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

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

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

Rationale and design of TransplantLines:a prospective cohort study and biobank of solid organ transplant recipients

Introduction In the past decades, short-term results after solid organ transplantation have markedly improved. Disappointingly, this has not been accompanied by parallel improvements in long-term outcomes after transplantation. To improve graft and recipient outcomes, identification of potentially modifiable risk factors and development of biomarkers are required. We provide the rationale and design of a large prospective cohort study of solid organ transplant recipients (TransplantLines). Methods and analysis TransplantLines is designed as a single-centre, prospective cohort study and biobank including all different types of solid organ transplant recipients as well as living organ donors. Data will be collected from transplant candidates before transplantation, during transplantation, at 3 months, 6 months, 1 year, 2 years and 5 years, and subsequently every 5 years after transplantation. Data from living organ donors will be collected before donation, during donation, at 3 months, 1 year and 5 years after donation, and subsequently every 5 years. The primary outcomes are mortality and graft failure. The secondary outcomes will be cause-specific mortality, cause-specific graft failure and rejection. The tertiary outcomes will be other health problems, including diabetes, obesity, hypertension, hypercholesterolaemia and cardiovascular disease, and disturbances that relate to quality of life, that is, physical and psychological functioning, including quality of sleep, and neurological problems such as tremor and polyneuropathy. Ethics and dissemination Ethical approval has been obtained from the relevant local ethics committee. The TransplantLines cohort study is designed to deliver pioneering insights into transplantation and donation outcomes. The study design allows comprehensive data collection on perioperative care, nutrition, social and psychological functioning, and biochemical parameters. This may provide a rationale for future intervention strategies to more individualised, patient-centred transplant care and individualisation of treatment

Beta-glucan incorporated into a fruit drink effectively lowers serum LDL-cholesterol concentrations

Background: beta-Glucan can reduce serum concentrations of total and LDL cholesterol. The mechanism of this action is not clear, however, and it is difficult to predict the cholesterol-lowering effect of a food product enriched with beta-glucan. Objectives: We examined the effects of a beta-glucan-enriched fruit juice on serum lipids and lipoproteins and on markers of cholesterol absorption (serum concentrations of plant sterols) and synthesis (serum concentrations of lathosierol). In addition, we measured effects on lipid-soluble antioxidants. Design: After a 3-wk run-in period, healthy subjects consumed daily a fruit drink providing 5 g rice starch [placebo (control) group; n = 22] or beta-glucan from oats (n = 25) for 5 wk (parallel design). At the end of the run-in period and at the end of the intervention, blood samples were taken for analysis of lipids and lipoproteins, noncholesterol sterols, and fat-soluble antioxidants. Changes between the end of the run-in period and the end of the intervention were calculated for each subject. Differences in changes between the groups were analyzed statistically. Results: The differences between the control and beta-glucan groups in the chance in serum concentrations of total and LDL cholesterol, respectively, were -4.8% (P = 0.012) and -7.7% (P = 0.005). The differences between the groups in the change in serum concentrations of lathosterol and sitosterol were -13% (P = 0.023) and -11 % (P = 0.030), respectively. No significant effects were found on fat-soluble antioxidants. Conclusions: beta-Glucan lowers serum concentrations of total and LDL cholesterol when incorporated into a fruit drink. A reduced cholesterol absorption contributes to the cholesterol-lowering effect of beta-glucan without affecting plasma concentrations of lipid-soluble antioxidants

Beta-glucan incorporated into a fruit drink effectively lowers serum LDL-cholesterol concentrations

BACKGROUND: beta-Glucan can reduce serum concentrations of total and LDL cholesterol. The mechanism of this action is not clear, however, and it is difficult to predict the cholesterol-lowering effect of a food product enriched with beta-glucan. OBJECTIVES: We examined the effects of a beta-glucan-enriched fruit juice on serum lipids and lipoproteins and on markers of cholesterol absorption (serum concentrations of plant sterols) and synthesis (serum concentrations of lathosterol). In addition, we measured effects on lipid-soluble antioxidants. DESIGN: After a 3-wk run-in period, healthy subjects consumed daily a fruit drink providing 5 g rice starch [placebo (control) group; n = 22] or beta-glucan from oats (n = 25) for 5 wk (parallel design). At the end of the run-in period and at the end of the intervention, blood samples were taken for analysis of lipids and lipoproteins, noncholesterol sterols, and fat-soluble antioxidants. Changes between the end of the run-in period and the end of the intervention were calculated for each subject. Differences in changes between the groups were analyzed statistically. RESULTS: The differences between the control and beta-glucan groups in the change in serum concentrations of total and LDL cholesterol, respectively, were -4.8% (P = 0.012) and -7.7% (P = 0.005). The differences between the groups in the change in serum concentrations of lathosterol and sitosterol were -13% (P = 0.023) and -11% (P = 0.030), respectively. No significant effects were found on fat-soluble antioxidants. CONCLUSIONS: Beta-glucan lowers serum concentrations of total and LDL cholesterol when incorporated into a fruit drink. A reduced cholesterol absorption contributes to the cholesterol-lowering effect of beta-glucan without affecting plasma concentrations of lipid-soluble antioxidants