Chi Kin Chan

Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces

Abstract The approximate solvability of a generalized system for relaxed cocoercive nonlinear variational inequality in Hilbert spaces is studied, based on the convergence of projection methods. The results presented in this paper extend and improve the main results of [R.U. Verma, Generalized system for relaxed cocoercive variational inequalities and its projection methods, J. Optim. Theory Appl. 121 (1) (2004) 203–210; R.U. Verma, Generalized class of partial relaxed monotonicity and its connections, Adv. Nonlinear Var. Inequal. 7 (2) (2004) 155–164; R.U. Verma, General convergence analysis for two-step projection methods and applications to variational problems, Appl. Math. Lett. 18 (11) (2005) 1286–1292; N.H. Xiu, J.Z. Zhang, Local convergence analysis of projection type algorithms: Unified approach, J. Optim. Theory Appl. 115 (2002) 211–230; H. Nie, Z. Liu, K.H. Kim, S.M. Kang, A system of nonlinear variational inequalities involving strongly monotone and pseudocontractive mappings, Adv. Nonlinear Var. Inequal. 6 (2) (2003) 91–99].

Application of a mixed simulated annealing-genetic algorithm heuristic for the two-dimensional orthogonal packing problem

Abstract In this paper a pure meta-heuristic (genetic algorithm) and a mixed meta-heuristic (simulated annealing-genetic algorithm) were applied to two-dimensional orthogonal packing problems and the results were compared. The major motivation for applying a modified genetic algorithm is as an attempt to alleviate the problem of pre-mature convergence. We found that in the long run, the mixed heuristic produces better results; while the pure heuristic produces only “good” results, but produces them faster.

Regulation of Src Homology 2-containing Tyrosine Phosphatase 1 during Activation of Human Neutrophils ROLE OF PROTEIN KINASE C

The tyrosine phosphorylation of several proteins induced in neutrophils by soluble and particulate stimuli is thought to be crucial for initiating antimicrobial responses. Although activation of tyrosine kinases is thought to mediate this event, the role of tyrosine phosphatases in the initiation and modulation of neutrophil responses remains largely undefined. We investigated the role of Src homology 2-containing tyrosine phosphatase 1 (SHP-1; also known as protein tyrosine phosphatase 1C (PTP1C), hematopoetic cell phosphatase, PTP-N6, and SHPTP-1), a phosphatase expressed primarily in hemopoietic cells, in the activation of human neutrophils. SHP-1 mRNA and protein were detected in these cells, and the enzyme was found to be predominantly localized to the cytosol in unstimulated cells. Following stimulation with neutrophil agonists such as phorbol ester, chemotactic peptide, or opsonized zymosan, a fraction of the phosphatase redistributed to the cytoskeleton. Agonist treatment also induced significant decreases (30-60%) in SHP-1 activity, which correlated temporally with increases in the cellular phosphotyrosine content. Phosphorylation of SHP-1 on serine residues was associated with the inhibition of its enzymatic activity, suggesting a causal relationship. Accordingly, both the agonist-evoked phosphorylation of SHP-1 and the inhibition of its catalytic activity were blocked by treatment with bisindolylmaleimide I, a potent and specific inhibitor of protein kinase C (PKC) activity. Immunoprecipitated SHP-1 was found to be phosphorylated efficiently by purified PKC in vitro. Such phosphorylation also caused a decrease in the phosphatase activity of SHP-1. Together, these data suggest that inhibition of SHP-1 by PKC-mediated serine phosphorylation plays a role in facilitating the accumulation of tyrosine-phosphorylated proteins following neutrophil stimulation. These findings provide a new link between the PKC and tyrosine phosphorylation branches of the signaling cascade that triggers antimicrobial responses in human neutrophils.

Leveraging the supply chain flexibility of third party logistics - Hybrid knowledge-based system approach

Nowadays, intensified globalization and consequent competitive pressures have reemphasized the importance of third party logistics (3PL) in managing logistics processes as well as customer and supplier relationships within the supply chain management (SCM). However, 3PL providers and their upstream and downstream parties within the whole chain have usually interacted as disconnected entities in the logistics performance management process. Despite the increased interest in using and improving logistics information systems, the number of researchers investigating the design and implementation of this process in close detail is still very small. This paper proposes an intelligent performance measurement system (K-LPMS) for measuring the performance of 3PL providers and their upstream and downstream supply chain partners. With the help of K-LPMS, 3PL providers are capable to fulfil different customers supply chain service requirement through accessing the capability of each SC partners and reconfigure SC network. This paper describes the structure of K-LPMS and its features. The results of testing and applying the tool in companies are presented. This paper concludes by discussing the implications of this research for managers, and identifying directions for future research.

Modified block iterative algorithm for Quasi-ϕ-asymptotically nonexpansive mappings and equilibrium problem in banach spaces

Abstract The purpose of this paper is to propose a modified block iterative algorithm for find a common element of the set of common fixed points of an infinite family of quasi-ϕ-asymptotically nonexpansive mappings and the set of an equilibrium problem. Under suitable conditions, some strong convergence theorems are established in a uniformly smooth and strictly convex Banach space with the Kadec–Klee property. As an application, at the end of the paper a numerical example is given. The results presented in the paper improve and extend the corresponding results in Qin et al. [Convergence theorems of common elements for equilibrium problems and fixed point problem in Banach spaces, J. Comput. Appl. Math., 225, 2009, 20–30], Zhou et al. [Convergence theorems of a modified hybrid algorithm for a family of quasi-ϕ-asymptotically nonexpansive mappings, J. Appl. Math. Compt., 17 March, 2009, doi:10.1007/s12190-009-0263-4], Takahashi and Zembayshi [Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Nonlinear Anal., 70, 2009, 45–57], Wattanawitoon and Kumam [Strong convergence theorems by a new hybrid projection algorithm for fixed point problem and equilibrium problems of two relatively quasi-nonexpansive mappings, Nonlinear Anal. Hybrid Syst., 3, 2009, 11–20] and Matsushita and Takahashi [A strong convergence theorem for relatively nonexpansive mappings in Banach spaces, J. Approx. Theory, 134, 2005, 257–266] and others.

