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Global Solutions to Nonconvex Problems by Evolution of Hamilton-Jacobi PDEs
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作者 Howard Heaton Samy Wu Fung Stanley Osher 《Communications on Applied Mathematics and Computation》 EI 2024年第2期790-810,共21页
Computing tasks may often be posed as optimization problems.The objective functions for real-world scenarios are often nonconvex and/or nondifferentiable.State-of-the-art methods for solving these problems typically o... Computing tasks may often be posed as optimization problems.The objective functions for real-world scenarios are often nonconvex and/or nondifferentiable.State-of-the-art methods for solving these problems typically only guarantee convergence to local minima.This work presents Hamilton-Jacobi-based Moreau adaptive descent(HJ-MAD),a zero-order algorithm with guaranteed convergence to global minima,assuming continuity of the objective function.The core idea is to compute gradients of the Moreau envelope of the objective(which is"piece-wise convex")with adaptive smoothing parameters.Gradients of the Moreau envelope(i.e.,proximal operators)are approximated via the Hopf-Lax formula for the viscous Hamilton-Jacobi equation.Our numerical examples illustrate global convergence. 展开更多
关键词 Global optimization Moreau envelope HAMILTON-JACOBI Hopf-Lax-Cole-Hopf Proximals zero-order optimization
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以LiB_(3)O_(5)为模板设计深紫外零级波片材料
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作者 张志远 徐蝶 +3 位作者 Abudukadi Tudi 杨志华 韩树娟 潘世烈 《Science China Materials》 SCIE EI CAS CSCD 2024年第3期914-920,共7页
以著名的LiB_(3)O_(5)为模板,通过增强其结构中B_(2)O_(5)的夹角使双折射更小,在封闭体系中通过高温溶液法获得了两种新的用于制造零级波片的双折射晶体Li_(2)MLaB_(18)O_(30)(M=Rb,Cs).有趣的是,相邻的B_(2)O_(5)接近垂直排列,使得它... 以著名的LiB_(3)O_(5)为模板,通过增强其结构中B_(2)O_(5)的夹角使双折射更小,在封闭体系中通过高温溶液法获得了两种新的用于制造零级波片的双折射晶体Li_(2)MLaB_(18)O_(30)(M=Rb,Cs).有趣的是,相邻的B_(2)O_(5)接近垂直排列,使得它们表现出比商用石英晶体(Δn~0.0092在可见光区域)小得多的双折射率(分别为0.0032@532 nm和0.0027@532 nm).此外,Li_(2)MLaB_(18)O_(30)(M=Rb,Cs)晶体的紫外截止边均低于200 nm,表明它们可用作深紫外区域的零级波片材料. 展开更多
关键词 tiny birefringence zero-order waveplate deep-ultraviolet region angle of B_(2)O_(5)
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On the Parameterization of Convective Entrainment: Inherent Relationships among Entrainment Parameters in Bulk Models 被引量:2
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作者 孙鉴泞 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2009年第5期1005-1014,共10页
In this paper, the equilibrium entrainment into a shear-free, linearly stratified atmosphere is discussed under the framework of bulk models, namely, the zero-order jump model (ZOM) and the first-order jump model (... In this paper, the equilibrium entrainment into a shear-free, linearly stratified atmosphere is discussed under the framework of bulk models, namely, the zero-order jump model (ZOM) and the first-order jump model (FOM). The parameterizations for the dimensionless entrainment rate versus the convective Richard- son number in the two models are compared. Based on the assumption that the parameterized entrainment rates in ZOM and FOM should be the same, the inherent relationships among the entrainment parameters in the bulk models are revealed. These relationships are supported by tank experiments and large-eddy sim- ulations. The validity of these inherent relationships indicates that, for a convective boundary layer growing into a linearly stratified free atmosphere, the only dominant factors of the growth rate are the turbulent buoyancy in the mixed layer and the stratification in the free atmosphere. In the point of the similarity view, the former is characterized by turbulent temperature and mixing length scales (mixed layer depth), and the latter is characterized by the lapse rate of potential temperature in the free atmosphere. Thus, the commonly-used Richardson number scheme for the parameterization of the entrainment rate is just as an equivalent description. The variability of the total entrainment flux ratio in FOM, which is connected with the entrainment zone thickness, can implicitly describe the effect of the stratification in the free atmosphere, but the entrainment zone thickness is not an independent parameter. These results demonstrate the validity of the hypothesis that there exists a similarity limit in which the mixed layer depth is the only lengthscale. 展开更多
