78 research outputs found
On Capital Dependent Dynamics of Knowledge
We investigate the dynamics of growth models in terms of dynamical system
theory. We analyse some forms of knowledge and its influence on economic
growth. We assume that the rate of change of knowledge depends on both the rate
of change of physical and human capital. First, we study model with constant
savings. The model with optimised behaviour of households is also considered.
We show that the model where the rate of change of knowledge depends only on
the rate of change of physical capital can be reduced to the form of the
two-dimensional autonomous dynamical system. All possible evolutional paths and
the stability of solutions in the phase space are discussed in details. We
obtain that the rate of growth of capital, consumption and output are greater
in the case of capital dependent rate of change of knowledge.Comment: 11 pages, 5 figures; presented at 2nd Polish Symposium on Econo- and
Sociophysics, Krakow, Poland, 21-22 April 2006; to be published in Acta Phys.
Pol.
Conference report: Academic conference “Perspektywy kształcenia nauczycieli języków specjalistycznych w Polsce” (Perspectives on educating LSP teachers in Poland), Institute of Applied Linguistics of Adam Mickiewicz University in Poznań, 20th October 2020
Conference report: Academic conference “Perspektywy kształcenia nauczycieli języków specjalistycznych w Polsce” (Perspectives on educating LSP teachers in Poland), Institute of Applied Linguistics of Adam Mickiewicz University in Poznań, 20th October 2020
Phantom cosmology as a simple model with dynamical complexity
We study the Friedmann-Robertson-Walker model with phantom fields modelled in
terms of scalar fields. We apply the Ziglin theory of integrability and find
that the flat model is nonintegrable. Then we cannot expect to determine simple
analytical solutions of the Einstein equations. We demonstrate that there is
only a discrete set of parameters where this model is integrable. For
comparison we describe the phantoms fields in terms of the barotropic equation
of state. It is shown that in the contrast to the phantoms modelled as scalar
fields, the dynamics is always integrable and phase portraits are constructed.
In this case we find the duality relation.Comment: RevTeX4, 11 pages, 2 figures; rewritten (v.2); new section on complex
dynamics in cases with and without spontaneous symmetry breaking (v.3); this
new section on numerical analysis of complex dynamics was dropped, upload to
match version in PRE (v.4
Lyapunov function for cosmological dynamical system
We prove the asymptotic global stability of the de Sitter solution in the Friedmann-Robertson-Walker conservative and dissipative cosmology. In the proof we construct a Lyapunov function in an exact form and establish its relationship with the first integral of dynamical system determining evolution of the flat Universe. Our result is that de-Sitter solution is asymptotically stable solution for general form of equation of state p = (ρ, H), where dependence on the Hubble function H means that the effect of dissipation are included
From Directive Guidance to Mentoring
This paper aims at presenting the practical approaches to chosen forms of support of self-reliance gaining process of young people coming from different forms of foster care. The most important forms of support include vocational counselling practiced during the realisation of the following projects by the Academy of Management in Lodz in the period of 2004 – 2012.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
Idea dynamicznego Wszechświata : style myślowe w kosmologii
Patrząc na korzenie współczesnej kosmologii odnajdujemy dwie ważne okoliczności: przejście z kosmologii na podstawie koncepcji czasoprzestrzeni newtonowskiej do kosmologii relatywistycznej i akceptacji idei dynamicznego relatywistycznego wszechświata. Uważamy, że podczas gdy pierwsza jest rewolucją naukową w sensie Kuhna, druga nie ma takiego charakteru. Powodem jest to, że przejście od statycznego Wszechświata Einsteina do Friedmanna dynamicznego Wszechświata odbywa się na fundamentach stworzonych przez ogólną teorię względności. Teoretyczna możliwość dynamicznego wszechświata jest naturalną konsekwencją ogólnej koncepcji względności krzywizny czasoprzestrzeni, ale nie została uznana od samego początku, gdyż Einstein był przekonany, że Wszechświat jest statyczny i nie istnieje rozwiązanie, zgodne z rozszerzającym się wszechświatem. Uważamy, że koncepcja Flecka stylu myślowego jest bardziej adekwatna w rekonstrukcji bardzo skomplikowanego procesu tworzenia się dynamicznego relatywistycznego obrazu Wszechświata (Weltbilt).Looking at the roots of modern cosmology we find two important circumstances: the transition from cosmology based on the Newtonian concept of space-time to relativistic cosmology and the acceptance of the idea of dynamical relativistic Universe. We argue that while the former is a scientific revolution in the Kuhn’s sense, the latter has no such a character. The reason is that the transition from Einstein’s static to Friedmann’s dynamic Universe takes place on foundations set up by general relativity theory. The theoretical possibility of dynamic Universe is a natural consequence of general relativity concept of curvature space-time, but it was not recognized from the very beginning, when Einstein was convinced that the Universe is static and did not admit the solutions of expanding Universe. We argue that Fleck’s conception of thought style is more adequate to reconstruct the very complicated process of the dynamical relativistic picture of the Universe (‘Weltbilt’) formation
Constraints on a Cardassian model from SNIa data - revisited
We discuss some observational constraints resulting only from SNIa
observations, imposed on the behavior of the original flat Cardassian model,
and its extension with the curvature term included. We test the models using
the Perlmutter SN Ia data as well as the new Knop and Tonry samples. We
estimate the Cardassian model parameters using the best-fitting procedure and
the likelihood method. In the fitting procedure we use the density variables
for matter, Cardassian fluid and curvature, and include the errors in redshift
measurements. For the Perlmutter sample in the non-flat Cardassian model we
obtain the high or normal matter density universe (),
while for the flat Cardassian model we have the high density universe. For
sample A in the high density universe we also find the negative values of
estimates of which can be interpreted as the phantom fluid effect. For the
likelihood method we get that a nearly flat universe is preferred. We show
that, if we assume that the matter density is 0.3, then in the
flat Cardassian model, which corresponds to the Perlmutter model with the
cosmological constant. Testing with the Knop and Tonry SN Ia samples show no
significant differences.Comment: RevTeX4, 14 pages, 8 figures; new supernovae data by Knop (v.2) and
Tonry (v.3) were used for the model estimatio
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