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Robust Control System Design Using Proportional Plus Partial Derivative State Feedback 被引量:4
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作者 DUAN Guang-Ren ZHANG Biao 《自动化学报》 EI CSCD 北大核心 2007年第5期506-510,共5页
经由为矩阵对的概括特征值敏感问题的比例的正部分衍生物状态反馈和结果把线性系统基于为描述符建议的一般参量的 eigenstructure 赋值结果,到在开环的系统矩阵的使不安的元素的靠近环的特征值敏感的参量的表示被获得。为有在经由反馈... 经由为矩阵对的概括特征值敏感问题的比例的正部分衍生物状态反馈和结果把线性系统基于为描述符建议的一般参量的 eigenstructure 赋值结果,到在开环的系统矩阵的使不安的元素的靠近环的特征值敏感的参量的表示被获得。为有在经由反馈当时是的比例的正部分衍生物状态的线性系统建议了的描述符的最小的敏感的特征值赋值的一个有效算法。算法不包含回到过程,并且允许靠近环的特征值方便地在需要的区域以内被优化。一个例子表明它的有效性和简洁。 展开更多
关键词 鲁棒控制系统 线性系统 特征值 比例偏导数状态反馈
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Solution of Partial Derivative Equations of Poisson and Klein-Gordon with Neumann Conditions as a Generalized Problem of Two-Dimensional Moments
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作者 Maria B. Pintarelli 《Journal of Applied Mathematics and Physics》 2020年第8期1606-1614,共9页
It will be shown that finding solutions from the Poisson and Klein-Gordon equations under Neumann conditions are equivalent to solving an integral equation, which can be treated as a generalized two-dimensional moment... It will be shown that finding solutions from the Poisson and Klein-Gordon equations under Neumann conditions are equivalent to solving an integral equation, which can be treated as a generalized two-dimensional moment problem over a domain that is considered rectangular. The method consists to solve the integral equation numerically using the two-dimensional inverse moments problem techniques. We illustrate the different cases with examples. 展开更多
关键词 Equation in Poisson partial derivatives Klein-Gordon Equation Integral Equations Generalized Moment Problem
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Curvularin derivatives from hydrothermal vent sediment fungus Penicillium sp.HL-50 guided by molecular networking and their antiinflammatory activity 被引量:2
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作者 Chunxue Yu Zixuan Xia +6 位作者 Zhipeng Xu Xiyang Tang Wenjuan Ding Jihua Wei Danmei Tian Bin Wu Jinshan Tang 《Chinese Journal of Natural Medicines》 2025年第1期119-128,共10页
Guided by molecular networking,nine novel curvularin derivatives(1-9)and 16 known analogs(10-25)were isolated from the hydrothermal vent sediment fungus Penicillium sp.HL-50.Notably,compounds 5-7 represented a hybrid ... Guided by molecular networking,nine novel curvularin derivatives(1-9)and 16 known analogs(10-25)were isolated from the hydrothermal vent sediment fungus Penicillium sp.HL-50.Notably,compounds 5-7 represented a hybrid of curvularin and purine.The structures and absolute configurations of compounds 1-9 were elucidated via nuclear magnetic resonance(NMR)spectroscopy,X-ray diffraction,electronic circular dichroism(ECD)calculations,^(13)C NMR calculation,modified Mosher's method,and chemical derivatization.Investigation of anti-inflammatory activities revealed that compounds 7-9,11,12,14,15,and 18 exhibited significant suppressive effects against lipopolysaccharide(LPS)-induced nitric oxide(NO)production in murine macrophage RAW264.7 cells,with IC_(50)values ranging from 0.44 to 4.40μmol·L^(-1).Furthermore,these bioactive compounds were found to suppress the expression of inflammation-related proteins,including inducible NO synthase(i NOS),cyclooxygenase-2(COX-2),NLR family pyrin domain-containing protein 3(NLRP3),and nuclear factor kappa-B(NF-κB).Additional studies demonstrated that the novel compound 7 possessed potent antiinflammatory activity by inhibiting the transcription of inflammation-related genes,downregulating the expression of inflammation-related proteins,and inhibiting the release of inflammatory cytokines,indicating its potential application in the treatment of inflammatory diseases. 展开更多
关键词 Penicillium sp.HL-50 Curvularin derivatives Molecular networking Anti-inflammatory activity
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An attractive analytical technique for coupled system of fractional partial differential equations in shallow water waves with conformable derivative 被引量:4
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作者 Mohammed Al-Smadi Omar Abu Arqub Samir Hadid 《Communications in Theoretical Physics》 SCIE CAS CSCD 2020年第8期1-17,共17页
Mathematical simulation of nonlinear physical and abstract systems is a very vital process for predicting the solution behavior of fractional partial differential equations(FPDEs)corresponding to different application... Mathematical simulation of nonlinear physical and abstract systems is a very vital process for predicting the solution behavior of fractional partial differential equations(FPDEs)corresponding to different applications in science and engineering. In this paper, an attractive reliable analytical technique, the conformable residual power series, is implemented for constructing approximate series solutions for a class of nonlinear coupled FPDEs arising in fluid mechanics and fluid flow, which are often designed to demonstrate the behavior of weakly nonlinear and long waves and describe the interaction of shallow water waves. In the proposed technique the n-truncated representation is substituted into the original system and it is assumed the(n-1) conformable derivative of the residuum is zero. This allows us to estimate coefficients of truncation and successively add the subordinate terms in the multiple fractional power series with a rapidly convergent form. The influence, capacity, and feasibility of the presented approach are verified by testing some real-world applications. Finally, highlights and some closing comments are attached. 展开更多
