Notes from Langlois--Prelude to Thoughts on Sustainability

Prelude to a Kiss

We consider expanding maps of the circle with an almost neutral fixed point c. In this setting the ergodic averages of a smooth observable A satisfy the Central Limit Theorem. If A(c) = 0 we show that the expectation and the variance behave as the square root of the multiplier of c times rapidly oscillating functions of parameters.

Notes on Dictyuchus species (Stramenopila, Oomycetes) from Anzali lagoon, Iran

Nine Dictyuchus isolates were obtained from floating and decaying twigs and leaves in Anzali lagoon, Anzali County, Guilan province, Iran. They are interestingly distinguished from current Dictyuchus species by the presence of dictyoid and achlyoid type of zoospore discharge, abundant fusiform and spherical gemma, and the absence of any sexual apparatus. In addition, phylogene...

Notes on some Encyrtidae (Hymenoptera: Chalcidoidea) from Iran

زنبور‌های خانواده‌یEncyrtidae از عوامل موفق در کنترل آفات گیاهی و به ویژه شپشک‌های آرد‌آلود می‌باشند. در مطالعات انجام شده در سال‌های 85-1381 که به منظور شناسایی پارازیتوییدهای شپشک‌های آردآلود در استان فارس انجام گرفت، از این خانواده و زیرخانواده‌ی Tetracneminae، گونه‌های Gyranusoidea indica Shafee, Alam & Agarwal از روی شپشک آرد‌آلود Maconellicoccus hirsutus (Green) روی توت سفید در جهرم،Anagy...

Notes on Complexity Theory Notes Taken From

I assume that most students have encountered Turing machines before. (Students who have not may want to look at Sipser’s book [3].) A Turing machine is defined by an integer k ≥ 1, a finite set of states Q, an alphabet Γ, and a transition function δ : Q×Γk → Q×Γk−1×{L, S,R}k where: • k is the number of (infinite, one-dimensional) tapes used by the machine. In the general case we have k ≥ 3 and ...

Judging Statutes: Thoughts on Statutory Interpretation and Notes for a Project on the Internal Revenue Code