Let H be a finite-dimensional bialgebra. In this paper, we prove that the category LR(H) of Yetter-Drinfeld-Long bimodules, introduced by F.Panaite, F.Van Oystaeyen (2008), is isomorphic to the Yetter-Drinfeld category H⊗H H⊗H YD over the tensor product bialgebra H H∗ as monoidal categories. Moreover if H is a finite-dimensional Hopf algebra with bijective antipode, the isomorphism is braided. Finally, as an application of this category isomorphism, we give two results., Daowei Lu, Shuanhong Wang., and Seznam literatury
This paper highlighs the contribution of Philipp Lenard (Nobel Prize winner 1905) to the understanding of luminescence and reviews his main results in the field. In particular, the experimental spectroscopic technique introduced by Lenard and the properties of the so-called Lenard phosphors are discussed., Ivan Pelant, Jan Valenta., and Obsahuje seznam literatury
It is known that for a nonempty topological space X and a nonsingleton complete lattice Y endowed with the Scott topology, the partially ordered set [X, Y ] of all continuous functions from X into Y is a continuous lattice if and only if both Y and the open set lattice OX are continuous lattices. This result extends to certain classes of Z-distributive lattices, where Z is a subset system replacing the system D of all directed subsets (for which the D-distributive complete lattices are just the continuous ones). In particular, it is shown that if [X, Y ] is a complete lattice then it is supercontinuous (i.e. completely distributive) iff both Y and OX are supercontinuous. Moreover, the Scott topology on Y is the only one making that equivalence true for all spaces X with completely distributive topology. On the way to these results, we find necessary and sufficient conditions for [X, Y ] to be complete, and some new, purely topological characterizations of continuous lattices by continuity conditions on their (infinitary) lattice operations.
Krátké zamyšlení nad souvislostí struktury krystalů a jejich vlastnostmi a nad fyzikálními a geometrickými principy difrakce rentgenového záření., The article contains a brief contemplation on the relationship between the structure and properties of crystals and on physical and geometrical principles of X-ray diffraction., Václav Valvoda., and Obsahuje seznam literatury