Bivariate systems of polynomial equations with roots of high multiplicity

Given a bivariate system of polynomial equations with fixed support sets [Formula: see text] it is natural to ask which multiplicities its solutions can have. We prove that there exists a system with a solution of multiplicity [Formula: see text] for all [Formula: see text] in the range [Formula: see text], where [Formula: see text] is the set of all integral vectors that shift B to a subset of [Formula: see text]. As an application, we classify all pairs [Formula: see text] such that the system supported at [Formula: see text] does not have a solution of multiplicity higher than [Formula: see text].

Cartan Triples

We introduce the class of Cartan triples as a generalization of the notion of a Cartan MASA in a von Neumann algebra. We obtain a one-to-one correspondence between Cartan triples and certain Clifford extensions of inverse semigroups. Moreover, there is a spectral theorem describing bimodules in terms of their support sets in the fundamental inverse semigroup and, as a corollary, an extension of Aoi’s theorem to this setting. This context contains that of Fulman’s generalization of Cartan MASAs and we discuss his generalization in an appendix.

Supporting Special Education Teacher Induction Through High-Leverage Practices

Induction is designed to support teachers’ effectiveness, improve their students’ learning, and foster their retention. We consider how high-leverage practices (HLPs) might provide an instructional framework for special education teacher (SET) induction. With sensemaking theory as a conceptual foundation, we posit that, by structuring induction experiences and instructional conditions around HLPs, schools and districts can send more coherent messages about effective instruction, thereby easing new SETs’ efforts to make sense of their roles. We first provide a brief review of research on new SETs’ experiences. Next, we consider how specific induction components (i.e., professional development and mentoring, teacher evaluation, and collaboration) and instructional conditions (i.e., collaboration, instructional curricula and resources, and schedules) might be structured to support SETs’ learning of and use of these HLPs. We conclude with considerations for researchers and practitioners.

The Indian Origin of Romani people as a Founding Myth in Eastern European Museums

The article analyses three museums – the Muzeum Romské Kultury in Czech Republic, the Muzej Romské Kulture in Serbia, and the Roma Ethnographic Museum in Poland – can be considered as elements of the Romani Nationalism. The main objective is to reflect on how these museums support a broad narrative about a common Indian origin of Gypsy/Romani populations. It is discussed how the aforementioned museums – by means of their exhibitions, websites, events or other any kind of official production – support sets of representations which allow a formation of an umbrella rhetoric about the groups known, taken and self-ascribed as Gypsies and/or Roma. The said rhetoric, then, is able to shelter all different groups within this population in a holistic manner, based on a narrative formed by essentializations, exoticizations and generalizations. The utmost layer of such practices it is an elaboration of a founding myth of their Indian Origins. This paper understands throughout that museums have a role in the process in which the concept of Roma is generalized in an attempt to rewrite and relabel Gypsy memory as a Roma history. Hence, considering the plurality that characterise the Gypsy/Romani people, it was necessary to articulate common aspects – whether truthful or not, is not the target of this article to discuss – which would legitimise this new identity, a Roma identity. This paper relies on the theories about memory, museology, sociomuseology, and the theory of representations. Key-words: Gypsy/Roma; Museums; Indian Origins; Nationalism.

Computing Repairs of Inconsistent DL-Programs over EL Ontologies

Description Logic (DL) ontologies and non-monotonic rules are two prominent Knowledge Representation (KR) formalisms with complementary features that are essential for various applications. Nonmonotonic Description Logic (DL) programs combine these formalisms thus providing support for rule-based reasoning on top of DL ontologies using a well-defined query interface represented by so-called DL-atoms. Unfortunately, interaction of the rules and the ontology may incur inconsistencies such that a DL-program lacks answer sets (i.e., models), and thus yields no information. This issue is addressed by recently defined repair answer sets, for computing which an effective practical algorithm was proposed for DL-Lite A ontologies that reduces a repair computation to constraint matching based on so-called support sets. However, the algorithm exploits particular features of DL-Lite A and can not be readily applied to repairing DL-programs over other prominent DLs like EL. compared to DL-Lite A , in EL support sets may neither be small nor only few support sets might exist, and completeness of the algorithm may need to be given up when the support information is bounded. We thus provide an approach for computing repairs for DL-programs over EL ontologies based on partial (incomplete) support families. The latter are constructed using datalog query rewriting techniques as well as ontology approximation based on logical difference between EL-terminologies. We show how the maximal size and number of support sets for a given DL-atom can be estimated by analyzing the properties of a support hypergraph, which characterizes a relevant set of TBox axioms needed for query derivation. We present a declarative implementation of the repair approach and experimentally evaluate it on a set of benchmark problems; the promising results witness practical feasibility of our repair approach.