If the matrix measure of connection weight of Hopfield-type continuous feedback neural network is less than the reciprocal of maximal product of resistance and gain constants, then the network system is globally and exponentially stable. The above reciprocal is a sharp upper bound of matrix measure of connection weight which guarantees that the above conclusion holds. The above result answers partially the open problem proposed by Vidyasagar recently, i. e whether neural network with "nearly" symmetric connection weight can exhibit limit cycles. The relation between the network time constant and the global exponential convergence rate is pointed out, and application to optimization computation of our results is also given.
{"title":"Global exponential stability of Hopfield-type neural network and its applications","authors":"Xuebin Liang, Wu Lide","doi":"10.1360/YA1995-38-6-757","DOIUrl":"https://doi.org/10.1360/YA1995-38-6-757","url":null,"abstract":"If the matrix measure of connection weight of Hopfield-type continuous feedback neural network is less than the reciprocal of maximal product of resistance and gain constants, then the network system is globally and exponentially stable. The above reciprocal is a sharp upper bound of matrix measure of connection weight which guarantees that the above conclusion holds. The above result answers partially the open problem proposed by Vidyasagar recently, i. e whether neural network with \"nearly\" symmetric connection weight can exhibit limit cycles. The relation between the network time constant and the global exponential convergence rate is pointed out, and application to optimization computation of our results is also given.","PeriodicalId":256661,"journal":{"name":"Science in China Series A-Mathematics, Physics, Astronomy & Technological Science","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116863775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For the shift a of the symbolic space ∑ N there exists a subset (called a chaotic set for σ) C of ∑N whose Hausdorff dimension is 1 everywhere (i.e. the Hausdorff dimension of the intersection of C and every non-empty open set of the symbolic space ∑ N is 1), satisfying the condition for any non-empty subset A of the set C, and for any continuous map F: A→∑N there exists a strictly increasing sequence {r n } of positive integers such that the sequence {σ (x)} converges to F(x) for any x∈A. On the other hand, it is shown that in ∑ N every chaotic set for σ has 1-dimensional Hausdorff measure 0.
{"title":"Hausdorff Dimension of a Chaotic Set of Shift of a Symbolic Space.","authors":"Xiong Jincheng","doi":"10.1360/YA1995-38-6-696","DOIUrl":"https://doi.org/10.1360/YA1995-38-6-696","url":null,"abstract":"For the shift a of the symbolic space ∑ N there exists a subset (called a chaotic set for σ) C of ∑N whose Hausdorff dimension is 1 everywhere (i.e. the Hausdorff dimension of the intersection of C and every non-empty open set of the symbolic space ∑ N is 1), satisfying the condition for any non-empty subset A of the set C, and for any continuous map F: A→∑N there exists a strictly increasing sequence {r n } of positive integers such that the sequence {σ (x)} converges to F(x) for any x∈A. On the other hand, it is shown that in ∑ N every chaotic set for σ has 1-dimensional Hausdorff measure 0.","PeriodicalId":256661,"journal":{"name":"Science in China Series A-Mathematics, Physics, Astronomy & Technological Science","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133501698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Suppose B is a sufficiently large positive constant, e is a sufficiently small positive constant, N is a sufficiently large natural number, and A = N 7/81+e. It is proved that all even numbers in ( N, N + A ) with O(Alog-BN) exceptions are Goldbach numbers.
假设B是一个足够大的正常数，e是一个足够小的正常数，N是一个足够大的自然数，a = N 7/81+e。证明了(N, N + A)中除0 (Alog-BN)个例外的所有偶数都是哥德巴赫数。
{"title":"Goldbach numbers in short intervals","authors":"Li Hongze","doi":"10.1360/YA1995-38-6-641","DOIUrl":"https://doi.org/10.1360/YA1995-38-6-641","url":null,"abstract":"Suppose B is a sufficiently large positive constant, e is a sufficiently small positive constant, N is a sufficiently large natural number, and A = N 7/81+e. It is proved that all even numbers in ( N, N + A ) with O(Alog-BN) exceptions are Goldbach numbers.","PeriodicalId":256661,"journal":{"name":"Science in China Series A-Mathematics, Physics, Astronomy & Technological Science","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122567189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The area stability of CNN system is instigated and the existence of its periodic solution is given.
