New strange fulleroids are built up by using the three classical composite map operations: tripling (leapfrog Le), quadrupling (chamfering Q) and septupling (capra Ca) on the starting structure dodecahedron. These transforms belong to the icosahedral symmetry group and show interesting mathematical and (possible) physico-chemical properties. Topological symmetry data of the presented cages are ...

I propose a model of radiative charged-lepton and neutrino masses with A4 symmetry. The soft breaking of A4 to Z3 lepton triality is accomplished by dimension-three terms. The breaking of Z3 by dimension-two terms allows cobimaximal neutrino mixing (θ13 6= 0, θ23 = π/4, δCP = ±π/2) to be realized with only very small finite calculable deviations from the residual Z3 lepton triality. This constr...

Symmetry is a fundamental organizational concept in art as well as science. To develop and exploit this concept to its fullest, it must be given a precise mathematical formulation. This has been a primary motivation for developing the branch of mathematics known as “group theory.” There are many kinds of symmetry, but the symmetries of rigid bodies are the most important and useful, because the...

Animations are discussed for a range of geometric dissections. These include a variety of twist-hinged dissections, some swing-hinged dissections, dissections of squares and cubes corresponding to a certain integer identities, folding dissections of multi-level regular polygons, and folding dissections of multi-level polyominoes. Artistic issues pertaining to these dissections and animations ar...

The partition function of QCD is studied in the Leutwyler–Smilga scaling regime for an arbitrary number of quark flavors and masses including the contributions from all winding numbers. For Nf = 2 and degenerate quark masses, the partition function becomes independent of the quark masses at θ = π and subsequently the scalar chiral condensate vanishes. There is a discontinuity at θ = π in the fi...

Numerical simulations are performed on different lattice sizes of chiral U(1) and SU(2) scalar-fermion models with explicit mirror pairs of fermions in the broken symmetry phase. Relevance of these models to the electroweak theory is discussed. Shift symmetry of the action is exploited to decouple the unwanted mirror-fermion. Upper and lower bounds on the renormalized scalar mass as a function ...

Superconducting cosmic strings may be viewed as wires of thickness 1/Λ with Λ = 1016 TeV. We show that the weak interactions will spread out the current to distances r = (1/MZ) ln(I/MZ), where I is the magnitude of the current in the string. Consequences for the scattering of light by these strings is presented. Symmetry breaking at scales of Λ = 10 TeV, or higher, may induce strings that behav...

    Nature is characterized by its chaotic behavior. Mathematics is considered one of the appropriate tools to achieve the best definition of possible its chaos variables and process. Classical mathematics deals with the numbers as static and meaningless, but chaos mathematics deals with it as dynamic evolutionary, and value- added. This paper attempts to introduce the transportation problem re...

When the Higgs sector of the standard model is replaced by a flavor doublet of color sextet quarks, dynamical electroweak symmetry breaking occurs, with the electroweak scale identified as the sextet chiral scale. Above the electroweak scale QCD is almost scale-invariant, leading to the high-momentum enhancement of both the sextet chiral condensate and instanton interactions. The instanton inte...