We study the canonical Krugman (1979) trade model with non-CES preferences that yield autarky at finite costs. prove a non-monotone impact of gradual liberalization. At first, near autarky, emerging reduces world welfare, while free it becomes large enough to be beneficial (Krugman's result). This non-monotonicity persists under heterogenous firms. The harmful small-scale is explained by variab...

The problem of finding a longest increasing subsequence (LIS) is a well known task in sequence processing. There are many variants of the basic task. We discuss a recently introduced variant of LIS, a minimal height longest increasing subsequence problem and propose a new algorithm for it, which improves its time complexity. Moreover, we define a family of similar problems and introduce algorit...

Let Ln be the length of the longest increasing subsequence of a random permutation of the numbers 1, . . . , n, for the uniform distribution on the set of permutations. We discuss the “hydrodynamical approach” to the analysis of the limit behavior, which probably started with Hammersley (1972), and was subsequently further developed by several authors. We also give two proofs of an exact (non-a...

Two-dimensional Lorentzian geometry has recently found application in some models of nonrelativistic systems, most profitably for the process of boarding an aeroplane. The duration of the boarding process is assumed to be a result of passengers standing in the isle and blocking each others’ way. According to this model, the expected boarding time is equal to the length of the longest timelike g...

New algorithm for finding longest increasing subsequence is discussed. This algorithm is based on the ideas of idempotent mathematic and uses Max-Plus idempotent semiring. Problem of finding longest increasing subsequence is reformulated in a matrix form and solved with linear algebra.

Sperm competition theory predicts that males should increase their expenditure on the ejaculate with increasing risk of sperm competition, but decrease their expenditure with increasing intensity. There is accumulating evidence for sperm competition theory, based on examinations of testes size and/or the numbers of sperm ejaculated. However, recent studies suggest that ejaculate quality can als...

Gaining entrance to a four-year college or university, particularly a selective institution, has become increasingly competitive over the last several decades. We document this phenomenon and show how it has varied across different parts of the student ability distribution and across region, with the most pronounced increases in competition being found among higher-ability students and in the N...