Weighted Lorentz estimates for parabolic equations with non-standard growth on rough domains

The main aim of this paper is to prove the Calderón–Zygmund estimates for a general nonlinear parabolic equation of p(x, t)-Laplacian type in the weighted Lorentz spaces. Note that we only require some mild conditions on the nonlinearity of coefficients and the underlying domain. The result for these nonlinear parabolic equations is new even in the particular case when the growth p(x, t) is a constant.     

A new lignan glycoside from the aerial parts and cytotoxic investigation of Uvaria rufa

Chemical investigation of the aerial parts of Uvaria rufa (Dunal) Blume collected from Vietnam yielded one new lignan glycoside, ufaside (1), along with six known compounds, oxoanolobine (2), ergosta-4,6,8(14),22-tetraen-3-one (3), catechin (4), epicatechin (5), daucosterol (6) and glutin-5-en-3-one (7). Their chemical structures were determined by using NMR, HR-MS spectroscopic analyses and in comparison with the reported data. A cytotoxic analysis of U. rufa herb extracts was performed for the first time using nine human cancer cell lines (MCF-7, MDA-MB-231, LNCaP, MKN7, SW480, KB, LU-1, HepG2 and HL-60) derived from different tumour types. Of these seven constituents, compounds 2 and 3 displayed moderate cytotoxicity against the human lung adenocarcinoma cell line (LU-1) with IC₅₀ values of 9.22 ± 1.02 μg/mL and 10.21 ± 1.16 μg/mL, respectively.     

Modeling of the water network at protein-RNA interfaces

Water plays an important role in the mediation of biomolecular interactions. Thus, accurate prediction and evaluation of water-mediated interactions is an important element in the computational design of interfaces involving proteins, RNA, and DNA. Here, we use an algorithm (WATGEN) to predict the locations of interfacial water molecules for a data set of 224 protein-RNA interfaces. The accuracy of the prediction is validated against water molecules present in the X-ray structures of 105 of these complexes. The complexity of the water networks is deconvoluted through definition of the characteristics of each water molecule based on its bridging properties between the protein and RNA and on its depth in the interface with respect to the bulk solvent. This approach has the potential for scoring the water network for incorporation into the computational design of protein-RNA complexes.     

Three-dimensional structural analysis of eukaryotic flagella/cilia by electron cryo-tomography

Electron cryo-tomography is a potential approach to analyzing the three-dimensional conformation of frozen hydrated biological macromolecules using electron microscopy. Since projections of each individual object illuminated from different orientations are merged, electron tomography is capable of structural analysis of such heterogeneous environments as in vivo or with polymorphism, although radiation damage and the missing wedge are severe problems. Here, recent results on the structure of eukaryotic flagella, which is an ATP-driven bending organelle, from green algae Chlamydomonas are presented. Tomographic analysis reveals asymmetric molecular arrangements, especially that of the dynein motor proteins, in flagella, giving insight into the mechanism of planar asymmetric bending motion. Methodological challenges to obtaining higher-resolution structures from this technique are also discussed.     

Immobilization of molecularly imprinted polymer nanoparticles in electrospun poly(vinyl alcohol) nanofibers

We describe the fabrication of polymer nanofibers with entrapped molecularly imprinted polymer (MIP) nanoparticles and study their possible use in a fluorescence-based biosensor application. The MIP was imprinted with the fluorescent amino acid derivative dansyl-L-phenylalanine. Poly(vinyl alcohol) was used as a support for MIP nanoparticles because it is water-soluble and can be spun into very thin fibers. The fibers were characterized by atomic force microscopy and optical microscopy, and fluorescence microscopy was used for the characterization of target binding to the MIP. The fibers show close to 100% recovery upon extraction and rebinding of the target molecule. The selectivity of the system has been demonstrated through competitive binding experiments with nonfluorescent analogues boc-L-phenylalanine and boc-D-phenylalanine.     

