Search results for: Feng Zhou
207 A Neighborhood Condition for Fractional k-deleted Graphs
Authors: Sizhong Zhou, Hongxia Liu
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Abstract–Let k ≥ 3 be an integer, and let G be a graph of order n with n ≥ 9k +3- 42(k - 1)2 + 2. Then a spanning subgraph F of G is called a k-factor if dF (x) = k for each x ∈ V (G). A fractional k-factor is a way of assigning weights to the edges of a graph G (with all weights between 0 and 1) such that for each vertex the sum of the weights of the edges incident with that vertex is k. A graph G is a fractional k-deleted graph if there exists a fractional k-factor after deleting any edge of G. In this paper, it is proved that G is a fractional k-deleted graph if G satisfies δ(G) ≥ k + 1 and |NG(x) ∪ NG(y)| ≥ 1 2 (n + k - 2) for each pair of nonadjacent vertices x, y of G.
Keywords: Graph, minimum degree, neighborhood union, fractional k-factor, fractional k-deleted graph.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1065206 A Schur Method for Solving Projected Continuous-Time Sylvester Equations
Authors: Yiqin Lin, Liang Bao, Qinghua Wu, Liping Zhou
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In this paper, we propose a direct method based on the real Schur factorization for solving the projected Sylvester equation with relatively small size. The algebraic formula of the solution of the projected continuous-time Sylvester equation is presented. The computational cost of the direct method is estimated. Numerical experiments show that this direct method has high accuracy.Keywords: Projected Sylvester equation, Schur factorization, Spectral projection, Direct method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1825205 The Causation and Solution of Ringing Effect in DCT-based Video Coding
Authors: Yu Yuan, David Feng, Yu-Zhuo Zhong
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Ringing effect is one of the most annoying visual artifacts in digital video. It is a significant factor of subjective quality deterioration. However, there is a widely-accepted misunderstanding of its cause. In this paper, we propose a reasonable interpretation of the cause of ringing effect. Based on the interpretation, we suggest further two methods to reduce ringing effect in DCT-based video coding. The methods adaptively adjust quantizers according to video features. Our experiments proved that the methods could efficiently improve subjective quality with acceptable additional computing costs.Keywords: ringing effect, video coding, subjective quality, DCT.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1756204 A New Algorithm for Determining the Leading Coefficient of in the Parabolic Equation
Authors: Shiping Zhou, Minggen Cui
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This paper investigates the inverse problem of determining the unknown time-dependent leading coefficient in the parabolic equation using the usual conditions of the direct problem and an additional condition. An algorithm is developed for solving numerically the inverse problem using the technique of space decomposition in a reproducing kernel space. The leading coefficients can be solved by a lower triangular linear system. Numerical experiments are presented to show the efficiency of the proposed methods.Keywords: parabolic equations, coefficient inverse problem, reproducing kernel.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1580203 A Robust Audio Fingerprinting Algorithm in MP3 Compressed Domain
Authors: Ruili Zhou, Yuesheng Zhu
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In this paper, a new robust audio fingerprinting algorithm in MP3 compressed domain is proposed with high robustness to time scale modification (TSM). Instead of simply employing short-term information of the MP3 stream, the new algorithm extracts the long-term features in MP3 compressed domain by using the modulation frequency analysis. Our experiment has demonstrated that the proposed method can achieve a hit rate of above 95% in audio retrieval and resist the attack of 20% TSM. It has lower bit error rate (BER) performance compared to the other algorithms. The proposed algorithm can also be used in other compressed domains, such as AAC.Keywords: Audio Fingerprinting, MP3, Modulation Frequency, TSM
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2195202 Development of Energy Management System Based on Internet of Things Technique
Authors: Wen-Jye Shyr, Chia-Ming Lin, Hung-Yun Feng
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The purpose of this study was to develop an energy management system for university campuses based on the Internet of Things (IoT) technique. The proposed IoT technique based on WebAccess is used via network browser Internet Explore and applies TCP/IP protocol. The case study of IoT for lighting energy usage management system was proposed. Structure of proposed IoT technique included perception layer, equipment layer, control layer, application layer and network layer.
