Synthesis of tripodal aza crown ether calix[4]arenes and their supramolecular chemistry with transition-, alkali metal ions and anions

Tripodal aza crown ether calix[4]arenes, 5a, 5b, 6a and 6b, have been synthesized. The structure of protonated 5a was elucidated by X-ray crystallography to be a self-threaded rotaxane. Complexation studies of 5a and 5b towards anions using Na⁺ as countercation were carried out by ¹H NMR titration in dimethylsulfoxide-d₆ and the mixture of chloroform-d and methanol-d₄, respectively. Ligands 5a and 5b were able to form 1:1 complexes with Br⁻, I⁻ and NO₃⁻ and the complexation stability varied as follows: NO₃⁻>I⁻>Br⁻. The effect of countercation on anion complexation was also investigated. The results showed that the association constants of 5a towards Br⁻ in the presence of various cations varied as K⁺>Bu₄N⁺>Na⁺. The enhancement in anion complexation ability of 5a may result from the rearrangement of the tripodal ammonium unit in the presence of K⁺. The neutral forms, 6a and 6b, were able to form complexes with transition metal ions such as Co²⁺, Ni²⁺, Cu²⁺ and Zn²⁺. The stability of the complexes followed the sequence: Ni²⁺2+Cu²⁺Zn²⁺. Compounds 6a and 6b may, therefore, potentially be used as either transition metal ion or anion receptors that can be controlled by pH of the solution.     

Hydrogen bonding in labdane diterpenoids, labda-7,12(E),14-triene-17-oic acid and labda-12(Z),14,17-triene-18-oic acid

Two labdane diterpenoids, labda-7,12(E),14-triene-17-oic acid (1) and labda-12(Z),14,17-triene-18-oic acid (2), C₂₀H₃₀O₂, have been isolated from Croton oblongifolius. Both 1 and 2 crystallized in the monoclinic system, space group C2, with cell dimensions of a = 21.912(1) Å, b = 7.4002(4) Å, c = 11.5079(7) Å, = 101.999(1)^o and a = 21.308(2) Å, b = 11.9067(9) Å, c = 7.5606(6) Å, = 100.763(1)^o, respectively. Compound 1, a rare example of carboxylic group bound to a cyclohexene ring, forms an infinite intermolecular hydrogen-bonded polymer [O1 O2(–x + 1/2, y + 1/2, –z + 2) 2.697(2) Å], whereas molecules of compound 2 are linked to form an asymmetric hydrogen-bonded dimer [O1 O2(–x, y, –z) 2.657(3) Å].     

AN EXTRAGRADIENT METHOD FOR RELAXED COCOERCIVE VARIATIONAL INEQUALITY AND EQUILIBRIUM PROBLEMS

The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of an equilibrium problem and the set of solutions of the variational inequality prob- lem for a relaxed cocoercive and Lipschitz continuous mapping in Hilbert spaces. Then, we show that the sequence converges strongly to a common element of the above three sets under some parameter controlling conditions, which are connected with Yao, Liou, Yao[17], Takahashi[12] and many others.     

A general iterative method for solving equilibrium problems, variational inequality problems and fixed point problems of an infinite family of nonexpansive mappings

In this paper, we introduce and analyze a new general iterative scheme by the viscosity approximation method for finding the common element of the set of equilibrium problems, the set of fixed points of an infinite family of nonexpansive mappings and the set solutions of the variational inequality problems for an ξ-inverse-strongly monotone mapping in Hilbert spaces. We show that the sequence converge strongly to a common element of the above three sets under some parameters controlling conditions. The result extends and improves a recent result of Chang et al. (Nonlinear Anal. 70:3307–3319, 2009) and many others.     

(Triphenylarsine)iodinemonobromine: a charge‐transfer adduct in which arsenic selectively bonds to iodine

The title molecule, (iodobromo)triphenylarsenic(III), [As(BrI)(C₆H₅)₃], has a dart shape, with the phenyl rings arranged in a propeller conformation [I—As—C—C 61.3 (4), 43.8 (4) and 54.1 (4)°]. There is no indication that the halogen atoms have mixed site occupancies. Packing forces displace the I atom away from one phenyl ring [I—As—C 117.3 (2)°] towards the other two [I—As—C 109.8 (2) and 108.3 (2)°] and produce an even more pronounced leaning of the terminal bromine [As—I—Br 174.78 (2)°].     

Crystal structure of diethoxynitrobenzene-p-tert-butylcalix [4]arene⋅2(CH3)2C=O: Evidence of intra- and intermolecular CH/π interactions forced by crystal packing

Diethoxynitrobenzene-p-tert-butylcalix[4]arene2(CH₃)₂C=O crystallized in the monoclinic system, space group P2₁/c, with cell dimensions a = 16.1437(2) Å, b = 21.0292(2) Å, c = 18.9685(3) Å and = 110.308(1)°. The asymmetric unit consists of a diethoxynitrobenzene-p-tert-butylcalix[4]arene molecule and two solvated acetone molecules. Besides the usual CH/ interaction between p-tert-butylcalix[4]arene cavity and a solvated acetone, this structure shows the intra- and intermolecular CH/ interactions among a nitrobenzene ring, ethylene bridge of the ethoxynitrobenzene side chain and a solvated acetone molecule.     

An extragradient method for relaxed cocoercive variational inequality and equilibrium problems

The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of a countable family of nonexpansivemappings, the set of an equilibrium problem and the set of solutions of the variational inequality problem for a relaxed cocoercive and Lipschitz continuous mapping in Hilbert spaces. Then, we show that the sequence converges strongly to a common element of the above three sets under some parameter controlling conditions, which are connected with Yao, Liou, Yao, Takahashi and many others.