Stable blow-up dynamics in the -critical and -supercritical generalized Hartree equation

We study stable blow-up dynamics in the generalized Hartree equation with radial symmetry, which is a Schrödinger-type equation with a nonlocal, convolution-type nonlinearity: First, we consider the -critical case in dimensions and obtain that a generic blow-up has a self-similar structure and exhibits not only the square root blowup rate , but also the log-log correction (via asymptotic analysis and functional fitting), thus, behaving similarly to the stable blow-up regime in the -critical nonlinear Schrödinger equation. In this setting, we also study blow-up profiles and show that generic blow-up solutions converge to the rescaled , a ground state solution of the elliptic equation . We also consider the -supercritical case in dimensions . We derive the profile equation for the self-similar blow-up and establish the existence and local uniqueness of its solutions. As in the NLS -supercritical regime, the profile equation exhibits branches of nonoscillating, polynomially decaying (multi-bump) solutions. A numerical scheme of putting constraints into solving the corresponding ordinary differential equation is applied during the process of finding the multi-bump solutions. Direct numerical simulation of solutions to the generalized Hartree equation by the dynamic rescaling method indicates that the is the profile for the stable blow-up. In this supercritical case, we obtain the blow-up rate without any correction. This blow-up happens at the focusing level , and thus, numerically observable (unlike the -critical case). In summary, we find that the results are similar to the behavior of stable self-similar blowup solutions in the corresponding settings for the nonlinear Schrödinger equation. Consequently, one may expect that the form of the nonlinearity in the Schrödinger-type equations is not essential in the stable formation of singularities.     

Elucidating the Nature of the External Acid Sites of ZSM-5 Zeolites Using NMR Probe Molecules

The identification of acid and nonacid species at the external surface of zeolites remains a major challenge, in contrast to the extensively-studied internal acid sites. Here, it is shown that the synthesis of zeolite ZSM-5 samples with distinct particle sizes, combined with solid-state NMR and computational studies of trimethylphosphine oxide (TMPO) adsorption, provides insight into the chemical species on the external surface of the zeolite crystals. ¹H–³¹P HETCOR NMR spectra of TMPO-loaded zeolites exhibit a broad correlation peak at δ_P ∼35–55 ppm and δ_H ∼5–12 ppm assigned to external SiOH species. Pore-mouth Brønsted acid sites exhibit ³¹P and ¹H NMR resonances and adsorption energies close to those reported for internal acid sites interacting with TMPO. The presence of an external tricoordinate Al-Lewis site interacting strongly with TMPO is suggested, resulting in ³¹P resonances that overlap with the peaks usually ascribed to the interaction of TMPO with Brønsted sites.     

Exploring the Interplay between Drug Release and Targeting of Lipid-Like Polymer Nanoparticles Loaded with Doxorubicin

Targeted delivery of doxorubicin still poses a challenge with regards to the quantities reaching the target site as well as the specificity of the uptake. In the present approach, two colloidal nanocarrier systems, NanoCore-6.4 and NanoCore-7.4, loaded with doxorubicin and characterized by different drug release behaviors were evaluated in vitro and in vivo. The nanoparticles utilize a specific surface design to modulate the lipid corona by attracting blood-borne apolipoproteins involved in the endogenous transport of chylomicrons across the blood–brain barrier. When applying this strategy, the fine balance between drug release and carrier accumulation is responsible for targeted delivery. Drug release experiments in an aqueous medium resulted in a difference in drug release of approximately 20%, while a 10% difference was found in human serum. This difference affected the partitioning of doxorubicin in human blood and was reflected by the outcome of the pharmacokinetic study in rats. For the fast-releasing formulation NanoCore-6.4, the AUC_0→1h was significantly lower (2999.1 ng × h/mL) than the one of NanoCore-7.4 (3589.5 ng × h/mL). A compartmental analysis using the physiologically-based nanocarrier biopharmaceutics model indicated a significant difference in the release behavior and targeting capability. A fraction of approximately 7.310–7.615% of NanoCore-7.4 was available for drug targeting, while for NanoCore-6.4 only 5.740–6.057% of the injected doxorubicin was accumulated. Although the targeting capabilities indicate bioequivalent behavior, they provide evidence for the quality-by-design approach followed in formulation development.     

Effect of non-covalent interactions in 2,5-di-Me-pyrazine-di-N-oxide - methanol – Carbon nanotube electrocatalytic system

Catalytic oxidation of methanol (MeOH) in the absence of noble metals and noble metal oxides as catalysts, and the use of metal-free materials are inexpensive and attractive process for practical use in electrocatalysis, sensors, and in direct methanol fuel cells. In previous works, it was found that the use of single-walled (SWCNT) or multi-walled (MWCNT) carbon nanotube paper electrodes instead of GC increases the catalytic efficiency of organic compounds oxidation in the presence of aromatic di-N-oxides by several times. In this work, the effect of non-covalent interactions on the catalytic efficiency of MeOH oxidation in the presence of 2,5-di-Me-pyrazine-di-N-oxide (Pyr₁) in 0.1 M Bu₄NClO₄ solution in acetonitrile at SWCNT and MWСNT paper electrodes was studied by the methods of quantum chemical modeling, Raman spectroscopy, and using electrochemical data. New factors determined the features of mechanism of MeOH oxidation on CNT electrodes and lead to an increase in the catalytic efficiency of the electrode process in comparison with the GC electrode were established.     

Light-Driven Catalyst-Free Access to Phthalazines: Entry to Antiviral Model Drugs by Merging Domino Reactions**

We report the development of a metal-free four-step one-pot synthetic strategy to access high-value functionalized phthalazines using o-methyl benzophenones as starting compounds. Combining a light-mediated enolization of o-methyl benzophenones/Diels-Alder reaction domino process with a subsequent deprotection/aromatization domino reaction in one-pot leads to sustainable and efficient organic synthesis. The tangible advantages, i. e., absence of catalysts or additives, utilization of commercially available and/or easily accessible substrates, mild reaction conditions, simplicity, and single work-up procedure, make this combined process highly appealing for the direct construction of various 1-aryl-phthalazines. Importantly, in vitro bioactivity evaluation of these newly prepared heterocyclic compounds demonstrated a strong antiviral efficacy against major human pathogens like HCMV and SARS-CoV-2.     

3D Study of the Morphology and Dynamics of Zeolite Nucleation

The principle aspects and constraints of the dynamics and kinetics of zeolite nucleation in hydrogel systems are analyzed on the basis of a model Na‐rich aluminosilicate system. A detailed time‐series EMT‐type zeolite crystallization study in the model hydrogel system was performed to elucidate the topological and temporal aspects of zeolite nucleation. A comprehensive set of analytical tools and methods was employed to analyze the gel evolution and complement the primary methods of transmission electron microscopy (TEM) and nuclear magnetic resonance (NMR) spectroscopy. TEM tomography reveals that the initial gel particles exhibit a core–shell structure. Zeolite nucleation is topologically limited to this shell structure and the kinetics of nucleation is controlled by the shell integrity. The induction period extends to the moment when the shell is consumed and the bulk solution can react with the core of the gel particles. These new findings, in particular the importance of the gel particle shell in zeolite nucleation, can be used to control the growth process and properties of zeolites formed in hydrogels.