Differential forms on Carnot groups

The main goal of this thesis is to understand and link together some of the early works by Michel Rumin and Pierre Julg. The work is centered around the so-called Rumin complex, which is a construction in subRiemannian geometry. A Carnot manifold is a manifold endowed with a horizontal distribution. If further a metric is given, one gets a subRiemannian manifold. Such data arise in different contexts, such as: - formulation of the second principle of thermodynamics; - optimal control; - propagation of singularities for sums of squares of vector fields; - real hypersurfaces in complex manifolds; - ideal boundaries of rank one symmetric spaces; - asymptotic geometry of nilpotent groups; - modelization of human vision. Differential forms on a Carnot manifold have weights, which produces a filtered complex. In view of applications to nilpotent groups, Rumin has defined a substitute for the de Rham complex, adapted to this filtration. The presence of a filtered complex also suggests the use of the formal machinery of spectral sequences in the study of cohomology. The goal was indeed to understand the link between Rumin's operator and the differentials which appear in the various spectral sequences we have worked with: - the weight spectral sequence; - a special spectral sequence introduced by Julg and called by him Forman's spectral sequence; - Forman's spectral sequence (which turns out to be unrelated to the previous one). We will see that in general Rumin's operator depends on choices. However, in some special cases, it does not because it has an alternative interpretation as a differential in a natural spectral sequence. After defining Carnot groups and analysing their main properties, we will introduce the concept of weights of forms which will produce a splitting on the exterior differential operator d. We shall see how the Rumin complex arises from this splitting and proceed to carry out the complete computations in some key examples. From the third chapter onwards we will focus on Julg's paper, describing his new filtration and its relationship with the weight spectral sequence. We will study the connection between the spectral sequences and Rumin's complex in the n-dimensional Heisenberg group and the 7-dimensional quaternionic Heisenberg group and then generalize the result to Carnot groups using the weight filtration. Finally, we shall explain why Julg required the independence of choices in some special Rumin operators, introducing the Szego map and describing its main properties.

Rare and complicated forms of infantile hemangiomas: new therapeutic outlooks

Infantile hemangiomas (IHs) are the most common benign neoplastic pathology of childhood; their natural history generally involves three phases: after the onset, which usually occurs in the first weeks of life, there is the proliferation phase where the IH reaches its maximum development and it is followed by the spontaneous involution which leads to the IH regression. The duration and the extent of these phases may vary widely even though in most of the cases the involution process begins around twelve months of life and the regression, complete or partial, is completed around seventh-ninth year of life. The majority of the IHs does not require any treatment. However, 10%-20% is likely to develop serious complications, functional impairments or aesthetic alterations and entail a timely treatment. Although there is no treatment protocol currently shared, therapies usually used in cases with a complication risk consist in: systemic or intralesional steroids as a first choice; interferon α, vincristine and/or bleomicin as second or third choice and/or surgical treatment. Propranolol, a non-selective beta-blocker, has been used for cardiovascular diseases even in childhood for decades. Since 2008 it has been widely used in the IHs treatment, although it is still "off-label". In literature there are hundreds of cases and some clinical studies that show the effectiveness and safety of this drug for this indication. Thanks to a multidisciplinary team (Dermatologists, Cardiologists, Paediatricians, and Radiologists) of S. Orsola-Malpighi Hospital, a clinical study, which has been previously approved by the ethics committee, is carried out in order to evaluate the efficacy and safety of systemic propranolol in the treatment of IHs in paediatric age. At the end of 2012, 78 patients underwent this treatment: the results we have obtained so far show a good efficacy and safety profile in agreement with the data provided by the literature.

Solubility and permeability as in vitro predictors for in vivo performance of fenofibrate IR solid dosage forms

This current work focused on the simulation of in vivo dissolution and permeation in order to be able to predict the in vivo performance of orally administered fenofibrate immediate release formulations. Therefore, the effects of the formulation surfactants on in vivo solubility and permeation of fenofibrate under physiologically relevant excipient concentrations were emphasized.rnIt was shown that the surfactant sodium dodecyl sulfate (SDS) may decrease rather than increase the solubility of fenofibrate in vivo. This was related to the interference of SDS with the vesicular system of the biorelevant medium, FaSSIFmod, and therefore its solubilization capacity. rnMoreover, in vitro permeation studies revealed that SDS concentrations inversely correlated with fenofibrate permeability. Through combination of the observed permeation and solubility data a good in vitro/in vivo correlation regarding Cmax values in humans could be established for five fenofibrate formulations which were based on the same manufacturing technique.rnBesides the experimental part, the major characteristics and their potential implementation in a dissolution/permeation device were discussed based on the promising realization of the in vitro solubility and permeation methods. rn

Optimization of molecular and crystalline forms of drugs, agrochemicals, pesticides in relation to activity, bioavailability, patentability and to the fabrication of polymorphs, solvates, co-crystals with green chemistry methods

