We present a short and simple proof of the recent result of Yang and Wang [12]. Stimulated by their idea, two geometric parameters Uax(ε) and βx (ε), both related to Gao's modulus of U-convexity of a Banach sp...We present a short and simple proof of the recent result of Yang and Wang [12]. Stimulated by their idea, two geometric parameters Uax(ε) and βx (ε), both related to Gao's modulus of U-convexity of a Banach space X, are introduced. Their properties and the relationships with normal structure are studied. Some existing results involving normal structure and fixed points for non-expansive mappings in Banach spaces are improved.展开更多
Aiming to increase the efficiency of gem design and manufacturing, a new method in computer-aided-design (CAD) of convex faceted gem cuts (CFGC) based on Half-edge data structure (HDS), including the algorithms for th...Aiming to increase the efficiency of gem design and manufacturing, a new method in computer-aided-design (CAD) of convex faceted gem cuts (CFGC) based on Half-edge data structure (HDS), including the algorithms for the implementation is presented in this work. By using object-oriented methods, geometrical elements of CFGC are classified and responding geometrical feature classes are established. Each class is implemented and embedded based on the gem process. Matrix arithmetic and analytical geometry are used to derive the affine transformation and the cutting algorithm. Based on the demand for a diversity of gem cuts, CAD functions both for free-style faceted cuts and parametric designs of typical cuts and visualization and human-computer interactions of the CAD system including two-dimensional and three-dimensional interactions have been realized which enhances the flexibility and universality of the CAD system. Furthermore, data in this CAD system can also be used directly by the gem CAM module, which will promote the gem CAD/CAM integration.展开更多
In this article, the authors study a generalized modulus of convexity, δ(α) (ε). Certain related geometrical properties of this modulus are analyzed. Their main result is that Banach space X has uniform normal ...In this article, the authors study a generalized modulus of convexity, δ(α) (ε). Certain related geometrical properties of this modulus are analyzed. Their main result is that Banach space X has uniform normal structure if there exists ε, 0 ≤e≤ 1, such that δ^(α)(1+ε ) 〉 (1- α)ε.展开更多
In lhis paper we draw some coincidence and common fixed point theorems fornonlinear hybrid contraction mappings on probabilistic metric spaces with a convexstructure.
Casing parts are regarded as key components of aero-engines.Most casing parts are attached to convex structures of diferent shapes,whose heights range from hundreds of microns to tens of millimeters.Using profling blo...Casing parts are regarded as key components of aero-engines.Most casing parts are attached to convex structures of diferent shapes,whose heights range from hundreds of microns to tens of millimeters.Using profling blocky electrodes for electrochemical machining(ECM)of casing parts is a commonly adopted method,especially when highly convex structures.However,with an increase in the convex structure height,the fow felds of the machining areas become more complex,and short circuits may occur at any time.In this study,a method to improve the fow feld characteristics within a machining area by adjusting the backwater pressure is proposed and validated through simulation and experiment analyses.The simulation results demonstrated that the back-pressure method can signifcantly improve the uniformity of the fow feld around the convex structure compared with the extraction and open outlet modes.Subsequently,the back-pressure value was optimized at 0.5 MPa according to the simulation results.The experimental results showed that using the optimized back-pressure parameters,the cathode feed-rate increased from 0.6 to 0.7 mm/min,and a 16.1 mm tall convex structure was successfully machined.This indicates that the back-pressure method is suitable and efective for electrochemical machining of highly convex structures with blocky electrodes.In this study,we propose a method to improve the electrochemical machining stability of a convex structure on a casing surface using backwater pressure,which has achieved remarkable results.展开更多
Let X be a Banach space, S(X) be the unit sphere of X, φ be a function: S(X)→ S(X *) such that φ(x)∈ x, and v φ(ε) =inf 1-12x+y: x,y∈S(X), and 〈φ(x), x-y 〉≥ε, 0≤ε≤2, whe...Let X be a Banach space, S(X) be the unit sphere of X, φ be a function: S(X)→ S(X *) such that φ(x)∈ x, and v φ(ε) =inf 1-12x+y: x,y∈S(X), and 〈φ(x), x-y 〉≥ε, 0≤ε≤2, where x is the set of norm 1 supporting functionals of S(X) at x. A geometric concept, modulus of V convexity V(ε)= sup {V φ(ε), for all φ: S(X)→S(X *)}, is introduced; the properties of V(ε) and the relationship between V(ε) and other geometric concepts are discussed. The main result is that V12>0 implies normal structure.展开更多
