In this work, we study the Klein–Gordon oscillator with equal scalar and vector potentials in a topologically charged Ellis–Bronnikov wormhole space-time background. The behaviour of relativistic field is studied position-dependent mass via transformation [Formula: see text] potential through minimal substitution wave equation. Simplifying equation for three different types potential, such as l...

Cardinal’s matrix version of the Sebastiao e Silva polynomial root-finder rapidly approximates the roots as the eigenvalues of the associated Frobenius matrix. We preserve rapid convergence to the roots but amend the algorithm to allow input polynomials with multiple roots and root clusters. As in Cardinal’s algorithm, we repeatedly square the Frobenius matrix in nearly linear arithmetic time p...

We apply Frobenius integrability theorem in the search of invariants for one-dimensional Hamiltonian systems with a time-dependent potential. We obtain several classes of potential functions for which Frobenius theorem assures the existence of a two-dimensional foliation to which the motion is constrained. In particular, we derive a new infinite class of potentials for which the motion is assur...

In this paper we consider Artinian modules over power series rings endowed with a Frobenius map. We describe a method for finding the set of all prime annihilators of submodules which are preserved by the given Frobenius map and on which the Frobenius map is not nilpotent. This extends the algorithm by Karl Schwede and the first author, which solved this problem for submodules of the injective ...

We extend categorical semantics of monadic programming to reversible computing, by considering monoidal closed dagger categories: the dagger gives reversibility, whereas closure gives higher-order expressivity. We demonstrate that Frobenius monads model the appropriate notion of coherence between the dagger and closure by reinforcing Cayley’s theorem; by proving that effectful computations (Kle...

k field, algebraically closed G finite group Definitions (1) A representation of G over k of degree n is a homomorphism of groups ρ : G→GLn(k), or equivalently, a kG-module structure for an n-dimensional k vector space M , where kG is the group algebra. (2) A representation M is irreducible if it is a simple kG-module, and indecomposable if M 6= N1 ⊕ N2 for any non-trivial submodules N1, N2. No...

Let E be an elementary abelian p-group of rank r and let k be a field of characteristic p. We introduce functors Fi from finitely generated kE-modules of constant Jordan type to vector bundles over projective space Pr−1. The fibers of the functors Fi encode complete information about the Jordan type of the module. We prove that given any vector bundle F of rank s on Pr−1, there is a kE-module M...

Let E ∼= (Z/p)r (r ≥ 2) be an elementary abelian p-group and let k be an algebraically closed field of characteristic p. A finite dimensional kE-module M is said to have constant Jordan type if the restriction of M to every cyclic shifted subgroup of kE has the same Jordan canonical form. I shall begin by discussing theorems and conjectures which restrict the possible Jordan canonical form. The...

LetM be a smooth oriented manifold. The homology ofM has the structure of a Frobenius algebra. This paper shows that on chain level there is a Frobenius-like algebra structure, whose homology gives the Frobenius algebra of M . Moreover, associated to any Frobeniuslike algebra, there is a chain complex whose homology has the structure of a Gerstenhaber algebra and a Batalin-Vilkovisky algebra. A...