Keywords: Energy management, IoT technique, Sensor, WebAccess
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1137201 The Relation of College Students- Process of Study and Creativity: The Mediating Effect of Creative Self-Efficacy
Authors: Chih-Feng Chuang, Shih-Ching Shiu, Chao-Jen Cheng
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The purpose of this study was to investigate the relationships among students- process of study, creative self-efficacy and creativity while attending college. A total of 60 students enrolled in Hsiuping Institute of Technology in central Taiwan were selected as samples for the study. The instruments for this study included three questionnaires to explore the aforesaid aspects. This researchers tested creative self-efficacy and process of study, and creativity with Pearson correlation and hierarchical regression analyses. The major findings of this research are (1) the process of study had direct positive predictability on creativity, and (2) the relationship between process of study and creativity is partially mediated by creative self-efficacy.Keywords: Process of study, Creative self-efficacy, Creativity
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1738200 Design a Three-dimensional Pursuit Guidance Law with Feedback Linearization Method
Authors: Chien-Chun Kung, Feng-Lung Chiang, Kuei-Yi Chen
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In this paper, we will implement three-dimensional pursuit guidance law with feedback linearization control method and study the effects of parameters. First, we introduce guidance laws and equations of motion of a missile. Pursuit guidance law is our highlight. We apply feedback linearization control method to obtain the accelerations to implement pursuit guidance law. The solution makes warhead direction follow with line-of-sight. Final, the simulation results show that the exact solution derived in this paper is correct and some factors e.g. control gain, time delay, are important to implement pursuit guidance law.
Keywords: Pursuit guidance law, feedback linearization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2527199 Real-time ROI Acquisition for Unsupervised and Touch-less Palmprint
Authors: Yi Feng, Jingwen Li, Lei Huang, Changping Liu
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In this paper we proposed a novel method to acquire the ROI (Region of interest) of unsupervised and touch-less palmprint captured from a web camera in real-time. We use Viola-Jones approach and skin model to get the target area in real time. Then an innovative course-to-fine approach to detect the key points on the hand is described. A new algorithm is used to find the candidate key points coarsely and quickly. In finely stage, we verify the hand key points with the shape context descriptor. To make the user much comfortable, it can process the hand image with different poses, even the hand is closed. Experiments show promising result by using the proposed method in various conditions.Keywords: Palmprint recoginition, hand detection, touch-lesspalmprint, ROI localization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1725198 Approximation Incremental Training Algorithm Based on a Changeable Training Set
Authors: Yi-Fan Zhu, Wei Zhang, Xuan Zhou, Qun Li, Yong-Lin Lei
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The quick training algorithms and accurate solution procedure for incremental learning aim at improving the efficiency of training of SVR, whereas there are some disadvantages for them, i.e. the nonconvergence of the formers for changeable training set and the inefficiency of the latter for a massive dataset. In order to handle the problems, a new training algorithm for a changeable training set, named Approximation Incremental Training Algorithm (AITA), was proposed. This paper explored the reason of nonconvergence theoretically and discussed the realization of AITA, and finally demonstrated the benefits of AITA both on precision and efficiency.Keywords: support vector regression, incremental learning, changeable training set, quick training algorithm, accurate solutionprocedure
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1483197 A Intelligent Inference Model about Complex Systems- Stability: Inspiration from Nature
Authors: Naiqin Feng, Yuhui Qiu, Yingshan Zhang, Fang Wang
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A logic model for analyzing complex systems- stability is very useful to many areas of sciences. In the real world, we are enlightened from some natural phenomena such as “biosphere", “food chain", “ecological balance" etc. By research and practice, and taking advantage of the orthogonality and symmetry defined by the theory of multilateral matrices, we put forward a logic analysis model of stability of complex systems with three relations, and prove it by means of mathematics. This logic model is usually successful in analyzing stability of a complex system. The structure of the logic model is not only clear and simple, but also can be easily used to research and solve many stability problems of complex systems. As an application, some examples are given.Keywords: Complex system, logic model, relation, stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1327196 Graphical Approach for Targeting Work Exchange Networks
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Depressurization and pressurization streams in industrial systems constitute a work exchange network (WEN). In this paper, a novel graphical approach for targeting energy conservation potential of a WEN is proposed. Through constructing the composite work curves in the pressure-work diagram and assuming all of the mechanical energy of the depressurization streams is recovered by expanders, the maximum work target of a WEN can be determined via the proposed targeting steps. A WEN in an ammonia production process is used as a case study to illustrate the applicability of the proposed graphical approach.Keywords: Expanders, Graphical approach, Pressure-work diagram, Work exchange network, Work target
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1501195 Unsupervised Image Segmentation Based on Fuzzy Connectedness with Sale Space Theory
Authors: Yuanjie Zheng, Jie Yang, Yue Zhou
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In this paper, we propose an approach of unsupervised segmentation with fuzzy connectedness. Valid seeds are first specified by an unsupervised method based on scale space theory. A region is then extracted for each seed with a relative object extraction method of fuzzy connectedness. Afterwards, regions are merged according to the values between them of an introduced measure. Some theorems and propositions are also provided to show the reasonableness of the measure for doing mergence. Experiment results on a synthetic image, a color image and a large amount of MR images of our method are reported.Keywords: Image segmentation, unsupervised imagesegmentation, fuzzy connectedness, scale space.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1340194 Delay-range-Dependent Exponential Synchronization of Lur-e Systems with Markovian Switching
Authors: Xia Zhou, Shouming Zhong
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The problem of delay-range-dependent exponential synchronization is investigated for Lur-e master-slave systems with delay feedback control and Markovian switching. Using Lyapunov- Krasovskii functional and nonsingular M-matrix method, novel delayrange- dependent exponential synchronization in mean square criterions are established. The systems discussed in this paper is advanced system, and takes all the features of interval systems, Itˆo equations, Markovian switching, time-varying delay, as well as the environmental noise, into account. Finally, an example is given to show the validity of the main result.
