Analytic structure of solutions to multiconfiguration equations

We study the regularity at the positions of the (fixed) nuclei of solutions to (non-relativistic) multiconfiguration equations (including Hartree--Fock) of Coulomb systems. We prove the following: Let {phi_1,...,phi_M} be any solution to the rank--M multiconfiguration equations for a molecule with L fixed nuclei at R_1,...,R_L in R^3. Then, for any j in {1,...,M} and k in {1,...,L}, there exists a neighbourhood U_{j,k} in R^3 of R_k, and functions phi^{(1)}_{j,k}, phi^{(2)}_{j,k}, real analytic in U_{j,k}, such that phi_j(x) = phi^{(1)}_{j,k}(x) + |x - R_k| phi^{(2)}_{j,k}(x), x in U_{j,k} A similar result holds for the corresponding electron density. The proof uses the Kustaanheimo--Stiefel transformation, as applied earlier by the authors to the study of the eigenfunctions of the Schr"odinger operator of atoms and molecules near two-particle coalescence points.Comment: 15 page

New exercise-integrated technology can monitor the dosage and quality of exercise performed against an elastic resistance band by adolescents with patellofemoral pain:an observational study

Question: Is the exercise-integrated Bandcizer™ system feasible for recording exercise dosage (time under tension (TUT) and repetitions) and pain scores among adolescents with patellofemoral pain? Do adolescents practise the exercises as prescribed (TUT and repetitions)? Do adolescents accurately report the exercises they do in an exercise diary? Design: Observational feasibility study. Participants: Twenty adolescents between 15 and 19 years of age with patellofemoral pain. Intervention: Participants were prescribed three exercise sessions per week (one with and two without supervision) for 6 weeks. The exercises included three hip and one knee exercise with an elastic resistance band. Participants were instructed to perform three sets with a predefined TUT (3 seconds concentric; 2 seconds isometric; 3 seconds eccentric; 2 seconds pause), equating to 80 seconds for 10 repetitions (one set). Outcome measures: The exercise-integrated system consisted of a sensor attached to the elastic resistance band that was connected to the Bandtrainer app on an electronic tablet device. Pain intensity was reported on a visual analogue scale on the app. Participants also completed a self-report exercise diary. Results: No major problems were reported with the system. Participants performed 2541 exercise sets during the 6 weeks; 5% were performed with the predefined TUT (ie, within 10 seconds of the 80-second target) and 90% were performed below the target TUT. On average, the participants received 15% of the instructed exercise dosage based on TUT. The exercise dosage reported in the exercise diaries was 2.3 times higher than the TUT data from the electronic system. Pain intensity was successfully collected in 100% of the exercise sets. Conclusion: The system was feasible for adolescents with patellofemoral pain. The system made it possible to capture detailed data about the TUT, repetitions and sets during home-based exercises together with pain intensity before and after each exercise. [Rathleff MS, Bandholm T, McGirr KA, Harring SI, Sørensen AS, Thorborg K (2016) New exercise-integrated technology can monitor the dosage and quality of exercise performed against an elastic resistance band by adolescents with patellofemoral pain: an observational study. Journal of Physiotherapy 62: 159–163

Resonating Valence Bond Theory of Coupled Heisenberg Chains

Using numerical results from a density matrix renormalization group study as a guide, we develop a resonating valence bond (RVB) theory for coupled Heisenberg chains. We argue that simple topological effects mandate a short-range RVB description of systems with an even number of chains $n_c$, with a spin gap, short-range correlations, and confinement of topological spin defects. Odd-$n_c$ systems have long-range RVB ground states, no gap, and power-law correlations.Comment: 11 pages and 6 postscript figures, RevTeX 3.0, UCI-CMTHE-94-02 (Revised version

Using remote substituents to control solution structure and anion binding in lanthanide complexes.

A study of the anion-binding properties of three structurally related lanthanide complexes, which all contain chemically identical anion-binding motifs, has revealed dramatic differences in their anion affinity. These arise as a consequence of changes in the substitution pattern on the periphery of the molecule, at a substantial distance from the binding pocket. Herein, we explore these remote substituent effects and explain the observed behaviour through discussion of the way in which remote substituents can influence and control the global structure of a molecule through their demands upon conformational space. Peripheral modifications to a binuclear lanthanide motif derived from α,α′-bis(DO3 Ayl)-m-xylene are shown to result in dramatic changes to the binding constant for isophthalate. In this system, the parent compound displays considerable conformational flexibility, yet can be assumed to bind to isophthalate through a well-defined conformer. Addition of steric bulk remote from the binding site restricts conformational mobility, giving rise to an increase in binding constant on entropic grounds as long as the ideal binding conformation is not excluded from the available range of conformers

Nanoparticle metrology of silica colloids and super-resolution studies using the ADOTA fluorophore

We describe how a new fluorescent dye, methyl ADOTA (N-methyl-azadioxatriangulenium tetrafluoroborate), is an improvement on dyes reported previously for measuring silica nanoparticle size in sols using the decay of fluorescence anisotropy. Me(thyl)-ADOTA possesses the unusual combination of having a red emission and a long fluorescence lifetime of ~ 20 ns, leaving it better-placed to reveal particle sizes at the upper end of the 1-10 nm measurement range. For stable LUDOX colloids, Me-ADOTA is shown to offer higher measurement precision in ≤ 1/30th of the measurement time required for dyes previously used. In measurement times of only ~ 20 mins nanoparticle radii for LUDOX SM-AS, AM and AS-40 of 4.6 ± 0.3 nm, 5.9 ± 0.2 nm and 11.1 ± 1.1 nm, are in good agreement with two of the manufacturer’s values of 3.5 nm, 6 nm and 11 nm respectively. Unlike the Si-ADOTA (N-(4-(triethoxysilylethyl)urea-phenyl-) ADOTA tetrafluoroborate) derivative containing a reactive trimetoxysilane group, Me-ADOTA is shown to not induce aggregation of colloidal silica. Measurements on nanoparticles growing in an acidic silica hydrogel at pH 0.94, prior to the gel time of ~ 50 hr, reveals an average nanoparticle size up to ~ 6.3 nm, significantly larger than the 4.5 nm reported previously. The difference is most certainly due to the longer fluorescence lifetime of Me-ADOTA (~ 20 ns) revealing the presence of larger particles. Studies of growing silica clusters in an alcogel of tetraethyl orthosilicate (TEOS) were able to resolve a monotonically increasing average radius of 1.42 ± 0.10 nm to 1.81 ± 0.14 nm over a period of 48 hr. We have also assessed a carboxylic acid derivative of ADOTA (N-(3-carboxypropylene)-ADOTA tetrafluoroborate - Acid-ADOTA) using dSTORM super-resolution microscopy. Although demonstrating high photochemical stability and blinking, its lower brightness and relative propensity to aggregate limits Acid-ADOTA’s use for dSTORM