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Strong Convergence Theorems for Strictly Asymptotically Pseudocontractive Mappings in Hilbert Spaces

Acta Mathematica Sinica,English Series 2011年第7期27卷 1367-1378页

作者： shi sheng zhang Department of Mathematics Yibin University Yibin 644007 P. R. China

The purpose of this paper is by using CSQ method to study the strong convergence problem of iterative sequences for a pair of strictly asymptotically pseudocontractive mappings to approximate a common fixed point in a Hilbert space. Under suitable conditions some strong convergence theorems are proved. The results presented in the paper are new which extend and improve some recent results of Acedo and Xu [Iterative methods for strict pseudo-contractions in Hilbert spaces. Nonlinear Anal., 67（7）, 2258-2271 （2007）], Kim and Xu [Strong convergence of modified Mann iterations for asymptoti- cally nonexpansive mappings and semigroups. Nonlinear Anal., 64, 1140-1152 （2006）], Martinez-Yanes and Xu [Strong convergence of the CQ method for fixed point iteration processes. Nonlinear Anal., 64, 2400-2411 （2006）], Nakajo and Takahashi pings and nonexpansive semigroups. J. Math [Strong convergence theorems for nonexpansive map- Anal. Appl., 279, 372-379 （2003）], Marino and Xu [Weak and strong convergence theorems for strict pseudocontractions in Hilbert spaces. J. Math. Anal. Appl., 329（1）, 336-346 （2007）], Osilike et al. [Demiclosedness principle and convergence theorems for k-strictly asymptotically pseudocontractive maps. J. Math. Anal. Appl., 326, 1334-1345 （2007）], Liu [Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings. Nonlinear Anal., 26（11）, 1835-1842 （1996）], Osilike et al. [Fixed points of demi-contractive mappings in arbitrary Banach spaces. Panamer Math. J., 12（2）, 77-88 （2002）], Gu [The new composite implicit iteration process strictly pseudocontractive mappings. J. Math with errors for common fixed points of a finite family of Anal. Appl., 329, 766-776 （2007）].

关键词： Strictly asymptotically pseudocontractive mapping strictly pseudocontractive mapping of Browder Petryshyn type CSQ methods common fixed point

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Weak Convergence Theorem for Lipschizian Pseudocontraction Semigroups in Banach Spaces

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Acta Mathematica Sinica,English Series 2010年第2期26卷 337-344页

作者： shi sheng zhang Department of Mathematics Yibin University Yibin 644007 Sichuan P. R. China

The purpose of this paper is to study the weak convergence problems of the irnplicity iteration process for Lipschitzian pseudocontraction semigroups in general Banach spaces. The results presented in this paper extend and improve the corresponding results of Zhou [Nonlinear Anal., 68, 2977-2983 （2008）], Chen, et ah [J. Math. Anal. Appl., 314, 701 709 （2006）], Xu and Ori [Numer. Funct. Anal. Optim, 22, 767-773 （2001）] and Osilike [J. Math. Anal. Appl., 294, 73-81 （2004）]. Keywords

关键词： Lipschitzian pseudocontraction semigroup demi-closed principle common fixed point Opial condition strongly pseudocontractive mapping implicit iteration process

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Study of the deformed halo nucleus^(31)Ne with Glauber model based on microscopic self-consistent structures

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Science China(Physics,Mechanics & Astronomy) 2022年第6期65卷 67-75页

作者： shi-Yi Zhong shi-sheng zhang Xiang-Xiang Sun Michael S.Smith School of Physics Beihang UniversityBeijing 100191China School of Nuclear Science and Technology University of Chinese Academy of SciencesBeijing 100049China Physics Division Oak Ridge National LaboratoryOak Ridge 378^(31)-6354USA

