Related papers: On the algebraic non-integrability of the Halphen …

Many distinct problems give birth to Darboux-Halphen system of differential equations and here we review some of them. The first is the classical problem presented by Darboux and later solved by Halphen concerning finding infinite number of…

First order algebraic differential equations are considered. An necessary condition for a first order algebraic differential equation to have a rational general solution is given: the algebraic genus of the equation should be zero.…

The new method for obtaining a variety of extensions of Hermite polynomials is given. As a first example a family of orthogonal polynomial systems which includes the generalized Hermite polynomials is considered. Apparently, either these…

The conjecture that every modular lattice is integral is disproved.

It is a fundamental result in commutative algebra and invariant theory that a finitely generated graded module over a commutative finitely generated graded algebra has rational Hilbert series, and consequently the Hilbert series of the…

We focus on a chaotic differential system in 3-dimension, including an absolute term and a line of equilibrium points. Which describes in the following This system has an implementation in electronic components. The first purpose of this…

We show that, if PA has no non-standard models, then P=/=NP. We then give an elementary proof that PA has no non-standard models.

The aim of this short note is to communicate an example of a finite-dimensional Hopf algebra that does not admit a modular pair in involution in the sense of Connes and Moscovici.

In this paper, we characterize all the irreducible Darboux polynomials and polynomial first integrals of FitzHugh-Nagumo (F-N) system. The method of the weight homogeneous polynomials and the characteristic curves is widely used to give a…

In this study, the solution of the Hamilton-Jacobi equation (HJE) with holonomic Hamiltonian is investigated in terms of the first integrals of the corresponding Hamiltonian system. Holonomic functions are related to a specific type of…

In this paper we study the integrability of the Hamiltonian system associated to the fourth Painlev\'{e} equation. We prove that one two parametric family of this Hamiltonian system is not integrable in the sense of the Liouville-Arnold…

In this note, we prove the irrationality of $\zeta(5)$ and generalize the method to prove the irrationality of all higher odd zeta values. Our proof relies on the method of contradiction, existence of solution of a system of Linear…

We proved a conjecture of D. Freed that there are no non-trivial complete special Kaehler manifolds.

In [11] Sklinos proved that any uncountable free group is not $\aleph_1$-homogenenous. This was later generalized by Belegradek in [1] to torsion-free residually finite relatively free groups, leaving open whether the assumption of residual…

There exists a complete atomless Boolean algebra that has no proper atomless complete subalgebra.

In this paper we study some fragments without implications of the (Hilbert) full Lambek logic $\mathbf{HFL}$ and also some fragments without implications of some of the substructural extensions of that logic. To do this, we perform an…

We show that for any pair of non-trivial finite groups, their coproduct in the category of finite groups is not representable.

We prove that no nilpotent Lie algebra admits an invariant generalized Kaehler structure. This is done by showing that a certain differential graded algebra associated to a generalized complex manifold is formal in the generalized Kaehler…

In this note, we prove some non-existence results for Dirichlet problems of complex Hessian equations. The non-existence results are proved using the Pohozaev method. We also prove existence results for radially symmetric solutions. The…

An algebraic technique is presented that does not use results of model theory and makes it possible to construct a general Galois theory of arbitrary nonlinear systems of partial differential equations. The algebraic technique is based on…