Educational Problems in Writing Chemical Formulae and Equations

The difficulties existing for many pupils in the areas of formulae and equations and the belief that many of these problems were due to maturity barriers, led to the inauguration of this study in 1970. A preliminary survey was made of the situation extant in 1970 concerning these topics. This revealed a very confused picture with wide variation of teacher approach. The most obvious problem was one of over-complexity in formulae and equations. Teachers were teaching with little or no regard for the developmental ideas of Piaget et al. This problem was investigated at school level by a test based on a Gagne net for the writing of formulae and by a questionnaire. This test was examined in depth and confirmed the indications gathered in the preliminary survey. Pupils did not appear to reason logically when writing formulae but rather committed certain common formulae to memory, and failure at one step in the thought process did not appear to affect performance in the next. The very high number of pupils unable to handle proportion (71%) calculations from equations (97%) was disturbing, (the problem may be purely mathematical,) and many pupils showed a lack of understanding of even the most basic principles e.g. nomenclature, formation,of ions. Pupils seemed able to cope with individual steps in e. g. formula writing, but could not handle all the material "en bloc" when it was presented in a very short time (2-3 months). This meant that overall performance was very poor (28% correct). A re-run of part of this test confirmed these results. The questionnaire revealed that pupils tended to underestimate the difficulty of many topics and that teachers were more consistent than them in their estimates of difficulty. The teaching order of the 'O' grade course in Chemistry was then examined in the light of the degree of complexity in formulae and equations needed for each section. A revised teaching order, which was basically 'organic first' was drawn up using the principle of gradual revelation of these topics. To evaluate this revised order a maturity study was set up, having both experimental and control groups. The progress of the groups was monitored by a series of short tests, the results of which, and the 1973 'O' grade examination in Chemistry were analysed. No significant differences were found, but following the revised order did not disadvantage pupils over those following the standard orders. In fact there was some evidence to show that the revised order had achieved for these pupils, a higher level of understanding on the more difficult topics, especially calculations from equations and the mole. They also were more consistent in their level of performance on writing formulae. A detailed analysis of the last test (an overall revision of the work) was carried out and showed the same problems as were evident in the Gagne study e. g. interpretation of nomenclature such as the difference between - IDE and - ITE compounds. Some topics appeared to be still beyond the majority of pupils e. g. (i) extrapolation from Na2CO3 to Na2SiO3 (12%) (ii) writing balanced equations (20%) (iii) calculations from equations (20%). However pupils did seem to grasp the mathematical rules for formulae writing reasonably competently. A similar questionnaire to that used in the first investigation revealed that in general the revised group found the course easier than the control groups and that pupils now overestimated the difficulty of those topics previously underestimated. A final survey in 1974 showed a situation on the one hand eased by the removal of a recall barrier in formula writing and on the other worsened by the choice of the correct level of complexity of formulae to be used in any questions being left to the pupil. Recommendations were made for lessening the amount of conceptually difficult material (Piaget Stage 3) in the 'O' grade syllabus and its replacement by work involving lower order skills, including purely practical ones

Global analysis by hidden symmetry

Hidden symmetry of a G'-space X is defined by an extension of the G'-action on X to that of a group G containing G' as a subgroup. In this setting, we study the relationship between the three objects: (A) global analysis on X by using representations of G (hidden symmetry); (B) global analysis on X by using representations of G'; (C) branching laws of representations of G when restricted to the subgroup G'. We explain a trick which transfers results for finite-dimensional representations in the compact setting to those for infinite-dimensional representations in the noncompact setting when $X_C$ is $G_C$-spherical. Applications to branching problems of unitary representations, and to spectral analysis on pseudo-Riemannian locally symmetric spaces are also discussed.Comment: Special volume in honor of Roger Howe on the occasion of his 70th birthda

Ultrafast control of inelastic tunneling in a double semiconductor quantum

In a semiconductor-based double quantum well (QW) coupled to a degree of freedom with an internal dynamics, we demonstrate that the electronic motion is controllable within femtoseconds by applying appropriately shaped electromagnetic pulses. In particular, we consider a pulse-driven AlxGa1-xAs based symmetric double QW coupled to uniformly distributed or localized vibrational modes and present analytical results for the lowest two levels. These predictions are assessed and generalized by full-fledged numerical simulations showing that localization and time-stabilization of the driven electron dynamics is indeed possible under the conditions identified here, even with a simultaneous excitations of vibrational modes.Comment: to be published in Appl.Phys.Let

Testing the Master Constraint Programme for Loop Quantum Gravity III. SL(2,R) Models

This is the third paper in our series of five in which we test the Master Constraint Programme for solving the Hamiltonian constraint in Loop Quantum Gravity. In this work we analyze models which, despite the fact that the phase space is finite dimensional, are much more complicated than in the second paper: These are systems with an SL(2,\Rl) gauge symmetry and the complications arise because non -- compact semisimple Lie groups are not amenable (have no finite translation invariant measure). This leads to severe obstacles in the refined algebraic quantization programme (group averaging) and we see a trace of that in the fact that the spectrum of the Master Constraint does not contain the point zero. However, the minimum of the spectrum is of order $\hbar^2$ which can be interpreted as a normal ordering constant arising from first class constraints (while second class systems lead to $\hbar$ normal ordering constants). The physical Hilbert space can then be be obtained after subtracting this normal ordering correction.Comment: 33 pages, no figure

