On the Well-Posedness and Long Time Behavior of the Hall-magnetohydrodynamics System

We study the incompressible Hall-MHD system, an important model in plasma physics akin to the Navier-Stokes equations, using harmonic analysis tools. Chapter \ref{intro} consists of an introduction of the Hall-MHD system and its derivation from a two-fluid Euler-Maxwell system, along with a review of the mathematical preliminaries. Chapter \ref{w} concerns the well-posedness of the Hall-MHD system. For completeness, a proof of the global-in-time existence of the Leray-Hopf type weak solutions is included. In addition, we include a proof of the regularity criterion in \cite{D1}, which is of particular interest as it highlights the dissipation wavenumbers formulated via Littlewood-Paley theory. We then exploit the regularizing effect of diffusion and use a classical fixed point theorem to prove local-in-time existence of solutions to the generalized Hall-MHD system in certain Besov spaces as well as global-in-time existence of solutions to the hyper-dissipative electron MHD equations for small initial data in critical Besov spaces. Long time behaviour of solutions to the Hall-MHD system is studied in Chapter \ref{l}. We reproduce the proof of algebraic decay of weak solutions to the fully dissipative Hall-MHD system in \cite{CS1}; we then present our study of strong solutions to the Hall-MHD systems with mere one diffusion featuring the Fourier splitting technique. Under certain moderate assumptions, we show that the magnetic energy decays to $0$ and the kinetic energy converges to a certain constant in the resistive inviscid case, while the opposite happens in the viscous non-resistive case. Inspired by \cite{CDK}, we study the long time behaviour of solutions to the Hall-MHD system from the viewpoint of the determining Fourier modes. Via Littlewood-Paley theory, we formulate the determining wavenumbers, which bounds the low frequencies essential to the long time behaviour of the solutions. The fact that the determining wavenumbers can be estimated in a certain average sense suggests that the Hall-MHD system has finite degrees of freedom in a certain sense

Accelerated Path-Following Iterative Shrinkage Thresholding Algorithm With Application to Semiparametric Graph Estimation

<p>We propose an accelerated path-following iterative shrinkage thresholding algorithm (APISTA) for solving high-dimensional sparse nonconvex learning problems. The main difference between APISTA and the path-following iterative shrinkage thresholding algorithm (PISTA) is that APISTA exploits an additional coordinate descent subroutine to boost the computational performance. Such a modification, though simple, has profound impact: APISTA not only enjoys the same theoretical guarantee as that of PISTA, that is, APISTA attains a linear rate of convergence to a unique sparse local optimum with good statistical properties, but also significantly outperforms PISTA in empirical benchmarks. As an application, we apply APISTA to solve a family of nonconvex optimization problems motivated by estimating sparse semiparametric graphical models. APISTA allows us to obtain new statistical recovery results that do not exist in the existing literature. Thorough numerical results are provided to back up our theory.</p

A Stereoselective Ring-Closing Glycosylation via Nonglycosylating Pathway

Two glycosyl partners were first coupled with as ester linkage, which upon reductive acetylation produced an α-acetoxy ether group. The subsequent activation with TfOH triggered the ring-closing process and provided the corresponding glycosidic bond in high β-selectivity without relying on neighboring group participation

Reactive Transport Mechanism for Organic Oxidation during Electrochemical Filtration: Mass-Transfer, Physical Adsorption, and Electron-Transfer