In small-sample problems, determining and controlling the errors of ordinary rigid convex set models are difficult. Therefore, a new uncertainty model called the fuzzy convex set(FCS) model is built and investigated...In small-sample problems, determining and controlling the errors of ordinary rigid convex set models are difficult. Therefore, a new uncertainty model called the fuzzy convex set(FCS) model is built and investigated in detail. An approach was developed to analyze the fuzzy properties of the structural eigenvalues with FCS constraints. Through this method, the approximate possibility distribution of the structural eigenvalue can be obtained. Furthermore, based on the symmetric F-programming theory, the conditional maximum and minimum values for the structural eigenvalue are presented, which can serve as nonfuzzy quantitative indicators for fuzzy problems. A practical application is provided to demonstrate the practicability and effectiveness of the proposed methods.展开更多
A computing method for estimating the upper and lower bounds of the response of structures with uncertainties is presented. The uncertain parameters are described by the convex model. A numerical example of the frame ...A computing method for estimating the upper and lower bounds of the response of structures with uncertainties is presented. The uncertain parameters are described by the convex model. A numerical example of the frame structure is given to illustrate the effectiveness of this method.展开更多
In this note, we investigate the generalized modulus of convexity δ(λ) and the generalized modulus smoothness p(λ). We obtain some estimates of these moduli for X=lp. We obtain inequalities between WCS coeffici...In this note, we investigate the generalized modulus of convexity δ(λ) and the generalized modulus smoothness p(λ). We obtain some estimates of these moduli for X=lp. We obtain inequalities between WCS coefficient of a KSthe sequence space X and δX(λ). We show that, for a wide class of class the sequence spaces X, if for some ε∈(0, 9/10] holds δx(e) 〉 1/3(1- √3/2)ε, then X has normal structure.展开更多
Since unmanned ground vehicles often encounter concave and convex obstacles in wild ground, a filtering algorithm using line structured light to detect these long distance obstacles is proposed. For the line structure...Since unmanned ground vehicles often encounter concave and convex obstacles in wild ground, a filtering algorithm using line structured light to detect these long distance obstacles is proposed. For the line structured light image, a ranked-order based adaptively extremum median (RAEM) filter algorithm on salt and pepper noise is presented. In the algorithm, firstly effective points and noise points in a filtering window are differentiated; then the gray values of noise points are replaced by the medium of gray values of the effective pixels, with the efficient points' gray values unchanged; in the end this algorithm is proved to be efficient by experiments. Experimental resuits demonstrate that the image blur, resulting into proposed algorithm can remove noise points effectively and minimize the protecting the edge information as much as possible.展开更多
Key frame extraction based on sparse coding can reduce the redundancy of continuous frames and concisely express the entire video.However,how to develop a key frame extraction algorithm that can automatically extract ...Key frame extraction based on sparse coding can reduce the redundancy of continuous frames and concisely express the entire video.However,how to develop a key frame extraction algorithm that can automatically extract a few frames with a low reconstruction error remains a challenge.In this paper,we propose a novel model of structured sparse-codingbased key frame extraction,wherein a nonconvex group log-regularizer is used with strong sparsity and a low reconstruction error.To automatically extract key frames,a decomposition scheme is designed to separate the sparse coefficient matrix by rows.The rows enforced by the nonconvex group log-regularizer become zero or nonzero,leading to the learning of the structured sparse coefficient matrix.To solve the nonconvex problems due to the log-regularizer,the difference of convex algorithm(DCA)is employed to decompose the log-regularizer into the difference of two convex functions related to the l1 norm,which can be directly obtained through the proximal operator.Therefore,an efficient structured sparse coding algorithm with the group log-regularizer for key frame extraction is developed,which can automatically extract a few frames directly from the video to represent the entire video with a low reconstruction error.Experimental results demonstrate that the proposed algorithm can extract more accurate key frames from most Sum Me videos compared to the stateof-the-art methods.Furthermore,the proposed algorithm can obtain a higher compression with a nearly 18% increase compared to sparse modeling representation selection(SMRS)and an 8% increase compared to SC-det on the VSUMM dataset.展开更多