关键词 nonlinear coupled system fractional partial differential equations residual power series method conformable fractional derivative
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Importance Analysis of a Multi-state System Based on Direct Partial Logic Derivatives and Multi-valued Decision Diagrams 被引量:1
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作者 古莹奎 李晶 《Journal of Donghua University(English Edition)》 EI CAS 2014年第6期789-792,共4页
Importance analysis quantifies the critical degree of individual component. Compared with the traditional binary state system,importance analysis of the multi-state system is more aligned with the practice. Because th... Importance analysis quantifies the critical degree of individual component. Compared with the traditional binary state system,importance analysis of the multi-state system is more aligned with the practice. Because the multi-valued decision diagram( MDD) can reflect the relationship between the components and the system state bilaterally, it was introduced into the reliability calculation of the multi-state system( MSS). The building method,simplified criteria,and path search and probability algorithm of MSS structure function MDD were given,and the reliability of the system was calculated. The computing methods of importance based on MDD and direct partial logic derivatives( DPLD) were presented. The diesel engine fuel supply system was taken as an example to illustrate the proposed method. The results show that not only the probability of the system in each state can be easily obtained,but also the influence degree of each component and its state on the system reliability can be obtained,which is conducive to the condition monitoring and structure optimization of the system. 展开更多
关键词 multi-state system(MSS) importance analysis reliability multi-valued decision diagram(MDD) direct partial logic derivative(DPLD) diesel engine fuel supply system
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Event-Based Networked Predictive Control of Cyber-Physical Systems with Delays and DoS Attacks
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作者 Wencheng Luo Pingli Lu +1 位作者 Changkun Du Haikuo Liu 《IEEE/CAA Journal of Automatica Sinica》 2025年第6期1295-1297,共3页
Dear Editor,This letter studies the stabilization control issue of cyber-physical systems with time-varying delays and aperiodic denial-of-service(DoS)attacks.To address the calculation overload issue caused by networ... Dear Editor,This letter studies the stabilization control issue of cyber-physical systems with time-varying delays and aperiodic denial-of-service(DoS)attacks.To address the calculation overload issue caused by networked predictive control(NPC)approach,an event-based NPC method is proposed.Within the proposed method,the negative effects of time-varying delays and DoS attacks on system performance are compensated.Then,sufficient and necessary conditions are derived to ensure the stability of the closed-loop system.In the end,simulation results are provided to demonstrate the validity of presented method. 展开更多
关键词 cyber physical systems dos attacks necessary conditions derived denial service attacks time varying delays event based networked predictive control stabilization control calculation overload
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Distributed Cooperative Regulation for Networked Re-Entrant Manufacturing Systems
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作者 Chenguang Liu Qing Gao +1 位作者 Wei Wang Jinhu Lü 《IEEE/CAA Journal of Automatica Sinica》 2025年第3期636-638,共3页
Dear Editor,This letter focuses on the distributed cooperative regulation problem for a class of networked re-entrant manufacturing systems(RMSs).The networked system is structured with a three-tier architecture:the p... Dear Editor,This letter focuses on the distributed cooperative regulation problem for a class of networked re-entrant manufacturing systems(RMSs).The networked system is structured with a three-tier architecture:the production line,the manufacturing layer and the workshop layer.The dynamics of re-entrant production lines are governed by hyperbolic partial differential equations(PDEs)based on the law of mass conservation. 展开更多
关键词 production line networked re entrant manufacturing systems three tier architecture production linethe distributed cooperative regulation hyperbolic partial differential equations pdes based distributed cooperative regulation problem manufacturing layer
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FMCSNet: Mobile Devices-Oriented Lightweight Multi-Scale Object Detection via Fast Multi-Scale Channel Shuffling Network Model
