As in the case of the associahedron and cyclohedron, the permutohedron can also be defined as an appropriate compactification of a configuration space of points on an interval or on a circle. The construction of the compactification endows the permutohedron with a projection to the cyclohedron, and the cyclohedron with a projection to the associahedron. We show that the preimages of any point via these projections might not be homeomorphic to (a cell decomposition of) a disk, but are still contractible. We briefly explain an application of this result to the study of knot spaces from the point of view of the Goodwillie-Weiss manifold calculus.

We investigate correlation between gauge coupling unification, fermion mass spectrum, proton decay, perturbativity and ultraviolet cutoff within an SU(5) grand unified theory with minimal scalar content and an extra adjoint representation of fermions. We find strong correlation between the upper bound on the mass of both the bosonic and fermionic SU(2) triplets and the cutoff. The upper bound on the mass of fermionic triplet responsible for Type III seesaw mechanism is 102.1 GeV for the Planck scale cutoff. In that case both the idea of grand unification and nature of seesaw mechanism could be tested at future collider experiments through the production of those particles. Moreover, the prediction for the proton decay lifetime is at most an order of magnitude away from the present experimental limits. If the cutoff is lowered these predictions change significantly. In the most general scenario, if one does (not) neglect a freedom in the quark and lepton mixing angles, the upper bound on the fermionic triplet mass is at 105.4 GeV (1010 GeV). Since the predictions of the model critically depend on the presence of the higher-dimensional operators and corresponding cutoff we address the issue of their possible origin and also propose alternative scenarios that implement the hybrid seesaw framework of the original proposal.

Islamic manuscript books had an over-eminent role in the spreading of literacy and dissemination of knowledge of Islamic provenance in Bosnia and Herzegovina not only among ulemah circles but rather among ordinary people in general. Those facts are proved by several thousands of such books which are preserved in national and foreign collections, most famous among them being preserved in Gazy Husrev-bey’s library in Sarajevo and Bašagić’s collection in Bratislava, Slovakia. Authentic evidence of the possession and use of Islamic manuscripts in Bosnia and Herzegovina during Ottoman Empire, which ended in 1878, are comprised in sijjils of shariah law. Sijjyl is a collection of court records of certain territorial-administrative area which resulted out of a professional judicial practice in a certain time period. These documents are peculiar civilization registers whose content includes various topics – currently unavoidable study of political, economic, social and cultural history of a town or a wider region. The above mentioned facts suggest the importance of the catalogues of Islamic manuscripts and archive registers dating from Ottoman-empire period in Bosnia and Herzegovina.

SUMMARY The objective of this investigation was to determine the distribution within EUROP classes and carcass traits (weight and measurements, dressing percentage, shares of separated fat and dissected muscle, fat, bone and tendon tissues) of young Simmental bulls (n=13) and heifers (n=13), which were produced as Croatian baby beef designed for export. The EUROP classification showed a favourable conformation of both, bulls and heifers with about one third of carcasses graded as highest E class. The heifer’s fatness was less favourable and almost half of carcasses were classified as high fat class (4) and thus less valid. The amount of trimmed carcass fat was higher (P>0.001) in heifers than in bulls (6.68 % vs. 4.70 %) as well as the share of fat tissue after carcass dissection (10.58 % vs. 7.27 %). The share of muscle tissue in the carcass was higher (P>0.001) in bulls compared to heifers (70.45 % vs. 67.09 %). The bulls also showed a longer (P>0.05) carcass length (135.66 cm vs. 132.07 cm), as well as a larger (P>0.001) perimeter of the leg (122.65 cm vs. 116.38 cm) in comparison with heifers. The differences between bulls and heifers in dressing percentage, leg length, shares of Milanese cut, bone and tendon tissue in the carcass were small and not significant (P>0.05).

Pt/gamma-Al2O3 catalysts were prepared using hydroxyl-terminated generation four (G4OH) PAMAM dendrimers as the templating agents and the various steps of the preparation process were monitored by extended X-ray absorption fine structure (EXAFS) spectroscopy. The EXAFS results indicate that, upon hydrolysis, chlorine ligands in the H(2)PtCl(6) and K(2)PtCl(4) precursors were partially replaced by aquo ligands to form [PtCl3(H2O)3]+ and [PtCl2(H2O)2] species, respectively. The results further suggest that, after interaction of such species with the dendrimer molecules, chlorine ligands from the first coordination shell of Pt were replaced by nitrogen atoms from the dendrimer interior, indicating that complexation took place. This process was accompanied by a substantial transfer of electron density from the dendrimer to platinum, indicating that the dendrimer plays the role of a ligand. Following treatment of the H(2)PtCl(6)/G4OH and K(2)PtCl(4)/G4OH complexes with NaBH4, no substantial changes were observed in the electronic or coordination environment of platinum, indicating that metal nanoparticles were not formed during this step under our experimental conditions. However, when the reduction treatment was performed with H2, the formation of extremely small platinum clusters, incorporating no more than four Pt atoms was observed. The nuclearity of these clusters depends on the length of the hydrogen treatment. These Pt species remained strongly bonded to the dendrimer. Formation of larger platinum nanoparticles, with an average diameter of approximately 10 A, was finally observed after the deposition and drying of the H(2)PtCl(6)/G4OH nanocomposites on a gamma-Al(2)O(3) surface, suggesting that the formation of such nanoparticles may be related to the collapse of the dendrimer structure. The platinum nanoparticles formed appear to have high mobility because subsequent thermal treatment in O2/H2, used to remove the dendrimer component, led to further sintering.