The Dirac equation γ<sub>μ</sub>(δ<sub>μ</sub>-eA<sub>μ</sub>)Ψ=mc<sup>2</sup>Ψ describes the bound states of the electron under the action of external potentials...The Dirac equation γ<sub>μ</sub>(δ<sub>μ</sub>-eA<sub>μ</sub>)Ψ=mc<sup>2</sup>Ψ describes the bound states of the electron under the action of external potentials, A<sub>μ</sub>. We assumed that the fundamental form of the Dirac equation γ<sub>μ</sub>(δ<sub>μ</sub>-S<sub>μ</sub>)Ψ=0 should describe the stable particles (the electron, the proton and the dark-matter-particle (dmp)) bound to themselves under the action of their own potentials S<sub>μ</sub>. The new equation reveals that self energy is consequence of self action, it also reveals that the spin angular momentum is consequence of the dynamic structure of the stable particles. The quantitative results are the determination of their relative masses as well as the determination of the electromagnetic coupling constant.展开更多
以专利引证网络为载体,从知识基因稳定性、遗传性以及变异性等基本特征出发,提出一种基于subject-action-object三元组的知识基因提取方法.应用连接度算法分析专利引证关系,挖掘引证专利和被引专利之间继承和发展的知识流,建立知识进化...以专利引证网络为载体,从知识基因稳定性、遗传性以及变异性等基本特征出发,提出一种基于subject-action-object三元组的知识基因提取方法.应用连接度算法分析专利引证关系,挖掘引证专利和被引专利之间继承和发展的知识流,建立知识进化轨迹;利用文本语法分析技术,从专利权利要求书中提取subject-action-object三元组;基于语义词库WordNet进行语义加工,计算语义相似度,合并同义的subject-action-object三元组,绘制知识基因图谱.从美国专利数据库中采集了5 073项1975—1999年授权的数据挖掘领域的相关专利,分析了专利的地区分布情况和年度分布情况.从NBER(National Bureau of Economic Research)的专利数据集中查询得到专利引证关系,利用网络分析软件Pajek构建专利引证网络,作为实验数据样本,对所提出的知识基因提取方法进行验证.实验结果表明:所提取的subject-action-object三元组具备了知识基因稳定性、遗传性和变异性等特征,可以作为知识基因的一种表现形式.展开更多
The snap-action behavior of a Ni-Ti alloy disc which is controlled by combination of a nonlinear stress field and temperature has been studied.After treatment for two-way shape memory,all shape memory strain of snap-a...The snap-action behavior of a Ni-Ti alloy disc which is controlled by combination of a nonlinear stress field and temperature has been studied.After treatment for two-way shape memory,all shape memory strain of snap-action finishes abruptly at a certain temperature within an interval of less than 1 ms.The results of resistance measurement and in-situ X-ray diffraction indicate that the snap-action strain is mainly resulted from the snap-action β (?)R transformation.展开更多
To alleviate the information overload in the product design process,this work proposes a multiaction-based method for constructing knowledge map. Since the relationships of knowledge are implicit in the collected user...To alleviate the information overload in the product design process,this work proposes a multiaction-based method for constructing knowledge map. Since the relationships of knowledge are implicit in the collected user activities,the method calculates the similarity according to the collected user activities.Three concepts,including knowledge,action and user,are explained first. Based on this,the similarity calculation method is illustrated in detail. The dependencies of actions and relations of the user are considered in the calculation method. Further,the approach of applying the constructed knowledge map to alleviate information overload is proposed. At last,the proposed method is validated by a knowledge search and result comparison experiment.展开更多
Segal’s chronometric theory is based on a space-time D, which might be viewed as a Lie group with a causal structure defined by an invariant Lorentzian form on the Lie algebra u(2). Similarly, the space-time F is rea...Segal’s chronometric theory is based on a space-time D, which might be viewed as a Lie group with a causal structure defined by an invariant Lorentzian form on the Lie algebra u(2). Similarly, the space-time F is realized as the Lie group with a causal structure defined by an invariant Lorentzian form on u(1,1). Two Lie groups G, GF are introduced as representations of SU(2,2): they are related via conjugation by a certain matrix Win Gl(4). The linear-fractional action of G on D is well-known to be global, conformal, and it plays a crucial role in the analysis on space-time bundles carried out by Paneitz and Segal in the 1980’s. This analysis was based on the parallelizing group U(2). In the paper, singularities’ general (“geometric”) description of the linear-fractional conformal GF-action on F is given and specific examples are presented. The results call for the analysis of space-time bundles based on U(1,1) as the parallelizing group. Certain key stages of such an analysis are suggested.展开更多