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作者 Lijuan Huang Xianyi Liu +1 位作者 Jinping Liu Pengfei Xu 《Computers, Materials & Continua》 2026年第1期1292-1311,共20页
The ubiquity of mobile devices has driven advancements in mobile object detection.However,challenges in multi-scale object detection in open,complex environments persist due to limited computational resources.Traditio... The ubiquity of mobile devices has driven advancements in mobile object detection.However,challenges in multi-scale object detection in open,complex environments persist due to limited computational resources.Traditional approaches like network compression,quantization,and lightweight design often sacrifice accuracy or feature representation robustness.This article introduces the Fast Multi-scale Channel Shuffling Network(FMCSNet),a novel lightweight detection model optimized for mobile devices.FMCSNet integrates a fully convolutional Multilayer Perceptron(MLP)module,offering global perception without significantly increasing parameters,effectively bridging the gap between CNNs and Vision Transformers.FMCSNet achieves a delicate balance between computation and accuracy mainly by two key modules:the ShiftMLP module,including a shift operation and an MLP module,and a Partial group Convolutional(PGConv)module,reducing computation while enhancing information exchange between channels.With a computational complexity of 1.4G FLOPs and 1.3M parameters,FMCSNet outperforms CNN-based and DWConv-based ShuffleNetv2 by 1%and 4.5%mAP on the Pascal VOC 2007 dataset,respectively.Additionally,FMCSNet achieves a mAP of 30.0(0.5:0.95 IoU threshold)with only 2.5G FLOPs and 2.0M parameters.It achieves 32 FPS on low-performance i5-series CPUs,meeting real-time detection requirements.The versatility of the PGConv module’s adaptability across scenarios further highlights FMCSNet as a promising solution for real-time mobile object detection. 展开更多
关键词 Object detection lightweight network partial group convolution multilayer perceptron
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An Improved PID Controller Based on Artificial Neural Networks for Cathodic Protection of Steel in Chlorinated Media
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作者 JoséArturo Ramírez-Fernández Henevith G.Méndez-Figueroa +3 位作者 Sebastián Ossandón Ricardo Galván-Martínez MiguelÁngel Hernández-Pérez Ricardo Orozco-Cruz 《Computers, Materials & Continua》 2026年第3期624-640,共17页
In this study,artificial neural networks(ANNs)were implemented to determine design parameters for an impressed current cathodic protection(ICCP)prototype.An ASTM A36 steel plate was tested in 3.5%NaCl solution,seawate... In this study,artificial neural networks(ANNs)were implemented to determine design parameters for an impressed current cathodic protection(ICCP)prototype.An ASTM A36 steel plate was tested in 3.5%NaCl solution,seawater,and NS4 using electrochemical impedance spectroscopy(EIS)to monitor the evolution of the substrate surface,which affects the current required to reach the protection potential(Eprot).Experimental data were collected as training datasets and analyzed using statistical methods,including box plots and correlation matrices.Subsequently,ANNs were applied to predict the current demand at different exposure times,enabling the estimation of electrochemical parameters(limiting voltage values)that can be used to optimize a self-regulating ICCP system.The obtained electrochemical parameters were then used,through Particle Swarm Optimization(PSO),to fine-tune an ANN-based proportional-integral-derivative(PID)controller for the ICCP system. 展开更多
关键词 Artificial neural networks(ANNs) corrosion impressed current cathodic protection(ICCP) proportional integral derivative(PID)corrosion control particle swarm optimization(PSO) statistical analysis
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Estimation of partial derivative functionals with application to human mortality data analysis 被引量:1
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作者 Tao Zhang Zhaohai Li +1 位作者 Aiyi Liu Qingzhao Zhang 《Science China Mathematics》 SCIE CSCD 2021年第9期2117-2140,共24页
To better describe and understand the time dynamics in functional data analysis,it is often desirable to recover the partial derivatives of the random surface.A novel approach is proposed based on marginal functional ... To better describe and understand the time dynamics in functional data analysis,it is often desirable to recover the partial derivatives of the random surface.A novel approach is proposed based on marginal functional principal component analysis to derive the representation for partial derivatives.To obtain the Karhunen-Lo`eve expansion of the partial derivatives,an adaptive estimation is explored.Asymptotic results of the proposed estimates are established.Simulation studies show that the proposed methods perform well in finite samples.Application to the human mortality data reveals informative time dynamics in mortality rates. 展开更多
