In this paper,we first establish the sharp two-sided heat kernel estimates and the gradient estimate for the truncated fractional Laplacian under gradient perturbation S^(b):=△^(α/2)+b·▽,where △^(α/2) is the...In this paper,we first establish the sharp two-sided heat kernel estimates and the gradient estimate for the truncated fractional Laplacian under gradient perturbation S^(b):=△^(α/2)+b·▽,where △^(α/2) is the truncated fractional Laplacian,α∈(1,2) and b ∈ K_(d)^(α-1).In the second part,for a more general finite range jump process,we present some sufficient conditions to allow that the two sided estimates of the heat kernel are comparable to the Poisson type function for large distance |x-y|in short time.展开更多
The motion equation of the rotor suspended by active magnetic bearing (AMB)is given in this paper after considering the nonlinear characteristics of the force.Fromthe response equation resulted from this Eq.we gained ...The motion equation of the rotor suspended by active magnetic bearing (AMB)is given in this paper after considering the nonlinear characteristics of the force.Fromthe response equation resulted from this Eq.we gained the functions of the jump ra-nge,and examined the effects of the A MB's parameters.展开更多
基金Partially supported by NSFC(Grant Nos.11731009 and 11401025)。
文摘In this paper,we first establish the sharp two-sided heat kernel estimates and the gradient estimate for the truncated fractional Laplacian under gradient perturbation S^(b):=△^(α/2)+b·▽,where △^(α/2) is the truncated fractional Laplacian,α∈(1,2) and b ∈ K_(d)^(α-1).In the second part,for a more general finite range jump process,we present some sufficient conditions to allow that the two sided estimates of the heat kernel are comparable to the Poisson type function for large distance |x-y|in short time.
文摘The motion equation of the rotor suspended by active magnetic bearing (AMB)is given in this paper after considering the nonlinear characteristics of the force.Fromthe response equation resulted from this Eq.we gained the functions of the jump ra-nge,and examined the effects of the A MB's parameters.
