The Euclidean algorithm on the natural numbers ℕ = {0,1,…} can be specified succinctly by the recursive programwhere rem is the remainder in the division of a by b, the unique natural number r such that for some natural number q,It is an algorithm from the remainder function rem, meaning that in computing its time complexity function cε, we assume that the values rem are provided on demand by some “oracle” in one “time unit”. It is easy to prove thatMuch (...) more is known about cε, but this simple-to-prove upper bound suggests the proper formulation of the Euclidean's optimality among its peers—algorithms from rem:Conjecture. If an algorithm α computes gcd from rem with time complexity cα, then there is a rational number r > 0 such that for infinitely many pairs a > b > 1, cα > r log2a. (shrink)

The Euclidean algorithm on the natural numbers ℕ = {0,1,…} can be specified succinctly by the recursive programwhere rem is the remainder in the division of a by b, the unique natural number r such that for some natural number q,It is an algorithm from the remainder function rem, meaning that in computing its time complexity function cε, we assume that the values rem are provided on demand by some “oracle” in one “time unit”. It is easy to prove thatMuch (...) more is known about cε, but this simple-to-prove upper bound suggests the proper formulation of the Euclidean's optimality among its peers—algorithms from rem:Conjecture. If an algorithm α computes gcd from rem with time complexity cα, then there is a rational number r > 0 such that for infinitely many pairs a > b > 1, cα > r log2a. (shrink)

Boys and men tend to underperform in language education, and they are also underrepresented in language-related fields. Research suggests that stereotypes can affect students’ performance and sense of belonging in academic subjects and test settings via stereotype threat. For example, girls and women sometimes underperform on math tests following reminders that math is for boys. We sought to test whether stereotypes that women have better language skills than men would affect men. In a series of four experiments (N = 542), (...) we tested the effect of explicit stereotype threats on men’s performance in language-related tasks, and their sense of belonging to language-related domains. We found little evidence for stereotype threat effects on men in language. Bayesian analysis suggested that the null hypothesis was consistently more likely than the alternative, and mini-meta analyses showed effect sizes near zero. Future research should explore other explanations for gender gaps in language. (shrink)

Let T be a complete o-minimal extension of the theory of real closed fields. We characterize the convex hulls of elementary substructures of models of T and show that the residue field of such a convex hull has a natural expansion to a model of T. We give a quantifier elimination relative to T for the theory of pairs (R, V) where $\mathscr{R} \models T$ and V ≠ R is the convex hull of an elementary substructure of R. We deduce (...) that the theory of such pairs is complete and weakly o-minimal. We also give a quantifier elimination relative to T for the theory of pairs (R, N) with R a model of T and N a proper elementary substructure that is Dedekind complete in R. We deduce that the theory of such "tame" pairs is complete. (shrink)

Сборник содержит материалы докладов участников межвузовской конференции, посвященной проблемам связи философии, культуры и истории, влиянию социально-культурологических аспектов на развитие философских идей.

В книгу вошли расширенные версии докладов, представленных на конференции "Научная жизнь Северного Кавказа в условиях социально-политических трансформаций XX века", проведенная 24-26 сентября 2009 года. Для специалистов.

Книга рассчитана на тех, кто по своей специальности занимается философией, литературоведением и в дальнейшем углубят свои знания в этом вопросе, а также для широкого круга читателей.

Эта книга поможет пролить свет на метафизическое осмысление философии истории, подведет к более глубокому пониманию сущности добра и зла, предложенному известным русским философом и мыслителем Н. Ф. Федоровым.