Maciej Radziejewski

Fractal analysis of flow of the river Warta

Abstract A long time series (170 years) of daily flows of the river Warta (Poland) are subject to fractal analysis. A binary variable (renewal stream) illustrating excursions of the process of flow is examined. The raw series is subject to de-seasonalization and normalization. Fractal dimensions of crossings of Warta flows are determined using a novel variant of the box-counting method. Temporal variability of the flow process is studied by determination of fractal dimensions for shifted horizons of 10 or 30 years length. Spectral properties are compared between the time series of flows, and the fractional Brownian motion which describes both the fractal structure of the process and the Hurst phenomenon. The approach may be useful in further studies of non-stationary of the process of flow, analysis of extreme hydrological events and synthetic flow generation.

Projections of Future Anthropogenic Climate Change

This chapter focuses on summarising projections of future anthropogenic climate change for the Baltic Sea Basin. This includes the science of climate change and how future projections are made, taking into account anthropogenic influence on greenhouse gases (GHG). Looking forward to-ward future climates requires using state-of-the-art modelling tools to represent climate processes.

Weakly half-factorial sets in finite abelian groups

Abstract We investigate weakly half-factorial sets in finite abelian groups, a concept introduced by J. Śliwa to study half-factorial sets. We fully characterize weakly half-factorial sets in a given group, and determine the maximum cardinality of such a set. This leads to several new results on half-factorial sets; in particular we solve a problem of W. Narkiewicz in some special cases. We also study the arithmetical consequences of weakly-half-factoriality in terms of factorization lengths in block monoids.

About Trend Detection in River Floods

This chapter reviews some methods for studying changes in the occurrence of extreme river flows. Some general background information on change detection is given. Changes in various characteristics of high flows are investigated using a variety of approaches. Although many cases of statistically significant changes are found, they go in different directions and are of different character in different regions. There does not seem to be a clear, uniform signal of change, except for, possibly, the occurrence of most extreme flows that seems to be increasing in the recent decades.

Independence of Hecke zeta functions of finite order over normal fields

We study oscillations of the remainder term corresponding to the counting functions of the sets of elements with unique factorization length in semigroups of algebraic numbers such as the semigroup of algebraic integers or totally positive algebraic integers in a given normal field K. The results imply existence of oscillations when the exponent of the class group of the semigroup in question is sufficiently large depending on the fields degree. In particular, when K is a quadratic field or a normal cubic field oscillations exist whenever the class group is not isomorphic to C 2 a ⊕ C 3 b ⊕ C 4 c for nonnegative integers a,b,c. The main part of this study is concerned with the problem of multiplicative independence of Hecke zeta functions. We also show that there are infinitely many fields whose Dedekind zeta function has infinitely many nontrivial multiple zeros.