Schaeffer Hall

The Duffin-schaeffer Conjecture with Extra Divergence

Throughout this note we will use the following standard notation from elementary number theory: p denotes a prime number, μ(n) is the Möbius function, φ(n) is the Euler phi function, ω(n) denotes the number of distinct prime divisors of n, and τ(n) is the number of positive integers which divide n. Also we use λ to denote Lebesgue measure on R/Z and dimX to denote the Hausdorff dimension of a s...

The Markoff-Duffin-Schaeffer inequalities abstracted.

The kth Markoff-Duffin-Schaeffer inequality provides a bound for the maximum, over the interval -1 </= x </= 1, of the kth derivative of a normalized polynomial of degree n. The bound is the corresponding maximum of the Chebyshev polynomial of degree n, T = cos(n cos(-1)x). The requisite normalization is over the values of the polynomial at the n + 1 points where T achieves its extremal values....

اثر هال (hall effect)

Eretmoptera Murphyi Schaeffer (diptera: Chironomjdae), an Apparently Parthenogenetic Antarctic Midge

Chironomid midges are amongst the most abundant and diverse holo­ metabolous insects of the Antarctic and sub-Antarctic. Eretmoptera murphyi Schaeffer, 1914, has been enigmatic to systematists since the first discovery of adult females on South Georgia. The rediscovery of the species as a suspected introduction to Signy Island (South Orkney Islands) allows the description of the immature stages...

Timothy Hall

The emergence of lexico-grammatical productivity has been a central issue in the field of Second Language Acquisition (SLA). Ellis (2002) proposed that formulaic chunks of language are one resource for the learner to develop such productivity. This exploratory study sought to determine whether formulaic language chunks were observed in the oral production of three adult beginner learners of Eng...