Generalized Fourier transforms arising from the enveloping algebras of sl(2) and osp(1|2)

The Howe dual pair (sl(2),O(m)) allows the characterization of the classical Fourier transform (FT) on the space of rapidly decreasing functions as the exponential of a well-chosen element of sl(2) such that the Helmholtz relations are satisfied. In this paper we first investigate what happens when instead we consider exponentials of elements of the universal enveloping algebra of sl(2). This leads to a complete class of generalized Fourier transforms, that all satisfy properties similar to the classical FT. There is moreover a finite subset of transforms which very closely resemble the FT. We obtain operator exponential expressions for all these transforms by making extensive use of the theory of integer-valued polynomials. We also find a plane wave decomposition of their integral kernel and establish uncertainty principles. In important special cases we even obtain closed formulas for the integral kernels. In the second part of the paper, the same problem is considered for the dual pair (osp(1|2),Spin(m)), in the context of the Dirac operator. This connects our results with the Clifford-Fourier transform studied in previous work.Comment: Second version, changes in title, introduction and section

Exact solution of the position-dependent effective mass and angular frequency Schr\"odinger equation: harmonic oscillator model with quantized confinement parameter

We present an exact solution of a confined model of the non-relativistic quantum harmonic oscillator, where the effective mass and the angular frequency are dependent on the position. The free Hamiltonian of the proposed model has the form of the BenDaniel--Duke kinetic energy operator. The position-dependency of the mass and the angular frequency is such that the homogeneous nature of the harmonic oscillator force constant $k$ and hence the regular harmonic oscillator potential is preserved. As a consequence thereof, a quantization of the confinement parameter is observed. It is shown that the discrete energy spectrum of the confined harmonic oscillator with position-dependent mass and angular frequency is finite, has a non-equidistant form and depends on the confinement parameter. The wave functions of the stationary states of the confined oscillator with position-dependent mass and angular frequency are expressed in terms of the associated Legendre or Gegenbauer polynomials. In the limit where the confinement parameter tends to $\infty$, both the energy spectrum and the wave functions converge to the well-known equidistant energy spectrum and the wave functions of the stationary non-relativistic harmonic oscillator expressed in terms of Hermite polynomials. The position-dependent effective mass and angular frequency also become constant under this limit

Normstelling verspreidbare baggerspecie

Bij de huidige normstelling is het mogelijk dat bij het toepassen of verspreiden van baggerspecie landbouwpercelen niet meer voldoen of in de toekomst gaan voldoen aan de criteria voor landbouwkundig gebruik. In dit onderzoek zijn nieuwe normen afgeleid waardoor landbouwkundig gebruik gewaarborgd wordt. Er is nagegaan wat de consequenties van de voorgestelde normen zijn op de hoeveelheid te verspreiden baggerspecie. Gebruik makende van deze rapportage zullen de uiteindelijke normen beleidsmatig worden vastgesteld

Physical Activity and the Development of Post-Transplant Diabetes Mellitus, and Cardiovascular- and All-Cause Mortality in Renal Transplant Recipients

(1) Background: Little is currently known about the health impacts of daily-life moderate-to-vigorous physical activity (MVPA) in relation to the development of post-transplant diabetes mellitus (PTDM) and the long-term survival of renal transplant recipients (RTRs). (2) Methods: We analyzed self-reported data on MVPA within non-occupational and occupational domains, estimated with the SQUASH questionnaire, from a prospective cohort study of RTRs (n = 650) with a functioning graft exceeding 1 year. PTDM diagnoses were based on plasma glucose levels (>= 126 mg/dL), HbA1c (>= 6.5%), and the use of antidiabetic medication. Mortality data were retrieved from patient files up to the end of September 2015. (3) Results: During a median follow-up period of 5.3 years, 50 patients (10%) developed PTDM and 129 (19.8%) died. Of these deaths, 53 (8.9%) were caused by cardiovascular disease. Cox regression analyses showed that higher MVPA levels among patients were associated with a lower risk of PTDM (hazard ratio (HR); 95% confidence interval (95%CI) = 0.49; 0.25-0.96, p = 0.04), cardiovascular- (0.34; 0.15-0.77, p = 0.01), and all-cause mortality (0.37; 0.24-0.58, p <0.001) compared with No-MVPA patients, independently of age, sex, and kidney function parameters. Associations of MVPA with cardiovascular and all-cause mortality remained significant and materially unchanged following further adjustments made for transplant characteristics, lifestyle factors, metabolic parameters, medication use, and creatinine excretion (muscle mass). However, the association between MVPA and PTDM was no longer significant after we adjusted for metabolic confounders and glucose levels. (4) Conclusion: Higher MVPA levels are associated with long-term health outcomes in RTRs

