This paper gives several fundamental theorems for the stability, uniform stability, asymptotic stability and uniform asymptotic stability. Those theorems allow the derivative of Lyapunov functions to be positive on ce...This paper gives several fundamental theorems for the stability, uniform stability, asymptotic stability and uniform asymptotic stability. Those theorems allow the derivative of Lyapunov functions to be positive on certain sets,relax the restriction about the rate of change of state variable in a system to be bounded in Marachkov's theorem and extend the related results in [4—7].展开更多
[Objective] This study aimed to conduct correspondence cluster analysis of the trace elements in Chinese wolfberry from Qinghai and Ningxia regions, and to investigate the relationship among the quality of the wolfber...[Objective] This study aimed to conduct correspondence cluster analysis of the trace elements in Chinese wolfberry from Qinghai and Ningxia regions, and to investigate the relationship among the quality of the wolfberry samples, the composition of trace elements and the sample sources. [Method] The determined contents of trace elements and ratios of zinc to copper (Zn/Cu) of wolfberry from 11 different producing areas of Qinghai and Ningxia regions were adopted to construct the raw measurement data matrix, to analyze the distribution characteristics of the trace ele- ments in wolfberry from Qinghai and Ningxia by using the corresponding cluster analysis method. [Result] The quality of wolfberry samples in 7hongning County, Zhongwei City, Pingluo County, Shizuishan City, Heicheng Town of Ningxia Hui Au-tonomous Region and Hehuang Valley, Golmud City of Qinghai Province is mainly related to the contents of Zn and Mn; Zn/Cu greatly affects the quality of Chinese wolfberry in Dulan County of Qinghai Province; Fe has great effect on the quality of Chinese wolfberry in Yinchuan City of Ningxia Hui Autonomous Region; Cu greatly affects the quality of Chinese wolfberry in Nuomuhong Village of Qinghai Province and a wolfberry research institute in Ningxia. [Conclusion] The relationship between the quality of wolfberry from different producing areas and the trace elements was investigated, which provides theoretical and practical basis for the cultivation, har- vesting, processing, and further development and utilization of Chinese wolfberry resources from different producing areas.展开更多
By utilizing a fixed point theorem on cone, some new results on the existence ofpositive periodic solutions for nonautonomous differential equations with delay are derived.
A wide range of quantum systems are time-invariant and the corresponding dynamics is dic- tated by linear differential equations with constant coefficients. Although simple in math- ematical concept, the integration o...A wide range of quantum systems are time-invariant and the corresponding dynamics is dic- tated by linear differential equations with constant coefficients. Although simple in math- ematical concept, the integration of these equations is usually complicated in practice for complex systems, where both the computational time and the memory storage become limit- ing factors. For this reason, low-storage Runge-Kutta methods become increasingly popular for the time integration. This work suggests a series of s-stage sth-order explicit Runge- Kutta methods specific for autonomous linear equations, which only requires two times of the memory storage for the state vector. We also introduce a 13-stage eighth-order scheme for autonomous linear equations, which has optimized stability region and is reduced to a fifth-order method for general equations. These methods exhibit significant performance improvements over the previous general-purpose low-stage schemes. As an example, we ap- ply the integrator to simulate the non-Markovian exciton dynamics in a 15-site linear chain consisting of perylene-bisimide derivatives.展开更多
We study an autonomous system of first order ordinary differential equations based on the vector product. We show that the system is completely integrable by constructing the first integrals.The connection with Nambu ...We study an autonomous system of first order ordinary differential equations based on the vector product. We show that the system is completely integrable by constructing the first integrals.The connection with Nambu mechanics is established.The extension to higher dimensions is also discussed.展开更多
By means of theory of toplogical degree in nonlinear functional analysis combining with qualitative analysis method in ordinary differential equations, we discuss the existence of nontrivial periodic orbits for higher...By means of theory of toplogical degree in nonlinear functional analysis combining with qualitative analysis method in ordinary differential equations, we discuss the existence of nontrivial periodic orbits for higher dimensional autonomous system with small perturbations.展开更多
The author studied the existence of positive solutions of the delay logistic difference equation Δ y n=p ny n(1-y τ(n) ), n =0,1,2,.... where { p n } is a sequence of positive real numbers, { τ(n) } is a nondecreas...The author studied the existence of positive solutions of the delay logistic difference equation Δ y n=p ny n(1-y τ(n) ), n =0,1,2,.... where { p n } is a sequence of positive real numbers, { τ(n) } is a nondecreasing sequence of integers, τ(n)<n and lim n →∞ τ(n) =∞. A sufficient condition for the existence of positive solutions of the equation was given.展开更多