The exotic deformed nucleus^(31)Ne is studied with an approach that combines self-consistent structure and reaction *** deformed relativistic Hartree-Bogoliubov theory in continuum(DRHBc)is utilized to demonstrate that deformation and pairing correlations give rise to a halo structure with a large-amplitude p-wave configuration in^(31)*** the valence nucleon wave functions and angle-averaged density distributions of ^(30)Ne from this theory are used as input for the Glauber reaction model to study the observables of neutron-rich neon isotopes to search halo *** NL1 effective interaction,our predictions of the reaction cross sections for these exotic neon isotopes on a carbon target can better reproduce the experimental data than those from the relativistic mean field model for a spherical shape with resonances and pairing correlation contributions,and are roughly 3.3%(∼50 mb)larger than those with Gaussian function-fitted densities of the core *** calculated one-neutron removal cross section at 240 MeV/nucleon,and the inclusive longitudinal momentum distribution of the 30Ne residues from the^(31)Ne breakup reaction are largely improved over previous theoretical predictions and agree well with *** reaction evalu-ations indicate a dilute density distribution in coordinate space and are a canonical signature of a halo ***,our predictions with the NL3 and PK1 effective interactions give slightly better descriptions of reaction observables for exotic neon isotopes.

关键词： halo relativistic model Glauber model reaction cross section momentum distribution

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Charge radii of potassium isotopes in the RMF(BCS)^(*) approach

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Chinese Physics C 2022年第5期46卷 108-115页

作者： Rong An shi-sheng zhang Li-sheng Geng Feng-Shou zhang Key Laboratory of Beam Technology of Ministry of Education Institute of Radiation TechnologyBeijing Academy of Science and TechnologyBeijing 100875China Key Laboratory of Beam Technology of Ministry of Education College of Nuclear Science and TechnologyBeijing Normal UniversityBeijing 100875China School of Physics Beihang UniversityBeijing 100191China Beijing Key Laboratory of Advanced Nuclear Materials and Physics Beihang UniversityBeijing 102206China School of Physics and Microelectronics Zhengzhou UniversityZhengzhouHenan 450001China Center of Theoretical Nuclear Physics National Laboratory of Heavy Ion Accelerator of LanzhouLanzhou 730000China

We apply the recently proposed RMF(BCS)*ansatz to study the charge radii of the potassium isotopic chain up to^(52)*** is shown that the experimental data can be reproduced rather well,qualitatively similar to the Fayans nuclear density functional theory,but with a slightly better description of the odd-even staggerings(OES).Nonetheless,both methods fail for ^(50)K and to a lesser extent for ^(48,52)*** is shown that if these nuclei are deformed with aβ_(20)≈−0.2,then one can obtain results consistent with experiments for both charge radii and *** argue that beyond-mean-field studies are needed to properly describe the charge radii of these three nuclei,particularly for ^(50)K.

关键词： relativistic mean field theory charge radius odd-even staggering

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The complex momentum representation approach and its application to low‑lying resonances in 17 O and^(29,31)F

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Nuclear Science and Techniques 2023年第1期34卷 43-50页

作者： Si‑Zhe Xu shi‑sheng zhang Xiao‑Qian Jiang Michael Scott Smith School of Physics Beihang UniversityBeijing 100191China Physics Division Oak Ridge National LaboratoryOak RidgeTN 37831‑6354USA

Approaches for predicting low-lying resonances,uniformly treating bound,and resonant levels have been a long-standing goal in nuclear ***,we explored the viability of the complex momentum representation(CMR)approach coupled with new *** focus on predicting the energy of the low-lying 2p_(3∕2)resonance in 17 O,which is critical for s-process nucleosynthesis and missing in previous theoretical *** a Woods-Saxon potential based on the Koning-Delaroche optical model and constrained by the experimental one-neutron separation energy,we successfully predicted the resonant energy of this level for the first *** predictions of the bound levels and 1d_(3∕2)resonance agree well with the measurement ***,we utilize this approach to study the near-threshold resonances that play a role when forming a two-neutron halo in^(29,31)*** found that the CMR-based predictions of the bound-level energies and unbound 1f7∕2 level agree well with the results obtained using the scattering phase shift ***,we successfully found a solution for the 2p_(3∕2)resonance with energy just above the threshold,which is decisive for halo formation.