Keywords: Synchronization, delay-range-dependent, Markov chain, generalized Itō's formula, brownian motion, M-matrix.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1566193 Some New Inequalities for Eigenvalues of the Hadamard Product and the Fan Product of Matrices
Authors: Jing Li, Guang Zhou
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Let A and B be nonnegative matrices. A new upper bound on the spectral radius ρ(A◦B) is obtained. Meanwhile, a new lower bound on the smallest eigenvalue q(AB) for the Fan product, and a new lower bound on the minimum eigenvalue q(B ◦A−1) for the Hadamard product of B and A−1 of two nonsingular M-matrices A and B are given. Some results of comparison are also given in theory. To illustrate our results, numerical examples are considered.
Keywords: Hadamard product, Fan product; nonnegative matrix, M-matrix, Spectral radius, Minimum eigenvalue, 1-path cover.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1894192 The Care Management Network as an Effective Intervention in Mitigating the Risks of Hypertension
Authors: Feng-Chuan Pan, Fang-Yue Liu
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Hospitals in southern Hualien teamed with the Hypertension Joint Care Network. Working with the network, the team provided a special designed health education to the individual who had been identified as a hypertension patient in the outpatient department. Some metabolism improvements achieved. This is a retrospective study by purposively taking 106 patients from a hospital between 2008 and 2010. Records of before and after education intervention of the objects was collected and analyzed to see the how the intervention affected the patients- hypertension control via clinical parameter monitoring. The results showed that the clinical indicators, the LDL-C, the cholesterol and the systolic blood pressure were significantly improved. The study provides evidence for the effectiveness of the network in controlling hypertension.Keywords: hypertension, joint care management network, cardiovascular diseases, metabolic syndrome.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1729191 Image Sensor Matrix High Speed Simulation
Authors: Z. Feng, V. Viswanathan, D. Navarro, I. O'Connor
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This paper presents a new high speed simulation methodology to solve the long simulation time problem of CMOS image sensor matrix. Generally, for integrating the pixel matrix in SOC and simulating the system performance, designers try to model the pixel in various modeling languages such as VHDL-AMS, SystemC or Matlab. We introduce a new alternative method based on spice model in cadence design platform to achieve accuracy and reduce simulation time. The simulation results indicate that the pixel output voltage maximum error is at 0.7812% and time consumption reduces from 2.2 days to 13 minutes achieving about 240X speed-up for the 256x256 pixel matrix.
Keywords: CMOS image sensor, high speed simulation, image sensor matrix simulation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2013190 Improved Robust Stability Criteria of a Class of Neutral Lur’e Systems with Interval Time-Varying Delays
Authors: Longqiao Zhou, Zixin Liu, Shu Lü
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This paper addresses the robust stability problem of a class of delayed neutral Lur’e systems. Combined with the property of convex function and double integral Jensen inequality, a new tripe integral Lyapunov functional is constructed to derive some new stability criteria. Compared with some related results, the new criteria established in this paper are less conservative. Finally, two numerical examples are presented to illustrate the validity of the main results.
