Cross-section and rate coefficient calculation for electron impact excitation, ionisation and dissociation of H2 and OH molecules

The weighted total cross-section (WTCS) theory is used to calculate electron impact excitation, ionisation and dissociation cross-sections and rate coefficients of OH, H₂, OH⁺, H₂ ⁺, OH^- and H₂ ^- diatomic molecules in the temperature range 1500–15000 K. Calculations are performed for H₂(X, B, C), OH(X, A, B), H₂ ⁺(X), OH⁺(X, a, A, b, c), H₂ ^-(X) and OH^-(X) electronic states for which Dunham coefficients are available. Rate coefficients are calculated from WTCS assuming Maxwellian energy distribution functions for electrons and heavy particles. One and two temperature (θ_e and θ_g respectively for electron and heavy particles kinetic temperatures) results are presented and fitting parameters (a, b and c) are given for each reaction rate coefficient: k(θ) = a (θ^b)exp (-c/θ).     

Elementary Operators and Completely Positive Linear Maps

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Generic pairs of SU-rank 1 structures

For a supersimple SU-rank 1 theory T we introduce the notion of a generic elementary pair of models of T (generic T-pair). We show that the theory T^* of all generic T-pairs is complete and supersimple. In the strongly minimal case, T^* coincides with the theory of infinite dimensional pairs, which was used in (S. Buechler, Pseudoprojective strongly minimal sets are locally projective, J. Symbolic Logic 56(4) (1991) 1184–1194) to study the geometric properties of T. In our SU-rank 1 setting, we use T^* for the same purpose. In particular, we obtain a characterization of linearity for SU-rank 1 structures by giving several equivalent conditions on T^*, find a “weak” version of local modularity which is equivalent to linearity, show that linearity coincides with 1-basedness, and use the generic pairs to “recover” projective geometries over division rings from non-trivial linear SU-rank 1 structures.     

What “counts” as algebra in the eyes of preservice elementary teachers?

This study examined conceptions of algebra held by 30 preservice elementary teachers. In addition to exploring participants’ general “definitions” of algebra, this study examined, in particular, their analyses of tasks designed to engage students in relational thinking or a deep understanding of the equal sign as well as student work on these tasks. Findings from this study suggest that preservice elementary teachers’ conceptions of algebra as subject matter are rather narrow. Most preservice teachers equated algebra with the manipulation of symbols. Very few identified other forms of reasoning - in particular, relational thinking - with the algebra label. Several participants made comments implying that student strategies that demonstrate traditional symbol manipulation might be valued more than those that demonstrate relational thinking, suggesting that what is viewed as algebra is what will be valued in the classroom. This possibility, along with implications for mathematics teacher education, will be discussed.     

A system architecture for parallel analysis of flux-balanced metabolic pathways

Elementary flux mode (EFM) analysis is a well-studied method in constraint-based modeling of metabolic networks. In EFM analysis, a network is decomposed into minimal functional pathways based on the assumption of balanced metabolic fluxes. In this paper, a system architecture is proposed that approximately models the functionality of metabolic networks. The AND/OR graph model is used to represent the metabolic network and each processing element in the system emulates the functionality of a metabolite. The system is implemented on a graphics processing unit (GPU) as the hardware platform using CUDA environment. The proposed architecture takes advantage of the inherent parallelism in the network structure in terms of both pathway and metabolite traversal. The function of each element is defined such that it can find flux-balanced pathways. Pathways in both small and large metabolic networks are applied to the proposed architecture and the results are discussed.     

Equation structure and the meaning of the equal sign: The impact of task selection in eliciting elementary students’ understandings

This paper reports results from a written assessment given to 290 third-, fourth-, and fifth-grade students prior to any instructional intervention. We share and discuss students’ responses to items addressing their understanding of equation structure and the meaning of the equal sign. We found that many students held an operational conception of the equal sign and had difficulty recognizing underlying structure in arithmetic equations. Some students, however, were able to recognize underlying structure on particular tasks. Our findings can inform early algebra efforts by highlighting the prevalence of the operational view and by identifying tasks that have the potential to help students begin to think about equations in a structural way at the very beginning of their early algebra experiences.     

How chemistry shifts horizons: element, substance, and the essential

In 1931 eminent chemist Fritz Paneth maintained that the modern notion of “element” is closely related to (and as “metaphysical” as) the concept of element used by the ancients (e.g., Aristotle). On that basis, the element chlorine (properly so-called) is not the elementary substance dichlorine, but rather chlorine as it is in carbon tetrachloride. The fact that pure chemicals are called “substances” in English (and closely related words are so used in other European languages) derives from philosophical compromises made by grammarians in the late Roman Empire (particularly Priscian [fl. ~520 CE]). When the main features of the constitution of isotopes became clear in the first half of the twentieth century, the formal (IUPAC) definition of a “chemical element” was changed. The features that are “essential” to being an element had previously been “transcendental” (“beyond the sphere of consciousness”) but, by the mid-twentieth century the defining characteristics of elements, as such, had come to be understood in detail. This amounts to a shift in a “horizon of invisibility” brought about by progress in chemistry and related sciences. Similarly, chemical insight is relevant to currently-open philosophical problems, such as the status of “the bundle theory” of the coherence of properties in concrete individuals.

On quotients of generalized Euclidean group rings

Let R = ?[C] be the integral group ring of a finite cyclic group C. Dennis et al. [4 Dennis, K., Magurn, B., Vaserstein, L. (1984). Generalized Euclidean group rings. J. Reine Angew. Math. 351:113–128.[Web of Science ®] , [Google Scholar]] proved that R is a generalized Euclidean ring in the sense of Cohn [3 Cohn, P. M. (1966). On the structure of the GL₂ of a ring. Inst. Hautes Études Sci. Publ. Math. 30:5–53.[Crossref] , [Google Scholar]], i.e., SL_n(R) is generated by the elementary matrices for all n. We prove that every proper quotient of R is also a generalized Euclidean ring.     

Pure patterns of order 2

We provide mutual elementary recursive order isomorphisms between classical ordinal notations, based on Skolem hulling, and notations from pure elementary patterns of resemblance of order 2, showing that the latter characterize the proof-theoretic ordinal $1^{\infty }$ of the fragment ${\mathrm{\Pi }}_1^1$–${\mathrm{CA}}_0$ of second order number theory, or equivalently the set theory $\mathrm{KP}{?}_0$. As a corollary, we prove that Carlson's result on the well-quasi orderedness of respecting forests of order 2 implies transfinite induction up to the ordinal $1^{\infty }$. We expect that our approach will facilitate analysis of more powerful systems of patterns.