An electrochemical carbon nanotube (CNT) filter has been reported to be effective for the adsorptive removal and oxidation of aqueous organic compounds. Here, we complete a detailed investigation of the aqueous dye oxidation reactive transport mechanism during electrochemical filtration. Similar to batch electrolysis, mass transfer, physical adsorption, and electron transfer are found to be three primary steps in the overall electrochemical filtration organic oxidation mechanism. Mass transfer was quantitatively examined by chronoamperometry and normal pulse voltammetry and determined to be increased 6-fold during electrochemical filtration as compared to batch electrochemistry. Convection-enhanced mass transfer to the electrode surface is determined to be the primary factor for increased current density and organic oxidation during electrochemical filtration. Physical adsorption of the organics onto the CNTs was evaluated using temperature-dependent batch adsorption and electrochemical filtration experiments. The electrochemical filtration kinetics were observed to have a minor negative temperature-dependence. Electron transfer was examined by challenging the electrochemical filter with a range of increasing dye concentrations until the mass transfer and adsorption processes were saturated. Upon surface site saturation, the electron transfer rates were determined to be 8.5 × 10¹⁵, 6.3 × 10¹⁶, and 1.3 × 10¹⁷ e^– s^–1 m^–2 at anode potentials of 0.35, 0.77, and 1.50 V, respectively. The electron transfer mechanism was also investigated and direct electron transfer was determined to be the dominant methyl orange oxidation mechanism at all evaluated anode potentials with an increasing contribution from indirect oxidation processes at potentials ≥1.0 V. The anode potential dependent maximum electron transfer rate is also observed to be affected by the polarity of the organic charge indicating electromigration is also active. In summary, electrochemical filtration is advantageous as compared to batch electrolysis due to the liquid flow through the electrode resulting in convection-enhanced transfer of the target molecule to the electrode surface

Positive Semidefinite Rank-Based Correlation Matrix Estimation With Application to Semiparametric Graph Estimation

<div><p>Many statistical methods gain robustness and flexibility by sacrificing convenient computational structures. In this article, we illustrate this fundamental tradeoff by studying a semiparametric graph estimation problem in high dimensions. We explain how novel computational techniques help to solve this type of problem. In particular, we propose a nonparanormal neighborhood pursuit algorithm to estimate high-dimensional semiparametric graphical models with theoretical guarantees. Moreover, we provide an alternative view to analyze the tradeoff between computational efficiency and statistical error under a smoothing optimization framework. Though this article focuses on the problem of graph estimation, the proposed methodology is widely applicable to other problems with similar structures. We also report thorough experimental results on text, stock, and genomic datasets.</p></div

Bismuth-Doped Tin Oxide-Coated Carbon Nanotube Network: Improved Anode Stability and Efficiency for Flow-Through Organic Electrooxidation

In this study, a binder-free, porous, and conductive 3D carbon-nanotube (CNT) network uniformly coated with bismuth-doped tin oxide (BTO) nanoparticles was prepared via a simple electrosorption–hydrothermal method and utilized for the electrooxidative filtration of organics. The BTO-CNT nanocomposite was characterized by scanning electron microscopy, thermogravimetric analysis, transmission electron microscopy, X-ray photoelectron spectroscopy, linear sweep voltammetry, and Tafel analysis. The submonolayer BTO coating is composed of 3.9 ± 1.5 nm diameter nanoparticles (NPs). The oxygen-evolution potential of the BTO-CNT nanocomposite was determined to be 1.71 V (vs Ag/AgCl), which is 440 mV higher than an uncoated CNT anode. Anodic stability, characterized by CNT oxidative corrosion to form dissolved species, indicated that the BTO-CNT incurred negligible corrosion up to V_anode = 2.2 V, whereas the uncoated CNT was compromised at V_anode ≥ 1.4 V. The effect of metal oxide-nanoparticle coating on anodic performance was initially studied by oxalate oxidation followed by total organic carbon (TOC) and chemical oxygen demand (COD) analysis. The BTO-CNT displayed the best performance, with ∼98% oxalate oxidation (1.2 s filter residence time) and current efficiencies in the range of 32 to >99%. The BTO-CNT anode energy consumption was 25.7 kW h kgCOD^–1 at ∼93% TOC removal and 8.6 kW h kgCOD^–1 at ∼50% TOC removal, comparable to state-of-the-art oxalate oxidation processes (22.5–81.7 kW h kgCOD^–1). The improved reactivity, current efficiency, and energy consumption are attributed to the increased conductivity, oxygen-evolution potential, and stability of the BTO-CNT anode. The effectiveness and efficiency of the BTO-CNT anode as compared to the uncoated CNT was further investigated by the electrooxidative filtration of ethanol, methanol, formaldehyde, and formate, and it was determined to have TOC removals 2 to 8 times greater, mineralization current efficiencies 1.5 to 3.5 times greater, and energy consumption 4 to 5 times less than the uncoated CNT anode. Electrooxidation and anode passivation mechanisms are discussed

Physical interaction between mitochondrial p38β and MnSOD <i>in vivo</i>.

