in this paper, we first collect the earlier results about some graph operations and then wepresent applications of these results in working with chemical graphs.

Large sets of baryon interpolating field operators are developed for use in lattice QCD studies of baryons with zero momentum. Operators are classified according to the double-valued irreducible representations of the octahedral group. At first, three-quark smeared, local operators are constructed for each isospin and strangeness and they are classified according to their symmetry with respect ...

Inspired by Bondarenko’s counter-example to Borsuk’s conjecture, we notice some strongly regular graphs that provide examples of ball packings whose chromatic numbers are significantly higher than the dimensions. In particular, from generalized quadrangles we obtain unit ball packings in dimension q3 − q2 + q with chromatic number q3 + 1, where q is a prime power. This improves the previous low...

We derive necessary and sufficient conditions for an ambiskew polynomial ring to have a Hopf algebra structure of a certain type. This construction generalizes many known Hopf algebras, for example U(sl2), Uq(sl2) and the enveloping algebra of the 3-dimensional Heisenberg Lie algebra. In a torsion-free case we describe the finite-dimensional simple modules, in particular their dimensions and pr...

We present a supersymmetric model of fermion masses with SU(4)×SU(2)2×U(1)X gauge group with matter in fundamental and antisymmetric tensor representations only. The up, down, charged lepton and neutrino Yukawa matrices are distinguished by different Clebsch-Gordan coefficients due to contracting over SU(4) and SU(2)R indices. We obtain a hierarchical light neutrino mass spectrum with bi-large ...

We use Clebsch potentials and an action principle to derive a complete closed system of gauge-invariant equations for sound superposed on a general background flow. Our system reduces to the Unruh [Phys. Rev. Lett. 46 (1981) 1351] and Pierce [J. Acoust. Soc. Am. 87 (1990) 2292] wave equations when the flow is irrotational, or slowly varying. We illustrate our formalism by applying it to waves p...

This article deals with a quantum-mechanical system which generalizes the ordinary isotropic harmonic oscillator system. We give the coefficients connecting the polar and Cartesian bases for D = 2 and the coefficients connecting the Cartesian and cylindrical bases as well as the cylindrical and spherical bases for D = 3. These interbasis expansion coefficients are found to be analytic continuat...

Generalized Hamiltonian formalism including generalized Poisson brackets and Lie-Poisson brackets is presented in Section II. Gyroviscous magnetohydrodynamics is treated as a relevant example in Euler and Clebsch variables. Section III is devoted to a short review of functional integration containing the definition and a discussion of ambiguities and methods of evaluation. The main part of the ...