On Convergence Rate in the Gauss–Kuzmin Problem for Grotesque Continued Fractions

 We give an infinite-order-chain representation of the sequence of the incomplete quotients of the grotesque continued fraction expansion. Together with the ergodic behaviour of a certain homogeneous random system with complete connections, this allows us to prove a Gauss–Kuzmin-type theorem for this expansion. Finally, we derive a two-dimensional Gauss–Kuzmin theorem and also obtain an estimate of the convergence rate. (Received 9 October 2000; in revised form 27 March 2001)     

Synthesis,characterization, molecular docking studies and in vitro screening of new metal complexes with Schiff base as antimicrobial and antiproliferative agents

A series of Cu(II), Co(II), Pd(II), Pt(II), Zn(II), Cd(II) and Fe(III) complexes were designed and synthesized using Schiff base 1‐phenyl‐2,3‐dimethyl‐4‐(N‐3‐formyl‐6‐methylchromone)‐3‐pyrazolin‐5‐one (HL). The new metal complexes were investigated using various physicochemical techniques including elemental and thermal analyses, molar electric conductivity and magnetic susceptibility measurements, as well as spectroscopic methods. Also, the crystal structures of ligand HL and the Pd(II) complex were determined using single‐crystal X‐ray diffraction analysis. For all compounds, the antimicrobial activity was studied against a series of standard strains: Staphylococcus aureus, Bacillus cereus, Enterococcus faecalis, Escherichia coli, Acinetobacter baumannii, Candida albicans, Candida krusei and Cryptococcus neoformans. The in vitro antiproliferative activity of the ligand and complexes was evaluated against ten cancer cell lines: MSC, A375, B16 4A5, HT‐29, MCF‐7, HEp‐2, BxPC‐3, RD, MDCK and L20B. At 10 μM concentration a significant cytotoxic effect of the Co(II), Pd(II) and Cd(II) complexes was observed against B16 4A5 murine melanoma cells. The Zn(II) complex is active against HEp‐2, RD and MDCK cancer cell lines, where IC₅₀ values vary between 1.0 and 77.6 and for BxPC‐3 the activity index versus doxorubicin is 3.7 times higher.     

Strategies to Improve the Thermo-Oxidative Stability of Sunflower Oil by Exploiting the Antioxidant Potential of Blueberries Processing Byproducts

This research was conducted in order to establish the effectiveness of two freeze-dried extracts obtained from blueberry processing byproducts resulting from juice manufacturing compared to butylated hydroxytoluene (BHT) in delaying the lipid oxidation of sunflower oil subjected to high-temperature convective heating at 180 °C up to 12 h under simulated frying conditions. The fruits were harvested from spontaneous flora of two regions of Romania, Arieseni (Alba County) and Paltinis (Sibiu County) and the blueberry byproducts extracts (BBE) were noted according to the origin place as ABBE and PBBE. The progress of lipid thermo-oxidation was investigated in terms of peroxide value (PV), p-anisidine value (p-AV), the response of TBA-malondialdehyde interactions assessed by thiobarbituric acid (TBA) method, the total oxidation (TOTOX) value and inhibition of oil oxidation (IO). The recorded data highlighted that BBE exhibit a high inhibitory response on lipid thermo-oxidation. The inhibitory effect was concentration-dependent, thus, the degree of lipid oxidation was in reverse related to the BBE dose. The exposure of the oil samples supplemented with 800 ppm BBE (ABBE, PBBE) to a high-temperature heating for 12 h led to a significant decrease of the assessed indices compared to additives-free sunflower oil sample as follows: PV (46%; 45%), p-AV (21%; 17%), TOTOX (27%; 24%), TBA value (25%; 11%). Regarding the impact of the origin on the potential of BBE to inhibit the lipid oxidative degradation, it was noted that ABBE derived from blueberries grown in a region with a milder climate with moderate precipitations and higher temperatures showed a stronger inhibitory effect on lipid thermo-oxidation than PBBE. A moderate level of 500 ppm BBE inhibited the lipid oxidation similar to 200 ppm BHT. The reported results reveal that BBE represent efficient natural antioxidants that could be successfully applied to improve the thermo-oxidative stability of sunflower oil used in various high-temperature food applications.     

