Stokes Matrices and Monodromy of the Quantum Cohomology of Projective Spaces

We compute Stokes matrices and monodromy for the quantum cohomology of projective spaces. We prove that the Stokes' matrix of the quantum cohomology coincides with the Gram matrix in the theory of derived categories of coherent sheaves.Comment: 50 pages, 6 Postscript figure

Tabulation of PVI Transcendents and Parametrization Formulas (August 17, 2011)

The critical and asymptotic behaviors of solutions of the sixth Painlev\'e equation PVI, obtained in the framework of the monodromy preserving deformation method, and their explicit parametrization in terms of monodromy data, are tabulated.Comment: 30 pages, 1 figure; Nonlinearity 201

Inverse Problem for semisimple Frobenius Manifolds, Monodromy Data and the Painleve' VI Equation

We study critical behaviour and connection problem for a Painleve' 6 equation. We construct solutions of WDVV eqs. using the isomonodromic deformation method and the Painleve' equations. We find algebraic solutions of WDVV and Gromov-Witten invariants of projective space.Comment: 131 pages 16 figure

On the Logarithmic Asymptotics of the Sixth Painleve' Equation (Summer 2007)

We study the solutions of the sixth Painlev\'e equation with a logarithmic asymptotic behavior at a critical point. We compute the monodromy group associated to the solutions by the method of monodromy preserving deformations and we characterize the asymptotic behavior in terms of the monodromy itself.Comment: LaTeX with 8 figure

Stokes matrices for the quantum differential equations of some Fano varieties

The classical Stokes matrices for the quantum differential equation of projective n-space are computed, using multisummation and the so-called monodromy identity. Thus, we recover the results of D. Guzzetti that confirm Dubrovin's conjecture for projective spaces. The same method yields explicit formulas for the Stokes matrices of the quantum differential equations of smooth Fano hypersurfaces in projective n-space and for weighted projective spaces.Comment: 20 pages. Introduction has been changed. Small corrections in the tex

Trascendenti di Painlevé e integrabilità

In questo scritto verrà analizzato come sia possibile definire nuove funzioni speciali attraverso la soluzione di equazioni differenziali e sviluppare metodi per conoscerne le proprietà di interesse, quando le equazioni stesse godono della così detta proprietà di Painlevé. In particolare, introdurremo le sei equazioni di Painlevé. Ciò permette di stabilire una nozione di integrabilità che si differenzia da quella nota in meccanica classica (riduzione delle equazioni del moto a delle integrazioni), e che è molto importante per diversi modelli della fisica matematica contemporane

Deformations with a resonant irregular singularity

I review topics of my talk in Alcal\ue1, inspired by the paper [1]. An isomonodromic system with irregular singularity at z= 1e (and Fuchsian at z=0) is considered, such that z= 1e becomes resonant for some values of the deformation parameters. Namely, the eigenvalues of the leading matrix at z= 1e coalesce along a locus in the space of deformation parameters. I give a complete extension of the isomonodromy deformation theory in this case

Landslide societal risk in Portugal in the period 1865-2015

The existence of reliable databases on natural disasters is crucial to study mortality due to natural hazards in terms of temporal trends, spatial distribution and epidemiological topics. Features on fatalities caused by different types of hazards can be found for instance in natural hazard databases (e.g. EM-DAT, DISASTER) based on documental sources, demographic statistics, death certificates from hospitals and civil protection authorities. There are some constraints in the inclusion criteria of mortality data in natural disasters databases. For instance, the EM-DAT only record natural disasters that have caused at least 10 fatalities, while the Portuguese DISASTER database includes every occurrence that caused fatalities regardless of their number. In Portugal, social impacts caused by landslides occurred in the period 1865-2015 are gathered in the DISASTER database. This database includes social consequences (fatalities, injuries, missing people, evacuated people and homeless people) caused by landslides referred in newspapers. The DISASTER database contains 289 damaging landslides that caused 238 fatalities. In the present work we explore the mortality patterns resulting from damaging landslides in the country for an extended period. In this work we aim to: (i) analyse the spatio-temporal analysis of damaging landslides occurred in the last 155 years; (ii) analyse the frequency and the temporal evolution of fatal landslides; (iii) analyse the spatio-temporal distribution of fatalities generated by landslides; (iii) identify the most deadly landside types; (iv) verify gender tendencies in mortality resulting from landslides; and (v) evaluate the individual and societal risk. Individual risk is evaluated computing mortality rates for landslides, which are calculated based on the annual average population and the annual average of fatalities. The societal risk is evaluated by plotting the annual frequency of landslide cases that generated fatalities (F-N curves). The results demonstrate the absence of any exponential growth in time of both landslide cases and landslide mortality in Portugal. The highest number of landslide cases and related mortalities occurred in the period of 1935-1969 in relation to very wet years. After this period, the number of landslide mortalities decreased, although fatalities remained higher than those registered in the period of 1865-1934. The landslide fatalities mainly occurred in the north of the Tagus valley where the geologic and geomorphologic conditions are more prone to landslides. The Lisbon area registered a mortality hotspot, which is explained by natural conditions combined with the high exposure of population to landslide risk. In the South of Portugal landslide fatalities are constrained to coastal cliffs reflecting a careless intensive use of the coastal areas for tourism. Falls and flows were responsible for the highest number of fatalities associated with landslides. Males were found to have the highest frequency of fatalities and fatalities inside buildings were dominant, mostly in rural areas. In conclusion, the spatial patterns of landslide mortality can be related to the unequal distribution of predisposing conditions to landslides, changes in the land use and exposure and social vulnerability to landslide hazards.N/