研究了CNN系统的区域稳定性，并给出了其周期解的存在性。
{"title":"Mathematical theory of cellular neural networks (II)","authors":"Liao Xiao-xin","doi":"10.1360/YA1995-38-5-542","DOIUrl":"https://doi.org/10.1360/YA1995-38-5-542","url":null,"abstract":"The area stability of CNN system is instigated and the existence of its periodic solution is given.","PeriodicalId":256661,"journal":{"name":"Science in China Series A-Mathematics, Physics, Astronomy & Technological Science","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115451660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"自对偶杨-Mills场的正则约化——Ernst引力方程","authors":"葛墨林, 王磊","doi":"10.1360/ZA1995-25-5-478","DOIUrl":"https://doi.org/10.1360/ZA1995-25-5-478","url":null,"abstract":"","PeriodicalId":256661,"journal":{"name":"Science in China Series A-Mathematics, Physics, Astronomy & Technological Science","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121518916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
使用Dobrushin唯一性准则及第一Neumann特征值估计,给出了自旋空间为带边紧流形的随机Ising模型Gibbs态唯一的若干充分条件.此外,还研究了无穷维反射扩散过程的 L 2 指数收敛.
使用Dobrushin唯一性准则及第一Neumann特征值估计,给出了自旋空间为带边紧流形的随机Ising模型Gibbs态唯一的若干充分条件.此外,还研究了无穷维反射扩散过程的 L 2 指数收敛.
{"title":"Gibbs态的唯一性与无穷维反射扩散过程的 L 2 收敛","authors":"王凤雨","doi":"10.1360/ZA1995-25-4-359","DOIUrl":"https://doi.org/10.1360/ZA1995-25-4-359","url":null,"abstract":"使用Dobrushin唯一性准则及第一Neumann特征值估计,给出了自旋空间为带边紧流形的随机Ising模型Gibbs态唯一的若干充分条件.此外,还研究了无穷维反射扩散过程的 L 2 指数收敛.","PeriodicalId":256661,"journal":{"name":"Science in China Series A-Mathematics, Physics, Astronomy & Technological Science","volume":"111 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115485155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Improvements to the mathematical-physical model of discrete sound field of multi-propeller aircraft have been made by using aeroacoustic analogy method, which considers the effects of fuselage boundary as well as the interference process of the multiple propeller sound field. The calculated results illustrate the effects of fuselage on the propeller sound field, the 'beating noise' phenomenon and the principle of noise control of synchrophaser system. The model for boundaries with arbitrary shapes can also be used to calculate the effects of rigid boundaries in other harmonic sound fields. Results for sound scattering of a rigid sphere in a planar harmonic wave calculated by using this model are satisfactorily coincident with those by the analytical method.
{"title":"Some improvements to the model of discrete sound field nearby multi-propeller aircraft","authors":"Wang Tongqing, Li Xiaodong, Z. Sheng","doi":"10.1360/YA1995-38-3-376","DOIUrl":"https://doi.org/10.1360/YA1995-38-3-376","url":null,"abstract":"Improvements to the mathematical-physical model of discrete sound field of multi-propeller aircraft have been made by using aeroacoustic analogy method, which considers the effects of fuselage boundary as well as the interference process of the multiple propeller sound field. The calculated results illustrate the effects of fuselage on the propeller sound field, the 'beating noise' phenomenon and the principle of noise control of synchrophaser system. The model for boundaries with arbitrary shapes can also be used to calculate the effects of rigid boundaries in other harmonic sound fields. Results for sound scattering of a rigid sphere in a planar harmonic wave calculated by using this model are satisfactorily coincident with those by the analytical method.","PeriodicalId":256661,"journal":{"name":"Science in China Series A-Mathematics, Physics, Astronomy & Technological Science","volume":"93 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121743361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
从周期参数激励系统——Mathieu-Duffing方程的时间对称性出发,讨论了它的1/2亚谐分叉,利用Liapunov-Schmidt约化导出了 Z 2等变的代数分叉方程,并建立与此对应的分析方法: Z 2等变的奇点理论,得到了1/2亚谐分叉的全体分叉图,数值计算验证了这些结果.
