Hasil untuk "math.AC"

Tahmin Mahmud, Hang Gao

Kyriakos Keremedis, Eleftherios Tachtsis, Eliza Wajch

AbstractA topological space is iso-dense if it has a dense set of isolated points, and it is scattered if each of its non-empty subspaces has an isolated point. In $$\textbf{ZF}$$ ZF (i.e. Zermelo–Fraenkel set theory without the Axiom of Choice ($$\textbf{AC}$$ AC )), basic properties of iso-dense spaces are investigated. A new permutation model is constructed, in which there exists a discrete weakly Dedekind-finite space having the Cantor set as a remainder; the result is transferable to $$\textbf{ZF}$$ ZF . This settles an open problem posed by Keremedis, Tachtsis and Wajch in 2021. A metrization theorem for a class of quasi-metric spaces is deduced. The statement “Every compact scattered metrizable space is separable” and several other statements about metric iso-dense spaces are shown to be equivalent to the axiom of countable choice for families of finite sets. Results related to the open problem of the set-theoretic strength of the statement “Every non-discrete compact metrizable space contains an infinite compact scattered subspace” are also included.

Tahmin Mahmud, Hang Gao

<p>The isolated AC-AC/DC-AC/AC-DC matrix converter (MC) is an innovative topology with several benefits including minimum current harmonics, nearly unity power factor, <em>four quadrant</em> (4Q) operation, and bidirectional power flow, making it an ideal choice for energy conversion techniques. Unlike any other AC-AC/DC-AC/AC-DC topologies, the MC topology necessitates electrical <em>medium-frequency</em> (MF)/<em>high-frequency</em> (HF) isolation in order to offer single-stage power conversion. MF/HF power conversion topology has numerous advantages such as high-power density, reduced weight, and low noise while preserving converter’s efficiency, cost, and reliability. This paper aims to report an extensive analysis and classification of different conventional isolated single-stage AC-AC converter, DC-AC inverter, and AC-DC rectifier topologies along with their modified system architecture. In this paper, the AC-AC/DC-AC/AC-DC topologies are classified based on their system architecture, AC-side or DC-side drive techniques, and other subvariants. Our primary objective of this study is to impart a clear understanding of the overarching framework and principles of the isolated AC-AC/DC-AC/AC-DC MC topologies and stimulate the creation of new topologies that cater to specific grid-interconnection requirement.</p>

JAMES GILLESPIE

We introduce what is meant by an AC-Gorenstein ring. It is a generalized notion of Gorenstein ring that is compatible with the Gorenstein AC-injective and Gorenstein AC-projective modules of Bravo–Gillespie–Hovey. It is also compatible with the notion of $n$ -coherent rings introduced by Bravo–Perez. So a $0$ -coherent AC-Gorenstein ring is precisely a usual Gorenstein ring in the sense of Iwanaga, while a $1$ -coherent AC-Gorenstein ring is precisely a Ding–Chen ring. We show that any AC-Gorenstein ring admits a stable module category that is compactly generated and is the homotopy category of two Quillen equivalent abelian model category structures. One is projective with cofibrant objects that are Gorenstein AC-projective modules while the other is an injective model structure with fibrant objects that are Gorenstein AC-injectives.

James Gillespie

A. Mironov, A. Morozov, L. Vinet

Zbigniew Leyk

John Ernest

S. P. Ponomarëv

George A. Elliott

M. B. Ghaemi

M. Stern

Amitayu Banerjee, Zalán Molnár, Alexa Gopaulsingh

Narayanaswamy P. R. Iyer

Tianya Cao, Zhongkui Liu, Xiaoyan Yang

Goncalo Oliveira

AC Okoroafor, GU Achi

Abel Klein, Olivier Lenoble, Peter Müller

B.T. Fijalkowski

A.D. SNEYD