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.     

Thorium(IV)-selenate clusters containing an octanuclear Th(IV) hydroxide/oxide core

Four Th(IV) hydroxide/oxide clusters have been synthesized from aqueous solution. The structures of [Th(8)(μ(3)-O)(4)(μ(2)-OH)(8)(H(2)O)(15)(SeO(4))(8)·7.5H(2)O] (1), [Th(8)(μ(3)-O)(4)(μ(2)-OH)(8)(H(2)O)(17)(SeO(4))(8)·nH(2)O] (2), [Th(9)(μ(3)-O)(4)(μ(2)-OH)(8)(H(2)O)(21)(SeO(4))(10)] (3), and Th(9)(μ(3)-O)(4)(μ(2)-OH)(8)(H(2)O)(21)(SeO(4))(10)·nH(2)O (4) were determined using single crystal X-ray diffraction. Each structure consists of an octanuclear core, [Th(8)O(4)(OH)(8)](16+), that is built from eight Th(IV) atoms (four Th in a plane and two up and two down) linked by four "inner" μ(3)-O and eight "outer" μ(2)-OH groups. Compounds 3 and 4 additionally contain mononuclear [Th(H(2)O)(5)(SeO(4))(4)](4-) units that link the octamers into an extended structure. The octanuclear units are invariably complexed by two selenate anions that sit in two cavities formed by four planar Th(IV) and four extra-planar Th(IV) atoms, thus making [Th(8)O(4)(OH)(8)(SeO(4))(2)](12+) a common building block in 1-4. However, changes in hydration as well selenate coordination give rise to structural differences that are observed in the extended structures of 1-4. The compounds were also characterized by Raman spectroscopy. Density functional theory calculations were performed to predict the geometries, vibrational frequencies, and relative energies of different structures. Details of the calculated structures are in good agreement with experimental results, and the calculated frequencies were used to assign the experimental Raman spectra. On the basis of an analysis of the DFT results, the compound Th(8)O(8)(OH)(4)(SeO(4))(6) was predicted to be a strong gas phase acid but is reduced to a weak acid in aqueous solution. Of the species studied computationally, the dication Th(8)O(6)(OH)(6)(SeO(6))(6)(2+) is predicted to be the most stable in aqueous solution at 298 K followed by the monocation Th(8)O(7)(OH)(5)(SeO(6))(6)(+).     

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.     

Free energies for degradation reactions of 1,2,3-trichloropropane from ab initio electronic structure theory

Electronic structure methods were used to calculate the gas and aqueous phase reaction energies for reductive dechlorination (i.e., hydrogenolysis), reductive β-elimination, dehydrochlorination, and nucleophilic substitution by OH? of 1,2,3-trichloropropane. The thermochemical properties ΔH(f)°(298.15 K), S°(298.15 K, 1 bar), and ΔG(S)(298.15 K, 1 bar) were calculated by using ab initio electronic structure calculations, isodesmic reactions schemes, gas-phase entropy estimates, and continuum solvation models for 1,2,3-trichloropropane and several likely degradation products: CH3?CHCl?CH2Cl, CH2Cl?CH2?CH2Cl, C?H2?CHCl?CH2Cl, CH2Cl?C?H?CH2Cl, CH2═CCl?CH2Cl, cis-CHCl═CH?CH2Cl, trans-CHCl═CH?CH2Cl, CH2═CH?CH2Cl, CH2Cl?CHCl?CH2OH, CH2Cl?CHOH?CH2Cl, CH2═CCl?CH2OH, CH2═COH?CH2Cl, cis-CHOH═CH?CH2Cl, trans-CHOH═CH?CH2Cl, CH(═O)?CH2?CH2Cl, and CH3?C(═O)?CH2Cl. On the basis of these thermochemical estimates, together with a Fe(II)/Fe(III) chemical equilibrium model for natural reducing environments, all of the reactions studied were predicted to be very favorable in the standard state and under a wide range of pH conditions. The most favorable reaction was reductive β-elimination (ΔG(rxn)° ≈ ?32 kcal/mol), followed closely by reductive dechlorination (ΔG(rxn)° ≈ ?27 kcal/mol), dehydrochlorination (ΔG(rxn)° ≈ ?27 kcal/mol), and nucleophilic substitution by OH? (ΔG(rxn)° ≈ ?25 kcal/mol). For both reduction reactions studied, it was found that the first electron-transfer step, yielding the intermediate C?H2?CHCl?CH2Cl and the CH2Cl?C?H?CH2Cl species, was not favorable in the standard state (ΔG(rxn)° ≈ +15 kcal/mol) and was predicted to occur only at relatively high pH values. This result suggests that reduction by natural attenuation is unlikely.     

Spectroscopic and energetic properties of thorium(IV) molecular clusters with a hexanuclear core

The spectral and energetic properties of three polynuclear thorium(IV) molecular complexes Th(6)(OH)(4)O(4)(H(2)O)(6)(HCOO)(12)·nH(2)O (1), Th(6)(OH)(4)O(4)(H(2)O)(6)(CH(3)COO)(12)·nH(2)O (2), and Th(6)(OH)(4)O(4)(H(2)O)(6)(ClCH(2)COO)(12)·4H(2)O (3) have been studied. Each complex has a hexanuclear core with six 9-coordinate Th(IV) cations bridged by four μ(3)-hydroxo and four μ(3)-oxo groups. The +12 core is stabilized by twelve bridging carboxylate functionalized organic acid (formate, acetate, and chloroacetate) units. The calculated (1)H NMR chemical shifts for the four μ(3)-hydroxo, water, and formate protons are reported and compared to the experimental values. The vibrational frequencies were calculated to aid in the assignment of the observed Raman bands. The Mulliken and NBO (natural bond orbital) charges are calculated for the Th clusters. The Th atoms are positive and the bridging O and O(H) are negative. The analysis of the calculated highest-occupied and lowest-unoccupied molecular orbitals (HOMO and LUMO) is reported. The average water complexation energies, the gas phase, the aqueous and dimethylsulfoxide (DMSO) acidities were predicted, and the Th clusters are found to be mild to strong acids in gas phase yet they behave as weak acids in solution.     

New Grafted Copolymers Carrying Betaine Units Based on Gellan and N-Vinylimidazole as Precursors for Design of Drug Delivery Systems

New grafted copolymers possessing structural units of 1-vinyl-3-(1-carboxymethyl) imidazolium betaine were obtained by graft copolymerization of N-vinylimidazole onto gellan gum followed by the polymer-analogous reactions on grafted polymer with the highest grafting percentage using sodium chloroacetate as the betainization agent. The grafted copolymers were prepared using ammonium persulfate/N,N,N′,N′ tetramethylethylenediamine in a nitrogen atmosphere. The grafting reaction conditions were optimized by changing one of the following reaction parameters: initiator concentration, monomer concentration, polymer concentration, reaction time or temperature, while the other parameters remained constant. The highest grafting yield was obtained under the following reaction conditions: c_i = 0.08 mol/L, c_m = 0.8 mol/L, c_p = 8 g/L, t_r = 4 h and T = 50 °C. The kinetics of the graft copolymerization of N-vinylimidazole onto gellan was discussed and a suitable reaction mechanism was proposed. The evidence of the grafting reaction was confirmed through FTIR spectroscopy, X-ray diffraction, ¹H-NMR spectroscopy and scanning electron microscopy. The grafted copolymer with betaine structure was obtained by a nucleophilic substitution reaction where the betainization agent was sodium chloroacetate. Preliminary results prove the ability of the grafted copolymers to bind amphoteric drugs (cefotaxime) and, therefore, the possibility of developing the new sustained drug release systems.