从周期参数激励系统——Mathieu-Duffing方程的时间对称性出发,讨论了它的1/2亚谐分叉,利用Liapunov-Schmidt约化导出了 Z 2等变的代数分叉方程,并建立与此对应的分析方法: Z 2等变的奇点理论,得到了1/2亚谐分叉的全体分叉图,数值计算验证了这些结果.
{"title":"Z 2 等变奇点理论及参激系统的1/2亚谐分叉","authors":"何国威, 方同","doi":"10.1360/ZA1995-25-3-296","DOIUrl":"https://doi.org/10.1360/ZA1995-25-3-296","url":null,"abstract":"从周期参数激励系统——Mathieu-Duffing方程的时间对称性出发,讨论了它的1/2亚谐分叉,利用Liapunov-Schmidt约化导出了 Z 2等变的代数分叉方程,并建立与此对应的分析方法: Z 2等变的奇点理论,得到了1/2亚谐分叉的全体分叉图,数值计算验证了这些结果.","PeriodicalId":256661,"journal":{"name":"Science in China Series A-Mathematics, Physics, Astronomy & Technological Science","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121646583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
在HT-6B TOKAMAK装置上,利用低混杂波驱动电流实现了等离子体约束改善,粒子约束时间增加2～6倍,等离子体内能增加一倍,低混杂波驱动电流改善约束存在一密度窗口:n e =(0.3～1.5)×10 13 cm -3 ,约束改善时伴随着边界快扰动的抑制和边界电子温度梯度的增大,此约束改善的功率阈值较低,最后讨论了此约束改善的物理机制,分析表明此约束改善现象可能是低混杂波在等离子体内产生一定数量具有一定能量的高能电子所造成.
在HT-6B TOKAMAK装置上,利用低混杂波驱动电流实现了等离子体约束改善,粒子约束时间增加2～6倍,等离子体内能增加一倍,低混杂波驱动电流改善约束存在一密度窗口:n e =(0.3～1.5)×10 13 cm -3 ,约束改善时伴随着边界快扰动的抑制和边界电子温度梯度的增大,此约束改善的功率阈值较低,最后讨论了此约束改善的物理机制,分析表明此约束改善现象可能是低混杂波在等离子体内产生一定数量具有一定能量的高能电子所造成.
{"title":"HT-6B TOKAMAK装置利用低混杂波驱动电流实现约束改善","authors":"邓传宝, 谢纪康, 黄荣, 方瑜德, 秦品健, 郭德全","doi":"10.1360/ZA1995-25-2-192","DOIUrl":"https://doi.org/10.1360/ZA1995-25-2-192","url":null,"abstract":"在HT-6B TOKAMAK装置上,利用低混杂波驱动电流实现了等离子体约束改善,粒子约束时间增加2～6倍,等离子体内能增加一倍,低混杂波驱动电流改善约束存在一密度窗口:n e =(0.3～1.5)×10 13 cm -3 ,约束改善时伴随着边界快扰动的抑制和边界电子温度梯度的增大,此约束改善的功率阈值较低,最后讨论了此约束改善的物理机制,分析表明此约束改善现象可能是低混杂波在等离子体内产生一定数量具有一定能量的高能电子所造成.","PeriodicalId":256661,"journal":{"name":"Science in China Series A-Mathematics, Physics, Astronomy & Technological Science","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126818845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"量子化腔体-原子系统的Born-Oppenheimer近似与原子态隧穿的定域化控制","authors":"孙昌璞","doi":"10.1360/ZA1995-25-2-155","DOIUrl":"https://doi.org/10.1360/ZA1995-25-2-155","url":null,"abstract":"应用广义Born-Oppenheimer近似理论,研究了单模腔场中二能级原子状态隧道效应的定域化控制问题,定量地分析了相干态腔场中原子手征态隧道效应的非绝热影响,给出了实现定域化的条件,还讨论了温度变化对原子态隧道效应的影响.","PeriodicalId":256661,"journal":{"name":"Science in China Series A-Mathematics, Physics, Astronomy & Technological Science","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117342862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：