A novel co-rotating electrochemical machining method is proposed for fabricating convex structures on the inner surface of a revolving part.The electrodes motion and material removal method of co-rotating electrochemi...A novel co-rotating electrochemical machining method is proposed for fabricating convex structures on the inner surface of a revolving part.The electrodes motion and material removal method of co-rotating electrochemical machining are different from traditional electrochemical machining.An equivalent kinematic model is established to analyze the novel electrodes motion,since the anode and cathode rotate in the same direction while the cathode simultaneously feeds along the line of centres.According to the kinematic equations of the electrodes and Faraday’s law,a material removal model is established to simulate the evolution of the anode profile in co-rotating electrochemical machining.The simulation results indicate that the machining accuracy of the convex structure is strongly affected by the angular velocity ratio and the radius of the cathode tool.An increase of the angular velocity ratio can improve the machining accuracy of a convex structure.A small difference in the radius of the cathode tool will cause changes in the shape of the sidewalls of the convex structure.The width of the cathode window affects only the width of the convex structure and the inclination a of the sidewall.A relation between the width of the cathode window and the width of the convex structure was obtained.The formation process for a convex structure under electrochemical dissolution was revealed.Based on the simulation results,the optimal angular velocity ratio and cathode radius were selected for an experimental verification,and 12 convex structures were simultaneously fabricated on the inner surface of a thin-walled revolving part.The experimental results are in good agreement with the simulation results,which verifies the correctness of the theoretical analysis.Therefore,inner surface co-rotating electrochemical machining is an effective method for fabricating convex structures on the inner surface of a revolving part.展开更多
文摘We present a short and simple proof of the recent result of Yang and Wang [12]. Stimulated by their idea, two geometric parameters Uax(ε) and βx (ε), both related to Gao's modulus of U-convexity of a Banach space X, are introduced. Their properties and the relationships with normal structure are studied. Some existing results involving normal structure and fixed points for non-expansive mappings in Banach spaces are improved.
基金Supported by the National Natural Science Foundation of China(21576240)Experimental Technology Research Program of China University of Geosciences(Key Program)(SJ-201422)
文摘Aiming to increase the efficiency of gem design and manufacturing, a new method in computer-aided-design (CAD) of convex faceted gem cuts (CFGC) based on Half-edge data structure (HDS), including the algorithms for the implementation is presented in this work. By using object-oriented methods, geometrical elements of CFGC are classified and responding geometrical feature classes are established. Each class is implemented and embedded based on the gem process. Matrix arithmetic and analytical geometry are used to derive the affine transformation and the cutting algorithm. Based on the demand for a diversity of gem cuts, CAD functions both for free-style faceted cuts and parametric designs of typical cuts and visualization and human-computer interactions of the CAD system including two-dimensional and three-dimensional interactions have been realized which enhances the flexibility and universality of the CAD system. Furthermore, data in this CAD system can also be used directly by the gem CAM module, which will promote the gem CAD/CAM integration.
基金Supported by Education Foundation of Henan Province(2003110006)
文摘In this article, the authors study a generalized modulus of convexity, δ(α) (ε). Certain related geometrical properties of this modulus are analyzed. Their main result is that Banach space X has uniform normal structure if there exists ε, 0 ≤e≤ 1, such that δ^(α)(1+ε ) 〉 (1- α)ε.