(4,4) superfield supergravity

We present the N=4 superspace constraints for the two-dimensional (2d) off-shell (4,4) supergravity with the superfield strengths expressed in terms of a (4,4) twisted (scalar) multiplet TM-I, as well as the corresponding component results, in a form suitable for applications. The constraints are shown to be invariant under the N=4 super-Weyl transformations, whose N=4 superfield parameters form another twisted (scalar) multiplet TM-II. To solve the constraints, we propose the Ansatz which makes the N=4 superconformal flatness of the N=4 supergravity curved superspace manifest. The locally (4,4) supersymmetric TM-I matter couplings, with the potential terms resulting from spontaneous supersymmetry breaking, are constructed. We also find the full (4,4) superconformally invariant (improved) TM-II matter action. The latter can be extended to the (4,4) locally supersymmetric Liouville action which is suitable for describing (4,4) supersymmetric non-critical strings.Comment: 32 pages, LaTeX, revised version (one reference added, and one Appendix is reduced

Automatic Abstraction for Congruences

One approach to verifying bit-twiddling algorithms is to derive invariants between the bits that constitute the variables of a program. Such invariants can often be described with systems of congruences where in each equation $\vec{c} \cdot \vec{x} = d \mod m$, (unknown variable m)$is a power of two,$\vec{c}$is a vector of integer coefficients, and$\vec{x}$ is a vector of propositional variables (bits). Because of the low-level nature of these invariants and the large number of bits that are involved, it is important that the transfer functions can be derived automatically. We address this problem, showing how an analysis for bit-level congruence relationships can be decoupled into two parts: (1) a SAT-based abstraction (compilation) step which can be automated, and (2) an interpretation step that requires no SAT-solving. We exploit triangular matrix forms to derive transfer functions efficiently, even in the presence of large numbers of bits. Finally we propose program transformations that improve the analysis results

Impure Aspects of Supersymmetric Wilson Loops

We study a general class of supersymmetric Wilson loops operator in N = 4 super Yang-Mills theory, obtained as orbits of conformal transformations. These loops are the natural generalization of the familiar circular Wilson-Maldacena operator and their supersymmetric properties are encoded into a Killing spinor that is not pure. We present a systematic analysis of their scalar couplings and of the preserved supercharges, modulo the action of the global symmetry group, both in the compact and in the non-compact case. The quantum behavior of their expectation value is also addressed, in the simplest case of the Lissajous contours: explicit computations at weak-coupling, through Feynman diagrams expansion, and at strong-coupling, by means of AdS/CFT correspondence, suggest the possibility of an exact evaluation.Comment: 40 pages, 4 figure

Supersymmetric Quantum Corrections and Poisson-Lie T-Duality

The quantum actions of the (4,4) supersymmetric non-linear sigma model and its dual in the Abelian case are constructed by using the background superfield method. The propagators of the quantum superfield and its dual and the gauge fixing actions of the original and dual (4,4) supersymmetric sigma models are determined. On the other hand, the BRST transformations are used to obtain the quantum dual action of the (4,4) supersymmetric non-linear sigma model in the sense of Poisson-Lie T-dualityComment: 18 page

(Super)twistors and (super)strings

The Lagrangian formulation of the D=4 bosonic string and superstring in terms of the (super)twistors is considered. The (super)twistor form of the equations of motion is derived and the kappa-symmetry transformation for the supertwistors is given. It is shown that the covariant kappa-symmetry gauge fixation results in the action quadratic in the (super)twistor variables.Comment: LaTeX, 17 page

Pea3 Transcription Factors and Wnt1-Induced Mouse Mammary Neoplasia

The role of the PEA3 subfamily of Ets transcription factors in breast neoplasia is controversial. Although overexpression of PEA3 (E1AF/ETV4), and of the related factors ERM (ETV5) and ER81 (ETV1), have been observed in human and mouse breast tumors, PEA3 factors have also been ascribed a tumor suppressor function. Here, we utilized the MMTV/Wnt1 mouse strain to further interrogate the role of PEA3 transcription factors in mammary tumorigenesis based on our previous observation that Pea3 is highly expressed in MMTV/Wnt1 mammary tumors. Pea3 expression in mouse mammary tissues was visualized using a Pea3NLSlacZ reporter strain. In normal mammary glands, Pea3 expression is predominantly confined to myoepithelial cells. Wnt1 transgene expression induced marked amplification of this cell compartment in nontumorous mammary glands, accompanied by an apparent increase in Pea3 expression. The pattern of Pea3 expression in MMTV/Wnt1 mammary glands recapitulated the cellular profile of activated β-catenin/TCF signaling, which was visualized using both β-catenin immunohistochemistry and the β-catenin/TCF-responsive reporter Axin2NLSlacZ. To test the requirement for PEA3 factors in Wnt1-induced tumorigenesis, we employed a mammary-targeted dominant negative PEA3 transgene, ΔNPEA3En. Expression of ΔNPEA3En delayed early-onset tumor formation in MMTV/Wnt1 virgin females (P = 0.03), suggesting a requirement for PEA3 factor function for Wnt1-driven tumor formation. Consistent with this observation, expression of the ΔNPEA3En transgene was profoundly reduced in mammary tumors compared to nontumorous mammary glands from bigenic MMTV/Wnt1, MMTV/ΔNPEA3En mice (P = 0.01). Our data provide the first description of Wnt1-mediated expansion of the Pea3-expressing myoepithelial compartment in nontumorous mammary glands. Consistent with this observation, mammary myoepithelium was selectively responsive to Wnt1. Together these data suggest the MMTV/Wnt1 strain as a potential model of basal breast cancer. Furthermore, this study provides evidence for a protumorigenic role of PEA3 factors in breast neoplasia, and supports targeting the PEA3 transcription factor family in breast cancer