Objective.To summarize the experience of minim ally invasive treatment in 520patie nts with intracranial aneurysms on a retrospective study.Methods.The measures used in the treatment of520patients were reviewed in ter...Objective.To summarize the experience of minim ally invasive treatment in 520patie nts with intracranial aneurysms on a retrospective study.Methods.The measures used in the treatment of520patients were reviewed in terms o f timing of surgery,induced-hypotensive anesthesia,b rain protection combined with temporal occlusion of the feeding artery,exter-nal drainage of CSF,dynamic monitoring of intracranial pressure,blood flow velocity,serum osmolality and CT scanning,anti-vasospasm therapy a s well as selected interventional en dovascular embolization of aneurysms.Results.Of the 520patients,485were treated with either direct clipping or endov ascular embolization and35patients were treated non-surgic ally.In 449patients undergoing dir ect clipping and 36undergoing endov ascu-lar embolization,intraoperative r upture of aneurysm occurred in 27(6.0%)and 0%,respectively.Death oc-curred in 13(2.6%),hemiplegia in 8(1.6%),and vegetative state in 2(0.4%).The operative mortality of direct clipping was 3.8%in 210patie nts before 1990and 1.8%in 275patien ts after 1990(36patients undergo-ing endovascular embolization,the operative mortality was 0%).Conclusion.The outcome of patients with intracranial aneurysms can be markedly impr oved and the opera-tive mortality can be lowered by mini mally invasive treatment.展开更多
In this paper, a class of non-autonomous functional integro-differential stochastic equations in a real separable Hilbert space is studied. When the operators A(t) satisfy Acquistapace-Terreni conditions, and with s...In this paper, a class of non-autonomous functional integro-differential stochastic equations in a real separable Hilbert space is studied. When the operators A(t) satisfy Acquistapace-Terreni conditions, and with some suitable assumptions, the existence and uniqueness of a square-mean almost periodic mild solution to the equations are obtained.展开更多
This paper presents a simple and rigorous solution procedure of residue harmonic balance for predicting the accurate approximation of certain autonomous ordinary differential systems.In this solution procedure,no smal...This paper presents a simple and rigorous solution procedure of residue harmonic balance for predicting the accurate approximation of certain autonomous ordinary differential systems.In this solution procedure,no small parameter is assumed.The harmonic residue of balance equation is separated in two parts at each step.The first part has the same number of Fourier terms as the present order of approximation and the remaining part is used in the subsequent improvement.The corrections are governed by linear ordinary differential equation so that they can be solved easily by means of harmonic balance method again.Three kinds of different differential equations involving general,fractional and delay ordinary differential systems are given as numerical examples respectively.Highly accurate limited cycle frequency and amplitude are captured.The results match well with the exact solutions or numerical solutions for a wide range of control parameters.Comparison with those available shows that the residue harmonic balance solution procedure is very effective for these autonomous differential systems.Moreover,the present method works not only in predicting the amplitude but also the frequency of bifurcated period solution for delay ordinary differential equation.展开更多
This paper presents some existence theorems on almost periodic solutions for almost periodicneutral functional differential equation and its perturbed systems by means of Liapunov functional, and extends the correspon...This paper presents some existence theorems on almost periodic solutions for almost periodicneutral functional differential equation and its perturbed systems by means of Liapunov functional, and extends the corresponding results in 12,4,5,10,11].展开更多
文摘This paper gives several fundamental theorems for the stability, uniform stability, asymptotic stability and uniform asymptotic stability. Those theorems allow the derivative of Lyapunov functions to be positive on certain sets,relax the restriction about the rate of change of state variable in a system to be bounded in Marachkov's theorem and extend the related results in [4—7].
文摘[Objective] This study aimed to conduct correspondence cluster analysis of the trace elements in Chinese wolfberry from Qinghai and Ningxia regions, and to investigate the relationship among the quality of the wolfberry samples, the composition of trace elements and the sample sources. [Method] The determined contents of trace elements and ratios of zinc to copper (Zn/Cu) of wolfberry from 11 different producing areas of Qinghai and Ningxia regions were adopted to construct the raw measurement data matrix, to analyze the distribution characteristics of the trace ele- ments in wolfberry from Qinghai and Ningxia by using the corresponding cluster analysis method. [Result] The quality of wolfberry samples in 7hongning County, Zhongwei City, Pingluo County, Shizuishan City, Heicheng Town of Ningxia Hui Au-tonomous Region and Hehuang Valley, Golmud City of Qinghai Province is mainly related to the contents of Zn and Mn; Zn/Cu greatly affects the quality of Chinese wolfberry in Dulan County of Qinghai Province; Fe has great effect on the quality of Chinese wolfberry in Yinchuan City of Ningxia Hui Autonomous Region; Cu greatly affects the quality of Chinese wolfberry in Nuomuhong Village of Qinghai Province and a wolfberry research institute in Ningxia. [Conclusion] The relationship between the quality of wolfberry from different producing areas and the trace elements was investigated, which provides theoretical and practical basis for the cultivation, har- vesting, processing, and further development and utilization of Chinese wolfberry resources from different producing areas.
基金Supported by the Natural Science Foundation of Guangdong Province(032469)
文摘By utilizing a fixed point theorem on cone, some new results on the existence ofpositive periodic solutions for nonautonomous differential equations with delay are derived.
