Related papers: When any three solutions are independent

This article is interested in internality to the constants of systems of autonomous algebraic ordinary differential equations. Roughly, this means determining when can all solutions of such a system be written as a rational function of…

Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…

We indicate a way of distinguishing between structures, for which, two structures are said to be separable.Being separable implies being non-isomorphic. We show that for any first order theory $T$ in a countable language, if it has an…

In [2], an exhaustive construction is achieved for the class of all 4-dimensional unital division algebras over finite fields of odd order, whose left nucleus is not minimal and whose automorphism group contains Klein's four-group. We…

We study unitary multigraded non-associative algebras R generated by an ordered set X over a field K of characteristic 0 such that the mappings d_k: x_l->delta_{kl}, x_k,x_l in X, can be extended to derivations of R. The class of these…

Generalising and unifying the known theorems for difference and differential fields, it is shown that for every finite free ${\mathbb S}$-algebra ${\mathcal D}$ over a field $A$ of characteristic zero the theory of ${\mathcal D}$-fields has…

We consider an ordinary nonlinear differential equation with generalized coefficients as an equation in differentials in algebra of new generalized functions. Then the solution of such equation will be a new generalized function. In the…

Let $(x_1,y_1),\ldots,(x_n,y_n)$ be distinct non-constant and non-degenerate solutions of the classical Lotka-Volterra system \begin{equation}\notag \begin{split} x'&= axy + bx\\ y'&= cxy + dy, \end{split} \end{equation} where…

The work considers a system of fractional order partial differential equations. The existence and uniqueness theorems for the classical solution of initial-boundary value problems are proved in two cases: 1) the right-hand side of the…

We show that the rational homotopy type of the complement of a toric arrangement is completely determined by two sets of combinatorial data. This is obtained by introducing a differential graded algebra over Q whose minimal model is…

In this paper by exploiting critical point theory, the existence of two distinct nontrivial solutions for a nonlinear algebraic system with a parameter is established. Our goal is achieved by requiring an appropriate behavior of the…

Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…

We consider entropically regularized, semi-discrete versions of variational problems on the set of probability measures involving optimal transport as well as other terms. We prove that the solutions can be characterized by well-posed…

Let k a characteristic zero field. We give a characterization for the finite quiver k-algebras, based on double derivations. More precisely, we prove that if an associative and unitary k-algebra have a family of double derivations…

We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data…

It is proved that for any finite dimensional representation of a prime order group over the field of rational numbers, polynomial invariants of degree at most $3$ separate the orbits. A result providing an upper degree bound for separating…

By means of classical fixed point index, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of Hammerstein integral equations where the nonlinearities are allowed to…

We generalize two of our previous results on abelian definable groups in $p$-adically closed fields to the non-abelian case. First, we show that if $G$ is a definable group that is not definably compact, then $G$ has a one-dimensional…

Regular groups and fields are common generalizations of minimal and quasi-minimal groups and fields, so the conjectures that minimal or quasi-minimal fields are algebraically closed have their common generalization to the conjecture that…

After tersely reviewing the various meanings that can be given to the property of a system of nonlinear ODEs to be solvable, we identify a special case of the system of two first-order ODEs with homogeneous quadratic right-hand sides which…