A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces

In this paper, we introduce two iterative schemes by the general iterative method for finding a common element of the set of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. Then, we prove two strong convergence theorems for nonexpansive mappings to solve a unique solution of the variational inequality which is the optimality condition for the minimization problem. These results extended and improved the corresponding results of Marino and Xu [G. Marino, H.K. Xu, A general iterative method for nonexpansive mapping in Hilbert spaces, J. Math. Anal. Appl. 318 (2006) 43-52], S. Takahashi and W. Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (1) (2007) 506-515], and many others.     

Extraction of Phenolic and Flavonoid Compounds from Mung Bean (Vigna radiata L.) Seed Coat by Pressurized Liquid Extraction

Mung bean seed coat (MBC) is a by-product of the mung bean processing industry. It contains a large number of phenolic compounds with therapeutic anti-inflammatory, anti-diabetic and antioxidant properties. This research aimed to investigate the optimum conditions for phenolic and flavonoid extraction from MBC by pressurized liquid extraction (PLE). Response surface methodology (RSM) was used to study the effects of temperature (80–160 °C), pressure (1200–1800 psi) and ethanol concentration (5–95%) on total phenolic content (TPC), total flavonoid content (TFC) and 2,2′-azinobis(3-ethylbenzothiazoline-6-sulfonic acid) scavenging activity (ABTS). Scale-up extraction was also performed. The optimum conditions for extraction were 160 °C, 1300 psi and 50% ethanol. Under optimum conditions, the TPC was 55.27 ± 1.14 mg gallic acid equivalent (GAE)/g MBC, TFC was 34.04 ± 0.72 mg catechin equivalent (CE)/g MBC and ABTS scavenging activity was 195.05 ± 2.29 mg trolox equivalent (TE)/g MBC. The TFC and ABTS scavenging activity of the extracts obtained at the pilot scale (10 L) was not significantly different from the laboratory scale, while TPC was significantly increased. The freeze-dried MBC extract contained vitexin and isovitexin 130.53 ± 17.89, 21.21 ± 3.22 mg/g extract, respectively. In conclusion, PLE was able to extract phenolics, flavonoids with ABTS scavenging activity from MBC with the prospect for future scale-up for food industry.     

Self-Assembly of 1D Double-Chain and 3D Diamondoid Networks of Lanthanide Coordination Polymers through In Situ-Generated Ligands: High-Pressure CO2 Adsorption and Photoluminescence Properties

Two new lanthanide-based coordination polymers, [Sm₂(bzz)(ben)₆(H₂O)₃]·0.5H₂O (1) and [Eu(bbz)(ben)₃] (2), were synthesized and characterized. The described products were formed from in situ-generated benzoate (ben) and N’-benzoylbenzohydrazide (bbz) ligands, which were the products of transformation of originally added benzhydrazide (bzz) under hydrothermal conditions. Compound 1 exhibits a one-dimensional (1D) double-chain structure built up from the connection of the central Sm³⁺ ions with a mixture of bzz and ben ligands. On the other hand, 2 features a 3D network with a 4-connected (6⁶) dia topology constructed from dinuclear [Eu₂(ben)₆] secondary building units and bbz linkers. High-pressure CO₂ sorption studies of activated 1 show that maximum uptake increases to exceptionally high values of 376.7 cm³ g⁻¹ (42.5 wt%) under a pressure of 50 bar at 298 K with good recyclability. Meanwhile, 2 shows a typical red emission in the solid state at room temperature with the decay lifetime of 1.2 ms.     

Unprecedented Reverse Volume Expansion in Spin-Transition Crystals

The current craze for research around the spin crossover phenomenon can be justified to some extent by the mechanical properties due to the decrease of volume associated with the transition of the metal ion from the HS state to the LS state. As demonstrated here, the molecular complex [Fe(PM-pBrA)₂(NCS)₂] exhibits, on the contrary, an increase of the unit-cell volume from HS to LS. This counter-intuitive and unprecedented behavior that concerns both the thermal and the photoexcited spin conversions is revealed by a combination of single-crystal and powder X-ray diffraction complemented by magnetic measurements. Interestingly, this abnormal volume change appears concomitant with the wide rotation of a phenyl ring which induces a drastic modification, though reversible, of the structural packing within the crystal. In addition, the light-induced HS state obtained through the Light-Induced Excited Spin-State Trapping shows a remarkably high relaxation temperature, namely T(LIESST), of 109 K, one of the highest so far reported. The above set of quite unusual characteristics opens up new fields of possibilities within the development of spin crossover materials.     

New reference material for analysis of elements in glutinous rice produced at the National Institute of Metrology (Thailand)

Reference materials play an important role for evaluating the accuracy of analytical results, and are essential parts of good laboratory practice. They represent a key tool for quality control of chemical analyses. In Thailand, the demand of food and environmental reference materials is constantly increasing, and the National Institute of Metrology (NIMT, Thailand) is responding to the urgent needs for affordable materials, which require collaborative efforts at the national level. This paper describes the preparation of a new glutinous rice reference material, along with homogeneity and stability studies and the analytical work carried out for the certification of the contents of inorganic elements. The incurred material was collected from an actual rice paddy field. Material preparation along with homogeneity and stability testing were carried out at the Environmental Research Training Centre (ERTC). The homogeneity study was designed to have three experimental conditions; (A) 10 bottles of candidate materials being analyzed each with 2 replicates, (B) 20 bottles with 2 replicates, (C) 10 bottles with 7 replicates, in order to study the suitable treatments for homogeneity testing in the reference material production. It was shown that a minimum number of 10 bottles with duplicate analyses are enough to demonstrate the homogeneity of candidate reference material. Certification of a candidate reference material in a single laboratory using reference method was confirmed with an interlaboratory comparison participated by a certain number of well recognized testing laboratories in Thailand. Further elaborative results will be discussed.     

