On the flow map for 2D Euler equations with unbounded vorticity

In Part I, we construct a class of examples of initial velocities for which the unique solution to the Euler equations in the plane has an associated flow map that lies in no Holder space of positive exponent for any positive time. In Part II, we explore inverse problems that arise in attempting to construct an example of an initial velocity producing an arbitrarily poor modulus of continuity of the flow map.Comment: http://iopscience.iop.org/0951-7715/24/9/013/ for published versio

THE AFTERCARE SURVEY:Assessment and intervention practices after brain tumour surgery in Europe

Introduction People with gliomas need specialized neurosurgical, neuro-oncological, psycho-oncological, and neuropsychological care. The role of language and cognitive recovery and rehabilitation in patients’ well-being and resumption of work is crucial, but there are no clear guidelines for the ideal timing and character of assessments and interventions. The goal of the present work was to describe representative (neuro)psychological practices implemented after brain surgery in Europe. Methods An online survey was addressed to professionals working with individuals after brain surgery. We inquired about the assessments and interventions and the involvement of caregivers. Additionally, we asked about recommendations for an ideal assessment and intervention plan. Results Thirty-eight European centres completed the survey. Thirty of them offered at least one post-surgical (neuro)psychological assessment, mainly for language and cognition, especially during the early recovery stage and at long-term. Twenty-eight of the participating centres offered post-surgical therapies. Patients who stand the highest chances of being included in evaluation and therapy post-surgically are those who underwent awake brain surgery, harboured a low-grade glioma, or showed poor recovery. Nearly half of the respondents offer support programs to caregivers, and all teams recommend them. Treatments differed between these offered to individuals with low-grade glioma versus those with high-grade glioma. The figure of caregiver is not yet fully recognized in the recovery phase. Conclusion We stress the need for more complete rehabilitation plans, including the emotional and health-related aspects of recovery. In respondents´ opinions, assessment and rehabilitation plans should also be individually tailored and goal-directed (e.g., professional reinsertion)

Remarks on the Cauchy functional equation and variations of it

This paper examines various aspects related to the Cauchy functional equation $f(x+y)=f(x)+f(y)$, a fundamental equation in the theory of functional equations. In particular, it considers its solvability and its stability relative to subsets of multi-dimensional Euclidean spaces and tori. Several new types of regularity conditions are introduced, such as a one in which a complex exponent of the unknown function is locally measurable. An initial value approach to analyzing this equation is considered too and it yields a few by-products, such as the existence of a non-constant real function having an uncountable set of periods which are linearly independent over the rationals. The analysis is extended to related equations such as the Jensen equation, the multiplicative Cauchy equation, and the Pexider equation. The paper also includes a rather comprehensive survey of the history of the Cauchy equation.Comment: To appear in Aequationes Mathematicae (important remark: the acknowledgments section in the official paper exists, but it appears before the appendix and not before the references as in the arXiv version); correction of a minor inaccuracy in Lemma 3.2 and the initial value proof of Theorem 2.1; a few small improvements in various sections; added thank

On continuity of iteration semigroups on metric paces

The article contains no abstrac

Sur la solution générale l’équation fonctionnelle φ(x)⋅φ(f(x))=0\varphi(x)\cdot\varphi (f(x)) = 0

The article contains no abstrac

Prospect for anthelminthic plants in the Ivory Coast using ethnobotanical criteria

Sixty plant species were collected in the Ivory Coast on the basis of an ethnobotanical literature using the following three criteria: activity against worms, diarrhoea and/or abdominal pain. Eighty six plant extracts were prepared using 90% ethanol and tested for potential anthelminthic activities with a larvicidal test of Haemonchus contortus. 25.6% of the extracts showed a high activity, 12.8% were active or marginally active and the remaining 61.6% were inactive. The fact that a relatively high percentage of the plants species (50%) had an activity can be explained by the initial preselection of the plants on the basis of ethnobotanical indications

Overview of Sun photometer measurements of aerosol properties in Scandinavia and Svalbard

An overview on the data of columnar aerosol properties measured in Northern Europe is provided. Apart from the necessary data gathered in the Arctic, the knowledge of the aerosol loading in nearby areas (e.g. sub-Arctic) is of maximum interest to achieve a correct analysis of the Arctic aerosols and transport patterns. This work evaluates data from operational sites with sun photometer measurements belonging either to national or international networks (AERONET, GAW-PFR) and programs conducted in Scandi- navia and Svalbard. We enumerate a list of sites, measurement type and periods together with observed aerosol properties. An evaluation and analysis of aerosol data was carried out with a review of previous results as well. Aerosol optical depth (AOD) and Ångström exponent (AE) are the current parameters with suf␣cient long-term records for a ␣rst evaluation of aerosol properties. AOD (500 nm) ranges from 0.08 to 0.10 in Arctic and sub-Arctic sites (Ny-Ålesund: 0.09; Andenes: 0.10; Sodankylä: 0.08), and it is somewhat higher in more populated areas in Southern Scandinavia (AOD about 0.10e0.12 at 500 nm). On the Norwegian coast, aerosols show larger mean size (AE � 1.2 at Andenes) than in Finland, with continental climate (AE � 1.5 at Sodankylä). Columnar particle size distributions and related parameters derived from inversion of sun/sky radiances were also investigated. This work makes special emphasis in the joint and collaborative effort of the various groups from different countries involved in this study. Part of the measurements presented here were involved in the IPY projects Polar-AOD and POLARCAT

A general class of iterative equations on the unit circle

summary:A class of functional equations with nonlinear iterates is discussed on the unit circle ${\mathbb{T}}^1$. By lifting maps on ${\mathbb{T}}^1$ and maps on the torus ${\mathbb{T}}^n$ to Euclidean spaces and extending their restrictions to a compact interval or cube, we prove existence, uniqueness and stability for their continuous solutions