<p>(A) Cellular localization of p38β in neonatal rat cardiomyocytes. The white scale bar represents 25 μm. (B) Cellular localization of p38β in the left ventricle of the female mouse heart. The white scale bar represents 25 μm. (C) Immunoblotting of a cytosolic marker, PGM1, in the cytosolic fraction and of p38β and MnSOD in the mitochondrial fraction from OVX female heart, with Cox IV as a mitochondrial marker. (D) Immunoblotting of MnSOD in the p38β-immunoprecipitate and immunoblotting of p38β in the MnSOD-immunoprecipitate from the mitochondrial fractions in the OVX hearts of the indicated treatment groups. NS IgG, nonspecific IgG input. Lysate, unfractionated LV homogenate. DAPI, 4’,6-diamidino-2-phenylindole; PGM1, phosphoglucomutase-1; MnSOD, manganese superoxide dismutase; COX IV, cytochrome c oxidase subunit IV; E2, 17β-estradiol; IP, immunoprecipitation.</p

Titanium Dioxide-Coated Carbon Nanotube Network Filter for Rapid and Effective Arsenic Sorption

In this study, a TiO₂-coated carbon nanotube (CNT) network filter was prepared via a simple filtration–steam hydrolysis method and evaluated with respect to aqueous arsenic removal. The TiO₂ coating was 5.5 ± 2.7 nm thick, completely covered the CNT network surface, and had a specific surface area of 196 m² g^–1, which was ∼2-fold greater than that of the CNT network. The TiO₂–CNT As sorption kinetics increased with both increasing flow rate and cell potential, with increasing flow rate having a significantly stronger effect. At 6 mL min^–1 in the absence of potential and in recirculation mode, the first-order As sorption rate constants were 4.3 and 4.4 s^–1 for As­(III) and As­(V), respectively. The TiO₂–CNT electro-assisted equilibrium sorption capacities at a cell potential of 2 V for effluent [As] = 10 ppb in single-pass mode were 1.8 and 1.3 mg g^–1 for As­(III) and As­(V), respectively. The enhanced TiO₂–CNT filter As sorption kinetics and capacity result from increased mass transport due to internal convection and pore radius range, improved sorption site accessibility due to porosity and TiO₂ dispersion, and reduced TiO₂ negative surface charge due to anodic capacitance. Groundwater samples containing 44 ppb As were treated by single-pass filtration, and 12500 bed volumes (residence time of 4.5 s; 127 L m^–2 h^–1; 5.8 mg m^–2 h^–1) were filtered prior to the effluent As level reaching >10 ppb. A spent TiO₂ filter was successfully regenerated by 5 mM NaOH for both As­(III) and As­(V)

The effect of E2 on myocardial infarct size, p38β activation and MnSOD expression.

<p>(A) Representative TTC staining of the heart sections in OVX mice with or without E2 supplementation. (B) The phosphorylation of p38β in the left ventricle of OVX mice with or without E2. (C) The protein level of MnSOD in the left ventricle of OVX mice with or without E2 supplementation.*<i>P</i><0.05 vs. Sham; ^† <i>P</i><0.05 vs. I/R; n = 3 in each group. E2, 17β-estradiol; I/R, ischemia/reperfusion; MnSOD, manganese superoxide dismutase.</p

The effect of E2 on the mitochondrial p38β activation and MnSOD activity.

<p>(A) Western blots and quantitative analysis of p-p38β and total p38β in mitochondria isolated from the left ventricle of the indicated treatment groups of OVX mice. (B) The protein level of MnSOD in mitochondria isolated from the left ventricle of the indicated treatment groups of OVX mice. (C) The activity of MnSOD in mitochondria isolated from the left ventricle of the indicated treatment groups of OVX mice.*<i>P</i><0.05 vs. Sham; ^† <i>P</i><0.05 vs. I/R; n = 3 in each group. E2, 17β-estradiol; I/R, ischemia/reperfusion; MnSOD, manganese superoxide dismutase, COX IV, cytochrome <i>c</i> oxidase subunit IV.</p