On The Negative Pell Equation

The negative pell equation represented by the binary quadratic equationnbspnbsp is analyzed for its non-zero distinct integer solutions. A few interesting relations among the solutions are presented. Employing the solutions of the equation under consideration, the integer solutions for a few choices of hyperbola and parabola are obtained

2-(6-Chloro-2,3,4,9-tetra­hydro-1H-carbazol-1-yl­idene)propane­dinitrile

The mol­ecular conformation of the title compound, C15H10ClN3, is stabilized by an intra­molecular N—H⋯N hydrogen bond with an S(7) ring motif. The crystal packing is controlled by N—H⋯N and C—H⋯N inter­molecular inter­actions. One of the methyl­ene groups of the cyclo­hexene ring is disordered over two positions with refined occupancies of 0.457 (12) and 0.543 (12)

6-Bromo-2-(3-phenyl­allyl­idene)-2,3,4,9-tetra­hydro-1H-carbazol-1-one

Mol­ecules of the title compound, C21H16BrNO, are linked through pairs of N—H⋯O inter­molecular hydrogen bonds into centrosymmetric R 2 2(10) dimers. One of the C atoms of the cyclohex-2-enone ring is disordered with refined occupancies of 0.61 (2) and 0.39 (2)

Insecticidal and biting deterrent activities of magnolia grandiflora essential oils and selected pure compounds against aedes aegypti

© 2020 by the authors. In our natural products screening program for mosquitoes, we tested essential oils extracted from different plant parts of Magnolia grandiflora L. for their insecticidal and biting deterrent activities against Aedes aegypti. Biting deterrence of seeds essential oil with biting deterrence index value of 0.89 was similar to N,N-diethyl-3-methylbenzamide (DEET). All the other oils were active above the solvent control but the activity was significantly lower than DEET. Based on GC-MS analysis, three pure compounds that were only present in the essential oil of seed were further investigated to identify the compounds responsible for biting deterrent activity. 1-Decanol with PNB value of 0.8 was similar to DEET (PNB = 0.8), whereas 1-octanol with PNB value of 0.64 showed biting deterrence lower than 1-decanol and DEET. The activity of 1-heptanol with PNB value of 0.36 was similar to the negative control. Since 1-decanol, which was 3.3% of the seed essential oil, showed biting deterrence similar to DEET as a pure compound, this compound might be responsible for the activity of this oil. In in vitro A & K bioassay, 1-decanol with MED value of 6.25 showed higher repellency than DEET (MED = 12.5). Essential oils of immature and mature fruit showed high toxicity whereas leaf, flower, and seeds essential oils gave only 20%, 0%, and 50% mortality, respectively, at the highest dose of 125 ppm. 1-Decanol with LC50 of 4.8 ppm was the most toxic compound

6-Bromo-2-[(E)-thio­phen-2-yl­methyl­idene]-2,3,4,9-tetra­hydro-1H-carbazol-1-one

In the title compound, C17H12BrNOS, the cyclo­hexene ring deviates only slightly from planarity (r.m.s. deviation for non-H atoms = 0.047 Å). In the crystal, the mol­ecules are linked into centro­symmetric R 2 2(10) dimers via pairs of N—H⋯O hydrogen bonds. The thio­phene ring is disordered over two positions rotated by 180° and with a site-occupation factor of 0.843 (4) for the major occupied site

Schinus molle: anatomy of leaves and stems, chemical composition and insecticidal activities of volatile oil against bed bug (Cimex lectularius)

