The present paper deals with a free boundary problem modeling the growth process of necrotic multi-layer tumors. We prove the existence of flat stationary solutions and determine the linearization of our model at such an equilibrium. Finally, we compute the solutions of the stationary linearized problem and comment on bifurcation.

(1968). L'ENCYCLIQUE HUMANAE VITAE ET L'ENSEIGNEMENT DE VATICAN II SUR LE MARIAGE ET LA FAMILLE (GAUDIUM ET SPES) Bijdragen: Vol. 29, No. 4, pp. 351-368.

Le propos de cette étude est d’explorer l’interface entre religion traditionnelle africaine et christianisme à l’aide d’une catégorie particulière de sources: les témoignages oraux d’un groupe de femmes chrétiennes de Sobantu, un township sud-africain. Peut-on adhérer à la religion chrétienne sans trahir son identité africaine? Souvent, mais pas toujours, en référence à la position de leur Église respective, chacune de ces femmes se forme une opinion sur cette question difficile.

We investigate two formalizations of Optimality Theory, a successful paradigm in linguistics.We first give an order-theoretic counterpart for the data and processinvolved in candidate evaluation.Basically, we represent each constraint as a function that assigns every candidate a degree of violation.As for the second formalization, we define (after Samek-Lodovici and Prince) constraints as operations that select the best candidates out of a set of candidates.We prove that these two formalizations are equivalent (accordingly, there is no loss of generality with using violation (...) marks and dispensing with them is only apparent).Importantly, we show that the second formalization is equivalent with a class of operations over sets of formulas in a given logical language.As a result, we prove that Optimality Theory can be characterized by certain cumulative logics.So, applying Optimality Theory is shown to be reasoning by the rules of cumulative logics. (shrink)

Standard quantum theory is inadequate to explain the mechanisms by which potential becomes actual. It is inadequate and therefore unable to describe generation of events. Niels Bohr emphasized long ago that the classical part of the world is necessary. John Bell stressed the same point: that “measurement≓ cannot even be defined within the standard quantum theory, and he sought a solution within hidden variable theories and his concept of “beables.≓Today it is customary to try to explain emergence of the classical (...) world through a decoherence mechanism due to “environment.≓ But, we believe, as it was with the concept of measurement, “environment≓ itself cannot be defined within the standard quantum theory.We have proposed a semiphenomenological solution to this problem by introducing explicitly, from the very beginning, classical degrees of freedom, and by coupling these degrees of freedom, through a Lindblad type coupling, to the quantum world. The resulting theory, we call “event-enhanced quantum theory.≓ EEQT allows us to describe an event-generating mechanism for individual quantum systems under continuous observation. The objections of John Bell are met and precise definitions of an “experiment≓ and of a “measurement≓ have been given within EEQT. However EEQT is, essentially, a nonrelativistic theory.In the present paper we extend the ideas of L. P. Horwitz and C. Piron and we propose a relativistic version of EEQT, with an event-generating algorithm for spin one-half particle detectors. The algorithm is based on proper time formulation of the relalivistic quantum theory. Although we use indefinite metric, all the probabilities controlling the random process of the detector clicks are nonnegative. (shrink)

Trees architectural study shows gradients in the meristematic activity. This activity is described by the number of internodes per growth unit, which is considered as the output of a dynamic random process. Several species were observed, which led us to propose and then estimate some mathematical models. Computing the functioning of a tree in a given environment therefore involves finding the probability function of the meristems and following the evolution of the parameters of this law along the botanical gradients (order, (...) trend, acrotony) within its architecture. (shrink)

Dogmatic Metaphysics and Tschirnhaus's M ethodology MARTIN SCHONFELD ACCORDING TO STANDARD COMMENTARIES, Tschirnhaus's main work, Medicina mentis, ~ supposedly furnished the methodological basis for the Leibnizian-Wolffian metaphysics. ~ Christian Wolff and his disciples, at any rate, preferred to think so. Wolff taught classes on Tschirnhaus and claimed that he had developed his own tenets on the basis of Tschirnhaus's ideas; Johann Christoph Gottsched praised the Medicina mentis as the basic methodology of the Wolffian enlightenment.3 Mirroring these views, W. Wundt and (...) H. J. de Vleeschauwer saw in Tschirnhaus the inventor of the "geometric method" adopted by the School Philosophers.4 According to M. ' Medicina Mentis, sive Tentamen genuinae Logicae, in qua disseritur de Methodo detegendi incoKaitas veritates, Amsterdam, 1687. Second and revised edition, Medicina Mentis, sive Artis inveniendi Praecepta generalia, Leipzig, 1695. ~For example, cf. Wilhelm Windelband, Geschichte der Philosophie, 3~o-33 and 356; Friedrich Ueberweg, Grundriss der Geschichte der Philosophie, III: ~95-97, 3 x~ 34o-43; A. Robert Caponigri, A History of Western Philosophy (Notre Dame/London: University of Notre Dame.. (shrink)