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Commuting Solutions of a Quadratic Matrix Equation for Nilpotent Matrices

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Algebra Colloquium 2018年第1期25卷 31-44页

作者： Qixiang Dong jiu ding Qianglian Huang School of Mathematical Sciences Yangzhou University Yangzhou Jiangsu 225002 China Department of Mathematics University of Southern Mississippi Hattiesburg MS 39406 USA

We solve the quadratic matrix equation AXA = XAX with a given nilpotent matrix A, to find all commuting solutions. We first provide a key lemma, and consider the special case that A has only one Jordan block to motivate the idea for the general case. Our main result gives the structure of all the commuting solutions of the equation with an arbitrary nilpotent matrix.

关键词： quadratic matrix equation nilpotent matrix Jordan canonical form Toeplitz matrix commuting solution

A Maximum Entropy Method Based on Orthogonal Polynomials for Frobenius-Perron Operators

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Advances in Applied Mathematics and Mechanics 2011年第2期3卷 204-218页

作者： jiu ding Noah H.Rhee Department of Mathematics The University of Southern MississippiHattiesburgMS 39406-5045USA Department of Mathematics and Statistics University of Missouri-Kansas CityKansas CityMO 64110-2499USA

Let S:[0,1]→[0,1]be a chaotic map and let f^(∗)be a stationary density of the Frobenius-Perron operator PS:L^(1)→L^(1)associated with *** develop a numerical algorithm for approximating f^(∗),using the maximum entropy approach to an under-determined moment problem and the Chebyshev polynomials for the stability *** experiments show considerable improvements to both the original maximum entropy method and the discrete maximum entropy method.

关键词： Frobenius-Perron operator stationary density maximum entropy orthogonal polynomials Chebyshev polynomials

On Polynomial Maximum EntropyMethod for ClassicalMoment Problem

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Advances in Applied Mathematics and Mechanics 2016年第1期8卷 117-127页

作者： jiu ding Noah H.Rhee Chenhua Zhang Department of Mathematics The University of Southern MississippiHattiesburgMS 39406-5045USA Department ofMathematics and Statistics University ofMissouri–Kansas CityKansas CityMO 64110-2499USA

The maximum entropy method for the Hausdorff moment problem suffers from ill conditioning as it uses monomial basis{1,x,x2,···,xn}.Themaximum entropy method for the Chebyshev moment probelm was studied to overcome this drawback in[4].In this paper we review and modify the maximum entropy method for the Hausdorff and Chebyshev moment problems studied in[4]and present the maximum entropy method for the Legendre moment *** also give the algorithms of converting the Hausdorff moments into the Chebyshev and Lengendre moments,respectively,and utilizing the corresponding maximum entropy method.

关键词： Classical moment problem monomials Chebyshev polynomials Legendre polynomials

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秸秆纤维加筋黄土三轴剪切特性试验

长江科学院院报 2024年第1期41卷 136-142页

作者：张琬丁九龙李波陈泽一薛一峰赵玮西安理工大学土木建筑工程学院西安710048 陕西省水利电力勘测设计研究院水电工程分院西安710001

为了探明秸秆纤维加筋黄土的剪切力学特性,开展三轴剪切试验和电镜扫描试验,研究纤维掺量、纤维长度和土体含水率对秸秆纤维加筋黄土应力-应变特性和抗剪强度的影响,并分析加筋机理。结果表明:加入秸秆纤维主要通过增加土体黏聚力以有... 详细信息

为了探明秸秆纤维加筋黄土的剪切力学特性,开展三轴剪切试验和电镜扫描试验,研究纤维掺量、纤维长度和土体含水率对秸秆纤维加筋黄土应力-应变特性和抗剪强度的影响,并分析加筋机理。结果表明:加入秸秆纤维主要通过增加土体黏聚力以有效提升黄土的抗剪强度,但不会改变黄土偏应力-应变曲线的类型及特征,仍表现为应变硬化型;秸秆纤维的最佳掺量和长度分别为0.3%和10 mm,当纤维掺量和长度超过最佳值时,土体中存在过多的软弱结构面会削弱加筋土体的整体性,筋土间黏结和摩擦作用降低,土体抗剪强度减小;加筋黄土的最佳含水率为素黄土的最优含水率,含水率超过最佳值后,筋土表面结合水膜增厚,筋土间润滑作用增强、摩擦力减弱,土体抗剪强度降低。

