On the covering dimension of the set of solutions of some nonlinear equations

We prove an abstract theorem whose sole hypothesis is that the degree of a certain map is nonzero and whose parametric equations are studied using cohomological mconclusions imply sharp, multidimensional continuation results. Applications are given to nonlinear partial differential equations

Complementing maps, continuation and global bifurcation

We state, and indicate some of the consequences of, a theorem whose sole assumption is the nonvanishing of the Leray- Schauder degree of a compact vector field, and whose conclusions yield multidimensional existence, continuation and bifurcation result

Structure and dimension of global branches of solutions to multiparameter nonlinear equations

A general study of the dimension and connectivity properties of branches of solutions of equations depending on n-parameters are studied using the homotopy properties of 0-epi maps

Complementing maps, continuation and global bifurcation

We state, and indicate some of the consequences of, a theorem whose sole assumption is the nonvanishing of the Leray- Schauder degree of a compact vector field, and whose conclusions yield multidimensional existence, continuation and bifurcation result

Comparison of different Aethalometer correction schemes and a reference multi-wavelength absorption technique for ambient aerosol data

Deriving absorption coefficients from Aethalometer attenuation data requires different corrections to compensate for artifacts related to filter-loading effects, scattering by filter fibers, and scattering by aerosol particles. In this study, two different correction schemes were applied to seven-wavelength Aethalometer data, using multi-angle absorption photometer (MAAP) data as a reference absorption measurement at 637 nm. The compensation algorithms were compared to five-wavelength offline absorption measurements obtained with a multi-wavelength absorbance analyzer (MWAA), which serves as a multiple-wavelength reference measurement. The online measurements took place in the Amazon rainforest, from the wet-to-dry transition season to the dry season (June\u2013September 2014). The mean absorption coefficient (at 637 nm) during this period was 1.8 +/-2.1Mm-1, with a maximum of 15.9Mm-1. Under these conditions, the filter-loading compensation was negligible. One of the correction schemes was found to artificially increase the short-wavelength absorption coefficients. It was found that accounting for the aerosol optical properties in the scattering compensation significantly affects the absorption \uc5ngstr\uf6m exponent (\ue5ABS/ retrievals. Proper Aethalometer data compensation schemes are crucial to retrieve the correct \ue5ABS, which is commonly implemented in brown carbon contribution calculations. Additionally, we found that the wavelength dependence of uncompensated Aethalometer attenuation data significantly correlates with the \ue5ABS retrieved from offline MWAA measurements

On the connectivity properties of the solution setof parametrized families of compact vector fields,

Using products in cohomology connected n-dimensional branches of zeroes of compact vector fields covering the parameter space are foun

Global several parameter bifurcation and continuation theorems: A unified approach via complementing maps

We use the concept of complementing map in order to present a unified approach to the continuation principle, global implicit function theorem and global bifurcation results for compact vector fields depending on several parameters