Nonlinear obstacle problems with double phase in the borderline case

In this paper we study a double phase problem with an irregular obstacle. The energy functional under consideration is characterized by the fact that both ellipticity and growth switch between a type of polynomial and a type of logarithm, which can be regarded as a borderline case of the double phase functional with $(p,q)$-growth. We obtain an optimal global Calderón–Zygmund type estimate for the obstacle problem with double phase in the borderline case.     

Synthesis and cytotoxic evaluation of novel brominated N-alkyl pyrano[3,2-c]quinolinones

A novel series of 6-alkyl-4-bromopyrano[3,2-c]quinoline-2,5-diones ( 2a–c ), 6-alkyl-3,4-dibromopyrano[3,2-c]quinoline-2,5-diones ( 4a–c ), and 6-alkyl-3-amino-bromopyrano[3,2-c]quinoline-2,5-diones ( 6a–c ) were synthesized via appropriate conventional methods and in good yields. The structures of target compounds were approved by elemental analysis, IR, ¹H NMR, ¹³C NMR, and mass spectrometry. The antitumor inhibitory activities of the new compounds were evaluated on several cancer cell lines, A-549 (human lung cancer), HCT-116 (human colon cancer), MCF-7 (breast cancer), and HePG-2 (human liver cancer). Moreover, 50% inhibitory concentrations, IC₅₀, were established. 5-Fluorouracil was used as a positive control in the viability assay. The screening results showed that most of the examined compounds exposed powerful inhibition activity toward various cell lines. Particularly, Compound 4c exhibited higher cytotoxic activity against four tumor cell lines than the reference drug, 5-fluorouracil, with significantly lower IC₅₀ values. Accordingly, most of the synthesized compounds would be a better prospective growth in the anticancer drug discovery.     

Synthesis,reactions, and antioxidant activity of 3-(pyrrol-1-yl)-4,6-dimethyl selenolo[2,3-b]pyridine derivatives

Ethyl 4,6-dimethyl-3-(pyrrol-1-yl) selenolo[2,3-b]pyridine-2-carboxylate (2) was synthesized by the reaction of previously prepared ethyl 3-amino-4,6-dimethyl selenolo[2,3-b]pyridine-2-carboxylate (1) with 2,5-dimethoxytetrahydrofuran in acetic acid. The pyrrolyl ester (2) was converted into the corresponding carbohydrazide 3 which reacted with acetyl acetone, aromatic aldehydes, carbon disulfide in pyridine, and sodium nitrite to afford the corresponding dimethyl pyrazolyl 4, arylidene carbohydrazides 5a–d, oxadiazolyl thiole 6, and caboazide compound 8, respectively. The carboazide 8 reacted with different alcohols and amines to give the corresponding carbamates 9a–c and the aryl urea derivatives 10a–d. Heating of carboazide 8 in dry xylene afforded the pyridoselenolo-pyrrolopyrazinone 11. The latter compound was used as a versatile starting precursor for synthesis of other pyridoselenolo-pyrrolopyrazine compounds. The newly synthesized compounds and their derivatives were characterized by elemental analysis and spectroscopy (IR, ¹H-NMR, and mass spectra). Some of the newly synthesized pyrrolyl selenolopyridine compounds showed remarkable antioxidant activity compared to ascorbic acid.     

Global gradient estimates for non-uniformly elliptic equations

We consider a nonlinear and non-uniformly elliptic problem in divergence form on a bounded domain. The problem under consideration is characterized by the fact that its ellipticity rate and growth radically change with the position, which provides a model for describing a feature of strongly anisotropic materials. We establish the global Calderón–Zygmund type estimates for the distributional solution in the case that the boundary of the domain is of class \(C^{1,\beta }\) for some \(\beta >0\).     

Spin-trapping of ligated boryl radicals

Amine- and phosphine-boryl radicals add to 2-methyl-2-nitrosopropane, 2,4,6-tri-t-butylnitrosobenzene, and phenyl-N-t-butylnitrone to give nitroxide spin-adducts and the application of these spin-trapping reactions as mechanistic probes is described.     

Co-existence of long- and short-range magnetic correlations in holmium-erbium superlattices

The effect of competing crystal-field anisotropies on magnetic order has been investigated in a series of Ho/Er superlattices using a combination of x-ray and neutron scattering techniques. For temperatures in the interval T_N(Er)≤T≤T_N(Ho) the Ho basal-plane order propagates coherently through the paramagnetic Er over a typical length scale of 1000 Å. At low temperatures the Ho moments retain their bulk-like helical configuration, whereas the magnetic structure in the Er blocks has both basal-plane and c-axis components. Below T_N(Er), the coherence length of the basal-plane order decreases on cooling, while the longitudinal component of the Er moments fails to order across the Ho block. It is argued that these results require an extension of current models of indirect exchange in superlattices to explicitly include the superlattice band structure.     

On Adequate Transversals

We consider adequate transversals of abundant semigroups and prove that, in a particular case, there is a natural embedding of an inverse transversal within a certain regular subsemigroup. We also introduce the concepts of simplistic, perfect, and quasi-adequate transversal and provide a number of interesting connections between these.     

Regularity results of the thin obstacle problem for the p(x)-Laplacian

We study thin obstacle problems involving the energy functional with $p(x)$-growth. We prove higher integrability and Hölder regularity for the gradient of minimizers of the thin obstacle problems under the assumption that the variable exponent $p(x)$ is Hölder continuous.     

Precisely Controlled Multidimensional Covalent Frameworks: Polymerization of Supramolecular Colloids

Rapid and selective removal of micropollutants from water is important for the reuse of water resources. Despite hollow frameworks with specific functionalized porous walls for the selective adsorption based on a series of interactions, tailoring a stable shape of nanometer- and micrometer-sized architectures for the removal of specific pollutants remains a challenge. Here, exactly controlled sheets, tubes, and spherical frameworks were presented from the crosslinking of supramolecular colloids in polar solvents. The frameworks strongly depended on the architecture of original supramolecular colloids. As the entropy of colloids increased, the initial laminar framework rolled up into hollow tubules, and then further curled into hollow spheres. These shape-persistent frameworks showed unprecedented selectivity as well as specific recognition for the shape of pollutants, thus contributing to efficient pollutant separation.     

Two-dimensionally well-ordered multilayer structures in thin films of a brush polypeptide

In this study, we report the first production of two-dimensionally well-ordered molecular multilayers (i.e., with a well-defined molecular lamellar structure) based on the antiparallel beta-sheet chain conformation in thin films of a brush polypeptide, poly(S-n-hexadecyl-dl-homocysteine) (PHHC), through the use of a simple spin-coating process and the quantitative structural and property analysis of the thin films using a grazing incidence X-ray scattering technique combined with Fourier transform infrared spectroscopy and differential scanning calorimetry. These analyses provide detailed information about the structure and molecular conformation of the self-assembled lamellae in the PHHC thin film, which is not easily obtained using conventional techniques. Moreover, we used the in situ measurements carried out at various temperatures and the data analyses to establish mechanisms for the evolution of the self-assembled lamellar structures in the film and for their melting. In addition, we propose molecular structure models of the PHHC polymer molecules in the thin film at various temperatures.