Fine Gradings of Low-Rank Complex Lie Algebras and of Their Real Forms

In this review paper, we treat the topic of fine gradings of Lie algebras. This concept is important not only for investigating the structural properties of the algebras, but, on top of that, the fine gradings are often used as the starting point for studying graded contractions or deformations of the algebras. One basic question tackled in the work is the relation between the terms 'grading' and 'group grading'. Although these terms have originally been claimed to coincide for simple Lie algebras, it was revealed later that the proof of this assertion was incorrect. Therefore, the crucial statements about one-to-one correspondence between fine gradings and MAD-groups had to be revised and re-formulated for fine group gradings instead. However, there is still a hypothesis that the terms 'grading' and 'group grading' coincide for simple complex Lie algebras. We use the MAD-groups as the main tool for finding fine group gradings of the complex Lie algebras $A_3 \cong D_3$, $B_2 \cong C_2$, and $D_2$. Besides, we develop also other methods for finding the fine (group) gradings. They are useful especially for the real forms of the complex algebras, on which they deliver richer results than the MAD-groups. Systematic use is made of the faithful representations of the three Lie algebras by $4\times 4$ matrices: $A_3 = sl(4,\mathbb C)$, $C_2 = sp(4,\mathbb C)$, $D_2 = o(4,\mathbb C)$. The inclusions $sl(4,\mathbb C)\supset sp(4,\mathbb C)$ and $sl(4,\mathbb C) \supset o(4,\mathbb C)$ are important in our presentation, since they allow to employ one of the methods which considerably simplifies the calculations when finding the fine group gradings of the subalgebras $sp(4,\mathbb C)$ and $o(4,\mathbb C)$.Comment: This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

The range and the structure of subsidies in agriculture companies reaching a different economical level

The paper deals with a range and a structure of subsidies in agricultural companies reach a different economic level and farm in different natural conditions. The research realized within a set of 109 agricultural companies of NUTS II South-East throughout the years 2001-2003 shows that the endowment support of field economy had the same extent in the main (subsidies for 1 ha of agricultural land and for one worker), both in the group of different economic level and in the group of agricultural companies running their own business in different natural conditions during this period. The structure of subsidies, in a view-point of their special purpose, is a bit different among the companies running businesses in less favored areas (LFA), namely in a higher share of subsidies supporting a non-production asset, ecological agriculture and beef-raising.Agricultural companies, subsidies, economical level of companies, natural conditions, Agricultural and Food Policy,

Changes of Employment in Enterprises in the South-Moravian Region during and after Economic Recession

In the period 2008–2010, the labour market of the European Union was significantly affected by the economic recession, which impacted economic development in all regions of the Czech Republic including the South Moravian Region. Impacts of the economic recession in the labour market were primarily reflected on decline of vacant work places, an increase in job seekers, and thus an increase in the unemployment rate, as well as an increase in long-term unemployment,etc. Enterprises in the region are responding to this situation in different ways, but all have to flexibly adapt – increase or decrease – the number of employees and production as movements in the labour market have been very significant for the past four years. In 2011 and 2012, the economic recession was not discussed anymore. However, has it already finished? The analysis of movements in the labour market, especially comparison of plans and reality in enterprises during and after economic recession is the aim of the paper

Overview of Parallel Platforms for Common High Performance Computing

The paper deals with various parallel platforms used for high performance computing in the signal processing domain. More precisely, the methods exploiting the multicores central processing units such as message passing interface and OpenMP are taken into account. The properties of the programming methods are experimentally proved in the application of a fast Fourier transform and a discrete cosine transform and they are compared with the possibilities of MATLAB's built-in functions and Texas Instruments digital signal processors with very long instruction word architectures. New FFT and DCT implementations were proposed and tested. The implementation phase was compared with CPU based computing methods and with possibilities of the Texas Instruments digital signal processing library on C6747 floating-point DSPs. The optimal combination of computing methods in the signal processing domain and new, fast routines' implementation is proposed as well

Institutional Conditionality and State Compliance: The Czech and Slovak Accession to NATO and the EU

This dissertation studies the interaction between international institutions and nation states. More specifically, it examines how the membership conditionality of the North Atlantic Treaty Organization (NATO) and the European Union (EU) was adopted by candidate states. It uses the Czech and Slovak accessions to NATO and the EU to argue that, in order to understand the external phenomenon of conditionality, we need to study its effects within states. Critical to this process is national leadership. National leaders determine whether and how conditionality is implemented. Furthermore, this dissertation asserts that successful compliance with NATO and EU conditionality is decisively determined by the extent to which leaders perceive compliance with institutional norms and rules to be in their interest, as well as by the extent to which their normative stance is aligned with the norms contained within NATO and EU conditionality. Elites favorably disposed towards membership are a sine qua non for successful compliance with conditionality. The case studies offer a detailed analysis of the dynamics of the accession process in the Czech Republic and Slovakia. What becomes apparent is the failure of either a purely rationalist or a purely constructivist explanation to capture the empirical phenomenon of compliance with conditionality. Neither approach can adequately accommodate the mix of material and ideational preferences that drives a state\u27s response to conditionality. This dissertation therefore advocates the employment of a more comprehensive analytical approach that transcends the traditional dichotomy between the two schools of thought and takes both rational and normative motivations of state behavior into consideration in order to explain the complexity of state behavior

