HKT manifolds: Hodge theory, formality and balanced metrics

Let $(M,I,J,K,\Omega)$ be a compact HKT manifold and denote with $\partial$ the conjugate Dolbeault operator with respect to $I$, $\partial_J:=J^{-1}\overline\partial J$, $\partial^\Lambda:=[\partial,\Lambda]$ where $\Lambda$ is the adjoint of $L:=\Omega\wedge-$. Under suitable assumptions, we study Hodge theory for the complexes $(A^{\bullet,0},\partial,\partial_J)$ and $(A^{\bullet,0},\partial,\partial^\Lambda)$ showing a similar behavior to K\"ahler manifolds. In particular, several relations among the Laplacians, the spaces of harmonic forms and the associated cohomology groups, together with Hard Lefschetz properties, are proved. Moreover, we show that for a compact HKT $\mathrm{SL}(n,\mathbb{H})$-manifold the differential graded algebra $(A^{\bullet,0},\partial)$ is formal and this will lead to an obstruction for the existence of an HKT $\mathrm{SL}(n,\mathbb{H})$-structure $(I,J,K,\Omega)$ on a compact complex manifold $(M,I)$. Finally, balanced HKT structures on solvmanifolds are studied.Comment: 17 pages. Comments are welcom

The quaternionic Calabi conjecture on abelian hypercomplex nilmanifolds viewed as tori fibrations

We study the quaternionic Calabi-Yau problem in HKT geometry introduced by Alesker and Verbitsky on 8-dimensional 2-step nilmanifolds with an abelian hypercomplex structure. We show that the quaternionic Monge-Amp\`ere equation on these manifolds can always be solved for every data which is invariant by the action of a 3-dimensional torus.Comment: 20 pages, to appear in IMR

A remark on the quaternionic Monge-Amp\`ere equation on foliated manifolds

We study the quaternionic Monge-Amp\`ere equation on HKT manifolds admitting an HKT foliation having corank 4. We show that in this setting the quaternionic Monge-Amp\`ere equation has always a unique solution for every basic datum. This approach includes the study of the equation on SU(3).Comment: 12 pages, last version to appear in Proc. Amer. Math. So

The parabolic quaternionic Calabi-Yau equation on hyperk\"ahler manifolds

We show that the parabolic quaternionic Monge-Amp\`ere equation on a compact hyperk\"ahler manifold has always a long-time solution which once normalized converges smoothly to a solution of the quaternionic Monge-Amp\`ere equation. This is the same setting in which Dinew and Sroka prove the conjecture of Alesker and Verbitsky. We also introduce an analogue of the Chern-Ricci flow in hyperhermitian manifolds.Comment: This is a new version of the paper "The Calabi-Yau theorem on Hypercomplex manifolds", which was withdrawn due to a crucial mistake in a key Lemma. In this new version we fix the mistake by introducing the extra assumption of the existence of a background hyperk\"ahler metri

A parabolic approach to the Calabi-Yau problem in HKT geometry

We consider the natural generalization of the parabolic Monge-Amp\`ere equation to HKT geometry. We prove that in the compact case the equation has always a short-time solution and when the hypercomplex manifold is locally flat and admits a hyperk\"ahler metric, then the equation has a long-time solution whose normalization converges to a solution of the quaternionic Monge-Amp\`ere equation introduced by Alesker and Verbitsky. The result gives an alternative proof of a theorem of Alesker.Comment: 15 pages. Revisited version. To appear in Math.

Alternanza scuola-lavoro: condizioni di riuscita

The approval of the reform of the school system, (Law no. 107/2015), introducesin Italy the school-work alternation. For the first time the “culture ofwork” is inserted systematically in schools’ curriculas with the aim ofpreparing students for a better employability after diploma and a more consciousentry into the labor market. The authors analyze and explain the historical,social and cultural context in which the reform is introduced and therole of educational partnerships within the school-work alternation’sprocesses can and should take place with the involvement and the sharedresponsibility of educational actors and economic ones. The study also indicatessome possible critical questions for the diffusion of school-work alternationprocesses and gives reference models to be set in the territories.L’approvazione della riforma del sistema scolastico italiano, con Legge n.107/2015, introduce in Italia l’alternanza scuola-lavoro obbligatoria. Per laprima volta la cultura del lavoro rientra sistematicamente nei programmiscolastici con l’obiettivo di preparare gli studenti sotto il profilo delle competenzeper migliorare la loro occupabilità e un ingresso più consapevolenel mercato del lavoro. Gli autori analizzano e spiegano il contesto storico,sociale e culturale in cui la riforma si introduce e presentano un quadro dipartnership formative entro il quale i processi di alternanza possono e devonosvolgersi con il coinvolgimento e la corresponsabilità sia degli attoriformativi che degli attori economici. Lo studio indica inoltre alcune possibilicriticità per la diffusione dei percorsi di alternanza e modelli di riferimentoda riprodurre nei territori

