图的不变量点稳定数是最近的热点问题之一,它被应用于设计算法解决图论的某些特定问题。设f是图不变量,图G的f-点稳定数vsf(G)定义为使得f(G−V′)≠f(G)成立的最小点子集V′的基数。在本文中,通过不变量f的性质,讨论笛卡尔积图的f-点稳...图的不变量点稳定数是最近的热点问题之一,它被应用于设计算法解决图论的某些特定问题。设f是图不变量,图G的f-点稳定数vsf(G)定义为使得f(G−V′)≠f(G)成立的最小点子集V′的基数。在本文中,通过不变量f的性质,讨论笛卡尔积图的f-点稳定数的界。The invariant vertex stability number of graph is one of the recent hot topics, which is applied to design algorithms to solve certain problems in graph theory. Let fbe an invariant of graphs, and the f-vertex stability number vsf(G)of a graph Gis defined as the cardinality of the minimum vertex subset V′such that f(G−V′)≠f(G). In this paper, we discuss the bounds of the f-vertex stability number for Cartesian product graphs through the properties of the invariant f.展开更多
Underground energy and resource development,deep underground energy storage and other projects involve the global stability of multiple interconnected cavern groups under internal and external dynamic disturbances.An ...Underground energy and resource development,deep underground energy storage and other projects involve the global stability of multiple interconnected cavern groups under internal and external dynamic disturbances.An evaluation method of the global stability coefficient of underground caverns based on static overload and dynamic overload was proposed.Firstly,the global failure criterion for caverns was defined based on its band connection of plastic-strain between multi-caverns.Then,overloading calculation of the boundary geostress and seismic intensity on the caverns model was carried out,and the critical unstable state of multi-caverns can be identified,if the plastic-strain band appeared between caverns during these overloading processes.Thus,the global stability coefficient for the multi-caverns under static loading and earthquake was obtained based on the corresponding overloading coefficient.Practical analysis for the Yingliangbao(YLB)hydraulic caverns indicated that this method can not only effectively obtain the global stability coefficient of caverns under static and dynamic earthquake conditions,but also identify the caverns’high-risk zone of local instability through localized plastic strain of surrounding rock.This study can provide some reference for the layout design and seismic optimization of underground cavern group.展开更多
This paper investigates the stability and bifurcation phenomena of a cholera transmission model in which individuals who have recovered from the disease may become susceptible again.The threshold for determining disea...This paper investigates the stability and bifurcation phenomena of a cholera transmission model in which individuals who have recovered from the disease may become susceptible again.The threshold for determining disease prevalence is established,and the parameter conditions for the existence of equilibria are discussed.The Routh-Hurwitz criterion is applied to demonstrate the local asymptotic stability of equilibria.By utilizing composite matrices and geometric techniques,the global dynamic behavior of the endemic equilibrium is investigated,and the sufficient conditions for its global asymptotic stability are derived.Furthermore,the disease-free equilibrium is a saddle-node when the basic reproductive number is 1,and tthe transcritical bifurcation in this case is discussed.展开更多
Abundant herbaceous and shrub roots play an important role in preventing water and soil erosion and increasing shallow slope stability. In order to make a quantitative analysis on the contribution of root system to sl...Abundant herbaceous and shrub roots play an important role in preventing water and soil erosion and increasing shallow slope stability. In order to make a quantitative analysis on the contribution of root system to slope stability under dif- ferent slope gradient, an unconsolidated and undrained triaxial compression test was conducted to measure the shear strengths of soil and root-soil composite in the two slopes in eastern Qinghai Province. In addition, under the protection of plant roots, the effect of gradient on stability of soil slope was investigated by limit equilibrium method. The results showed that the stability coefficient of soil slope planted with two kinds of brush was decreased with the increase in slope gradient, and the sta- bility coefficient increment of soil slope containing Atriplex canescens roots was higher than that containing Caragana korshinskii roots. When the slope gradient ranged from 25° to 50°, the stability coefficient of soil slope planted with Atriplex canescens or Caragana korshinskii ranged from 0.80 to 1.38. However, when the slope gradient exceeded 55°, the increment of stability coefficient of soil slope became small.展开更多
