Invariants and Infinitesimal Transformations for Contact Sub-Lorentzian Structures on 3-Dimensional Manifolds

In this article we develop some elementary aspects of a theory of symmetry in sub-Lorentzian geometry. First of all we construct invariants characterizing isometric classes of sub-Lorentzian contact 3 manifolds. Next we characterize vector fields which generate isometric and conformal symmetries in general sub-Lorentzian manifolds. We then focus attention back to the case where the underlying manifold is a contact 3 manifold and more specifically when the manifold is also a Lie group and the structure is left-invariant

Invariants of contact sub-pseudo-Riemannian structures and Einstein-Weyl geometry

We consider local geometry of sub-pseudo-Riemannian structures on contact manifolds. We construct fundamental invariants of the structures and show that the structures give rise to Einstein-Weyl geometries in dimension 3, provided that certain additional conditions are satisfied

3-dimensional left-invariant sub-Lorentzian contact structures

We provide a classification of ts-invariant sub-Lorentzian structures on 3 dimensional contact Lie groups. Our approach is based on invariants arising form the construction of a normal Cartan connection. \ua9 2016 Elsevier B.V

Procesy rozwoju województwa mazowieckiego a suburbanizacja

Celem niniejszego opracowania jest przedstawienie zróżnicowania rozwoju województwa mazowieckiego i jego wpływu na procesy suburbanizacji. Intensywna migracja na tereny otaczające Warszawę spowodowała nasilenie ruchu budowlanego (budowa mieszkań, obiektów usługowych, infrastruktury), co pociągnęło za sobą przemiany w sferze gospodarczej i w użytkowaniu ziemi.Udostępnienie publikacji Wydawnictwa Uniwersytetu Łódzkiego finansowane w ramach projektu „Doskonałość naukowa kluczem do doskonałości kształcenia”. Projekt realizowany jest ze środków Europejskiego Funduszu Społecznego w ramach Programu Operacyjnego Wiedza Edukacja Rozwój; nr umowy: POWER.03.05.00-00-Z092/17-00. Książka finansowana ze środków Wydziału Nauk Geograficznych Uniwersytetu Łódzkiego

Spatiotemporal complexity patterns of resting‐state bioelectrical activity explain fluid intelligence : sex matters

Neural complexity is thought to be associated with efficient information processing but the exact nature of this relation remains unclear. Here, the relationship of fluid intelligence (gf) with the resting‐state EEG (rsEEG) complexity over different timescales and different electrodes was investigated. A 6‐min rsEEG blocks of eyes open were analyzed. The results of 119 subjects (57 men, mean age = 22.85 ± 2.84 years) were examined using multivariate multiscale sample entropy (mMSE) that quantifies changes in information richness of rsEEG in multiple data channels at fine and coarse timescales. gf factor was extracted from six intelligence tests. Partial least square regression analysis revealed that mainly predictors of the rsEEG complexity at coarse timescales in the frontoparietal network (FPN) and the temporo‐parietal complexities at fine timescales were relevant to higher gf. Sex differently affected the relationship between fluid intelligence and EEG complexity at rest. In men, gf was mainly positively related to the complexity at coarse timescales in the FPN. Furthermore, at fine and coarse timescales positive relations in the parietal region were revealed. In women, positive relations with gf were mostly observed for the overall and the coarse complexity in the FPN, whereas negative associations with gf were found for the complexity at fine timescales in the parietal and centro‐temporal region. These outcomes indicate that two separate time pathways (corresponding to fine and coarse timescales) used to characterize rsEEG complexity (expressed by mMSE features) are beneficial for effective information processing