关键词：加筋黄土秸秆纤维三轴剪切试验电镜扫描力学特性

数字普惠金融对乡村振兴的影响研究——基于建设环境中介效应的分析

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长春金融高等专科学校学报 2024年第3期 38-51页

作者：于春荣贾依帆丁义久长春大学经济学院吉林长春130022

为了研究数字普惠金融对乡村振兴的影响以及产生影响的具体路径,选取2011—2019年我国30个省、自治区、直辖市的面板数据,构建乡村振兴的衡量指标体系,将建设环境作为中介变量进行实证分析。实证结果表明,数字普惠金融可以通过改善乡村... 详细信息

为了研究数字普惠金融对乡村振兴的影响以及产生影响的具体路径,选取2011—2019年我国30个省、自治区、直辖市的面板数据,构建乡村振兴的衡量指标体系,将建设环境作为中介变量进行实证分析。实证结果表明,数字普惠金融可以通过改善乡村建设环境推动乡村振兴发展。此外,研究发现数字普惠金融的不同维度、不同业务对乡村振兴建设产生不同程度的影响。在分维度层面,数字普惠金融的覆盖广度、使用深度对乡村振兴建设的促进作用较大;在业务层面,信贷业务的发展对乡村振兴建设具有较强的正向促进作用。

关键词：数字普惠金融乡村振兴中介效应

Brazed joints of CBN grains and AISI 1045 steel with AgCuTi-TiC mixed powder as filler materials

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International Journal of Minerals,Metallurgy and Materials 2011年第6期18卷 717-724页

作者： Wen-feng ding jiu-hua Xu Zhen-zhen Chen Hong-hua Su Yu-can Fu College of Mechanical and Electrical Engineering Nanjing University of Aeronautics and Astronautics Nanjing 210016 China

The brazing process of cubic boron nitride （CBN） grains and AISI 1045 steel with AgCuTi-TiC mixed powder as a filler material was carried *** joining strength and the interfacial microstructure were *** experimental results indicate that the spreading of the molten filler material on AISI 1045 steel is decreased with the increase of TiC content.A good interface is formed between the TiC particulates and AgCuTi alloy through the wetting *** the case of AgCuTi＋16wt% TiC,the strength of the brazed steel-to-steel joints reached the highest value of 95MPa dependent upon the reinforcement effect of TiC particles within the filler *** resultants of TiB2,TiB,and TiN are produced at the interface of the CBN grains and the AgCuTi-TiC filler layer by virtue of the interdiffusion of B,N,and Ti atoms.

关键词： grinding wheels cubic boron nitride brazing filler metals shear strength interfaces

Estimation of earth pressure against retaining walls with different limited displacement modes based on elastic theory

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Journal of Mountain Science 2022年第1期19卷 289-304页

作者： ZHANG Le DANG Fa-ning WANG Xu ding jiu-long GAO Jun ZHANG Yu School of Civil Engineering and Architecture Xi’an University of TechnologyXi’an 710048China State Key Laboratory of Eco-hydraulics in Northwest Arid Region Xi’an University of TechnologyXi’an 710048China Shaanxi Key Laboratory of Loess Mechanics and Engineering Xi’an University of TechnologyXi’an 710048China

The earth pressure acting on retaining walls due to creep and consolidation is under limited equilibrium conditions(limited displacement). Linear elastic constitutive theory can be applied to determine earth pressure distribution along retaining walls under limited displacement condition. In addition,tangent modulus in Duncan-Chang nonlinear elastic model was introduced to reflect the variations of soil modulus with confining pressure, and boundary strains were derived from Rankine active earth pressure, Rankine passive earth pressure, static earth pressure and principal stress direction *** to the above four boundary strains, earth pressure on retaining walls was divided into five state zones. By comparing the calculation results obtained from the equations proposed in this paper with those of experimental tests, the following conclusions can be drawn: earth pressure distribution was always nonlinear along retaining walls for translation displacement(T mode), rotation displacement around wall base(RB mode), and translation + rotation displacement around wall base(RBT mode). Also,calculated earth pressure distributions along with the depth of wall were found to be consistent with measured values under three displacement ***, a parametric study was carried out to evaluate the effects of internal friction angle and backfill soil cohesion on earth pressure. It could be seen from the above series of studies that the earth pressure equations derived in this work could be well applied in practical engineering in designing retaining walls.

