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

A Plane Rational Map with Chebyshev-like Dynamics

This paper concerns a specific rational map of two complex variables whose dynamics are closely related to those of the well known one variable Chebyshev map. The goal is to obtain a complete description of the dynamics of the map, something that is rarely possible for such examples and then go on to study dynamics of some nearby perturbations

Circular RNA 0000654 facilitates the growth of gastric cancer cells through absorbing microRNA-149-5p to up-regulate inhibin-beta A

Circular (circ) RNAs are differentially expressed in gastric cancer (GC) and participate in the biological growth of tumor cells. Given that, investigations were performed to unravel the function of circ_0000654 in GC. GC tissue and normal tissue specimens were obtained, in which circ_0000654, microRNA (miR)-149-5p, and inhibin-beta A (INHBA) levels were examined. GC cell line (BGC-823) was transfected to alter circ_0000654 and miR-149-5p expression, thereby observing cell malignancy. Stably-transfected BGC-823 cells were injected into nude mice to observe tumor growth in vivo. The interaction circ_0000654, miR-149-5p, and INHBA was validated. circ_0000654 and INHBA were up-regulated but miR-149-5p was down-regulated in GC. circ_0000654 absorbed miR-149-5p to target INHBA. Silencing circ_0000654inhibited the progress of GC cell biology. Oppositely, restoring circ_0000654 enhanced the growth of GC cells. Inhibiting miR-149-5p rescued down-regulated circ_0000654-induced anti-tumor effect on GC. circ_0000654 silence or miR-149-5p overexpression limited the growth of GC tumors in vivo. Obviously, circ_0000654 facilitates the growth of GC cells through absorbing miR-149-5p to up-regulate INHBA.</p

MicroRNA-886 suppresses osteosarcoma cell proliferation and its maturation is suppressed by long non-coding RNA OXCT1-AS1

This study aimed to investigate the roles of microRNA-886 (miR-886) and long non-coding RNA (lncRNA) OXCT1-AS1 in osteosarcoma (OS). We predicted that they might interact with each other. The expression of OXCT1-AS1 and miR-886 (mature and premature) in osteosarcoma and paired non-tumor tissues from 66 OS patients was negatively correlated. Overexpression and silencing assays showed that OXCT1-AS1 suppresses miR-886 maturation. RNA–RNA pulldown and subcellular fractionation assays demonstrated the direct interaction between OXCT1-AS1 and miR-886. BrdU proliferation assays revealed that OXCT1-AS1 promoted OS cell proliferation, and miR-886 reduced the enhancing effects of OXCT1-AS1 on OS cell proliferation. Western blot showed that OXCT1-AS1 had no effects on the levels of epithelial–mesenchymal transition biomarkers. Overall, OXCT1-AS1 suppresses miR-886 maturation to promote OS cell proliferation.</p

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

Kernel Meets Sieve: Post-Regularization Confidence Bands for Sparse Additive Model

We develop a novel procedure for constructing confidence bands for components of a sparse additive model. Our procedure is based on a new kernel-sieve hybrid estimator that combines two most popular nonparametric estimation methods in the literature, the kernel regression and the spline method, and is of interest in its own right. Existing methods for fitting sparse additive model are primarily based on sieve estimators, while the literature on confidence bands for nonparametric models are primarily based upon kernel or local polynomial estimators. Our kernel-sieve hybrid estimator combines the best of both worlds and allows us to provide a simple procedure for constructing confidence bands in high-dimensional sparse additive models. We prove that the confidence bands are asymptotically honest by studying approximation with a Gaussian process. Thorough numerical results on both synthetic data and real-world neuroscience data are provided to demonstrate the efficacy of the theory. Supplementary materials for this article are available online.</p

EFFECTS OF EXERCISE ON HUMAN ENERGY METABOLISM IN HIGH TEMPERATURE AND HIGH HUMIDITY ENVIRONMENT

ABSTRACT Introduction Many exercise enthusiasts have started participating in sports in the high-temperature environment in recent years due to the increasing popularity of these sports habits. However, their scientific studies still have a gap in their safety and effectiveness. Objective Measure the energy supply characteristics of fat and sugar oxidation during exercise in different high-temperature and humidity environments. Methods 20 healthy adult subjects were exposed to fixed-intensity exercise for 20 minutes at 30-33 oC, 20% relative humidity (RH), and 50% RH, respectively. Results Under the silent exposure condition, compared with RH 20% and RH 50% under high temperature, sugar oxidation was significantly increased (P</div

Aliskiren attenuates cardiac dysfunction by modulation of the mTOR and apoptosis pathways

Aliskiren (ALS) is well known for its antihypertensive properties. However, the potential underlying the molecular mechanism and the anti-hypertrophic effect of ALS have not yet been fully elucidated. The aim of the present study was to investigate the role of ALS in mammalian target of rapamycin (mTOR) and apoptosis signaling using in vivo and in vitro models of cardiac hypertrophy. A rat model of cardiac hypertrophy was induced by isoproterenol treatment (5 mg·kg-1·day-1) for 4 weeks, with or without ALS treatment at 20 mg·kg-1·day-1. The expression of hypertrophic, fibrotic, and apoptotic markers was determined by RT-qPCR. The protein expression of apoptotic markers mTOR and p-mTOR was assessed by western blot analysis. The proliferation of H9C2 cells was monitored using the MTS assay. Cell apoptosis was analyzed using flow cytometry. In vivo, isoproterenol-treated rats exhibited worse cardiac function, whereas ALS treatment reversed these dysfunctions, which were associated with changes in p-mTOR, Bcl-2, Bax, and cleaved caspase-3 expression, as well as the number of apoptotic cells. In vitro, H9C2 cardiomyocyte viability was significantly inhibited and cardiac hypertrophy was induced by Ang II administration, but ALS reversed Ang II-induced H9C2 cardiomyocyte hypertrophy and death. Furthermore, Ang II triggered the activation of the mTOR and apoptosis pathways in hypertrophic cardiomyocytes that were inhibited by ALS treatment. These results indicated that ALS alleviated cardiac hypertrophy through inhibition of the mTOR and apoptosis pathways in cardiomyocytes.</div