Diliberto–Straus algorithm for the uniform approximation by a sum of two algebras

In 1951, Diliberto and Straus [5] proposed a levelling algorithm for the uniform approximation of a bivariate function, defined on a rectangle with sides parallel to the coordinate axes, by sums of univariate functions. In the current paper, we consider the problem of approximation of a continuous function defined on a compact Hausdorff space by a sum of two closed algebras containing constants. Under reasonable assumptions, we show the convergence of the Diliberto–Straus algorithm. For the approximation by sums of univariate functions, it follows that Diliberto–Straus’s original result holds for a large class of compact convex sets.     

Helical silica nanotubes: Nanofabrication architecture,transfer of helix and chirality to silica nanotubes

A series of neutral gelators and cationic amphiphiles derived from 1,2 diphenylethylenediamine (I) and 1,2-cyclohexanediamine (II) was synthesised. Helical silica nanotubes were prepared utilising these organic gelators through sol-gel polycondensation of tetraethoxy silane, (TEOS-silica source). Right- and left-handed helical nanotubes respectively were obtained from a 1: 1 mass mixture of optically active, (1S,2S)-III-(1S,2S)-V neutral gelator and (1S,2S)-IV-(1S,2S)-VI cationic amphiphile and a 1: 1 mass mixture of optically active, (1R,2R)-III-(1R,2R)-V neutral gelator and (1R,2R)-IV-(1R,2R)-VI cationic amphiphile, indicating that the handedness of the helical nanotubes varied with the change in the neutral gelator precursors used. The nanotubes were characterised by SEM images.     

Monitoring protein distributions based on patterns generated by protein adsorption behavior in a microfluidic channel

We report a unique monitoring technique of protein distributions based on distinctive patterns generated by protein adsorption behavior on a solid surface in a microfluidic channel. Bare gold and COOH-modified self-assembled monolayer (SAM) sensing surfaces were pre-adsorbed with one of four different proteins: lysozyme, albumin, transferrin, or IgG. Each surface provides a thermodynamically governed platform for immobilizing proteins and generates analyte-specific response patterns. Each surface has its own thermodynamic energy governing pre-adsorbed protein behaviors, so that sample proteins react with the pre-adsorbed ones to different extents depending on their sizes, isoelectric points (pI), and characteristics of the sensing surfaces. Modified surfaces were mounted and monitored in real time using surface plasmon resonance (SPR). Buffer-prepared sample matrices (α1-antitrypsin, haptoglobin, C-reactive protein (CRP), and IgM) characterized protein response patterns. Each surface generated distinctive patterns based on individual SPR angle shifts. We classified each sample with 95% accuracy using linear discriminant analysis (LDA). Our method also discriminated between different concentrations of CRP in the cocktail sample, detecting concentrations as low as 1 nM with 91.7% accuracy. This technique may be integrated with a microfluidic lab-on-a-chip system and monitor the distribution of a specific group of proteins in human serum.     

pH-Sensitive pentablock copolymer nanocapsules as nontoxic and efficient gene carriers

A biodegradable amphiphilic pentablock copolymer PAE‐PCL‐PEG‐PCL‐PAE with a pH‐sensitive unit was synthesized for use as a nontoxic, biodegradable carrier for gene delivery by forming nanocapsules entrapping nucleic acid drugs. The PAE block can interact with plasmid DNA to form polyelectrolyte complexes in an acidic environment. At physiological pH, the PAE blocks are deprotonated and form an insoluble skin, resulting in the formation of nanocapsules that encapsulate plasmid DNA. The surface charges of the nanocapsules became almost neutral at pH = 7.4, and their size ranged from 210 to 280 nm. The nanocapsule maintained most of its transfection efficiency even in the presence of serum. These nanocapsules are therefore potential carriers for systemic gene therapy.

     

Phosphorescent sensor for biological mobile zinc

A new phosphorescent zinc sensor (ZIrF) was constructed, based on an Ir(III) complex bearing two 2-(2,4-difluorophenyl)pyridine (dfppy) cyclometalating ligands and a neutral 1,10-phenanthroline (phen) ligand. A zinc-specific di(2-picolyl)amine (DPA) receptor was introduced at the 4-position of the phen ligand via a methylene linker. The cationic Ir(III) complex exhibited dual phosphorescence bands in CH(3)CN solutions originating from blue and yellow emission of the dfppy and phen ligands, respectively. Zinc coordination selectively enhanced the latter, affording a phosphorescence ratiometric response. Electrochemical techniques, quantum chemical calculations, and steady-state and femtosecond spectroscopy were employed to establish a photophysical mechanism for this phosphorescence response. The studies revealed that zinc coordination perturbs nonemissive processes of photoinduced electron transfer and intraligand charge-transfer transition occurring between DPA and phen. ZIrF can detect zinc ions in a reversible and selective manner in buffered solution (pH 7.0, 25 mM PIPES) with K(d) = 11 nM and pK(a) = 4.16. Enhanced signal-to-noise ratios were achieved by time-gated acquisition of long-lived phosphorescence signals. The sensor was applied to image biological free zinc ions in live A549 cells by confocal laser scanning microscopy. A fluorescence lifetime imaging microscope detected an increase in photoluminescence lifetime for zinc-treated A549 cells as compared to controls. ZIrF is the first successful phosphorescent sensor that detects zinc ions in biological samples.     

