Environment conditions and biological innovations in the european agrarian growth, 1819-1939

The circumstances that were the driving forces behind Europe's economic growth beginning in the 19th century are diverse, and not easily prioritized. Until the 1970's, specifically, in Economy and Economic History, attention was focused on different institutional and technological variables, and various regularities were proposed. Nevertheless, new studies also underlined that the evolution of economic activity could not be understood considering only the new production possibilities offered by market economies. As a result, today it is also accepted that those processes can not be explained without considering two additional circumstances: the energy flows that sustained them, and the changes undergone in their transformation In this context, a question arises that takes on special importance. Which was the influence of the biological change in the economic growth?. A part of the flows of energy must be made into food, and this transformation can only happen with the participation.

In search of mathematical primitives for deriving universal projective hash families

We provide some guidelines for deriving new projective hash families of cryptographic interest. Our main building blocks are so called group action systems; we explore what properties of this mathematical primitives may lead to the construction of cryptographically useful projective hash families. We point out different directions towards new constructions, deviating from known proposals arising from Cramer and Shoup's seminal work.

The automorphism group of a free-by-cyclic group in rank 2

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Linear stochastic differential algebraic equations with constant coefficients

We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson and Fernique). We provide sufficient conditions for the law of the variables of the solution process to be absolutely continuous with respect to Lebesgue measure.

Clarke critical values of subanalytic Lipschitz continuous functions

We prove that any subanalytic locally Lipschitz function has the Sard property. Such functions are typically nonsmooth and their lack of regularity necessitates the choice of some generalized notion of gradient and of critical point. In our framework these notions are defined in terms of the Clarke and of the convex-stable subdifferentials. The main result of this note asserts that for any subanalytic locally Lipschitz function the set of its Clarke critical values is locally finite. The proof relies on Pawlucki's extension of the Puiseuxlemma. In the last section we give an example of a continuous subanalytic function which is not constant on a segment of "broadly critical" points, that is, points for which we can find arbitrarily short convex combinations of gradients at nearby points.