A novel one‐dimensional double‐chain‐like ZnII coordination polymer: poly[bis(1‐benzyl‐1H‐imidazole‐κN3)tris(μ‐cyanido‐κ2C:N)(cyanido‐κC)disilver(I)zinc(II)]

One of most interesting systems of coordination polymers constructed from the first‐row transition metals is the porous Zn^II coordination polymer system, but the numbers of such polymers containing N‐donor linkers are still limited. The title double‐chain‐like Zn^II coordination polymer, [Ag₂Zn(CN)₄(C₁₀H₁₀N₂)₂]_n, presents a one‐dimensional linear coordination polymer structure in which Zn^II ions are linked by bridging anionic dicyanidoargentate(I) units along the crystallographic b axis and each Zn^II ion is additionally coordinated by a terminal dicyanidoargentate(I) unit and two terminal 1‐benzyl‐1H‐imidazole (BZI) ligands, giving a five‐coordinated Zn^II ion. Interestingly, there are strong intermolecular Ag^I…Ag^I interactions between terminal and bridging dicyanidoargentate(I) units and C—H…π interactions between the phenyl rings of BZI ligands of adjacent one‐dimensional linear chains, providing a one‐dimensional linear double‐chain‐like structure. The supramolecular three‐dimensional framework is stabilized by C—H…π interactions between the phenyl rings of BZI ligands and by Ag^I…Ag^I interactions between adjacent double chains. The photoluminescence properties have been studied.     

Flow boiling heat transfer of R134a in the multiport minichannel heat exchangers

The flow boiling heat transfer characteristics of R134a in the multiport minichannel heat exchangers are presented. The heat exchanger was designed as the counter flow tube-in-tube heat exchanger with refrigerant flowing in the inner tube and hot water in the gap between the outer and inner tubes. Two inner tubes were made from extruded multiport aluminium with the internal hydraulic diameter of 1.1 mm for 14 numbers of channels and 1.2 mm for eight numbers of channels. The outer surface areas of two inner test sections are 5979 mm² and 6171 m², while the inner surface areas are 13,545 mm² and 8856 mm² for 14 and eight numbers of channels, respectively. The outer tube of heat exchanger was made from circular acrylic tube with an internal hydraulic diameter of 25.4 mm. The experiments were performed at the heat fluxes between 15 and 65 kW/m², mass flux of refrigerant between 300 and 800 kg/m² s and saturation pressure ranging from 4 to 6 bar. For instance the boiling curve, average heat transfer coefficients are discussed. The comparison results of two test sections with different the number of channels are investigated. The results are also compared with nine existing correlations. The new correlation for predicting the heat transfer coefficient was also proposed.     

Evaporation heat transfer and flow characteristics of R-134a flowing through internally grooved tubes

This article describes experimental investigations of the heat transfer coefficient and pressure drop of R-134a flowing inside internally grooved tubes. The test tubes are one smooth tube and four grooved tubes. All test tubes are made from type 304 stainless steel, have an inner diameter of 7.1 mm, are 2,000 mm long and are installed horizontally. The test section is uniformly heated by a DC power supply to create evaporation conditions. The groove depth of all grooved tubes is fixed at 0.2 mm. The experimental conditions are conducted at saturation temperatures of 20, 25 and 30°C, heat fluxes of 5, 10 and 15 kW/m², and mass fluxes of 300, 500 and 700 kg/m² s. The effects of groove pitch, mass flux, heat flux, and saturation temperature on heat transfer coefficient and frictional pressure drop are discussed. The results illustrate that the grooved tubes have a significant effect on the heat transfer coefficient and frictional pressure drop augmentations.     

The general iterative methods for nonexpansive mappings in Banach spaces

In this paper, we introduce a general iterative approximation method for finding a common fixed point of a countable family of nonexpansive mappings which is a unique solution of some variational inequality. We prove the strong convergence theorems of such iterative scheme in a reflexive Banach space which admits a weakly continuous duality mapping. As applications, at the end of the paper, we apply our results to the problem of finding a zero of an accretive operator. The main result extends various results existing in the current literature.     

Strong convergence of the iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems of an infinite family of nonexpansive mappings

In this paper, we introduce an iterative scheme based on the extragradient approximation method for finding a common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of solutions of a mixed equilibrium problem, and the set of solutions of the variational inequality problem for a monotone L-Lipschitz continuous mapping in a real Hilbert space. Then, the strong convergence theorem is proved under some parameters controlling conditions. Applications to optimization problems are given. The results obtained in this paper improve and extend the recent ones announced by Wangkeeree [R. Wangkeeree, An extragradient approximation method for equilibrium problems and fixed point problems of a countable family of nonexpansive mappings, Fixed Point Theory and Applications (2008) 17. doi:10.1155/2008/134148. Article ID 134148], Kumam and Katchang [P. Kumam, P. Katchang, A viscosity of extragradient approximation method for finding equilibrium problems, variational inequalities and fixed point problems for nonexpansive mappings, Nonlinear Anal. Hybrid Syst. (2009) doi:10.1016/j.nahs.2009.03.006] and many others.