This paper studies how well computable functions can be approximated by their Fourier series. To this end, we equip the space of Lp-computable functions with a size notion, by introducing Lp-computable Baire categories. We show that Lp-computable Baire categories satisfy the following three basic properties. Singleton sets {f } are meager, suitable infinite unions of meager sets are meager, and the whole space of Lp-computable functions is not meager. We give an alternative characterization of meager sets via Banach-Mazur (...) games. We study the convergence of Fourier series for Lp-computable functions and show that whereas for every p > 1, the Fourier series of every Lp-computable function f converges to f in the Lp norm, the set of L1-computable functions whose Fourier series does not diverge almost everywhere is meager. (shrink)

We define the effective integrability of Fine-computable functions and effectivize some fundamental limit theorems in the theory of Lebesgue integrals such as the Bounded Convergence Theorem, the Dominated Convergence Theorem, and the Second Mean Value Theorem. It is also proved that the Walsh-Fourier coefficients of an effectively integrable Fine-computable function form a Euclidian computable sequence of reals which converges effectively to zero. This property of convergence is the effectivization of the Walsh-Riemann-Lebesgue Theorem. The article is closed with the effective (...) version of Dirichlet's test. (shrink)

Beyond being the first substantial publication on Fourier, this work contains the text of Fourier's seminal paper of 1807 on the propagation of heat, marking the first time it has ever appeared in print. This paper incorporates many of the mathematical creations on which Fourier's fame rests, including derivation of the diffusion equation, the separation of the treatment of surface phenomena from internal phenomena, the use of boundary values and initial conditions, and the development of "Fourier (...) series" and the so-called "Bessel functions."When submitted to the examiners of the Institut de France, the originality of the paper and the surprising nature of some of its mathematical revelations caused great controversy, and it was denied publication both in 1807 and in later years. Fourier had the support, among the examiners, of Laplace and Monge, but Lagrange was adamantly in opposition, so that Fourier's work did not appear in print until 1822, reworked into book form.Fourier's mathematical discoveries are intimately related to his interest in the solution of physical problems and their experimental verification. The mathematical methods he developed in connection with heat diffusion apply to physical situations far beyond the boundaries of this area. Generally, Fourier may be credited with one of the first major extensions of mathematical physics beyond the applications of Newton's laws of motion and universal gravitation.The opening biographical chapter of this book follows Fourier's career up to the submission of the 1807 paper, and the two closing chapters take up his life and work from that point on. Fourier had strong political motivations and spent much of his life in the public service. These chapters trace his political difficulties, both before and after 1807, when he was the prefect of a department of France and was subjected to the dislocations of Napoleon's ups and downs. These chapters also describe aspects of the turbulent but productive development of French science from the Revolution to 1830.The core of the book presents the paper of 1807 in its original French and with the original notation. Grattan-Guinness has divided the paper into sections by the sequence of the problems taken up, and he introduces and, where necessary, closes each section with commentary relevant to Fourier's later work in these areas. The paper itself (cllows the chronology of Fourier's discoveries, and among the topics treated are, in this order: heat diffusion between disjoint bodies and in continuous bodies; the appearance of partial differential equations; the special solution for the lamina; sine and cosine series for an arbitrary function; reflections on the vibrating string problem; solution for the annulus; the full Fourier series for an arbitrary function; reflections on n-body analysis; solution for the sphere; solution for the cylinder; steady-state diffusion in the rectangular prism; time-dependent diffusion in the cube; and Fourier's experimental work. (shrink)

Die vorliegende Auswahl von Texten des französischen Sozialphilosophen und Gesellschaftstheoretikers Charles Fourier (1772-1837) hat zwei Schwerpunkte: Zum einen thematisiert sie die wesentlichen Aspekte und die gedankliche Struktur von Fouriers weitreichendem Œuvre; zum anderen macht sie verständlich, welche Überlegungen Fouriers für heutige Theoretikerinnen und Theoretiker anregend oder anschlussfähig sind. Zu den Themen, die Fourier in den im vorliegenden Band publizierten Schriften behandelt, zählen das Ideal einer exakten Sozialwissenschaft; die Grundlagen der Anthropologie; die „neue Welt“ der Liebe und des Konsums; (...) die Relevanz der Arbeit für ein gelingendes Leben; die Grundstruktur nicht-entfremdeter Gesellschaften; sowie die Kritik an der Philosophie und den Gesellschaftswissenschaften, insbesondere der Ökonomik. Zahlreiche der im Band versammelten Texte werden erstmals auf Deutsch veröffentlicht. (shrink)

Objective: To evaluate feasibility of the guidelines of the Groupe Francophone de Réanimation et Urgence Pédiatriques for limitation of treatments in the paediatric intensive care unit .Design: A 2-year prospective survey.Setting: A 12-bed PICU at the Hôpital Jeanne de Flandre, Lille, France.Patients: Were included when limitation of treatments was expected.Results: Of 967 children admitted, 55 were included with a 2-day median delay. They were younger than others , had a higher paediatric risk of mortality score , and a higher paediatric (...) overall performance category score at admission ; all p<0.002. 34 children died. A limitation decision was made without meeting for 7 children who died: 6 received do-not-resuscitate orders and 1 received withholding decision. Decision-making meetings were organised for 31 children, and the following decisions were made: 12 DNROs , 4 withholding , with 14 withdrawing and 1 continuing treatment . After limitation, 21 children died and 10 survived . 13 procedures were interrupted because of death and 11 because of clinical improvement . Parents’ opinions were obtained after 4 family conferences , 3 days after inclusion. The first meeting was planned for 6 days after inclusion and held on the 7th day after inclusion; 80% of parents were immediately informed of the decision, which was implemented after half a day.Conclusions: GFRUPs procedure was applicable in most cases. The main difficulties were anticipating the correct date for the meeting and involving nurses in the procedure. Children for whom the procedure was interrupted because of clinical improvement and who survived in poor condition without a formal decision pointed out the need for medical criteria for questioning, which should systematically lead to a formal decision-making process. (shrink)

