This paper presents a multi-ANN approximation approach to approximate complex non-linear function. Comparing with single-ANN methods the proposed approach improves and increases the approximation and generalization ab...This paper presents a multi-ANN approximation approach to approximate complex non-linear function. Comparing with single-ANN methods the proposed approach improves and increases the approximation and generalization ability, and adaptability greatly in learning processes of networks. The simulation results have been shown that the method can be applied to the modeling and identification of complex dynamic control systems.展开更多
In this paper, we solve the quadratic p-functional inequalities ……where p is a fixed complex number with ｜P｜ 〈 1, and^where p is a fixed complex number with ｜P｜ 〈 2^-1.Using the direct method, we prove the Hye...In this paper, we solve the quadratic p-functional inequalities ……where p is a fixed complex number with ｜P｜ 〈 1, and^where p is a fixed complex number with ｜P｜ 〈 2^-1.Using the direct method, we prove the Hyers-Ulam stability of the quadratic p-functional inequalities （0.1） and （0.2） in complex Banach spaces and prove the Hyers-Ulam stability of quadratic p-functional equations associated with the quadratic p-functional inequalities （0.1） and （0.2） in complex Banach spaces.展开更多
We prove, using the fixed point approach, some results on hyperstability （in normed spaces） of the equation that defines the generalization of p-Wright affine functions and show that they yield a simple characteriza...We prove, using the fixed point approach, some results on hyperstability （in normed spaces） of the equation that defines the generalization of p-Wright affine functions and show that they yield a simple characterization of the complex inner product spaces.展开更多
In this paper, we present a new representation of gamma function as a series of complex delta functions. We establish the convergence of this representation in the sense of distributions. It turns out that the gamma f...In this paper, we present a new representation of gamma function as a series of complex delta functions. We establish the convergence of this representation in the sense of distributions. It turns out that the gamma function can be defined over a space of complex test functions of slow growth denoted by Z. Some properties of gamma function are discussed by using the properties of delta function.展开更多
The complex Banach spaces X with values in which every bounded holomorphic function in the unit hall B of C-d(d > 1) has boundary limits almost surely are exactly the spaces with the analytic Radon-Nikodym property...The complex Banach spaces X with values in which every bounded holomorphic function in the unit hall B of C-d(d > 1) has boundary limits almost surely are exactly the spaces with the analytic Radon-Nikodym property. The proof is based on inner Hardy martingales introduced here. The inner Hardy martingales are constructed in terms of inner functions in B and are reasonable discrete approximations for the image processes of the holomorphic Brownian motion under X-valued holomorphic functions in B.展开更多
Extension of classical Mandelbrojt’s criterion for normality to several complex variables is given. Some inequalities for holomorphic functions which omit values 0 and 1 are obtained.
In the complex n-dimensional projective space CP^n. let λ_p(=4p(p+n)) be the eigen vaiue of the Laplace-Beltrami operator and H_p be the space of all eigen functions of eigen value λ_p. The reproducing kernel h_p(z,...In the complex n-dimensional projective space CP^n. let λ_p(=4p(p+n)) be the eigen vaiue of the Laplace-Beltrami operator and H_p be the space of all eigen functions of eigen value λ_p. The reproducing kernel h_p(z, w) of H_p is constructed explicitly in this paper. and a system of complete orthogohal functions of H_p is construncted from h_p(z, w)(p=1,2…).展开更多
文摘This paper presents a multi-ANN approximation approach to approximate complex non-linear function. Comparing with single-ANN methods the proposed approach improves and increases the approximation and generalization ability, and adaptability greatly in learning processes of networks. The simulation results have been shown that the method can be applied to the modeling and identification of complex dynamic control systems.
基金supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education,Science and Technology(NRF-2012R1A1A2004299)
文摘In this paper, we solve the quadratic p-functional inequalities ……where p is a fixed complex number with ｜P｜ 〈 1, and^where p is a fixed complex number with ｜P｜ 〈 2^-1.Using the direct method, we prove the Hyers-Ulam stability of the quadratic p-functional inequalities （0.1） and （0.2） in complex Banach spaces and prove the Hyers-Ulam stability of quadratic p-functional equations associated with the quadratic p-functional inequalities （0.1） and （0.2） in complex Banach spaces.
文摘We prove, using the fixed point approach, some results on hyperstability （in normed spaces） of the equation that defines the generalization of p-Wright affine functions and show that they yield a simple characterization of the complex inner product spaces.
文摘In this paper, we present a new representation of gamma function as a series of complex delta functions. We establish the convergence of this representation in the sense of distributions. It turns out that the gamma function can be defined over a space of complex test functions of slow growth denoted by Z. Some properties of gamma function are discussed by using the properties of delta function.
文摘The complex Banach spaces X with values in which every bounded holomorphic function in the unit hall B of C-d(d > 1) has boundary limits almost surely are exactly the spaces with the analytic Radon-Nikodym property. The proof is based on inner Hardy martingales introduced here. The inner Hardy martingales are constructed in terms of inner functions in B and are reasonable discrete approximations for the image processes of the holomorphic Brownian motion under X-valued holomorphic functions in B.
文摘Extension of classical Mandelbrojt’s criterion for normality to several complex variables is given. Some inequalities for holomorphic functions which omit values 0 and 1 are obtained.
文摘In the complex n-dimensional projective space CP^n. let λ_p(=4p(p+n)) be the eigen vaiue of the Laplace-Beltrami operator and H_p be the space of all eigen functions of eigen value λ_p. The reproducing kernel h_p(z, w) of H_p is constructed explicitly in this paper. and a system of complete orthogohal functions of H_p is construncted from h_p(z, w)(p=1,2…).