Slider-Pinning Rigidity: a Maxwell–Laman-Type Theorem

We define and study slider-pinning rigidity, giving a complete combinatorial characterization. This is done via direction-slider networks, which are a generalization of Whiteley’s direction networks.     

Elisapterosin F: a polycyclic gorgonian-derived diterpene with a facially amphiphilic structure

Analysis of the terpene metabolites of Pseudopterogorgia elisabethae collected in San Andrés island, Colombia has resulted in the discovery of a novel metabolite, elisapterosin F (1). The tangled molecular structure of 1, which was elucidated after extensive spectroscopic data interpretation, possesses hydrophilic and hydrophobic groups located on two opposite faces, rather than at two ends as in the more conventional head/tail amphiphiles.     

The whole is more than the sum of its parts: Modeling community-level effects of UVR in marine ecosystems

The effect of UVB radiation (UVBR, 290-320 nm) on the dynamics of the lower levels of the marine plankton community was modeled. The model was built using differential equations and shows a good fit to experimental data collected in mesocosms (defined as large enclosures of 1500 L filled with natural marine waters). Some unexpected results appear to be possible by indirect effects in prey (bacteria, phytoplankton and heterotrophic flagellates). In particular, apparent competition appears between small phytoplankton and bacteria. This effect is caused by a shared predator (ciliates). Another remarkable effect is an increase in bacteria and flagellates populations due to enhanced UVBR. This effect is similar to that observed under mesocosm experimental conditions and is related to the decrease of predation due to the direct damage to predators (ciliates) by UVBR. The effect of UVBR changing interaction coefficients may be dramatic on the community structure, producing big changes in equilibrium populations, as demonstrated by sensitivity analysis of the model. In order to generalize these results to field conditions it will be necessary to increase model complexity and include extra organic mater sources, mixing and sinking effects and predation by large zooplankton. This work shows that UVBR may produce community global responses that are consequence of both direct and indirect effects among populations.     

Pressurized liquid extraction of cyclitols and sugars: optimization of extraction parameters and selective separation

Cyclitols and sugars were obtained as a mixture from Medicago sativa L., in a comparative study by using maceration, and pressurized liquid extraction, as a modern and green extraction techniques. The influence of extraction parameters including: extraction temperature, time and number of cycles on the content of sugars and cyclitols was investigated based on response surface methodology. The highest total amount of sugars and cyclitols (62.27 ± 2.30 and 50.35 ± 0.77 mg/g of dry material, respectively) was obtained when extraction was performed at 88°C, for 22 min, in two cycles. The methodology used involved extraction, purification, selective separation (using yeast and anion exchange resin) and derivatization, followed by gas chromatography ‐mass spectrometry analysis. The use of yeast treatment realized an effective fractionation of cyclitols and sugars, which allowed the removal of most sugars. The involvement of anion exchange resin after yeast allowed the removal of sugar alcohols and lactose, together with other sugar traces remained and to obtain a solution containing six cyclitols. The recrystallization of dry residue after solvent evaporation, from ethanol, allowed us to obtain 14.65 mg of white pure crystals identified with NMR spectroscopy, liquid chromatography with mass spectrometry, gas chromatography with mass spectrometry, optical rotation and melting point as analysis D‐pinitol.     

Ferromagnetic resonance study of NiCuAl alloys

The results of magnetic measurements and ferromagnetic resonance study on Ni_0.87Cu_0.13?xAl_x and Ni_0.77Cu_0.23?xAl_x alloys with x ? 10 at 10 % Al are reported. The saturation magnetization and the Curie temperatures are linearly dependent on the mean electronic concentration of the CuAl matrix. The ferromagnetic resonance measurements show that the g values are not dependent on composition, g = 2.19 ± 0.01. The magnetic behaviour of NiCuAl alloys is analysed in the coherent potential approximation.