Keywords: Lur’e system, Convex function, Jensen integral inequality, Triple-integral method, Exponential stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1517189 FPGA Implement of a Vision Based Lane Departure Warning System
Authors: Yu Ren Lin, Yi Feng Su
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Using vision based solution in intelligent vehicle application often needs large memory to handle video stream and image process which increase complexity of hardware and software. In this paper, we present a FPGA implement of a vision based lane departure warning system. By taking frame of videos, the line gradient of line is estimated and the lane marks are found. By analysis the position of lane mark, departure of vehicle will be detected in time. This idea has been implemented in Xilinx Spartan6 FPGA. The lane departure warning system used 39% logic resources and no memory of the device. The average availability is 92.5%. The frame rate is more than 30 frames per second (fps).
Keywords: Lane departure warning system, image, FPGA.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2075188 An Adaptive Least-squares Mixed Finite Element Method for Pseudo-parabolic Integro-differential Equations
Authors: Zilong Feng, Hong Li, Yang Liu, Siriguleng He
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In this article, an adaptive least-squares mixed finite element method is studied for pseudo-parabolic integro-differential equations. The solutions of least-squares mixed weak formulation and mixed finite element are proved. A posteriori error estimator is constructed based on the least-squares functional and the posteriori errors are obtained.
Keywords: Pseudo-parabolic integro-differential equation, least squares mixed finite element method, adaptive method, a posteriori error estimates.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1318187 Geographic Profiling Based on Multi-point Centrography with K-means Clustering
Authors: Jiaji Zhou, Le Liang, Long Chen
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Geographic Profiling has successfully assisted investigations for serial crimes. Considering the multi-cluster feature of serial criminal spots, we propose a Multi-point Centrography model as a natural extension of Single-point Centrography for geographic profiling. K-means clustering is first performed on the data samples and then Single-point Centrography is adopted to derive a probability distribution on each cluster. Finally, a weighted combinations of each distribution is formed to make next-crime spot prediction. Experimental study on real cases demonstrates the effectiveness of our proposed model.
Keywords: Geographic profiling, Centrography model, K-means algorithm
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2085186 The Catalytic Properties of PtSn/Al2O3 for Acetic Acid Hydrogenation
Authors: Mingchuan Zhou, Haitao Zhang, Hongfang Ma, Weiyong Ying
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Alumina supported platinum and tin catalysts with different loadings of Pt and Sn were prepared and characterized by low temperature N2 adsorption/desorption, H2-temperature programed reduction and CO pulse chemisorption. Pt and Sn below 1% loading were suitable for acetic acid hydrogenation. The best performance over 0.75Pt1Sn/Al2O3 can reach 87.55% conversion of acetic acid and 47.39% selectivity of ethanol. The operating conditions of acetic acid hydrogenation over 1Pt1Sn/Al2O3 were investigated. High reaction temperature can enhance the conversion of acetic acid, but it decreased total selectivity of ethanol and acetyl acetate. High pressure and low weight hourly space velocity were beneficial to both conversion of acetic acid and selectivity to ethanol.
Keywords: Acetic acid, hydrogenation, PtSn, operating condition.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1245185 Determinants of E-Government Services Adoption from the African Students’ Perspective
Authors: Isaac Kofi Mensah, Jianing Mi, Cheng Feng
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The patronage of e-government services (demand side of e-government) is vital to the successful implementation of e-government initiatives. The purpose of this study is to explore the predictors determining the willingness of African students in China to adopt and use e-government services. The Unified Theory of Acceptance and Use of Technology (UTAUT) will be used as the theoretical foundation for this research. Research instrument will be developed and administered to 500 African students in China. Factors such as performance expectancy, effort expectancy, social influence, facilitating conditions and culture will be investigated to determine its significant impact on the willingness to use e-government services. This study is a research in progress. The outcome of this study will provide valuable recommendations to improve the provision of public services through e-government.
Keywords: E-government, e-government services, predictors UTAUT.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1249184 The Dividend Payments for General Claim Size Distributions under Interest Rate
Authors: Li-Li Li, Jinghai Feng, Lixin Song
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This paper evaluates the dividend payments for general claim size distributions in the presence of a dividend barrier. The surplus of a company is modeled using the classical risk process perturbed by diffusion, and in addition, it is assumed to accrue interest at a constant rate. After presenting the integro-differential equation with initial conditions that dividend payments satisfies, the paper derives a useful expression of the dividend payments by employing the theory of Volterra equation. Furthermore, the optimal value of dividend barrier is found. Finally, numerical examples illustrate the optimality of optimal dividend barrier and the effects of parameters on dividend payments.Keywords: Dividend payout, Integro-differential equation, Jumpdiffusion model, Volterra equation
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1799183 Component Comparison of Polyaluminum Chloride Produced from Various Methods
Authors: Wen Po Cheng, Chia Yun Chung, Ruey Fang Yu, Chao Feng Chen
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The main objective of this research was to study the differences of aluminum hydrolytic products between two PACl preparation methods. These two methods were the acidification process of freshly formed amorphous Al(OH)3 and the conventional alkalization process of aluminum chloride solution. According to Ferron test and 27Al NMR analysis of those two PACl preparation procedures, the reaction rate constant (k) values and Al13 percentage of acid addition process at high basicity value were both lower than those values of the alkaline addition process. The results showed that the molecular structure and size distribution of the aluminum species in both preparing methods were suspected to be significantly different at high basicity value.
