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THE OHM-RUSH CONTENT FUNCTION III: COMPLETION, GLOBALIZATION, AND POWER-CONTENT ALGEBRAS
Epstein, Neil,Shapiro, Jay Korean Mathematical Society 2021 대한수학회지 Vol.58 No.6
One says that a ring homomorphism R → S is Ohm-Rush if extension commutes with arbitrary intersection of ideals, or equivalently if for any element f ∈ S, there is a unique smallest ideal of R whose extension to S contains f, called the content of f. For Noetherian local rings, we analyze whether the completion map is Ohm-Rush. We show that the answer is typically 'yes' in dimension one, but 'no' in higher dimension, and in any case it coincides with the content map having good algebraic properties. We then analyze the question of when the Ohm-Rush property globalizes in faithfully flat modules and algebras over a 1-dimensional Noetherian domain, culminating both in a positive result and a counterexample. Finally, we introduce a notion that we show is strictly between the Ohm-Rush property and the weak content algebra property.
The Transition from Orality to Literacy - The Homeric Poems, especially the lliad
( Katharina Epstein ) 연세대학교 인문학연구원 2018 人文科學 Vol.114 No.-
본 논문은 구술성과 문자성 사이에 위치하는 『일리아드』를 중심으로 호머시편들의 주요한 문제들을 다룬다. 이와 관련된 증거들이 희소하고 또 불확실한 탓에 많은 문제들은 여전히 해결되지 않은 채 남아 있다. 『일리아드』에서는 구술성과 문자성의 특징이 동시에 발견된다. 이를 함께 고려하면, 『일리아드』가 구술문화 전통에 강한 영향을 받았지만, 동시에 기원전 7세기 전반부의 글쓰기 (writing, 기록)에 힘입어 지어졌다는 가설을 지지할 수 있다. 『일리아드』 6권 160ff에서 발견되는 모호한 서술은 의도적인 것으로, 그것은 『일리아드』가 (구술방식이 아니라) 글쓰기(기록)에 의해 지어졌다는 주장에 대해 찬성이나 반대의 증거가 될 수 없다. 그러한 서술은 『일리아드』의 시인이 아킬레우스와 헥토르의 시대에 대해 모순적인 이미지를 만들어내었던 것처럼, 일종의 시적 프로젝트의 일환으로 간주할 때 가장 잘 이해될 수 있다. This article addresses some major questions about the place of the Homeric poems, especially the Iliad, between orality and literacy. Due to the scarcity and often dubious quality of the evidence, many questions must remain open. Features both of orality and of literacy can be discerned in the Iliad. Taken together, they support the hypothesis that the Iliad is heavily influenced by an oral tradition, but was composed with the aid of writing in the first half of the 7<sup>th</sup> century B.C. The deliberately obscure depiction of writing in Il. 6.160ff. cannot be used as evidence for or against a composition of the Iliad in writing. This depiction, just like the historically inconsistent image the Iliadic poet creates of the age of Achilles and Hector, is best understood as part of his poetic project.
ArthurJ.Epstein,Fang-ChiHsu,Nan-RongChiou,VladimirN.Prigodin 한국물리학회 2002 Current Applied Physics Vol.2 No.4
The field effect devices prepared completely from conducting polymers, especially poly(3,4-ethylenedioxythiophene)/poly(styrene sulfonic acid) (PEDOT/PSS), were studied. Normally in a conductive ‘‘on’’ state, the transistor-like device has a transition to a substantially less conductive ‘‘off’’ state at an applied positive gate voltage, typically 15–25 V. The current ratio Ioff=Ion can exceed 104 at room temperature. We have found that the field effect is strongly temperature dependent and is substantially reduced upon decreasing the temperature by only a 10 C. This loss of current reduction upon application of a gate voltage is not due to the temperature dependence of the electrical conductivity of polymers of which the devices are made. The temperature dependence of the dc conductivity of the PEDOT/PSS follows the variable range hopping law both before and after application of the gate voltage, though with an increased activation energy, T0. We suggest that the conducting polymer is near the metal–insulator transition and that the field effect in the device is related to the electric field modulating this transition in the region underneath the gate electrode. The transition is controlled and leveraged by ion motion. The time dynamics of the current with the gate modulation strongly supports our conjecture. We demonstrate the generality of the phenomena by presenting similar results for devices fabricated from the conducting polypyrrole doped with Cl.