Positive solution for singular boundary value problems

AbstractA sufficient condition for the existence of positive solutions of the nonlinear boundary value problem u″(t) + f(t, u(t)) = 0, 0<t<, u′(0) = u(1) = 0is constructed, where f : [0, 1) × (0, ∞) → (0, ∞) is continuous, f(t, u) is locally Lipschitz continuous, and f(t, u)u is strictly decreasing in u > 0 for each t ∈ (0, 1)

1-Carboxymethyl-1′-carboxylatomethyl-3,3′-[p-phenylenebis(oxymethylene)]dipyridinium bromide dihydrate

In the crystal structure of the title salt, C22H21N2O6 +·Br−·2H2O, pairs of betaine mol­ecules are bridged by protons (the bridging proton is disordered), forming strong and symmetrical O—H⋯O hydrogen bonds, leading to an infinite chain along the b axis. The water mol­ecules are linked to the betaine mol­ecule and the bromide ion through O—H⋯O and O—H⋯Br inter­actions. The central ring, located on an inversion centre, makes dihedral angles of 1.2 (2)° with the outer rings. One of the carboxylic acid groups is deprotonated

catena-Poly[[[diaqua­copper(II)]-μ-2,2′-{[p-phenyl­enebis(oxymethyl­ene)]bis­(pyridinium-3,1-di­yl)}diacetate] dibromide]

The title centrosymmetric coordination polymer, {[Cu(C22H20N2O6)(H2O)2]Br2}n, formed by the reaction of the flexible double betaine ligand 2,2′-{[p-phenyl­enebis(oxymethyl­ene)]bis­(pyridine-3,1-di­yl)}diacetic acid with CuBr2, contains a Cu(II) atom ( symmetry) which is surrounded by two water molecules and bridged by two anions in a square-planar coordination. In the crystal, polymeric zigzag chains are linked via O—H⋯Br inter­actions, forming a two-dimensional network extending parallel to (011)

Alpha-mangostin and beta-mangostin from Cratoxylum laucum.

Our continuing interest in xanthones and anthraquinones from the Cratoxylum genus has led us to look at Cratoxylum glaucum. This resulted in the isolation of alpha-mangostin (1), beta-mangostin (2), fuscaxanthone C (3), 3-geranyloxy-6-methyl-1,8-dihydroxyanthraquinone (4), beta-sitosterol (5), 1,8-dihydroxy-3-methoxy-6-methylanthraquinone (6), stigmasterol (7), friedelin (8) and betulinic acid (9). Structural elucidations of these compounds were achieved by using ID and 2D NMR spectroscopic experiments. Cytotoxic assays indicated that the hexane and ethyl acetate extracts demonstrated cytotoxicity against the MCF7 cancer cell line. Meanwhile, the ethyl acetate and methanol extracts of C. glaucum inhibited the HL-60 cancer cell line activity

catena-Poly[[[tetra­aqua­cadmium(II)]-μ-3,3′-[p-phenyl­enebis(oxymethyl­ene)]bis­(1-pyridinioacetate)] dinitrate hemihydrate]

In the title polymeric coordination complex, {[Cd(C22H20N2O6)(H2O)4](NO3)2·0.5H2O}n, obtained from the self-assembly of the flexible double betaine 3,3′-[p-phenyl­enebis(oxymethyl­ene)]bis­(1-pyridinioacetate) with cadmium nitrate, both the octa­hedrally coordinated CdII cation and the substituted betaine ligand lie on inversion centres. The chains constructed through the trans-related acetate groups of the ligand are inter-connected via O—H⋯O hydrogen bonds involving coordinated aqua ligands, the nitrate anions and the partial-occupancy (0.25) water mol­ecule of solvation, forming a three-dimensional structure

Fixed-point theorems in fuzzy real line

AbstractSome sufficient conditions for the existence of fixed points of increasing operators in fuzzy real line RL are given. We also establish some coupled quasi-fixed-point theorems of mixed monotone operators in fuzzy real line RL

Xanthones from Calophyllum inophyllum

Repeated separation and purification of fractions from the crude chloroform extract of Calophyllum inophyllum via column chromatography afforded five known xanthone caloxanthones A, B, C, macluraxanthone and pyranojacareubin. Structural elucidations and determination of the isolated compounds were supported by spectral analyses obtained by subjecting the compounds to various spectroscopic techniques. The chloroform extract, when tested against RAW264.7 cells for anti-inflammatory potentials, exhibited the most promising activity with an IC50 value of 14.81±0.04 µg/mL compared to moderate activities shown by the ethyl acetate and n-hexane extracts. Antimicrobial tests showed that the n-hexane and chloroform extracts acted moderately against Staphylococcus epidermidis S273 and Bacillus subtilis B145