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.

The present study examines the work of a group of medical scientists as they identify interpretative ‘pitfalls’ – recurrent sources of error – in the use of a new radiographic technique, formulate suggestions on how these pitfalls can be avoided and communicate their findings in the form of a scientific publication. The analysis focuses on a session in which previously diagnosed cases are discussed, and demonstrates the ways in which a certain source of diagnostic error gradually emerges as a taken-for-granted (...) in the interaction. An increased sense of recognition, recurrence and typicality is discernible in the treatment of the cases. Talk characterized by expansions and elaborations, displays of understanding in the form of reformulations, understanding checks, and so on, leave room for brief typifications and reifications of interpretative difficulties in characteristics of the imaging technique. Topical treatment of perception and interpretation, as well as embodied engagement, become decreasingly salient. It is argued that the abstracted formulations in the published text rely on the case-by-case working up of generality from particularity; from individualized accounts of why ‘I’ interpreted the image in a certain way to proffered generalizations achieved through articulated perceptions of a generalized ‘one’. If these proffers are ratified, a potential ground is established for the consensual formulation of a pitfall. The formulation of novel instructions is consequently made relevant, projecting a re-instructed diagnostic practice. (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 $\mathbb {C}$.

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)

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)

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)

1. In his paper “On Denoting” Russell points out what he calls a puzzle every satisfactory theory of denoting will have to solve. Of the three sentences George IV. wished to know whether Scott was the author of WaverleyScott is the author of WaverleyGeorge IV. wished to know whether Scott was Scott the first two, and, are presumably true, while the third,, is presumably false. The reason given for considering this arrangement of truth values a puzzle is that the ‘is’ (...) in signifies identity; that the proper name ‘Scott’ and the descriptive phrase ‘the author of Waverley’ denote the same object; and that, therefore, if the latter is replaced by the former in the true sentence, the resulting sentence,, should again be true. Yet is false, or, as one also says, the context considered is nonextensional with respect to this replacement. (shrink)

This paper does not purport to present a fully developed argument. Rather, it intends to delineate, in broad strokes and in a synoptic manner, the total frame of reference of Scientific Empiricism as far as it is necessary for an integration of the several contributory clarifications of the complex, usually referred to as the psychophysical problem. Several considerations seem to justify such an attempt. It is desirable, from time to time, to free the results of logical and methodological analysis from (...) their specialized contexts. Only thus can they be presented in a way which brings to the fore their continuity with more traditionally worded epistemological thought. By doing this such a presentation should also help to dissolve the current objections of formalism, scientism, and philosophical irrelevance so frequently based on misunderstanding. It is only fair to admit, however, that these misunderstandings have been facilitated by the preoccupation with the technical, and the brevity with regard to the nontechnical, which characterize the modern analysts. (shrink)

Inflammatory mediators have an established role in inducing insulin resistance and promoting hyperglycemia. In turn, hyperglycemia has been argued to drive immune cell dysfunction as a result of mitochondrial dysfunction. Here, the authors review the evidence challenging this view. First, it is pointed out that inflammatory mediators are known to induce altered mitochondrial function. In this regard, critical care patients suffer both an elevated inflammatory tone as well as hyperglycemia, rendering it difficult to distinguish between the effects of inflammation and (...) hyperglycemia. Second, emerging evidence indicates that a decrease in mitochondrial respiration and an increase in reactive oxygen species (ROS) production are not necessarily manifestations of pathology, but adaptations taking shape as the mitochondria is abdicating its adenosine triphosphate (ATP)‐producing function (which is taken over by glycolysis) and instead becomes “retooled” for an immunological role. Collectively, these observations challenge the commonly held belief that acute hyperglycemia induces mitochondrial damage leading to immune cell dysfunction. (shrink)

In a recent article P. Henle gave an analysis of the notion of emergence. His inquiry deals with what he calls, quite appropriately, the emergence of characteristics. Such emergence, that is, the emergence of qualities and relations is undoubtedly the primary connotation of the term, and I feel that Henle has been very successful in clarifying it. The purpose of the present paper is to discuss in some detail one special aspect of Henle's analysis. This is done because the precise (...) formulation of this particular aspect sheds light on the notion of elementarism. And the opposite of this notion, holism or organicism, belongs undoubtedly to the variety of fused and confused meanings the idea of emergence has come to cover. (shrink)