We use tools of mathematical logic to analyse the notion of a path on a complex algebraic variety, and are led to formulate a “rigidity” property of fundamental groups specific to algebraic varieties, as well as to define a bona fide topology closely related to etale topology. These appear as criteria for ℵ1-categoricity, or rather stability and homogeneity, of the formal countable language we propose to describe homotopy classes of paths on a variety, or equivalently, its universal covering space.Technically, for (...) a variety A defined over a finite field extension of the field Q of rational numbers, we introduce a countable language L describing the universal covering space of A, or, equivalently, homotopy classes of paths in A. Under some assumptions on A source we show that the universal covering space of A is an analytic Zariski structure [26]), and present an Lω1ω)-sentence axiomatising the class containing the structure and that is stable and homogeneous over elementary submodels. The “rigidity” condition on fundamental groups says that projection of the fundamental group of a variety is the fundamental group of the projection, up to finite index and under some irreducibility assumptions, and is used to prove that the projection of an irreducible closed set is closed in the analytic Zariski structure.In particular, we define an analytic Zariski structure on the universal covering space of an Abelian variety defined over a finite extension of the field Q of rational numbers. (shrink)

We describe approximation algorithms for MAX SAT with performance ratios arbitrarily close to 1, in particular, when performance ratios exceed the limits of polynomial-time approximation. Namely, given a polynomial-time α-approximation algorithm , we construct an -approximation algorithm . The algorithm runs in time of the order ck, where k is the number of clauses in the input formula and c is a constant depending on α. Thus we estimate the cost of improving a performance ratio. Similar constructions for MAX 2SAT (...) and MAX 3SAT are also described. Taking known algorithms as , we obtain particular upper bounds on the running time of. (shrink)

Collection of works on literature theory, translated into Mongolian language.

Kant's Critique of Pure Reason, his main work of theoretical philosophy, frequently uses metaphors from law. In this first book-length study in English of Kant's legal metaphors and their role in the first Critique, Sofie Møller shows that they are central to Kant's account of reason. Through an analysis of the legal metaphors in their entirety, she demonstrates that Kant conceives of reason as having a structure mirroring that of a legal system in a natural right framework. Her study shows (...) that Kant's aim is to make cognisers become similar to authorized judges within such a system, by proving the legitimacy of the laws and the conditions under which valid judgments can be pronounced. These elements consolidate her conclusion that reason's systematicity is legal systematicity. (shrink)

A detailed attempt to ground the topological properties of time in the laws of micro- and macro-physical processes. The reversible processes of mechanics are used to define an order among temporally separated events, which is invariant under reversals of time direction. So long as consideration is limited to a single isolated system, a time ensemble, the transfer of the reversibility of the constituent processes of such a system to the system as a whole makes it impossible to define time direction (...) by means of the entropy curve. The directionality of time, accordingly, can only be defined as the direction of the entropy increase of multiple systems, of a space ensemble. A macrostatistical definition of time direction is then based upon the causal relation. The author's view of causation is non-deterministic: the conjunction of two events is caused if they occur together more frequently than can be expected from their chance coincidence. Reichenbach's analyses and arguments are careful and thorough; the book as a whole is a solid achievement. -- M. F. (shrink)

Listening to someone from some distance in a crowded room you may experience the following phenomenon: when looking at them speak, you may both hear and see where the source of the sounds is; but when your eyes are turned elsewhere, you may no longer be able to detect exactly where the voice must be coming from. With your eyes again fixed on the speaker, and the movement of her lips a clear sense of the source of the sound will (...) return. This ‘ventriloquist’ effect reflects the ways in which visual cognition can dominate auditory perception. And this phenomenological observation is one what you can verify or disconfirm in your own case just by the slightest reflection on what it is like for you to listen to someone with or without visual contact with them. (shrink)

This volume offers the first-ever complete English translation of Leibniz’s Dissertatio De Arte Combinatoria together with a critical edition of the original Latin text on fa...

Our research is based on a rather large "library" of various works by M. Drahomanov, which contains his views on religion. Among them: Paradise and Progress, From the History of Relations Between Church and State in Western Europe, Faith and Public Affairs, Fight for Spiritual Power and Freedom of Conscience in the 16th - 17th Centuries,, "Church and State in the Roman Empire", "The Status and Tasks of the Science of Ancient History," "Evangelical Faith in Old England," "Populism and Popular (...) Progress in Austrian Rus, Austrian-Russian Remembrance," "Pious The Legend of the Bulgarians "," The Issues of Religious Freedom in Russia, "" On the Brotherhood of the Baptist or the Baptist in Ukraine, "" The Foreword, " Shevchenko, Ukrainianophiles and Socialism "," Wonderful thoughts about the Ukrainian national affair "," Zazdri gods "," Slavic variants of one Gospel legend "," Resurrection of Christ ", etc. (shrink)

Dünyada müxtəlif dillər mövcuddur. Hal-hazırda əlavə xarici dil öyrənməyə maraq artmaqdadır. Təbii ki bu hər bir şəxsin öz istəyinə və seçiminə bağlıdır. Yəni hər kəs, hər hansı bir dili öyrəndiyi zaman, qarşısında iki məqsəd dayanır; ya o dili sevir, ya da o dili öyrənmək onun üçün lazımdır. Hər bir vətəndaşın borcudur ki, əvvəlcə öz ana dilini mükəmməl şəkildə öyrənsin. Lakin elm və texnologiyanın yüksək inkişaf etdiyi bir zamanda yalnız ana dilini bilmək kifayət etmir. İnsanın hər bir sahədə inkişafı üçün bacardığı (...) qədər başqa dillərə də yiyələnməsi artıq zəruridir. Yeni dil öyrənmənin faydaları çoxdur, yaddaşın güclənməsinə, söz ehtiyatının artmasına, nitqin gözəlləşməsinə səbəb olur. Həmçinin yeni dil öyrənməklə, insanın özünə güvəni artır, ünsiyyət dairəsi genişlənir. Bununla insan yalnız yeni sözlər deyil, yeni mədəniyyətlərlə də tanış olur və nəticədə dünyagörüşü artır. (shrink)