关键词 zero-order jump model first-order jump model convective Richardson number entrainmentrate lengthscale
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Asymptotic Smoothing Effect of Solutions to Davey-Stewartson Systems on the Whole Plane 被引量:2
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作者 Cai Di ZHAO Yong Sheng LI Sheng Fan ZHOU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第11期2043-2060,共18页
This paper discusses the Cauchy problem of elliptic-elliptic-type Davey-Stewartson systems with zero-order dissipation on R^2. Making use of the Fourier spectral projector, together with a long time comparison between... This paper discusses the Cauchy problem of elliptic-elliptic-type Davey-Stewartson systems with zero-order dissipation on R^2. Making use of the Fourier spectral projector, together with a long time comparison between the solutions to the Davey-Stewartson systems and to an auxiliary problem, we prove that the global attractor in H^1 (R^2) for the addressed Davey-Stewartson systems is a compact subset of H^2(R^2), and thus reveal the asymptotic smoothing effect of the solutions for the systems. 展开更多
关键词 Davey-Stewartson systems asymptotic smoothing effect global attractor zero-order dissipation
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Value Distribution of Meromorphic Solutions of Some q-Difference Equations 被引量:2
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作者 Xiu Min ZHENG Zong Xuan CHEN 《Journal of Mathematical Research and Exposition》 CSCD 2011年第4期698-704,共7页
In this paper, we consider the value distribution of meromorphic solutions of order zero of some kind of q-difference equations and examples are also given to elaborate our results.
关键词 q-difference equation meromorphic solution zero-order.
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q-平移差分多项式和推广了的q-平移差分方程亚纯解的一些性质 被引量:3
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作者 涂金 郑秀敏 《数学物理学报(A辑)》 CSCD 北大核心 2013年第5期951-959,共9页
研究了某些推广了的q-平移差分方程亚纯解的增长性.还研究了q-平移差分多项式的值分布,这些结果可以视为复微分多项式对应结果的q-平移差分模拟.亦给出了一些例子说明所得结果的精确性.
关键词 q-平移差分方程 q-平移差分多项式 亚纯解 零级
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Online fault recognition of electric power cable in coal mine based on the minimum risk neural network 被引量:2
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作者 汪梅 STATHAKI Tania 《Journal of Coal Science & Engineering(China)》 2008年第3期492-496,共5页
Firstly,the concepts of the traveling wave entropy and the feature function of traveling wave entropy were defined.Then the statistic characters of the traveling wave entropy feature function,mean value and variance w... Firstly,the concepts of the traveling wave entropy and the feature function of traveling wave entropy were defined.Then the statistic characters of the traveling wave entropy feature function,mean value and variance were analyzed after the zero-order component of the traveling wave of online cable was selected to serve as the observed object.Finally,the new recognition algorithm of minimum risk neural network was pre- sented.The simulation experiments show that the recognitions of the early fault states can be completed correctly by using the proposed recognition algorithm.The classes of cable faults include in 1-phase ground faults,and the 2-phase short circuit faults or ground faults and the 3-phase short circuit faults or ground faults,open circuit.The fault resistance range is 1×10^(-1)~1×10~9Ω. 展开更多
关键词 minimum risk neural network traveling wave entropy zero-order component online cable recognition algorithm early fault
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Application of D-Optimal Study Design with Contour Surface Response for Designing Sustained Release Gliclazide Matrix Tablets 被引量:1
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作者 Chien Nguyen John Mark Christensen Thuy Nguyen 《Pharmacology & Pharmacy》 2014年第7期620-635,共16页
