In this paper best approximation by reciprocals of functions of a subspace U_n=span (u_1,…,u_n)satisfying coefficient constraints is considered.We present a characterization of best approximations.When(u_1,…,u_n)is ...In this paper best approximation by reciprocals of functions of a subspace U_n=span (u_1,…,u_n)satisfying coefficient constraints is considered.We present a characterization of best approximations.When(u_1,…,u_n)is a Descartes system an explicit characterization of best approximations by equioscillations is given.Existence and uniqueness results are shown. Moreover,the theory is applied to best approximaitons by reciprocals of polynomials.展开更多
To provide a computational efficient forward model with moderate accuracy for rapid 3D optical tomography in small volumes,radiative transport in the delta-P1 approximation combined with the approximation of the recip...To provide a computational efficient forward model with moderate accuracy for rapid 3D optical tomography in small volumes,radiative transport in the delta-P1 approximation combined with the approximation of the reciprocity was examined.Perturbations of optical signals caused by absorption and fluorescence heterogeneities submerged in a resin-based liquid phantom with background parameters close to rat brain tissues were measured using a recently constructed laminar optical tomography system.These measured perturbations were used to examine the theoretically calculated fluence perturbations based on the delta-P1 approximation and the reciprocity approximation.Results show that the errors between the predicted and measured data are acceptable,especially for fluorescence perturbations.展开更多
Let S^1-1,q≥2,be the surface of the unit sphere in the Euclidean space R^1,f（x）∈L^p（S^q-1）,f（x）≥0,f absohutely unegual to 0,1≤p≤＋∞,Then,it is proved in the present paper that there is a spherical harmonic...Let S^1-1,q≥2,be the surface of the unit sphere in the Euclidean space R^1,f（x）∈L^p（S^q-1）,f（x）≥0,f absohutely unegual to 0,1≤p≤＋∞,Then,it is proved in the present paper that there is a spherical harmonics PN（x） of order≤N and a constant C〉0 such that where ω（f,δ）L^p=sup 0〈t≤δ‖St（f）-f‖L^p is a kind of moduli of continuity and ^‖f-1/PN‖L^p≤Cω（f,N^-1）L^p,St（f,μ）=1/｜S^q-2｜Sin^2λt ∫-μμ’=t f（μ＇）dμ＇ is a translation operator.展开更多
文摘In this paper best approximation by reciprocals of functions of a subspace U_n=span (u_1,…,u_n)satisfying coefficient constraints is considered.We present a characterization of best approximations.When(u_1,…,u_n)is a Descartes system an explicit characterization of best approximations by equioscillations is given.Existence and uniqueness results are shown. Moreover,the theory is applied to best approximaitons by reciprocals of polynomials.
文摘To provide a computational efficient forward model with moderate accuracy for rapid 3D optical tomography in small volumes,radiative transport in the delta-P1 approximation combined with the approximation of the reciprocity was examined.Perturbations of optical signals caused by absorption and fluorescence heterogeneities submerged in a resin-based liquid phantom with background parameters close to rat brain tissues were measured using a recently constructed laminar optical tomography system.These measured perturbations were used to examine the theoretically calculated fluence perturbations based on the delta-P1 approximation and the reciprocity approximation.Results show that the errors between the predicted and measured data are acceptable,especially for fluorescence perturbations.
基金Supported by the National Natural Science Foundation of China （No.10371024）, the Natural Science of Zhejiang Province （No. Y604003） and the Doctor Foundation of Ningbo City （No.2004A620017）.
文摘Let S^1-1,q≥2,be the surface of the unit sphere in the Euclidean space R^1,f（x）∈L^p（S^q-1）,f（x）≥0,f absohutely unegual to 0,1≤p≤＋∞,Then,it is proved in the present paper that there is a spherical harmonics PN（x） of order≤N and a constant C〉0 such that where ω（f,δ）L^p=sup 0〈t≤δ‖St（f）-f‖L^p is a kind of moduli of continuity and ^‖f-1/PN‖L^p≤Cω（f,N^-1）L^p,St（f,μ）=1/｜S^q-2｜Sin^2λt ∫-μμ’=t f（μ＇）dμ＇ is a translation operator.
