Using the methods of the theory of formal symmetries, we obtain new easily verifiable sufficient conditions for a recursion operator to produce a hierarchy of local generalized symmetries. An important advantage of our approach is that under certain mild assumptions it allows to bypass the cumbersome check of hereditariness of the recursion operator in question, what is particularly useful for ...

A subgroup of the automorphism group a graph acts half-arc-transitively on if it transitively vertex-set and edge-set but not arc-set graph. If full half-arc-transitively, is said to be half-arc-transitive. In 1994 Gardiner Praeger introduced two families tetravalent arc-transitive graphs, called C±1 C±ε that play prominent role in characterization graphs admitting an automorphisms with normal ...

We generalize the exact predictive regularity of symmetry groups to give an algebraic theory patterns, building from a core principle future equivalence. For topological patterns in fully-discrete one-dimensional systems, equivalence uniquely specifies minimal semiautomaton. demonstrate how latter and its semigroup algebra generalizes translation partial hidden symmetries. This generalization i...

Bäcklund’s Theorem, which characterizes contact transformations, is generalized to give an analogous characterization of “internal symmetries” of systems of differential equations. For a wide class of systems of differential equations, every internal symmetry comes from a first order generalized symmetry and, conversely, every first order generalized symmetry satisfying certain explicit contact...

It is well known that x-translation and t-translation invariance of (1) leads to the following symmetries: ux, ut of the KdV equation (1). In order to find more generalized symmetries, the concepts of recursion operators or strong symmetries, and hereditary symmetries were introduced by Olver and Fuchssteiner and used to find these symmetries [1, 2]. Furthermore, Galilean invariance of the KdV ...

different symmetries play a role in understanding the meaning of a sentence. syntacticians have been aware of this issue and have used a variety of symmetries in their analyses. when the arabic syntax became familiar with the aristotelian logic and received some philosophical issues, most of the syntacticians focused upon the arabic symmetry and few attentions were directed towards other symmet...

Symmetries of the auto-cumulant function (the generalization of the auto-covariance function) of a kth-order stationary time series are derived through a connection with the symmetric group of degree k. Using theory of group representations, symmetries of the auto-cumulant function are demystified and lag-window functions are symmetrized to satisfy these symmetries. A generalized Gabr-Rao optim...

Analytic-bilinear approach is used to study continuous and discrete non-isospectral symmetries of the generalized KP hierarchy. It is shown that Möbius symmetry transformation for the singular manifold equation leads to continuous or discrete non-isospectral symmetry of the basic (scalar or multicomponent KP) hierarchy connected with binary Bäcklund transformation. A more general class of multi...