Metric Versus Topological Receptive Entropy of Semigroup Actions

We study the receptive metric entropy for semigroup actions on probability spaces, inspired by a similar notion of topological entropy introduced by Hofmann and Stoyanov (Adv Math 115:54–98, 1995). We analyze its basic properties and its relation with the classical metric entropy. In the case of semigroup actions on compact metric spaces we compare the receptive metric entropy with the receptive topological entropy looking for a Variational Principle. With this aim we propose several characterizations of the receptive topological entropy. Finally we introduce a receptive local metric entropy inspired by a notion by Bowen generalized in the classical setting of amenable group actions by Zheng and Chen, and we prove partial versions of the Brin–Katok Formula and the local Variational Principle.

Baltasar Gracián: El concepto de interés propio como guía de la acción humana

The work of Baltasar Gracián, one of the great writers of the Spanish Golden Age, has been interesting for philologists, moral philosophers and political theorists but it has hardly been relevant for economists. This paper explores the writings of this great author of the baroque period in order to emphasize the analysis of human nature derived from his work. Gracián suggested a very similar notion to that used by other Spanish contemporaries: one which possessed a great number of the qualities of the homo oeconomicus, an abstract conception of the human being which most of the economists will subsequently embrace.

Some Generalizations of Non-Unique Fixed Point Theorems of Ćirić-type for (Φ, ψ)-Hybrid Contractive Mappings

In this article, we establish some non-unique fixed point theorems of Ćirić’s type for (Φ, ψ)–hybrid contractive mappings by using a similar notion to that of the paper [M. Akram, A.A. Zafar and A.A. Siddiqui, A general class of contractions: A–contractions, Novi Sad J. Math. 38 (2008), no. 1, 25–33]. Our results generalize, extend and improve several ones in the literature.

A general concept of multiple fixed point for mappings defined on spaces with a distance

Our main aim in this paper is to introduce a general concept of multidimensional fixed point of a mapping in spaces with distance and establish various multidimensional fixed point results. This new concept simplifies the similar notion from [A. Roldan, J. Martinez-Moreno, C. Roldan, Multidimensional fixed point theorems in partially ordered complete metric spaces, J. Math. Anal. Appl. 396 (2012), 536–545]. The obtained multiple fixed point theorems extend, generalise and unify many related results in literature.

The Medievals

Medieval philosophers used the language of cause and effect as frequently as philosophers do now. Viewed very, very broadly, they had in mind a similar notion, at least when they were speaking of efficient causality (and even the three other types of Aristotelian cause — material, formal, and final — can be brought loosely under this concept): causes are in some sense prior to their effects, which they produce and the existence of which they explain. Viewed more closely, medieval notions of causality are sharply different from contemporary ones, and these differences are especially evident in explicit discussions of causation. This article discusses the idea of essential causation. It looks at the aspect of medieval thought about causation that seems to come closest to the modern debates instigated by Hume, the supposed medieval occasionalists such as the Islamic thinker al-Ghazali (1058–1111) and the Parisian Arts Master and student of theology, Nicholas of Autrecourt (d. 1369), and the critiques of occasionalism offered by Averroes (c.1126–98), who wrote in Muslim Spain, and Aquinas.

A note on homomorphisms of Hilbert algebras

We give a representation theorem for Hilbert algebras by means of ordered sets and characterize the homomorphisms of Hilbert algebras in terms of applications defined between the sets of all irreducible deductive systems of the associated algebras. For this purpose we introduce the notion of order-ideal in a Hilbert algebra and we prove a separation theorem. We also define the concept of semi-homomorphism as a generalization of the similar notion of Boolean algebras and we study its relation with the homomorphism and with the deductive systems.

Chronometers and Units in Early Archaeology and Paleontology

Early in the nineteenth century, geologist Charles Lyell reasoned that successively older faunas would contain progressively more extinct species and younger faunas relatively more extant species. The present, with one-hundred percent extant species, was the chronological anchor. In archaeology a similar notion underpins the direct historical approach: Successively older cultures will contain progressively fewer of the cultural traits found in extant cultures and relatively more prehistoric traits. As in Lyell’s scheme, the chronological anchor is the present. When A. L. Kroeber invented frequency seriation in the second decade of the twentieth century, he retained the present as a chronological anchor but reasoned that the oldest cultural manifestation would contain the highest percentage of a variant, or what came to be known as a "style," of an ancient trait, and successively younger cultural manifestations would have progressively lower percentages of that variant. The principle of overlapping permitted building sequences of fossils and artifacts, but differences in the units that allowed the chronometers to be operationalized reveal significant epistemological variation in how historical research is undertaken. This variation should be of considerable interest to paleobiologists and archaeologists alike, especially given recent archaeological interest in creating and explaining historical lineages of artifacts.

On braid monodromies of non-simple braided surfaces

A braided surface of degree m is a compact oriented surface S embedded in a bidisk such that is a branched covering map of degree m and , where is the projection. It was defined L. Rudolph [14, 16] with some applications to knot theory, cf. [13, 14, 15, 16, 17, 18]. A similar notion was defined O. Ya. Viro: A (closed) 2-dimensional braid in R4 is a closed oriented surface F embedded in R4 such that and pr2 │F: F → S2 is a branched covering map, where is the tubular neighbourhood of a standard 2-sphere in R4. It is related to 2-knot theory, cf. [8, 9, 10]. Braided surfaces and 2-dimensional braids are called simple if their associated branched covering maps are simple. Simple braided surfaces and simple 2-dimensional braids are investigated in some articles, [5, 8, 9, 14, 16], etc. This paper treats of non-simple braided surfaces in the piecewise linear category. For braided surfaces a natural weak equivalence relation, called braid ambient isotopy, appears essentially although it is not important for classical dimensionai braids Artin's argument [1].

Correspondences of completely regular semigroups and -isomorphisms of semigroups

A correspondence of a semigroup S is any subsemigroup of S × S, and the set of all correspondences of S, with the operations of composition and involution and the relation of set-theoretic inclusion, forms the bundle of correspondences of S, denoted by (S). For semigroups S and T, any isomorphism of (S) onto (T) is called a -isomorphism of S upon T. Similar notion can be introduced for other types of algebras and in the general frame of category theory. The principal goal of this paper is to study -isomorphisms of completely regular semigroups (that is, unions of groups) and of one other interesting class of semigroups.

The Right to Income

This paper argues for a right to income based on a conception of the integrity of the individual. It first justifies the argument through the notion of social need developed by Hegel, contrasting that idea with the notion of subsistence in classical political economy and of needs and wants in the neoclassical economics. It then reexamines Locke’s labor theory of property and argues that its intuitive strength actually relies on a similar notion of individual integrity, not on labor pre se. The paper concludes by applying this notion of rightful acquisition of property to the situation of production by capital and explores some policy implications of a right to income.