Let f be a tree map,P(f) the set of periodic points of f and CR(f) the set of chain recurrent points of f. In this paper,the notion of division for invariant closed subsets of a tree map is introduced.It is proved th...Let f be a tree map,P(f) the set of periodic points of f and CR(f) the set of chain recurrent points of f. In this paper,the notion of division for invariant closed subsets of a tree map is introduced.It is proved that: (1) f has zero topological entropy if and only if for any x∈CR(f)-P(f) and each natural number s the orbit of x under f s has a division; (2) If f has zero topological entropy,then for any x∈CR(f)-P(f) the ω-limit set of x is an infinite minimal set.展开更多
Let and f:Xn→Xn be a continuous map. If f is a second descendible map, then P(f) is closed if and only if one of the following hold: 1);2) For any z ε R (f), there exists a yεw (z,f) ∩ P(f) such that every point o...Let and f:Xn→Xn be a continuous map. If f is a second descendible map, then P(f) is closed if and only if one of the following hold: 1);2) For any z ε R (f), there exists a yεw (z,f) ∩ P(f) such that every point of the set orb (y,f) is a isolated point of the set w (z,f);3) For any z ε R(f), the set w (z,f) is finite;4) For any z ε R(f), the set w' (z,f) is finite. The consult give another condition of f with closed periodic set other than [1].展开更多
Repeated respiratory tract infection is a frequently-occurring disease during childhood. At present, western medicine doctors generally adopt anti-infectives and immunomodulators to treat the disease, while traditiona...Repeated respiratory tract infection is a frequently-occurring disease during childhood. At present, western medicine doctors generally adopt anti-infectives and immunomodulators to treat the disease, while traditional Chinese medicine doctors mainly administer decoction of Chinese herbs. The authors treated 46 cases of repeated respiratory tract infection from March 1990 to April 1996 by applying mild-moxibustion over points on the back with satisfactory therapeutic results. A report follows.Clinical Data All the 86 cases were outpatients in our hospital with duration of common cold for over 10 days and characterized by relapse of respiratory tract infection. There were over 7-time relapse of respiratory tract infection on each case within a year. Eighty-six cases were randomly divided into treatment group (46 cases) and control group (40 cases). Of the 46 cases in the treatment group, 22 were boys and 24 girls. 17 cases (36.9%) were 6 months to 4 years old, 18 (39.1%) 4 to 6 years, and 11 (23.9%) 6 to 12 years. Among the 40 cases in the control group, 19 cases were boys and 21 girls.展开更多
Objective： To explore the correlation between single acupoints used and the recurrence rate of cystitis among cystitis-prone women receiving acupuncture as a prophylactic treatment. Methods： In all, 58 cystitis-pron...Objective： To explore the correlation between single acupoints used and the recurrence rate of cystitis among cystitis-prone women receiving acupuncture as a prophylactic treatment. Methods： In all, 58 cystitis-prone women were included in the analysis. Customised acupuncture treatments were given twice a week, over 4 weeks. The main effect parameter was the number of cystitis episodes during the 6-month observation time. Residual urine was measured at baseline, 2, 4 and 6 months using portable ultrasound equipment. Sympathetic and vagotone nerve activities were measured by using skin conductance and respiratory sinus arrhythmia, respectively. Results： The main acupoints used for patients with Kidney （Shen） qi/yang deficiency were Shenshu （BL23）, Taixi （KI3）, Zhongji （CV3）, Sanyinjiao （SP6） and Pangguangshu （BL2.8）, compared with Taichong （LR3）, CV3, BL28, Yinlingquan （SP9） and SP6 for Liver （Gan） qi stagnation, and SP6, CV3, BL28, Zusanli （ST36） and SP9 for Spleen （Pi） qi/yang deficiency patients. The combination BL23 and KI3 were used in 16 women, 13 of which were Kidney pattern related patients. When used, the number of symptomatic episodes were reduced to a third compared with what occurred in the 42 women where this combination was not used （3/16 vs. 28/42, P〈0.05）. BL23 application correlated to a significant reduction in residual urine measured a few days after treatment. Patients with the pattern of Spleen qi/yang deficiency had an initial increase in residual urine after treatments. Conclusion： Treating Kidney pattern related patients with the combination of BL23 and KI3 resulted in far better outcome than other points/combination of points for other Chinese medicine diagnoses. The acupoint SP6 may be less indicated than previously assumed when treating cvstitis-Drone women DroDhvlacticalIv.展开更多
From 1996 to 1999, the author treated 103 cases of primary trigeminal neuralgia by point-injection with lidocaine, VB1 and VB12, and obtained quite good therapeutic results. A report follows.
