Comments on The Co-emergence of Machine Techniques, Paper-and-Pencil Techniques, and Theoretical Reflection

We comment on the paper The co-emergence of machine techniques, paper-and-pencil techniques, and theoretical reflection: A study of CAS use in secondary school algebra by Carolyn Kieran and Paul Drijvers. We look at aspects of Kieran and Drijvers' analysis with regard to ‚task-technique-theory’ in the light of a model of abstraction in context and suggest that this re-viewing brings mutual analytic benefits.     

Crystal structure of 3,3-dichloro-N-p-methoxyphenyl-4-(2-phenylstryl)-2-azetidinone.

3,3-Dichloro-N-p-methoxyphenyl-4-(2-phenylstryl)-2-azetidinone (C22H15Cl2NO2) was studied by X-Ray analysis, which indicated a monoclinic space group, P2(1)/c, with a = 9.619(5), b = 13.879(4), c = 14.161(5)A, beta = 100.16(3)degrees, V = 1860.8(13)A3, Z = 4, Dc = 1.414 g cm(-3), micro(Mo Kalpha) = 0.366 mm(-1) and F000 = 816. The structure was solved by direct methods and refined to R = 0.041 for 4026 reflections [I > 2sigma(I). The beta-lactam ring (2-azetidinone) has antimicrobial affects. The substituents of the methoxyphenyl and phenyl substituents do not change the activity property of the beta-lactam ring, and the activity properties depend on the planarity of the beta-lactam ring.     

Non-linear vibrations of a simple-simple beam with a non-ideal support in between

A simply supported Euler-Bernoulli beam with an intermediate support is considered. Non-linear terms due to immovable end conditions leading to stretching of the beam are included in the equations of motion. The concept of non-ideal boundary conditions is applied to the beam problem. In accordance, the intermediate support is assumed to allow small deflections. An approximate analytical solution of the problem is found using the method of multiple scales, a perturbation technique. Ideal and non-ideal frequencies as well as frequency-response curves are contrasted.     

Stream function finite element solution of Stokes flow with penalties

A finite element method for solution of the stream function formulation of Stokes flow is developed. The method involves complete cubic non-conforming (C⁰) triangular Hermite elements. This element fails the patch test. To correct the element and produce a convergent method we employ a penalty method to weakly enforce the desired continuity constraint on the normal derivative across the inter-element boundaries. Successful use of the method is demonstrated to require reduced integration of the inter-element penalty with a 1-point Gauss rule. Error estimates relate the optimal choice of penalty parameter to mesh size and are corroborated by numerical convergence studies. The need for reduced integration is interpreted using rank relations for an associated hybrid method.     

Approximate renormalization group calculation of cubic crossover

The cross-over exponent for an anisotropic cubic perturbation is calculated for all n > 1 and d = 3. It is found that the isotropic fixed point is unstable for $\text{n ? 2.3}$.     

Temperature effect on the partition and dimerization constant of benzoic acid

Making use of the regular solution theory with binary coefficients, the partition of benzole acid between aqueous benzene phases was investigated. ΔH, ΔS and ΔG thermodynamic functions associated with the hydration-corrected partition and dimerization were calculated. It was found that the partition was spontaneous at high temperatures and of the hydrates of benzoic acid, the monohydrate monomer was dominant at high temperatures.     

Light charged particle emission and fission in238U+238U collisions at 1,740 MeV

Inclusive⁴He and⁴H energy spectra and heavy fragment coincidence correlations have been measured for reactions of 7.31 MeV/u²³⁸U with²³⁸U and^?197Au targets. The H/He production cross sections are in the range 15–26 mb, and their emission spectra are very similar for the two systems. The observed strong kinematic shifts with angle are reproduced in shape and magnitude by Monte Carlo simulations of particle evaporation from projectile-like and target-like fragments, indicating competition between charged particle emission and sequential fission. No evidence is found for high energy charged particle emission associated with ultra-highZ composite systems. Heavy fragment measurements indicate an abundance of quasielastic and deeply inelastic reaction fragments, as well as sequential fission of target and projectile nuclei. For²³⁸U nuclei, the fission occurs predominantly in an asymmetric mode, reminiscent of fission at low excitation energy. For²³⁸+²³⁸U reactions in the vicinity of the grazing angle, the frequency of single sequential fission (with survival of the partner fragment) is twice as large as double sequential fission in which both the target and projectile undergo fission. In²³⁸U+¹⁹⁷Au reactions, the survival probability of the heavy fragments is even greater. The surprisingly high survival probabilities of high-Z fragments imply a preponderance of very soft collisions in these very-heavy-ion reactions, at least at energies not very far over the Coulomb barrier.     

Experimental vibrational spectra (Raman,infrared) and DFT calculations on monomeric and dimeric structures of 2‐ and 6‐bromonicotinic acid

In this work, the Fourier transform infrared and Raman spectra of 2‐bromonicotinic acid and 6‐bromonicotinic acid (abbreviated as 2‐BrNA and 6‐BrNA, C₆H₄BrNO₂) have been recorded in the region 4000–400 and 3500–50 cm⁻¹. The optimum molecular geometry, normal mode wavenumbers, infrared intensities and Raman scattering activities, corresponding vibrational assignments and intermolecular hydrogen bonds were investigated with the help of B3LYP density functional theory (DFT) method using 6‐311++G(d,p) basis set. Reliable vibrational assignments were made on the basis of total energy distribution (TED) calculated with scaled quantum mechanical (SQM) method. From the calculations, the molecules are predicted to exist predominantly as the C1 conformer. Copyright © 2009 John Wiley & Sons, Ltd.