Local approximation of observables and commutator bounds

We discuss conditional expectations that can be used as generalizations of the partial trace for quantum systems with an infinite-dimensional Hilbert space of states

Decay bounds on eigenfunctions and the singular spectrum of unbounded Jacobi matrices

Bounds on the exponential decay of generalized eigenfunctions of bounded and unbounded selfadjoint Jacobi matrices are established. Two cases are considered separately: (i) the case in which the spectral parameter lies in a general gap of the spectrum of the Jacobi matrix and (ii) the case of a lower semi-bounded Jacobi matrix with values of the spectral parameter below the spectrum. It is demonstrated by examples that both results are sharp. We apply these results to obtain a "many barriers-type" criterion for the existence of square-summable generalized eigenfunctions of an unbounded Jacobi matrix at almost every value of the spectral parameter in suitable open sets. As an application, we provide examples of unbounded Jacobi matrices with a spectral mobility edge.Comment: This is a substantially revised and expanded version of 0711.4035v

Asymptotics of large eigenvalues for a class of band matrices

We investigate the asymptotic behaviour of large eigenvalues for a class of finite difference self-adjoint operators with compact resolvent in $l^2$

Postpregnancy glycemic control and weight changes in type 1 diabetic women

OBJECTIVE - Pregnancy in type 1 diabetes requires excellent glycemic control. Most pregnant type 1 diabetic women achieve normoglycemia; however, there is scarce data on their postdelivery characteristics. We aimed to examine postpregnancy glycemic control and weight changes in type 1 diabetes. RESEARCH DESIGN AND METHODS - We identified and followed (median 20 months) 254 women with singleton pregnancies receiving postdelivery medical care at a single institution. RESULTS - Study subjects were 28.3 6 4.7 years of age (mean 6 SD), with a diabetes duration of 12.0 6 7.7 years. Mean A1C before conception was 6.9 6 1.4%, and preconception weight and BMI were 64.4 6 10.0 kg and 23.9 6 3.3 kg/m2, respectively. Mean A1C decreased during pregnancy, reaching 5.7 6 0.8% in the third trimester. We observed a mean weight gain of 14.4 6 6.5 kg during pregnancy. Within 6 months after delivery, A1C increased by 0.8% (P , 0.0001) compared with the last trimester, and body weight and BMI were 4.4 kg and 2.5 kg/m2 higher (P , 0.0001) compared with the preconception baseline. A1C further deteriorated by 0.8% until the end of follow-up. For women in the "pregnancy planning" program (n = 117), A1C .12 months after delivery was worse compared with before conception (7.1 vs. 6.5%, P = 0.0018), whereas in women with unplanned pregnancies, it was similar to the pregestational levels (7.3 vs.7.4%, P = 0.59). Weight and BMI in the entire study group did not return to prepregnancy levels and were 2.5 kg (P = 0.0079) and 0.9 kg/m2 higher (P = 0.0058). CONCLUSIONS - In this clinical observation, type 1 diabetic women showed postpregnancy deterioration in glycemic control and were unable to return to prepregnancy weight. Type 1 diabetic women seem to require special attention after delivery to meet therapeutic targets

Risk of macrosomia remains glucose-dependent in a cohort of women with pregestational type 1 diabetes and good glycemic control

Macrosomia risk remains high in type 1 diabetes (T1DM) complicated pregnancies. A linear relationship between macrosomia risk and glycated hemoglobin A(1c) (HbA(1c)) was described; however, low range of HbA(1c) has not been studied. We aimed to identify risk factors and examine the impact of HbA(1c) on the occurrence of macrosomia in newborns of T1DM women from a cohort with good glycemic control. In this observational retrospective one-center study we analyzed records of 510 consecutive T1DM pregnancies (1998–2012). The analyzed group consisted of 375 term singleton pregnancies. We used multiple regression models to examine the impact of HbA(1c) and self-monitored glucose in each trimester on the risk of macrosomia and birth weight. The median age of T1DM women was 28 years, median T1DM duration—11 years, median pregestational BMI—23.3 kg/m(2). Median birth weight reached 3520 g (1st and 3rd quartiles 3150 and 3960, respectively) at median 39 weeks of gestation. There were 85 (22.7 %) macrosomic (>4000 g) newborns. Median HbA(1c) levels in the 1st, 2nd, and 3rd trimester were 6.4, 5.7, and 5.6 %. Third trimester HbA(1c), mean fasting self-monitored glucose and maternal age were independent predictors of birth weight and macrosomia. There was a linear relationship between 3rd trimester HbA(1c) and macrosomia risk in HbA(1c) range from 4.5 to 7.0 %. Macrosomia in children of T1DM mothers was common despite excellent metabolic control. Glycemia during the 3rd trimester was predominantly responsible for this condition

On Unbounded Composition Operators in L2L^2-Spaces

Fundamental properties of unbounded composition operators in $L^2$-spaces are studied. Characterizations of normal and quasinormal composition operators are provided. Formally normal composition operators are shown to be normal. Composition operators generating Stieltjes moment sequences are completely characterized. The unbounded counterparts of the celebrated Lambert's characterizations of subnormality of bounded composition operators are shown to be false. Various illustrative examples are supplied