One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. One of the best-known examples is that of the Fermat hypothesis, which was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the creation of a whole field of knowledge, but it was proved only after several hundred years. This book, based on the author's lectures, presents several new directions of mathematical research. (...) All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither proved nor disproved. The hypotheses range from geometry and topology (statistics of plane curves and smooth functions) to combinatorics (combinatorial complexity and random permutations) to algebra and number theory (continuous fractions and Galois groups). For each subject, the author describes the problem and presents numerical results that led him to a particular conjecture. In the majority of cases there is an indication of how the readers can approach the formulated conjectures (at least by conducting more numerical experiments). Written in Arnold's unique style, the book is intended for a wide range of mathematicians, from high school students interested in exploring unusual areas of mathematics on their own, to college and graduate students, to researchers interested in gaining a new, somewhat nontraditional perspective on doing mathematics. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI). (shrink)

The research of the thermal state of workers is associated with s ome ethical difficulties. The research work uses the method of rewards and bonuses for respondents. This argues the relevance of the discussion about the ethical principles of conducting hygienic and physiological studies in conditions of manufacturing.

In this article, we provide a description of the good in health promotion based on an empirical study of health promotion practices in New South Wales, the most populous state in Australia. We found that practitioners were unified by a vision of the good in health promotion that had substantive and procedural dimensions. Substantively, the good in health promotion was teleological: it inhered in meliorism, an intention to promote health, which was understood holistically and situated in places and environments, a (...) commitment to primary rather than secondary prevention and engagement with communities more than individuals. Procedurally, the good in health promotion arose from qualities of practices that they developed over time in respectful relationships, were flexible and responsive to communities, built capabilities in communities and were sustainable. We discuss our findings with reference to Martha Nussbaum’s normative list of functional capabilities for a good human life, David Buchanan’s vision for health promotion ethics and common concerns in health promotion ethics regarding the relationship between paternalism and freedom. Our thick, vague conception of the good in health promotion, founded in the values and practical reason of people engaged daily in health promotion work, contributes to the development of a more complete theory of health promotion ethics. (shrink)

The decade that has elapsed since the flight of the world's first cosmonaut, Iu. A. Gagarin, has been marked by considerable successes in mastering the cosmos. Lengthy orbital flights and lunar expeditions are already being conducted. Automatic stations are studying the moon, Mars, Venus, and cosmic space. And although we understand that the major trumphs in space are still ahead of us and that today we are merely at the start of the cosmic era, it is nonetheless already possible, in (...) this year of the tenth anniversary of the first human space flight, to draw certain conclusions and discuss the results of human intrusion into the expanses of the universe. (shrink)

We present a novel variant of decision making based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intentions, which allows us to describe a variety of interesting fallacies and anomalies that have been reported to particularize the decision making of real human beings. The theory characterizes entangled decision making, non-commutativity of subsequent decisions, and intention interference. We demonstrate how the violation of the Savage’s sure-thing principle, known (...) as the disjunction effect, can be explained quantitatively as a result of the interference of intentions, when making decisions under uncertainty. The disjunction effects, observed in experiments, are accurately predicted using a theorem on interference alternation that we derive, which connects aversion-to-uncertainty to the appearance of negative interference terms suppressing the probability of actions. The conjunction fallacy is also explained by the presence of the interference terms. A series of experiments are analyzed and shown to be in excellent agreement with a priori evaluation of interference effects. The conjunction fallacy is also shown to be a sufficient condition for the disjunction effect, and novel experiments testing the combined interplay between the two effects are suggested. (shrink)

Istoryko-filosofichni ret︠s︡ept︠s︡iï antychnosti -- Antychnistʹ v akademichniĭ filosofsʹkiĭ osviti -- F.O. Zelenohorsʹkyĭ i P.E. Leĭkfelʹd i︠a︡k universytetsʹki profesory.

Kuznet︠s︡ov, I. V. Kategorii︠a︡ prichinnosti i ee poznavatelʹnoe znachenie.--Shali︠u︡tin, S. M. Ob otrazhenii kak obshchem svoĭstve materii.--I︠U︡rgelenas, D. I. Teorii︠a︡ otrazhenii︠a︡ i poni︠a︡tie informat︠s︡ii.--Korneeva, A. I. Vozrastai︠u︡shchai︠a︡ rolʹ logicheskogo myshlenii︠a︡ v poznanii mira.--Klimashevskiĭ, G. Teoretiko-poznavatelʹnai︠a︡ rolʹ myslennogo ėksperimenta v fizike.-- Podosetnik, V. M. Gnoseologicheskoe znachenie faktov v poznanii obshchestvennykh i︠a︡vleniĭ.

Предназначено для студентов художественных вузов и факультетов, а также для учащихся профессиональных учебных заведений художественного профиля.

Idealizm Platona -- Skholastika XIX veka -- Pchëly -- Russkoepravitelʹstvo pod pokrovitelʹstvom Shedo-Ferroti -- Russkiĭ Don-Kikhot -- Ocherki iz istorii truda -- Progress v mire zhivotnykh i rasteniĭ -- Populi︠a︡rizatory otrit︠s︡atelʹnykh doktrin -- Genrikh Geĭne -- Mysli︠a︡shchiĭ proletariat.