Metric connections with parallel twistor-free torsion

The torsion of every metric connection on a Riemannian manifold has three components: one totally skew-symmetric, one of vectorial type and one of twistorial type, which is also called the traceless cyclic component. In this paper we classify complete simply connected Riemannian manifolds carrying a metric connection whose torsion is parallel, has nonzero vectorial component and vanishing twistorial component.

Цифровая синергетика взаимодействия внутригодовой активности экономической деятельности и годовой динамики валового внутреннего продукта

According to the results of the decomposition of the observed levels of quarterly GDP indicators statistically relevant components of its dynamics are identified: the dynamic component of seasonal cyclic nature, the trend-cyclic component, and that of short-term fluctuations. A methodology is suggested for studying the impact of within-year economic activity energy on the dynamics of annual GDP indicators. The research analytics was tested on the actual materials of annual and quarterly indicators of the Gross Domestic Product of the Republic of Belarus over the period of 2009–2017.

MONEY LAUNDERING RISK IN DEVELOPING AND TRANSITIVE ECONOMIES: ANALYSIS OF CYCLIC COMPONENT OF TIME SERIES

Money laundering has become a global threat to the international stability and security, leading both to economic and social upheavals, and to an increase in terrorist threats. Therefore, an objective necessity arises for a more detailed study of the money laundering within the scope of its developmental patterns and time-dependent behaviour. The study mission is the development of a theoretical framework and methodological support for modelling the cyclic component of the money laundering risk. The correlation and regression are used for isolating the cyclic component. In turn, the Fourier harmonic analysis allows specifying the cyclic component. Additionally, we carried out a decomposition of time series, analysis of its volatility and persistence using the Hurst exponent. We determined the peaks, downturns and duration of the money laundering cycles in the developed economies and economies in transition, and established the possibility of predicting this process in the medium term. We proved the internationalization of the money laundering and the similarity of behaviour of trends that characterize it both for developed economies among themselves and between groups of countries. The further scientific research is needed within the framework of the imposition of trends in the development of the money laundering processes of some countries on others and the formation of international medium-term anti-fraud strategies.

Primary cyclic matrices in irreducible matrix subalgebras

Primary cyclic matrices were used (but not named) by Holt and Rees in their version of Parker’s MEAT-AXE algorithm to test irreducibility of finite matrix groups and algebras. They are matrices X with at least one cyclic component in the primary decomposition of the underlying vector space as an X-module. Let {\operatorname{M}(c,q^{b})} be an irreducible subalgebra of {\operatorname{M}(n,q)}, where {n=bc>c}. We prove a generalisation of the Kung–Stong cycle index theorem, and use it to obtain a lower bound for the proportion of primary cyclic matrices in {\operatorname{M}(c,q^{b})}. This extends work of Glasby and the second author on the case {b=1}.

Ion-pair recognition by a neutral [2]rotaxane based on a bis-calix[4]pyrrole cyclic component

In this work we report our investigations on the synthesis and binding properties of a [2]rotaxane acting as an efficient heteroditopic receptor for onium salts in CHCl3 solution.