We characterize strict Mittag-Leffler modules in terms of free realizations of positive primitive formulas, and rings over which projectives are trivial in terms of various notions of separability of strict Mittag-Leffler modules. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

The main theorem characterizes Mittag-Leffler modules as ‘positively atomic’ modules . This is applied to reduced products of Mittag-Leffler modules and pure-semisimple.

It is known that C. G. J. Jacobi wrote his first two letters to E. E. Kummer in the year 1834. Thanks to a find in the archive of the Mittag-Leffler Institute there is now the missing link , Kummer’s reply letter to Jacobi’s first letter. This letter seems to be the earliest one from Kummer still in existence (at least to a mathematician). Kummer tells in his letter about his situation as a teacher in Liegnitz, gives further (...) a version of his later paper on the summation of slowly convergent series and discusses Euler’s summation formula in connection with the practice of its use in numerical calculations. The article contains the complete texts of the three letters (up to those parts in Kummer’s letter identically contained in his published article) together with a commentary on their contents. (shrink)

Working in an o-minimal expansion of the real field, we investigate when a germ of a complex analytic function has a definable analytic continuation to its Mittag–Leffler star. As an application we show that any algebro-logarithmic function that is complex analytic in a neighborhood of the origin in $\mathbb {C}$ has an analytic continuation to all but finitely many points in $\mathbb {C}$.

It is often thought that desire-based versions of reasons internalism, according to which our practical reasons depend on what we desire, are committed to denying that we have any categorical reasons. I shall argue, however, that such theories are committed to a universal desire which gives rise to an unexpected categorical reason – a reason to know our surroundings. I will arrive at this conclusion by using Fichte’s argument for thinking that security from unpredictable and powerful forces of nature is (...) constitutive of agency. Fichte thinks this is the case because we ought to aim at knowledge of our surroundings, and such environments uniquely facilitate it. I show that his argument fails, but the point that we ought to aim at – or desire – such knowledge is fundamentally sound. This aim can then be leveraged to generate a categorical reason when embedded in an account of agency typically embraced by internalists. (shrink)

In this work, ZZ transformation is combined with the Adomian decomposition method to solve the dynamical system of fractional order. The derivative of fractional order is represented in the Atangana–Baleanu derivative. The numerical examples are combined for their approximate-analytical solution. It is explored using graphs that indicate that the actual and approximation results are close to each other, demonstrating the method’s usefulness. Fractional-order solutions are the most in line with the dynamics of the targeted problems, and they provide an endless (...) number of options for an optimal mathematical model solution for a particular physical phenomenon. This analytical approach produces a series form solution that is quickly convergent to exact solutions. The acquired results suggest that the novel analytical solution technique is simple to use and very successful at assessing complicated problems that arise in related fields of research and technology. (shrink)

We characterize rings over which every cotorsion module is pure injective in terms of certain descending chain conditions and the Ziegler spectrum, which renders the classes of von Neumann regular rings and of pure semisimple rings as two possible extremes. As preparation, descriptions of pure projective and Mittag–Leffler preenvelopes with respect to so-called definable subcategories and of pure generation for such are derived, which may be of interest on their own. Infinitary axiomatizations lead to coherence results previously known (...) for the special case of flat modules. Along with pseudoflat modules we introduce quasiflat modules, which arise naturally in the model-theoretic and the category-theoretic contexts. (shrink)

This book examines the life and work of mathematician Giovanni Battista Guccia, founder of the Circolo Matematico di Palermo and its renowned journal, the Rendiconti del Circolo matematico di Palermo. The authors describe how Guccia, an Italian geometer, was able to establish a mathematical society in Sicily in the late nineteenth century, which by 1914 would grow to become the largest and most international in the world, with one of the most influential journals of the time. The book highlights the (...) challenges faced by Guccia in creating an international society in isolated Palermo, and places Guccia’s activities in the wider European context through comparisons with the formation of the London Mathematical Society and the creation of Mittag-Leffler’s Acta Mathematica in Stockholm. Based on extensive searches in European archives, this scholarly work follows both historical and scientific treads, and will appeal to those interested in the history of mathematics and science in general. (shrink)

Written over the last 18 months of his life and inspired by his interest in G. E. Moore's defence of common sense, this much discussed volume collects Wittgenstein's reflections on knowledge and certainty, on what it is to know a proposition for sure.