A diffeomorphism is non-uniformly partially hyperbolic if it preserves an ergodic measure with at least one zero Lyapunov exponent.We prove that a C^(1)-smooth Z^(d)-action has the quasishadowing property if one of th...A diffeomorphism is non-uniformly partially hyperbolic if it preserves an ergodic measure with at least one zero Lyapunov exponent.We prove that a C^(1)-smooth Z^(d)-action has the quasishadowing property if one of the generators is C^(1+α)(α>0)non-uniformly partially hyperbolic.展开更多
In this paper,forward expansiveness and entropies of"subsystems"2)of Z^(k)_(+)-actions are investigated.Letαbe a Z^(k)_(+)-action on a compact metric space.For each 1≤j≤k-1,denote G^(j)_(+)={V+:=V∩R^(k)_...In this paper,forward expansiveness and entropies of"subsystems"2)of Z^(k)_(+)-actions are investigated.Letαbe a Z^(k)_(+)-action on a compact metric space.For each 1≤j≤k-1,denote G^(j)_(+)={V+:=V∩R^(k)_(+):V is a j-dimensional subspace of R^(k)}.We consider the forward expansiveness and entropies forαalong V+∈G^(j)_(+).Adapting the technique of"coding",which was introduced by M.Boyle and D.Lind to investigate expansive subdynamics of Z^(k)-actions,to the Z^(k)_(+)cases,we show that the set E^(j)_(+)(α)of forward expansive j-dimensional V_(+)is open in G^(j)_(+).The topological entropy and measure-theoretic entropy of j-dimensional subsystems ofαare both continuous in E^(j)_(+)(α),and moreover,a variational principle relating them is obtained.For a 1-dimensional ray L∈G^(+)_(1),we relate the 1-dimensional subsystem ofαalong L to an i.i.d.random transformation.Applying the techniques of random dynamical systems we investigate the entropy theory of 1-dimensional subsystems.In particular,we propose the notion of preimage entropy(including topological and measure-theoretical versions)via the preimage structure ofαalong L.We show that the preimage entropy coincides with the classical entropy along any L∈E1+(α)for topological and measure-theoretical versions respectively.Meanwhile,a formula relating the measure-theoretical directional preimage entropy and the folding entropy of the generators is obtained.展开更多
文摘The Dirac equation γ<sub>μ</sub>(δ<sub>μ</sub>-eA<sub>μ</sub>)Ψ=mc<sup>2</sup>Ψ describes the bound states of the electron under the action of external potentials, A<sub>μ</sub>. We assumed that the fundamental form of the Dirac equation γ<sub>μ</sub>(δ<sub>μ</sub>-S<sub>μ</sub>)Ψ=0 should describe the stable particles (the electron, the proton and the dark-matter-particle (dmp)) bound to themselves under the action of their own potentials S<sub>μ</sub>. The new equation reveals that self energy is consequence of self action, it also reveals that the spin angular momentum is consequence of the dynamic structure of the stable particles. The quantitative results are the determination of their relative masses as well as the determination of the electromagnetic coupling constant.
文摘以专利引证网络为载体,从知识基因稳定性、遗传性以及变异性等基本特征出发,提出一种基于subject-action-object三元组的知识基因提取方法.应用连接度算法分析专利引证关系,挖掘引证专利和被引专利之间继承和发展的知识流,建立知识进化轨迹;利用文本语法分析技术,从专利权利要求书中提取subject-action-object三元组;基于语义词库WordNet进行语义加工,计算语义相似度,合并同义的subject-action-object三元组,绘制知识基因图谱.从美国专利数据库中采集了5 073项1975—1999年授权的数据挖掘领域的相关专利,分析了专利的地区分布情况和年度分布情况.从NBER(National Bureau of Economic Research)的专利数据集中查询得到专利引证关系,利用网络分析软件Pajek构建专利引证网络,作为实验数据样本,对所提出的知识基因提取方法进行验证.实验结果表明:所提取的subject-action-object三元组具备了知识基因稳定性、遗传性和变异性等特征,可以作为知识基因的一种表现形式.