Nanopore wall effect on surface tension of methane

Local pressure is known to be anisotropic across the interfaces separating fluids in equilibrium. Tangential pressure profiles show characteristic negative peaks as a result of surface tension forces parallel to the interface. Nearby attractive forces parallel to the interface are larger than the repulsive forces and, hence, constitute the surface tension. In this work, using molecular dynamics simulations of methane inside nano-scale pores, we show this surface tension behaviour could be significantly influenced by confinement effects. The layering structure, characterised by damped oscillations in local liquid density and tangential pressures, extends deep into the pore and can be a few nanometers thick. The surface tension is measured numerically using local pressures across the interface. Results show that the tension is smaller under confinement and becomes a variable in small pores, mainly controlled by the thickness of the liquid density layering (or liquid saturation) and the pore width. If the liquid saturation inside the pore is high enough, the vapour–liquid interface is not interfered by the pore wall and the surface tension remains the same as the bulk values. The results are important for understanding phase change and multi-phase transport phenomena in nanoporous materials.     

On Locally Nilpotent Subgroups of GL 1(D)

In this article we study locally nilpotent subgroups of D*: = GL ₁(D), where D is a division ring. It is proved that every locally nilpotent subnormal subgroup of D* is central. If D is algebraic over its centre then every locally solvable subnormal subgroup of D* is central. Also, in this case, it is shown that every locally nilpotent maximal subgroup of D* can occur as the multiplicative group of some maximal subfield of D.     

A note on the existence of non-cyclic free subgroups in division rings

A division ring D is said to be weakly locally finite if for every finite subset ${S \subset D}$ , the division subring of D generated by S is centrally finite. It is known that the class of weakly locally finite division rings strictly contains the class of locally finite division rings. In this note we prove that every non-central subnormal subgroup of the multiplicative group of a weakly locally finite division ring contains a non-cyclic free subgroup. This generalizes the previous result by Gonçalves for centrally finite division rings.     

Polysaccharide- and β-Cyclodextrin-Based Chiral Selectors for Enantiomer Resolution: Recent Developments and Applications

Polysaccharides, oligosaccharides, and their derivatives, particularly of amylose, cellulose, chitosan, and β-cyclodextrin, are well-known chiral selectors (CSs) of chiral stationary phases (CSPs) in chromatography, because they can separate a wide range of enantiomers. Typically, such CSPs are prepared by physically coating, or chemically immobilizing the polysaccharide and β-cyclodextrin derivatives onto inert silica gel carriers as chromatographic support. Over the past few years, new chiral selectors have been introduced, and progressive methods to prepare CSPs have been exploited. Also, chiral recognition mechanisms, which play a crucial role in the investigation of chiral separations, have been better elucidated. Further insights into the broad functional performance of commercially available chiral column materials and/or the respective newly developed chiral phase materials on enantiomeric separation (ES) have been gained. This review summarizes the recent developments in CSs, CSP preparation, chiral recognition mechanisms, and enantiomeric separation methods, based on polysaccharides and β-cyclodextrins as CSs, with a focus on the years 2019–2020 of this rapidly developing field.     

CI Reactive Black 5 dye as a visible crosslinker to improve physical properties of lyocell fabrics

Bi-functional reactive dyes have been used for reducing the fibrillation of lyocell fibres. The sole influence of CI Reactive Black 5 dye on the fibrillation tendency of lyocell single jersey knitted fabrics was investigated by dyeing with different concentrations (35 g/L for medium shade and 70 g/L for dark shade), dyeing without dyestuff and by decolouration process after each dyeing. The fibrillation tendency of lyocell fibres was accessed by means of fibre wet abrasion resistance and fibrillation number. Nitrogen content was used as indication of the amount of reactive dye in fabrics during dyeing and decolouration processes. The correlation between fibre fibrillation tendency and colour values of fabrics was found. Due to the fibrillation reduction, pilling formation in dyed lyocell fabrics was improved. As colour values can estimate the dye fixation and reduction in fabrics, reactive dye can be used as a visible marker for crosslinking effect on lyocell fabrics.