Synthesis of cationic quantum dots via a two-step ligand exchange process

A new class of quaternary ammonium derivatives has been used to synthesize cationic CdSe/ZnS quantum dots with exceptional stability in water as well as in biological media.     

Molecular properties of water-unextractable proteoglycans from Hypsizygus marmoreus and their in vitro immunomodulatory activities

Four proteoglycans were sequentially extracted from Hypsizygus marmoreus using 0.1 M NaOH (alkali-soluble proteoglycans [F1] and alkali-insoluble proteoglycans [F3]) and 0.1 M HCl (acid-soluble proteoglycans [F2] and acid-insoluble proteoglycans [F4]), and their structures and immunomodulatory activities were investigated. The proteoglycans were found to contain carbohydrates (19.8-82.4%) with various amounts of proteins (7.7-67.3%), and glucose was the major monosaccharide unit present, along with trace amounts of galactose. The molecular weights (Mw) and the radius of gyration (Rg) of these proteoglycans showed ranges of 16 × 10(4)-19,545 × 10(4) g/mol and 35-148 nm, respectively, showing significant variations in their molecular conformations. The backbones of F1 and F2 were mainly connected through a-(1→3), (1→4) and b-(1→6)-glycosidic linkages with some branches. The F1 and F2 proteoglycans significantly stimulated Raw264.7 cells to release nitric oxide (NO), prostaglandin E2 (PGE(2)) and various cytokines, such as IL-1β, TNF-α and IL-6 by inducing their mRNA expressions.     

Inviscid Models Generalizing the Two-dimensional Euler and the Surface Quasi-geostrophic Equations

Any classical solution of the two-dimensional incompressible Euler equation is global in time. However, it remains an outstanding open problem whether classical solutions of the surface quasi-geostrophic (SQG) equation preserve their regularity for all time. This paper studies solutions of a family of active scalar equations in which each component u _j of the velocity field u is determined by the scalar θ through \({u_j =\mathcal{R}\Lambda^{-1}P(\Lambda) \theta}\) , where \({\mathcal{R}}\) is a Riesz transform and Λ = (?Δ)^1/2. The two-dimensional Euler vorticity equation corresponds to the special case P(Λ) = I while the SQG equation corresponds to the case P(Λ) = Λ. We develop tools to bound \({\|\nabla u||_{L^\infty}}\) for a general class of operators P and establish the global regularity for the Loglog-Euler equation for which P(Λ) = (log(I + log(I ? Δ))) ^γ with 0 ≦ γ ≦ 1. In addition, a regularity criterion for the model corresponding to P(Λ) = Λ ^β with 0 ≦ β ≦ 1 is also obtained.     

Anticancer Activity of 2-O-caffeoyl Alphitolic Acid Extracted from the Lichen,Usnea barbata 2017-KL-10

Colorectal cancer is one of the life-threatening ailments causing high mortality and morbidity worldwide. Despite the innovation in medical genetics, the prognosis for metastatic colorectal cancer in patients remains unsatisfactory. Recently, lichens have attracted the attention of researchers in the search for targets to fight against cancer. Lichens are considered mines of thousands of metabolites. Researchers have reported that lichen-derived metabolites demonstrated biological effects, such as anticancer, antiviral, anti-inflammatory, antibacterial, analgesic, antipyretic, antiproliferative, and cytotoxic, on various cell lines. However, the exploration of the biological activities of lichens’ metabolites is limited. Thus, the main objective of our study was to evaluate the anticancer effect of secondary metabolites isolated from lichen (Usnea barbata 2017-KL-10) on the human colorectal cancer cell line HCT116. In this study, 2OCAA exhibited concentration-dependent anticancer activities by suppressing antiapoptotic genes, such as MCL-1, and inducing apoptotic genes, such as BAX, TP53, and CDKN1A(p21). Moreover, 2OCAA inhibited the migration and invasion of colorectal cancer cells in a concentration-dependent manner. Taken together, these data suggest that 2OCAA is a better therapeutic candidate for colorectal cancer.     

Influence of TiO2 nanotube morphology and TiCl4 treatment on the charge transfer in dye-sensitized solar cells

Dye-sensitized solar cells (DSSCs) were fabricated using TiO₂ nanoparticles (NPs), TiO₂ nanotube arrays (NTAs), and surface-modified NTAs with a TiCl₄ treatment. The photovoltaic efficiencies of the DSSCs using TiO₂ NP, NTA, and TiCl₄-treated NTA electrodes are 4.25, 4.74, and 7.47 %, respectively. The highest performance was observed with a TiCl₄-treated TiO₂ NTA photoanode, although in the case of the latter two electrodes, the amounts of N719 dye adsorbed were similar and 68 % of that of the NP electrode. Electrochemical impedance measurements show that the overall resistance, including the charge–transfer resistance, was smaller with NTA morphologies than with NP morphologies. We suggest that a different electron transfer mechanism along the one-dimensional nanostructure of the TiO₂ NTAs contributes to the smaller charge–transfer resistance, resulting in a higher short circuit current (J _sc), even at lower dye adsorption. Furthermore, the TiCl₄-treated NTAs showed even smaller charge–transfer resistance, resulting in the highest J _sc value, because the downward shift in the conduction band edge improves the electron injection efficiency from the excited dye into the TiCl₄-treated TiO₂ electrodes.