Poincare' normal forms and simple compact Lie groups

We classify the possible behaviour of Poincar\'e-Dulac normal forms for dynamical systems in $R^n$ with nonvanishing linear part and which are equivariant under (the fundamental representation of) all the simple compact Lie algebras and thus the corresponding simple compact Lie groups. The ``renormalized forms'' (in the sense of previous work by the author) of these systems is also discussed; in this way we are able to simplify the classification and moreover to analyze systems with zero linear part. We also briefly discuss the convergence of the normalizing transformations.Comment: 17 pages; minor corrections in revised versio

On the relation between standard and μ\mu-symmetries for PDEs

We give a geometrical interpretation of the notion of $\mu$-prolongations of vector fields and of the related concept of $\mu$-symmetry for partial differential equations (extending to PDEs the notion of $\lambda$-symmetry for ODEs). We give in particular a result concerning the relationship between $\mu$-symmetries and standard exact symmetries. The notion is also extended to the case of conditional and partial symmetries, and we analyze the relation between local $\mu$-symmetries and nonlocal standard symmetries.Comment: 25 pages, no figures, latex. to be published in J. Phys.

Antioxidant and UV-Blocking Functionalized Poly(Butylene Succinate) Films

The introduction of a limited number of functional groups on poly(butylene succinate) (PBS) chains by covalent bonding can impart new properties to the polymer without modifying its thermal and mechanical properties. In pursuit of a viable approach to obtain light- and heat-stabilized PBS samples, the nitroxide radical coupling (NRC) reaction between PBS macroradicals and the 3,5-di-tert-butyl-4-hydroxybenzoyl-2,2,6,6-tetramethylpiperidine-1-oxyl radical (BHB-TEMPO), a functionalizing agent bearing a sterically-hindered antioxidant phenol moiety, is here proposed. The reaction was initiated by peroxide and carried out in solution and in a melt. The functionalized materials were characterized by UV-visible spectroscopy (UV-Vis), proton nuclear magnetic resonance (1H-NMR), and size exclusion chromatography (SEC) analysis to gain structural information and by thermal gravimetric analysis (TGA) and differential scanning calorimetry (DSC) to investigate the thermal properties. In addition, films of the samples were subjected to thermal and photo-oxidative aging to assess their resistance to degradative processes. Finally, the PBS film with the highest degree of functionalization showed the ability to protect β-carotene, a molecule found in food and drugs and that is very sensitive to UV light, from degradation. This result suggests the use of this material (either alone or blended with other biopolyesters) for biodegradable and compostable active packaging

On the notion of conditional symmetry of differential equations

Symmetry properties of PDE's are considered within a systematic and unifying scheme: particular attention is devoted to the notion of conditional symmetry, leading to the distinction and a precise characterization of the notions of ``true'' and ``weak'' conditional symmetry. Their relationship with exact and partial symmetries is also discussed. An extensive use of ``symmetry-adapted'' variables is made; several clarifying examples, including the case of Boussinesq equation, are also provided.Comment: 18 page

“Intestinal-Type” Vulvar Adenocarcinoma: A Review of the MITO Rare Tumors Group

Intestinal-type adenocarcinoma (VAIt) represents a sporadic variant of vulvar carcinoma. It appears frequently localized to epithelial glands in the vulvar region, and it probably derives from cloacal remnants persisting in the adult. We performed a systematic review of the limited cases reported in the literature, with the intent to assess the specific peculiarities of this rare neoplasia and to state consistent management recommendations. The principal histological VAIt characteristic is that it resembles mucinous colonic carcinomas. Therefore, immunohistochemical workup, with different tumor markers including CK20, CDX2, and CK7 staining, is needed. To confirm vulvar origin, a thorough diagnostic, and radiological examination is required to rule out other primary malignancies. The gold standard of treatment for VAIt is surgery, with local excision with tumor-free margins. Lymph node staging is an option advised if the tumor size is >2 cm or if lymph node metastases are suspected on imaging. On the other hand, the role of neoadjuvant therapy is still in doubt, but a good response to adjuvant chemotherapy treatments has been described in both advanced and recurrent diseases. Sometimes, VAIt behavior can be unpredictable, with relapses even after many years, so more experiences and longer follow-up periods are needed to elucidate the best therapeutic management and its long-term prognosis

Events in a Non-Commutative Space-Time

We treat the events determined by a quantum physical state in a noncommutative space-time, generalizing the analogous treatment in the usual Minkowski space-time based on positive-operator-valued measures (POVMs). We consider in detail the model proposed by Snyder in 1947 and calculate the POVMs defined on the real line that describe the measurement of a single coordinate. The approximate joint measurement of all the four space-time coordinates is described in terms of a generalized Wigner function (GWF). We derive lower bounds for the dispersion of the coordinate observables and discuss the covariance of the model under the Poincare' group. The unusual transformation law of the coordinates under space-time translations is interpreted as a failure of the absolute character of the concept of space-time coincidence. The model shows that a minimal length is compatible with Lorents covariance.Comment: 13 pages, revtex. Introductory part shortened and some arguments made more clea

Surgical site infection after caesarean section. Space for post-discharge surveillance improvements and reliable comparisons

Surgical site infections (SSI) after caesarean section (CS) represent a substantial health system concern. Surveying SSI has been associated with a reduction in SSI incidence. We report the findings of three (2008, 2011 and 2013) regional active SSI surveillances after CS in community hospital of the Latium region determining the incidence of SSI. Each CS was surveyed for SSI occurrence by trained staff up to 30 post-operative days, and association of SSI with relevant characteristics was assessed using binomial logistic regression. A total of 3,685 CS were included in the study. A complete 30 day post-operation follow-up was achieved in over 94% of procedures. Overall 145 SSI were observed (3.9% cumulative incidence) of which 131 (90.3%) were superficial and 14 (9.7%) complex (deep or organ/space) SSI; overall 129 SSI (of which 89.9% superficial) were diagnosed post-discharge. Only higher NNIS score was significantly associated with SSI occurrence in the regression analysis. Our work provides the first regional data on CS-associated SSI incidence, highlighting the need for a post-discharge surveillance which should assure 30 days post-operation to not miss data on complex SSI, as well as being less labour intensive

Continuous Symmetries of Difference Equations

Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study difference equations. We show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners. One is to use generalized symmetries acting on solutions of difference equations, but leaving the lattice invariant. The other is to restrict to point symmetries, but to allow them to also transform the lattice.Comment: Review articl