Fukui’s DNA problem is a long-range target of the international and interdisciplinary joint project initiated by Kenichi Fukui in 1992, whose underlying motive has been to cultivate a new interdisciplinary region between chemistry and mathematics for a future development of theoretical chemistry. “Can the conductivity and other properties of a single-walled carbon nanotube be analyzed in the setting of a *-algebra equipped with a complete metric?” This metric problem is fundamental to proceed towards a solution of Fukui’s DNA problem. To affirmatively solve this metric problem, we establish, here in this paper, the new notion of normed repeat space fancyscriptXr(q, d, p){fancyscript{X}_{r}(q, d, p)}. The normed repeat space fancyscriptXr(q, d, p){fancyscript{X}_{r}(q, d, p)} is an intermediate theoretical device to shift from periodic polymers to aperiodic polymers like DNA and RNA in the above-mentioned Fukui Project. The space fancyscriptXr(q, d, p){fancyscript{X}_{r}(q, d, p)} is a Banach algebra for all 1 ≤ p ≤ ∞, and fancyscriptXr(q, d, p){fancyscript{X}_{r}(q, d, p)} forms a C*-algebra for p = 2. Here, polymer moiety size number q and dimension number d are arbitrarily given positive integers. The generalized repeat space fancyscriptXr(q, d){fancyscript{X}_{r}(q, d)} is included in the normed repeat space fancyscriptXr(q, d, p){fancyscript{X}_{r}(q, d, p)}, which in turn is included in one of its super spaces fancyscriptXB(q, d, p){fancyscript{X}_{B}(q, d, p)} so that aperiodic polymers can be represented and investigated in the setting of this super space fancyscriptXB(q, d, p){fancyscript{X}_{B}(q, d, p)}.
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机译:福井的DNA问题是福井健一(Kenichi Fukui)在1992年发起的国际和跨学科联合项目的长期目标,该项目的主要动机是在化学和数学之间建立一个新的跨学科领域,以促进理论化学的未来发展。 “能否在配备完整度量的*代数的背景下分析单壁碳纳米管的电导率和其他特性?”这个度量标准问题是解决福井DNA问题的基础。为了肯定地解决该度量问题,我们在本文中建立了范数重复空间fancyscriptX r sub>(q,d,p){fancyscript {X} _ {r}(q, d,p)}。范数重复空间fancyscriptX r sub>(q,d,p){fancyscript {X} _ {r}(q,d,p)}是从周期性聚合物转变为非周期性聚合物的中间理论装置就像上述福井计划中的DNA和RNA一样。空间fancyscriptX r sub>(q,d,p){fancyscript {X} _ {r}(q,d,p)}是所有1≤p≤∞的Banach代数,并且fancyscriptX < sub> r sub>(q,d,p){fancyscript {X} _ {r}(q,d,p)}形成一个C *-代数,其中p = 2。维数d任意为正整数。范式重复空间fancyscriptX r sub>()中包含广义重复空间fancyscriptX r sub>(q,d){fancyscript {X} _ {r}(q,d)} q,d,p){fancyscript {X} _ {r}(q,d,p)},反过来又包含在其超空间之一fancyscriptX B sub>(q,d,p ){fancyscript {X} _ {B}(q,d,p)},以便可以在此超空间fancyscriptX B sub>(q,d,p)的背景下表示和研究非周期性聚合物{fancyscript {X} _ {B}(q,d,p)}。
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