An optimized formulation of a sustained release tablet of Gliclazide was developed. The use of Doptimal design with a polynomial statistical model to analyze dissolution data reduced the number of laboratory tests req... An optimized formulation of a sustained release tablet of Gliclazide was developed. The use of Doptimal design with a polynomial statistical model to analyze dissolution data reduced the number of laboratory tests required to obtain an optimal dosage form. The final formulation contained 22 mg of Methocel&regE15LV, 16.5 mg Methocel&regE15 and 10.0 mg of Dibasic Calcium Phosphate per 30 mg Gliclazide sustained release tablet. Dissolution studies performed on tablets from 5000 tablet test batches released greater than 90 percent of loaded drug in eight hours. Drug release from the optimized tablets followed a pattern more closely similar to zero-order than other mechanisms of drug release tested. Storage of tablets in accelerated and ambient conditions for 6 and 12 months respectively did not alter any of the physico-chemical properties, drug release or the drug release rate compared to initial observations and dissolution data of the prepared tablets. The addition of potassium phosphate and monosodium phosphate to the tablet reduced the effect pH has on Gliclazide dissolution compared to the commercially available product. 展开更多
关键词 GLICLAZIDE SUSTAINED RELEASE D-Optimal zero-order RESPONSE Surface Modified RELEASE
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单位圆盘上全纯映照模的精细Schwarz引理 被引量:2
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作者 张宇芳 徐庆华 《数学物理学报(A辑)》 CSCD 北大核心 2017年第1期18-25,共8页
记DC为单位圆盘,B^p={z∈C^n:n∑i=1|z_i|~p<1},1<p<+∞.该文证明了若f∈H_m(D,B^p),则|▽||f||(z)≤m|z|^(m-1)/1-|z|^(2m)(1-||f(z)||~2),z∈D.同时,当p为偶数时,该文也讨论了相应的极值问题,所得结论推广了一些相关结果.
关键词 全纯映照 m阶零点 SCHWARZ引理
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Axial acoustic radiation force on an elastic spherical shell near an impedance boundary for zero-order quasi-Bessel-Gauss beam 被引量:2
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作者 Yu-Chen Zang Wei-Jun Lin +1 位作者 Chang Su Peng-Fei Wu 《Chinese Physics B》 SCIE EI CAS CSCD 2021年第4期305-318,共14页
Shell structures have increasingly widespread applications in biomedical ultrasound fields such as contrast agents and drug delivery,which requires the precise prediction of the acoustic radiation force under various ... Shell structures have increasingly widespread applications in biomedical ultrasound fields such as contrast agents and drug delivery,which requires the precise prediction of the acoustic radiation force under various circumstances to improve the system efficiency.The acoustic radiation force exerted by a zero-order quasi-Bessel-Gauss beam on an elastic spherical shell near an impedance boundary is theoretically and numerically studied in this study.By means of the finite series method and the image theory,a zero-order quasi-Bessel-Gauss beam is expanded in terms of spherical harmonic functions,and the exact solution of the acoustic radiation force is derived based on the acoustic scattering theory.The acoustic radiation force function,which represents the radiation force per unit energy density and per unit cross-sectional surface,is especially investigated.Some simulated results for a polymethyl methacrylate shell and an aluminum shell are provided to illustrate the behavior of acoustic radiation force in this case.The simulated results show the oscillatory property and the negative radiation force caused by the impedance boundary.An appropriate relative thickness of the shell can generate sharp peaks for a polymethyl methacrylate shell.Strong radiation force can be obtained at small half-cone angles and the beam waist only affects the results at high frequencies.Considering that the quasi-Bessel-Gauss beam possesses both the energy focusing property and the non-diffracting advantage,this study is expected to be useful in the development of acoustic tweezers,contrast agent micro-shells,and drug delivery applications. 展开更多
关键词 acoustic radiation force zero-order quasi-Bessel-Gauss beam impedance boundary elastic spherical shell
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平面上零级Dirichlet级数和随机Dirichlet级数的上下级 被引量:1
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作者 曹月波 杨祺 田宏根 《数学杂志》 CSCD 北大核心 2011年第5期945-951,共7页
本文对平面上的零级Dirichlet级数和随机Dirichlet级数的上下级进行了研究.利用Newton多边形,在一定条件下得到了Dirichlet级数和随机Dirichlet级数的上下级与其系数的重要关系.推广了平面上的零级Dirichlet级数和随机Dirichlet级数的... 本文对平面上的零级Dirichlet级数和随机Dirichlet级数的上下级进行了研究.利用Newton多边形,在一定条件下得到了Dirichlet级数和随机Dirichlet级数的上下级与其系数的重要关系.推广了平面上的零级Dirichlet级数和随机Dirichlet级数的增长性的研究范围. 展开更多
