Estimation of NO2 and SO2 concentration changes in Europe from meteorological data with Neural Network

<p>Chemical substances of anthropogenic and natural origin released into the atmosphere affect air quality and, as a consequence, the health of the population. As a result, there is a demand for reliable air quality simulations and future scenarios investigating the effects of emission reduction measures. Due to high computational costs, the prediction of concentrations of chemical substances with discretized atmospheric chemistry transport models (CTM) is still a great challenge. An alternative to the cumbersome numerical estimates is a computationally efficient neural network (NN). The design of the NN is much simpler than a CTM and allows approximating any bounded continuous function (i.e., concentration time series) with the desired accuracy. In particular, the NN trained on a set of CTM estimates can produce similar to CTM estimates up to the approximation error. We test the ability of a NN to produce CTM concentration estimates with the example of daily mean summer NO2 and SO2 concentrations. The measures of success in these tests are the difference in the consumption of computational resources and the difference between NN and CTM concentration estimates. Relying on the fact that after spin-up, CTM estimates are independent of the initial concentrations, we show that recurrent NN can also spin-up and predict atmospheric chemical state without having input concentration data. Moreover, we show that if the emission scenario does not change significantly from year to year, the NN can predict daily mean concentrations from meteorological data only.</p>

EXISTENCE OF S-ASYMPTOTICALLY ω-PERIODIC SOLUTIONS FOR ABSTRACT NEUTRAL EQUATIONS

A bounded continuous function $u:[0,\infty )\to X$ is said to be S-asymptotically ω-periodic if $ \lim _{t\to \infty }[ u(t+\omega ) -u(t)]=0$. This paper is devoted to study the existence and qualitative properties of S-asymptotically ω-periodic mild solutions for some classes of abstract neutral functional differential equations with infinite delay. Furthermore, applications to partial differential equations are given.

Characterizations of vector-valued weakly almost periodic functions

We characterize the weak almost periodicity of a vector-valued, bounded, continuous function. We show that if the range of the function is relatively weakly compact, then the relative weak compactness of its right orbit is equivalent to that of its left orbit. At the same time, we give the function some other equivalent properties.

The Fourier transform of vector-valued functions

For each natural number n, let un(x)=(1—cos nx)/πnx2(xɛℝ). It is well–known that a bounded continuous function f on the real line ℝ is the Fourier transform of an integrable function on ℝ if and only if the functions Φn(f) (n= 1, 2,…), defined byform a Cauchy sequence in the space L1(ℝ) (cf. [2]). Such a characterization, which can be extended to functions defined on a locally compact Abelian group more general than ℝ, is based on the fact that the space L1(ℝ) is complete with respect to convergence in mean.

Non-Extendability of Bounded Continuous Functions

If X is a dense subspace of Y, much is known about the question of when every bounded continuous real-valued function on X extends to a continuous function on Y. Indeed, this is one of the central topics of [5]. In this paper we are interested in the opposite question: When are there continuous bounded real-valued functions on X which extend to no point of Y – X? (Of course, we cannot hope that every function on X fails to extend since the restrictions to X of continuous functions on Y extend to Y.) In this paper, we show that if Y is a compact metric space and if X is a dense subset of Y, then X admits a bounded continuous function which extends to no point of Y – X if and only if X is completely metrizable. We also show that for certain spaces Y and dense subsets X, the set of bounded functions on X which extend to a point of Y – X form a first category subset of C*(X).