Keywords: Polyaluminum chloride, Al13, amorphous aluminum hydroxide, Ferron test.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1508182 A New Robust Stability Criterion for Dynamical Neural Networks with Mixed Time Delays
Authors: Guang Zhou, Shouming Zhong
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In this paper, we investigate the problem of the existence, uniqueness and global asymptotic stability of the equilibrium point for a class of neural networks, the neutral system has mixed time delays and parameter uncertainties. Under the assumption that the activation functions are globally Lipschitz continuous, we drive a new criterion for the robust stability of a class of neural networks with time delays by utilizing the Lyapunov stability theorems and the Homomorphic mapping theorem. Numerical examples are given to illustrate the effectiveness and the advantage of the proposed main results.
Keywords: Neural networks, Delayed systems, Lyapunov function, Stability analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1584181 Numerical Study on the Effect of Spudcan Penetration on the Jacket Platform
Authors: Xiangming Ge, Bing Pan, Wei He, Hao Chen, Yong Zhou, Jiayao Wu, Weijiang Chu
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How the extraction and penetration of spudcan affect the performance of the adjacent pile foundation supporting the jacket platform was studied in the program FLAC3D depending on a wind farm project in Bohai sea. The simulations were conducted at the end of the spudcan penetration, which induced a pockmark in the seabed. The effects of the distance between the pile foundation and the pockmark were studied. The displacement at the mudline arose when the pockmark was closer. The bearing capacity of this jacket platform with deep pile foundations has been less influenced by the process of spudcan penetration, which can induce severe stresses on the pile foundation. The induced rotation was also satisfied with the serviceability constraints.
Keywords: Offshore foundation, pile-soil interaction, spudcan penetration, FLAC3D.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 365180 Selection of Rayleigh Damping Coefficients for Seismic Response Analysis of Soil Layers
Authors: Huai-Feng Wang, Meng-Lin Lou, Ru-Lin Zhang
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One good analysis method in seismic response analysis is direct time integration, which widely adopts Rayleigh damping. An approach is presented for selection of Rayleigh damping coefficients to be used in seismic analyses to produce a response that is consistent with Modal damping response. In the presented approach, the expression of the error of peak response, acquired through complete quadratic combination method, and Rayleigh damping coefficients was set up and then the coefficients were produced by minimizing the error. Two finite element modes of soil layers, excited by 28 seismic waves, were used to demonstrate the feasibility and validity.Keywords: Rayleigh damping, modal damping, damping coefficients, seismic response analysis.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2917179 Evaluation of Chromium Contamination in the Sediments of Jen-Gen River Mouth, Taiwan
Authors: Chiu-Wen Chen, Chih-Feng Chen, Cheng-Di Dong
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This study was conducted using the data collected at the mouth of Jen-Gen River to investigate and analyze chromium (Cr) contained in the sediments, and to evaluate the accumulation of Cr and the degree of its potential risk. The results show that samples collected at all monitoring stations near the mouth of Jen-Gen River contain 92–567 mg/kg of Cr with average of 366±166 mg/kg. The spatial distribution of Cr reveals that the Cr concentration is relatively high in the river mouth region, and gradually diminishes toward the harbor region. This indicates that upstream industrial and municipal wastewater discharges along the river bank are major sources of pollution. The accumulation factor and potential ecological risk index indicate that the sedimentation at Jen-Gen River mouth has the most serious degree of Cr accumulation and the highest ecological potential risk.
Keywords: chromium, sediment, river mouth, enrichment factor
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1300178 Ten Limit Cycles in a Quintic Lyapunov System
Authors: Li Feng
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In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated.With the help of computer algebra system MATHEMATICA, the first 10 quasi Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 10 small amplitude limit cycles created from the three order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems. At last, we give an system which could bifurcate 10 limit circles.
Keywords: Three-order nilpotent critical point, center-focus problem, bifurcation of limit cycles, Quasi-Lyapunov constant.
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