A simple and effective method is proposed to derive the three-dimensional electric potential induced by a point singularity of any type in an N-phase dielectric medium composed of N-2 intermediate dielectric layers of...A simple and effective method is proposed to derive the three-dimensional electric potential induced by a point singularity of any type in an N-phase dielectric medium composed of N-2 intermediate dielectric layers of equal thickness encased in two semi-infinite dielectric media. The point singularity can include a point charge or a point electric dipole. The original boundary value problem for the N-phase medium is reduced to the determination of a single unknown three-dimensional harmonic function through satisfaction of the continuity conditions across all of the N-1 perfect planar interfaces. The single harmonic function can be completely determined after analytically solving the resulting linear recurrence relations, which are independent of the type and the specific location of the singularity. When the singularity is a point charge, we obtain the self-energy of the point charge expressed in terms of a single function and the Coulomb force on the point charge expressed in terms of the negative derivative of this function.展开更多
Let X denote a compact metric space with distance d and F ： X×R→ X or Ft ： X→X denote a C0-flow. From the point of view of ergodic theory, all important dynamical behaviors take place on a full measure set. T...Let X denote a compact metric space with distance d and F ： X×R→ X or Ft ： X→X denote a C0-flow. From the point of view of ergodic theory, all important dynamical behaviors take place on a full measure set. The aim of this paper is to introduce the notion of Banach upper density recurrent points and to show that the closure of the set of all Banach upper density recurrent points equals the measure center or the minimal center of attraction for a C0-flow. Moreover, we give an example to show that the set of quasi-weakly almost periodic points can be included properly in the set of Banach upper density recurrent points, and point out that the set of Banach upper density recurrent points can be included properly in the set of recurrent points.展开更多
The purpose of this paper is to show that for one-sided symbolic systems,there exists an uncountable distributionally scrambled set contained in the set of proper positive upper Banach density recurrent points.
基金the National Natural Science Foundation of China(1 996 1 0 0 1 ) and SF of Guangxi(0 1 3 5 0 2 7)
文摘Let f be a tree map,P(f) the set of periodic points of f and CR(f) the set of chain recurrent points of f. In this paper,the notion of division for invariant closed subsets of a tree map is introduced.It is proved that: (1) f has zero topological entropy if and only if for any x∈CR(f)-P(f) and each natural number s the orbit of x under f s has a division; (2) If f has zero topological entropy,then for any x∈CR(f)-P(f) the ω-limit set of x is an infinite minimal set.
文摘Let and f:Xn→Xn be a continuous map. If f is a second descendible map, then P(f) is closed if and only if one of the following hold: 1);2) For any z ε R (f), there exists a yεw (z,f) ∩ P(f) such that every point of the set orb (y,f) is a isolated point of the set w (z,f);3) For any z ε R(f), the set w (z,f) is finite;4) For any z ε R(f), the set w' (z,f) is finite. The consult give another condition of f with closed periodic set other than [1].
文摘Repeated respiratory tract infection is a frequently-occurring disease during childhood. At present, western medicine doctors generally adopt anti-infectives and immunomodulators to treat the disease, while traditional Chinese medicine doctors mainly administer decoction of Chinese herbs. The authors treated 46 cases of repeated respiratory tract infection from March 1990 to April 1996 by applying mild-moxibustion over points on the back with satisfactory therapeutic results. A report follows.Clinical Data All the 86 cases were outpatients in our hospital with duration of common cold for over 10 days and characterized by relapse of respiratory tract infection. There were over 7-time relapse of respiratory tract infection on each case within a year. Eighty-six cases were randomly divided into treatment group (46 cases) and control group (40 cases). Of the 46 cases in the treatment group, 22 were boys and 24 girls. 17 cases (36.9%) were 6 months to 4 years old, 18 (39.1%) 4 to 6 years, and 11 (23.9%) 6 to 12 years. Among the 40 cases in the control group, 19 cases were boys and 21 girls.