© 2019 by the authors The investigation of the constituents that were isolated from Turnera diffusa (damiana) for their inhibitory activities against recombinant human monoamine oxidases (MAO-A and MAO-B) in vitro identified acacetin 7-methyl ether as a potent selective inhibitor of MAO-B (IC50 = 198 nM). Acacetin 7-methyl ether (also known as 5-hydroxy-40, 7-dimethoxyflavone) is a naturally occurring flavone that is present in many plants and vegetables. Acacetin 7-methyl ether was four-fold less potent as an inhibitor of MAO-B when compared to acacetin (IC50 = 50 nM). However, acacetin 7-methyl ether was \u3e500-fold selective against MAO-B over MAO-A as compared to only two-fold selectivity shown by acacetin. Even though the IC50 for inhibition of MAO-B by acacetin 7-methyl ether was ~four-fold higher than that of the standard drug deprenyl (i.e., SelegilineTM or ZelaparTM, a selective MAO-B inhibitor), acacetin 7-methyl ether’s selectivity for MAO-B over MAO-A inhibition was greater than that of deprenyl (\u3e500- vs. 450-fold). The binding of acacetin 7-methyl ether to MAO-B was reversible and time-independent, as revealed by enzyme-inhibitor complex equilibrium dialysis assays. The investigation on the enzyme inhibition-kinetics analysis with varying concentrations of acacetin 7-methyl ether and the substrate (kynuramine) suggested a competitive mechanism of inhibition of MAO-B by acacetin 7-methyl ether with Ki value of 45 nM. The docking scores and binding-free energies of acacetin 7-methyl ether to the X-ray crystal structures of MAO-A and MAO-B confirmed the selectivity of binding of this molecule to MAO-B over MAO-A. In addition, molecular dynamics results also revealed that acacetin 7-methyl ether formed a stable and strong complex with MAO-B. The selective inhibition of MAO-B suggests further investigations on acacetin 7-methyl as a potential new drug lead for the treatment of neurodegenerative disorders, including Parkinson’s disease

Antimicrobial Constituents from Machaerium Pers.: Inhibitory Activities and Synergism of Machaeriols and Machaeridiols against Methicillin-Resistant Staphylococcus aureus, Vancomycin-Resistant Enterococcus faecium, and Permeabilized Gram-Negative Pathogens

Two new epimeric bibenzylated monoterpenes machaerifurogerol (1a) and 5-epi-machaerifurogerol (1b), and four known isoflavonoids (+)-vestitol (2), 7-O-methylvestitol (3), (+)-medicarpin (4), and 3,8-dihydroxy-9-methoxypterocarpan (5) were isolated from Machaerium Pers. This plant was previously assigned as Machaerium multiflorum Spruce, from which machaeriols A-D (6-9) and machaeridiols A-C (10-12) were reported, and all were then re-isolated, except the minor compound 9, for a comprehensive antimicrobial activity evaluation. Structures of the isolated compounds were determined by full NMR and mass spectroscopic data. Among the isolated compounds, the mixture 10 + 11 was the most active with an MIC value of 1.25 μg/mL against methicillin-resistant Staphylococcus aureus (MRSA) strains BAA 1696, -1708, -1717, -33591, and vancomycin-resistant Enterococcus faecium (VRE 700221) and E. faecalis (VRE 51299) and vancomycin-sensitive E. faecalis (VSE 29212). Compounds 6-8 and 10-12 were found to be more potent against MRSA 1708, and 6, 11, and 12 against VRE 700221, than the drug control ciprofloxacin and vancomycin. A combination study using an in vitro Checkerboard method was carried out for machaeriols (7 or 8) and machaeridiols (11 or 12), which exhibited a strong synergistic activity of 12 + 8 (MIC 0.156 and 0.625 µg/mL), with \u3e32- and \u3e8-fold reduction of MIC\u27s, compared to 12, against MRSA 1708 and -1717, respectively. In the presence of sub-inhibitory concentrations on polymyxin B nonapeptide (PMBN), compounds 10 + 11, 11, 12, and 8 showed activity in the range of 0.5-8 µg/mL for two strains of Acinetobacter baumannii, 2-16 µg/mL against Pseudomonas aeruginosa PAO1, and 2 µg/mL against Escherichia coli NCTC 12923, but were inactive (MIC \u3e 64 µg/mL) against the two isolates of Klebsiella pneumoniae