关键词： Neutron capture Low-lying resonance Complex momentum representation Resonance energy

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Neutron drip line of Z=9–11 isotopic chains

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Chinese Physics C 2020年第7期44卷 87-94页

作者： Rong An Guo-Fang Shen shi-sheng zhang Li-sheng Geng School of Physics Beihang UniversityBeijing 100191China Beijing Key Laboratory of Advanced Nuclear Materials and Physics Beihang UniversityBeijing 100191China Beijing Advanced Innovation Center for Big Data-based Precision Medicine Beihang UniversityBeijing 100191China School of Physics and Microelectronics Zhengzhou UniversityZhengzhouHenan 450001China

A recent experimental breakthrough identified the last bound neutron-rich nuclei in fluorine and neon *** on this finding,we perform a theoretical study of Z=9,10,11,12 isotopes in the relativistic mean field(RMF)*** mean field parameters are assumed from the PK1 parameterization,and the pairing correlation is described by the particle number conservation BCS(FBCS)method recently formulated in the RMF *** show that the FBCS approach plays an essential role in reproducing experimental results of fluorine and neon ***,we predict 39Na and 40Mg to be the last bound neutron-rich nuclei in sodium and magnesium isotopes.

关键词： drip line relativistic mean field theory particle number conservation

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Comparison of visual effects of FS-LASIK for myopia centered on the coaxially sighted corneal light reflex or the line of sight

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International Journal of Ophthalmology(English edition) 2017年第4期10卷 624-631页

作者： Jing zhang shi-sheng zhang Qin Yu Jing-Cai Lian Department of Ophthalmology Shanghai Ninth People's Hospital Shanghai Jiaotong University School of MedicineShanghai 200011 China New Vision Eye Clinic Shanghai 200011 China Shanghai Xinshijie Zhongxing Eye Hospital School of MedicineShanghai Tongji University Shanghai 200070 China

AIM：To compare visual quality after femtosecond laser in situ keratomileusis（FS-LASIK）,between the coaxially sighted corneal light reflex（CSCLR） group and conventional ablation line of sight（LOS） ***：In total,243 eyes（122 patients） were treated with centration on the CSCLR（visual axis） and 238 eyes（119 patients） treated with centration on the pupil center（LOS）.Postoperative outcomes [uncorrected visual acuity（UCVA）,best spectacle-corrected visual acuity（BSCVA）],safety index,efficacy index,refractive outcome,ablation center distance from the visual axis,corneal high-order aberrations,subjective discomfort glare and shadowing incidence rate,and contrast sensitivity at 1,3,and 6mo were measured and ***：The mean age was 27.77±7.1y in the CSCLR group and 26.03±7.70 y in the LOS ***,the manifest refraction spherical equivalent（MRSE） was-6.68±2.60 D in the CSCLR group and-6.65±2.68 D in the LOS *** postoperative UCVA,BSCVA,MRSE（-0.03±0.263 D in the CSCLR group,-0.05±0.265 D in the LOS group）,efficacy index（1.04,1.03）,and safety index（1.09,1.08） were not significantly different between the groups（all P〉0.05）.In total,3% lost one line and more of BSCVA in the CSCLR group,as 9% in the LOS group postoperatively（P〈0.05）.The ablation center deviation was 0.20±0.15 mm from the visual axis（Pentacam system default setting;range,0-0.75 mm） in the CSCLR group,and 0.43±0.22 mm（range,0-1.32 mm） in the LOS group（P〈0.0001）.Statistically significant greater augmentationof total corneal higher-order aberrations（0.15±0.10 μm and 0.20±0.12 μm respectively,P=0.03） and vertical and horizontal coma（P〈0.0001） were noted in the LOS *** discomfort glare and shadowing incidence rates were 8.59% and 17.5% in the CSCLR and LOS groups,respectively（P〈0.05）.The 1-month postoperative contrast sensitivity visual acuity in the CSCLR group was significantly higher than that in the LOS group on contrast（100%,25%,10%） with a dark background,but there

