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.

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

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 geometry of lambda-symmetries, and PDEs reduction

We give a geometrical characterization of $\lambda$-prolongations of vector fields, and hence of $\lambda$-symmetries of ODEs. This allows an extension to the case of PDEs and systems of PDEs; in this context the central object is a horizontal one-form $\mu$, and we speak of $\mu$-prolongations of vector fields and $\mu$-symmetries of PDEs. We show that these are as good as standard symmetries in providing symmetry reduction of PDEs and systems, and explicit invariant solutions

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

Noether theorem for mu-symmetries

We give a version of Noether theorem adapted to the framework of mu-symmetries; this extends to such case recent work by Muriel, Romero and Olver in the framework of lambda-symmetries, and connects mu-symmetries of a Lagrangian to a suitably modified conservation law. In some cases this "mu-conservation law'' actually reduces to a standard one; we also note a relation between mu-symmetries and conditional invariants. We also consider the case where the variational principle is itself formulated as requiring vanishing variation under mu-prolonged variation fields, leading to modified Euler-Lagrange equations. In this setting mu-symmetries of the Lagrangian correspond to standard conservation laws as in the standard Noether theorem. We finally propose some applications and examples.Comment: 28 pages, to appear in J. Phys.

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