Reviewing Integrated Science and Mathematics: The Search for Evidence and Definitions From New Perspectives

Based upon current research needs indicated from recent literature reviews, this integrative review concentrates on two of the perceived major impediments to integrating science and mathematics: The lack of evidence to support integration and the lack of a definition for integration. Using mixed methodology, this review found quantitative evidence favoring integration from a meta-analysis of 31 studies of student achievement, qualitative evidence revealing the existence of multiple forms of integration, and historical evidence of publishing patterns from across the 20th century. The forms of integration were identified and defined; differential effects were identified both between forms and between science and mathematics when the forms were analyzed by effect size. Additional research implications and suggestions for future research were also identified.     

Kinetic study of the reaction of chlorine atoms with CF3I and the reactions of CF3 radicals with O2, Cl2 and NO at 296 K

The kinetics of the gas-phase reaction of Cl atoms with CF₃I have been studied relative to the reaction of Cl atoms with CH₄ over the temperature range 271–363 K. Using k(Cl + CH₄) = 9.6 × 10^?12 exp(?2680/RT) cm³ molecule^?1 s^?1, we derive k(Cl + CF₃I) = 6.25 × 10^?11 exp(?2970/RT) in which E_a has units of cal mol^?1. CF₃ radicals are produced from the reaction of Cl with CF₃I in a yield which was indistinguishable from 100%. Other relative rate constant ratios measured at 296 K during these experiments were k(Cl + C₂F₅I)/k(Cl + CF₃I) = 11.0 ± 0.6 and k(Cl + C₂F₅I)/k(Cl + C₂H₅Cl) = 0.49 ± 0.02. The reaction of CF₃ radicals with Cl₂ was studied relative to that with O₂ at pressures from 4 to 700 torr of N₂ diluent. By using the published absolute rate constants for k(CF₃ + O₂) at 1–10 torr to calibrate the pressure dependence of these relative rate constants, values of the low- and high-pressure limiting rate constants have been determined at 296 K using a Troe expression: k₀(CF₃ + O₂) = (4.8 ± 1.2) × 10^?29 cm⁶ molecule^?2 s^?1; k_∞(CF₃ + O₂) = (3.95 ± 0.25) × 10^?12 cm³ molecule^?1 s^?1; F_c = 0.46. The value of the rate constant k(CF₃ + Cl₂) was determined to be (3.5 ± 0.4) × 10^?14 cm³ molecule^?1 s^?1 at 296 K. The reaction of Cl atoms with CF₃I is a convenient way to prepare CF₃ radicals for laboratory study. © 1995 John Wiley & Sons, Inc.     

Electromagnetic response of thin disks

Summary The electromagnetic response of a thin disk with finite conductivity in free space to an arbitrary sinusoidal primary magnetic field is solved through use of an orthogonal expansion in Bessel functions. The eddy currents induced in the disk and the secondary magnetic field are calculated for various locations of a dipole generating the primary field and for different values of the induction number. Numerical computation is done only in the final stages of the analysis so that little computing time is needed to obtain detailed results.

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Zusammenfassung Der elektromagnetische Effekt einer von einem beliebigen sinusförmigen magnetischen Feld angeregten dünnen Scheibe endlicher Leitfähigkeit im Vakuum wird beschrieben unter Benutzung einer orthogonalen Entwicklung in Besselsche Funktionen. In der Scheibe induzierte Wirbelströme und das sekundäre Magnetfeld werden für verschiedene Orte eines Dipols der das Primärfeld erzeugt, und für verschiedene Induktions-Koeffizienten berechnet. Numerische Berechnungen werden nur in der letzten Phase der Analyse durchgeführt, so daß nur wenig Rechenzeit benötigt wird um konkrete Ergebnisse zu erhalten.

     

Using steered molecular dynamics to study the interaction between ADP and the nucleotide-binding domain of yeast Hsp70 protein Ssa1

Genetics experiments have identified six mutations located in the subdomain IA (A17V, R23H, G32D, G32S, R34K, V372I) of Ssa1 that influence propagation of the yeast [PSI⁺] prion. However, the underlining molecular mechanisms of these mutations are still unclear. The six mutation sites are present in the IA subdomain of the nucleotide-binding domain (NBD). The ATPase subdomain IA is a critical mediator of inter-domain allostery in Hsp70 molecular chaperones, so the mutation and changes in this subdomain may influence the function of the substrate-binding domain. In addition, ADP release is a rate-limiting step of the ATPase cycle and dysregulation of the ATPase cycle influences the propagation of the yeast [PSI⁺] prion. In this work, steered molecular dynamics (SMD) simulations were performed to explore the interaction between ADP and NBD. Results suggest that during the SMD simulations, hydrophobic interactions are predominant and variations in the binding state of ADP within the mutants is a potential reason for in vivo effects on yeast [PSI⁺] prion propagation. Additionally, we identify the primary residues in the ATPase domain that directly constitute the main hydrophobic interaction network and directly influence the ADP interaction state with the NBD of Ssa1. Furthermore, this in silico analysis reaffirms the importance of previously experimentally-determined residues in the Hsp70 ATPase domain involved in ADP binding and also identifies new residues potentially involved in this process.     