文摘In lhis paper we draw some coincidence and common fixed point theorems fornonlinear hybrid contraction mappings on probabilistic metric spaces with a convexstructure.
基金Supported by National Natural Science Foundation of China(Grant No.51775484)China Postdoctoral Science Foundation(Grant No.2020M670791).
文摘Casing parts are regarded as key components of aero-engines.Most casing parts are attached to convex structures of diferent shapes,whose heights range from hundreds of microns to tens of millimeters.Using profling blocky electrodes for electrochemical machining(ECM)of casing parts is a commonly adopted method,especially when highly convex structures.However,with an increase in the convex structure height,the fow felds of the machining areas become more complex,and short circuits may occur at any time.In this study,a method to improve the fow feld characteristics within a machining area by adjusting the backwater pressure is proposed and validated through simulation and experiment analyses.The simulation results demonstrated that the back-pressure method can signifcantly improve the uniformity of the fow feld around the convex structure compared with the extraction and open outlet modes.Subsequently,the back-pressure value was optimized at 0.5 MPa according to the simulation results.The experimental results showed that using the optimized back-pressure parameters,the cathode feed-rate increased from 0.6 to 0.7 mm/min,and a 16.1 mm tall convex structure was successfully machined.This indicates that the back-pressure method is suitable and efective for electrochemical machining of highly convex structures with blocky electrodes.In this study,we propose a method to improve the electrochemical machining stability of a convex structure on a casing surface using backwater pressure,which has achieved remarkable results.
文摘Let X be a Banach space, S(X) be the unit sphere of X, φ be a function: S(X)→ S(X *) such that φ(x)∈ x, and v φ(ε) =inf 1-12x+y: x,y∈S(X), and 〈φ(x), x-y 〉≥ε, 0≤ε≤2, where x is the set of norm 1 supporting functionals of S(X) at x. A geometric concept, modulus of V convexity V(ε)= sup {V φ(ε), for all φ: S(X)→S(X *)}, is introduced; the properties of V(ε) and the relationship between V(ε) and other geometric concepts are discussed. The main result is that V12>0 implies normal structure.
基金supported by the National Natural Science Foundation of China (Grant 51509254)
文摘In small-sample problems, determining and controlling the errors of ordinary rigid convex set models are difficult. Therefore, a new uncertainty model called the fuzzy convex set(FCS) model is built and investigated in detail. An approach was developed to analyze the fuzzy properties of the structural eigenvalues with FCS constraints. Through this method, the approximate possibility distribution of the structural eigenvalue can be obtained. Furthermore, based on the symmetric F-programming theory, the conditional maximum and minimum values for the structural eigenvalue are presented, which can serve as nonfuzzy quantitative indicators for fuzzy problems. A practical application is provided to demonstrate the practicability and effectiveness of the proposed methods.
基金Project supported by the National Natural Science Foundation of China(No.10132010)the Foundation of Committee on Science Technology of Shanghai(No.00QA14013)
文摘A computing method for estimating the upper and lower bounds of the response of structures with uncertainties is presented. The uncertain parameters are described by the convex model. A numerical example of the frame structure is given to illustrate the effectiveness of this method.
基金supported by National Fund for Scientific Research of the Bulgarian Ministry of Education and Science, Contract MM-1401/04
文摘In this note, we investigate the generalized modulus of convexity δ(λ) and the generalized modulus smoothness p(λ). We obtain some estimates of these moduli for X=lp. We obtain inequalities between WCS coefficient of a KSthe sequence space X and δX(λ). We show that, for a wide class of class the sequence spaces X, if for some ε∈(0, 9/10] holds δx(e) 〉 1/3(1- √3/2)ε, then X has normal structure.