关键词 DIRICHLET级数 增长性 零级 型函数 下级
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Improved Grid Relaxation with Zero-Order Integrators
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作者 Jan Mueller Hans-Georg Matuttis 《Journal of Applied Mathematics and Physics》 2021年第6期1257-1270,共14页
In this research, we have improved a relaxation method for triangular meshes intended for finite element fluid simulations which contain discrete element particles. The triangle edges are treated as springs which rela... In this research, we have improved a relaxation method for triangular meshes intended for finite element fluid simulations which contain discrete element particles. The triangle edges are treated as springs which relax their lengths towards a “better” force equilibrium where the triangles are closer to equilateral shape. The actual kernel is an improved zero order integrator which is able to follow reconfigurations of the particles faster than earlier methods. The improved relaxation allows larger timesteps in the flow simulation and leads to more stable, faster mesh reconfigurations for fast moving particles in the flow. Additionally, this demonstrates how integrators of the same order zero can nevertheless have different convergence speeds towards 展开更多
关键词 zero-order Solver EQUILIBRATION Grid Generation Fluid Mechanics
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Circular Obstacle Avoidance Control of the Compass-Type Biped Robot Based on a Blending Method of Discrete Mechanics and Nonlinear Optimization
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作者 Tatsuya Kai 《International Journal of Modern Nonlinear Theory and Application》 2015年第3期179-189,共11页
This paper considers an obstacle avoidance control problem for the compass-type biped robot, especially circular obstacles are dealt with. First, a sufficient condition such that the swing leg does not collide the cir... This paper considers an obstacle avoidance control problem for the compass-type biped robot, especially circular obstacles are dealt with. First, a sufficient condition such that the swing leg does not collide the circular obstacle is derived. Next, an optimal control problem for the discrete compass-type robot is formulated and a solving method of the problem by the sequential quadratic programming is presented in order to calculate a discrete control input. Then, a transformation method that converts a discrete control input into a continuous zero-order hold input via discrete Lagrange-d’ Alembert principle is explained. From the results of numerical simulations, it turns out that obstacle avoidance control for the continuous compass-type robot can be achieved by the proposed method. 展开更多
关键词 Discrete Mechanics Compass-Type BIPED Robot OBSTACLE Avoidance CONTROL Nonlinear Optimization zero-order HOLD Input
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A STUDY OF ELECTROCHEMICAL REDUCTION OF SAFRANINE T AND THE ELECTROGENERATED FREE RADICAL TRACING BY ESR
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作者 彭美蓉 胡志彬 《Science China Chemistry》 SCIE EI CAS 1990年第12期1409-1417,共9页
A study of the electrochemical reduction behavior of safranine T by means of electrochemical methods coupled with ESR (electron spin resonance) is presented. Through an 'in situ' tracing of the 1-electron redu... A study of the electrochemical reduction behavior of safranine T by means of electrochemical methods coupled with ESR (electron spin resonance) is presented. Through an 'in situ' tracing of the 1-electron reduction intermediate—free radical, the structure of the free radical has been deduced. During the electrochemical reduction the free radical went through a post-electrolysis chemical decay including parallel steps of zero and first order reactions. This fact gives further support and experimental ascertainment of the viewpoint that some electrode processes are clearly related to the enzymatic catalyses^([1]). In accordance with the chemical behavior of safranine T free radicals at various concentrations and at different potentials the authors have advanced a scheme of reaction mechanism and evaluated the kinetic parameters of the reation steps by simulating the experimental curves. 展开更多