This book, published in 1986, addresses questions concerned with a central normative principle in contemporary assessments of economic policies and systems. What does 'consumer sovereignty' mean? Is consumer sovereignty an appropriate principle for the optimization and evaluation of the design and performance of economic policies, institutions and systems? If not, what is a more appropriate principle? The author argues that the conception of consumer sovereignty has to be broadened so that it is not limited to the market mechanism but includes (...) environmental, work and social preferences. However, even this version runs into serious difficulties as the principle of consumer sovereignty still relies on too subjectivist a conception of the interests of individuals to be suitable for the evaluation of economic institutions. An alternative basis for such evaluation is 'human interests' that are not contingent on particular economic systems, After considering various possibilities, a basic-needs approach is proposed and its use in economic evaluation illustrated. (shrink)

This study examines BDI logics in the context of Gabbay's fibring semantics. We show that dovetailing can be adopted as a semantic methodology to combine BDI logics. We develop a set of interaction axioms that can capture static as well as dynamic aspects of the mental states in BDI systems, using Catach's incestual schema G^[a, b, c, d]. Further we exemplify the constraints required on fibring function to capture the semantics of interactions among modalities. The advantages of having a fibred (...) approach is discussed in the final section. (shrink)

We show that in 1929 Cartan and Einstein almost produced a theory in which the electromagnetic (EM) field constitutes the time-like 2-form part of the torsion of Finslerian teleparallel connections on pseudo-Riemannian metrics. The primitive state of the theory of these connections would not, and did not, permit Cartan and Einstein to realize how their torsion field equations contained the Maxwell system and how the Finslerian torsion contains the EM field. Cartan and Einstein discussed curvature field equations, though failing to (...) focus on the fact that teleparallelism automatically implies gravitational field equations with torsion terms as source, both in first and second order. We further show that the first-order contribution of the EM field to the source of the gravitational field may play havoc with the remeasurement of Newton's gravitational constant, even if the experiment is electrically grounded. These results are also used as support for the thesis that there is an alternative to the present way of dealing with the great theoretical questions of physics. On the practical side, the inconveniences faced in measuring G may be greatly compensated by the possibility of manipulating spacetime with electric fields at the first-order level. (shrink)

Plotinus (204/5–270 CE) was the first and greatest of Neoplatonic philosophers. His writings were edited by his disciple Porphyry, who published them sometime between 301 and 305 CE in six sets of nine treatises each (Enneads), with a biography of his master in which he also explains his editorial principles.

Open peer commentary on the article “The Autopoiesis of Social Systems and its Criticisms” by Hugo Cadenas & Marcelo Arnold. Upshot: I discuss two aspects of Cadenas & Arnold’s target article. The first concerns some clarifications of the sociological importance of the concept of autopoiesis and the second the criticisms of this concept and its applications in the social sciences.

En 2011 el señor Mario Posada Ochoa donó a la Universidad EAFIT una extensa y poco conocida colección de arte; acaso unos cuantos amigos habrían visto de cerca las 480 obras que recibió la Universidad, de artistas como Segundo Angelvis, Inés Acevedo Bernal, Sergio Trujillo Magnenat, Luis A. Rengifo y Ramón Vásquez, entre otros. Algunas de ellas carecían de la firma del autor o de un dato que comprobara la autoría, y estaban deterioradas, más que por el tiempo, por el (...) improvisado bodegaje: don Mario las había guardado durante cuarenta años en su hermosa casa de Maracaibo, en el centro de la ciudad. En Extensión Cultural de EAFIT han procurado, desde entonces, conservar este legado. (shrink)

The Platonic Commentators.—After Cicero the Academy is no more than a few names to us for nearly five centuries. The nearest that we get to contact with it in this period is in the writings of Plutarch. He was himself a student there, and was well read in the books of Plato and the commentaries thereon.