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A Note on P-Sasakian Manifold
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作者 杨明升 张明 《Chinese Quarterly Journal of Mathematics》 CSCD 1997年第2期95-98, ,共4页
In this paper,we give a necessary and sufficient condition for a P-Sasakian manifold to be a SP-Sasakian manifold and prove a P-Sasakian manifold of constant curvature - 1 is a SP-Sasakian manifold.
关键词 p-sasakian manifold Sp-sasakian manifold
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Numerical manifold method for thermo-mechanical coupling simulation of fractured rock mass 被引量:1
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作者 Jiawei Liang Defu Tong +3 位作者 Fei Tan Xiongwei Yi Junpeng Zou Jiahe Lv 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2024年第6期1977-1992,共16页
As a calculation method based on the Galerkin variation,the numerical manifold method(NMM)adopts a double covering system,which can easily deal with discontinuous deformation problems and has a high calculation accura... As a calculation method based on the Galerkin variation,the numerical manifold method(NMM)adopts a double covering system,which can easily deal with discontinuous deformation problems and has a high calculation accuracy.Aiming at the thermo-mechanical(TM)coupling problem of fractured rock masses,this study uses the NMM to simulate the processes of crack initiation and propagation in a rock mass under the influence of temperature field,deduces related system equations,and proposes a penalty function method to deal with boundary conditions.Numerical examples are employed to confirm the effectiveness and high accuracy of this method.By the thermal stress analysis of a thick-walled cylinder(TWC),the simulation of cracking in the TWC under heating and cooling conditions,and the simulation of thermal cracking of the SwedishÄspöPillar Stability Experiment(APSE)rock column,the thermal stress,and TM coupling are obtained.The numerical simulation results are in good agreement with the test data and other numerical results,thus verifying the effectiveness of the NMM in dealing with thermal stress and crack propagation problems of fractured rock masses. 展开更多
关键词 Heat conduction Fractured rock mass Crack propagation Galerkin variation Numerical manifold method(NMM)
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Delineating homogeneous domains of fractured rocks using topological manifolds and deep learning
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作者 Yongqiang Liu Jianping Chen +3 位作者 Fujun Zhou Jiewei Zhan Wanglai Xu Jianhua Yan 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2024年第8期2996-3013,共18页
Determining homogeneous domains statistically is helpful for engineering geological modeling and rock mass stability evaluation.In this text,a technique that can integrate lithology,geotechnical and structural informa... Determining homogeneous domains statistically is helpful for engineering geological modeling and rock mass stability evaluation.In this text,a technique that can integrate lithology,geotechnical and structural information is proposed to delineate homogeneous domains.This technique is then applied to a high and steep slope along a road.First,geological and geotechnical domains were described based on lithology,faults,and shear zones.Next,topological manifolds were used to eliminate the incompatibility between orientations and other parameters(i.e.trace length and roughness)so that the data concerning various properties of each discontinuity can be matched and characterized in the same Euclidean space.Thus,the influence of implicit combined effect in between parameter sequences on the homogeneous domains could be considered.Deep learning technique was employed to quantify abstract features of the characterization images of discontinuity properties,and to assess the similarity of rock mass structures.The results show that the technique can effectively distinguish structural variations and outperform conventional methods.It can handle multisource engineering geological information and multiple discontinuity parameters.This technique can also minimize the interference of human factors and delineate homogeneous domains based on orientations or multi-parameter with arbitrary distributions to satisfy different engineering requirements. 展开更多
关键词 Homogeneous domain Geological domain Geotechnical domain Structural domain Topological manifold Deep learning
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A STABILITY RESULT FOR TRANSLATINGSPACELIKE GRAPHS IN LORENTZ MANIFOLDS
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作者 高雅 毛井 吴传喜 《Acta Mathematica Scientia》 SCIE CSCD 2024年第2期474-483,共10页
In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piece... In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piecewise smooth boundary,and ℝ denotes the Euclidean 1-space.We prove an interesting stability result for translating spacelike graphs in M^(n)×ℝ under a conformal transformation. 展开更多
关键词 mean curvature flow spacelike graphs translating spacelike graphs maximal spacelike graphs constant mean curvature Lorentz manifolds
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Isometric Immersions of Lightlike Warped Product Manifolds