The exponential stability of a class of neural networks with continuously distributed delays is investigated by employing a novel Lyapunov-Krasovskii functional. Through introducing some free-weighting matrices and th...The exponential stability of a class of neural networks with continuously distributed delays is investigated by employing a novel Lyapunov-Krasovskii functional. Through introducing some free-weighting matrices and the equivalent descriptor form, a delay-dependent stability criterion is established for the addressed systems. The condition is expressed in terms of a linear matrix inequality （LMI）, and it can be checked by resorting to the LMI in the Matlab toolbox. In addition, the proposed stability criteria do not require the monotonicity of the activation functions and the derivative of a time-varying delay being less than 1, which generalize and improve earlier methods. Finally, numerical examples are given to show the effectiveness of the obtained methods.展开更多
The cadmium（Ⅱ）-glycine system was studied by the two experimental techniques, ion sensitive electrode （ISE） and differential pulse polarography （DPP）, and the experimental data obtained were used by a unified m...The cadmium（Ⅱ）-glycine system was studied by the two experimental techniques, ion sensitive electrode （ISE） and differential pulse polarography （DPP）, and the experimental data obtained were used by a unified mathematical treatment to calculate the complex stability constants. The combination of the two techniques is of many advantages as ISE can be performed at low [LT]：[MT] ratios and significantly higher [MT], whereas DPP could be used well at large [LT]：[MT] ratios and much smaller [MT]. This makes it possible to study a metal-ligand system in a relatively broader range of experimental conditions that, in turn, provides more information about the metakligand system of interest. Applying the unified mathematical treatment to the cadmium-glycine system, two new complexes MHL and ML2（OH） as well as three complexes ML, ML2 and ML3, reported in literatures, could be modeled and all their stability constants have been refined.展开更多
A complete closed-loop third order s-domain model is analyzed for a frequency synthesizer. Based on the model and root-locus technique, the procedure for parameters design is described, and the relationship between th...A complete closed-loop third order s-domain model is analyzed for a frequency synthesizer. Based on the model and root-locus technique, the procedure for parameters design is described, and the relationship between the process,voltage,and temperature variation of parameters and the loop stability is quantitatively analyzed. A variation margin is proposed for stability compensation. Furthermore,a simple adjustable current cell in the charge pump is proposed for additional stability compensation and a novel VCO with linear gain is adopted to limit the total variation. A fully integrated frequency synthesizer from 1 to 1.05GHz with 250kHz channel resolution is implemented to verify the methods.展开更多
文摘图的不变量点稳定数是最近的热点问题之一,它被应用于设计算法解决图论的某些特定问题。设f是图不变量,图G的f-点稳定数vsf(G)定义为使得f(G−V′)≠f(G)成立的最小点子集V′的基数。在本文中,通过不变量f的性质,讨论笛卡尔积图的f-点稳定数的界。The invariant vertex stability number of graph is one of the recent hot topics, which is applied to design algorithms to solve certain problems in graph theory. Let fbe an invariant of graphs, and the f-vertex stability number vsf(G)of a graph Gis defined as the cardinality of the minimum vertex subset V′such that f(G−V′)≠f(G). In this paper, we discuss the bounds of the f-vertex stability number for Cartesian product graphs through the properties of the invariant f.
基金Project(2023YFC2907204)supported by the National Key Research and Development Program of ChinaProject(52325905)supported by the National Natural Science Foundation of ChinaProject(DJ-HXGG-2023-16)supported by the Key Technology Research Projects of Power China。
文摘Underground energy and resource development,deep underground energy storage and other projects involve the global stability of multiple interconnected cavern groups under internal and external dynamic disturbances.An evaluation method of the global stability coefficient of underground caverns based on static overload and dynamic overload was proposed.Firstly,the global failure criterion for caverns was defined based on its band connection of plastic-strain between multi-caverns.Then,overloading calculation of the boundary geostress and seismic intensity on the caverns model was carried out,and the critical unstable state of multi-caverns can be identified,if the plastic-strain band appeared between caverns during these overloading processes.Thus,the global stability coefficient for the multi-caverns under static loading and earthquake was obtained based on the corresponding overloading coefficient.Practical analysis for the Yingliangbao(YLB)hydraulic caverns indicated that this method can not only effectively obtain the global stability coefficient of caverns under static and dynamic earthquake conditions,but also identify the caverns’high-risk zone of local instability through localized plastic strain of surrounding rock.This study can provide some reference for the layout design and seismic optimization of underground cavern group.
