7,609 research outputs found
On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie
A new description of the universal Whitham hierarchy in terms of a
factorization problem in the Lie group of canonical transformations is
provided. This scheme allows us to give a natural description of dressing
transformations, string equations and additional symmetries for the Whitham
hierarchy. We show how to dress any given solution and prove that any solution
of the hierarchy may be undressed, and therefore comes from a factorization of
a canonical transformation. A particulary important function, related to the
-function, appears as a potential of the hierarchy. We introduce a class
of string equations which extends and contains previous classes of string
equations considered by Krichever and by Takasaki and Takebe. The scheme is
also applied for an convenient derivation of additional symmetries. Moreover,
new functional symmetries of the Zakharov extension of the Benney gas equations
are given and the action of additional symmetries over the potential in terms
of linear PDEs is characterized
On the Whitham hierarchy: dressing scheme, string equations and additional symmetrie
A new description of the universal Whitham hierarchy in terms of a
factorization problem in the Lie group of canonical transformations is
provided. This scheme allows us to give a natural description of dressing
transformations, string equations and additional symmetries for the Whitham
hierarchy. We show how to dress any given solution and prove that any solution
of the hierarchy may be undressed, and therefore comes from a factorization of
a canonical transformation. A particulary important function, related to the
-function, appears as a potential of the hierarchy. We introduce a class
of string equations which extends and contains previous classes of string
equations considered by Krichever and by Takasaki and Takebe. The scheme is
also applied for an convenient derivation of additional symmetries. Moreover,
new functional symmetries of the Zakharov extension of the Benney gas equations
are given and the action of additional symmetries over the potential in terms
of linear PDEs is characterized
Noise in neurons is message-dependent
Neuronal responses are conspicuously variable. We focus on one particular
aspect of that variability: the precision of action potential timing. We show
that for common models of noisy spike generation, elementary considerations
imply that such variability is a function of the input, and can be made
arbitrarily large or small by a suitable choice of inputs. Our considerations
are expected to extend to virtually any mechanism of spike generation, and we
illustrate them with data from the visual pathway. Thus, a simplification
usually made in the application of information theory to neural processing is
violated: noise {\sl is not independent of the message}. However, we also show
the existence of {\sl error-correcting} topologies, which can achieve better
timing reliability than their components.Comment: 6 pages,6 figures. Proceedings of the National Academy of Sciences
(in press
Herschel GASPS spectral observations of T Tauri stars in Taurus: unraveling far-infrared line emission from jets and discs
At early stages of stellar evolution young stars show powerful jets and/or
outflows that interact with protoplanetary discs and their surroundings.
Despite the scarce knowledge about the interaction of jets and/or outflows with
discs, spectroscopic studies based on Herschel and ISO data suggests that gas
shocked by jets and/or outflows can be traced by far-IR (FIR) emission in
certain sources. We want to provide a consistent catalogue of selected atomic
([OI] and [CII]) and molecular (CO, OH, and HO) line fluxes observed in
the FIR, separate and characterize the contribution from the jet and the disc
to the observed line emission, and place the observations in an evolutionary
picture. The atomic and molecular FIR (60-190 ) line emission of
protoplanetary discs around 76 T Tauri stars located in Taurus are analysed.
The observations were carried out within the Herschel key programme Gas in
Protoplanetary Systems (GASPS). The spectra were obtained with the
Photodetector Array Camera and Spectrometer (PACS). The sample is first divided
in outflow and non-outflow sources according to literature tabulations. With
the aid of archival stellar/disc and jet/outflow tracers and model predictions
(PDRs and shocks), correlations are explored to constrain the physical
mechanisms behind the observed line emission. The much higher detection rate of
emission lines in outflow sources and the compatibility of line ratios with
shock model predictions supports the idea of a dominant contribution from the
jet/outflow to the line emission, in particular at earlier stages of the
stellar evolution as the brightness of FIR lines depends in large part on the
specific evolutionary stage. [Abridged Abstract]Comment: 37 pages, 27 figures, accepted for publication in A&
`Interpolating' differential reductions of multidimensional integrable hierarchies
We transfer the scheme of constructing differential reductions, developed
recently for the case of the Manakov-Santini hierarchy, to the general
multidimensional case. We consider in more detail the four-dimensional case,
connected with the second heavenly equation and its generalization proposed by
Dunajski. We give a characterization of differential reductions in terms of the
Lax-Sato equations as well as in the framework of the dressing method based on
nonlinear Riemann-Hilbert problem.Comment: Based on the talk at NLPVI, Gallipoli, 15 page
Incidence of Hypertension in a Cohort of Spanish University Graduates:The SUN Study
Hypertension is a major public health problem. However,
no estimates of age- and sex-specific incidences are available
for the Spanish population. Our objective was to estimate
the incidence of hypertension in a cohort of university
graduates in Spain. We followed up 5648 individuals aged
25-65 years who were initially free of hypertension, diabetes,
and cardiovascular disease for a median of 30 months. New
diagnoses of hypertension were identified using mailed
questionnaires. We validated the self-reported diagnosis of
hypertension. In 18 250 person-years of follow-up, we
identified 248 new cases of hypertension. The unadjusted
incidences of hypertension in women and men were 8.2 per
1000 person-years (95% CI, 6.7-10.1) and 21.8 per 1000
person-years (95% CI, 18.6-25.4), respectively. The
cumulative probability of receiving a medical diagnosis of
hypertension by the age of 65 years was 50% among women
and 72% among men. In conclusion, we have provided new
evidence confirming that hypertension is one of the most
important public health problems in Spain
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