关键词 safranine T RADICAL TRACING by ESR zero-order DECAY
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Mean-Square Stabilization of Networked Sampled-Data Systems with Packet Losses:Critical Sampling Intervals
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作者 WANG Chao WANG Bingchang 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2022年第4期1278-1292,共15页
This paper studies the stabilizing problem of networked sampled-data linear systems with independent and identically distribution(i.i.d.) packet dropouts. First of all, for the sampled-data system without packet losse... This paper studies the stabilizing problem of networked sampled-data linear systems with independent and identically distribution(i.i.d.) packet dropouts. First of all, for the sampled-data system without packet losses, the necessary and sufficient conditions for the critical sampling intervals are given to ensure the mean square stability where zero order holder and generalized holder are adopted, respectively. Secondly, for the sampled-data system with i.i.d. packet losses, necessary and sufficient conditions for the critical sampling intervals are given to ensure the mean square stability where the zero order holder control is adopted. The random sampling framework is used to examine the case that the value of the control signal is not zero when the packet loss occurs, but the value of the previous control signal when the data packet is not lost. For the sampled-data system with i.i.d.packet losses, the range of the sampling interval is given to ensure the mean square stability where the generalized holder control is adopted. Some numerical simulations are provided to validate the theoretical results. 展开更多
关键词 Generalized hold i.i.d.packet dropout sampled-data linear system zero-order hold
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SIMULTANEOUS DETERMINATION OF NEODYMIUM AND PRASEODYMIUM BY ZERO-ORDER AND FOURTH-ORDER DFRIVATIVE SPECTROPHOTOMETRY
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作者 Nai Xing Wang Department of Applied Chemistry,Shandong University,Jinan,250100,Shandong,People’s Repulic of China 《Chinese Chemical Letters》 SCIE CAS CSCD 1991年第1期41-44,共4页
With derivative spectrophotometric method,the complexes of lanthanides with 2-(5-bromo-2-pyridylazo)-5-diethylaminophen- ol(5-Br-PADAP)in the presence of octylphenol poly(ethyleneg- lycol)ether(TX-100)were studied.It ... With derivative spectrophotometric method,the complexes of lanthanides with 2-(5-bromo-2-pyridylazo)-5-diethylaminophen- ol(5-Br-PADAP)in the presence of octylphenol poly(ethyleneg- lycol)ether(TX-100)were studied.It is found that the maximum absorption of fourth-order derivative spectra of the neodymium complex by 4f electron transitions is at 579(+)nm and 582(-)nm with molar derivative absorptivities of 5.2×10~3 1.mol^(-1).cm^(-1). The maximum absorption of the zero-order derivative spectra of the complexes for neodymium and praseodymium is at 580hm,the molar absorptivities are 1.47×10~5 l.mol^(-1).cm^(-1)for Nd and 1.26 ×10~5 l.mol^(-1).cm^(-1)for Pr.The component ratio of the complex is Nd:5-Br-PADAP=1:4.Beer's law is obeyed in the range of 0-3.75μg of Nd and Pr in 25ml of solution.The method has been used for the simultaneous determination of Nd and Pr in four synthetic samples and the results obtained are satisfactory. 展开更多
关键词 der SIMULTANEOUS DETERMINATION OF NEODYMIUM AND PRASEODYMIUM BY zero-order AND FOURTH-order DFRIVATIVE SPECTROPHOTOMETRY
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Phosphate and Nitrate Release from Mucky Mineral Soils
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作者 Michael A.Leblanc Léon E.Parent Gilles Gagné 《Open Journal of Soil Science》 2013年第2期107-114,共8页