关键词 bivariate functional data functional principal component analysis MORTALITY partial derivatives
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Distributed wireless quantum communication networks with partially entangled pairs 被引量:9
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作者 余旭涛 张在琛 徐进 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第1期66-73,共8页
Wireless quantum communication networks transfer quantum state by teleportation. Existing research focuses on maximal entangled pairs. In this paper, we analyse the distributed wireless quantum communication networks ... Wireless quantum communication networks transfer quantum state by teleportation. Existing research focuses on maximal entangled pairs. In this paper, we analyse the distributed wireless quantum communication networks with partially entangled pairs. A quantum routing scheme with multi-hop teleportation is proposed. With the proposed scheme, is not necessary for the quantum path to be consistent with the classical path. The quantum path and its associated classical path are established in a distributed way. Direct multi-hop teleportation is conducted on the selected path to transfer a quantum state from the source to the destination. Based on the feature of multi-hop teleportation using partially entangled pairs, if the node number of the quantum path is even, the destination node will add another teleportation at itself. We simulated the performance of distributed wireless quantum communication networks with a partially entangled state. The probability of transferring the quantum state successfully is statistically analyzed. Our work shows that multi-hop teleportation on distributed wireless quantum networks with partially entangled pairs is feasible. 展开更多
关键词 distributed wireless quantum communication networks partially entangled pairs routing multi-hop teleportation
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Mobility-Aware Partial Computation Offloading in Vehicular Networks: A Deep Reinforcement Learning Based Scheme 被引量:8
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作者 Jianfei Wang Tiejun Lv +1 位作者 Pingmu Huang P.Takis Mathiopoulos 《China Communications》 SCIE CSCD 2020年第10期31-49,共19页
Encouraged by next-generation networks and autonomous vehicle systems,vehicular networks must employ advanced technologies to guarantee personal safety,reduce traffic accidents and ease traffic jams.By leveraging the ... Encouraged by next-generation networks and autonomous vehicle systems,vehicular networks must employ advanced technologies to guarantee personal safety,reduce traffic accidents and ease traffic jams.By leveraging the computing ability at the network edge,multi-access edge computing(MEC)is a promising technique to tackle such challenges.Compared to traditional full offloading,partial offloading offers more flexibility in the perspective of application as well as deployment of such systems.Hence,in this paper,we investigate the application of partial computing offloading in-vehicle networks.In particular,by analyzing the structure of many emerging applications,e.g.,AR and online games,we convert the application structure into a sequential multi-component model.Focusing on shortening the application execution delay,we extend the optimization problem from the single-vehicle computing offloading(SVCOP)scenario to the multi-vehicle computing offloading(MVCOP)by taking multiple constraints into account.A deep reinforcement learning(DRL)based algorithm is proposed as a solution to this problem.Various performance evaluation results have shown that the proposed algorithm achieves superior performance as compared to existing offloading mechanisms in deducing application execution delay. 展开更多
关键词 partial offloading MEC fog computing vehicular networks D2D AR
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Quantum communication for satellite-to-ground networks with partially entangled states 被引量:1
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作者 陈娜 权东晓 +1 位作者 裴昌幸 杨宏 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第2期53-61,共9页
To realize practical wide-area quantum communication,a satellite-to-ground network with partially entangled states is developed in this paper.For efficiency and security reasons,the existing method of quantum communic... To realize practical wide-area quantum communication,a satellite-to-ground network with partially entangled states is developed in this paper.For efficiency and security reasons,the existing method of quantum communication in distributed wireless quantum networks with partially entangled states cannot be applied directly to the proposed quantum network.Based on this point,an efficient and secure quantum communication scheme with partially entangled states is presented.In our scheme,the source node performs teleportation only after an end-to-end entangled state has been established by entanglement swapping with partially entangled states.Thus,the security of quantum communication is guaranteed.The destination node recovers the transmitted quantum bit with the help of an auxiliary quantum bit and specially defined unitary matrices.Detailed calculations and simulation analyses show that the probability of successfully transferring a quantum bit in the presented scheme is high.In addition,the auxiliary quantum bit provides a heralded mechanism for successful communication.Based on the critical components that are presented in this article an efficient,secure,and practical wide-area quantum communication can be achieved. 展开更多
