Non‐constructive Properties of the Real Numbers

We study the relationship between various properties of the real numbers and weak choice principles.     

On the incremental singular value decomposition method to support unsteady adjoint-based optimization

This paper proposes and evaluates an approximation model based on an incremental Singular Value Decomposition (iSVD) algorithm, for unsteady flow field reconstructions, needed for integrating the unsteady adjoint equations backward in time, within a gradient-based optimization loop. Due to the iSVD algorithm, the computational cost of solving the unsteady adjoint equations is reduced considerably, without practically affecting the accuracy of the computed gradient. Approximations to the unsteady flow fields are constructed while solving the time-varying flow equations (moving forward in time) and used to reconstruct these fields during the backward-in-time integration of the continuous adjoint equations. Optimization results obtained using the proposed method are compared to those computed using the binomial checkpointing technique, which acts as the reference method. Test cases for both flow control and shape optimization problems are presented.     

Compact and Loeb Hausdorff spaces in \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathsf {ZF}$\end{document} and the axiom of choice for families of finite sets

Given a set X, $\mathsf {AC}^{\mathrm{fin}(X)}$ denotes the statement: “$[X]^{<\omega }\backslash \lbrace \varnothing \rbrace$ has a choice set” and $\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )$ denotes the family of all closed subsets of the topological space $\mathbf {2}^{X}$ whose definition depends on a finite subset of X. We study the interrelations between the statements $\mathsf {AC}^{\mathrm{fin}(X)},$ $\mathsf {AC}^{\mathrm{fin}([X]^{<\omega })},$ $\mathsf {AC}^{\mathrm{fin} (F_{n}(X,2))},$ $\mathsf {AC}^{\mathrm{fin}(\mathcal {\wp }(X))}$ and “$\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$has a choice set”. We show:

• (i) $\mathsf {AC}^{\mathrm{fin}(X)}$ iff $\mathsf {AC}^{\mathrm{fin}([X]^{<\omega } )}$ iff $\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$ has a choice set iff $\mathsf {AC}^{\mathrm{fin}(F_{n}(X,2))}$.
• (ii) $\mathsf {AC}_{\mathrm{fin}}$ ($\mathsf {AC}$ restricted to families of finite sets) iff for every set X, $\mathcal {C}_\mathrm{R}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$ has a choice set.
• (iii) $\mathsf {AC}_{\mathrm{fin}}$ does not imply “$\mathcal {K}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$ has a choice set($\mathcal {K}(\mathbf {X})$ is the family of all closed subsets of the space $\mathbf {X}$)
• (iv) $\mathcal {K}(\mathbf {2}^{X})\backslash \lbrace \varnothing \rbrace$ implies $\mathsf {AC}^{\mathrm{fin}(\mathcal {\wp }(X))}$ but $\mathsf {AC}^{\mathrm{fin}(X)}$ does not imply $\mathsf {AC}^{\mathrm{fin}(\mathcal {\wp }(X))}$.

We also show that “For every setX, “$\mathcal {K}\big (\mathbf {2}^{X}\big )\backslash \lbrace \varnothing \rbrace$has a choice set” iff “for every setX, $\mathcal {K}\big (\mathbf {[0,1]}^{X}\big )\backslash \lbrace \varnothing \rbrace$has a choice set” iff “for every product$\mathbf {X}$of finite discrete spaces,$\mathcal {K}(\mathbf {X})\backslash \lbrace \varnothing \rbrace$ has a choice set”.     

N@C60-porphyrin: a dyad of two radical centers

Dyads of endohedral nitrogen fullerene and porphyrin have been synthesized. In the two-radical-center dyad, the copper(II) tetraphenylporphyrin suppressed the electron spin resonance (ESR) signal of N@C(60) through intramolecular dipolar coupling with a strength of 27.0 MHz. Demetalation of the metalloporphyrin moiety of the dyad, which effectively turned the two-radical-center dyad into a single-radical-center dyad, recovered 82% of the ESR signal of N@C(60). Such mechanism of switching a spin state on and off could find use in molecular spintronics applications.     

Cationic liposomes in double emulsions for controlled release

In this paper, we report a facile way to fabricate biomimetic high performance optical hybrid films with excellent antireflective and antifogging properties by one-step spin-coating the mixture of mesoporous SiO(2) particles and SiO(2) sol. The production process of the films is easy, low-cost, and time-efficient. Mesoporous SiO(2) particles containing surfactants disperse in SiO(2) sol stably without any chemical modification, which decrease the effective refractive index and increase the transmittance of the films. In addition, such films possess superhydrophilic properties and exhibit high performance antifogging properties. Due to the good film forming performance of SiO(2) sol, mesoporous SiO(2) particles are embedded in the films and impart the films high mechanical stability and durability. The surface morphology of the films can maintain well after repeated friction, and the performances of antireflective and antifogging also do not change as well.     

CO2 selectivity of a 1D microporous adenine-based metal-organic framework synthesised in water

The coordination of adenine to Ni(2+) forms a dimer unit which can be linked by 3,5-pyrazoledicarboxylic acid into chains which assemble under hydrothermal conditions via hydrogen bonding into a robust porous network. The material displays selectivity for CO(2) over CH(4) and an isosteric heat which increases with guest loading.     

Elastic properties of the Ta–V system: bcc Ta0.33V0.67 and C15 TaV2

Resonant ultrasound spectroscopy was used to measure the elastic constants of bcc Ta_0.33V_0.67 over the temperature range 3.5–300?K; the results were compared to earlier measurements on C15 TaV₂. The temperature dependence of the polycrystalline shear modulus is completely different in the two phases; that of the bcc phase decreases with temperature whereas that of the C15 phases increases in an anomalous fashion. This difference is consistent with a model involving doubly-degenerate levels at the X point of the Brillouin zone in the C15 phase with the Fermi level lying near the doubly degenerate level. This model accounted for the unusual behaviour of the C15 phase. Debye temperatures were determined from the ultrasonic measurements: 295?K for the C15 phase and 315?K for the bcc phase.