159 research outputs found
On the relation between standard and -symmetries for PDEs
We give a geometrical interpretation of the notion of -prolongations of
vector fields and of the related concept of -symmetry for partial
differential equations (extending to PDEs the notion of -symmetry for
ODEs). We give in particular a result concerning the relationship between
-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 -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 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 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
On the geometry of lambda-symmetries, and PDEs reduction
We give a geometrical characterization of -prolongations of vector
fields, and hence of -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 , and we speak of -prolongations of vector fields
and -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 -symmetries and ODEs reduction
A reduction method of ODEs not possessing Lie point symmetries makes use of
the so called -symmetries (C. Muriel and J. L. Romero, \emph{IMA J.
Appl. Math.} \textbf{66}, 111-125, 2001). The notion of covering for an ODE
is used here to recover -symmetries of as
nonlocal symmetries. In this framework, by embedding into a
suitable system determined by the function ,
any -symmetry of can be recovered by a local symmetry of
. As a consequence, the reduction method of Muriel and
Romero follows from the standard method of reduction by differential invariants
applied to .Comment: 13 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
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.
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