<?xml version="1.0" encoding="UTF-8"?> <rss xmlns:dc="http://purl.org/dc/elements/1.1/" version="2.0"> <channel> <title>DSpace コミュニティ:</title> <link>http://hdl.handle.net/2433/24849</link> <description /> <pubDate>Wed, 26 Feb 2025 10:46:14 GMT</pubDate> <dc:date>2025-02-26T10:46:14Z</dc:date> <item> <title>Virtual classes via vanishing cycles</title> <link>http://hdl.handle.net/2433/291818</link> <description>タイトル: Virtual classes via vanishing cycles 著者: Kinjo, Tasuki 抄録: We develop a new method to construct the virtual fundamental classes for quasismooth derived schemes (and more generally, derived 1-Artin stacks) using the perverse sheaves of vanishing cycles on their —1-shifted cotangent spaces. It is based on the author’s previous work that can be regarded as a version of the Thom isomorphism for —1-shifted cotangent spaces. We use the Fourier–Sato transform to prove that our classes coincide with the virtual fundamental classes introduced by the work of Behrend–Fantechi and Li–Tian, under the schematic and quasiprojectivity assumption. We also discuss an approach to construct DT4 virtual classes for —2-shifted symplectic derived schemes using the perverse sheaves of vanishing cycles.</description> <pubDate>Wed, 22 Jan 2025 00:00:00 GMT</pubDate> <guid isPermaLink="false">http://hdl.handle.net/2433/291818</guid> <dc:date>2025-01-22T00:00:00Z</dc:date> </item> <item> <title>The centre of the modular affine vertex algebra</title> <link>http://hdl.handle.net/2433/291658</link> <description>タイトル: The centre of the modular affine vertex algebra 著者: Arakawa, Tomoyuki; Topley, Lewis; Villarreal, Juan J. 抄録: The Feigin–Frenkel theorem states that, over the complex numbers, the centre of the universal affine vertex algebra at the critical level is an infinite rank polynomial algebra. The first author and W. Wang observed that in positive characteristics, the universal affine vertex algebra contains a large central subalgebra known as the p-centre. They conjectured that at the critical level the centre should be generated by the Feigin–Frenkel centre and the p-centre. In this paper we prove the conjecture for classical simple Lie algebras for p larger than the Coxeter number, and for exceptional Lie algebras in large characteristics. Finally, we give an example which shows that at non-critical level the center is larger than the p-centre.</description> <pubDate>Sat, 01 Feb 2025 00:00:00 GMT</pubDate> <guid isPermaLink="false">http://hdl.handle.net/2433/291658</guid> <dc:date>2025-02-01T00:00:00Z</dc:date> </item> <item> <title>Introduction to Time-fractional Differential Equations: a sketch of theory (Innovation of the theory for evolution equations: developments via cross-disciplinary studies)</title> <link>http://hdl.handle.net/2433/291448</link> <description>タイトル: Introduction to Time-fractional Differential Equations: a sketch of theory (Innovation of the theory for evolution equations: developments via cross-disciplinary studies) 著者: Yamamoto, Masahiro 抄録: This article explains a partial shape of the complete theory for time-fractional differential equations, which is still under construction. First we define a fractional derivative with the order between O and 1 in suitable Sobolev spaces, and show some properties on fractional calculus. Then we establish theories for initial value problems and initial boundary value problems. Finally we discuss several remarkable properties for time-fractional differential equations. The article mainly aims at demonstrating a sketch of the total theory covering from fractional calculus to linear or nonlinear time-fractional partial differential equations, and so this article is not a survey and refers to other works for more details.</description> <pubDate>Thu, 01 Feb 2024 00:00:00 GMT</pubDate> <guid isPermaLink="false">http://hdl.handle.net/2433/291448</guid> <dc:date>2024-02-01T00:00:00Z</dc:date> </item> <item> <title>前方後方動的境界条件下でのCahn-Hilliard方程式について (発展方程式論の革新: 異分野との融合がもたらす理論の深化)</title> <link>http://hdl.handle.net/2433/291446</link> <description>タイトル: 前方後方動的境界条件下でのCahn-Hilliard方程式について (発展方程式論の革新: 異分野との融合がもたらす理論の深化) 著者: 深尾, 武史 抄録: この報告では，適切性やその周辺の研究が近年盛んにされている，動的境界条件下でのCahn-Hilliard方程式について，特に境界上での拡散項に対する粘性消滅の結果，“P. Colli, T. Fukao, and L. Scarpa, J. Evol. Equ., 22 (2022), Article number: 89, 31 pp.”と“P. Colli, T. Fukao, and L. Scarpa, SIAM J. Math. Anal., 54 (2022), 3292-3315”の紹介を中心にGMSモデルとLWモデルの2つについて概説を行う．これらの報告はPavia大学のPierluigi Colli氏とMilano工科大学のLuca Scarpa氏との共同研究に基づく．</description> <pubDate>Thu, 01 Feb 2024 00:00:00 GMT</pubDate> <guid isPermaLink="false">http://hdl.handle.net/2433/291446</guid> <dc:date>2024-02-01T00:00:00Z</dc:date> </item> </channel> </rss>