Ambarzumyan-type theorem for the Sturm-Liouville operator on the lasso graph

We consider the Sturm-Liouville operator on the lasso graph with a segment and a loop joined at one point, which has arbitrary length. The Ambarzumyan's theorem for the operator is proved, which says that if the eigenvalues of the operator coincide with those of the zero potential, then the potential is zero

Inverse problems for Dirac operators with a constant delay less than half of the interval

In this work, we consider Dirac-type operators with a constant delay less than half of the interval and not less than two-fifths of the interval. For our considered Dirac-type operators, two inverse spectral problems are studied. Specifically, reconstruction of two complex $L_{2}$-potentials is studied from complete spectra of two boundary value problems with one common Dirichlet boundary condition and Neumann boundary condition, respectively. We give answers to the full range of questions usually raised in the inverse spectral theory. That is, we give uniqueness, necessary and sufficient conditions of the solvability, reconstruction algorithm and uniform stability for our considered inverse problems.Comment: arXiv admin note: text overlap with arXiv:2204.08259 by other author

Prevalence and Anthropometric Risk of Metabolic Syndrome in Taiwanese Adolescents

Background. To evaluate the prevalence and the importance of anthropometric indexes on metabolic syndrome (MetS) among young adolescents in Taiwan. Methods. We conducted a cross sectional survey to obtain a representative sampling among Taipei adolescents in 2003, totally enrolled of 1,562 adolescents (764 boys and 798 girls) from age 11 to 15. We used modified NCEP-ATP III criteria to diagnose metabolic syndrome in young adolescents including: blood pressure ≧90th percentile, fasting glucose ≧90th, TG ≧ 90th, HDL-C ≦ 10th, and BMI or WC ≧ 90th according to age and gender specific recommendations. Results. The overall prevalence of MetS was 4.8% for boys and 3.9% for girls. BMI and WC were significantly associated with MetS for both boys and girls, even after adjusting for age, cigarette smoking, alcohol drinking and pubertal status. However, after further adjusting for BMI or WC, WC for boys (OR = 1.14, 95% CI = 1.05–1.24) and BMI for girls (OR = 1.36, 95% CI = 1.13–1.64) were significantly associated with MetS. Conclusions. Adolescents with abnormal BMI or waist circumference had 10 to 20 times higher odds of MetS when compared to normal subjects. Obesity, either general or central adiposity, may play an important role in the development of MetS among adolescents