关键词 satellite-to-ground quantum communication network partially entangled states entanglementswapping quantum teleportation
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DISTRIBUTED PARAMETER NEURAL NETWORKS FOR SOLVING PARTIAL DIFFERENTIAL EQUATIONS 被引量:1
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作者 Feng Dazheng Bao Zheng Jiao Licheng(Electronic Engineering Institute, Xidian University, Xi’an 710071) 《Journal of Electronics(China)》 1997年第2期186-190,共5页
Novel distributed parameter neural networks are proposed for solving partial differential equations, and their dynamic performances are studied in Hilbert space. The locally connected neural networks are obtained by s... Novel distributed parameter neural networks are proposed for solving partial differential equations, and their dynamic performances are studied in Hilbert space. The locally connected neural networks are obtained by separating distributed parameter neural networks. Two simulations are also given. Both theoretical and computed results illustrate that the distributed parameter neural networks are effective and efficient for solving partial differential equation problems. 展开更多
关键词 Distributed PARAMETER NEURAL network partial differential equation Stability Local CONNECTION
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Application of neural network model coupling with the partial least-squares method for forecasting watre yield of mine 被引量:2
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作者 陈南祥 曹连海 黄强 《Journal of Coal Science & Engineering(China)》 2005年第1期40-43,共4页
Scientific forecasting water yield of mine is of great significance to the safety production of mine and the colligated using of water resources. The paper established the forecasting model for water yield of mine, co... Scientific forecasting water yield of mine is of great significance to the safety production of mine and the colligated using of water resources. The paper established the forecasting model for water yield of mine, combining neural network with the partial least square method. Dealt with independent variables by the partial least square method, it can not only solve the relationship between independent variables but also reduce the input dimensions in neural network model, and then use the neural network which can solve the non-linear problem better. The result of an example shows that the prediction has higher precision in forecasting and fitting. 展开更多
关键词 water yield of mine partial least square method neural network forecasting model
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Prediction of Partial Ring Current Index Using LSTM Neural Network 被引量:1
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作者 LI Hui WANG Runze WANG Chi 《空间科学学报》 CAS CSCD 北大核心 2022年第5期873-883,共11页
The local time dependence of the geomagnetic disturbances during magnetic storms indicates the necessity of forecasting the localized magnetic storm indices.For the first time,we construct prediction models for the Su... The local time dependence of the geomagnetic disturbances during magnetic storms indicates the necessity of forecasting the localized magnetic storm indices.For the first time,we construct prediction models for the SuperMAG partial ring current indices(SMR-LT),with the advance time increasing from 1 h to 12 h by Long Short-Term Memory(LSTM)neural network.Generally,the prediction performance decreases with the advance time and is better for the SMR-06 index than for the SMR-00,SMR-12,and SMR-18 index.For the predictions with 12 h ahead,the correlation coefficient is 0.738,0.608,0.665,and 0.613,respectively.To avoid the over-represented effect of massive data during geomagnetic quiet periods,only the data during magnetic storms are used to train and test our models,and the improvement in prediction metrics increases with the advance time.For example,for predicting the storm-time SMR-06 index with 12 h ahead,the correlation coefficient and the prediction efficiency increases from 0.674 to 0.691,and from 0.349 to 0.455,respectively.The evaluation of the model performance for forecasting the storm intensity shows that the relative error for intense storms is usually less than the relative error for moderate storms. 展开更多
关键词 Geomagnetic storm partial Ring Current Index(PRCI) Artificial Neural network(ANN)
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Development a Spectrophotometric of Fe(Ⅲ), Al(Ⅲ) and Cu(Ⅱ) Using Eriochrome Cyanine R Ligand and Assessment of the Obtained Data by Partial Least-Squares and Artificial Neural Network Method-Application to Natural Waters
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作者 A. Hakan AKTAS 《光谱学与光谱分析》 SCIE EI CAS CSCD 北大核心 2018年第8期2638-2644,共7页
