Existence of positive solutions of a superlinear boundary value problem with indefinite weight

We deal with the existence of positive solutions for a two-point boundary value problem associated with the nonlinear second order equation $u''+a(x)g(u)=0$. The weight $a(x)$ is allowed to change its sign. We assume that the function $g\colon\mathopen{[}0,+\infty\mathclose{[}\to\mathbb{R}$ is continuous, $g(0)=0$ and satisfies suitable growth conditions, so as the case $g(s)=s^{p}$, with $p>1$, is covered. In particular we suppose that $g(s)/s$ is large near infinity, but we do not require that $g(s)$ is non-negative in a neighborhood of zero. Using a topological approach based on the Leray-Schauder degree we obtain a result of existence of at least a positive solution that improves previous existence theorems.Comment: 12 pages, 4 PNG figure

Educating for Autonomy: Liberalism and Autonomy in the Capabilities Approach

Martha Nussbaum grounds her version of the capabilities approach in political liberalism. In this paper, we argue that the capabilities approach, insofar as it genuinely values the things that persons can actually do and be, must be grounded in a hybrid account of liberalism: in order to show respect for adults, its justification must be political; in order to show respect for children, however, its implementation must include a commitment to comprehensive autonomy, one that ensures that children develop the skills necessary to make meaningful choices about whether or not to exercise their basic capabilities. Importantly, in order to show respect for parents who do not necessarily recognize autonomy as a value, we argue that the liberal state, via its system of public education, should take on the role of ensuring that all children within the state develop a sufficient degree of autonomy

Quantum correlations and distinguishability of quantum states

A survey of various concepts in quantum information is given, with a main emphasis on the distinguishability of quantum states and quantum correlations. Covered topics include generalized and least square measurements, state discrimination, quantum relative entropies, the Bures distance on the set of quantum states, the quantum Fisher information, the quantum Chernoff bound, bipartite entanglement, the quantum discord, and geometrical measures of quantum correlations. The article is intended both for physicists interested not only by collections of results but also by the mathematical methods justifying them, and for mathematicians looking for an up-to-date introductory course on these subjects, which are mainly developed in the physics literature.Comment: Review article, 103 pages, to appear in J. Math. Phys. 55 (special issue: non-equilibrium statistical mechanics, 2014

Intergenerational justice of what: welfare, resources or capabilities?

An important aspect of intergenerational justice concerns the specification of a 'currency of advantage' that can be used to evaluate distributive outcomes across time. Environmental theorists have introduced several innovative currencies of justice in recent years, such as ecological space and critical natural capital. However they have often downplayed the application of established currencies (such as welfare, resources or capabilities) to issues of futurity. After exploring the merits of a number of rival currencies, it is argued that the currency of 'capabilities to function' provides a promising basis for a theory of justice that takes seriously the rights and duties of intergenerational justice

Cyclic projectors and separation theorems in idempotent convex geometry

Semimodules over idempotent semirings like the max-plus or tropical semiring have much in common with convex cones. This analogy is particularly apparent in the case of subsemimodules of the n-fold cartesian product of the max-plus semiring it is known that one can separate a vector from a closed subsemimodule that does not contain it. We establish here a more general separation theorem, which applies to any finite collection of closed semimodules with a trivial intersection. In order to prove this theorem, we investigate the spectral properties of certain nonlinear operators called here idempotent cyclic projectors. These are idempotent analogues of the cyclic nearest-point projections known in convex analysis. The spectrum of idempotent cyclic projectors is characterized in terms of a suitable extension of Hilbert's projective metric. We deduce as a corollary of our main results the idempotent analogue of Helly's theorem.Comment: 20 pages, 1 figur

The Causal Structure of Emotions in Aristotle: Hylomorphism, Causal Interaction between Mind and Body, and Intentionality

Recently, a strong hylomorphic reading of Aristotelian emotions has been put forward, one that allegedly eliminates the problem of causal interaction between soul and body. Taking the presentation of emotions in de An. I 1 as a starting point and basic thread, but relying also on the discussion of Rh. II, I will argue that this reading only takes into account two of the four causes of emotions, and that, if all four of them are included into the picture, then a causal interaction of mind and body remains within Aristotelian emotions, independent of how strongly their hylomorphism is understood. Beyond the discussion with this recent reading, the analysis proposed of the fourfold causal structure of emotions is also intended as a hermeneutical starting point for a comprehensive analysis of particular emotions in Aristotle. Through the different causes Aristotle seems to account for many aspects of the complex phenomenon of emotion, including its physiological causes, its mental causes, and its intentional object

Hilbert geometry for convex polygonal domains

We prove in this paper that the Hilbert geometry associated with an open convex polygonal set is Lipschitz equivalent to Euclidean plane