Amalgamation and interpolation in ordered algebras

The first part of this paper provides a comprehensive and self-contained account of the interrelationships between algebraic properties of varieties and properties of their free algebras and equational consequence relations. In particular, proofs are given of known equivalences between the amalgamation property and the Robinson property, the congruence extension property and the extension property, and the flat amalgamation property and the deductive interpolation property, as well as various dependencies between these properties. These relationships are then exploited in the second part of the paper in order to provide new proofs of amalgamation and deductive interpolation for the varieties of lattice-ordered abelian groups and MV-algebras, and to determine important subvarieties of residuated lattices where these properties hold or fail. In particular, a full description is given of all subvarieties of commutative GMV-algebras possessing the amalgamation property.

The developmental and evolutionary origins of psychological essentialism lie in sortal object individuation

Cimpian & Salomon (C&S) present promising steps towards understanding the cognitive underpinnings of adult essentialism. However, their approach is less convincing regarding ontogenetic and evolutionary aspects. In contrast to C&S's claim, the so-called inherence heuristic, though perhaps vital in adult reasoning, seems an implausible candidate for the developmental and evolutionary foundations of psychological essentialism. A more plausible candidate is kind-based object individuation that already embodies essentialist modes of thinking and that is present in infants and nonhuman primates.

Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.

Die Nationalversammlung aufgelöst: Eine Thronrede: Wenn ich ein König wäre, der noch vor wenigen Wochen in der unseligsten Verblendung 14 Stunden lang sein Volk beschießen ließ ...

Welsch (Projektbearbeiter): Wenn Friedrich Wilhelm IV. seine eigenen Versprechungen vom März 1848 ernst nähme, müßte er seine Minister entlassen, die Nationalversammlung auflösen und selbst zurücktreten: "... das Volk soll Männer berufen, die an den Gräbern des Friedrichshains das Mark der Revolution empfangen." Verfaßt von dem Berliner Philologiestudenten und Aktivisten des Demokratischen Klubs Edmund Monecke und veröffentlicht in der Form einer (fiktiven) Thronrede. Datierung des Flugblatts nach Friedländer, S. 164

Preußens Bartholomäusnacht: Nein, wir wollen keinen König, der sein Volk kartätschen ließ, Der die Bittenden mit Hohne fort von seiner Schwelle stieß ...

Welsch (Projektbearbeiter): Rachegedicht an die Adresse Friedrich Wilhelms IV. nach den Berliner Barrikadenkämpfen vom 18. und 19. März 1848: "Zittre nun, du Menschenschlächter, vor der blut'gen Rechenschaft! Diese Saat, die du gesäet, wird zur Ernte blutig reifen, Wenn die Völker zu dem Schwerte mit dem starken Arme greifen."

The Jewish Bogey by Lucien Wolf, London - The History of a Lie, study by Herman Bernstein, New York [Rezension]

Paul Nathan

Rational invariants on the space of all structures of algebras on a two-dimensional vector space

Rational invariants on the space of all structures of algebras on a two-dimensional vector space

Solution of optimal continuous low-thrust transfer using Lie transforms

This paper addresses the problem of optimal constant continuous low-thrust transfer in the context of the restricted two-body problem (R2BP). Using the Pontryagin’s principle, the problem is formulated as a two point boundary value problem (TPBVP) for a Hamiltonian system. Lie transforms obtained through the Deprit method allow us to obtain the canonical mapping of the phase flow as a series in terms of the order of magnitude of the thrust applied. The reachable set of states starting from a given initial condition using optimal control policy is obtained analytically. In addition, a particular optimal transfer can be computed as the solution of a non-linear algebraic equation. Se investiga el uso de series y transformadas de Lie en problemas de optimización de trayectorias de satélites impulsados por motores de bajo empuje

Orientation in operator algebras

A concept of orientation is relevant for the passage from Jordan structure to associative structure in operator algebras. The research reported in this paper bridges the approach of Connes for von Neumann algebras and ourselves for C*-algebras in a general theory of orientation that is of geometric nature and is related to dynamics.

The Lie That Tells the Truth: Creating Truth in Fiction and the Novel Delivering Hope

What makes fiction believable is the truth behind the words. This Capstone Project explores the ways in which authors put the truth on the page while simultaneously fabricating stories. The Reflective Paper examines writing techniques used to make the reader trust the story and the storyteller. The Creative Capstone is the result of applying these craft skills to Delivering Hope, a novel in progress about a critically ill baby bringing a dysfunctional family back together. The author relies on her personal experience of high- risk pregnancy and preterm birth to help create truth in her fiction.

Weighted composition operators on the predual and dual Banach spaces of Beurling algebras on Z

Let vv be a weight sequence on ZZ and let ψ,φψ,φ be complex-valued functions on ZZ such that φ(Z)⊂Zφ(Z)⊂Z. In this paper we study the boundedness, compactness and weak compactness of weighted composition operators Cψ,φCψ,φ on predual Banach spaces c0(Z,1/v)c0(Z,1/v) and dual Banach spaces ℓ∞(Z,1/v)ℓ∞(Z,1/v) of Beurling algebras ℓ1(Z,v)ℓ1(Z,v).