Simultaneous determination of heavy metal cations and accurate quantitative prediction of them are of great interest in analytical chemistry.This work has focused on a comprehensive comparison of partial least squares... Simultaneous determination of heavy metal cations and accurate quantitative prediction of them are of great interest in analytical chemistry.This work has focused on a comprehensive comparison of partial least squares(PLS-1)and artificial neural networks(ANN)as two types of chemometric methods.For this purpose,aluminum,iron and copper were studied as three analytes whose UV-Vis absorption spectra highly overlap each other.Accordance with determined parameters(ligand concentration,pH,waiting times,the relationship between absorbance and concentration of metal ion effect and foreign ions)are provided and the optimum conditions.After establishing the optimum conditions for Fe^(3+),Al^(3+) and Cu^(2+) containing mixtures spectrophotometric determinations and the data calibration method of least squares(PLS-1)regression,and artificial neural network(ANN)methods were used.Chemometric methods are applied in a fast,simple,and the results are applicable. 展开更多
关键词 UV-Vis spectrophotometry partial least squares Artificial neural network ALUMINUM IRON COPPER
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Non-derivative solution to nonlinear dynamic optimal design of class two for deformation network monitoring
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作者 陶华学 郭金运 《中国有色金属学会会刊:英文版》 CSCD 2000年第4期551-554,共4页
Based on the nonlinear error equation of deformation network monitoring, the mathematical model of nonlinear dynamic optimal design of class two was put forward for the deformation network monitoring, in which the tar... Based on the nonlinear error equation of deformation network monitoring, the mathematical model of nonlinear dynamic optimal design of class two was put forward for the deformation network monitoring, in which the target function is the accuracy criterion and the constraint conditions are the network’s sensitivity, reliability and observing cost. Meanwhile a new non derivative solution to the nonlinear dynamic optimal design of class two was also put forward. The solving model uses the difference to stand for the first derivative of functions and solves the revised feasible direction to get the optimal solution to unknown parameters. It can not only make the solution to converge on the minimum point of the constraint problem, but decrease the calculating load. 展开更多
关键词 DEFORMATION network monitoring NONLINEAR dynamic optimal design non derivative ANALYTIC method.
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A Partially Non-Cryptographic Security Routing Protocol in Mobile Ad Hoc Networks
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作者 CHEN Jing CUI Guohua 《Wuhan University Journal of Natural Sciences》 CAS 2006年第6期1781-1784,共4页
In this paper, we propose a partially non-cryptographic security routing protocol (PNCSR) that protects both routing and data forwarding operations through the same reactive approach. PNCSR only apply public-key cry... In this paper, we propose a partially non-cryptographic security routing protocol (PNCSR) that protects both routing and data forwarding operations through the same reactive approach. PNCSR only apply public-key cryptographic system in managing token, but it doesn't utilize any cryptographic primitives on the routing messages. In PNCSR, each node is fair. Local neighboring nodes collaboratively monitor each other and sustain each other. It also uses a novel credit strategy which additively increases the token lifetime each time a node renews its token. We also analyze the storage, computation, and communication overhead of PNCSR, and provide a simple yet meaningful overhead comparison. Finally, the simulation results show the effectiveness of PNCSR in various situations. 展开更多
关键词 ad hoc network security routing protocol partially non-cryptographic
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On the partial stability of nonlinear impulsive Caputo fractional systems
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作者 Boulbaba Ghanmi Saifeddine Ghnimi 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第2期166-179,共14页
In this work,stability with respect to part of the variables of nonlinear impulsive Caputo fractional differential equations is investigated.Some effective sufficient conditions of stability,uniform stability,asymptot... In this work,stability with respect to part of the variables of nonlinear impulsive Caputo fractional differential equations is investigated.Some effective sufficient conditions of stability,uniform stability,asymptotic uniform stability and Mittag Leffler stability.The approach presented is based on the specially introduced piecewise continuous Lyapunov functions.Furthermore,some numerical examples are given to show the effectiveness of our obtained theoretical results. 展开更多
关键词 impulsive fractional differential equations Mittag-Leffler function partial stability Caputo derivative
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