18 resultados para wave equation
Resumo:
Background: Type 2 diabetes patients have a 2-4 fold risk of cardiovascular disease (CVD) compared to the general population. In type 2 diabetes, several CVD risk factors have been identified, including obesity, hypertension, hyperglycemia, proteinuria, sedentary lifestyle and dyslipidemia. Although much of the excess CVD risk can be attributed to these risk factors, a significant proportion is still unknown. Aims: To assess in middle-aged type 2 diabetic subjects the joint relations of several conventional and non-conventional CVD risk factors with respect to cardiovascular and total mortality. Subjects and methods: This thesis is part of a large prospective, population based East-West type 2 diabetes study that was launched in 1982-1984. It includes 1,059 middle-aged (45-64 years old) participants. At baseline, a thorough clinical examination and laboratory measurements were performed and an ECG was recorded. The latest follow-up study was performed 18 years later in January 2001 (when the subjects were 63-81 years old). The study endpoints were total mortality and mortality due to CVD, coronary heart disease (CHD) and stroke. Results: Physically more active patients had significantly reduced total, CVD and CHD mortality independent of high-sensitivity C-reactive protein (hs-CRP) levels unless proteinuria was present. Among physically active patients with a hs-CRP level >3 mg/L, the prognosis of CVD mortality was similar to patients with hs-CRP levels ≤3 mg/L. The worst prognosis was among physically inactive patients with hs-CRP levels >3 mg/L. Physically active patients with proteinuria had significantly increased total and CVD mortality by multivariate analyses. After adjustment for confounding factors, patients with proteinuria and a systolic BP <130 mmHg had a significant increase in total and CVD mortality compared to those with a systolic BP between 130 and 160 mmHg. The prognosis was similar in patients with a systolic BP <130 mmHg and ≥160 mmHg. Among patients without proteinuria, a systolic BP <130 mmHg was associated with a non-significant reduction in mortality. A P wave duration ≥114 ms was associated with a 2.5-fold increase in stroke mortality among patients with prevalent CHD or claudication. This finding persisted in multivariable analyses. Among patients with no comorbidities, there was no relationship between P wave duration and stroke mortality. Conclusions: Physical activity reduces total and CVD mortality in patients with type 2 diabetes without proteinuria or with elevated levels of hs-CRP, suggesting that the anti-inflammatory effect of physical activity can counteract increased CVD morbidity and mortality associated with a high CRP level. In patients with proteinuria the protective effect was not, however, present. Among patients with proteinuria, systolic BP <130 mmHg may increase mortality due to CVD. These results demonstrate the importance of early intervention to prevent CVD and to control all-cause mortality among patients with type 2 diabetes. The presence of proteinuria should be taken into account when defining the target systolic BP level for prevention of CVD deaths. A prolongation of the duration of the P wave was associated with increased stroke mortality among high-risk patients with type 2 diabetes. P wave duration is easy to measure and merits further examination to evaluate its importance for estimation of the risk of stroke among patients with type 2 diabetes.
Resumo:
In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.
Resumo:
In this work we look at two different 1-dimensional quantum systems. The potentials for these systems are a linear potential in an infinite well and an inverted harmonic oscillator in an infinite well. We will solve the Schrödinger equation for both of these systems and get the energy eigenvalues and eigenfunctions. The solutions are obtained by using the boundary conditions and numerical methods. The motivation for our study comes from experimental background. For the linear potential we have two different boundary conditions. The first one is the so called normal boundary condition in which the wave function goes to zero on the edge of the well. The second condition is called derivative boundary condition in which the derivative of the wave function goes to zero on the edge of the well. The actual solutions are Airy functions. In the case of the inverted oscillator the solutions are parabolic cylinder functions and they are solved only using the normal boundary condition. Both of the potentials are compared with the particle in a box solutions. We will also present figures and tables from which we can see how the solutions look like. The similarities and differences with the particle in a box solution are also shown visually. The figures and calculations are done using mathematical software. We will also compare the linear potential to a case where the infinite wall is only on the left side. For this case we will also show graphical information of the different properties. With the inverted harmonic oscillator we will take a closer look at the quantum mechanical tunneling. We present some of the history of the quantum tunneling theory, its developers and finally we show the Feynman path integral theory. This theory enables us to get the instanton solutions. The instanton solutions are a way to look at the tunneling properties of the quantum system. The results are compared with the solutions of the double-well potential which is very similar to our case as a quantum system. The solutions are obtained using the same methods which makes the comparison relatively easy. All in all we consider and go through some of the stages of the quantum theory. We also look at the different ways to interpret the theory. We also present the special functions that are needed in our solutions, and look at the properties and different relations to other special functions. It is essential to notice that it is possible to use different mathematical formalisms to get the desired result. The quantum theory has been built for over one hundred years and it has different approaches. Different aspects make it possible to look at different things.
