Search results for: Shiping Zhou
124 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 1580123 Zhou Enlai’s Impact to the Foreign Folicy of China
Authors: Nazira B. Boldurukova
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The main aim of this article is to give the information about life and social and diplomatic work of Zhou Enlai, to prove his identity in his impact to the history of the world; to show his place in the organization of internal and foreign policy and in the peaceful international relationships of China with other countries.
Keywords: China, foreign policy of China, identity, politician, diplomacy, Zhou Enlai.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2961122 Structure of Covering-based Rough Sets
Authors: Shiping Wang, Peiyong Zhu, William Zhu
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Rough set theory is a very effective tool to deal with granularity and vagueness in information systems. Covering-based rough set theory is an extension of classical rough set theory. In this paper, firstly we present the characteristics of the reducible element and the minimal description covering-based rough sets through downsets. Then we establish lattices and topological spaces in coveringbased rough sets through down-sets and up-sets. In this way, one can investigate covering-based rough sets from algebraic and topological points of view.
Keywords: Covering, poset, down-set, lattice, topological space, topological base.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1848121 Monitoring and Analysis of Bridge Crossing Ground Fissures
Authors: Zhiqing Zhang, Xiangong Zhou, Zihan Zhou
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Ground fissures can be seen in some cities all over the world. As a special urban geological disaster, ground fissures in Xi'an have caused great harm to infrastructure. Chang'an Road Interchange in Xi'an City is a bridge across ground fissures. The damage to Chang'an Road interchange is the most serious and typical. To study the influence of ground fissures on the bridge, we established a bridge monitoring system. The main monitoring items include elevation monitoring, structural displacement monitoring, etc. The monitoring results show that the typical failure is mainly reflected in the bridge deck damage caused by horizontal tension and vertical dislocation. For the construction of urban interchange spanning ground fissures, the interchange should be divided reasonably, a simple support structure with less restriction should be adopted, and the monitoring of supports should be strengthened to prevent the occurrence of beam falling.
Keywords: Bridge monitoring, ground fissures, typical disease, structural displacement.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 648120 Phase-Averaged Analysis of Three-Dimensional Vorticity in the Wake of Two Yawed Side-By-Side Circular Cylinders
Authors: T. Zhou, S. F. Mohd. Razali, Y. Zhou, H. Wang, L. Cheng
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Thewake flow behind two yawed side-by-sidecircular cylinders is investigated using athree-dimensional vorticity probe. Four yaw angles (α), namely, 0°, 15°, 30° and 45° and twocylinder spacing ratios T* of 1.7 and 3.0 were tested. For T* = 3.0, there exist two vortex streets and the cylinders behave as independent and isolated ones. The maximum contour value of the coherent streamwise vorticity ~* ωx is only about 10% of that of the spanwise vorticity ~* ωz . With the increase of α, ~* ωx increases whereas ~* ωz decreases. At α = 45°, ~* ωx is about 67% of ~* ωz .For T* = 1.7, only a single peak is detected in the energy spectrum. The spanwise vorticity contours have an organized pattern only at α = 0°. The maximum coherent vorticity contours of ~* ω x and ~* ωz for T* = 1.7 are about 30% and 7% of those for T* = 3.0.The independence principle (IP)in terms of Strouhal numbers is applicable in both wakes when α< 40°.
Keywords: Circular cylinder wake, vorticity, vortex shedding.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1795119 A Sufficient Condition for Graphs to Have Hamiltonian [a, b]-Factors
Authors: Sizhong Zhou
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Let a and b be nonnegative integers with 2 ≤ a < b, and let G be a Hamiltonian graph of order n with n ≥ (a+b−4)(a+b−2) b−2 . An [a, b]-factor F of G is called a Hamiltonian [a, b]-factor if F contains a Hamiltonian cycle. In this paper, it is proved that G has a Hamiltonian [a, b]-factor if |NG(X)| > (a−1)n+|X|−1 a+b−3 for every nonempty independent subset X of V (G) and δ(G) > (a−1)n+a+b−4 a+b−3 .