关键词： Linear elasticity Limited earth pressure Translation displacement Rotation displacement around wall base Rotation displacement Earth pressure state zone

A local refinement purely meshless scheme for time fractional nonlinear Schrodinger equation in irregular geometry region

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Chinese Physics B 2021年第2期30卷 164-175页

作者： Tao Jiang Rong-Rong Jiang Jin-Jing Huang jiu ding Jin-Lian Ren School of Mathematical Sciences Yangzhou UniversityYangzhou 225002China Department of Mathematics University of Southern MississippiHattiesburgMS 39406-5045USA

A local refinement hybrid scheme(LRCSPH-FDM)is proposed to solve the two-dimensional(2D)time fractional nonlinear Schrodinger equation(TF-NLSE)in regularly or irregularly shaped domains,and extends the scheme to predict the quantum mechanical properties governed by the time fractional Gross-Pitaevskii equation(TF-GPE)with the rotating Bose-Einstein *** is the first application of the purely meshless method to the TF-NLSE to the author’s *** proposed LRCSPH-FDM(which is based on a local refinement corrected SPH method combined with FDM)is derived by using the finite difference scheme(FDM)to discretize the Caputo TF term,followed by using a corrected smoothed particle hydrodynamics(CSPH)scheme continuously without using the kernel derivative to approximate the spatial ***,the local refinement technique is adopted to reduce the numerical *** numerical simulations,the complex irregular geometry is considered to show the flexibility of the purely meshless particle method and its advantages over the grid-based *** numerical convergence rate and merits of the proposed LRCSPH-FDM are illustrated by solving several 1D/2D(where 1D stands for one-dimensional)analytical TF-NLSEs in a rectangular region(with regular or irregular particle distribution)or in a region with irregular *** proposed method is then used to predict the complex nonlinear dynamic characters of 2D TF-NLSE/TF-GPE in a complex irregular domain,and the results from the posed method are compared with those from the *** the numerical results show that the present method has a good accuracy and flexible application capacity for the TF-NLSE/GPE in regions of a complex shape.

关键词： Caputo fractional derivative nonlinear Schrodinger/Gross-Pitaevskii equation corrected smoothed particle hydrodynamics irregularly domain

NUMERICAL STUDY OF HYDRODYNAMICS OF MULTIPLE TANDEM JETS IN CROSS FLOW

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Journal of Hydrodynamics 2011年第6期23卷 806-813页

作者： XIAO Yang TANG Hong-wu LIANG Dong-fang ZHANG jiu-ding State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering Nanjing 210098 China College of Water Conservancy and Hydropower Engineering Hohai University Nanjing 210098 China Department of Engineering University of Cambridge Cambridge UK

The hydrodynamics of a single jet and four tandem jets in a cross flow are simulated by using the Computational Fluid Dynamics （CFD） software Fluent. The realizable model is used to close the Reynolds-Averaged equations. The flow characteristics of the jets, including the jet trajectory, the velocity field and the turbulent kinetic energy are obtained with various jet-to-cross flow velocity ratios in the range of 2.38-17.88. It is shown that a single jet penetrates slightly deeper than the first jet in a jet group at the same , although the difference decreases with the decrease of . It is also found that the way in which the velo-city decays along the centerline of the jet is similar for both a single jet and the first jet in a group, and the speed of the decay increases with the decrease of . The downstream jets in a group are found to behave differently due to the sheltering effect of the first jet in the group. Compared with the first jet, the downstream jets penetrate deeper into the cross flow, and the velocity decays more slowly. The circulation zone between the two upstream jets in the front is stronger than those formed between the downstream jets. The Turbulent Kinetic Energy （TKE） sees a distinct double-peak across the cross-sections close to each nozzle, with low values in the jet core and high values in the shear layers. The double-peak gradually vanishes, as the shear layers of the jet merge further away from the nozzle, where the TKE assumes peaks at the jet centerline.

关键词： multiple tandem jets jet in cross flow realizable model flow dynamics