Our work clearly established that relatively simple supramolecular adducts of porphyrins, such as molecular squares, are suitable building blocks for the construction of more elaborate assemblies of higher order by axial coordination of bridging ligands.     

The kinetics of thiyl radical-induced reactions of monounsaturated fatty acid esters

The time-dependent isomerizations and thiol additions of several Z- and E-monounsaturated fatty acid methyl esters catalyzed by alkanethiyl radicals during gamma-radiolysis of tert-butyl alcohol solutions are analyzed on the basis of the radiation chemical yield of radicals and established rate data. This provides room-temperature rate constants for the reversible thiyl addition. Within experimental errors, they do not depend on the double bond position in the alkyl chains. Particularly noteworthy is the very fast beta-elimination of thiyl radicals from alkyl radicals which carry a second beta-substituent. It is supported by additional evidence obtained with a radical clock methodology, and the large preference of fragmentation to the E-isomers is attributed to different barriers for the formation of the E- and Z-transition states from the equilibrium radical structure.     

Analytical quality control for the determination of polychlorobiphenyls in environmental matrices

Analytical quality control procedures for ensuring reliable data in the determination of PCBs in environmental matrices are described. Several extraction procedures of PCBs from sediment samples are critically compared and recovery and reproducibility for PCBs determination in sediment and cod liver oil samples are evaluated. Extraction by 1:1n-hexane/acetone mixture in an ultrasonic bath and by supercritical fluids generally give a quantitative recovery and a coefficient of variation lower than 15%, while extraction by a Soxhlet system does not give such good results and requires much longer extraction times. Certified reference materials available from three international organizations, namely the Standards, Measurements and Testing programme of the European Union, the USA National Institute of Standards and Technology and the National Research Council of Canada were used. Finally, the on-going European Union QUASIMEME programme aimed at improving the analytical quality of marine pollution monitoring measurements of European laboratories is addressed.     

Universality in several-matrix models via approximate transport maps

We construct approximate transport maps for perturbative several-matrix models. As a consequence, we deduce that local statistics have the same asymptotic as in the case of independent GUE or GOE matrices (i.e., they are given by the sine-kernel in the bulk and the Tracy–Widom distribution at the edge), and we show averaged energy universality (i.e., universality for averages of m-points correlation functions around some energy level E in the bulk). As a corollary, these results yield universality for self-adjoint polynomials in several independent GUE or GOE matrices which are close to the identity.