Search results for "Theorem"
showing 10 items of 1250 documents
Emmy Noether’s Long Struggle to Habilitate in Göttingen
2020
Doctoral degrees have a long prehistory, but the modern Ph.D. first arose as part of an educational reform launched at the German universities. Over the course of the nineteenth century, this degree came to be awarded not merely to those who displayed a command of established knowledge in an academic field.
Diving into Math with Emmy Noether
2020
Some 100 years ago a notice appeared in the journal of the German Mathematical Society that read: “Dr. Emmy Noether has habilitated as a lecturer in mathematics at Gottingen University.” This quiet announcement was actually the resounding final chord in a long struggle that went on for four years and only ended on June 4, 1919, when Noether joined the Gottingen faculty.
National, regional, and global trends in systolic blood pressure since 1980: systematic analysis of health examination surveys and epidemiological st…
2011
Summary Background Data for trends in blood pressure are needed to understand the effects of its dietary, lifestyle, and pharmacological determinants; set intervention priorities; and evaluate national programmes. However, few worldwide analyses of trends in blood pressure have been done. We estimated worldwide trends in population mean systolic blood pressure (SBP). Methods We estimated trends and their uncertainties in mean SBP for adults 25 years and older in 199 countries and territories. We obtained data from published and unpublished health examination surveys and epidemiological studies (786 country-years and 5·4 million participants). For each sex, we used a Bayesian hierarchical mo…
National, regional, and global trends in serum total cholesterol since 1980: systematic analysis of health examination surveys and epidemiological st…
2011
Summary Background Data for trends in serum cholesterol are needed to understand the effects of its dietary, lifestyle, and pharmacological determinants; set intervention priorities; and evaluate national programmes. Previous analyses of trends in serum cholesterol were limited to a few countries, with no consistent and comparable global analysis. We estimated worldwide trends in population mean serum total cholesterol. Methods We estimated trends and their uncertainties in mean serum total cholesterol for adults 25 years and older in 199 countries and territories. We obtained data from published and unpublished health examination surveys and epidemiological studies (321 country-years and 3…
National, regional, and global trends in body-mass index since 1980: systematic analysis of health examination surveys and epidemiological studies wi…
2011
Summary Background Excess bodyweight is a major public health concern. However, few worldwide comparative analyses of long-term trends of body-mass index (BMI) have been done, and none have used recent national health examination surveys. We estimated worldwide trends in population mean BMI. Methods We estimated trends and their uncertainties of mean BMI for adults 20 years and older in 199 countries and territories. We obtained data from published and unpublished health examination surveys and epidemiological studies (960 country-years and 9·1 million participants). For each sex, we used a Bayesian hierarchical model to estimate mean BMI by age, country, and year, accounting for whether a …
Exact simulation of first exit times for one-dimensional diffusion processes
2019
International audience; The simulation of exit times for diffusion processes is a challenging task since it concerns many applications in different fields like mathematical finance, neuroscience, reliability horizontal ellipsis The usual procedure is to use discretization schemes which unfortunately introduce some error in the target distribution. Our aim is to present a new algorithm which simulates exactly the exit time for one-dimensional diffusions. This acceptance-rejection algorithm requires to simulate exactly the exit time of the Brownian motion on one side and the Brownian position at a given time, constrained not to have exit before, on the other side. Crucial tools in this study …
The Poincar\'e-Cartan Form in Superfield Theory
2018
An intrinsic description of the Hamilton-Cartan formalism for first-order Berezinian variational problems determined by a submersion of supermanifolds is given. This is achieved by studying the associated higher-order graded variational problem through the Poincar\'e-Cartan form. Noether theorem and examples from superfield theory and supermechanics are also discussed.
A consistent microscopic theory of collective motion in the framework of an ATDHF approach
1978
Based on merely two assumptions, namely the existence of a collective Hamiltonian and that the collective motion evolves along Slater determinants, we first derive a set of adiabatic time-dependent Hartree-Fock equations (ATDHF) which determine the collective path, the mass and the potential, second give a unique procedure for quantizing the resulting classical collective Hamiltonian, and third explain how to use the collective wavefunctions, which are eigenstates of the quantized Hamiltonian.
Conformality and $Q$-harmonicity in sub-Riemannian manifolds
2016
We prove the equivalence of several natural notions of conformal maps between sub-Riemannian manifolds. Our main contribution is in the setting of those manifolds that support a suitable regularity theory for subelliptic $p$-Laplacian operators. For such manifolds we prove a Liouville-type theorem, i.e., 1-quasiconformal maps are smooth. In particular, we prove that contact manifolds support the suitable regularity. The main new technical tools are a sub-Riemannian version of p-harmonic coordinates and a technique of propagation of regularity from horizontal layers.
Modelling the presence of disease under spatial misalignment using Bayesian latent Gaussian models.
2015
Modelling patterns of the spatial incidence of diseases using local environmental factors has been a growing problem in the last few years. Geostatistical models have become popular lately because they allow estimating and predicting the underlying disease risk and relating it with possible risk factors. Our approach to these models is based on the fact that the presence/absence of a disease can be expressed with a hierarchical Bayesian spatial model that incorporates the information provided by the geographical and environmental characteristics of the region of interest. Nevertheless, our main interest here is to tackle the misalignment problem arising when information about possible covar…