Pseudospherical surfaces on time scales: a geometric definition and the spectral approach

We define and discuss the notion of pseudospherical surfaces in asymptotic coordinates on time scales. Thus we extend well known notions of discrete pseudospherical surfaces and smooth pseudosperical surfaces on more exotic domains (e.g, the Cantor set). In particular, we present a new expression for the discrete Gaussian curvature which turns out to be valid for asymptotic nets on any time scale. We show that asymptotic Chebyshev nets on an arbitrary time scale have constant negative Gaussian curvature. We present also the quaternion-valued spectral problem (the Lax pair) and the Darboux-Backlund transformation for pseudospherical surfaces (in asymptotic coordinates) on arbitrary time scales.Comment: 20 page

Global warming – causes, effects and climate change prevention

Efekt cieplarniany stał się w ostatnich latach jednym z głównych problemów świata. Globalne ocieplenie wpływa negatywnie na środowisko. Wiele gatunków roślin i zwierząt, które nie mogą przystosować się do zmian klimatycznych może wyginąć. Wpływa ono także niekorzystnie na ekonomię i infrastrukturę państw. Organizowane są liczne konferencje odnośnie zmiany klimatu, których celem jest poszukiwanie rozwiązań służących redukcji emisji gazów cieplarnianych. Na konferencjach w Kioto i Paryżu powstały protokoły odnośnie ograniczenia emisji tych gazów. Protokół paryski przedstawia długoterminową strategię przeciwdziałania globalnemu ociepleniu. Zakłada on redukcję gazów cieplarnianych do roku 2050, o co najmniej o 60% w odniesieniu do roku 2010.The greenhouse effect has become one of the major problems of the world in recent years. Global warming has a negative effect on the environment. Many species of plants and animal that cannot adapt to climate change could become extinct. It also affect negatively on the economy and infrastructure of states. Numerous conferences relating to climate change are organized, aimed at finding solutions to reduce greenhouse gas emissions. At conferences in Kyoto and Paris protocols were created concerning the limitation of emissions of these gases. Paris Protocol represents a longterm strategy to combat global warming. It assumes the reduction of greenhouse gases by 2050, at least 60% for 2010

Spectroscopic (IR, Raman, NMR), thermal and theoretical (DFT) study of alkali metal dipicolinates (2,6) and quinolinates (2,3)

AbstractIn the presented work the thermal, theoretical (DFT) and spectroscopic (IR, Raman, NMR) properties of alkali metal complexes with quinolinic acid (2,3-pyridinedicarboxylic acid) and dipicolinic acid (2,6-pyridinedicarboxylic acid) were studied. The IR and Raman spectra were registered and analyzed in the range of 400–4000cm−1. 1H NMR and 13C NMR spectra of analyzed compounds have been registered and assigned. The electronic charge distribution for the studied acids and their salts with lithium, sodium and potassium was calculated. All the calculations were done in the frame of density functional theory (DFT) using 6-311++G(d,p) basis set. The thermal decomposition of the analyzed compounds was done