An application of solvable structures to the reduction ODEs with a lack local symmetries is given. Solvable considered here are all defined in nonlocal extension, or covering space, given ODE. Examples procedure provided.

Abstract Let G be a finite group. Denoting by $$\textrm{cd}(G)$$ cd ( G ) the set of degrees irreducible complex characters , we consider character degree graph : this is (simple undirected) whose vertices are prime divisors numbe...

Using supersymmetric quantum mechanics we develop a new method for constructing quasi-exactly solvable (QES) potentials with two known eigenstates. This method is extended for constructing conditionally-exactly solvable potentials (CES). The considered QES potentials at certain values of parameters become exactly solvable and can be treated as CES ones.

A bstract This paper is an attempt to extend the recent understanding of Page curve for evaporating black holes more general systems coupled a heat bath. Although calculating von Neumann entropy by replica trick usually challenge, we have identified two solvable cases. For initial section curve, sum up perturbation series in system-bath coupling ? ; most interesting contribution order 2 s , whe...

We prove that every countable group with solvable power problem embeds into a finitely presented 2-generated group with solvable power and conjugacy problems.

In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable and an array of powerful new approximation methods for handling potentials which are not exactly solvable. In this report, we review the theoretical formulat...

We examine the problem of finding rational points defined over solvable extensions on algebraic curves defined over general fields. We construct non-singular, geometrically irreducible projective curves without solvable points of genus g when g is at least 40 over fields of arbitrary characteristic. We prove that every smooth, geometrically irreducible projective curve of genus 0, 2, 3 or 4 def...