Related papers: Linear forms of a given Diophantine type

In this paper we study about the existence of solutions of certain kind of non-linear differential and differential-difference equations. We give partial answer to a problem which was asked by chen et al. in [13].

We survey some results on toric topology.

We study directions along which the norms of vectors are preserved under a linear map. In particular, we find families of matrices for which these directions are determined by integer vectors. We consider the two-dimensional case in detail,…

Some special solutions to the multidimensional Lam\'e and Bourlet type equations are constructed in an explicit form.

We present lifted linear relaxations of the OPF problem.

This paper concerns a nonlinear elliptic equation involving a critical Sobolev growth and a lower-order term. Under a Lions's condition, we prove the existence of at least one positive solution. Our approach consists in constructing a…

We survey results devoted to the lattice of varieties of monoids. Along with known results, some unpublished results are given with proofs. A number of open questions and problems are also formulated.

In this paper we prove the Dynamical Mordell-Lang Conjecture for polynomial endomorphisms of the affine plane.

We prove Landen's transformation by a direct elementary transformation of infinite series

We prove that any product of a family of pseudofinite structures is pseudofinite. The main tools are the fundamental results on products of first order structures due to Feferman and Vaught.

We develop the metric theory of Diophantine approximation on homogeneous varieties of semisimple algebraic groups and prove results analogous to the classical Khinchin and Jarnik theorems. In full generality our results establish…

In this paper we investigate the metrical theory of Diophantine approximation associated with linear forms that are simultaneously small for infinitely many integer vectors; i.e. forms which are close to the origin. A complete…

In this paper we deal with a non-linear Diophantine equation which arises from the determinant computation of an integer matrix. We show how to find a solution, when it exists. We define an equivalence relation and show how the set of all…

We prove a formula relating the fermionic forms and the Poincare polynomials of quiver varieties associated to a finite quiver. Applied to quivers of type ADE, our result implies a version of the fermionic conjecture of Lusztig.

Certain types of bilinearly defined sets in $\mathbb{R}^n$ exhibit a higher degree of linearity than what is apparent by inspection.

We prove that the uniform recurrence of morphic sequences is decidable. For this we show that the number of derived sequences of uniformly recurrent morphic sequences is bounded. As a corollary we obtain that uniformly recurrent morphic…

These notes represent an extended version of a talk I gave for the participants of the IMO 2009 and other interested people. We introduce diophantine equations and show evidence that it can be hard to solve them. Then we demonstrate how one…

Some diophantine aspects of projective toric varieties: We present several faces of projective toric varieties, of interest from the point of view of diophantine geometry. We make explicit the theory on a number of meaningful examples and…

We prove the long time existence of solutions of a Boussinesq system with strong topography variations.

We give evaluations in closed form of certain Lehmer-binomial series