Carbon and silicon pentagonal low-dimensional structures attract a great interest as they may lead to new exotic phenomena such as topologically protected phases or increased spin-orbit effects. However, no pure pentagonal phase has yet been realized for any of them. Here we unveil through extensive density functional theory calculations and scanning tunnelling microscope simulations, confronte...

Resting cyst and motile thecate cell stages of three heterotrophic Protoperidinium oblongum, Protoperidinium sp and Protoperidinium claudicans were assessed. Cysts were isolated from sediment collected from southeast coast of Iran. Individual live cysts were incubated under optimal conditions for germination. Results showed that Protoperidinium oblongum cysts were pentagonal smooth walled and t...

In this paper we give the history of Leonhard Euler's work on the pentagonal number theorem, and his applications of the pentagonal number theorem to the divisor function, partition function and divergent series. We have attempted to give an exhaustive review of all of Euler's correspondence and publications about the pentagonal number theorem and his applications of it. Comprehensus: In hoc di...

We prove a general pentagonal sieve theorem that has corollaries such as the following First the number of pairs of partitions of n that have no parts in common is p n p n p n p n p n Second if two unlabeled rooted forests of the same number of vertices are chosen i u a r then the probability that they have no common tree is Third if f g are two monic polynomials of the same degree over the eld...

Academic insignia of the Faculty Chemical Technology UCT Prague have a history and are used in academic ceremonies (graduation, ceremonial scientific councils, awarding honorary doctorates, etc.). Insignia consists single chain with medal scepter. They made gold-plated silver decorated natural synthetic precious stones. The central motif head sceptre is pentagonal dodecahedron cut from sulphide...

A pentagonal geometry PENT( k , r) is a partial linear space, where every line incident with points, point r lines, and for each x, there precisely those points that are not collinear x. Here we generalize the concept by allowing x to form set of Steiner system S ( 2 w ) whose blocks lines geometry.