基金Supported by the National Natural Science Foundation of China(61273346)the National Defense Key Fundamental Research Program of China(A20130010)the Program for the Fundamental Research of Beijing Institute of Technology(2016CX02010)
文摘Since unmanned ground vehicles often encounter concave and convex obstacles in wild ground, a filtering algorithm using line structured light to detect these long distance obstacles is proposed. For the line structured light image, a ranked-order based adaptively extremum median (RAEM) filter algorithm on salt and pepper noise is presented. In the algorithm, firstly effective points and noise points in a filtering window are differentiated; then the gray values of noise points are replaced by the medium of gray values of the effective pixels, with the efficient points' gray values unchanged; in the end this algorithm is proved to be efficient by experiments. Experimental resuits demonstrate that the image blur, resulting into proposed algorithm can remove noise points effectively and minimize the protecting the edge information as much as possible.
基金supported in part by the National Natural Science Foundation of China(61903090,61727810,62073086,62076077,61803096,U191140003)the Guangzhou Science and Technology Program Project(202002030289)Japan Society for the Promotion of Science(JSPS)KAKENHI(18K18083)。
文摘Key frame extraction based on sparse coding can reduce the redundancy of continuous frames and concisely express the entire video.However,how to develop a key frame extraction algorithm that can automatically extract a few frames with a low reconstruction error remains a challenge.In this paper,we propose a novel model of structured sparse-codingbased key frame extraction,wherein a nonconvex group log-regularizer is used with strong sparsity and a low reconstruction error.To automatically extract key frames,a decomposition scheme is designed to separate the sparse coefficient matrix by rows.The rows enforced by the nonconvex group log-regularizer become zero or nonzero,leading to the learning of the structured sparse coefficient matrix.To solve the nonconvex problems due to the log-regularizer,the difference of convex algorithm(DCA)is employed to decompose the log-regularizer into the difference of two convex functions related to the l1 norm,which can be directly obtained through the proximal operator.Therefore,an efficient structured sparse coding algorithm with the group log-regularizer for key frame extraction is developed,which can automatically extract a few frames directly from the video to represent the entire video with a low reconstruction error.Experimental results demonstrate that the proposed algorithm can extract more accurate key frames from most Sum Me videos compared to the stateof-the-art methods.Furthermore,the proposed algorithm can obtain a higher compression with a nearly 18% increase compared to sparse modeling representation selection(SMRS)and an 8% increase compared to SC-det on the VSUMM dataset.
基金supported by the National Natural Science Foundation of China(No.52175414)National Natural Science Foundation of China for Creative Research Groups(No.51921003)the China Postdoctoral Science Foundation(No.2019M661833).
文摘A novel co-rotating electrochemical machining method is proposed for fabricating convex structures on the inner surface of a revolving part.The electrodes motion and material removal method of co-rotating electrochemical machining are different from traditional electrochemical machining.An equivalent kinematic model is established to analyze the novel electrodes motion,since the anode and cathode rotate in the same direction while the cathode simultaneously feeds along the line of centres.According to the kinematic equations of the electrodes and Faraday’s law,a material removal model is established to simulate the evolution of the anode profile in co-rotating electrochemical machining.The simulation results indicate that the machining accuracy of the convex structure is strongly affected by the angular velocity ratio and the radius of the cathode tool.An increase of the angular velocity ratio can improve the machining accuracy of a convex structure.A small difference in the radius of the cathode tool will cause changes in the shape of the sidewalls of the convex structure.The width of the cathode window affects only the width of the convex structure and the inclination a of the sidewall.A relation between the width of the cathode window and the width of the convex structure was obtained.The formation process for a convex structure under electrochemical dissolution was revealed.Based on the simulation results,the optimal angular velocity ratio and cathode radius were selected for an experimental verification,and 12 convex structures were simultaneously fabricated on the inner surface of a thin-walled revolving part.The experimental results are in good agreement with the simulation results,which verifies the correctness of the theoretical analysis.Therefore,inner surface co-rotating electrochemical machining is an effective method for fabricating convex structures on the inner surface of a revolving part.