Looking Back in Mathematical Modeling: Classroom Observations and Instructional Strategies

Theorists often characterize modeling as a cyclic problem-solving process. One builds the model, assesses its validity with regard to the underlying problem situation, and revises accordingly. The process halts when, in the opinion of the modeler, the model generates a valid solution to the underlying problem. Recent research suggests that students, like experts, employ cyclic modeling processes. Extensive observations of university and high school students’ modeling efforts, however, suggest the use of linear rather than cyclic modeling strategies. That is, novice modelers often fail to look back or revise their initial models. This paper offers empirical evidence on behalf of the linear modeling theory and identifies five factors that promote the use of linear modeling strategies: students’ conceptions of models and the modeling process, the perceived objectives of the modeling activity, constraints on time and resources, statistical misconceptions, and an overall lack of interest. The paper concludes with several promising instructional strategies (strategies that address students’ difficulties and promote reflective modeling behavior), as well as suggestions for future research.     

Maximin share and minimax envy in fair-division problems

For fair-division or cake-cutting problems with value functions which are normalized positive measures (i.e., the values are probability measures) maximin-share and minimax-envy inequalities are derived for both continuous and discrete measures. The tools used include classical and recent basic convexity results, as well as ad hoc constructions. Examples are given to show that the envy-minimizing criterion is not Pareto optimal, even if the values are mutually absolutely continuous. In the discrete measure case, sufficient conditions are obtained to guarantee the existence of envy-free partitions.     

Comparison between biokinetics of inhaled plutonium nitrate and gadolinium oxide in humans and animals

Due to the paucity of human data after inhalation of different chemical forms of radionuclides, the implications for human exposure are often based on animal studies. This paper describes biokinetic studies of plutonium nitrate and gadolinium oxide in human volunteers and rats. The results, together with information from other studies with radionuclides, suggests that animal studies can be used with advantage for assessing the biokinetic behavior in humans, and for providing guidance on the assessment of intake and optimal monitoring regimens.     

Stable attachment of redox groups for modified electrodes via cyanuric chloride

Methylaminopropylviologen (MAV) was covalently attached to glassy carbon electrodes via cyuranic chloride. X-ray photoelectron spectroscopy (XPS) analysis confirmed the presence of bound MAV on the electrode surfaces. Electrochemical experiments of these electrodes indicated that the bound MAV was stable and electrochemically active for extended periods of time in aqueous media. The surface coverage of MAV was in the range, of 2.0–3.0×10^?10 mol cm^?2.     

A non-sulfide scheme of inorganic qualitative microanalysis

Summary A non-sulfide scheme of inorganic qualitative microanalysis is presented with solutions of HCl, CH₃COONa, H₂SO₄, and NaOH as group reagents. Color reactions (spot tests) are also included in this scheme. The purpose of this new approach to qualitative analysis is to eliminate disagreeable odor and corosive action of hydrogen sulfide as also to introduce complete group separations leading to more definite analytical results.

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Zusammenfassung Ein Schema für die qualitative anorganische Analyse ohne Schwefelwasserstoff mit Salzsäure, Na-Acetat, Schwefelsäure und Natronlauge als Gruppenreagenzien wird vorgelegt. Farbreaktionen (Tüpfelproben) werden im Laufe des Analysenganges verwendet. Die Geruchsbelästigung und die Korrosion durch Schwefelwasserstoff wird vermieden und gleichzeitig eine Gruppentrennung mit eindeutigeren Ergebnissen erzielt.

     

Vector two-point functions in maximally symmetric spaces

We obtain massive and massless vector two-point functions in maximally symmetric spaces (and vacua) of any number of dimensions. These include de Sitter space and anti-de Sitter space, and their Euclidean analogsS ⁿ andH ⁿ. Our method is based on a simple way of constructing every possible maximally symmetric bitensorT _a...bc...d(x, x) which carries tangent-space indicesa...b atx andc...d atx.     

Coherent effects in energy transport in model dendritic structures investigated by ultrafast fluorescence anisotropy spectroscopy

Measurements of ultrafast fluorescence anisotropy decay in model branched dendritic molecules of different symmetry are reported. These molecules contain the fundamental branching center units of larger dendrimer macromolecules with either three (C(3))- or four (T(d), tetrahedral)-fold symmetry. The anisotropy for a tetrahedral system is found to decay on a subpicosecond time scale (880 fs). This decay can be qualitatively explained by F?rster-type incoherent energy migration between chromophores. Alternatively, for a nitrogen-centered trimer system, the fluorescence anisotropy decay time (35 fs) is found to be much shorter than that of the tetramers, and the decay cannot be attributed to an incoherent hopping mechanism. In this case, a coherent interchromophore energy transport mechanism should be considered. The mechanism of the ultrafast energy migration process in the branched systems is interpreted by use of a phenomenological quantum mechanical model, which examines the two extreme cases of incoherent and coherent interactions.