Chiral separation and analysis of antifungal drugs by chromatographic and electromigration techniques: Results achieved in 2010–2020

AbstractThe determination and separation of enantiomers is an interesting and important topic of research in various fields, e.g., biochemistry, food science, pharmaceutical industry, environment, etc. Although these compounds possess identical physicochemical properties, a pair of enantiomers often has different pharmacological, toxicological, and metabolic activities. For this reason, chiral discrimination by using chromatographic and electromigration techniques has become an urgent need in the pharmaceutical field. This review intends to offer the "state of the art" about the separation of chiral antifungal drugs and several related precursors by both liquid and gas chromatography, as well as electromigration methods. This overview is organized into two sections. The first one describes general considerations on chiral antifungal drugs. The second part deals with the main analytical methods for the enantiomeric discrimination of these drugs, including a brief description of chiral selectors and stationary phases. Moreover, many recent applications attesting the great interest of analytical chemists in the field of enantiomeric separation are presented

Application of a Low Transition Temperature Mixture for the Dispersive Liquid-Liquid Microextraction of Illicit Drugs from Urine Samples

The use of psychoactive substances is a serious problem in today's society and reliable methods of analysis are necessary to confirm their occurrence in biological matrices. In this work, a green sample preparation technique prior to HPLC-MS analysis was successfully applied to the extraction of 14 illicit drugs from urine samples. The isolation procedure was a dispersive liquid-liquid microextraction based on the use of a low transition temperature mixture (LTTM), composed of choline chloride and sesamol in a molar ratio 1:3 as the extracting solvent. This mixture was classified as LTTM after a thorough investigation carried out by FTIR and DSC, which recorded a glass transition temperature at −71 °C. The extraction procedure was optimized and validated according to the main Food and Drug Administration (FDA) guidelines for bioanalytical methods, obtaining good figures of merit for all parameters: the estimated lower limit of quantitation (LLOQ) values were between 0.01 µg L−1 (bk-MMBDB) and 0.37 µg L−1 (PMA); recoveries, evaluated at very low spike levels (in the ng-µg L−1 range), spanned from 55% (MBDB) to 100% (bk-MMBDB and MDPV); finally, both within-run and between-run precisions were lower than 20% (LLOQ) and 15% (10xLLOQ)

Chemotherapy and palliative care near end-of life: Examining the appropriateness at a cancer institute for colorectal cancer patients

Background: Appropriate cessation of chemotherapy and timely referral of patients to hospice services are crucial for the quality of care near death. We investigated the quality of care in our Cancer Institute in very advanced metastatic colorectal cancer patients treated in real life. Patients and Methods: We performed a retrospective analysis of electronic medical data of patients with metastatic colorectal cancer who were candidates for chemotherapy during the study period (1 January 2007-30 June 2014) and died before 31 December 2014. Quality-of-cancer-care indicators were calculated for the overuse of chemotherapy and referral to hospice. Predictive factors of chemotherapy discontinuation and hospice referral in end-of life care were investigated using parametric and nonparametric methods. Results: Of the 365 patients who died before 31 December 2014, 26 (7.1%) received chemotherapy in the last 14 days of life and 36 (9.8%) started a new chemotherapy regimen in the last 30 days of life. Factors associated with the overuse of chemotherapy were being < 70 years of age for both indicators and not having received advanced chemotherapy treatments for the former indicator. The majority of patients (74.7%) had access to hospice services, of whom only a small percentage (7.2%) accessed them very near to death. Conclusions: According to the criteria used, our Institute provides a good quality of cancer care for dying colorectal cancer patients, measured by the use of chemotherapy and referral to hospice in their last days of life