This doctorate was funded by the Regione Emilia Romagna, within a Spinner PhD project coordinated by the University of Parma, and involving the universities of Bologna, Ferrara and Modena. The aim of the project was: - Production of polymorphs, solvates, hydrates and co-crystals of active pharmaceutical ingredients (APIs) and agrochemicals with green chemistry methods; - Optimization of molecular and crystalline forms of APIs and pesticides in relation to activity, bioavailability and patentability. In the last decades, a growing interest in the solid-state properties of drugs in addition to their solution chemistry has blossomed. The achievement of the desired and/or the more stable polymorph during the production process can be a challenge for the industry. The study of crystalline forms could be a valuable step to produce new polymorphs and/or co-crystals with better physical-chemical properties such as solubility, permeability, thermal stability, habit, bulk density, compressibility, friability, hygroscopicity and dissolution rate in order to have potential industrial applications. Selected APIs (active pharmaceutical ingredients) were studied and their relationship between crystal structure and properties investigated, both in the solid state and in solution. Polymorph screening and synthesis of solvates and molecular/ionic co-crystals were performed according to green chemistry principles. Part of this project was developed in collaboration with chemical/pharmaceutical companies such as BASF (Germany) and UCB (Belgium). We focused on on the optimization of conditions and parameters of crystallization processes (additives, concentration, temperature), and on the synthesis and characterization of ionic co-crystals. Moreover, during a four-months research period in the laboratories of Professor Nair Rodriguez-Hormedo (University of Michigan), the stability in aqueous solution at the equilibrium of ionic co-crystals (ICCs) of the API piracetam was investigated, to understand the relationship between their solid-state and solution properties, in view of future design of new crystalline drugs with predefined solid and solution properties.

Real forms of Lie algebras and Lie superalgebras

In questa tesi abbiamo studiato le forme reali di algebre e superalgebre di Lie. Il lavoro si suddivide in tre capitoli diversi, il primo è di introduzione alle algebre di Lie e serve per dare le prime basi di questa teoria e le notazioni. Nel secondo capitolo abbiamo introdotto le algebre compatte e le forme reali. Abbiamo visto come sono correlate tra di loro tramite strumenti potenti come l'involuzione di Cartan e relativa decomposizione ed i diagrammi di Vogan e abbiamo introdotto un algoritmo chiamato "push the button" utile per verificare se due diagrammi di Vogan sono equivalenti. Il terzo capitolo segue la struttura dei primi due, inizialmente abbiamo introdotto le superalgebre di Lie con relativi sistemi di radici e abbiamo proseguito studiando le relative forme reali, diagrammi di Vogan e abbiamo introdotto anche qua l'algoritmo "push the button".

Glucagon-like peptide-1 versus somatostatin receptor targeting reveals 2 distinct forms of malignant insulinomas

Glucagon-like peptide-1 (GLP-1) receptor imaging is superior to somatostatin receptor subtype 2 (sst(2)) imaging in localizing benign insulinomas. Here, the role of GLP-1 and sst(2) receptor imaging in the management of malignant insulinoma patients was investigated.

Numerical Computation of a Certain Dirichlet Series Attached to Siegel Modular Forms of Degree Two

The Rankin convolution type Dirichlet series D-F,D-G(s) of Siegel modular forms F and G of degree two, which was introduced by Kohnen and the second author, is computed numerically for various F and G. In particular, we prove that the series D-F,D-G(s), which shares the same functional equation and analytic behavior with the spinor L-functions of eigenforms of the same weight are not linear combinations of those. In order to conduct these experiments a numerical method to compute the Petersson scalar products of Jacobi Forms is developed and discussed in detail.

The co-evolution of development needs and IOR forms: development by committee in Bosnia

This work highlights opportunities and obstacles to success in four task forces typically found at different times in states of conflict, transition, and development. They include: refugee return, media issues, privatization of state-owned enterprises, and efforts to promote business development. Based on over 180 in-depth interviews and observations of dozens of meetings during five lengthy field research trips to the Bosnian region between 1999 and 2005, this manuscript analyzes how these four task forces differed in terms of context, strategy, organization, and management in an attempt to understand the co-evolution of international development needs and the interorganizational forms that address them.

"Framing Counterspaces: Forms and Meanings of Graffiti in Berlin's Linguistic Landscape"

Street art and graffiti are integral parts of Berlin’s urban space, which has undergone dramatic transformations in the past two decades. Graffiti texts constitute a critical comment on these urban transformations. This talk analyzes the connection between the phenomenon of street art and trajectories in urban planning in post-wall Berlin. My current research explores the meaning of various forms of street art (such as graffiti, posters, sticker art, stencils) as texts in Berlin’s linguistic landscape. Linguistic Landscape research pays critical attention to language, words, and images displayed and exposed in public spaces. The field of Linguistic Landscapes has only recently begun to include graffiti texts in analyses of text and space to fully comprehend the semiotics of the street. In the case of Germany’s capital, graffiti writing enters into a critical dialogue with the environment and provides a readable text to understand the city.

Pond-Women Revelations: The Subaltern Registers in Maithil Women's Expressive Forms

Ponds are ubiquitous in the Maithil region of Nepal, and they figure prominently in folk narratives and ceremonial paintings produced by women there. I argue that in Maithil women's folktales, as in their paintings, the trope of ponds shifts the imaginative register toward women's perspectives and the importance of women's knowledge and influence in shaping Maithil society, even as this register shift occurs within plots featuring male protagonists. I argue further that in the absence of a habit of exegesis in their expressive arts, and given the cross-referential, dialogic nature of expressive practices, a methodology that draws into interpretive conversation the multitude of expressive forms exercised by Maithil women enhances analytical access to Maithil women's collective perspectives on their social and cosmological worlds.