Keywords: graph, minimum degree, neighborhood, [a, b]-factor, Hamiltonian [a, b]-factor.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1234118 Hamiltonian Factors in Hamiltonian Graphs
Authors: Sizhong Zhou, Bingyuan Pu
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Let G be a Hamiltonian graph. A factor F of G is called a Hamiltonian factor if F contains a Hamiltonian cycle. In this paper, two sufficient conditions are given, which are two neighborhood conditions for a Hamiltonian graph G to have a Hamiltonian factor.Keywords: graph, neighborhood, factor, Hamiltonian factor.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1172117 [a, b]-Factors Excluding Some Specified Edges In Graphs
Authors: Sizhong Zhou, Bingyuan Pu
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Let G be a graph of order n, and let a, b and m be positive integers with 1 ≤ a<b. An [a, b]-factor of G is defined as a spanning subgraph F of G such that a ≤ dF (x) ≤ b for each x ∈ V (G). In this paper, it is proved that if n ≥ (a+b−1+√(a+b+1)m−2)2−1 b and δ(G) > n + a + b − 2 √bn+ 1, then for any subgraph H of G with m edges, G has an [a, b]-factor F such that E(H)∩ E(F) = ∅. This result is an extension of thatof Egawa [2].
Keywords: graph, minimum degree, [a, b]-factor.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1100116 Transformerless AC-DC Converter
Authors: Saisundar. S., I Made Darmayuda, Zhou Jun, Krishna Mainali, Simon Ng Sheung Yan, Eran Ofek
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This paper compares the recent transformerless ACDC power converter architectures and provides an assessment of each. A prototype of one of the transformerless AC-DC converter architecture is also presented depicting the feasibility of a small form factor, power supply design. In this paper component selection guidelines to achieve high efficiency AC-DC power conversion are also discussed.Keywords: AC-DC converter, digitally controlled, switched mode power supply, transformerless.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 5783115 A Convenient Part Library Based On SolidWorks Platform
Authors: Wei Liu, Xionghui Zhou, Qiang Niu, Yunhao Ni
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3D part library is an ideal approach to reuse the existing design and thus facilitates the modeling process, which will enhance the efficiency. In this paper, we implemented the thought on the SolidWorks platform. The system supports the functions of type and parameter selection, 3D template driving and part assembly. Finally, BOM is exported in Excel format. Experiment shows that our method can satisfy the requirement of die and mold designers.
Keywords: Intelligent, SolidWorks, automatic assembly, part library.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2147114 Study on Rural Landscape Design Method under the Background of the Population Diversification
Authors: Z. Zhou, Q. Chen, S. Wu
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Population diversification phenomena becomes quite common in villages located in China’s developed coastal area. Based on the analysis of the traditional rural society and its landscape characteristics, and in consideration of diversified landscape requirements due to the population diversification, with dual ideas of heritage and innovation, methods for rural landscape design were explored by taking Duxuao Village in Zhejiang Province of China as an example.
Keywords: Rural landscape, Population diversification, Landscape design.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2254113 A Comprehensive Analysis for Widespread use of Electric Vehicles
Authors: Yu Zhou, Zhaoyang Dong, Xiaomei Zhao
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This paper mainly investigates the environmental and economic impacts of worldwide use of electric vehicles. It can be concluded that governments have good reason to promote the use of electric vehicles. First, the global vehicles population is evaluated with the help of grey forecasting model and the amount of oil saving is estimated through approximate calculation. After that, based on the game theory, the amount and types of electricity generation needed by electronic vehicles are established. Finally, some conclusions on the government-s attitudes are drawn.Keywords: electronic vehicles, grey prediction, game theory
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1655112 Low Power Digital System for Reconfigurable Neural Recording System
Authors: Peng Li, Jun Zhou, Xin Liu, Chee Keong Ho, Xiaodan Zou, Minkyu Je
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A digital system is proposed for low power 100- channel neural recording system in this paper, which consists of 100 amplifiers, 100 analog-to-digital converters (ADC), digital controller and baseband, transceiver for data link and RF command link. The proposed system is designed in a 0.18 μm CMOS process and 65 nm CMOS process.Keywords: multiplex, neural recording, synchronization, transceiver
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1652111 Notes on Fractional k-Covered Graphs
Authors: Sizhong Zhou, Yang Xu
