Before examining de Moivre's contributions to the science of mathematics, this article reviews the source materials, consisting of the printed works and the correspondence of de Moivre, and constructs his biography from them. The analytical part examines de Moivre's contributions and achievements in the study of equations, series, and the calculus of probability. De Moivre contributed to the continuing development from Viète to Abel and Galois of the theory of solving equations by means of constructing particular equations, the roots of (...) which can be written in the form $$\sqrt[n]{{a + \sqrt b }} + \sqrt[n]{{a - \sqrt b }}$$. He also discovered the reciprocal equations. In the course of this work de Moivre discovered an expression equivalent to (cos α+i sin α) n =cos n α+i sin n α and, following Cotes, he succeeded in expressing the nth roots of unity in trigonometric form. In the theory of series, de Moivre developed a polynomial theorem encom-passing Newton's binomial theorem and, in particular, a theorem of recurrent series useful in the calculus of probability. The demands of the calculus of probability led de Moivre to an approximation for the binomial coefficients $$\left( {_m^n } \right)$$ for large values of n. The interaction between de Moivre and James Stirling, particularly in regard to the asymptotic series for log (n!), is treated at length. This work supplied the foundation for de Moivre's limit theorem for the binomial distribution. The calculus of probability, which occupied him from 1708 onward, became in time ever more the center of de Moivre's inquiries. Proceeding from contemporary collections of gambling exercises, de Moivre, by introducing an explicit measure of probability for the so-called Laplace experiments, found the beginnings of a theory of probability. De Moivre expanded the classic application of probability calculus to games of chance by addressing himself to the problem of annuities and by adopting Halley's work with its conception of “Probability of life”. De Moivre was the first to publish a mathematically formulated law for the decrements of life derived from mortality tables. (shrink)

The standard model for mereotopological structures are Boolean subalgebras of the complete Boolean algebra of regular closed subsets of a nonempty connected regular T 0 topological space with an additional "contact relation" C defined by xCy x ØA (possibly) more general class of models is provided by the Region Connection Calculus (RCC) of Randell et al. We show that the basic operations of the relational calculus on a "contact relation" generate at least 25 relations in any model of the RCC, (...) and hence, in any standard model of mereotopology. It follows that the expressiveness of the RCC in relational logic is much greater than the original 8 RCC base relations might suggest. We also interpret these 25 relations in the the standard model of the collection of regular open sets in the two-dimensional Euclidean plane. (shrink)

The recent piece ‘When Does Catholic Social Teaching Imply a Duty to be Vaccinated for the Common Good?’ by Stephen M.A. Bow (29 [4], 304–321) provides 12 criteria for the duty to vaccinate in acco...

Das Leben ist ein fundamentales Phänomen unserer Welt. In der Theologie war das Leben immer schon eine zentrale Größe, eng verbunden mit dem Schöpfungshandeln Gottes. Für die Philosophie ist es eine bleibende Herausforderung, das Leben begrifflich zu fassen. In der Ausdifferenzierung der modernen Wissenschaften gibt es einen eigenen Wissenschaftszweig, den der Biologie, der sich mit den vielfältigen Formen des Lebens beschäftigt. Doch ist nach wie vor unbekannt, wie Leben überhaupt entstehen konnte. Die Beiträge dieses Buches widmen sich dem Lebensbegriff und (...) gehen seiner Bedeutungsvielfalt und Rätselhaftigkeit nach: Wie nähern sich die unterschiedlichen Disziplinen heute dem Leben? Welches Verhältnis hat das Leben zu fundamentalen Werten? Gibt es einen Zusammenhang zwischen dem Leben und der Zeit oder zwischen dem Leben und dem Bewusstsein? (shrink)

Electronic sports and other variants of ‘digital sports’ have increased in popularity all over the world and may even come to challenge hegemonic concepts of sport. More relevant than the apparent opposition between ‘physical’ and ‘non-physical’ is the question what kind of embodiment is manifested within virtual environments. In this paper, we argue that eSports do require the learning and performance of motor skills and that embodiment within a virtual environment may be considered playful or even athletic. The type of (...) skills that might be tested can even be considered fundamental movement skills. Under appropriate educational supervision, with knowledge of the game, eSports can be utilized for the development of specific elements of digital literacy. Although motor skills are a defining characteristic of eSports, we do not argue that eSports should be integrated within PE. These arguments have not so much to do with the status of physicality present, but with differences in t... (shrink)

The Kosovo conflict -- The Israeli-Palestinian conflict -- The conflict in the Democratic Republic of Congo.

