A description of direct simulation of crosswind loads caused by critical vortex excitation and the response of the structure to these loads are presented in this paper. Tower-like structures of circular cross-sections are considered. A proposed mathematical model of vortex excitation has been numerically implemented and a selfserving computer program was created for the purpose. This software, cooperating with the FEM system, allows for a simulation of a crosswind load and lateral response in real time, meaning that at each time step of the calculations the load is generated using information regarding displacements seen beforehand. A detailed description of the mathematical model is neglected in this paper, which is focused on numerical simulations. WAWS and AR methods are used in simulations.

This article aims at constructing a new method for testing the statistical significance of seasonal fluctuations for non-stationary processes. The constructed test is based on a method of subsampling and on the spectral theory of Almost Periodically Correlated (APC) time series. In the article we consider an equation of a nonstationary process, containing a component which includes seasonal fluctuations and business cycle fluctuations, both described by an almost periodic function. We build subsampling test justifying the significance of frequencies obtained from the Fourier representation of the unconditional expectation of the process.

The empirical usefulness of the constructed test is examined for selected macroeconomic data. The article studies survey indicators of economic climate in industry, retail trade and consumption for European countries.

We discuss the empirical importance of long term cyclical effects in the volatility of financial returns. Following Amado and Teräsvirta (2009), ČiŽek and Spokoiny (2009) and others, we consider a general conditionally heteroscedastic process with stationarity property distorted by a deterministic function that governs the possible time variability of the unconditional variance. The function proposed in this paper can be interpreted as a finite Fourier approximation of an Almost Periodic (AP) function as defined by Corduneanu (1989). The resulting model has a particular form of a GARCH process with time varying parameters, intensively discussed in the recent literature.

In the empirical analyses we apply a generalisation of the Bayesian AR(1)-GARCH model for daily returns of S&P500, covering the period of sixty years of US postwar economy, including the recently observed global financial crisis. The results of a formal Bayesian model comparison clearly indicate the existence of significant long term cyclical patterns in volatility with a strongly supported periodic component corresponding to a 14 year cycle. Our main results are invariant with respect to the changes of the conditional distribution from Normal to Student-tand to the changes of the volatility equation from regular GARCH to the Asymmetric GARCH.

This paper presents new directions in the modeling of electric arc furnaces. This work is devoted to an overview of new approaches based on random differential equations, artificial neural networks, chaos theory, and fractional calculus. The foundation of proposed solutions consists of an instantaneous power balance equation related to the electric arc phenomenon. The emphasis is mostly placed on the conclusions that come from a novel interpretation of the equation coefficients.