On proofs of the general density theorem

We show that if is a compact manifold, then there is a residual subset of the set of homeomorphisms on with the property that if , then the periodic points of are dense in its chain recurrent set. This result was first announced in [4], but a flaw in that argument was noted in [1], where a different proof was given. It was recently noted in [5] that this new argument only serves to show that the density of periodic points in the chain recurrent set is generic in the closure of the set of diffeomorphisms. We show how to patch the original argument from [4] to prove the result.

     

Functional groups expressed as graphs extracted from the Laplacian of the electron density

The valence charge concentration shell, as determined by the Laplacian of the electron density, is used as a source of quantum topological graphs, called L‐graphs. A considerable number of such graphs are extracted from the ab initio wave functions of 31 molecules calculated at the B3LYP/6‐311+G(2d,p)//B3LYP/6‐311+G(2d,p) level, covering common functional groups in organic chemistry. We show how L‐graphs can be constructed from a largely transferable subgraph called atomic L‐graph. We investigate the topological stability of the L‐graphs as a function of the basis set. Reliable and consistent atomic L‐graphs are only obtained with basis sets of triple‐zeta quality or higher. The recurrence of invariant motifs or subgraphs in the L‐graphs enables the isolation of 16 atomic L‐graphs. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

NMR paramagnetic relaxation due to the S=5/2 complex, Fe(III)-(tetra-p-sulfonatophenyl)porphyrin: central role of the tetragonal fourth-order zero-field splitting interaction

The metalloporphyrins, Me-TSPP [Me=Cr(III), Mn(III), Mn(II), Fe(III), and TSPP=meso-(tetra-p-sulfonatophenyl)porphyrin], which possess electron spins S=3/2, 2, 5/2, and 5/2, respectively, comprise an important series of model systems for mechanistic studies of NMR paramagnetic relaxation enhancement (NMR-PRE). For these S>1/2 spin systems, the NMR-PRE depends critically on the detailed form of the zero-field splitting (zfs) tensor. We report the results of experimental and theoretical studies of the NMR relaxation mechanism associated with Fe(III)-TSPP, a spin 5/2 complex for which the overall zfs is relatively large (D approximately = 10 cm(-1)). A comparison of experimental data with spin dynamics simulations shows that the primary determinant of the shape of the magnetic relaxation dispersion profile of the water proton R1 is the tetragonal fourth-order component of the zfs tensor. The relaxation mechanism, which has not previously been described, is a consequence of zfs-induced mixing of the spin eigenfunctions of adjacent Kramers doublets. We have also investigated the magnetic-field dependence of electron-spin relaxation for S=5/2 in the presence of a large zfs, such as occurs in Fe(III)-TSPP. Calculations show that field dependence of this kind is suppressed in the vicinity of the zfs limit, in agreement with observation.     

Ru(II) and Os(II) nucleosides and oligonucleotides: synthesis and properties

A general and versatile method for the site-specific incorporation of polypyridine Ru(II) and Os(II) complexes into DNA oligonucleotides using solid-phase phosphoramidite chemistry is reported. Novel nucleosides containing a [(bpy)(2)M(3-ethynyl-1,10-phenanthroline)](2+) (M = Ru, Os) metal center covalently attached to the 5-position in 2'-deoxyuridine are synthesized, and their electrochemical as well as photophysical properties are studied. The Ru(II) nucleoside exhibits a rather long-lived excited state in phosphate buffer pH 7.0 (tau = 1.08 micros) associated with a relatively high emission quantum efficiency (phi = 0.051). The solvent dependence of the absorption and emission spectra is consistent with an emissive MLCT state where charge localization takes place on the extended heterocycle-linked phenanthroline. In contrast, the Os(II)-containing nucleoside is quite nonemissive in aqueous environment (tau = 0.027 micros, phi = 1 x 10(-4)). The metal-containing nucleosides are converted into their phosphoramidites and are utilized for the high-yield preparation of modified oligonucleotides. The novel oligonucleotides, characterized by absorption and emission spectroscopy, enzymatic digestion, and electrophoresis, form stable duplexes. Circular dichroism spectra confirm that the global conformation of the double helix is not altered by the presence of these polypyridyl complexes in the major groove. Metal-containing phosphoramidites with predetermined absolute configuration at the octahedral coordination center are synthesized and utilized for the synthesis of diasteromerically pure metal-containing DNA oligonucleotides. Emission spectroscopy suggests a higher protection of the Delta metal center from the bulk solvent and better accommodation within the major groove.     

Gas phase UV and IR absorption spectra of CxF2x+1CHO (x = 1-4)

The UV and IR spectra of C_xF_2x+1CHO (x = 1-4) were investigated using computational and experimental techniques. C_xF_2x+1CHO (x = 1-4) have broad UV absorption features centered at 300-310 nm. The maximum absorption cross-section increases significantly and shifts slightly to the red with increased length of the C_xF_2x+1 group: CF₃CHO, 3.10 × 10⁻²⁰ (300 nm); C₂F₅CHO, 6.25 × 10⁻²⁰ (308 nm); C₃F₇CHO, 8.96 × 10⁻²⁰ (309 nm); and C₄F₉CHO, 10.9 × 10⁻²⁰ (309 nm). IR spectra for C_xF_2x+1CHO were recorded, calculated, and assigned. Results are discussed with respect to the literature data and to the atmospheric fate of CxF2x+1CHO.