A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization

We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an inviscid regularization of the Euler equations known as the 3D Euler–Voigt equations, which are known to be globally well-posed. Moreover, simulations of the 3D Euler–Voigt equations also require less resolution than simulations of the 3D Euler equations for fixed values of the regularization parameter \(\alpha >0\). Therefore, the new blow-up criteria allow one to gain information about possible singularity formation in the 3D Euler equations indirectly, namely by simulating the better-behaved 3D Euler–Voigt equations. The new criteria are only known to be sufficient criterion for blow-up. Therefore, to test the robustness of the inviscid-regularization approach, we also investigate analogous criteria for blow-up of the 1D Burgers equation, where blow-up is well known to occur.     

Base-Pairing Properties of Double-Headed Nucleotides

Nucleotides that contain two nucleobases (double-headed nucleotides) have the potential to condense the information of two separate nucleotides into one. This presupposes that both bases must successfully pair with a cognate strand. Here, double-headed nucleotides that feature cytosine, guanine, thymine, adenine, hypoxanthine, and diaminopurine linked to the C2′-position of an arabinose scaffold were developed and examined in full detail. These monomeric units were efficiently prepared by convergent synthesis and incorporated into DNA oligonucleotides by means of the automated phosphoramidite method. Their pairing efficiency was assessed by UV-based melting-temperature analysis in several contexts and extensive molecular dynamics studies. Altogether, the results show that these double-headed nucleotides have a well-defined structure and invariably behave as functional dinucleotide mimics in DNA duplexes.     

Altered Lipid Composition of Secretory Cells Following Exposure to Zinc Can Be Correlated to Changes in Exocytosis

A micromolar concentration of zinc has been shown to significantly change the dynamics of exocytosis as well as the vesicle contents in a model cell line, providing direct evidence that zinc regulates neurotransmitter release. To provide insight into how zinc modulates these exocytotic processes, neurotransmitter release and vesicle content were compared with single cell amperometry and intracellular impact vesicle cytometry with a range of zinc concentrations. Additionally, time-of-flight secondary ion mass spectrometry (ToF-SIMS) images of lipid distributions in the cell membrane after zinc treatment correlate to changes in exocytosis. By combining electrochemical techniques and mass spectrometry imaging, we proposed a mechanism by which zinc changes the fusion pore and the rate of neurotransmitter release by changing lipid distributions and results in the modulation of synaptic strength and plasticity.     

Gapmer Antisense Oligonucleotides Containing 2′,3′-Dideoxy-2′-fluoro-3′-C-hydroxymethyl-β-d-lyxofuranosyl Nucleotides Display Site-Specific RNase H Cleavage and Induce Gene Silencing

Off-target effects remain a significant challenge in the therapeutic use of gapmer antisense oligonucleotides (AONs). Over the years various modifications have been synthesized and incorporated into AONs, however, precise control of RNase H-induced cleavage and target sequence selectivity has yet to be realized. Herein, the synthesis of the uracil and cytosine derivatives of a novel class of 2′-deoxy-2′-fluoro-3′-C-hydroxymethyl-β-d -lyxo-configured nucleotides has been accomplished and the target molecules have been incorporated into AONs. Experiments on exonuclease degradation showed improved nucleolytic stability relative to the unmodified control. Upon the introduction of one or two of the novel 2′-fluoro-3′-C-hydroxymethyl nucleotides as modifications in the gap region of a gapmer AON was associated with efficient RNase H-mediated cleavage of the RNA strand of the corresponding AON:RNA duplex. Notably, a tailored single cleavage event could be engineered depending on the positioning of a single modification. The effect of single mismatched base pairs was scanned along the full gap region demonstrating that the modification enables a remarkable specificity of RNase H cleavage. A cell-based model system was used to demonstrate the potential of gapmer AONs containing the novel modification to mediate gene silencing.     

Photoluminescence of Seven-Coordinate Zirconium and Hafnium Complexes with 2,2′-Pyridylpyrrolide Ligands

Luminescent seven-coordinated zirconium and hafnium complexes bearing three mono-anionic 2,2′-pyridylpyrrolide ligands and one chloride were synthesized. Solid-state structures and the dynamic behaviors in solution were probed by X-ray crystallography and variable temperature ¹H NMR experiments, respectively. Absorption spectroscopy and time-dependent density functional theory (TD-DFT) calculations supported a hybrid of ligand-to-metal charge transfer (LMCT)/ligand-to-ligand charge transfer (LLCT) for the visible light absorption band. The complexes (^MePMP^Me)₃MCl (M=Zr, Hf, ^MePMP^Me=3,5-dimethyl-2-(2-pyridyl)pyrrolide) are emissive in solution at room temperature upon irradiation with visible light due to a combination of phosphorescence and fluorescence characterized by excited state lifetimes in the μs and low to sub-ns timescale, respectively. Electrochemical experiments revealed that the zirconium complex possesses a reversible redox event under highly reducing condition (−2.29 V vs. Fc^+/0).     

Two Theorems on Convergence of Schrödinger Means

Journal of Fourier Analysis and Applications - Localization and convergence almost everywhere of Schrödinger means are studied.     

IR Tools: a MATLAB package of iterative regularization methods and large-scale test problems

Numerical Algorithms - This paper describes a new MATLAB software package of iterative regularization methods and test problems for large-scale linear inverse problems. The software package, called...