基金the Norwegian Research Council and the Eckbos Legacy for funding the study
文摘Objective： To explore the correlation between single acupoints used and the recurrence rate of cystitis among cystitis-prone women receiving acupuncture as a prophylactic treatment. Methods： In all, 58 cystitis-prone women were included in the analysis. Customised acupuncture treatments were given twice a week, over 4 weeks. The main effect parameter was the number of cystitis episodes during the 6-month observation time. Residual urine was measured at baseline, 2, 4 and 6 months using portable ultrasound equipment. Sympathetic and vagotone nerve activities were measured by using skin conductance and respiratory sinus arrhythmia, respectively. Results： The main acupoints used for patients with Kidney （Shen） qi/yang deficiency were Shenshu （BL23）, Taixi （KI3）, Zhongji （CV3）, Sanyinjiao （SP6） and Pangguangshu （BL2.8）, compared with Taichong （LR3）, CV3, BL28, Yinlingquan （SP9） and SP6 for Liver （Gan） qi stagnation, and SP6, CV3, BL28, Zusanli （ST36） and SP9 for Spleen （Pi） qi/yang deficiency patients. The combination BL23 and KI3 were used in 16 women, 13 of which were Kidney pattern related patients. When used, the number of symptomatic episodes were reduced to a third compared with what occurred in the 42 women where this combination was not used （3/16 vs. 28/42, P〈0.05）. BL23 application correlated to a significant reduction in residual urine measured a few days after treatment. Patients with the pattern of Spleen qi/yang deficiency had an initial increase in residual urine after treatments. Conclusion： Treating Kidney pattern related patients with the combination of BL23 and KI3 resulted in far better outcome than other points/combination of points for other Chinese medicine diagnoses. The acupoint SP6 may be less indicated than previously assumed when treating cvstitis-Drone women DroDhvlacticalIv.
文摘From 1996 to 1999, the author treated 103 cases of primary trigeminal neuralgia by point-injection with lidocaine, VB1 and VB12, and obtained quite good therapeutic results. A report follows.
基金Project supported by the National Natural Science Foundation of China(No.11272121)the Natural Sciences and Engineering Research Council of Canada(No.RGPIN-2017-c3716115112)
文摘A simple and effective method is proposed to derive the three-dimensional electric potential induced by a point singularity of any type in an N-phase dielectric medium composed of N-2 intermediate dielectric layers of equal thickness encased in two semi-infinite dielectric media. The point singularity can include a point charge or a point electric dipole. The original boundary value problem for the N-phase medium is reduced to the determination of a single unknown three-dimensional harmonic function through satisfaction of the continuity conditions across all of the N-1 perfect planar interfaces. The single harmonic function can be completely determined after analytically solving the resulting linear recurrence relations, which are independent of the type and the specific location of the singularity. When the singularity is a point charge, we obtain the self-energy of the point charge expressed in terms of a single function and the Coulomb force on the point charge expressed in terms of the negative derivative of this function.
基金Supported by National Natural Science Foundations of China(Grant Nos.11261039,11661054)National Natural Science Foundation of Jiangxi(Grant No.20132BAB201009)
文摘Let X denote a compact metric space with distance d and F ： X×R→ X or Ft ： X→X denote a C0-flow. From the point of view of ergodic theory, all important dynamical behaviors take place on a full measure set. The aim of this paper is to introduce the notion of Banach upper density recurrent points and to show that the closure of the set of all Banach upper density recurrent points equals the measure center or the minimal center of attraction for a C0-flow. Moreover, we give an example to show that the set of quasi-weakly almost periodic points can be included properly in the set of Banach upper density recurrent points, and point out that the set of Banach upper density recurrent points can be included properly in the set of recurrent points.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11661054 and 11261039)
文摘The purpose of this paper is to show that for one-sided symbolic systems,there exists an uncountable distributionally scrambled set contained in the set of proper positive upper Banach density recurrent points.
