We introduce a plan toward a perfect list of convex pentagons that can tile the whole plane in edge-to-edge manner. Our strategy is based on Bagina’s Proposition, and is direct and primitive: Generating all candidates of pentagonal tiles (several hundreds in number), classify them into the known 14 types, geometrically impossible cases, the cases that do not generate an edge-to-edge pentagonal ...

In this paper, microstrip patch antennas with six different shapes i. e. rectangular, circular, square, elliptical, pentagonal and hexagonal are implemented using Ansoft HFSS version 13. 0. 0 software. Antennas are designed on Rogers RT/duroid 5880 material with dielectric constant 2. 2 and thickness 3. 2 mm. The different performance parameters such as return loss, gain and bandwidth of these ...

Recently Zagier proved a remarkable q-series identity. We show that this identity can also be proved by modifying Franklin's classical proof of Euler's pentagonal number theorem.

Mammalian pyruvate dehydrogenase complex (PDC) is a key multi-enzyme assembly that is responsible for glucose homeostasis maintenance and conversion of pyruvate into acetyl-CoA. It comprises a central pentagonal dodecahedral core consisting of two subunit types (E2 and E3BP) to which peripheral enzymes (E1 and E3) bind tightly but non-covalently. Currently, there are two conflicting models of P...

The Pb(II )atom in the title compound, {[Pb(2)(C(7)H(6)NO(2))(4)]}(n), is chelated by two 3-aminobenzoato ligands in a distorted pentagonal-bipyramidal coordination geometry with five oxygen donors in the equatorial positions, one nitro-gen donor and one oxygen donor in the axial positions. Two mol-ecules are linked through a centre of inversion, forming a dinuclear entity. These entities are l...

The Pb(II) atom in the polymeric title compound, {[Pb(C(13)H(11)N(4)O)(CH(3)OH)(2)]ClO(4)}(n), is coordinated by an N'-[1-(pyridin-2-yl-κN)ethyl-idene]isonicotinohydrazidate ligand via O,N,N'-donors and simultaneously bridged by a neighbouring ligand via the isonicotinoyl N atom; two additional sites are occupied by methanol O atoms. The resultant supra-molecular chain is a zigzag along the c a...