A collection of articles about P.A. Sorokin's work are preceded by a Russian translation of selected chapters of his 1947 work "Society, culture and personality" and a collection of correspondence (also translated into Russian) between him and Robert Merton.

Razdel I. Obnovlencheskoe dvizhenie -- Razdel II. Politicheskiĭ islam -- Razdel III. Mezhdu neomodernizmom i islamizmom : otdelʹnye proekty -- Zakli︠u︡chenie.

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)

Tijdens zijn bewogen leven schreef Dirck Volckertsz Coornhert (1522-1590) vele teksten en voerde hij talloze gesprekken. Zijn doel: zijn medemensen overtuigen van het belang om niet slaafs achter anderen aan te lopen maar zélf na te denken. Want elk mens heeft voldoende redelijke vermogens om het leven zelfstandig vorm te geven en het goede te doen. De Kruidhofjes bevat twee bundels met dialogen – gesprekken die Coornhert zelf voerde of onderweg heeft gehoord. De dialogen zijn te zien als medicijnen tegen (...) wat Coornhert zag als de ziekte van zijn tijd: onnadenkendheid en religieuze scherpslijperij. Enerzijds probeert Coornhert obstakels voor een goed en gelukkig persoonlijk leven weg te halen. Hier gaat het vooral om het bestrijden van onbegrip en onwetendheid. Anderzijds probeert Coornhert obstakels voor vreedzaam samenleven op te ruimen. Dat is de reden waarom nogal wat dialogen ingaan op religieuze kwesties als kerkbezoek, de mis en kerkelijke ceremonies; onenigheid over deze onderwerpen vormde immers de belangrijkste oorzaak van de heftige onderdrukking, vervolging en oorlog in de zestiende eeuw. Dit verklaart ook de felheid van veel van de dialogen. Discussies over religieuze denkbeelden en gebruiken waren niet zomaar interessant tijdverdrijf voor bij de borrel. Het ging ergens om: om de waarheid, je zielenheil en de inrichting van de maatschappij. In 45 dialogen probeert Coornhert zo zijn medemens te motiveren tot eerlijkheid naar zichzelf en verdraagzaamheid naar de ander. (shrink)

The Hamilton–Jacobi (HJ) equation for the action function plays a fundamental role in classical mechanics. A known consequence of the HJ equation is a blow-up of a disturbed free-particle solution. Following the idea of Sivashinsky, we formulate an extension of the HJ equation in which perturbations eventually evolve into a finite autosoliton associated with an elementary particle. A novel element of the model is stability of the autosoliton. We link uncertainties in the position and momentum of a particle to a (...) width and amplitude of the autosoliton. We formulate restrictions on the coefficients of the model and compare the model with some existing theories of extended elementary objects. (shrink)