Solving the multi-buyer joint replenishment problem with a modified genetic algorithm

The joint replenishment problem (JRP) is a multi-item inventory problem. The objective is to develop inventory policies that minimize the total costs (comprised of holding cost and setup cost) over the planning horizon. In this paper, we look at the multi-buyer, multi-item version of the JRP. We propose a new modified genetic algorithm which is very efficient. Tests are conducted on problems from a leading bank in Hong Kong and from the literature.

A modified halpern-type iteration algorithm for totally quasi-ϕ-asymptotically nonexpansive mappings with applications

Abstract The purpose of this article is to modify the Halpern-type iteration algorithm for total quasi- ϕ -asymptotically nonexpansive mapping to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding results of [X.L. Qin, Y.J. Cho, S.M. Kang, H. Y. Zhou, Convergence of a modified Halpern-type iterative algorithm for quasi- ϕ -nonexpansive mappings, Appl. Math. Lett. 22 (2009) 1051–1055], [Z.M. Wang, Y.F. Su, D.X. Wang, Y.C. Dong, A modified Halpern-type iteration algorithm for a family of hemi-relative nonexpansive mappings and systems of equilibrium problems in Banach spaces, J. Comput. Appl. Math. 235 (2011) 2364–2371], [Y.F. Su, H.K. Xu, X. Zhang, Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications, Nonlinear Anal. 73 (2010) 3890–3906], [C. Martinez-Yanes, H.K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006) 2400–2411] and others.

Demiclosed principle and Δ-convergence theorems for total asymptotically nonexpansive mappings in CAT(0) spaces☆

Abstract The purpose of this paper is to introduce the concept of total asymptotically nonexpansive mappings and to prove the demiclosed principle for this kind of mappings in CAT(0) spaces. As a consequence, we obtain a Δ -convergence theorem of the Krasnoselskii – Mann type iteration for total asymptotically nonexpansive mappings in this setting. Our results extend and improve the corresponding recent results announced by many authors.

Approximation theorems for total quasi-ϕ-asymptotically nonexpansive mappings with applications☆

Abstract The purpose of this article is to prove some approximation theorems of common fixed points for countable families of total quasi-ϕ-asymptotically nonexpansive mappings which contain several kinds of mappings as its special cases in Banach spaces. In order to get the approximation theorems, the hybrid algorithms are presented and are used to approximate the common fixed points. Using this result, we also discuss the problem of strong convergence concerning the maximal monotone operators in a Banach space. The results of this article extend and improve the results of Matsushita and Takahashi [S. Matsushita, W. Takahashi, A strong convergence theorem for relatively nonexpansive mappings in Banach spaces, J. Approx. Theor. 134 (2005) 257–266], Plubtieng and Ungchittrakool [S. Plubtieng, K. Ungchittrakool, Hybrid iterative methods for convex feasibility problems and fixed point problems of relatively nonexpansive mappings in Banach spaces, J. Approx. Theor. 149 (2007) 103–115], Li, Su [H. Y. Li, Y. F. Su, Strong convergence theorems by a new hybrid for equilibrium problems and variational inequality problems, Nonlinear Anal. 72(2) (2010) 847-855], Su, Xu and Zhang [Y.F. Su, H.K. Xu, X. Zhang, Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications, Nonlinear Anal. 73 (2010) 3890–3960], Wang et al. [Z.M. Wang, Y.F. Su, D.X. Wang, Y.C. Dong, A modified Halpern-type iteration algorithm for a family of hemi-relative nonexpansive mappings and systems of equilibrium problems in Banach spaces, J. Comput. Appl. Math. 235 (2011) 2364–2371], Chang et al. [S.S. Chang, H.W. Joseph Lee, Chi Kin Chan, A new hybrid method for solving a generalized equilibrium problem solving a variational inequality problem and obtaining common fixed points in Banach spaces with applications, Nonlinear Anal. 73 (2010) 2260–2270], Chang et al. [S.S. Chang, C.K. Chan, H.W. Joseph Lee, Modified block iterative algorithm for quasi-ϕ-asymptotically nonexpansive mappings and equilibrium problem in Banach spaces, Appl. Math. Comput. 217 (2011) 7520–7530], Ofoedu and Malonza [E.U. Ofoedu, D.M. Malonza, Hybrid approximation of solutions of nonlinear operator equations and application to equation of Hammerstein-type, Appl. Math. Comput. 217 (2011) 6019–6030] and Yao et al. [Y.H. Yao, Y.C. Liou, S.M. Kang, Strong convergence of an iterative algorithm on an infinite countable family of nonexpansive mappings, Appl. Math. Comput. 208 (2009) 211–218].

The value of combining forecasts in inventory management – a case study in banking

Managing inventories in the face of uncertain stochastic demand requires an investment in safety stocks. These are related to the accuracy in forecasting future demands and the noise in the demand generation process. Reducing the demand forecasting error can free up capital and space, and reduce the operating costs of managing the inventories. A leading bank in Hong Kong consumes more than three hundred kinds of printed forms for its daily operations. A major problem of its inventory control system for the forms management is to forecast the monthly demand of these forms. In this study the idea of combining forecasts is introduced and its practical application is addressed. The individual forecasts come from well established time series models and the weights for combination are estimated with Quadratic Programming. The combined forecast is found to perform better than any of the individual forecasts.