Objective Compare outcome of dogs that did and did not receive fresh frozen plasma (FFP) for treatment of pancreatitis. Design Retrospective case series between 1995 and 2005. Setting University referral hospital. Animals Seventy-four dogs were enrolled with a total of 77 Cases as 2 dogs had repeat episodes of pancreatitis. Diagnosis of pancreatitis was based on clinical signs, physical examination, and abdominal ultrasonographic examination. Interventions The medical database was searched for dogs with a diagnosis of pancreatitis. Information collected included (...) signalment, vital signs, CBC, use of FFP, length of stay, use of antimicrobials and supplemental nutrition, surgical intervention, preexisting illness, evidence of a coagulopathy and outcome. Outcome was compared between those patients that did and did not receive FFP. Measurements and Main Results Fifty-nine dogs survived to discharge. Two dogs with repeat pancreatitis survived to discharge after each episode. Thirteen dogs died and 2 were euthanized. FFP was administered to 20 dogs. Two dogs that were hospitalized for repeat pancreatitis did not receive FFP. Seven of 20 (35%) cases that received plasma died or were euthanized compared with 6 of 57 (12%) cases that did not receive plasma. Plasma administration was significantly related to outcome (P<0.001). Severity of illness scores were difficult to assign, however, dogs meeting criteria for systemic inflammatory response syndrome were not more likely to receive FFP. Other therapies included supplemental nutrition, antimicrobials, and surgical intervention, which did not affect outcome. Conclusions Mortality rate for those dogs receiving plasma was higher than those that did not. Severity of illness scores were difficult to assign; however, preexisting illness, evidence of systemic inflammatory response syndrome, and presence of a coagulopathy were not significantly different between the groups that did and did not receive FFP. No benefit for administration of FFP was noted. Additional investigation should be performed to confirm this result. 2009 Veterinary Emergency and Critical Care Society. (shrink)

This article proposes a framework for the analysis of experienced discrimination in home mortgages. It addresses the problem of home mortgage lending discrimination in one of the richest areas of northern Italy. Employees of a local hospital were interviewed to study their perception of discriminatory behavior related to home financing. The analysis follows two steps. The first evaluates self-selection and the second focuses on the likelihood that applications are accepted by the bank. Findings show that discrimination is likely to appear (...) when the applicant’s nationality is considered. In addition to its findings, the study provides an original econometric model on a two-step procedure to test perceived discrimination and suggests a method and approach that may constitute a point of reference for those willing to study perceived discrimination. (shrink)

This chapter introduces the idea that computation is a key tool that can help us understand how the human brain works. Recent years have seen a revolution in the kinds of tasks computers can perform. Underlying these advances is the burgeoning field of machine learning, a branch of artificial intelligence, which aims at creating machines that can act without being programmed, learning from data and experience. Rather startlingly, it turns out that the same methods that allow us to make intelligent (...) machines also appear to hold the key to explaining how our brains work. In this chapter, we explore this exciting new field and some of the questions that it raises. (shrink)

Enūma eliš exhibits a masterful array of intertextual borrowings that makes it exceptional among Akkadian literary texts. In this paper I discuss “intertextu- ity” as an analytical category and its suitability and limitations for the study of ancient compositions. I consider three different levels of intertextuality and present instances from an assorted group of texts. I finally show how a variety of intertextual types that are usually found in isolation are combined in Enūma eliš to create an original piece.

The Material and Ideological Base of the Old Babylonian State: History, Economy, and Politics. By Lukáš Pecha. Lanham, MD: Lexington Books, 2018. Pp. xvii + 316. $115.

The text commonly known as the Babylonian Poem of Creation has attracted scholarly attention since it was first translated in the late nineteenth century, although critical editions have appeared only recently. In 2014 there was published a lengthy study on enūma eliš that presents a number of original approaches to the ancient composition. This new book is the subject of the following notes.

According to a growing trend in theoretical neuroscience, the human perceptual system is akin to a Bayesian machine. The aim of this article is to clearly articulate the claims that perception can be considered Bayesian inference and that the brain can be considered a Bayesian machine, some of the epistemological challenges to these claims; and some of the implications of these claims. We address two questions: (i) How are Bayesian models used in theoretical neuroscience? (ii) From the use of Bayesian (...) models in theoretical neuroscience, have we learned or can we hope to learn that perception is Bayesian inference or that the brain is a Bayesian machine? From actual practice in theoretical neuroscience, we argue for three claims. First, currently Bayesian models do not provide mechanistic explanations; instead they are useful devices for predicting and systematizing observational statements about people's performances in a variety of perceptual tasks. That is, currently we should have an instrumentalist attitude towards Bayesian models in neuroscience. Second, the inference typically drawn from Bayesian behavioural performance in a variety of perceptual tasks to underlying Bayesian mechanisms should be understood within the three-level framework laid out by David Marr ( [1982] ). Third, we can hope to learn that perception is Bayesian inference or that the brain is a Bayesian machine to the extent that Bayesian models will prove successful in yielding secure and informative predictions of both subjects' perceptual performance and features of the underlying neural mechanisms. (shrink)

Aims to show graduate students and researchers the vital benefits of integrating mathematics into their study and experience of the physical world. This book details numerous topics from the frontiers of modern physics and mathematics such as convergence, Green functions, complex analysis, Fourier series and Fourier transform, tensors, and others.