In this paper we consider the Feller property and the exponential ergodicity for general diffusion processes with state-dependent switching. We prove their Feller continuity by means of intro- ducing some auxiliary pr...In this paper we consider the Feller property and the exponential ergodicity for general diffusion processes with state-dependent switching. We prove their Feller continuity by means of intro- ducing some auxiliary processes and by making use of the Radon-Nikodym derivatives. Furthermore, we also prove their strong Feller continuity and their exponential ergodicity under some reasonable conditions.展开更多
We present a general formula to generate the family of odd-point ternary approximating subdivision schemes with a shape parameter for describing curves. The influence of parameter to the limit curves and the sufficien...We present a general formula to generate the family of odd-point ternary approximating subdivision schemes with a shape parameter for describing curves. The influence of parameter to the limit curves and the sufficient conditions of the continuities from C0 to C5 of 3- and 5-point schemes are discussed. Our family of 3-point and 5-point ternary schemes has higher order of derivative continuity than the family of 3-point and 5-point schemes presented by [Jian-ao Lian, On a-ary subdivision for curve design: II. 3-point and 5-point interpolatory schemes, Applications and Applied Mathematics: An International Journal, 3(2), 2008, 176-187]. Moreover, a 3-point ternary cubic B-spline is special case of our family of 3-point ternary scheme. The visual quality of schemes with examples is also demonstrated.展开更多
A new generalization of Stancu polynomials based on the q-integers and a nonnegative integer s is firstly introduced in this paper. Moreover, the shape-preserving and convergence properties of these polynomials are al...A new generalization of Stancu polynomials based on the q-integers and a nonnegative integer s is firstly introduced in this paper. Moreover, the shape-preserving and convergence properties of these polynomials are also investigated.展开更多
In this paper,we discuss the trajectory controllability of linear and nonlinear fractional dynamical systems represented by the fractional differential equations in the sense of Caputo fractional derivative by using t...In this paper,we discuss the trajectory controllability of linear and nonlinear fractional dynamical systems represented by the fractional differential equations in the sense of Caputo fractional derivative by using the Mittag-Leffler function and Gronwall-Bellman inequality.For the nonlinear system,we assume Lipschitz-type conditions on the nonlinearity.Examples are given to illustrate the theoretical results.展开更多
基金the National Natural Science Foundation of China (Grant No. 10671037)the Basic Research Foundation of Beijing Institute of Technology (Grant No. 200507A4203)
文摘In this paper we consider the Feller property and the exponential ergodicity for general diffusion processes with state-dependent switching. We prove their Feller continuity by means of intro- ducing some auxiliary processes and by making use of the Radon-Nikodym derivatives. Furthermore, we also prove their strong Feller continuity and their exponential ergodicity under some reasonable conditions.
文摘We present a general formula to generate the family of odd-point ternary approximating subdivision schemes with a shape parameter for describing curves. The influence of parameter to the limit curves and the sufficient conditions of the continuities from C0 to C5 of 3- and 5-point schemes are discussed. Our family of 3-point and 5-point ternary schemes has higher order of derivative continuity than the family of 3-point and 5-point schemes presented by [Jian-ao Lian, On a-ary subdivision for curve design: II. 3-point and 5-point interpolatory schemes, Applications and Applied Mathematics: An International Journal, 3(2), 2008, 176-187]. Moreover, a 3-point ternary cubic B-spline is special case of our family of 3-point ternary scheme. The visual quality of schemes with examples is also demonstrated.
文摘A new generalization of Stancu polynomials based on the q-integers and a nonnegative integer s is firstly introduced in this paper. Moreover, the shape-preserving and convergence properties of these polynomials are also investigated.
基金the National Board for Higher Mathematics(Department of Atomic Energy,India)for the financial support through the Post-Doctoral Fellowship[2/40(9)/2014/R&D-II/319]the Second author would like to thank the IIT Mandi for providing the financial support through the Seed Grant[IITMandi/SG/2015/05-01].
文摘In this paper,we discuss the trajectory controllability of linear and nonlinear fractional dynamical systems represented by the fractional differential equations in the sense of Caputo fractional derivative by using the Mittag-Leffler function and Gronwall-Bellman inequality.For the nonlinear system,we assume Lipschitz-type conditions on the nonlinearity.Examples are given to illustrate the theoretical results.
