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.

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

Local and nonlocal solvable structures in ODEs reduction

Solvable structures, likewise solvable algebras of local symmetries, can be used to integrate scalar ODEs by quadratures. Solvable structures, however, are particularly suitable for the integration of ODEs with a lack of local symmetries. In fact, under regularity assumptions, any given ODE always admits solvable structures even though finding them in general could be a very difficult task. In practice a noteworthy simplification may come by computing solvable structures which are adapted to some admitted symmetry algebra. In this paper we consider solvable structures adapted to local and nonlocal symmetry algebras of any order (i.e., classical and higher). In particular we introduce the notion of nonlocal solvable structure

Nonlocal aspects of λ\lambda-symmetries and ODEs reduction

A reduction method of ODEs not possessing Lie point symmetries makes use of the so called $\lambda$-symmetries (C. Muriel and J. L. Romero, \emph{IMA J. Appl. Math.} \textbf{66}, 111-125, 2001). The notion of covering for an ODE $\mathcal{Y}$ is used here to recover $\lambda$-symmetries of $\mathcal{Y}$ as nonlocal symmetries. In this framework, by embedding $\mathcal{Y}$ into a suitable system $\mathcal{Y}^{\prime}$ determined by the function $\lambda$, any $\lambda$-symmetry of $\mathcal{Y}$ can be recovered by a local symmetry of $\mathcal{Y}^{\prime}$. As a consequence, the reduction method of Muriel and Romero follows from the standard method of reduction by differential invariants applied to $\mathcal{Y}^{\prime}$.Comment: 13 page

Diet-induced Obesity In Rats Leads To A Decrease In Sperm Motility.

Obesity is rapidly becoming a worldwide epidemic that affects children and adults. Some studies have shown a relationship between obesity and infertility, but until now it remains controversial. Thus, the aim of the present study was to investigate the effect of high-fat diet-induced obesity on male reproductive parameters. In a first experiment, male Wistar rats were fed a high-fat diet (HFD) or standard chow (SD) for 15, 30 or 45 weeks, after which they were evaluated by adiposity index, serum leptin levels, reproductive organ weights and sperm counts. In a second experiment, rats received HFD or SD only for 15 weeks, long enough to cause obesity. Sexual hormones and sexual behavior were evaluated in these animals, as well as fertility after natural mating. Another group of rats was submitted to motility analysis and fertility evaluation after in utero insemination. After 15, 30 or 45 weeks, HFD-fed animals presented significant increases in obesity index and serum leptin levels. Reproductive organ weights and sperm counts in the testis and epididymis were similar between the two groups at all timepoints studied. Sexual behavior was not altered by the diet regimen, and HFD fertility after natural mating was also similar to SD-fed animals. Intergroup testosterone levels were also comparable, but estradiol levels were increased in HFD rats. Furthermore, sperm quality was reduced in HFD animals as evidenced by their decreased percentage of sperm with progressive movement. This altered motility parameter was followed by a trend toward reduction in fertility potential after artificial in utero insemination. The results reported herein showed that obesity can affect sperm quality, by reducing sperm motility, without affecting other sperm parameters. The low sperm quality caused a slight reduction in fertility potential, showing that obesity may lead to impairment in male fertility.93

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