文摘The snap-action behavior of a Ni-Ti alloy disc which is controlled by combination of a nonlinear stress field and temperature has been studied.After treatment for two-way shape memory,all shape memory strain of snap-action finishes abruptly at a certain temperature within an interval of less than 1 ms.The results of resistance measurement and in-situ X-ray diffraction indicate that the snap-action strain is mainly resulted from the snap-action β (?)R transformation.
基金Supported by the National Natural Science Foundation of China(51375049)National Defense Basic Scientific Research(A222011A222013)
文摘To alleviate the information overload in the product design process,this work proposes a multiaction-based method for constructing knowledge map. Since the relationships of knowledge are implicit in the collected user activities,the method calculates the similarity according to the collected user activities.Three concepts,including knowledge,action and user,are explained first. Based on this,the similarity calculation method is illustrated in detail. The dependencies of actions and relations of the user are considered in the calculation method. Further,the approach of applying the constructed knowledge map to alleviate information overload is proposed. At last,the proposed method is validated by a knowledge search and result comparison experiment.
文摘Segal’s chronometric theory is based on a space-time D, which might be viewed as a Lie group with a causal structure defined by an invariant Lorentzian form on the Lie algebra u(2). Similarly, the space-time F is realized as the Lie group with a causal structure defined by an invariant Lorentzian form on u(1,1). Two Lie groups G, GF are introduced as representations of SU(2,2): they are related via conjugation by a certain matrix Win Gl(4). The linear-fractional action of G on D is well-known to be global, conformal, and it plays a crucial role in the analysis on space-time bundles carried out by Paneitz and Segal in the 1980’s. This analysis was based on the parallelizing group U(2). In the paper, singularities’ general (“geometric”) description of the linear-fractional conformal GF-action on F is given and specific examples are presented. The results call for the analysis of space-time bundles based on U(1,1) as the parallelizing group. Certain key stages of such an analysis are suggested.
基金supported by the Science and Technology Research Program of Chongqing Municipal Education Commission(Grant No.KJQN202300802)the second author is supported by NSFC(Grant Nos.11801261,12071285)+1 种基金the third author is supported by NSFC(Grant Nos.11871120,12071082)Natural Science Foundation of Chongqing(Grant No.cstc2021jcyj-msxmX0299)。
文摘A diffeomorphism is non-uniformly partially hyperbolic if it preserves an ergodic measure with at least one zero Lyapunov exponent.We prove that a C^(1)-smooth Z^(d)-action has the quasishadowing property if one of the generators is C^(1+α)(α>0)non-uniformly partially hyperbolic.
基金Wang and Zhu are supported by NSFC (Grant Nos.11771118,11801336,12171400)Wang is also supported by China Postdoctoral Science Foundation (No.2021M691889)。
文摘In this paper,forward expansiveness and entropies of"subsystems"2)of Z^(k)_(+)-actions are investigated.Letαbe a Z^(k)_(+)-action on a compact metric space.For each 1≤j≤k-1,denote G^(j)_(+)={V+:=V∩R^(k)_(+):V is a j-dimensional subspace of R^(k)}.We consider the forward expansiveness and entropies forαalong V+∈G^(j)_(+).Adapting the technique of"coding",which was introduced by M.Boyle and D.Lind to investigate expansive subdynamics of Z^(k)-actions,to the Z^(k)_(+)cases,we show that the set E^(j)_(+)(α)of forward expansive j-dimensional V_(+)is open in G^(j)_(+).The topological entropy and measure-theoretic entropy of j-dimensional subsystems ofαare both continuous in E^(j)_(+)(α),and moreover,a variational principle relating them is obtained.For a 1-dimensional ray L∈G^(+)_(1),we relate the 1-dimensional subsystem ofαalong L to an i.i.d.random transformation.Applying the techniques of random dynamical systems we investigate the entropy theory of 1-dimensional subsystems.In particular,we propose the notion of preimage entropy(including topological and measure-theoretical versions)via the preimage structure ofαalong L.We show that the preimage entropy coincides with the classical entropy along any L∈E1+(α)for topological and measure-theoretical versions respectively.Meanwhile,a formula relating the measure-theoretical directional preimage entropy and the folding entropy of the generators is obtained.
