In this note we show that $B$-scrolls over null curves in a 3-dimensional Lorentzian space form $\bar{M}^3_1(c)$ are characterized as the only ruled surfaces with null rulings whose Gauss maps $G$ satisfy the condition $\Delta G=\Lambda G$, $\Lambda \:{X}(\bar{M})\rightarrow {X}(\bar{M})$ being a parallel endomorphism of ${X}(\bar{M})$.
This paper studies the uniqueness of meromorphic functions f n ∏ k i=1 (f (i) ) ni and g n ∏ k i=1 (g (i) ) ni that share two values, where n, nk, k ∈ N, ni ∈ N ∪ {0}, i = 1, 2, . . . , k − 1. The results significantly rectify, improve and generalize the results due to Cao and Zhang (2012).
We investigate the generalized Drazin inverse and the generalized resolvent in Banach algebras. The Laurent expansion of the generalized resolvent in Banach algebras is introduced. The Drazin index of a Banach algebra element is characterized in terms of the existence of a particularly chosen limit process. As an application, the computing of the Moore-Penrose inverse in $C^*$-algebras is considered. We investigate the generalized Drazin inverse as an outer inverse with prescribed range and kernel. Also, $2\times 2$ operator matrices are considered. As corollaries, we get some well-known results.
In this paper we examine some features of the global dynamics of the four-dimensional system created by Lou, Ruggeri and Ma in 2007 which describes the behavior of the AIDS-related cancer dynamic model in vivo. We give upper and lower ultimate bounds for concentrations of cell populations and the free HIV-1 involved in this model. We show for this dynamics that there is a positively invariant polytope and we find a few surfaces containing omega-limit sets for positive half trajectories in the positive orthant. Finally, we derive the main result of this work: sufficient conditions of ultimate cancer free behavior.
The article defines and explicates the concept of gold-plating, i.e. non-minimalistic transposition of EU directives. It describes its typical manifestations in legislative practice and elaborates when and why it should be avoided. It is submitted in the article that the Czech methodological transposition guidelines and RIA methodology insufficiently deal with the issue of gold-plating. Therefore, the article seeks to propose amendments to the relevant Czech methodology so as to limit the occurrence of unjustified gold-plating in Czech legislation.
This article shows that although EU Member States are quite unsuccessful when they plead many different grounds before the ECJ to justify the non-transposition of EU directives, there are still strikingly many grounds that can possibly justify non-transposition. This article also argues that although there are many good reasons for the ECJ to be very strict in accepting possible grounds justifying the non-transposition of EU directives, there was no good reason for the ECJ to reject as justifying basis one special case of the pointlessness of the transposition. Namely the pointlessness because an activity referred to in a directive does not yet exist in a Member State due to an EU law compatible national legal obstacle for such activity in that State.
Adult head structures of Lepicerus inaequalis were examined in detail and interpreted functionally and phylogenetically. The monogeneric family clearly belongs to Myxophaga. A moveable process on the left mandible is an autapomorphy of the suborder. Even though Lepiceridae is the "basal" sistergroup of the remaining three myxophagan families, it is likely the group which has accumulated most autapomorphic features, e.g. tuberculate surface structure, internalised antennal insertion, and a specific entognathous condition. Adults of Lepiceridae and other myxophagan groups possess several features which are also present in larvae (e.g., premental papillae, semimembranous mandibular lobe). This is probably related to a very similar life style and has nothing to do with "desembryonisation". Lepiceridae and other myxophagans share a complex and, likely, derived character of the feeding apparatus with many polyphagan groups (e.g., Staphyliniformia). The mandibles are equipped with large molae and setal brushes. The latter interact with hairy processes or lobes of the epi- and hypopharynx. This supports a sistergroup relationship between both suborders.