High-organic (mucky) mineral soils make a small proportion of the Canadian agricultural land but are highly productive, especially for organic farming. Although these high-quality soils may release large amounts of ni... High-organic (mucky) mineral soils make a small proportion of the Canadian agricultural land but are highly productive, especially for organic farming. Although these high-quality soils may release large amounts of nitrate and phosphate to the environment, there is yet no reliable agro-environmental indicator for managing N and P compared to the adjacent mineral and organic soils. Our objective was to quantify the N mineralization and P environmental risks of mucky mineral soils. Nine Canadian soil series (eight Orthic Humic Gleysols and one Terric Humisol with three variants) were analyzed for texture, pH(CaCl2), total C and N, oxalate and Mehlich-III (M-III) extractable P, Al and Fe, and water extractable P (Pw). Soil texture varied from loamy sand to heavy clay, organic carbon (OC) content ranged from 14 to 392 g·OC·kg-1, total N from 1.21 to 16.38 g·N·kg-1, and degree of P saturation (DPSM-III) as molar (P/[Al + γFe])M-III percentage between 0.3% and 11.3%. After 100 d of incubation, soils released 31 to 340 mg·N·kg-1. The N mineralization rate was closely correlated to organic matter content (r = 0.91, p Sandy to loamy soils released 1.2 - 1.8 kg·N·ha-1·d-1 compared to 1.6 - 2.4 kg·N·ha-1·d-1 for clayey soils, 2.0 - 2.8 kg·N·ha-1·d-1 for mucky clayey soils and 2.6 - 2.7 kg·N·ha-1·d-1 for Humisol. For (P/[Al + 3Fe])M-III ratios of mucky clayey soils below 4.5%, water-extractable P did not exceed threshold of 9.7 mg Pw L-1. Mucky clayey soils could be managed for N similarly to Humisol and for P with (P/[Al + 3Fe])M-III percentage not exceeding 4.5%. 展开更多
关键词 Degree of Phosphate Saturation Gleysol Humisol Organic Nitrogen Mineralization zero-order Kinetics
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某类差分微分多项式和差分微分方程亚纯解的性质
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作者 樊艺 《毕节学院学报(综合版)》 2014年第8期18-23,共6页
利用亚纯函数差分的Nevanlinna值分布理论,研究了一类平移差分微分多项式的零点分布和一类平移差分微分方程亚纯解的性质,推广和改进了一些文献的结论。
关键词 差分微分多项式 亚纯解 零级 零点
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Stability analysis for time delay control of nonlinear systems in discrete-time domain with a standard discretisation method
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作者 Jinoh LEE Gustavo A.MEDRANO-CERDA Je Hyung JUNG 《Control Theory and Technology》 EI CSCD 2020年第1期92-106,共15页
This paper provides stability analysis results for discretised time delay control(TDC)as implemented in a sampled data system with the standard form of zero-order hold.We first substantiate stability issues in discret... This paper provides stability analysis results for discretised time delay control(TDC)as implemented in a sampled data system with the standard form of zero-order hold.We first substantiate stability issues in discrete-time TDC using an example and propose sufficient stability criteria in the sense of Lyapunov.Important parameters significantly affecting the overall system stability are the sampling period,the desired trajectory and the selection of the reference model dynamics. 展开更多
关键词 Time delay control(TDC) discretisation stability analysis zero-order HOLD
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Method for eliminating zero-order image in digital holography
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作者 刘雯雯 康新 +1 位作者 戴宜全 何小元 《Journal of Southeast University(English Edition)》 EI CAS 2009年第1期113-116,共4页
For eliminating the zero-order image in digital holography, a new method using the differential of the hologram intensity instead of the hologram itself for numerical reconstruction is proposed. This method is based o... For eliminating the zero-order image in digital holography, a new method using the differential of the hologram intensity instead of the hologram itself for numerical reconstruction is proposed. This method is based on digital image processing. By analyzing the spatial spectrum of the off-axis digital hologram, it theoretically proves that the zero-order image can be effectively eliminated by differential before reconstruction. Then, the detected hologram is processed in the program with differential and reconstruction. Both the theoretical analysis and digital reconstruction results show that it can effectively eliminate the large bright spot in the center of the reconstructed image caused by the zero-order image, improve the image quality significantly, and render a better contrast of the reconstructed image. This method is very simple and convenient due to no superfluous optical elements and requiring only one time record. 展开更多
关键词 digital holography zero-order image digital image processing Fresnel integral
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