关键词： laser in situ keratomileusis ablation center line of sight coaxially sighted corneal light reflex

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Approximation of Nearest Common Fixed Point of Nonexpansive Mappings in Hilbert Spaces

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Acta Mathematica Sinica,English Series 2007年第10期23卷 1889-1896页

作者： shi sheng zhang H.W. JOSEPH LEE Chi Kin CHAN Department of Mathematics Yibin University Yibin 644007 P. R. China Department of Mathematics Sichuan University Chengdu 610064 P. R. China Department of Applied Mathematics The Hong Kong Polytechnic University Hung Horn Kowloon Hong Kong P. R. China

The purpose of this paper is to study the convergence problem of the iteration scheme xn＋l = λn＋1y ＋（1 - λn＋1）Tn＋1xn for a family of infinitely many nonexpansive mappings T1, T2,... in a Hilbert space. It is proved that under suitable conditions this iteration scheme converges strongly to the nearest common fixed point of this family of nonexpansive mappings. The results presented in this paper extend and improve some recent results.

关键词： common fixed point family of nonexpansive mappings nearest point projection iterative scheme

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Modified Block Iterative Method for Solving Convex Feasibility Problem, Equilibrium Problems and Variational Inequality Problems

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Acta Mathematica Sinica,English Series 2012年第4期28卷 741-758页

作者： shi sheng zhang Chi Kin CHAN H.W.JOSEPH LEE College of Statistics and Mathematics Yunnan Uniersity of Finance and Economics Department of Applied Mathematics The Hong Kong Polytechnic University

The purpose of this paper is by using the modified block iterative method to propose an algorithm for finding a common element in the intersection of the set of common fixed points of an infinite family of quasi-C-asymptotically nonexpansive and the set of solutions to an equilibrium problem and the set of solutions to a variational inequality. Under suitable conditions some strong convergence theorems are established in 2-uniformly convex and uniformly smooth Banach spaces. As applications we utilize the results presented in the paper to solving the convex feasibility problem （CFP） and zero point problem of maximal monotone mappings in Banach spaces. The results presented in the paper improve and extend the corresponding results announced by many authors.

关键词： Modified block iterative algorithm quasi-φ-asymptotically nonexpansive mapping quasi-φ-nonexpansive mapping relatively nonexpansive mapping generalized projection

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Effect of pairing correlation on low-lying quadrupole states in Sn isotopes

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Chinese Physics C 2021年第9期45卷 136-142页

作者： Shuai Sun shi-sheng zhang Zhen-Hua zhang Li-Gang Cao School of Mathematics and Physics North China Electric Power UniversityBeijing 102206China School of Physics Beihang UniversityBeijing 100191China Key Laboratory of Beam Technology of Ministry of Education College of Nuclear Science and TechnologyBeijing Normal UniversityBeijing 100875China Beijing Radiation Center Beijing 100875China

We examined the low-lying quadrupole states in Sn isotopes in the framework of fully self-consistent Hartree-Fock+BCS plus *** focus on the effect of the density-dependence of pairing interaction on the properties of the low-lying quadrupole *** SLy5 Skyrme interaction with surface,mixed,and volume pairings is employed in the calculations,*** find that the excitation energies and the corresponding reduced electric transition probabilities of the first 2^(+) state are different,given by the three pairing *** properties of the quasiparticle state,two-quasiparticle excitation energy,reduced transition amplitude,and transition densities in ^(112)Sn are analyzed in *** different mechanisms,the static and dynamical effects,of the pairing correlation are also *** results show that the surface,mixed,and volume pairings indeed affect the properties of the first 2^(+) state in the Sn isotopes.

关键词： density-dependence of pairing interaction low-lying quadrupole state Skyrme energy density functional

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