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作者 Domitien Ndayirukiye Cyriaque Atindogbe Gilbert Nibaruta 《Journal of Applied Mathematics and Physics》 2024年第7期2490-2505,共16页
In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3. Under the assumptions that the globally null warped ... In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3. Under the assumptions that the globally null warped product manifold has no points with the same constant sectional curvature c as the Lorentzian ambient, we show that such isometric immersion splits into warped product of isometric immersions. 展开更多
关键词 Lightlike Warped Product manifolds Globally Null Warped Products manifolds Lightlike Warped Product Isometric Immersions
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Galerkin-based quasi-smooth manifold element(QSME)method for anisotropic heat conduction problems in composites with complex geometry
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作者 Pan WANG Xiangcheng HAN +2 位作者 Weibin WEN Baolin WANG Jun LIANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2024年第1期137-154,共18页
The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element ... The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method(FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element(QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional(2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity.The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom(DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations. 展开更多
关键词 anisotropic heat conduction quasi-smooth manifold element(QSME) composite with complex geometry numerical simulation finite element method(FEM)
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Certain Curvature Conditions on P-Sasakian Manifolds Admitting a Quater-Symmetric Metric Connection 被引量:1
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作者 Uday Chand DE Peibiao ZHAO +1 位作者 Krishanu MANDAL Yanling HAN 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2020年第1期133-146,共14页
The authors consider a quarter-symmetric metric connection in a P-Sasakian manifold and study the second order parallel tensor in a P-Sasakian manifold with respect to the quarter-symmetric metric connection. Then Ric... The authors consider a quarter-symmetric metric connection in a P-Sasakian manifold and study the second order parallel tensor in a P-Sasakian manifold with respect to the quarter-symmetric metric connection. Then Ricci semisymmetric P-Sasakian manifold with respect to the quarter-symmetric metric connection is considered. Next the authors study ξ-concircularly flat P-Sasakian manifolds and concircularly semisymmetric P-Sasakian manifolds with respect to the quarter-symmetric metric connection. Furthermore, the authors study P-Sasakian manifolds satisfying the condition Z(ξ,Y)·S=0,where Z,S are the concircular curvature tensor and Ricci tensor respectively with respect to the quarter-symmetric metric connection. Finally, an example of a 5-dimensional P-Sasakian manifold admitting quarter-symmetric metric connection is constructed. 展开更多
关键词 Quarter-symmetric METRIC CONNECTION p-sasakian manifold RICCI semisymmetric manifold ξ-Concircularly flat Concircularly semisymmetric
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Secret Sharing Scheme Based on the Differential Manifold
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作者 Bin Li 《Applied Mathematics》 2023年第3期173-181,共9页
In this paper, the concepts of topological space and differential manifold are introduced, and it is proved that the surface determined by function F (x<sub>2</sub>, x<sub>2</sub>, …, x<sub... In this paper, the concepts of topological space and differential manifold are introduced, and it is proved that the surface determined by function F (x<sub>2</sub>, x<sub>2</sub>, …, x<sub>t</sub>) of class C<sup>r</sup> in Euelidean R<sup>t</sup> is a differential manifold. Using the intersection of the tangent plane and the hypernormal of the differential manifold to construct the shared master key of participants, an intuitive, secure and complete (t,n)-threshold secret sharing scheme is designed. The paper is proved to be safe, and the probability of successful attack of attackers is only 1/p<sup>t</sup><sup>-1</sup>. When the prime number p is sufficiently large, the probability is almost 0. The results show that this scheme has the characteristics of single-parameter representation of the master key in the geometric method, and is more practical and easy to implement than the Blakley threshold secret sharing scheme. 展开更多
关键词 Topological Space Differential manifold Secret Sharing Tangent Plane Hypernormal
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SOME CONVERGENCE PROBLEMS REGARDING THE FRACTIONAL SCHRODINGER PROPAGATOR ON NONCOMPACT MANIFOLDS
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作者 潘亚丽 《Acta Mathematica Scientia》 SCIE CSCD 2023年第5期2309-2319,共11页
Let L be the Laplace-Beltrami operator.On an n-dimensional(n≥2),complete,noncompact Riemannian manifold M,we prove that if 0<α<1,s>α/2 and f∈Hs(M),then the fractional Schr?dinger propagator e(it|L|α/2)(f... Let L be the Laplace-Beltrami operator.On an n-dimensional(n≥2),complete,noncompact Riemannian manifold M,we prove that if 0<α<1,s>α/2 and f∈Hs(M),then the fractional Schr?dinger propagator e(it|L|α/2)(f)(x)→f(x)a.e.as t→0.In addition,for when M is a Lie group,the rate of the convergence is also studied.These results are a non-trivial extension of results on Euclidean spaces and compact manifolds. 展开更多
