We show on the example of the discrete heat equation that for any given discrete derivative we can construct a nontrivial Leibniz rule suitable to find the symmetries of discrete equations. In this way we obtain a symmetry Lie algebra, defined in terms of shift operators, isomorphic to that of the continuous heat equation.

A method used recently to obtain a discrete formalism for classical fields with nonlocal actions preserving chiral symmetry and uniqueness of fermion fields yields a discrete version of Huygens’ principle with free discrete propagators that recover their continuum forms in certain limit.

In this paper we analyze some properties of the discrete copulas in terms of permutations. We observe the connection between discrete copulas and the empirical copulas, and then we analyze a statistic that indicates when the discrete copula is symmetric and obtain its main statistical properties under independence. The results obtained are useful in designing a nonparametric test for symmetry o...

We examine discrete gauge symmetries in axionic extensions of the SSM which provide a solution of the µ-problem. Automatic-PQ symmetry and proton stability are shown to be guaranteed by certain discrete symmetries. Focusing on the L-violating discrete symmetries we discuss two sources of neutrino masses and their relevance for the solar neutrino problem.

Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the controlled Lagrangian approach in the discrete context that are not present in the continuous theory. In particular, to make the discrete theory effective, one can m...

Recently a TeV-scale Supersymmetric Standard Model (TSSM) was proposed in which the gauge coupling unification is as precise (at one loop) as in the MSSM, and occurs in the TeV range. Proton stability in the TSSM is due to an anomaly free Z3 ⊗ Z3 discrete gauge symmetry, which is also essential for successfully generating neutrino masses in the desirable range. In this paper we show that the TS...

The cosmological and astrophysical implications of a shadow matter model which could also have interesting experimental consequences are examined. The model has identical microphysics for both the ordinary and shadow worlds but requires a macroscopic asymmetry from nucleosynthesis constraints. It is proposed that this macroscopic asymmetry can be generated at the quark-hadron phase transition. ...

In an attempt to understand the observed patterns of lepton and quark masses, models invoking a flavor symmetry Gf , under which the Standard Model generations are charged, have been proposed. One particularly successful symmetry, U(2), has been extensively discussed in the literature. The Yukawa matrices in models based on this symmetry reproduce the observed mass ratios in the lepton and quar...

The possibility exists that the early universe experienced a sequence of symmetry breaking phase transitions, which could have resulted in the production of defects, such as monopoles, cosmic strings, or domain walls [1–3]. Furthermore, it is possible that supersymmetry could have been physically realized during early epochs, becoming broken after defect formation, at a lower energy scale. It i...

The Karhunen-Loève spectrum of a discrete function can vary depending on how symmetry group objects are mapped to function minterms. For completely specified functions with a range space smaller than the cardinality of a symmetry group, we propose a technique to assign the symmetry group don’t cares to maximize the number of zero-valued KL spectral coefficients of the function. To evaluate thes...