This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers...This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers for any M> 0.Moreover,the limiting behavior of minimizers as M→∞ is also analyzed rigorously.展开更多
A novel method of renormalization called Pacman renormalization allows us to study (unicritical) Siegel functions through Pacman-type functions. It has been used to investigate the Siegel parameters with combinatorial...A novel method of renormalization called Pacman renormalization allows us to study (unicritical) Siegel functions through Pacman-type functions. It has been used to investigate the Siegel parameters with combinatorially periodic rotation number in the main cardioid of the Mandelbrot set. It is already known that it can be defined a Pacman renormalization operator such that for Siegel pacmen, with combinatorially periodic rotation numbers, the operator is compact, analytic and has a unique fixed point, at which it is hyperbolic with one-dimensional unstable manifold. In this paper we observe that this Pacman renormalization operator is compact and analytic at any Siegel Pacman or Siegel map with combinatorially bounded rotation number. This allows us to define a renormalization operator on the hybrid classes of the standard Siegel pacmen to which we built its horseshoe where the operator is topologically semiconjugated to the left shift on the space of bi-infinite sequences of natural numbers bounded by some constant.展开更多
We show an example of a bounded potential on the half-line obtained as the image of an Inverse Transformation Operator of the Bessel singular potential of the Reduced Radial Schrödinger Equation, and show us ...We show an example of a bounded potential on the half-line obtained as the image of an Inverse Transformation Operator of the Bessel singular potential of the Reduced Radial Schrödinger Equation, and show us the Estimates of the A(α) amplitude.展开更多
This paper investigates the error reachable set based stabilization problem for a class of discrete-time switched linear systems with bounded peak disturbances under persistent dwell-time(PDT)constraint.A double-clock...This paper investigates the error reachable set based stabilization problem for a class of discrete-time switched linear systems with bounded peak disturbances under persistent dwell-time(PDT)constraint.A double-clockdependent control scheme is presented that can split the disturbed switched system into a nominal system and an error system,and assign to each system a controller scheduled by a clock.A necessary and sufficient convex stability criterion is presented for the nominal system,and is further extended to the stabilization controller design with a nominal clock.In the presence of bounded peak disturbances,another stabilization controller with an error clock is developed for the error system,with the purpose of‘‘minimizing’’the reachable set of the error system by the ellipsoidal techniques.It is demonstrated that the disturbed system is also globally exponentially stable in the sense of converging to an over approximation of the reachable set of the error system,i.e.,a union of a family of bounding ellipsoids,that can also be regarded as the cross section of a tube containing the trajectories of the disturbed system.Two numerical examples are provided to verify the effectiveness of the developed results.展开更多
基金supported by the Graduate Education Innovation Funds(2022CXZZ088)at Central China Normal University in Chinasupported by the NSFC(12225106,11931012)the Fundamental Research Funds(CCNU22LJ002)for the Central Universities in China。
文摘This paper is concerned with the minimizers of L^(2)-subcritical constraint variar tional problems with spatially decaying nonlinearities in a bounded domain Ω of R~N(N≥1).We prove that the problem admits minimizers for any M> 0.Moreover,the limiting behavior of minimizers as M→∞ is also analyzed rigorously.
文摘A novel method of renormalization called Pacman renormalization allows us to study (unicritical) Siegel functions through Pacman-type functions. It has been used to investigate the Siegel parameters with combinatorially periodic rotation number in the main cardioid of the Mandelbrot set. It is already known that it can be defined a Pacman renormalization operator such that for Siegel pacmen, with combinatorially periodic rotation numbers, the operator is compact, analytic and has a unique fixed point, at which it is hyperbolic with one-dimensional unstable manifold. In this paper we observe that this Pacman renormalization operator is compact and analytic at any Siegel Pacman or Siegel map with combinatorially bounded rotation number. This allows us to define a renormalization operator on the hybrid classes of the standard Siegel pacmen to which we built its horseshoe where the operator is topologically semiconjugated to the left shift on the space of bi-infinite sequences of natural numbers bounded by some constant.
文摘We show an example of a bounded potential on the half-line obtained as the image of an Inverse Transformation Operator of the Bessel singular potential of the Reduced Radial Schrödinger Equation, and show us the Estimates of the A(α) amplitude.
基金supported by the Natural Sciences and Engineering Research Council of Canada(NSERC).
文摘This paper investigates the error reachable set based stabilization problem for a class of discrete-time switched linear systems with bounded peak disturbances under persistent dwell-time(PDT)constraint.A double-clockdependent control scheme is presented that can split the disturbed switched system into a nominal system and an error system,and assign to each system a controller scheduled by a clock.A necessary and sufficient convex stability criterion is presented for the nominal system,and is further extended to the stabilization controller design with a nominal clock.In the presence of bounded peak disturbances,another stabilization controller with an error clock is developed for the error system,with the purpose of‘‘minimizing’’the reachable set of the error system by the ellipsoidal techniques.It is demonstrated that the disturbed system is also globally exponentially stable in the sense of converging to an over approximation of the reachable set of the error system,i.e.,a union of a family of bounding ellipsoids,that can also be regarded as the cross section of a tube containing the trajectories of the disturbed system.Two numerical examples are provided to verify the effectiveness of the developed results.
