The symmetry of singular Hamiltonian differential operators is proved under the standard ＂definiteness condition＂, which is strictly weaker than the densely definite condition used by A. M. Krall. Meanwhile, some pr...The symmetry of singular Hamiltonian differential operators is proved under the standard ＂definiteness condition＂, which is strictly weaker than the densely definite condition used by A. M. Krall. Meanwhile, some properties of deficiency indices are given.展开更多
Iron deficiency anemia is one of the most prevalent nutritional deficiency worldwide. The commonly used cut-off values for identifying iron deficiency are extrapolated from older children and may not be suitable for i...Iron deficiency anemia is one of the most prevalent nutritional deficiency worldwide. The commonly used cut-off values for identifying iron deficiency are extrapolated from older children and may not be suitable for infants. Therefore, our study aimed to establish appropriate cut-off values for the evaluation of iron status in Chinese infants. Pregnant women who delivered at 〉37 gestational weeks with normal iron status were recruited. Later, infants with normal birth weight and who were breastfed in the first 4 months were selected. Blood samples were collected to assess hemoglobin, serum ferritin, soluble transferrin receptor, mean corpuscular volume and free erythrocyte protoporphyrin. Cut-offs of all iron indices were determined as the limit of 95% confidence interval.展开更多
In this paper, we have considered the general ordinary quasi-differential operators generated by a general quasi-differential expression τ<sub>p,q</sub> in L<sup>p</sup>w</sub>-spaces of...In this paper, we have considered the general ordinary quasi-differential operators generated by a general quasi-differential expression τ<sub>p,q</sub> in L<sup>p</sup>w</sub>-spaces of order n with complex coefficients and its formal adjoint τ<sup>+</sup><sub>q',p' </sub>in L<sup>p</sup>w</sub>-spaces for arbitrary p,q∈[1,∞). We have proved in the case of one singular end-point that all well-posed extensions of the minimal operator T<sub>0</sub> (τ<sub>p,q</sub>) generated by such expression τ<sub>p,q</sub> and their formal adjoint on the interval [a,b) with maximal deficiency indices have resolvents which are Hilbert-Schmidt integral operators and consequently have a wholly discrete spectrum. This implies that all the regularly solvable operators have all the standard essential spectra to be empty. Also, a number of results concerning the location of the point spectra and regularity fields of the operators generated by such expressions can be obtained. Some of these results are extensions or generalizations of those in the symmetric case, while others are new.展开更多
基金This work is supported by Ningbo Doctoral Science Foundation （No. 2004A620018）
文摘The symmetry of singular Hamiltonian differential operators is proved under the standard ＂definiteness condition＂, which is strictly weaker than the densely definite condition used by A. M. Krall. Meanwhile, some properties of deficiency indices are given.
基金supported by Natural Science Foundation of China(Grant No.30972483)The Chinese clinical trial registry number is ChiCTR-TRC-12002838
文摘Iron deficiency anemia is one of the most prevalent nutritional deficiency worldwide. The commonly used cut-off values for identifying iron deficiency are extrapolated from older children and may not be suitable for infants. Therefore, our study aimed to establish appropriate cut-off values for the evaluation of iron status in Chinese infants. Pregnant women who delivered at 〉37 gestational weeks with normal iron status were recruited. Later, infants with normal birth weight and who were breastfed in the first 4 months were selected. Blood samples were collected to assess hemoglobin, serum ferritin, soluble transferrin receptor, mean corpuscular volume and free erythrocyte protoporphyrin. Cut-offs of all iron indices were determined as the limit of 95% confidence interval.
文摘In this paper, we have considered the general ordinary quasi-differential operators generated by a general quasi-differential expression τ<sub>p,q</sub> in L<sup>p</sup>w</sub>-spaces of order n with complex coefficients and its formal adjoint τ<sup>+</sup><sub>q',p' </sub>in L<sup>p</sup>w</sub>-spaces for arbitrary p,q∈[1,∞). We have proved in the case of one singular end-point that all well-posed extensions of the minimal operator T<sub>0</sub> (τ<sub>p,q</sub>) generated by such expression τ<sub>p,q</sub> and their formal adjoint on the interval [a,b) with maximal deficiency indices have resolvents which are Hilbert-Schmidt integral operators and consequently have a wholly discrete spectrum. This implies that all the regularly solvable operators have all the standard essential spectra to be empty. Also, a number of results concerning the location of the point spectra and regularity fields of the operators generated by such expressions can be obtained. Some of these results are extensions or generalizations of those in the symmetric case, while others are new.
