In this paper, we have studied several classes of planar piecewise Hamiltonian systems with three zones separated by two parallel straight lines. Firstly, we give the maximal number of limit cycles in these classes of...In this paper, we have studied several classes of planar piecewise Hamiltonian systems with three zones separated by two parallel straight lines. Firstly, we give the maximal number of limit cycles in these classes of systems with a center in two zones and without equilibrium points in the other zone (or with a center in one zone and without equilibrium points in the other zones). In addition, we also give examples to illustrate that it can reach the maximal number.展开更多
The paper deals with a lossy transmission line terminated at both ends by non-linear RCL elements. The mixed problem for the hyperbolic system, describing the transmission line, to an initial value problem for a neutr...The paper deals with a lossy transmission line terminated at both ends by non-linear RCL elements. The mixed problem for the hyperbolic system, describing the transmission line, to an initial value problem for a neutral equation is reduced. Sufficient conditions for the existence and uniqueness of periodic regimes are formulated. The proof is based on the finding out of suitable operator whose fixed point is a periodic solution of the neutral equation. The method has a good rate of convergence of the successive approximations even for high frequencies.展开更多
Regarding the problem that the traditional straight-line generating has a low accuracy, we study straightline generating with the distance of point to line. We explore generating a line to approximate the ideal line a...Regarding the problem that the traditional straight-line generating has a low accuracy, we study straightline generating with the distance of point to line. We explore generating a line to approximate the ideal line and the issue is to pick out the pixel point of approximating the ideal line. The paper plays a significant scientific role in elucidating linear optimization norm and it lays a foundation for showing a straight line. The algorithm is valuable for computer graphics.展开更多
This paper studies a new class of two-dimensional rational maps exhibiting self-excited and hidden attractors. The mathematical model of these maps is firstly formulated by introducing a rational term. The analysis of...This paper studies a new class of two-dimensional rational maps exhibiting self-excited and hidden attractors. The mathematical model of these maps is firstly formulated by introducing a rational term. The analysis of existence and stability of the fixed points in these maps suggests that there are four types of fixed points, i.e., no fixed point, one single fixed point, two fixed points and a line of fixed points. To investigate the complex dynamics of these rational maps with different types of fixed points, numerical analysis tools, such as time histories, phase portraits, basins of attraction, Lyapunov exponent spectrum, Lyapunov(Kaplan–Yorke) dimension and bifurcation diagrams, are employed. Our extensive numerical simulations identify both self-excited and hidden attractors, which were rarely reported in the literature. Therefore, the multi-stability of these maps, especially the hidden one, is further explored in the present work.展开更多
In this work, we are concerned with the existence and multiplicity of positive solutions for singular boundary value problems on the half-line. Two problems from epi- demiology and combustion theory set on the positiv...In this work, we are concerned with the existence and multiplicity of positive solutions for singular boundary value problems on the half-line. Two problems from epi- demiology and combustion theory set on the positive half-line are investigated upper and lower solution techniques combined with fixed point index on cones in priate Banach spaces. The results complement recent ones in the literature. We use appropriate Banach spaces. The results complement recent ones in the literature.展开更多
The compactness criterion in l◇={x（·）∈l^∞（0,∞））｜lim t→∞ x（t）=x（∞）} is given and as an application,we study the existence of positive solutions of second order boundary value problems of differenc...The compactness criterion in l◇={x（·）∈l^∞（0,∞））｜lim t→∞ x（t）=x（∞）} is given and as an application,we study the existence of positive solutions of second order boundary value problems of difference equation on the half line by the fixedpoint theorem in cones.展开更多
文摘In this paper, we have studied several classes of planar piecewise Hamiltonian systems with three zones separated by two parallel straight lines. Firstly, we give the maximal number of limit cycles in these classes of systems with a center in two zones and without equilibrium points in the other zone (or with a center in one zone and without equilibrium points in the other zones). In addition, we also give examples to illustrate that it can reach the maximal number.
文摘The paper deals with a lossy transmission line terminated at both ends by non-linear RCL elements. The mixed problem for the hyperbolic system, describing the transmission line, to an initial value problem for a neutral equation is reduced. Sufficient conditions for the existence and uniqueness of periodic regimes are formulated. The proof is based on the finding out of suitable operator whose fixed point is a periodic solution of the neutral equation. The method has a good rate of convergence of the successive approximations even for high frequencies.
基金supported by Xi'an University of Architecture and Technology under Grant No. JC0818,JC09112 and 2011028
文摘Regarding the problem that the traditional straight-line generating has a low accuracy, we study straightline generating with the distance of point to line. We explore generating a line to approximate the ideal line and the issue is to pick out the pixel point of approximating the ideal line. The paper plays a significant scientific role in elucidating linear optimization norm and it lays a foundation for showing a straight line. The algorithm is valuable for computer graphics.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11672257, 11772306, 11972173, and 12172340)the 5th 333 High-level Personnel Training Project of Jiangsu Province of China (Grant No. BRA2018324)。
文摘This paper studies a new class of two-dimensional rational maps exhibiting self-excited and hidden attractors. The mathematical model of these maps is firstly formulated by introducing a rational term. The analysis of existence and stability of the fixed points in these maps suggests that there are four types of fixed points, i.e., no fixed point, one single fixed point, two fixed points and a line of fixed points. To investigate the complex dynamics of these rational maps with different types of fixed points, numerical analysis tools, such as time histories, phase portraits, basins of attraction, Lyapunov exponent spectrum, Lyapunov(Kaplan–Yorke) dimension and bifurcation diagrams, are employed. Our extensive numerical simulations identify both self-excited and hidden attractors, which were rarely reported in the literature. Therefore, the multi-stability of these maps, especially the hidden one, is further explored in the present work.
文摘In this work, we are concerned with the existence and multiplicity of positive solutions for singular boundary value problems on the half-line. Two problems from epi- demiology and combustion theory set on the positive half-line are investigated upper and lower solution techniques combined with fixed point index on cones in priate Banach spaces. The results complement recent ones in the literature. We use appropriate Banach spaces. The results complement recent ones in the literature.
基金The NSF(11626188,11671322)of ChinaGansu Provincial NSF(1606RJYA232)of China and NWNU-LKQN-15-16
文摘The compactness criterion in l◇={x（·）∈l^∞（0,∞））｜lim t→∞ x（t）=x（∞）} is given and as an application,we study the existence of positive solutions of second order boundary value problems of difference equation on the half line by the fixedpoint theorem in cones.
文摘海底控制点的GNSS-A定位精度受到测量船相对于海底控制点的航迹影响,本文针对圆形测量模式垂向几何结构较弱的问题,给出了一种新的基于嵌套圆的直线测量模式的分析方法,研究了直线测量模式的参数可估性,并给出了直线测量模式得到唯一解的条件.同时,详细分析了圆形测量模式下要增加十字航迹的原因,推导出圆加十字测量模式下获得海底控制点最优三维点位精度的走航半径约为1.15倍水深.理论分析表明,在圆形测量模式下增加直线航迹能够有效增强其几何结构,提升定位效能.此外,针对是否存在唯一的最优航迹进行了思考,并给出了相应的见解.最后,利用深海实测数据验证了理论推导的结果,圆加十字测量模式较圆形测量模式对海底控制点定位的精度提升可达1.4 cm.
