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The *reciprocal complement* $R(D)$ of an integral domain $D$ is the subring of its fraction field generated by the reciprocals of its nonzero elements. Many properties of $R(D)$ are determined when $D$ is a polynomial ring in $n\geq 2$ variables over
Externí odkaz:
http://arxiv.org/abs/2407.15637
Let $D$ be a two-dimensional regular local ring. We prove there is a one-to-one correspondence between closed connected sets in the space of valuation overrings of $D$ that dominate $D$ and the integrally closed local overrings of $D$ that are not es
Externí odkaz:
http://arxiv.org/abs/2406.10966
Let $F$ be a field, let $D$ be a local subring of $F$, and let Val$_F(D)$ be the space of valuation rings of $F$ that dominate $D$. We lift Zariski's connectedness theorem for fibers of a projective morphism to the Zariski-Riemann space of valuation
Externí odkaz:
http://arxiv.org/abs/2306.14833
Autor:
Guerrieri, Lorenzo, Loper, K. Alan
It is well-known that an integrally closed domain $D$ can be express as the intersection of its valuation overrings but, if $D$ is not a Pr\"{u}fer domain, the most of valuation overrings of $D$ cannot be seen as localizations of $D$. The Kronecker f
Externí odkaz:
http://arxiv.org/abs/2304.03723
Autor:
Pu Li, Qizhi Li, Wenye Tang, Weiqiang Wang, Wenfu Zhang, Brent E. Little, Sai Tek Chu, K. Alan Shore, Yuwen Qin, Yuncai Wang
Publikováno v:
Light: Science & Applications, Vol 13, Iss 1, Pp 1-8 (2024)
Abstract Random bit generators are critical for information security, cryptography, stochastic modeling, and simulations. Speed and scalability are key challenges faced by current physical random bit generation. Herein, we propose a massively paralle
Externí odkaz:
https://doaj.org/article/1a4302c70e554095bc6717712b1ccfd2
Autor:
Zhao, Jiamin, Li, Pu, Zhang, Xing, Gao, Zhensen, Jia, Zhiwei, Bogris, Adonis, Shore, K. Alan, Wang, Yuncai
We propose a simple and all-optical method for fast random number generation based on the laser mode hopping. Through periodically restarting a two-mode laser operating in the bistable state, a random number stream can be generated due to the spontan
Externí odkaz:
http://arxiv.org/abs/2201.07616
Publikováno v:
In Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena September 2024 186
Publikováno v:
In Optics Communications 15 May 2024 559