Studio sperimentale e conseguente analisi dei costi di processo per la produzione di bioplasticizzanti a partire da biodiesel

Nel 2016 il mercato globale dei plastificanti \ue8 stato pari a 8,4 milioni di tonnellate, di cui il 70% ricoperto dalla produzione di ftalati. L\u2019utilizzo di questi ultimi, nonostante le loro ottime propriet\ue0 chimico-fisiche (elevata solubilit\ue0 nella matrice polimerica, bassa volatilit\ue0 e bassi costi di produzione), pone problemi di salute e ha indotto l'Unione Europea nel Giugno 2017 a limitarne la percentuale nei prodotti plastici ad un livello inferiore allo 0,1% in peso. Gli oli vegetali epossidati (EVO) sono buoni candidati come sostituenti degli ftalati, specialmente quando applicati al cloruro di polivinile (PVC). Tali molecole possono venire prodotte grazie alla reazione, catalizzata da acido solforico, tra la frazione insatura di un olio vegetale e l'acido perossiacetico, che funge da vettore attivo di ossigeno e viene ottenuto dalla reazione di acido acetico e perossido di idrogeno. Tuttavia, la solubilit\ue0 degli EVO in PVC \ue8 bassa, il che rende questi prodotti solo parzialmente idonei come sostituti degli ftalati, la cui concentrazione tipica nel polimero varia dallo 0,5 al 45% in peso. Il biodiesel di soia epossidato (ESB) pu\uf2 essere proposto come alternativa agli EVO. Il biodiesel \ue8 una miscela di esteri metilici di acidi grassi, il cui peso molecolare \ue8 circa un terzo rispetto agli oli vegetali. Tale prodotto pu\uf2 essere portato alla forma epossidata e pu\uf2 cos\uec fungere da plastificante primario e quindi essere considerato adatto come sostituto degli ftalati. Nel presente lavoro si propone una strategia per la produzione di ESB a partire da biodiesel ricavato da olio di soia, tramite un\u2019operazione di distillazione seguita da reazione di epossidazione. L\u2019obiettivo di tale processo \ue8 la massimizzazione del contenuto di ossirano nel prodotto finale, grazie alla concentrazione delle molecole insature ottenute a valle della colonna di distillazione a seguito della rimozione della parte satura del biodiesel di partenza. Tale strategia permette di ottenere sperimentalmente prodotti che, dopo l\u2019ottimizzatione di specifici parametri operativi, risultano chimicamente idonei all\u2019utilizzo come bioplastificanti primari. Per potere stimare i costi di processo, \ue8 stata simulata la colonna di distillazione e il reattore di epossidazione usando un codice Python 3.0 che si interfaccia in modo autonomo con il software di simulazione PRO / II 9.3 (SimSci Schneider Electrics by AVEVA). Le equazioni cinetiche e lo stato di equilibrio liquido-liquido sono state risolte numericamente ad ogni istante temporale della reazione (la reazione avviene in un sistema bifasico liquido) tramite un codice MATLAB. I coefficienti di attivit\ue0 di ciascun componente sono stati calcolati utilizzando il modello UNIFAC. La stima dei costi di investimento ed operativi ha permesso, in ultimo, di definire le migliori condizioni tecno-economiche di produzione di ESB

Cyclic RGD peptidomimetics containing bifunctional diketopiperazine scaffolds as new potent integrin ligands

The synthesis of eight bifunctional diketopiperazine (DKP) scaffolds is described; these were formally derived from 2,3-diaminopropionic acid and aspartic acid (DKP-1-DKP-7) or glutamic acid (DKP-8) and feature an amine and a carboxylic acid functional group. The scaffolds differ in the configuration at the two stereocenters and the substitution at the diketopiperazinic nitrogen atoms. The bifunctional diketopiperazines were introduced into eight cyclic peptidomimetics containing the Arg-Gly-Asp (RGD) sequence. The resulting RGD peptidomimetics were screened for their ability to inhibit biotinylated vitronectin binding to the purified integrins \u3b1 v\u3b2 3 and \u3b1 v\u3b2 5, which are involved in tumor angiogenesis. Nanomolar IC 50 values were obtained for the RGD peptidomimetics derived from trans DKP scaffolds (DKP-2-DKP-8). Conformational studies of the cyclic RGD peptidomimetics by 1H NMR spectroscopy experiments (VT-NMR and NOESY spectroscopy) in aqueous solution and Monte Carlo/Stochastic Dynamics (MC/SD) simulations revealed that the highest affinity ligands display well-defined preferred conformations featuring intramolecular hydrogen-bonded turn motifs and an extended arrangement of the RGD sequence [C\u3b2(Arg)-C\u3b2(Asp) average distance 658.8 \uc5]. Docking studies were performed, starting from the representative conformations obtained from the MC/SD simulations and taking as a reference model the crystal structure of the extracellular segment of integrin \u3b1 v\u3b2 3 complexed with the cyclic pentapeptide, Cilengitide. The highest affinity ligands produced top-ranked poses conserving all the important interactions of the X-ray complex. Copyright \ua9 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim