The analysis of cutting regularity is provided through using and comparing two typical cooling liquids. It is proved that cutting regularity is greatly affected by cooling liquid＇s washing ability. Discharge characte...The analysis of cutting regularity is provided through using and comparing two typical cooling liquids. It is proved that cutting regularity is greatly affected by cooling liquid＇s washing ability. Discharge characteristics and theoretic analysis between two electrodes are also discussed based on discharge waveform. By using composite cooling liquid which has strong washing ability, the efficiency in the first stable cutting phase has reached more than 200 mm^2/min, and the roughness of the surface has reached Ra〈0.8 μm after the fourth cutting with more than 50 mm^2/min average cutting efficiency. It is pointed out that cutting situation of the wire cut electrical discharge machine with high wire traveling speed （HSWEDM） is better than the wire cut electrical discharge machine with low wire traveling speed （LSWEDM） in the condition of improving the cooling liquid washing ability. The machining indices of HSWEDM will be increased remarkably by using the composite cooling liquid.展开更多
Category is put to work in the non-associative realm in the article.We focus on atypical example of non-associative category.Its objects are octonionic bimodules,morphisms are octonionic para-linear maps,and compositi...Category is put to work in the non-associative realm in the article.We focus on atypical example of non-associative category.Its objects are octonionic bimodules,morphisms are octonionic para-linear maps,and compositions are non-associative in general.The octonionic para-linear map is the main object of octonionic Hilbert theory because of the octonionic Riesz representation theorem.An octonionic para-linear map f is in general not octonionic linear since it subjects to the rule Re(f(px)-pf(x))=0.The composition should be modified as f◎g(x):=f(g(x))-7∑j=1ejRe(f(g(e_(i)x))-f(e_(i)g(x)))j=1 so that it preserves the octonionic para-linearity.In this non-associative category,we introduce the Hom and Tensor functors which constitute an adjoint pair.We establish the Yoneda lemma in terms of the new notion of weak functor.To define the exactness in a non-associative category,we introduce the notion of the enveloping category via a universal property.This allows us to establish the exactness of the Hom functor and Tensor functor.展开更多
This paper is concerned with the composite row sparsity regularized(c RSR)minimization problem,which captures a number of important applications arising in machine learning,statistics,signal and image processing,and s...This paper is concerned with the composite row sparsity regularized(c RSR)minimization problem,which captures a number of important applications arising in machine learning,statistics,signal and image processing,and so forth.Due to the non-convexity and discontinuity of the composite row sparsity regularization term,the c RSR problem is NP-hard in general.In this paper,we study the optimality conditions of the c RSR problem and derive its stationary equation which is crucial to design efficient algorithms.Based on this stationary equation,an easy-to-implement Newton method is designed to solve the c RSR problem(Nc RSR).The quadratic convergence rate and iteration complexity estimation of Nc RSR are rigorously proved under some mild conditions.Furthermore,Nc RSR is used for solving the regularized clustering and trend filtering problems.Extensive experimental results illustrate that our approach has superior performance compared with the stateof-the-art methods.In particular,Nc RSR not only possesses perfect clustering performance and estimation accuracy but also is faster than all the compared methods.展开更多
基金Provincial Key Laboratory of Precision and Micro-Manufacturing Technology of Jiangsu,China(No.Z0601-052-02).
文摘The analysis of cutting regularity is provided through using and comparing two typical cooling liquids. It is proved that cutting regularity is greatly affected by cooling liquid＇s washing ability. Discharge characteristics and theoretic analysis between two electrodes are also discussed based on discharge waveform. By using composite cooling liquid which has strong washing ability, the efficiency in the first stable cutting phase has reached more than 200 mm^2/min, and the roughness of the surface has reached Ra〈0.8 μm after the fourth cutting with more than 50 mm^2/min average cutting efficiency. It is pointed out that cutting situation of the wire cut electrical discharge machine with high wire traveling speed （HSWEDM） is better than the wire cut electrical discharge machine with low wire traveling speed （LSWEDM） in the condition of improving the cooling liquid washing ability. The machining indices of HSWEDM will be increased remarkably by using the composite cooling liquid.
文摘Category is put to work in the non-associative realm in the article.We focus on atypical example of non-associative category.Its objects are octonionic bimodules,morphisms are octonionic para-linear maps,and compositions are non-associative in general.The octonionic para-linear map is the main object of octonionic Hilbert theory because of the octonionic Riesz representation theorem.An octonionic para-linear map f is in general not octonionic linear since it subjects to the rule Re(f(px)-pf(x))=0.The composition should be modified as f◎g(x):=f(g(x))-7∑j=1ejRe(f(g(e_(i)x))-f(e_(i)g(x)))j=1 so that it preserves the octonionic para-linearity.In this non-associative category,we introduce the Hom and Tensor functors which constitute an adjoint pair.We establish the Yoneda lemma in terms of the new notion of weak functor.To define the exactness in a non-associative category,we introduce the notion of the enveloping category via a universal property.This allows us to establish the exactness of the Hom functor and Tensor functor.
基金supported by the Project funded by China Postdoctoral Science Foundation(Grant No.2022M723327)National Natural Science Foundation of China(Grant Nos.12371322 and 12071022)。
文摘This paper is concerned with the composite row sparsity regularized(c RSR)minimization problem,which captures a number of important applications arising in machine learning,statistics,signal and image processing,and so forth.Due to the non-convexity and discontinuity of the composite row sparsity regularization term,the c RSR problem is NP-hard in general.In this paper,we study the optimality conditions of the c RSR problem and derive its stationary equation which is crucial to design efficient algorithms.Based on this stationary equation,an easy-to-implement Newton method is designed to solve the c RSR problem(Nc RSR).The quadratic convergence rate and iteration complexity estimation of Nc RSR are rigorously proved under some mild conditions.Furthermore,Nc RSR is used for solving the regularized clustering and trend filtering problems.Extensive experimental results illustrate that our approach has superior performance compared with the stateof-the-art methods.In particular,Nc RSR not only possesses perfect clustering performance and estimation accuracy but also is faster than all the compared methods.