Ações de gestão e infraestrutura na Embrapa Instrumentação Agropecuária visando sistemas de qualidade.

bitstream/CNPDIA-2009-09/11891/1/CT94_2008.pd

High Plasma Branched-Chain Amino Acids Are Associated with Higher Risk of Post-Transplant Diabetes Mellitus in Renal Transplant Recipients

Post-transplant diabetes mellitus (PTDM) is a serious complication in renal transplant recipients. Branched-chain amino acids (BCAAs) are involved in the pathogenesis of insulin resistance. We determined the association of plasma BCAAs with PTDM and included adult renal transplant recipients (>= 18 y) with a functioning graft for >= 1 year in this cross-sectional cohort study with prospective follow-up. Plasma BCAAs were measured in 518 subjects using nuclear magnetic resonance spectroscopy. We excluded subjects with a history of diabetes, leaving 368 non-diabetic renal transplant recipients eligible for analyses. Cox proportional hazards analyses were used to assess the association of BCAAs with the development of PTDM. Mean age was 51.1 +/- 13.6 y (53.6% men) and plasma BCAA was 377.6 +/- 82.5 mu M. During median follow-up of 5.3 (IQR, 4.2-6.0) y, 38 (9.8%) patients developed PTDM. BCAAs were associated with a higher risk of developing PTDM (HR: 1.43, 95% CI 1.08-1.89) per SD change (p = 0.01), independent of age and sex. Adjustment for other potential confounders did not significantly change this association, although adjustment for HbA1c eliminated it. The association was mediated to a considerable extent (53%) by HbA1c. The association was also modified by HbA1c; BCAAs were only associated with renal transplant recipients without prediabetes (HbA1c <5.7%). In conclusion, high concentrations of plasma BCAAs are associated with developing PTDM in renal transplant recipients. Alterations in BCAAs may represent an early predictive biomarker for PTDM

High Betaine, a Trimethylamine N-Oxide Related Metabolite, Is Prospectively Associated with Low Future Risk of Type 2 Diabetes Mellitus in the PREVEND Study

Background: Gut microbiota-related metabolites, trimethylamine-N-oxide (TMAO), choline, and betaine, have been shown to be associated with cardiovascular disease (CVD) risk. Moreover, lower plasma betaine concentrations have been reported in subjects with type 2 diabetes mellitus (T2DM). However, few studies have explored the association of betaine with incident T2DM, especially in the general population. The goals of this study were to evaluate the performance of a newly developed betaine assay and to prospectively explore the potential clinical associations of betaine and future risk of T2DM in a large population-based cohort. Methods: We developed a high-throughput, nuclear magnetic resonance (NMR) spectroscopy procedure for acquiring spectra that allow for the accurate quantification of plasma/serum betaine and TMAO. Assay performance for betaine quantification was assessed and Cox proportional hazards regression was employed to evaluate the association of betaine with incident T2DM in 4336 participants in the Prevention of Renal and Vascular End-Stage Disease (PREVEND) study. Results: Betaine assay results were linear (y = 1.02X - 3.75) over a wide range of concentrations (26.0-1135 mu M). The limit of blank (LOB), limit of detection (LOD) and limit of quantitation (LOQ) were 6.4, 8.9, and 13.2 mu M, respectively. Coefficients of variation for intra- and inter-assay precision ranged from 1.5-4.3% and 2.5-5.5%, respectively. Deming regression analysis of results produced by NMR and liquid chromatography coupled to tandem mass spectrometry(LC-MS/MS) revealed an R-2 value of 0.94 (Y = 1.08x - 1.89) and a small bias for higher values by NMR. The reference interval, in a cohort of apparently healthy adult participants (n = 501), was determined to be 23.8 to 74.7 mu M (mean of 42.9 +/- 12.6 mu M). In the PREVEND study (n = 4336, excluding subjects with T2DM at baseline), higher betaine was associated with older age and lower body mass index, total cholesterol, triglycerides, and hsCRP. During a median follow-up of 7.3 (interquartile range (IQR), 5.9-7.7) years, 224 new T2DM cases were ascertained. Cox proportional hazards regression models revealed that the highest tertile of betaine was associated with a lower incidence of T2DM. Hazard ratio (HR) for the crude model was 0.61 (95% CI: 0.44-0.85, p = 0.004). The association remained significant even after adjusting for multiple clinical covariates and T2DM risk factors, including fasting glucose. HR for the fully-adjusted model was 0.50 (95% CI: 0.32-0.80, p = 0.003). Conclusions: The newly developed NMR-based betaine assay exhibits performance characteristics that are consistent with usage in the clinical laboratory. Betaine levels may be useful for assessing the risk of future T2DM