In this article,we first establish an asymptotically sharp result on the higher order Fréchet derivatives for bounded holomorphic mappings f(x)=f(0)+∞∑s=1Dskf(0)(x^(sk))/(sk)!:B_(X)→B_(Y),where B_X is the unit...In this article,we first establish an asymptotically sharp result on the higher order Fréchet derivatives for bounded holomorphic mappings f(x)=f(0)+∞∑s=1Dskf(0)(x^(sk))/(sk)!:B_(X)→B_(Y),where B_X is the unit ball of X.We next give a sharp result on the first order Fréchet derivative for bounded holomorphic mappings F(X)=F(0+)∞∑s=KD^(s)f(0)(x^(8)/s!):B_(X)→B_(Y),where B_(X)is the unit ball of X.The results that we derive include some results in several complex variables,and extend the classical result in one complex variable to several complex variables.展开更多
To realize high-resolution digital beamforming(DBF)of ultra-wideband(UWB) signals, we propose a DBF method based on Carath ′eodory representation for delay compensation and array extrapolation. Delay compensation by ...To realize high-resolution digital beamforming(DBF)of ultra-wideband(UWB) signals, we propose a DBF method based on Carath ′eodory representation for delay compensation and array extrapolation. Delay compensation by Carath ′eodory representation could achieve high interpolation accuracy while using the single channel sampling technique. Array extrapolation by Carath ′eodory representation reformulates and extends each snapshot, consequently extends the aperture of the original uniform linear array(ULA) by several times and provides a better realtime performance than the existing aperture extrapolation utilizing vector extrapolation based on the two dimensional autoregressive(2-D AR) model. The UWB linear frequency modulated(LFM) signal is used for simulation analysis. Simulation results demonstrate that the proposed method is featured by a much higher spatial resolution than traditional DBF methods and lower sidelobes than using Lagrange fractional filters.展开更多
In this paper nonlinear boundary value problems for discontinuous delayed differen- tial equations are considered. Some existence and boundedness results of solutions are obtained via the method of upper and lower sol...In this paper nonlinear boundary value problems for discontinuous delayed differen- tial equations are considered. Some existence and boundedness results of solutions are obtained via the method of upper and lower solutions, which may be discontinuous. Our analysis can be applied to those phenomena from physics and control theory which have been successfully described by delayed differential equations with discontinuous functions, such as electric, pneu- matic, and hydraulic networks. It is also an important step to precede the design of control signals when finite-time or practical stability control are concerned.展开更多
By introducing the Carathéodory metric,we establish the Schwarz lemma at the boundary for holomorphic self-mappings on the unit p-ball B_(p)^(n) of C^(n).Furthermore,the boundary rigidity theorem for holomorphic ...By introducing the Carathéodory metric,we establish the Schwarz lemma at the boundary for holomorphic self-mappings on the unit p-ball B_(p)^(n) of C^(n).Furthermore,the boundary rigidity theorem for holomorphic self-mappings defined on B_(n)^(p) is obtained.These results cover the boundary Schwarz lemma and rigidity result for holomorphic self-mappings on the unit ball for p=2,and the unit polydisk for p=∞,respectively.展开更多
We study the periodic boundary value problems for nonlinear integro-differential equa- tions of Volterra type with Carathéodory functions. For two situations relative to lower and upper solutions α and β:αβ ...We study the periodic boundary value problems for nonlinear integro-differential equa- tions of Volterra type with Carathéodory functions. For two situations relative to lower and upper solutions α and β:αβ or β α, the existence of solutions and the monotone iterative method for establishing extreme solutions are considered.展开更多
基金supported by the NSFC(11871257,12071130)supported by the NSFC(11971165)。
文摘In this article,we first establish an asymptotically sharp result on the higher order Fréchet derivatives for bounded holomorphic mappings f(x)=f(0)+∞∑s=1Dskf(0)(x^(sk))/(sk)!:B_(X)→B_(Y),where B_X is the unit ball of X.We next give a sharp result on the first order Fréchet derivative for bounded holomorphic mappings F(X)=F(0+)∞∑s=KD^(s)f(0)(x^(8)/s!):B_(X)→B_(Y),where B_(X)is the unit ball of X.The results that we derive include some results in several complex variables,and extend the classical result in one complex variable to several complex variables.
基金Supported by The National Natural Science Foundation of China(10771171)555 Innovation Talent Project of Gansu Province(GS-555-CXRC)+1 种基金Technique Innovation Project of Northwest Normal University(NWNU-KJCXGC-212)Important Foundation of Dingxi Teachers College(TD2016ZD06)
基金supported by the National Natural Science Foundation of China(61271331 61571229)
文摘To realize high-resolution digital beamforming(DBF)of ultra-wideband(UWB) signals, we propose a DBF method based on Carath ′eodory representation for delay compensation and array extrapolation. Delay compensation by Carath ′eodory representation could achieve high interpolation accuracy while using the single channel sampling technique. Array extrapolation by Carath ′eodory representation reformulates and extends each snapshot, consequently extends the aperture of the original uniform linear array(ULA) by several times and provides a better realtime performance than the existing aperture extrapolation utilizing vector extrapolation based on the two dimensional autoregressive(2-D AR) model. The UWB linear frequency modulated(LFM) signal is used for simulation analysis. Simulation results demonstrate that the proposed method is featured by a much higher spatial resolution than traditional DBF methods and lower sidelobes than using Lagrange fractional filters.
基金Supported by the National Natural Science Foundation of China(Grants No.70703016 and No.10001024)Research Grant of the Business School of Nanjing University
文摘In this paper nonlinear boundary value problems for discontinuous delayed differen- tial equations are considered. Some existence and boundedness results of solutions are obtained via the method of upper and lower solutions, which may be discontinuous. Our analysis can be applied to those phenomena from physics and control theory which have been successfully described by delayed differential equations with discontinuous functions, such as electric, pneu- matic, and hydraulic networks. It is also an important step to precede the design of control signals when finite-time or practical stability control are concerned.
基金supported by the National Natural Science Foundation of China(12071161,11971165)supported by the National Natural Science Foundation of China(11971042)the Natural Science Foundation of Zhejiang Province(Z24A010005)。
文摘By introducing the Carathéodory metric,we establish the Schwarz lemma at the boundary for holomorphic self-mappings on the unit p-ball B_(p)^(n) of C^(n).Furthermore,the boundary rigidity theorem for holomorphic self-mappings defined on B_(n)^(p) is obtained.These results cover the boundary Schwarz lemma and rigidity result for holomorphic self-mappings on the unit ball for p=2,and the unit polydisk for p=∞,respectively.
基金Project supported by the National Natural Science Foundation of China
文摘We study the periodic boundary value problems for nonlinear integro-differential equa- tions of Volterra type with Carathéodory functions. For two situations relative to lower and upper solutions α and β:αβ or β α, the existence of solutions and the monotone iterative method for establishing extreme solutions are considered.
