A formal Frobenius theorem, which is an analog of the classical integrability theorem for smooth distributions, is proved and applied to generalize the argument shift method of A. S. Mishchenko and A. T. Fomenko to finite-dimensional Lie algebras over any field of characteristic zero. A completeness criterion for a commutative set of polynomials constructed by the formal argument shift method i...

The spectral radius of a matrix A is the maximum norm of all eigenvalues of A. In previous work we already formalized that for a complex matrix A, the values in A grow polynomially in n if and only if the spectral radius is at most one. One problem with the above characterization is the determination of all complex eigenvalues. In case A contains only non-negative real values, a simplification ...

This primarily expository article collects together some facts from the literature about the monodromy of differential equations on a p-adic (rigid analytic) annulus, though often with simpler proofs. These include Matsuda’s classification of quasiunipotent ∇-modules, the Christol-Mebkhout construction of the ramification filtration, and the Christol-Dwork Frobenius antecedent theorem. We also ...

In this article, we prove the following results. • We show a mirror theorem : the Frobenius manifold associated to the orbifold quantum cohomology of weighted projective space is isomorphic to the one attached to a specific Laurent polynomial, • We show a reconstruction theorem, that is, we can reconstruct in an algorithmic way the full genus 0 Gromov-Witten potential from the 3-point invariants.

In this note we prove a generalization of the Frobenius-Schur theorem for finite groups for the case of semisimple Hopf algebra over an algebraically closed field of characteristic 0. A similar result holds in characteristic p > 2 if the Hopf algebra is also cosemisimple. In fact we show a more general version for any finite-dimensional semisimple algebra with an involution; this more general r...

We give an integrability criterion for a projective limit of Banach distributions on Fr\'echet manifold which is manifolds. This leads to result involutive bundles sequence can be seen as version Frobenius Theorem in setting. As consequence, we obtain the third Lie theorem Fr\'echet-Lie group submersive groups. also application prolongations algebroid.

In the last two years Frobenius-Euler polynomials have gained renewed interest and were studied by several authors. This paper presents a novel approach to these polynomials by treating them as Appell polynomials. This allows to apply an elementary matrix representation based on a nilpotent creation matrix for proving some of the main properties of Frobenius-Euler polynomials in a straightforwa...

It is often stated that Frobenius quantales are necessarily unital. By taking negation as a primitive operation, we can define may not have unit. We develop the elementary theory of these structures and show, in particular, how to nuclei whose quotients quantales. This yields phase semantics representation theorem via Important examples arise from Raney’s notion tight Galois connection: endomap...

let x ,..., xn 1 be a random sample from a distribution with sample mean x and samplevariance s 2. in this paper we consider certain very general properties of the so-called “z-scores”x x s i n i ( − )/ : = 1,...., . a representation theorem is then given for z-scores obtained from an underlyingnormal population, together with a theorem for their limiting distribution as the sample size tends t...