An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings

In this paper, we propose an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a strict pseudo-contraction mapping in the setting of real Hilbert spaces. We establish some weak and strong convergence theorems of the sequences generated by our proposed scheme. Our results combine the ideas of Marino and Xu’s result [G. Marino, H.K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007) 336–346], and Takahashi and Takahashi’s result [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506–515]. In particular, necessary and sufficient conditions for strong convergence of our iterative scheme are obtained.     

Weak convergence theorems for a countable family of Lipschitzian mappings

This paper is concerned with convergence of an approximating common fixed point sequence of countable Lipschitzian mappings in a uniformly convex Banach space. We also establish weak convergence theorems for finding a common element of the set of fixed points, the set of solutions of an equilibrium problem, and the set of solutions of a variational inequality. With an appropriate setting, we obtain and improve the corresponding results recently proved by Moudafi [A. Moudafi, Weak convergence theorems for nonexpansive mappings and equilibrium problems. J. Nonlinear Convex Anal. 9 (2008) 37–43], Tada–Takahashi [A. Tada and W. Takahashi, Weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem. J. Optim. Theory Appl. 133 (2007) 359–370], and Plubtieng–Kumam [S. Plubtieng and P. Kumam, Weak convergence theorem for monotone mappings and a countable family of nonexpansive mappings. J. Comput. Appl. Math. (2008) doi:10.1016/j.cam.2008.05.045]. Some of our results are established with weaker assumptions.     

Equilibrium and <Superscript>1</Superscript>H NMR Kinetic Study of the Reactions of Dichlorido [S-Methyl-L-Cysteine(N,S)]Platinum(II) Complex with Some Relevant Biomolecules

The formation equilibria of the [Pt(SMC)(H₂O)₂]⁺ complex with some biologically relevant ligands such as L-methionine (L-met) and glutathione (GSH) were studied. The stoichiometry and stability constants of the formed complexes are reported, and the concentration distribution of the various complex species has been evaluated as a function of pH. The reaction between [PtCl₂(SMC)] and guanosine-5′-monophosphate (5′-GMP) was studied by ¹H NMR spectroscopy. The NMR spectra indicated that first step is the hydrolysis of the [PtCl₂(SMC)] complex and second step is the substitution of an aqua ligand, either in the cis or trans position with guanosine-5′-monophosphate in molar ratio 1:1. The values of rate constant showed faster substitution of coordinated H₂O in the trans position to the S donor atom of S-methyl-L-cysteine, whereas the slower reaction was assigned to the displacement of the cis coordinated aqua molecule. This is due to the strong trans labilization effect of coordinated sulfur. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

Measurement and prediction of tie-line data for mixtures of (water + 1-propanol + diisopropyl ether): LLE diagrams as a function of temperature

Tie-line data for ternary system of (water + 1-propanol + diisopropyl ether (DIPE)) were determined at T = (298.2, 308.2 and 313.2) K under atmospheric conditions. The ternary system exhibited type-I LLE behavior, as (DIPE + water) is the only liquid pair that is partially miscible. The experimental data for this system were predicted with the UNIFAC model with a root mean square deviation of 2.64%. The reliability of the experimental tie-line data was determined through the Othmer–Tobias and Hand plots. Distribution coefficients and separation factors were measured to evaluate the extracting capability of the solvents. The influence of temperature effect on the equilibrium characteristics and separation factor was found to be significant at the temperatures studied.     

A novel multi-directional multi-scroll chaotic system and its CCII+ circuit implementation

This paper proposes a generalized formula of multi-directional multi-scroll chaotic system. Based on the generalized formula, by adding the nonlinear functions, and controlling the parameters of system, multi-directional multi-scroll chaotic attractors with different order system can be generated. According to this method, the correctness of generalized formula is verified. Then, basic dynamic characteristics of the system including the fractal, equilibrium points, Poincaré section, Lyapunov exponent spectrum and bifurcation diagram are analyzed. Finally, a nine-dimensional chaotic circuit based on CCII₊ devices is designed, which verified the feasibility of the generalized formula and multi-directional multi-scroll chaotic circuit with CCII₊ devices.     

常压溶剂法合成抗氧剂3114反应热力学和动力学

研究了常压溶剂法一步合成抗氧剂3114反应热力学和动力学过程。控制温度在117±2℃,研究结果表明,反应是零级反应,反应速率常数为k=1．91×10^-3／min,反应的平衡常数为K=138．4（mol／L）^-6,反应活化能Ea=1366J／mol。     

Subleading long-range interactions and violations of finite size scaling

We study the behavior of systems in which the interaction contains a long-range component that does not dominate the critical behavior. Such a component is exemplified by the van der Waals force between molecules in a simple liquid-vapor system. In the context of the mean spherical model with periodic boundary conditions we are able to identify, for temperatures close above T _c, finite-size contributions due to the subleading term in the interaction that are dominant in this region decaying algebraically as a function of L. This mechanism goes beyond the standard formulation of the finite-size scaling but is to be expected in real physical systems. We also discuss other ways in which critical point behavior is modified that are of relevance for analysis of Monte Carlo simulations of such systems. Received 21 November 2000 and Received in final form 28 February 2001     

Core percolation in random graphs: a critical phenomena analysis

We study both numerically and analytically what happens to a random graph of average connectivity α when its leaves and their neighbors are removed iteratively up to the point when no leaf remains. The remnant is made of isolated vertices plus an induced subgraph we call the core. In the thermodynamic limit of an infinite random graph, we compute analytically the dynamics of leaf removal, the number of isolated vertices and the number of vertices and edges in the core. We show that a second order phase transition occurs at α = e = 2.718 ... : below the transition, the core is small but above the transition, it occupies a finite fraction of the initial graph. The finite size scaling properties are then studied numerically in detail in the critical region, and we propose a consistent set of critical exponents, which does not coincide with the set of standard percolation exponents for this model. We clarify several aspects in combinatorial optimization and spectral properties of the adjacency matrix of random graphs. Received 31 January 2001 and Received in final form 26 June 2001     

On balking from an empty queue

The intuition while observing the economy of queueing systems, is that one’s motivation to join the system, decreases with its level of congestion. Here we present a queueing model where sometimes the opposite is the case. The point of departure is the standard first-come first-served single server queue with Poisson arrivals. Customers commence service immediately if upon their arrival the server is idle. Otherwise, they are informed if the queue is empty or not. Then, they have to decide whether to join or not. We assume that the customers are homogeneous and when they consider whether to join or not, they assess their queueing costs against their reward due to service completion. As the whereabouts of customers interact, we look for the (possibly mixed) join/do not join Nash equilibrium strategy, a strategy that if adopted by all, then under the resulting steady-state conditions, no one has any incentive not to follow it oneself. We show that when the queue is empty then depending on the service distribution, both ‘avoid the crowd’ (ATC) and ‘follow the crowd’ (FTC) scenarios (as well as none-of-the-above) are possible. When the queue is not empty, the situation is always that of ATC. Also, we show that under Nash equilibrium it is possible (depending on the service distribution) that the joining probability when the queue is empty is smaller than it is when the queue is not empty. This research was supported by The Israel Science Foundation Grant No. 237/02.     

Study of Plasma MHD Equilibrium in HL-2A Tokamak

In an axisymmetric toroidal system, the MHD equilibrium Grad-Shafranov equation can be written as