Full ideals - Hong, J.; Lee, H.; Noh, S.; Rush, D.E. (Communications in Algebra, 2009)
Contractedness of m-primary integrally closed ideals played a central role in the development of Zariski's theory of integrally closed ideals in two-dimensional regular local rings (R, m). In such rings, the contracted m-primary ideals are known to be characterized by the property that I: m = I: x for some x ∈ m\m2. We call the ideals with this property full ideals and compare this class of ideals with the classes of m-full ideals, basically full ideals, and contracted ideals in higher dimensional regular local rings. The m-full ideals are easily seen to be full. In this article, we find a sufficient condition for a full ideal to be m-full. We also show the equivalence of the properties full, m-full, contracted, integrally closed, and normal, for the class of parameter ideals. We then find a sufficient condition for a basically full parameter ideal to be full. © Taylor & Francis Group, LLC.
6 citations (Crossref) [2023-10-31]
Keywords: Basically full ideal; Contracted ideal; Full ideal; Ideal with Rees property; Integrally closed ideal; dept.mat; m-Full ideal

Realistic reconfiguration of crystalline (and telecube) robots - Aloupis, Greg; Collette, Sebastien; Damian, Mirela; Demaine, Erik D; Elkhechen, Dania; Flatland, Robin; Langerman, Stefan; Orourke, Joseph; Pinciu, Val; Ramaswami, Suneeta; Sacristan, Vera; Wuhrer, Stefanie (International Workshop Algorithmic Foundations Robotics, 2009)
In this paper we propose novel algorithms for reconfiguring modular robots that are composed of n atoms. Each atom has the shape of a unit cube and can expand/contract each face by half a unit, as well as attach to or detach from faces of neighboring atoms. For universal reconfiguration, atoms must be arranged in 2×2×2 modules. We respect certain physical constraints: each atom reaches at most unit velocity and (via expansion) can displace at most one other atom. We require that one of the atoms can store a map of the target configuration. Our algorithms involve a total of O(n 2) such atom operations, which are performed in O(n) parallel steps. This improves on previous reconfiguration algorithms, which either use O(n 2) parallel steps [8,10,4] or do not respect the constraints mentioned above [1]. In fact, in the setting considered, our algorithms are optimal, in the sense that certain reconfigurations require Ω(n) parallel steps. A further advantage of our algorithms is that reconfiguration can take place within the union of the source and target configurations. © 2009 Springer-Verlag.
5 citations (Crossref) [2023-10-31] tex.type: Proceedings paper
Keywords: Algorithms; Atoms; Novel algorithm; Physical constraints; Reconfiguration algorithm; Robotics; Robots; Target configurations; dept.mat

The signature of the chern coefficients of local rings - Ghezzi, Laura; Hong, Jooyoun; Vasconcelos, Wolmer V (Mathematical Research Letters, 2009)
This paper considers the following conjecture: If R is an unmixed, equidimensionallocal ring that is a homomorphic image of a Cohen-Macaulay local ring, then for any ideal J generated by a system of parameters, the Chern coefficient e1(J) < 0 is equivalent to R being non Cohen-Macaulay. The conjecture is established if R is a homomorphic image of a Gorenstein ring, and for all universally catenary integral domains containing fields. Criteria for the detection of Cohen-Macaulayness in equi-generated graded modules are derived. © International Press 2009.
Citation Key Alias: lens.org/088-471-109-905-772 tex.type: [object Object]
Keywords: dept.mat; ⚠️ Invalid DOI

Leveraging summative assessment for formative purposes. - Vaden-Goad, Robert E (College Teaching, 2009)
The problem of motivation has received a great deal of attention, and many successful approaches have been developed. However, in areas such as introductory college mathematics, students often question their own potential for success. At the first sign of trouble, their fears are confirmed and many of them drop out, formally or informally. If a method could be found to improve persistence, motivational techniques would have an opportunity to succeed. In this article, the author describes a simple method to improve persistence using assessments that are normally already in place. Data are presented indicating that the method improves persistence and achievement. © 2009, Copyright Taylor & Francis Group, LLC.
4 citations (Crossref) [2023-10-31] Citation Key Alias: lens.org/110-474-222-109-603 tex.type: [object Object]
Keywords: classroom assessment; dept.mat; mathematics