21 research outputs found

    Water safety plans and climate change mitigation

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    [Excerpt] Definition Quality water at affordable prices for all is a key condition for the promotion of public health, environmental sustainability, and quality and safety of life. In a context of growing external uncertainties arising from changes in the climate and the environment, ensuring these conditions is an upward concern and is of utmost relevance to increase scientific research on the impacts of climate change on water quality modification and in minimization/mitigation strategies

    Remarks on the Cauchy functional equation and variations of it

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    This paper examines various aspects related to the Cauchy functional equation f(x+y)=f(x)+f(y)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

    A Survey of Examples of Convex Functions and Classifications of Normed Spaces

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    This paper represents a slightly extended version of the eponymous talk given at the VII Colloque Franco-Allemand d'Optimisation. My aim is to illustrate the tight connection between the sequential properties of a Banach space and the corresponding properties of the convex functions and sets which may or may not be defined on that space
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