In this paper, we consider the eigenvalue problem of a class of fourth-order operator matrices appearing in mechan- ics, including the geometric multiplicity, algebraic index, and algebraic multiplicity of the eigenva...In this paper, we consider the eigenvalue problem of a class of fourth-order operator matrices appearing in mechan- ics, including the geometric multiplicity, algebraic index, and algebraic multiplicity of the eigenvalue, the symplectic orthogonality, and completeness of eigen and root vector systems. The obtained results are applied to the plate bending problem.展开更多
This paper deals with a class of upper triangular infinite-dimensional Hamilto- nian operators appearing in the elasticity theory. The geometric multiplicity and algebraic index of the eigenvalue are investigated. Fur...This paper deals with a class of upper triangular infinite-dimensional Hamilto- nian operators appearing in the elasticity theory. The geometric multiplicity and algebraic index of the eigenvalue are investigated. Furthermore, the algebraic multiplicity of the eigenvalue is obtained. Based on these properties, the concrete completeness formulation of the system of eigenvectors or root vectors of the Hamiltonian operator is proposed. It is shown that the completeness is determined by the system of eigenvectors of the operator entries. Finally, the applications of the results to some problems in the elasticity theory are presented.展开更多
Objective: To estimate the presence and the quantity of endotoxin of periodontally involved root surfaces after root surface debridement.Methods: Ninety single rooted teeth with severe bone resorption were selected,wh...Objective: To estimate the presence and the quantity of endotoxin of periodontally involved root surfaces after root surface debridement.Methods: Ninety single rooted teeth with severe bone resorption were selected,which were scheduled for extraction.The teeth were randomly assigned into 3 groups.The teeth in the first group were served as control and they did not receive any debridement.The teeth in the second group were scaled and root planned with Gracey curettes.The teeth in the third group were debrided with the new ultrasonic device VectorTM-system(Dürr Dental).The endotoxin concentrations before and after debridement were assessed by Limulus Amebocyte Lysat(LAL).Results: The concentration of endotoxin of periodontally involved teeth in the control group was 0.825 EU/ml.Scaling and root planning resulted in a significant reduction of the values as follows: Gracey curettes 0.240 EU/ml,VectorTM-system 0.184 EU/ml.Conclusion: Scaling and root planning leads to obvious reduction of the endotoxin on periodontally involved root surfaces and VectorTM-system is comparatively more effective than Gracey curettes.展开更多
The authors investigate the completeness of the system of eigen or root vectors of the 2×2 upper triangular infinite-dimensional Hamiltonian operator H 0.First,the geometrical multiplicity and the algebraic index...The authors investigate the completeness of the system of eigen or root vectors of the 2×2 upper triangular infinite-dimensional Hamiltonian operator H 0.First,the geometrical multiplicity and the algebraic index of the eigenvalue of H0 are considered.Next,some necessary and sufficient conditions for the completeness of the system of eigen or root vectors of H0 are obtained.Finally,the obtained results are tested in several examples.展开更多
目的研究Vector系统进行牙周基础治疗的临床效果。方法采用口内自身对照方法,选择58例慢性牙周炎患者,口内A、D区设为试验组,B、C区设为对照组。所有患者行超声洁治后,试验组应用Vector系统行龈下刮治及根面平整术(scaling and root pla...目的研究Vector系统进行牙周基础治疗的临床效果。方法采用口内自身对照方法,选择58例慢性牙周炎患者,口内A、D区设为试验组,B、C区设为对照组。所有患者行超声洁治后,试验组应用Vector系统行龈下刮治及根面平整术(scaling and root planning,SRP),对照组应用Gracey刮治器械行SRP。对2组SRP的治疗时间,SRP前(基线期)及SRP后1、3、6个月的龈沟出血指数、探诊出血、探诊深度及附着水平进行比较,视觉模拟疼痛评级法(visual analogue scale,VAS)评定2组的疼痛程度。结果试验组每区的SRP治疗时间为(25.15±1.35)min,明显短于对照组的(40.11±1.08)min(Z=3.625,P<0.05)。SRP后各观察时点,2组的各项牙周指数较治疗前均有明显改善(P<0.05),但2组间各项牙周指数的差异均无统计学意义(P>0.05)。试验组SRP结束时(Zc=2.356,P<0.05)及治疗后1d(Zc=3.138,P<0.05)的VAS评分明显低于对照组。结论Vector系统能缩短临床操作时间,提高牙周基础治疗舒适度,有效改善慢性牙周炎的临床症状。展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 11061019 and 10962004)the Chunhui Program of Ministry of Education of China (Grant No. Z2009-1-01010)+1 种基金the Natural Science Foundation of Inner Mongolia, China(Grant Nos. 2010MS0110 and 2009BS0101)the Cultivation of Innovative Talent of ‘211 Project’ of Inner Mongolia University
文摘In this paper, we consider the eigenvalue problem of a class of fourth-order operator matrices appearing in mechan- ics, including the geometric multiplicity, algebraic index, and algebraic multiplicity of the eigenvalue, the symplectic orthogonality, and completeness of eigen and root vector systems. The obtained results are applied to the plate bending problem.
基金supported by the National Natural Science Foundation of China (Nos. 11061019,10962004,11101200,and 11026175)the Chunhui Program of Ministry of Education of China (No. Z2009-1-01010)+1 种基金the Natural Science Foundation of Inner Mongolia of China (No. 2010MS0110)the Cultivation of Innovative Talent of "211 Project" of Inner Mongolia University
文摘This paper deals with a class of upper triangular infinite-dimensional Hamilto- nian operators appearing in the elasticity theory. The geometric multiplicity and algebraic index of the eigenvalue are investigated. Furthermore, the algebraic multiplicity of the eigenvalue is obtained. Based on these properties, the concrete completeness formulation of the system of eigenvectors or root vectors of the Hamiltonian operator is proposed. It is shown that the completeness is determined by the system of eigenvectors of the operator entries. Finally, the applications of the results to some problems in the elasticity theory are presented.
文摘Objective: To estimate the presence and the quantity of endotoxin of periodontally involved root surfaces after root surface debridement.Methods: Ninety single rooted teeth with severe bone resorption were selected,which were scheduled for extraction.The teeth were randomly assigned into 3 groups.The teeth in the first group were served as control and they did not receive any debridement.The teeth in the second group were scaled and root planned with Gracey curettes.The teeth in the third group were debrided with the new ultrasonic device VectorTM-system(Dürr Dental).The endotoxin concentrations before and after debridement were assessed by Limulus Amebocyte Lysat(LAL).Results: The concentration of endotoxin of periodontally involved teeth in the control group was 0.825 EU/ml.Scaling and root planning resulted in a significant reduction of the values as follows: Gracey curettes 0.240 EU/ml,VectorTM-system 0.184 EU/ml.Conclusion: Scaling and root planning leads to obvious reduction of the endotoxin on periodontally involved root surfaces and VectorTM-system is comparatively more effective than Gracey curettes.
基金supported by the National Natural Science Foundation of China(Nos.10962004,11061019)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20070126002)+1 种基金the Chunhui Program of the Ministry of Education of China(No.Z2009-1-01010)the Natural Science Foundation of Inner Mongolia(Nos.2009BS0101,2010MS0110)
文摘The authors investigate the completeness of the system of eigen or root vectors of the 2×2 upper triangular infinite-dimensional Hamiltonian operator H 0.First,the geometrical multiplicity and the algebraic index of the eigenvalue of H0 are considered.Next,some necessary and sufficient conditions for the completeness of the system of eigen or root vectors of H0 are obtained.Finally,the obtained results are tested in several examples.