Embrioni riba kao alternativni model u toksikologiji: revijalni pregled

Povećan broj ksenobiotika ugrožava životnu sredinu. Ova bioaktivna jedinjenja dospevaju u vodenu sredinu na različite načine i imaju značajan uticaj na akvatični živi svet. Za procenu opasnosti i rizika industrijskih hemikalija, proizvoda zaštite bilja, biocida, dodataka u hrani i lekova koriste se testovi na životinjama. Akutni test toksičnosti za ribe je obavezni korak u procesu ispitivanja toksičnosti hemikalija. Međutim njihova ekotoksikološka relevantnost je pod znakom pitanja. Povrh toga ribe se u ovim testovima podvrgavaju značajnom bolu i patnji. U skladu sa filozofijom 3r (redukcija/smanjenje, refinement/prečišćavanje, replacement/zamena) embrioni riba se smatraju metodom zamene ili prečišćavanja budući da ovi razvojni stadijumi nisu zakonski zaštićeni (Direktiva 2010/63/EU) i izgleda da osećaju manju bol i patnju. Cilj ovog pregleda bio je da se sumiraju dostupni podaci o testovima toksičnosti na embrionima riba i ukaže na moguće perspektive korišćenja ovog modela u savremenoj toksikologiji. Princip testa toksičnosti sa embrionima riba zasniva se na izloženosti vijabilnih embriona ksenobioticima, od oplođenja do kraja embriogeneze. Test toksičnosti sa embrionima riba validiran je u OECD studiji i prihvaćen kao OECD TG 236 96-h test za procenu toksičnosti za embrione riba. Određuje se letalnost koja je označena koagulacijom embriona, nedostatkom somita, ispravljanja repa ili otkucaja srca. Povrh smrtnosti, složeniji pokazatelji kao što je razvoj očiju, prisustvo krvotoka ili razvojne malformacije mogu se uočiti na stadijumima izvaljenih eleutero embriona. Mogućnost praćenja različitih pokazatelja čini embrione riba odličnim modelom za ispitivanje i razumevanje mehanizama toksičnosti i indikatorom mogućih nepovoljnih i dugotrajnih efekata. Na osnovu izvedenih istraživanja, test toksičnosti sa embrionima riba je razumna alternativa akutnom testu toksičnosti na ribama. Raspon mogućih aplikacija je značajan i ima mnogo perspektiva u budućnosti: kao što je dalja identifikacija molekularnih markera – indikatora načina delovanja ili uspostavljanje veze među efektima u kratkotrajnim testovima sa embrionima i dugotrajnih efekata na individue. Test toksičnosti sa embrionima riba takođe može da doprinese smanjenju broja eksperimenata na životinjama što je jedan od osnovnih principa EU legislative u oblasti dobrobiti

An oxygen isotope record of lacustrine opal from a European Maar indicates climatic stability during the Last Interglacial

The penultimate temperate period, 127–110 ka before present (BP), bracketed by abrupt shifts of the global climate system initiating and terminating it, is considered as an analogue of the Holocene because of a similar low global ice‐volume. Ice core records as well as continental and marine records exhibit conflicting evidence concerning the climate variability within this period, the Last Interglacial. We present, for the first time, a high‐resolution record of oxygen isotopes in diatom opal of the Last Interglacial obtained from the Ribains Maar in France (44°50′09″N 3°49′16″E). Our results indicate that the Last Interglacial in southwestern Europe was generally a period of climatic stability. The record shows that the temperate period was initiated by an abrupt warm event followed midway by a minor climatic transition to a colder climate. An abrupt isotopic depletion that occurs simultaneously with abrupt changes in pollen and diatom assemblages marks the end of the temperate period, and is correlative with the Melisey I stadial. Variations in the isotopic composition of lake‐water related to the isotopic composition of precipitation and evaporation dominate the biogenic opal oxygen isotope record

Biostratigraphy and paleoecology of the Lower Cretaceous sediments in the Outer Western Carpathians (Silesian Unit, Czech Republic)

Almost black shale filling fissures in the Štramberk Limestone belonging to the Silesian Unit, Outer Western Carpathians contain prolific and poorly to moderately well preserved spores, pollen, organic-walled dinoflagellate cysts, foraminifers, and calcareous nannofossils. A detailed micropaleontological analysis of the proved stratigraphical interval from the Valanginian to the Albian indicated sedimentary conditions of brackish, restricted marine, shallow-marine and neritic sedimentation. Moreover, it drew attention to occasional influence from the Boreal province in the depositional area of the NW part of Tethys, especially during the Early Valanginian and Hauterivian, as supported by the presence of highlatitude nannofossils and organic-walled dinoflagellate cysts. Terrestrial miospores form a significant component of palynoassemblages and give evidence of continent proximity in the Valanginian-Barremian interval. Samples were acquired from isolated fissure fills in the Štramberk Limestone and, therefore, they do not represent a continuous section.Web of Science62433230