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A FIRST-ORDER SPLITTING METHOD FOR SOLVING A LARGE-SCALE COMPOSITE CONVEX OPTIMIZATION PROBLEM

Journal of Computational Mathematics 2019年第5期37卷 666-688页

作者： Yuchao Tang Guorong Wu chuanxi zhu School of Management Nanchang UniversityNanchang 330031China Department of Mathematics Nanchang UniversityNanchang 330031China Department of Radiology and BRIC University of North Carolina at Chapel HillNC27599USA

In this paper, we construct several efficient first-order splitting algorithms for solving a multi-block composite convex optimization problem. The objective function includes a smooth function with a Lipschitz continuous gradient, a proximable convex function that may be nonsmooth, and a finite sum composed of a proximable function and a bounded linear operator. To solve such an optimization problem, we transform it into the sum of three convex functions by defining an appropriate inner product space. Based on the dual forward-backward splitting algorithm and the primal-dual forward-backward splitting algorithm, we develop several iterative algorithms that involve only computing the gradient of the differentiable function and proximity operators of related convex functions. These iterative algorithms are matrix-inversion-free and completely splitting algorithms. Finally, we employ the proposed iterative algorithms to solve a regularized general prior image constrained compressed sensing model that is derived from computed tomography image reconstruction. Numerical results show that the proposed iterative algorithms outperform the compared algorithms including the alternating direction method of multipliers, the splitting primal-dual proximity algorithm, and the preconditioned splitting primal-dual proximity algorithm.

关键词： Forward-backward splitting method Primal-dual Dual Proximity operator

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Effects of Re, Ta, and W in [110] (001) dislocation core of γ/γ' interface to Ni-based superalloys: First-principles study

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Chinese Physics B 2020年第9期29卷 390-396页

作者： chuanxi zhu Tao Yu Central Iron and Steel Research Institute Beijing 100081China

The strengthening effects of alloying elements Re,Ta,and W in the[110](001)dislocation core of theγ/γ'interface are studied by first-principles *** the level of energy the substitution formation energies and the migration energies of alloying elements are computed and from the level of electron the differential charge density(DCD)and the partial density of states(PDOSs)are *** elements above are found to tend to substitute for Al sitesγ'phase by analyzing the substitution formation *** calculation results for the migration energies of alloying elements indicate that the stability of the[110](001)dislocation core is enhanced by adding Ta,W,and Re and the strengthening effect of Re is the *** results agree with the relevant *** electronic structure analysis indicates that the electronic interaction between Re-nearest neighbor(NN)Ni is the *** reason why the doped atoms have different strengthening effects in the[110](001)dislocation core is explained at the level of electron.

关键词： Ni-based superalloys dislocation structure electronic structure first-principles calculations

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Convergence of a Multistep Ishikawa Iteration Algorithm for a Finite Family of Lipschitz Mappings and Its Applications

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Journal of Mathematical Research with Applications 2013年第4期33卷 463-474页

作者： Yuchao TANG chuanxi zhu Department of Mathematics Nanchang University Department of Mathematics Xi'an Jiaotong University

The purpose of this paper is to investigate the problem of finding a common fixed point of Lipschitz mappings. We introduce a multistep Ishikawa iteration approximation method which is based upon the Ishikawa iteration method and the Noor iteration method, and we prove some necessary and sufficient conditions for the strong convergence of the iteration scheme to a common fixed point of a finite family of quasi-Lipschitz mappings and pseudocontractive mappings, respectively. In particular, we establish a strong convergence theorem of the sequence generated by the multistep Ishikawa scheme to a common fixed point of nonexpansive mappings. As applications, some numerical experiments of the multistep Ishikawa iteration algorithm are given to demonstrate the convergence results.

关键词： convex feasibility problem common fixed point problem Lipschitz mappings.

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Best Proximity Point Theorems for p-Proximal α-η-β-Quasi Contractions in Metric Spaces with w0-Distance

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Journal of Mathematical Research with Applications 2022年第1期42卷 95-110页

作者： Mengdi LIU Zhaoqi WU chuanxi zhu Chenggui YUAN Department of Mathematics Nanchang University Department of Mathematics Swansea University

In this paper, we propose a new class of non-self mappings called p-proximal α-η-β-quasi contraction, and introduce the concepts of α-proximal admissible mapping with respect to η and(α, d) regular mapping with respect to η. Based on these new notions, we study the existence and uniqueness of best proximity point for this kind of new contractions in metric spaces with w-distance and obtain a new theorem, which generalize and complement the results in [Ayari, M. I. et al. Fixed Point Theory Appl., 2017, 2017: 16] and [Ayari, M. I. et al. Fixed Point Theory Appl., 2019, 2019: 7]. We give an example to show the validity of our main ***, we obtain several consequences concerning about best proximity point and common fixed point results for two mappings, and we present an application of a corollary to discuss the solutions to a class of systems of Volterra type integral equations.

关键词： best proximity point $p$-proximal $\alpha - \eta - \beta $ quasi contraction ${\omega _0}$-distance $\alpha $-proximal admissible mapping with respect to $\eta $ $\left( {\alpha,d} \right)$ regular mapping with respect to η

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Inhibition of Botrytis cinerea and control of gray mold on table grapes by calcium propionate

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Food Quality and Safety 2021年第3期5卷 279-290页

作者： Chenxu Sun chuanxi zhu Ying Tang Dandan Ren Yunfei Cai Ganghan Zhou Yiwen Wang Ling Xu Pinkuan zhu School of Life Sciences East China Normal UniversityShanghaiChina

Objectives:The gray mold fungus Botrytis cinerea(***)infects a wide range of crops before and after harvest,causing huge losses *** mechanisms of *** in vitro and in plants by calcium propionate(CP),generally recognized as a safe substanee,are described in this *** and methods:Wild-type and transgenic mutant strains of *** were used in the study to evaluate the effects of CP on fun gal growth and developme nt in *** materials in cludi ng tomato leaves and table grapes were tested for con trolling efficie ncy of CP agai nst gray mold deterioration in ***:Mycelial growth of *** was inhibited by CP in a dose-dependent manner with occasional disruption of hyphal tips,causing cellular collapse and efflux of cell *** with fluorescein diacetate and propidium iodide indicated that CP decreased fungal cell *** efficiency of CP against *** was enhaneed by reducing *** contrast,the veil mutant,which exhibited deficiency in acid production,was more resista nt to CP,suggesti ng that inhibition of *** by CP is enhanced by the acidification ability of the fungus ***,CP inhibited infection cushion development by germlings of *** assays with tomato leaves and table grapes showed that CP inhibited decay development in both host ***,application of CP on grapes 3 days prior to harvest could contribute to management of deterioration caused by spontaneous fungal diseases during ***:CP can suppress hyphal growth,inhibit infection cushion development,and reduce the virulence of *** is thus promising for practical management of gray mold in fruit crops and merits further evaluation.

关键词： Necrotrophic pathogen virulence factor infection cushion green fluorescent protein generally recognized as safe.

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