The Analysis of the Effectiveness of Implementing Emission Reduction Measures in Improving Air Quality and Health of the Residents of a Selected Area of the Lower Silesian Voivodship

The case study selected in order to analyze and evaluate the effectiveness of implemented solutions for improving air quality with the WRF-CALMET/CALPUFF modeling system as an element of decision support was the subject of this paper. Its character can be considered unique due to its geographical location, topography and the functioning PGE GiEK S.A. Turów Power Complex (ELT), and, in particular, the PGE GiEK S.A. Turów Coal Mine (KWBT). The conducted analyses have defined three scenarios of emission changes: (1) scenario related to the activities of the energy complex resulting from the minimizing measures indicated in the report on the environmental impact of the mine, (2) scenario resulting from the so-called “anti-smog” regional resolution and (3) scenario compiling the abovementioned scenarios. According to the analyses, the lowest values of the annual mean PM2.5 concentration were noted in the eastern part of the studied area and did not exceed 14 µg/m3 (56% of the permissible level). The best results in improving air quality were proven for scenario 3, i.e., a 10% reduction in concentration values over the entire analyzed area of the commune. In the case of this scenario, as the most effective and health-promoting solution, only in 25% of the area was the improvement in the residents’ health below 5%, while the reduction in the estimated number of premature deaths by over 15% was observed in nearly one third of the studied area.

Convergence of the solutions of discounted Hamilton–Jacobi systems

We consider a weakly coupled system of discounted Hamilton–Jacobi equations set on a closed Riemannian manifold. We prove that the corresponding solutions converge to a specific solution of the limit system as the discount factor goes to 0. The analysis is based on a generalization of the theory of Mather minimizing measures for Hamilton–Jacobi systems and on suitable random representation formulae for the discounted solutions.

Action-Minimizing Invariant Measures for Tonelli Lagrangians

This chapter discusses the notion of action-minimizing measures, recalling the needed measure–theoretical material. In particular, this allows the definition of a first family of invariant sets, the so-called Mather sets. It discusses their main dynamical and symplectic properties, and introduces the minimal average actions, sometimes called Mather's α‎- and β‎-functions. A thorough discussion of their properties (differentiability, strict convexity or lack thereof) is provided and related to the dynamical and structural properties of the Mather sets. The chapter also describes these concepts in a concrete physical example: the simple pendulum.

Lower and upper bounds for the Lyapunov exponents of twisting dynamics: a relationship between the exponents and the angle of Oseledets’ splitting

We consider locally minimizing measures for conservative twist maps of the $d$-dimensional annulus and for Tonelli Hamiltonian flows defined on a cotangent bundle $T^*M$. For weakly hyperbolic measures of such type (i.e. measures with no zero Lyapunov exponents), we prove that the mean distance/angle between the stable and unstable Oseledets bundles gives an upper bound on the sum of the positive Lyapunov exponents and a lower bound on the smallest positive Lyapunov exponent. We also prove some more precise results.

Majorization of invariant measures for orientation-reversing maps

Let the invariant probability measures for an orientation-reversing weakly expanding map of the interval [0,1] be partially ordered by majorization. The minimal elements of the resulting poset are shown to be convex combinations of Dirac measures supported on two adjacent fixed points. A consequence is that if f:[0,1]→ℝ is strictly convex, then either its minimizing measure is unique and is a Dirac measure on a fixed point, or f has precisely two ergodic minimizing measures, namely Dirac measures on two adjacent fixed points. In the case where {0,1} is a period-two orbit, with corresponding invariant measure μ01, the maximal elements of the poset are shown to be convex combinations of μ01 with the Dirac measure on either the leftmost, or the rightmost, fixed point. This facilitates the identification of f-maximizing measures when f:[0,1]→ℝ is convex.