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A graph G is fractional k-covered if for each edge e of G, there exists a fractional k-factor h, such that h(e) = 1. If k = 2, then a fractional k-covered graph is called a fractional 2-covered graph. The binding number bind(G) is defined as follows, bind(G) = min{|NG(X)| |X| : ├ÿ = X Ôèå V (G),NG(X) = V (G)}. In this paper, it is proved that G is fractional 2-covered if δ(G) ≥ 4 and bind(G) > 5 3 .Keywords: graph, binding number, fractional k-factor, fractional k-covered graph.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1185110 On Fractional (k,m)-Deleted Graphs with Constrains Conditions
Authors: Sizhong Zhou, Hongxia Liu
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Let G be a graph of order n, and let k 2 and m 0 be two integers. Let h : E(G) [0, 1] be a function. If e∋x h(e) = k holds for each x V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh = {e E(G) : h(e) > 0}. A graph G is called a fractional (k,m)-deleted graph if there exists a fractional k-factor G[Fh] of G with indicator function h such that h(e) = 0 for any e E(H), where H is any subgraph of G with m edges. In this paper, it is proved that G is a fractional (k,m)-deleted graph if (G) k + m + m k+1 , n 4k2 + 2k − 6 + (4k 2 +6k−2)m−2 k−1 and max{dG(x), dG(y)} n 2 for any vertices x and y of G with dG(x, y) = 2. Furthermore, it is shown that the result in this paper is best possible in some sense.
Keywords: Graph, degree condition, fractional k-factor, fractional (k, m)-deleted graph.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1200109 Single Spectrum End Point Predict of BOF with SVM
Authors: Ling-fei Xu, Qi Zhao, Yan-ru Chen, Mu-chun Zhou, Meng Zhang, Shi-xue Xu
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SVM ( Support Vector Machine ) is a new method in the artificial neural network ( ANN ). In the steel making, how to use computer to predict the end point of BOF accuracy is a great problem. A lot of method and theory have been claimed, but most of the results is not satisfied. Now the hot topic in the BOF end point predicting is to use optical way the predict the end point in the BOF. And we found that there exist some regular in the characteristic curve of the flame from the mouse of pudding. And we can use SVM to predict end point of the BOF, just single spectrum intensity should be required as the input parameter. Moreover, its compatibility for the input space is better than the BP network.
Keywords: SVM, predict, BOF, single spectrum intensity.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1359108 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 1065107 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 1825106 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 2195105 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 1483104 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 1340103 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 1566102 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 1894101 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 1517100 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 208599 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 124598 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 158497 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 36596 Influence of Heat Transfer on Stability of Newtonian and Non-Newtonian Extending Films
Authors: Olus N. Boratav, Zheming Zheng, Chunfeng Zhou
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The stability of Newtonian and Non-Newtonian extending films under local or global heating or cooling conditions are considered. The thickness-averaged mass, momentum and energy equations with convective and radiative heat transfer are derived, both for Newtonian and non-Newtonian fluids (Maxwell, PTT and Giesekus models considered). The stability of the system is explored using either eigenvalue analysis or transient simulations. The results showed that the influence of heating and cooling on stability strongly depends on the magnitude of the Peclet number. Examples of stabilization or destabilization of heating or cooling are shown for Pe<< 1, and Pe = O(1) cases, for Newtonian and non-Newtonian flows.
Keywords: Extended films, stability, eigen-analysis for stability, transient response, polymer instability, Non-Newtonian fluids.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 165795 Application of Functional Network to Solving Classification Problems
Authors: Yong-Quan Zhou, Deng-Xu He, Zheng Nong
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In this paper two models using a functional network were employed to solving classification problem. Functional networks are generalized neural networks, which permit the specification of their initial topology using knowledge about the problem at hand. In this case, and after analyzing the available data and their relations, we systematically discuss a numerical analysis method used for functional network, and apply two functional network models to solving XOR problem. The XOR problem that cannot be solved with two-layered neural network can be solved by two-layered functional network, which reveals a potent computational power of functional networks, and the performance of the proposed model was validated using classification problems.Keywords: Functional network, neural network, XOR problem, classification, numerical analysis method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1309