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.     

Two types of explicit continued fractions

Summary Two types of explicit continued fractions are presented. The continued fractions of the first type include those discovered by Shallit in 1979 and 1982, which were later generalized by Pethő. They are further extended here using Peth\H o's method. The continued fractions of the second type include those whose partial denominators form an arithmetic progression as expounded by Lehmer in 1973. We give here another derivation based on a modification of Komatsu's method and derive its generalization. Similar results are also established for continued fractions in the field of formal series over a finite base field.     

Independence of continued fractions in the field of Laurent series

Criteria for independence, both algebraic and linear, are derived for continued fraction expansions of elements in the field of Laurent series. These criteria are then applied to examples involving elements recently discovered to have explicit series and continued fraction expansions. Communicated by Attila Pethő     

Exogenous Spermidine Alleviates UV-Induced Growth Inhibition of Synechocystis sp. PCC 6803 via Reduction of Hydrogen Peroxide and Malonaldehyde Levels

Effects of exogenously added spermidine (Spd) to UV-treated Synechocystis sp. PCC 6803 cultures on their growth, intracellular pigments, hydrogen peroxide (H₂O₂), malonaldehyde (MDA) contents, and antioxidant enzymes were investigated. Growth inhibition of cells subjected to 1-h UV-A, UV-B, and UV-C irradiation was abolished in culture added with 0.5 mM Spd. Both chlorophyll a and carotenoid contents were decreased under UV radiations in cells grown in BG₁₁ medium. However, the contents of these two pigments were slightly increased under UV radiations in Spd-supplemented cells with the consequence of enhanced oxygen evolution. Intracellular levels of H₂O₂ and MDA generated during 1-h UV irradiation were decreased when the culture medium contained 0.5 mM Spd. The antioxidative enzymes, catalase, and superoxide dismutase had a little or no response towards Spd supplementation under UV irradiation except for some increase in superoxide dismutase activity under UV-C. Total intracellular polyamines were decreased during Spd supplementation under UV stress; however, the cells showed a drastic increase in the amount of Put under this condition. Altogether, exogenous Spd is likely a potential compound that enables Synechocystis cells to cope with UV stress.     

A new hybrid iterative method for mixed equilibrium problems and variational inequality problem for relaxed cocoercive mappings with application to optimization problems

In this paper, we introduce and study a new hybrid iterative method for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of variational inequalities for a ξ-Lipschitz continuous and relaxed (m,v)-cocoercive mappings in Hilbert spaces. Then, we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm which solves some optimization problems under some suitable conditions. Our results extend and improve the recent results of Yao et al. [Y. Yao, M.A. Noor, S. Zainab and Y.C. Liou, Mixed equilibrium problems and optimization problems, J. Math. Anal. Appl (2009). doi:10.1016/j.jmaa.2008.12.005] and Gao and Guo [X. Gao and Y. Guo, Strong convergence theorem of a modified iterative algorithm for Mixed equilibrium problems in Hilbert spaces, J. Inequal. Appl. (2008). doi:10.1155/2008/454181] and many others.     

A general iterative method for addressing mixed equilibrium problems and optimization problems

In this paper, we introduce a new general iterative method for finding a common element of the set of solutions of a mixed equilibrium problem (MEP), the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of variational inequalities for a ξ-inverse-strongly monotone mapping in Hilbert spaces. Furthermore, we establish the strong convergence theorem for the iterative sequence generated by the proposed iterative algorithm under some suitable conditions, which solves some optimization problems. Our results extend and improve the recent results of Yao et al. [Y. Yao, M.A. Noor, S. Zainab, Y.C. Liou, Mixed equilibrium problems and optimization problems, J. Math. Anal. Appl. 354 (2009) 319-329; Y. Yao, M. A. Noor, Y.C. Liou, On iterative methods for equilibrium problems, Nonlinear Anal. 70 (1) (2009) 479-509] and many others.     

A convergence theorem based on a hybrid relaxed extragradient method for generalized equilibrium problems and fixed point problems of a finite family of nonexpansive mappings

The purpose of this paper is to consider a new hybrid relaxed extragradient method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of fixed points of a finite family of nonexpansive mappings and the set of solutions of variational inequalities for an inverse-strongly monotone mapping in Hilbert spaces. Then, we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm under some suitable conditions. Our results extend and improve the recent results of Cai and Hu [G. Cai, C.S. Hu, A hybrid approximation method for equilibrium and fixed point problems for a family of infinitely nonexpansive mappings and a monotone mapping, Nonlinear Anal. Hybrid Syst., 3(2009) 395–407], Kangtunyakarn and Suantai [A. Kangtunyakarn, S. Suantai, A new mapping for finding common solution of equilibrium problems and fixed point problems of finite family of nonexpansive mappings, Nonlinear Anal., 71(2009) 4448–4460] and Thianwan [S. Thianwan, Strong convergence theorems by hybrid methods for a finite family of nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal. Hybrid Syst., 3(2009) 605–614] and many others.     

Using an improved electrostatic precipitator for poultry dust removal

Pubic concerns related to particulate matter emissions from animal housing operations are increasing. The goal of this study was to custom develop a simple and low cost electrostatic precipitator (ESP) for poultry dust control. The performance of the improved electrostatic precipitator (iESP) to remove a test aerosol was evaluated under a series of operating voltages between ?60 kV and 60 kV. The mass and size distributions of the particles were measured by a cascade impactor. The overall dust removal efficiency ranged from 37% to 79% with the maximum efficiency obtained at ?30 kV. The iESP shows high removal efficiencies for particles less than 2.1 μm.     

Novel Acetogenins from the Leaves of Dasymaschalon sootepense

The hexane extract from the leaves of Dasymaschalon sootepense Craib (Annonaceae) showed strong cytotoxic activity against the L1210 tumor cell line. Activity-directed fractionation of the extract by column chromatography on silica gel and high-pressure liquid chromatography led to the isolation of the acetogenins 1 – 4 as the main active principles. The structures of the two novel structures named sootepensin A ( 1 ) and sootepensin B ( 2 ) were elucidated by spectroscopic analysis (UV, EI- and ESI-MS, 1D- and 2D-¹H- and ¹³C-NMR). The absolute configurations were established by 2D-NMR experiments utilizing Mosher esters. Two recently described compounds, tonkinin C ( 3 ) and tonkinesin C ( 4 ), were also isolated and are new to the genus Dasymaschalon. All four acetogenins were found to be highly cytotoxic against the L1210 tumor cell line.