基金This work is supported by the National Natural Science Foundation of China (No.21373064), the Program for Innovative Research Team of Guizhou Province (No.QKTD[2014]4021), and the Natural Sci- entific Foundation from Guizhou Provincial Department of Education (No.ZDXK[2014]IS). All the calculations were performed at Guizhou Provincial High- Performance Computing Center of Condensed Mate- rials and Molecular Simulation in Guizhou Education University.
文摘A wide range of quantum systems are time-invariant and the corresponding dynamics is dic- tated by linear differential equations with constant coefficients. Although simple in math- ematical concept, the integration of these equations is usually complicated in practice for complex systems, where both the computational time and the memory storage become limit- ing factors. For this reason, low-storage Runge-Kutta methods become increasingly popular for the time integration. This work suggests a series of s-stage sth-order explicit Runge- Kutta methods specific for autonomous linear equations, which only requires two times of the memory storage for the state vector. We also introduce a 13-stage eighth-order scheme for autonomous linear equations, which has optimized stability region and is reduced to a fifth-order method for general equations. These methods exhibit significant performance improvements over the previous general-purpose low-stage schemes. As an example, we ap- ply the integrator to simulate the non-Markovian exciton dynamics in a 15-site linear chain consisting of perylene-bisimide derivatives.
文摘We study an autonomous system of first order ordinary differential equations based on the vector product. We show that the system is completely integrable by constructing the first integrals.The connection with Nambu mechanics is established.The extension to higher dimensions is also discussed.
文摘By means of theory of toplogical degree in nonlinear functional analysis combining with qualitative analysis method in ordinary differential equations, we discuss the existence of nontrivial periodic orbits for higher dimensional autonomous system with small perturbations.
文摘The author studied the existence of positive solutions of the delay logistic difference equation Δ y n=p ny n(1-y τ(n) ), n =0,1,2,.... where { p n } is a sequence of positive real numbers, { τ(n) } is a nondecreasing sequence of integers, τ(n)<n and lim n →∞ τ(n) =∞. A sufficient condition for the existence of positive solutions of the equation was given.
文摘Objective.To summarize the experience of minim ally invasive treatment in 520patie nts with intracranial aneurysms on a retrospective study.Methods.The measures used in the treatment of520patients were reviewed in terms o f timing of surgery,induced-hypotensive anesthesia,b rain protection combined with temporal occlusion of the feeding artery,exter-nal drainage of CSF,dynamic monitoring of intracranial pressure,blood flow velocity,serum osmolality and CT scanning,anti-vasospasm therapy a s well as selected interventional en dovascular embolization of aneurysms.Results.Of the 520patients,485were treated with either direct clipping or endov ascular embolization and35patients were treated non-surgic ally.In 449patients undergoing dir ect clipping and 36undergoing endov ascu-lar embolization,intraoperative r upture of aneurysm occurred in 27(6.0%)and 0%,respectively.Death oc-curred in 13(2.6%),hemiplegia in 8(1.6%),and vegetative state in 2(0.4%).The operative mortality of direct clipping was 3.8%in 210patie nts before 1990and 1.8%in 275patien ts after 1990(36patients undergo-ing endovascular embolization,the operative mortality was 0%).Conclusion.The outcome of patients with intracranial aneurysms can be markedly impr oved and the opera-tive mortality can be lowered by mini mally invasive treatment.
基金Acknowledgement This article is funded by the National Natural Science Foundation of China (11161052), Guangxi Natural Science Foundation of China (201 ljjA10044) and Guangxi Education Hall Project (201012MS183)
文摘In this paper, a class of non-autonomous functional integro-differential stochastic equations in a real separable Hilbert space is studied. When the operators A(t) satisfy Acquistapace-Terreni conditions, and with some suitable assumptions, the existence and uniqueness of a square-mean almost periodic mild solution to the equations are obtained.
基金supported by the Natural Science Foundation of Shandong Province,China(Grant Nos.ZR2011AQ022 and ZR2012AL03)
文摘This paper presents a simple and rigorous solution procedure of residue harmonic balance for predicting the accurate approximation of certain autonomous ordinary differential systems.In this solution procedure,no small parameter is assumed.The harmonic residue of balance equation is separated in two parts at each step.The first part has the same number of Fourier terms as the present order of approximation and the remaining part is used in the subsequent improvement.The corrections are governed by linear ordinary differential equation so that they can be solved easily by means of harmonic balance method again.Three kinds of different differential equations involving general,fractional and delay ordinary differential systems are given as numerical examples respectively.Highly accurate limited cycle frequency and amplitude are captured.The results match well with the exact solutions or numerical solutions for a wide range of control parameters.Comparison with those available shows that the residue harmonic balance solution procedure is very effective for these autonomous differential systems.Moreover,the present method works not only in predicting the amplitude but also the frequency of bifurcated period solution for delay ordinary differential equation.
文摘This paper presents some existence theorems on almost periodic solutions for almost periodicneutral functional differential equation and its perturbed systems by means of Liapunov functional, and extends the corresponding results in 12,4,5,10,11].