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

Light absorption by phytoplankton in the Southern Baltic and Pomeranian lakes: mathematical expressions for remote sensing applications

The absorption properties of phytoplankton in surface waters of the Baltic Sea and coastal lakes are examined in the context of their relationships with the concentration of the main photosynthetic pigment, chlorophyll a. The analysis covers 425 sets of spectra of light absorption coefficients aph(l) and chlorophyll a concentrations Chla measured in 2006—2009 in various waters of the Baltic Sea (open and coastal waters, the Gulf of Gdańsk and the Pomeranian Bay, river mouths and the Szczecin Lagoon), as well as in three lakes in Pomerania, Poland (Obłęskie, Łebsko and Chotkowskie). In these waters the specific (i.e. normalized with respect to Chla) light absorption coefficient of phytoplankton aph *(l) varies over wide ranges, which differ according to wavelength. For example, aph *(440) takes values from 0.014 to 0.124 mg1 m2, but aph *(675) from 0.008 to 0.067 mg1 m2, whereby Chla ranges from 0.8 to 120 mg m3. From this analysis a mathematical description has been produced of the specific light absorption coefficient of phytoplankton aph *(l), based on which the dynamics of its variability in these waters and the absorption spectra in the 400—700 nm interval can be reconstructed with a low level of uncertainty (arithmetic statistical error: 4.09—10.21%, systematic error: 29.63—51.37%). The relationships derived here are applicable in local remote sensing algorithms used for monitoring the Baltic Sea and coastal lakes and can substantially improve the accuracy of the remotely determined optical and biogeochemical characteristics of these waters

Assessing Architecture Conformance to Coupling-Related Infrastructure-as-Code Best Practices: Metrics and Case Studies

Infrastructure as Code (IaC) is an IT practice that facilitates the management of the underlying infrastructure as software. It enables developers or operations teams to automatically manage, monitor, and provision resources rather than organize them manually. In many industries, this practice is widespread and has already been fully adopted. However, few studies provide techniques for evaluating architectural conformance in IaC deployments and, in particular, aspects such as loose coupling. This paper focuses on coupling-related patterns and practices such as deployment strategies and the structuring of IaC elements. Many best practices are documented in gray literature sources, such as practitioner books, blogs, and public repositories. Still, there are no approaches yet to automatically check conformance with such best practices. We propose an approach based on generic, technology-independent metrics tied to typical architectural design decisions for IaC-based practices in microservice deployments to support architecting in the context of continuous delivery practices. We present three case studies based on open-source microservice architectures to validate our approach

Domain-Specific Languages for Service-Oriented Architectures: An Explorative Study

Domain-specific languages (DSLs) are an important software development approach for many service-oriented architectures (SOAs). They promise to model the various SOA concerns in a suitable way for the various technical and non-technical stakeholders of a SOA. However, so far the research on SOA DSLs concentrates on novel technical contributions, and not much evidence or counter-evidence for the claims associated to SOA DSLs has been provided. In this paper, we present a qualitative, explorative study that provides an initial analysis of a number of such claims through a series of three prototyping experiments in which each experiment has developed, analyzed, and compared a set of DSLs for process-driven SOAs. Our result is to provide initial evidence for a number of popular claims about SOA DSLs which follow the model-driven software development (MDSD) approach, as well as a list of design trade-offs to be considered in the design decisions that must be made when developing a SOA DSL