On strongly stable normal operators in Krein spaces

For bounded normal operators in Krein spaces we give a necessary and sufficient condition for strong stability. The same result for unitary operators was obtained by M.G.Krein [1] (see also [2]). For selfadjoint operators we refer to the papers of P.Jonas, H.Langer [3] and H.Langer [4].     

On Strongly Stable Normal Operators in Krein Spaces

We give a necessary and sufficient condition for strong stability of bounded normal operators in Krein spaces. A similar result was obtained for unitary operators by M. G. Krein [1], and for selfadjoint operators by H. Langer [2], [3].     

Heritability and linkage study on heart rates in a Mongolian population

Elevated heart rate has been proposed as an independent risk factor for cardiovascular diseases, but their interrelationships are not well understood. In this study, we performed a genome-wide linkage scan in 1,026 individuals (mean age 30.6 years, 54.5% women) from 73 extended families of Mongolia and determined quantitative trait loci that influence heart rate. The DNA samples were genotyped using deCODE 1,039 microsatellite markers for 3 cM density genome-wide linkage scan. Correlation analysis was carried out to evaluate the correlation of the covariates and the heart rate. T-tests of the heart rate were also performed on sex, smoking and alcohol intake. Consequently, this model was used in a nonparametric genome-wide linkage analysis using variance component model to create a multipoint logarithm of odds (LOD) score and a corresponding P value. In the adjusted model, the heritability of heart rate was estimated as 0.32 (P<.0001) and a maximum multipoint LOD score of 2.03 was observed in 77 cM region at chromosome 18. The second largest LOD score of 1.52 was seen on chromosome 5 at 216 cM. Genes located on the specified locations in chromosomes 5 and 18 may be involved in the regulation of heart rate.