On Groups with Two Isomorphism Classes of Derived Subgroups

The structure of groups which have at most two isomorphism classes of derived subgroups (D-2-groups) is investigated. A complete description of D-2-groups is obtained in the case where the derived subgroup is finite: the solution leads an interesting number theoretic problem. In addition, detailed information is obtained about soluble D-2-groups, especially those with finite rank, where algebraic number fields play an important role. Also, detailed structural information about insoluble D-2-groups is found, and the locally free D-2-groups are characterized.

Teaching and aligning upper level mathematics classes to Michigan high school content expectations in an alternative education setting : approaches and issues

After teaching regular education secondary mathematics for seven years, I accepted a position in an alternative education high school. Over the next four years, the State of Michigan adopted new graduation requirements phasing in a mandate for all students to complete Geometry and Algebra 2 courses. Since many of my students were already struggling in Algebra 1, getting them through Geometry and Algebra 2 seemed like a daunting task. To better instruct my students, I wanted to know how other teachers in similar situations were addressing the new High School Content Expectations (HSCEs) in upper level mathematics. This study examines how thoroughly alternative education teachers in Michigan are addressing the HSCEs in their courses, what approaches they have found most effective, and what issues are preventing teachers and schools from successfully implementing the HSCEs. Twenty-six alternative high school educators completed an online survey that included a variety of questions regarding school characteristics, curriculum alignment, implementation approaches and issues. Follow-up phone interviews were conducted with four of these participants. The survey responses were used to categorize schools as successful, unsuccessful, and neutral schools in terms of meeting the HSCEs. Responses from schools in each category were compared to identify common approaches and issues among them and to identify significant differences between school groups. Data analysis showed that successful schools taught more of the HSCEs through a variety of instructional approaches, with an emphasis on varying the ways students learned the material. Individualized instruction was frequently mentioned by successful schools and was strikingly absent from unsuccessful school responses. The main obstacle to successful implementation of the HSCEs identified in the study was gaps in student knowledge. This caused pace of instruction to also be a significant issue. School representatives were fairly united against the belief that the Algebra 2 graduation requirement was appropriate for all alternative education students. Possible implications of these findings are discussed.

PARTITIONING THE BLOCKS OF A STEINER TRIPLE SYSTEM INTO PARTIAL PARALLEL CLASSES

Does there exist a Steiner Triple System on v points, whose blocks can be partitioned into partial parallel classes of size m, where m ≤ [v⁄3], m | b and b is the number of blocks of the STS(v)? We give the answer for 9 ≤ v ≤ 43. We also show that whenever 2|b, v ≡ 3 (mod 6) we can find an STS(v) whose blocks can be partitioned into partial parallel classes of size 2, and whenever 4|b , v ≡ 3 (mod 6), there exists an STS(v) whose blocks can be partitioned into partial parallel classes of size 4.

Family business: Multiple members of major phytohormone classes orchestrate plant stress responses

Low-molecular-weight compounds such as jasmonic, abscisic and salicylic acids are commonly thought to be regulators of plant stress responses. However, it is becoming clear that these molecules, often referred to as phytohormones, are only a part of bigger groups of compounds with biological activity. We propose that the concept of "hormone families" may help to better understand plant physiological responses by taking into account not only the alleged main regulators, but also their precursors, conjugates and catabolites. Novel approaches to profile potentially active compounds in plants are discussed.

Search for charged Higgs bosons through the violation of lepton universality in t art events using collision data at sqrts=7 TeV with the AT experiment

In several extensions of the Standard Model, the top quark can decay into a bottom quark and a light charged Higgs boson H+, t -> bH(+), in addition to the Standard Model decay t -> bW. Since W bosons decay to the three lepton generations equally, while H+ may predominantly decay into tau nu, charged Higgs bosons can be searched for using the violation of lepton universality in top quark decays. The analysis in this paper is based on 4.6 fb(-1) of proton-proton collision data at root s = 7 TeV collected by the ATLAS experiment at the Large Hadron Collider. Signatures containing leptons (e or mu) and/or a hadronically decaying tau (tau(had)) are used. Event yield ratios between e+ tau(had) and e + mu, as well as between mu + tau(had) and mu + e, final states are measured in the data and compared to predictions from simulations. This ratio-based method reduces the impact of systematic uncertainties in the analysis. No significant deviation from the Standard Model predictions is observed. With the assumption that the branching fraction B(H+ -> tau nu) is 100%, upper limits in the range 3.2%-4.4% can be placed on the branching fraction B(t -> bH(+)) for charged Higgs boson masses m(H+) in the range 90-140GeV. After combination with results from a search for charged Higgs bosons in t (t) over bar decays using the tau(had) + jets final state, upper limits on B(t -> bH(+)) can be set in the range 0.8%-3.4%, for m(H+) in the range 90-160GeV.