Model structures on modules over Ding-Chen rings

An $n$-FC ring is a left and right coherent ring whose left and right self FP-injective dimension is $n$. The work of Ding and Chen in \cite{ding and chen 93} and \cite{ding and chen 96} shows that these rings possess properties which generalize those of $n$-Gorenstein rings. In this paper we call a (left and right) coherent ring with finite (left and right) self FP-injective dimension a Ding-Chen ring. In case the ring is Noetherian these are exactly the Gorenstein rings. We look at classes of modules we call Ding projective, Ding injective and Ding flat which are meant as analogs to Enochs' Gorenstein projective, Gorenstein injective and Gorenstein flat modules. We develop basic properties of these modules. We then show that each of the standard model structures on Mod-$R$, when $R$ is a Gorenstein ring, generalizes to the Ding-Chen case. We show that when $R$ is a commutative Ding-Chen ring and $G$ is a finite group, the group ring $R[G]$ is a Ding-Chen ring.Comment: 12 page

Another remark on a result of Ding-Jost-Li-Wang

Let $(M,g)$ be a compact Riemann surface, $h$ be a positive smooth function on $M$. It is well known the functional $$J(u)=\frac{1}{2}\int_M|\nabla u|^2dv_g+8\pi\int_M udv_g-8\pi\log\int_Mhe^{u}dv_g$$ achieves its minimum under Ding-Jost-Li-Wang condition. This result was generalized to nonnegative $h$ by Yang and the author. Later, Sun and Zhu (arXiv:2012.12840) showed Ding-Jost-Li-Wang condition is also sufficient for $J$ achieves its minimum when $h$ changes sign, which was reproved later by Wang and Yang (J. Funct. Anal. 282: Paper No. 109449, 2022) and Li and Xu (Calc. Var. 61: Paper No. 143, 2022) respectively using flow approach. The aim of this note is to give a new proof of Sun and Zhu's result. Our proof is based on the variational method and the maximum principle.Comment: 13 pages. To appear on Proc. AM

Universal R-matrix Of The Super Yangian Double DY(gl(1|1))

Based on Drinfeld realization of super Yangian Double DY(gl(1|1)), its pairing relations and universal R-matrix are given. By taking evaluation representation of universal R-matrix, another realization $L^{\pm}(u)$ of DY(gl(1|1)) is obtained. These two realizations of DY(gl(1|1)) are related by the supersymmetric extension of Ding-Frenkel map.Comment: 6 pages, latex, no figure

Characterizations of Ding Injective Complexes

©2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ This document is the Accepted version of a Published Work that appeared in final form inBulletin of the Malaysian Mathematical Sciences Society. To access the final edited and published work see https://doi.org/10.1007/s40840-019-00807-8Let R be a ring and X a chain complex of R-modules. It is proven that if each term is Ding injective in R-Mod for all i in Z , and there exists an integer k such that each ZiX is Ding injective in R-Mod for all i>=k , then X is Ding injective in Ch(R) . If R is a left coherent ring, then a chain complex X is Ding injective if and only if each term is Ding injective in R-Mod for all i in Z

物自体と個物 : カント解釈の試み

Kant hat in seiner kritischen Zeit die transsubjektive Existenz vom Ding an sich, das das menschliche Gemut affiziert, nicht einmal bezweifelt. Aber der Gegensatz zwischen Ding an sich und Erscheinung ist ein Angriffspunkt aller Kant kritiker und eine Crux aller Kant-interpretation. Er stellt den Angelpunkt auch fur diejenigen Versuche dar, in denen die Bedeutung der ontologischen Probleme fur Kant herausgesftellt werden. Im folgenden Aufsatz nehmen wir das Ding an sich in Bezug auf das erscheinende Ding auf. Der Begriff "Erscheinung" zeigt schon eine Beziehung zu Etwas an, dessen unmittelbare Vorstellung zwar sinnlich ist, aber als solche das Ding an sich, d. h. ein von der Sinnlichkeit unabhangiger Gegenstand, sein muss. Also wird die Aufgabe "transzendentaler Aesthetik und Analytik" aus der "Kritik der reinen Vernunft" zuruckgeworfen auf die allgemeine Frage: Wie manifesfiert sich das Ding an sich in der Erscheinung? Von diesem Gesichtspunkt ausgehend mochten wir in dem Aufsatz die folgende 3 Themen erortern. 1. Ding an sich und Erscheinung 2. Die Frage der Empfindung 3. Ding an sich und Ich an sic

Perception of Phrase Boundaries and Prominent Syllables in German

Mixdorff H, Hönemann A, Ding H. Perception of Phrase Boundaries and Prominent Syllables in German. In: Proceedings of Nordic Prosody XI. 2012: 245-254