Search results for " secondary"
showing 10 items of 692 documents
$V$-filtrations in positive characteristic and test modules
2013
Let $R$ be a ring essentially of finite type over an $F$-finite field. Given an ideal $\mathfrak{a}$ and a principal Cartier module $M$ we introduce the notion of a $V$-filtration of $M$ along $\mathfrak{a}$. If $M$ is $F$-regular then this coincides with the test module filtration. We also show that the associated graded induces a functor $Gr^{[0,1]}$ from Cartier crystals to Cartier crystals supported on $V(\mathfrak{a})$. This functor commutes with finite pushforwards for principal ideals and with pullbacks along essentially \'etale morphisms. We also derive corresponding transformation rules for test modules generalizing previous results by Schwede and Tucker in the \'etale case (cf. ar…
Commensurability in Artin groups of spherical type
2019
Let $A$ and $A'$ be two Artin groups of spherical type, and let $A_1,\dots,A_p$ (resp. $A'_1,\dots,A'_q$) be the irreducible components of $A$ (resp. $A'$). We show that $A$ and $A'$ are commensurable if and only if $p=q$ and, up to permutation of the indices, $A_i$ and $A'_i$ are commensurable for every $i$. We prove that, if two Artin groups of spherical type are commensurable, then they have the same rank. For a fixed $n$, we give a complete classification of the irreducible Artin groups of rank $n$ that are commensurable with the group of type $A_n$. Note that it will remain 6 pairs of groups to compare to get the complete classification of Artin groups of spherical type up to commensur…
Density of Lipschitz functions in energy
2020
In this paper, we show that the density in energy of Lipschitz functions in a Sobolev space $N^{1,p}(X)$ holds for all $p\in [1,\infty)$ whenever the space $X$ is complete and separable and the measure is Radon and finite on balls. Emphatically, $p=1$ is allowed. We also give a few corollaries and pose questions for future work. The proof is direct and does not involve the usual flow techniques from prior work. It also yields a new approximation technique, which has not appeared in prior work. Notable with all of this is that we do not use any form of Poincar\'e inequality or doubling assumption. The techniques are flexible and suggest a unification of a variety of existing literature on th…
Imaginary Dialogues – In-service Teachers’ Steps Towards Mathematical Argumentation in Classroom Discourse
2018
The purpose of this qualitative study was to explore in-service teachers’ first experiences with imaginary dialogues – a form of mathematical writing where students are introduced to a written and unfinished dialogue between two imaginary persons discussing a mathematical problem. Students are supposed to continue working with the problem and to complete the initial dialogue between these persons. In-service teachers were enrolled in a continuing university education mathematics course. They were given the task to try out imaginary dialogues in their classes from grades 4 to 10. Based on in-service teachers’ responses in open-ended self-evaluation forms, the study examined how the in-servic…
Engaging Mathematical Reasoning-and-Proving: A Task, a Method, and a Taxonomy
2019
This article is the second paper in a series of papers on studies focusing on teaching mathematical reasoning-and-proving in elementary mathematics classroom. Participants are in-service teachers enrolled in a continuing university education program in mathematics. Results from the first paper suggested the method of imaginary dialogues to have the potential to support in-service teachers in engaging their students in mathematical reasoning-and-proving, and Balacheff’s taxonomy of proofs to support in-service teachers in identifying students’ argumentation. This study is on the following years’ in-service teachers in the program. It examines their perceptions of the usefulness of two consti…
Implementation of CLIL in Castilla-La Mancha (Spain) and teacher training
2009
This article is the result of the first stage of ongoing research in schools in the region of Castilla La-Mancha, a non bilingual region located in the centre of Spain, in order to ascertain the extent to which CLIL has been established as part of the general curriculum. We analysed schools of primary and secondary education in Cuenca, one of the region?s provinces, and contacted the teachers responsible for the ?Secciones Europeas? programme in a number of state primary schools and secondary education centres of the other four provinces which make up the region (Albacete, Ciudad Real, Guadalajara and Toledo). Through contact with the regional Department of Education responsible for the pro…
The tusk condition and Petrovski criterion for the normalized $p\mspace{1mu}$-parabolic equation
2017
We study boundary regularity for the normalized $p\mspace{1mu}$-parabolic equation in arbitrary bounded domains. Effros and Kazdan (Indiana Univ. Math. J. 20 (1970), 683-693) showed that the so-called tusk condition guarantees regularity for the heat equation. We generalize this result to the normalized $p\mspace{1mu}$-parabolic equation, and also obtain H\"older continuity. The tusk condition is a parabolic version of the exterior cone condition. We also obtain a sharp Petrovski criterion for the regularity of the latest moment of a domain. This criterion implies that the regularity of a boundary point is affected if one side of the equation is multiplied by a constant.
A new class of spaces with all finite powers Lindelof
2013
We consider a new class of open covers and classes of spaces defined from them, called "iota spaces". We explore their relationship with epsilon-spaces (that is, spaces having all finite powers Lindelof) and countable network weight. An example of a hereditarily epsilon-space whose square is not hereditarily Lindelof is provided.
The euro–dollar exchange rate and equity flows
2009
Abstract I examine equity flows between the US and the euro area and their impact on the euro–dollar exchange rate. I explain equity flows by examining the behavior of an international investor who maintains a minimum variance portfolio. An excess of euro area equity returns over US equity returns generates a flow of equity from the euro area to the US. The equity flow, the purchase of US equities by the euro-area residents, causes appreciation (depreciation) of the dollar (euro), while the purchase of euro area equities by US residents causes appreciation (depreciation) of the euro (dollar).
The Institutional Determinants of Private Equity Involvement in Business Groups The Case of Africa
2015
This study examines the governance attributes of post-IPO (initial public offering) retained ownership of private equity in business group constituent firms in contrast to their unaffiliated counterparts, in 202 newly listed firms in 22 emerging African economies. We adopt an actor centered institutional-theoretic perspective in rationalizing institutional voids and the advantages of maintained governance by both business angels (BA) and venture capital (VC) private equity. Our findings reveal private equity retain higher post-IPO ownership in business group constituents compared to unaffiliated firms and that this is inversely moderated in the context of improving institutional quality. Ou…