关键词 Schrodinger propagator noncompact manifolds SPECTRA
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Invariant manifold growth formula in cylindrical coordinates and its application for magnetically confined fusion
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作者 魏文崟 梁云峰 《Plasma Science and Technology》 SCIE EI CAS CSCD 2023年第9期51-67,共17页
For three-dimensional vector fields,the governing formula of invariant manifolds grown from a hyperbolic cycle is given in cylindrical coordinates.The initial growth directions depend on the Jacobians of Poincaré... For three-dimensional vector fields,the governing formula of invariant manifolds grown from a hyperbolic cycle is given in cylindrical coordinates.The initial growth directions depend on the Jacobians of Poincarémap on that cycle,for which an evolution formula is deduced to reveal the relationship among Jacobians of different Poincarésections.The evolution formula also applies to cycles in arbitrary finite n-dimensional autonomous continuous-time dynamical systems.Non-Möbiusian/Möbiusian saddle cycles and a dummy X-cycle are constructed analytically as demonstration.A real-world numeric example of analyzing a magnetic field timeslice on EAST is presented. 展开更多
关键词 magnetic topology TOKAMAK invariant manifold
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Fluid-Structure Coupled Analysis of the Transient Thermal Stress in an Exhaust Manifold
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作者 Liang Yi Wen Gang +2 位作者 Nenggui Pan Wangui Wang Shengshuai Mo 《Fluid Dynamics & Materials Processing》 EI 2023年第11期2777-2790,共14页
The development of thermal stress in the exhaust manifold of a gasoline engine is considered.The problem is addresses in the frame of a combined approach wherefluid and structure are coupled using the GT-POWER and STA... The development of thermal stress in the exhaust manifold of a gasoline engine is considered.The problem is addresses in the frame of a combined approach wherefluid and structure are coupled using the GT-POWER and STAR-CCM+software.First,the external characteristic curve of the engine is compared with a one-dimen-sional simulation model,then the parameters of the model are modified until the curve matches the available experimental values.GT-POWER is then used to transfer the inlet boundary data under transient conditions to STAR-CCM+in real-time.The temperature profiles of the inner and outer walls of the exhaust manifold are obtained in this way,together with the thermal stress and thermal deformation of the exhaust manifold itself.Using this information,the original model is improved through the addition of connections.Moreover,the local branch pipes are optimized,leading to significant improvements in terms of thermal stress and thermal deforma-tion of the exhaust manifold(a 7%reduction in the maximum thermal stress). 展开更多
关键词 Exhaust manifold fluid-structure coupling temperaturefield thermal stress
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A Discussion on the Establishment That a Fibre Metric on the Positive Definite Real Inner-Product of a Properly Embedded Smooth Submanifold Be Always Extended to a Riemannian Metric on the Positive Definite Real Inner-Product
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作者 Zhiwei Yan 《Advances in Pure Mathematics》 2023年第5期207-210,共4页
Let M be a smooth manifold and S ⊆ M a properly embedded smooth submanifold. Suppose that we have a fibre metric on TM|<sub>s</sub> i.e. a positive definite real inner-product on T<sub>p</sub>M... Let M be a smooth manifold and S ⊆ M a properly embedded smooth submanifold. Suppose that we have a fibre metric on TM|<sub>s</sub> i.e. a positive definite real inner-product on T<sub>p</sub>M for all p ∈ S, which depends smoothly on p ∈ S. The purpose of this article is to figure out that the fibre metric on TM|s</sub> can always be extended to a Riemannian metric on TM from a special perspective. 展开更多
关键词 Embedded Smooth manifold Superplane Riemannian Metric
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Experimental Investigation of Regular or Wavy Two-Phase Flow in a Manifold
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作者 Xiaowei Nie Lihui Ma +7 位作者 Yiqiu Xu Dong Sun Weibo Zheng Liang Zhou Xiaodong Wang Xiaohan Zhang Weijia Dong Yunfei Li 《Fluid Dynamics & Materials Processing》 EI 2023年第1期37-50,共14页
An experimental study was conducted to investigate the properties of stratified regular or wavy two-phase flow in two parallel separators located after a manifold.A total of 103 experiments with various gas and liquid... An experimental study was conducted to investigate the properties of stratified regular or wavy two-phase flow in two parallel separators located after a manifold.A total of 103 experiments with various gas and liquid velocity combinations in three inlet pipes were conducted,including 77 groups of outlet pipe resistance symmetry and 26 groups of outlet pipe resistance asymmetry trials.The experimental results have revealed that when the gas-liquid flow rate is low,the degree of uneven splitting is high,and“extreme”conditions are attained.When the superficial gas velocity is greater than that established in the extreme case,the direction of the liquid-phase displacement is reversed,while that of the gas remains unchanged.Thus,the degree of gas phase bias tends to be mitigated with an increase in the gas velocity,while the uneven splitting degree of liquid approaches 10%.Finally,varying the gas-phase outlet pipe resistance is shown to effectively change the gas-liquid two-phase flow distribution. 展开更多
