Linear convergence of accelerated conditional gradient algorithms in spaces of measures

A class of generalized conditional gradient algorithms for the solution of optimization problem in spaces of Radon measures is presented. The method iteratively inserts additional Dirac-delta functions and optimizes the corresponding coefficients. Under general assumptions, a sub-linear [see formula in PDF] rate in the objective functional is obtained, which is sharp in most cases. To improve efficiency, one can fully resolve the finite-dimensional subproblems occurring in each iteration of the method. We provide an analysis for the resulting procedure: under a structural assumption on the optimal solution, a linear [see formula in PDF] convergence rate is obtained locally.

The Brazilian nursing workforce faced with the international trends: an analysis in the International Year of Nursing

The article analyzes the condition of the Brazilian Nursing workforce when confronted with international trends. Diagnoses in publications by international organizations marked the confrontation of international trends with the reality of Brazilian Nursing, based on secondary research data. The analysis allows asserting that the Brazilian Nursing workforce follows international trends, essentially, because the social and sexual division of work and the foundations of the origin of Nursing as a capitalist occupation are maintained. At the same time, the historical-structural assumption of female proletarianization is based on the following: the disparities between men and women in pay and access to prominent positions in the market; combined inequalities across nations and regions in the supply of the labor market, which stimulates immigration of professionals; exploitation of older professionals, in the context of restricted access to retirement and labor rights; and exposure to violence and harassment, associated with the potential for overload and work intensification, which result in workers contracting diseases. In summary, it is observed that the pillars of female proletarianization and professionalization of Nursing remain in today's differentiated forms of workforce exploitation, being configured depending on the intersections of gender, racial-ethnicity, and regional-nationality.

Solutions of the differential inequality with a null Lagrangian: higher integrability and removability of singularities. I

The aim of this paper is to derive the self-improving property of integrability for derivatives of solutions of the differential inequality with a null Lagrangian. More precisely, we prove that the solution of the Sobolev class with some Sobolev exponent slightly smaller than the natural one determined by the structural assumption on the involved null Lagrangian actually belongs to the Sobolev class with some Sobolev exponent slightly larger than this natural exponent. We also apply this property to improve Holder regularity and stability theorems of [19].

Is Brownian Motion Really Necessary?

The mathematical treatment of models relying on pure jump processes is quite different from the treatment of models where a Brownian motion is present. For instance, risk management procedures, derivative pricing and portfolio optimization are all significantly altered, so there is interest from the mathematical finance side in finding out which model is more likely to have generated the data. This chapter provides explicit testing procedures to decide whether the Brownian motion is necessary to model the observed path, or whether the process is entirely driven by its jumps. The structural assumption is the same as in the previous two chapters, with the underlying process X being a one-dimensional Itô semimartingale, since in the multi-dimensional case we can again perform the test on each component separately.

NON-PERIODIC Γ-CONVERGENCE: APPLICATION TO A MAIN EXAMPLE OF A NON-FINER OSCILLATION OPERATOR IN HIGHER DIMENSION

We generalize, to a higher dimension, a main example of an operator that enjoys the NFO property introduced recently in [13]. It turns out that this issue is intimately connected to Γ-convergence of functionals in a non-periodic, general setting. Under a main structural assumption on the sequence of functionals, the Γ-convergence limit is computable. As a consequence of our analysis, we obtain the generalization just mentioned, opening thus the way to treat the existence for some nonlinear PDEs in divergence form.

REGULARITY OF SOLUTIONS TO CHARACTERISTIC INITIAL-BOUNDARY VALUE PROBLEMS FOR SYMMETRIZABLE SYSTEMS

We consider the initial-boundary value problem for linear Friedrichs symmetrizable systems with characteristic boundary of constant rank. We assume the existence of the strong L2 solution satisfying a suitable energy estimate, but we do not assume any structural assumption sufficient for existence, such as the fact that the boundary conditions are maximally dissipative or the Kreiss–Lopatinski condition. We show that this is enough in order to get the regularity of solutions, in the natural framework of weighted anisotropic Sobolev spaces, provided the data are sufficiently smooth.

QUALITATIVE BEHAVIOR OF SOLUTIONS OF A DEGENERATE NONLINEAR DRIFT-DIFFUSION MODEL FOR SEMICONDUCTORS

We are concerned with qualitative properties of transient solutions of a degenerate multi-dimensional quasi-hydrodynamic model for semiconductors with nonlinear diffusivities. For small time and sufficiently small initial and boundary data we show a local vanishing property of a solution. Furthermore it is shown that the carrier densities are bounded uniformly in time and are strictly positive uniformly in time if the recombination-generation rate satisfies some structural assumption. Finally we construct a Lyapunov functional in order to show convergence of the carrier distributions to the thermal equilibrium state as the time tends to infinity.