We discovered the new tiling patterns each of which is composed of a single kind of convex pentagon. Moreover, we propose a new concept of classification method of the tessellating convex pentagons, which is the only unsolved case among the corresponding tessellating convex polygon problems.

Reactions of 3,6-bis(2-pyridyl)-1,2,4,5-tetrazine (bptz) with solvated first-row transition metals M(II) (M(II) = Ni, Zn, Mn, Fe, Cu) have been explored with emphasis on the factors that influence the identity of the resulting cyclic products for Ni(II) and Zn(II). The relatively small anions, namely [ClO4]- and [BF4]-, lead to the formation of molecular squares [{M4(bptz)4(CH3CN)8} subsetX][X]...

The atomic processes associated with energy storage and release in irradiated graphite have long been subject to untested speculation. We examine structures and recombination routes for interstitial-vacancy (I-V) pairs in graphite. Interaction results in the formation of a new metastable defect (an intimate I-V pair) or a Stone-Wales defect. The intimate I-V pair, although 2.9 eV more stable th...

Forming a regular pentagon, decagon and pentagram using origami technique is based on the construction of approximately 36 angle by dint of A4 paper of format. The implemented method is “fold and cut”. We endeavored to obtain the polygons with the most accurate sides, i.e. with the minimal aberration of the interior angle. There is also considered an ideal paper format, which would provide the ...

An additional pancake-antipancake vortex pair is considered in the vortex lattice of layered superconductors. Within linear elastic continuum theory, the relaxation of the background lattice screens the long-range logarithmic interaction of the defect pair, reducing the factor ln(r0 /j) to ln(a/j) where r0 is the pair spacing, j the in-plane coherence length, and a the vortex spacing. The finit...

First-order phase transitions typically exhibit a significant hysteresis resulting for instance in boiling retardation and supercooling. The hysteresis arises, because nucleation of the new phase is activated. The free-energy change is positive until the nucleus reaches a critical size beyond which further growth is downhill. In practice, the barrier is often circumvented by the presence of het...

Fullerene-Like (FL) sulpho-carbide (CSx) compounds have been addressed by first principles calculations. Geometry optimization and cohesive energy results are presented for the relative stability of precursor species such as C2S, CS2, and C2S2 in isolated form. The energy cost for structural defects, arising from the substitution of C by S is also reported. Similar to previously synthesized FL-...