关键词 Uneven phase distribution two-phase flow manifold asymmetric resistance
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Representation of Physical Fields as Einstein Manifold
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作者 Vu B. Ho 《Journal of Applied Mathematics and Physics》 2023年第3期599-607,共9页
In this work we investigate the possibility to represent physical fields as Einstein manifold. Based on the Einstein field equations in general relativity, we establish a general formulation for determining the metric... In this work we investigate the possibility to represent physical fields as Einstein manifold. Based on the Einstein field equations in general relativity, we establish a general formulation for determining the metric tensor of the Einstein manifold that represents a physical field in terms of the energy-momentum tensor that characterises the physical field. As illustrations, we first apply the general formulation to represent the perfect fluid as Einstein manifold. However, from the established relation between the metric tensor and the energy-momentum tensor, we show that if the trace of the energy-momentum tensor associated with a physical field is equal to zero then the corresponding physical field cannot be represented as an Einstein manifold. This situation applies to the electromagnetic field since the trace of the energy-momentum of the electromagnetic field vanishes. Nevertheless, we show that a system that consists of the electromagnetic field and non-interacting charged particles can be represented as an Einstein manifold since the trace of the corresponding energy-momentum of the system no longer vanishes. As a further investigation, we show that it is also possible to represent physical fields as maximally symmetric spaces of constant scalar curvature. 展开更多
关键词 General Relativity Einstein manifold Energy-Momentum Tensor Electromagnetic Field Perfect Fluid Maximally Symmetric Spaces
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Dynamic Analogical Association Algorithm Based on Manifold Matching for Few-Shot Learning
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作者 Yuncong Peng Xiaolin Qin +2 位作者 Qianlei Wang Boyi Fu Yongxiang Gu 《Computer Systems Science & Engineering》 SCIE EI 2023年第7期1233-1247,共15页
At present,deep learning has been well applied in many fields.However,due to the high complexity of hypothesis space,numerous training samples are usually required to ensure the reliability of minimizing experience ri... At present,deep learning has been well applied in many fields.However,due to the high complexity of hypothesis space,numerous training samples are usually required to ensure the reliability of minimizing experience risk.Therefore,training a classifier with a small number of training examples is a challenging task.From a biological point of view,based on the assumption that rich prior knowledge and analogical association should enable human beings to quickly distinguish novel things from a few or even one example,we proposed a dynamic analogical association algorithm to make the model use only a few labeled samples for classification.To be specific,the algorithm search for knowledge structures similar to existing tasks in prior knowledge based on manifold matching,and combine sampling distributions to generate offsets instead of two sample points,thereby ensuring high confidence and significant contribution to the classification.The comparative results on two common benchmark datasets substantiate the superiority of the proposed method compared to existing data generation approaches for few-shot learning,and the effectiveness of the algorithm has been proved through ablation experiments. 展开更多
关键词 Few-shot learning manifold matching analogical association data generation
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Brain Functional Networks with Dynamic Hypergraph Manifold Regularization for Classification of End-Stage Renal Disease Associated with Mild Cognitive Impairment
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作者 Zhengtao Xi Chaofan Song +2 位作者 Jiahui Zheng Haifeng Shi Zhuqing Jiao 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第6期2243-2266,共24页
