On the Closure of Translation–Dilation Invariant Linear Spaces of Polynomials

Assume that a linear space of real polynomials in d variables is given which is translation and dilation invariant. We show that if a sequence in this space converges pointwise to a polynomial, then the limit polynomial belongs to the space, too.     

AFM study of conducting polymer polypyrrole nanoparticles formed by redox enzyme - glucose oxidase - initiated polymerisation

Redox enzyme – glucose oxidase E.C. 1.1.3.4 from Penecillum vitale (GOx) – initiated polypyrrole (Ppy) synthesis was applied for the formation of polypyrrole based nanoparticles. The increase in optical absorbance at λ = 460 nm was exploited for the monitoring of polypyrrole polymerisation process. The shape and size of the formed Ppy nanoparticles was also monitored by means of contact mode AFM. The highest increase in the diameter of the formed Ppy nanoparticles was detected during 15-day period. AFM imaging was performed in contact mode to investigate the shape and flexibility of particles deposited on the SiO₂ and Pt surfaces. Contact mode AFM investigations allowed us to conclude that after drying at 50 °C the formed Ppy particles are more flexibly deposited on the Pt electrode if compared to those deposited on the SiO₂ substrate. The application of well-shaped Ppy nanoparticles in biomedicine, chromatography and bioanalysis may be predicted.     

Pulsed amperometric detection of DNA with an ssDNA/polypyrrole-modified electrode

Pulsed amperometric detection (PAD) of target DNA with platinum electrodes modified by single-stranded DNA (ssDNA) entrapped within polypyrrole (ssDNA/Ppy) is reported for the first time. Single-stranded DNA 20-mers complementary to the target DNA were used to construct the DNA biosensors. Polymerase chain reaction (PCR) amplified bovine leukaemia virus (BLV) provirus DNA was used as target DNA. Electrochemical impedance spectroscopic (EIS) investigation of ssDNA/Ppy before and after incubation in target DNA-containing sample revealed significant changes in terms of an imaginary (Z) vs. a real (Z) component. The PAD results were in good agreement with EIS investigations. The PAD method was selected, because it does not require such sophisticated equipment as it is used to perform EIS and the results obtained can be more easily estimated. Optimum conditions for performing PAD and evaluating an analytical signal were elaborated. No label-binding step was necessary for detection of target DNA in PCR-amplified amplicons and detection time was reduced by as much as 30–35 min. The changes of PAD signals were at least 6–7 times higher if ssDNA/Ppy-modified electrodes instead of blank Ppy-modified electrodes were incubated in the target DNA solutions. If ssDNA/Ppy modified electrodes were incubated in non-complementary (control) DNA solution changes in PAD signals were smaller than those detected after incubation in complementary (target) DNA-containing solution by a factor of at least 6–8.     

Discretization and best approximation in Besov spaces

In this paper we prove a theorem about existence of best approximation in a class of spaces involving Besov spaces, via a discretization technique. It is a consequence of this theorem that rational functions and exponencial sums are proximinal subsets of B _∞,q ^a (π). It is also proved the proximinality of R _m ⁿ [a, b] in B _p,q ^a (π) for arbitrary p,q and a.     

Homobivalent Lamellarin-Like Schiff Bases: In Vitro Evaluation of Their Cancer Cell Cytotoxicity and Multitargeting Anti-Alzheimer’s Disease Potential

Marine alkaloids belonging to the lamellarins family, which incorporate a 5,6-dihydro-1-phenylpyrrolo[2,1-a]isoquinoline (DHPPIQ) moiety, possess various biological activities, spanning from antiviral and antibiotic activities to cytotoxicity against tumor cells and the reversal of multidrug resistance. Expanding a series of previously reported imino adducts of DHPPIQ 2-carbaldehyde, novel aliphatic and aromatic Schiff bases were synthesized and evaluated herein for their cytotoxicity in five diverse tumor cell lines. Most of the newly synthesized compounds were found noncytotoxic in the low micromolar range (<30 μM). Based on a Multi-fingerprint Similarity Search aLgorithm (MuSSeL), mainly conceived for making protein drug target prediction, some DHPPIQ derivatives, especially bis-DHPPIQ Schiff bases linked by a phenylene bridge, were prioritized as potential hits addressing Alzheimer’s disease-related target proteins, such as cholinesterases (ChEs) and monoamine oxidases (MAOs). In agreement with MuSSeL predictions, homobivalent para-phenylene DHPPIQ Schiff base 14 exhibited a noncompetitive/mixed inhibition of human acetylcholinesterase (AChE) with K_i in the low micromolar range (4.69 μM). Interestingly, besides a certain inhibition of MAO A (50% inhibition of the cell population growth (IC₅₀) = 12 μM), the bis-DHPPIQ 14 showed a good inhibitory activity on self-induced β-amyloid (Aβ)_1–40 aggregation (IC₅₀ = 13 μM), which resulted 3.5-fold stronger than the respective mono-DHPPIQ Schiff base 9.     

Square wave voltammetry based on determination of copper (II) ions by polyluteolin- and polykaempferol-modified electrodes

Applicability of square wave voltammetry for the determination of Cu(II) ions by PolyLut/GC and PolyKae/GC electrodes was evaluated in this study. For this luteolin and kaempferol were electrochemically polymerized on glassy carbon (GC) electrode surface in order to get polyluteolin and polykaempferol-modified glassy carbon electrodes (PolyLut/GC and PolyKae/GC, correspondingly). The formation of polyphenol layer on the GC electrode surface was evidenced by atomic force microscopy. Square wave voltammetry was found to be more sensitive in comparison with differential pulse voltammetry. It was determined that PolyLut/GC and PolyKae/GC electrodes offered great sensitivity towards Cu(II) ions with very low limit of detection, good reproducibility, sufficient stability and excellent selectivity of analytical signal.     

Structural diversity of interaction products of mucochloric acid and its derivatives with 1,2-ethanedithiol

The synthesis and characterization of previously unknown sulfur-containing products from the reaction of mucochloric acid (3,4-dichloro-5-hydroxy-2(5H)-furanone) and its 5-alkoxy derivatives with 1,2-ethanedithiol is reported. Under basic and acidic conditions both SH-groups of the reagent show nucleophilic activity, leading to the formation of substitution products of different structural types. Novel fused (7-hydroxy-2,3-dihydro[1,4]dithiino[2,3-c]furan-5(7H)-one) and spiro (9-chloro-6-methoxy-7-oxa-1,4-dithiaspiro[4.4]nonan-8-one) bicyclic compounds, as well as various bis-thioethers have been obtained and characterized by NMR spectroscopy and single crystal X-ray diffraction.