基金supported by the National Natural Science Foundation of China(No.12171337)the Central Government Guided Local Science and Technology Development Projects(No.2024ZYD0059)+1 种基金the Natural Science Foundation of Sichuan Province(No.2022NSFSC0529)the Open Research Fund Program of Data Recovery Key Laboratory of Sichuan Province(No.DRN2405)。
文摘This paper investigates the stability and bifurcation phenomena of a cholera transmission model in which individuals who have recovered from the disease may become susceptible again.The threshold for determining disease prevalence is established,and the parameter conditions for the existence of equilibria are discussed.The Routh-Hurwitz criterion is applied to demonstrate the local asymptotic stability of equilibria.By utilizing composite matrices and geometric techniques,the global dynamic behavior of the endemic equilibrium is investigated,and the sufficient conditions for its global asymptotic stability are derived.Furthermore,the disease-free equilibrium is a saddle-node when the basic reproductive number is 1,and tthe transcritical bifurcation in this case is discussed.
基金Supported by Scientific Research Fund for Middle-aged and Young Scientists of Qinghai University(2012-QGY-5)"123 High-level Personnel Training Project"of Qinghai UniversityProject of Geological Resources and Geological Engineering Innovation Team of Qinghai University(4056051201)~~
文摘Abundant herbaceous and shrub roots play an important role in preventing water and soil erosion and increasing shallow slope stability. In order to make a quantitative analysis on the contribution of root system to slope stability under dif- ferent slope gradient, an unconsolidated and undrained triaxial compression test was conducted to measure the shear strengths of soil and root-soil composite in the two slopes in eastern Qinghai Province. In addition, under the protection of plant roots, the effect of gradient on stability of soil slope was investigated by limit equilibrium method. The results showed that the stability coefficient of soil slope planted with two kinds of brush was decreased with the increase in slope gradient, and the sta- bility coefficient increment of soil slope containing Atriplex canescens roots was higher than that containing Caragana korshinskii roots. When the slope gradient ranged from 25° to 50°, the stability coefficient of soil slope planted with Atriplex canescens or Caragana korshinskii ranged from 0.80 to 1.38. However, when the slope gradient exceeded 55°, the increment of stability coefficient of soil slope became small.
基金The National Natural Science Foundation of China (No60574006)
文摘The exponential stability of a class of neural networks with continuously distributed delays is investigated by employing a novel Lyapunov-Krasovskii functional. Through introducing some free-weighting matrices and the equivalent descriptor form, a delay-dependent stability criterion is established for the addressed systems. The condition is expressed in terms of a linear matrix inequality （LMI）, and it can be checked by resorting to the LMI in the Matlab toolbox. In addition, the proposed stability criteria do not require the monotonicity of the activation functions and the derivative of a time-varying delay being less than 1, which generalize and improve earlier methods. Finally, numerical examples are given to show the effectiveness of the obtained methods.
文摘The cadmium（Ⅱ）-glycine system was studied by the two experimental techniques, ion sensitive electrode （ISE） and differential pulse polarography （DPP）, and the experimental data obtained were used by a unified mathematical treatment to calculate the complex stability constants. The combination of the two techniques is of many advantages as ISE can be performed at low [LT]：[MT] ratios and significantly higher [MT], whereas DPP could be used well at large [LT]：[MT] ratios and much smaller [MT]. This makes it possible to study a metal-ligand system in a relatively broader range of experimental conditions that, in turn, provides more information about the metakligand system of interest. Applying the unified mathematical treatment to the cadmium-glycine system, two new complexes MHL and ML2（OH） as well as three complexes ML, ML2 and ML3, reported in literatures, could be modeled and all their stability constants have been refined.
文摘A complete closed-loop third order s-domain model is analyzed for a frequency synthesizer. Based on the model and root-locus technique, the procedure for parameters design is described, and the relationship between the process,voltage,and temperature variation of parameters and the loop stability is quantitatively analyzed. A variation margin is proposed for stability compensation. Furthermore,a simple adjustable current cell in the charge pump is proposed for additional stability compensation and a novel VCO with linear gain is adopted to limit the total variation. A fully integrated frequency synthesizer from 1 to 1.05GHz with 250kHz channel resolution is implemented to verify the methods.
