A pentagonal geometry PENT (k, r) is a partial linear space, where every line, or block, incident with k points, point r lines, and for each x, there line precisely those points that are not collinear x. An opposite pair in consists of two parallel lines such on one the other line. We give direct construction an infinite sequence geometries block size 3 connected deficiency graphs. Also we pres...

A metallaborane of novel structure, [(Cp*Mo)(2)B(3)H(3)Se(2){Fe(CO)(2)}(2){Fe(CO)(3)}(2)] (2; Cp* = η(5)-C(5)Me(5)), with tetracapped pentagonal bipyramidal geometry, isolated from the reaction of [(Cp*Mo)(2)B(4)H(4)Se(2)], 1 with [Fe(2)(CO)(9)]; the title compound exhibit an 11-vertex closo-cage geometry, having eight skeletal electron pairs (sep) and 98 valence electrons, appropriate for its ...

Neural Network is and used to be a principal component of mathematics education. Many models have been developed in the literature for the description of the neural network. In this paper, we use fuzzy number choose the best machine for a job by Feed-Forward Neural Network.

Ordered graphene has been extensively studied. In this paper, we undertake a density functional study of topologically disordered analogs of graphene, in the formof a random network, consisting predominantly of hexagonal rings, but also including pentagons and heptagons. After some preliminaries with crystalline material, we relax various random network models and find that the presence of carb...

X iv :m at h/ 02 03 22 9v 1 [ m at h. C O ] 2 2 M ar 2 00 2 2000]Primary 05A19, 33D15 q-HYPERGEOMETRIC PROOFS OF POLYNOMIAL ANALOGUES OF THE TRIPLE PRODUCT IDENTITY, LEBESGUE’S IDENTITY AND EULER’S PENTAGONAL NUMBER THEOREM S. OLE WARNAAR Abstract. We present alternative, q-hypergeometric proofs of some polynomial analogues of classical q-series identities recently discovered by Alladi and Berk...

On the example of exceptional families of viruses we (i) show the existence of a completely new type of matter organization in nanoparticles, in which the regions with a chiral pentagonal quasicrystalline order of protein positions are arranged in a structure commensurate with the spherical topology and dodecahedral geometry, (ii) generalize the classical theory of quasicrystals (QCs) to explai...