An algebra A is uniform if for each ∅ ∈ Con A, every two classes of ∅ have the same cardinality. It was shown by W. Taylor that coherent varieties need not be uniform (and vice versa). We show that every coherent variety having transferable congruences is uniform.
The notion of a metric bead space was introduced in the preceding paper (L. Pasicki: Bead spaces and fixed point theorems, Topology Appl., vol. 156 (2009), 1811–1816) and it was proved there that every bounded set in such a space (provided the space is complete) has a unique central point. The bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces. It appears that normed bead spaces are identical with uniformly convex spaces. On the other hand the "metric" approach leads to new elementary conditions equivalent to the uniform convexity. The initial part of the paper contains the proof that discus spaces (they seem to have a richer structure) are identical with bead spaces.
The paper examines similarities between observer design as introduced in Automatic Control Theory and filter design as established in Signal Processing. It is shown in the paper that there are obvious connections between them in spite of different aims for their design. Therefore, it is prospective to make them be compatible from the structural point of view. Introduced error invariance and error convergence properties of both of them are unifying tools for their design. Lyapunov's stability theory, signal power, system energy and a power balance relation are other basic terms used in the paper.
Právo EU obsahuje nejpřísnější soubor pravidel týkajících se poskytování veřejných podpor podnikům, které na mezinárodní úrovni existují. Není proto překvapivé, že poslední finanční krize, jež vypukla v roce 2007, konfrontovala unijní právo veřejných podpor s jednou z nejzávažnějších výzev v historii EU. V atmosféře eskalace finanční krize – a volání po státních zásazích ve většině členských států – se ukázalo jako neudržitelné, aby veřejné podpory poskytované členskými státy finančním institucím včetně systémových byly Evropskou komisí posuzovány jako veřejné podpory pro podniky v obtížích, na které se za obvyklých okolností kladou přísné požadavky. Pod tlakem Rady EU a členských států přistoupila Evropská komise k vydání pěti právních aktů, které na dobu trvání finanční krize umožnily povolovat členským státům poskytování veřejných podpor finančním institucím za méně přísných podmínek podle čl. 107 odst. 3 písm. b) SFEU, k čemuž došlo v bezprecedentním rozsahu. Toto zmírnění však nebylo bezbřehé a postup Evropské komise měl, jak se zdá, málo rozumných alternativ. Zkušenosti z poslední finanční krize by každopádně měly vést k hlubší debatě o přístupu k řadě základních konceptů práva veřejných podpor EU, pro což by mohl dát potřebný prostor proces další modernizace unijního práva veřejných podpor spuštěný Evropskou komisí v květnu 2012. and EU law contains the strictest set of rules limiting granting aids to undertakings by States that do exist on international level. Consequently, it is not surprising that the recent financial crisis which broke out in 2007 has confronted EU law with one of the most serious challenges in its history. In the atmosphere of the escalating financial crisis and urgent calls for State interventions in most of the EU Member States, it turned out untenable for the European Commission to treat state aids to financial institutions, including the systemic ones, under the normal – and strict – rules on state aids to undertakings in difficulties.Under the pressure from the EU Council and the Member States, the European Commission proceeded to issuing five legal acts which have enabled the European Commission to permit Member States to grant aids to financial institutions under less strict conditions stemming from Article 107 (3) b TFEU and these aids have been actually permitted in an unprecedented extent.However, the ensuing moderation of EU state aids law has not been unlimited, apart from that the European Commission’s approach seems to have had few reasonable alternatives. Anyway, experience from the recent financial crisis should lead to a deeper debate on many of the basic notions and presumptions hitherto inherent to EU state aid law. The process of another modernization of EU state aid law – launched by the European Commission in May 2012 – might create needed space in this regard.
A so far unknown book printed by the Speyer printer Anastasius Nolt, the New Testament in the ‘biblia pauperum’ style, has been discovered in the Library of the Křivoklát Castle. It was published by Jakob Beringer, a Speyer cleric, who had had Luther’s translation of the New Testament issued in Strasbourg already in 1527 decorated with these woodcuts.