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

Perspectives on the Missiological Legacy of Martin Luther and the Protestant Reformation

Upon the occasion of the 500th anniversary Martin Luther’s publication of his 95 theses, this composite article brings together five perspectives on the missiological legacy of the reformer and the subsequent Protestant Reformation. The blend of voices makes clear that Luther and the subsequent Protestant Reformation do not have a simple missiological legacy but rather various legacies: theological, ecclesiological, political, and practical; some of which co-exist, and even collide, in the same ecclesiastical community. The scandalous legacy of a splintered and splintering church remains. Yet, demonstrations of mutual recognition, reciprocal respect, and genuine fellowship can be found in certain missiological circles

Isomorphism of graph classes related to the circular-ones property

We give a linear-time algorithm that checks for isomorphism between two 0-1 matrices that obey the circular-ones property. This algorithm leads to linear-time isomorphism algorithms for related graph classes, including Helly circular-arc graphs, \Gamma-circular-arc graphs, proper circular-arc graphs and convex-round graphs.Comment: 25 pages, 9 figure

Ten myths about character, virtue and virtue education – plus three well-founded misgivings

Initiatives to cultivate character and virtue in moral education at school continue to provoke sceptical responses. Most of those echo familiar misgivings about the notions of character, virtue and education in virtue – as unclear, redundant, old-fashioned, religious, paternalistic, anti-democratic, conservative, individualistic, relative and situation dependent. I expose those misgivings as ‘myths’, while at the same time acknowledging three better-founded historical, methodological and practical concerns about the notions in question

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

Tissue signals imprint ILC2 identity with anticipatory function.

Group 2 innate lymphoid cells (ILC2s) are distributed systemically and produce type 2 cytokines in response to a variety of stimuli, including the epithelial cytokines interleukin (IL)-25, IL-33, and thymic stromal lymphopoietin (TSLP). Transcriptional profiling of ILC2s from different tissues, however, grouped ILC2s according to their tissue of origin, even in the setting of combined IL-25-, IL-33-receptor-, and TSLP-receptor-deficiency. Single-cell profiling confirmed a tissue-organizing transcriptome and identified ILC2 subsets expressing distinct activating receptors, including the major subset of skin ILC2s, which were activated preferentially by IL-18. Tissue ILC2 subsets were unaltered in number and expression in germ-free mice, suggesting that endogenous, tissue-derived signals drive the maturation of ILC2 subsets by controlling expression of distinct patterns of activating receptors, thus anticipating tissue-specific perturbations occurring later in life

Robot rights? Towards a social-relational justification of moral consideration \ud

Should we grant rights to artificially intelligent robots? Most current and near-future robots do not meet the hard criteria set by deontological and utilitarian theory. Virtue ethics can avoid this problem with its indirect approach. However, both direct and indirect arguments for moral consideration rest on ontological features of entities, an approach which incurs several problems. In response to these difficulties, this paper taps into a different conceptual resource in order to be able to grant some degree of moral consideration to some intelligent social robots: it sketches a novel argument for moral consideration based on social relations. It is shown that to further develop this argument we need to revise our existing ontological and social-political frameworks. It is suggested that we need a social ecology, which may be developed by engaging with Western ecology and Eastern worldviews. Although this relational turn raises many difficult issues and requires more work, this paper provides a rough outline of an alternative approach to moral consideration that can assist us in shaping our relations to intelligent robots and, by extension, to all artificial and biological entities that appear to us as more than instruments for our human purpose

Linear instability criteria for ideal fluid flows subject to two subclasses of perturbations

In this paper we examine the linear stability of equilibrium solutions to incompressible Euler's equation in 2- and 3-dimensions. The space of perturbations is split into two classes - those that preserve the topology of vortex lines and those in the corresponding factor space. This classification of perturbations arises naturally from the geometric structure of hydrodynamics; our first class of perturbations is the tangent space to the co-adjoint orbit. Instability criteria for equilibrium solutions are established in the form of lower bounds for the essential spectral radius of the linear evolution operator restricted to each class of perturbation.Comment: 29 page