Cordial Volterra integral equations (CVIEs) from some applications models associated with a noncompact cordial Volterra integral operator are discussed in the recent years. A lot of real problems are effected by a del...Cordial Volterra integral equations (CVIEs) from some applications models associated with a noncompact cordial Volterra integral operator are discussed in the recent years. A lot of real problems are effected by a delayed history information. In this paper we investigate some properties of cordial Volterra integral operators influenced by a vanishing delay. It is shown that to replicate all eigenfunctions , or , the vanishing delay must be a proportional delay. For such a linear delay, the spectrum, eigenvalues and eigenfunctions of the operators and the existence, uniqueness and solution spaces of solutions are presented. For a nonlinear vanishing delay, we show a necessary and sufficient condition such that the operator is compact, which also yields the existence and uniqueness of solutions to CVIEs with the vanishing delay.展开更多
Amygdaloid nucleus(AMYG)could converge and integrate the signals from electroacupuncture(EA)at Neiguan(P 6)and acute myocardial ischemia(AMI)in rabbits.And EA could regulatethe changes in the discharge of single units...Amygdaloid nucleus(AMYG)could converge and integrate the signals from electroacupuncture(EA)at Neiguan(P 6)and acute myocardial ischemia(AMI)in rabbits.And EA could regulatethe changes in the discharge of single units in AMYG caused by AMI,that is,EA inhibited theincreased frequency,and reversed the decreased frequency.This suggested that AMYG is an im-portant link in correlation between the heart and the acupoint Neiguan,providing an experimen-tal basis for the Theory of Channel-Viscera Correlation.展开更多
文摘Cordial Volterra integral equations (CVIEs) from some applications models associated with a noncompact cordial Volterra integral operator are discussed in the recent years. A lot of real problems are effected by a delayed history information. In this paper we investigate some properties of cordial Volterra integral operators influenced by a vanishing delay. It is shown that to replicate all eigenfunctions , or , the vanishing delay must be a proportional delay. For such a linear delay, the spectrum, eigenvalues and eigenfunctions of the operators and the existence, uniqueness and solution spaces of solutions are presented. For a nonlinear vanishing delay, we show a necessary and sufficient condition such that the operator is compact, which also yields the existence and uniqueness of solutions to CVIEs with the vanishing delay.
基金The project was supported by National Natural Science Foundation of China.
文摘Amygdaloid nucleus(AMYG)could converge and integrate the signals from electroacupuncture(EA)at Neiguan(P 6)and acute myocardial ischemia(AMI)in rabbits.And EA could regulatethe changes in the discharge of single units in AMYG caused by AMI,that is,EA inhibited theincreased frequency,and reversed the decreased frequency.This suggested that AMYG is an im-portant link in correlation between the heart and the acupoint Neiguan,providing an experimen-tal basis for the Theory of Channel-Viscera Correlation.