The structure and function of brain networks have been altered in patients with end-stage renal disease(ESRD).Manifold regularization(MR)only considers the pairing relationship between two brain regions and cannot rep... The structure and function of brain networks have been altered in patients with end-stage renal disease(ESRD).Manifold regularization(MR)only considers the pairing relationship between two brain regions and cannot represent functional interactions or higher-order relationships between multiple brain regions.To solve this issue,we developed a method to construct a dynamic brain functional network(DBFN)based on dynamic hypergraph MR(DHMR)and applied it to the classification of ESRD associated with mild cognitive impairment(ESRDaMCI).The construction of DBFN with Pearson’s correlation(PC)was transformed into an optimization model.Node convolution and hyperedge convolution superposition were adopted to dynamically modify the hypergraph structure,and then got the dynamic hypergraph to form the manifold regular terms of the dynamic hypergraph.The DHMR and L_(1) norm regularization were introduced into the PC-based optimization model to obtain the final DHMR-based DBFN(DDBFN).Experiment results demonstrated the validity of the DDBFN method by comparing the classification results with several related brain functional network construction methods.Our work not only improves better classification performance but also reveals the discriminative regions of ESRDaMCI,providing a reference for clinical research and auxiliary diagnosis of concomitant cognitive impairments. 展开更多
关键词 End-stage renal disease mild cognitive impairment brain functional network dynamic hypergraph manifold regularization CLASSIFICATION
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Stability analysis of the projectile based on random center manifold reduction
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作者 Yong Huang Chunyan Yang 《Theoretical & Applied Mechanics Letters》 CAS CSCD 2023年第1期3-7,共5页
The center manifold method has been widely used in the field of stochastic dynamics as a dimensionality reduction method.This paper studied the angular motion stability of a projectile system under random disturbances... The center manifold method has been widely used in the field of stochastic dynamics as a dimensionality reduction method.This paper studied the angular motion stability of a projectile system under random disturbances.The random bifurcation of the projectile is studied using the idea of the Routh-Hurwitz stability criterion,the center manifold reduction,and the polar coordinates transformation.Then,an approximate analytical presentation for the stationary probability density function is found from the related Fokker–Planck equation.From the results,the random dynamical system of projectile generates three different dynamical behaviors with the changes of the bifurcation parameter and the noise strength,which can be a reference for projectile design. 展开更多
关键词 Center manifold reduction FPK equation Routh-Hurwitz stability criterion Projectile stability The polar coordinates transformation
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Two-Dimensional Manifolds with Computation V-Function of ODE Systems
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作者 Suqi Ma Bohan Ma Xinping Wang 《International Journal of Modern Nonlinear Theory and Application》 2023年第4期99-106,共8页
The computation of stable or unstable manifold of two-dimensional is developed, which is an efficient method in studying stable structure analysis of system character geometrically. The Lorentz stable manifold is comp... The computation of stable or unstable manifold of two-dimensional is developed, which is an efficient method in studying stable structure analysis of system character geometrically. The Lorentz stable manifold is computed by the fixed arclength method and the hyperbolic equilibrium is a saddle. The two-dimensional stable structure of Lorentz manifold is significant in people’s usual view. We also introduce the V-function to compute the V-manifold correspondingly. The defined V-function is smooth in the unstable direction of the manifold. Especially, the routh to period-doubling attractor on manifold surface is discussed too. 展开更多
关键词 Stable manifold Unstable manifold V-Function Attraction Boundary
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Manifold Structure Analysis of Tactical Network Traffic Matrix Based on Maximum Variance Unfolding Algorithm
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作者 Hao Shi Guofeng Wang +2 位作者 Rouxi Wang Jinshan Yang Kaishuan Shang 《Journal of Electronic Research and Application》 2023年第6期42-49,共8页
As modern weapons and equipment undergo increasing levels of informatization,intelligence,and networking,the topology and traffic characteristics of battlefield data networks built with tactical data links are becomin... As modern weapons and equipment undergo increasing levels of informatization,intelligence,and networking,the topology and traffic characteristics of battlefield data networks built with tactical data links are becoming progressively complex.In this paper,we employ a traffic matrix to model the tactical data link network.We propose a method that utilizes the Maximum Variance Unfolding(MVU)algorithm to conduct nonlinear dimensionality reduction analysis on high-dimensional open network traffic matrix datasets.This approach introduces novel ideas and methods for future applications,including traffic prediction and anomaly analysis in real battlefield network environments. 展开更多
关键词 manifold learning Maximum Variance Unfolding(MVU)algorithm Nonlinear dimensionality reduction
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油轮Manifolds及附属设备常见问题24问
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作者 宋红专 《中国水运》 2023年第11期43-45,共3页
在油轮的生产运营中,从初始的商务揽货问卷,填写Manifolds(货油管管头)及附属设备的相关参数;到靠泊前与码头的交换其参数;靠泊后接管和试压及完成货油的装卸;及随后的拆管,都少不了Manifolds及附属设备这个环节。
关键词 manifold(管头) Reducer(变径接头) Spool Piece(连接短管) 附属设备
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