Background Retraction is a mechanism for alerting readers to unreliable material and other problems in the published scientific and scholarly record. Retracted publications generally remain visible and searchable, but the intention of retraction is to mark them as “removed” from the citable record of scholarship. However, in practice, some retracted articles continue to be treated by researchers and the public as valid content as they are often unaware of the retraction. Research over the past decade has identified a number of (...) factors contributing to the unintentional spread of retracted research. The goal of the Reducing the Inadvertent Spread of Retracted Science: Shaping a Research and Implementation Agenda (RISRS) project was to develop an actionable agenda for reducing the inadvertent spread of retracted science. This included identifying how retraction status could be more thoroughly disseminated, and determining what actions are feasible and relevant for particular stakeholders who play a role in the distribution of knowledge. -/- Methods These recommendations were developed as part of a year-long process that included a scoping review of empirical literature and successive rounds of stakeholder consultation, culminating in a three-part online workshop that brought together a diverse body of 65 stakeholders in October–November 2020 to engage in collaborative problem solving and dialogue. Stakeholders held roles such as publishers, editors, researchers, librarians, standards developers, funding program officers, and technologists and worked for institutions such as universities, governmental agencies, funding organizations, publishing houses, libraries, standards organizations, and technology providers. Workshop discussions were seeded by materials derived from stakeholder interviews (N = 47) and short original discussion pieces contributed by stakeholders. The online workshop resulted in a set of recommendations to address the complexities of retracted research throughout the scholarly communications ecosystem. -/- Results The RISRS recommendations are: (1) Develop a systematic cross-industry approach to ensure the public availability of consistent, standardized, interoperable, and timely information about retractions; (2) Recommend a taxonomy of retraction categories/classifications and corresponding retraction metadata that can be adopted by all stakeholders; (3) Develop best practices for coordinating the retraction process to enable timely, fair, unbiased outcomes; and (4) Educate stakeholders about pre- and post-publication stewardship, including retraction and correction of the scholarly record. -/- Conclusions Our stakeholder engagement study led to 4 recommendations to address inadvertent citation of retracted research, and formation of a working group to develop the Communication of Retractions, Removals, and Expressions of Concern (CORREC) Recommended Practice. Further work will be needed to determine how well retractions are currently documented, how retraction of code and datasets impacts related publications, and to identify if retraction metadata (fails to) propagate. Outcomes of all this work should lead to ensuring retracted papers are never cited without awareness of the retraction, and that, in public fora outside of science, retracted papers are not treated as valid scientific outputs. (shrink)

"A splendidly illuminating book." —The New York Times Like it or not, George W. Bush has launched a revolution in American foreign policy. He has redefined how America engages the world, shedding the constraints that friends, allies, and international institutions once imposed on its freedom of action. In America Unbound, Ivo Daalder and James Lindsay caution that the Bush revolution comes with serious risks–and, at some point, we may find that America’s friends and allies will refuse to follow his lead, (...) leaving the U.S. unable to achieve its goals. This edition has been extensively revised and updated to include major policy changes and developments since the book’s original publication. (shrink)

What is the ontological status of a musical work? This paper enters the discussion of the question between Julian Dodd and Michael Morris. Dodd is a proponent of a type-token view, which is a version of Platonism. Morris has formulated an argument that purports to show that a musical work cannot be a token of a type. If successful, the argument presents a serious challenge for a type-token theorist with implications for Platonism as a whole. Morris’s argument is, however, problematic (...) in several respects. The aim of this paper is to identify the problems and weaken the strength of Morris’s argument, thus restoring the original appeal of a type-token view. (shrink)

Each information system leads to a hierarchy of binary relations on the object set in a natural way; these relational systems can serve as frames for the semantics of modal logics. While relations of indiscernibility and their logics have been frequently studied, the situation in the case of relations which distinguish objects is much less clear. In this paper, we present complete logical systems for relations of complementarity derived from information systems.

Jeder weiss, dass er sterben muss. Er weiss nur nicht wann. Wüsste er es, er könnte den Tod nicht mehr aus seinem Leben verdrängen. Dieses Buch geht von einer utopischen Situation aus: Durch eine gentechnische Analyse wird bei jedem Menschen gleich nach seiner Geburt festgestellt, wann sein "Endtag", also sein Todestag, sein wird. Frühere Todesfälle gibt es nur bei Unfall oder Mord, spätere nie. Das Wissen um den Endtag verändert das Leben jedes Einzelnen, die Familien, die Gesellschaft, Ausbildung, Beziehungen und (...) Lebensplanung, Laufbahnen im Beruf, das Rentensystem u.v.m. Was für die einen ein "Horrorszenario" sein kann, entpuppt sich für die anderen als ein Segen: Alle können ihren Lebensabend planen und zur rechten Zeit bewusst Abschied nehmen. Und an diesem Punkt wird das Szenario von Ivo W. Greiter zum Plädoyer: Versucht euch täglich bewusst zu sein und zu akzeptieren, dass Ihr nicht ewig leben werdet. Rechnet mit dem Tod, redet über das Sterben, räumt eure Sachen auf. Und: Der Tod kann seinen Schrecken verlieren, wenn er am Leben teilhaben darf. "Und immer wieder stellte ich mir die Frage: Wenn ich weiss, was ich ändern würde, wenn ich in vier Monaten sterben würde, warum ändere ich es dann nicht gleich?" DR. GREITER, geb. 1940, ist Rechtsanwalt in Innsbruck; er ist vielfach in Berufsverbänden und ehrenamtlich engagiert, so als österreichischer Vorsitzender der internationalen Juristenorganisation World Jurist Association, Washington, als Vizepräsident des Österreichischen Juristentages und des österreichischen Anwaltsvereins u. a.; von 1983 bis 1989 war Dr. Greiter Mitglied des Gemeinderates von Innsbruck und von 1993 bis 2010 französischer Honorarkonsul in Innsbruck. Er befasst sich unter anderem mit Rechtsfragen für Menschen über 66; zahlreiche sonstige fachbezogene Veröffentlichungen. (shrink)

Tradução do comentario tomista ao "De Hebdomadibus" de Boécio.

Let Uq be the quantum group associated to sl2 with char≠2 and qk not a root of unity. The article is devoted to the model-theoretic study of the quantum plane kq[x,y], considered as an -structure, where is the language of representations of Uq. It is proved that the lattice of definable k-subspaces of kq[x,y] is complemented. This is deduced from the same result for the Uq-module M, which is defined to be the direct sum of all finite dimensional representations of (...) Uq. It follows that the ring of definable scalars for the quantum plane is a von Neumann regular epimorphic ring extension of the quantum group Uq. (shrink)