Related papers: Remark on the Garnier system in two variables

We discuss various dualities, relating integrable systems and show that these dualities are explained in the framework of Hamiltonian and Poisson reductions. The dualities we study shed some light on the known integrable systems as well as…

We prove that a certain sequence of tau functions of the Garnier system satisfies Toda equation. We construct a class of algebraic solutions of the system by the use of Toda equation; then show that the associated tau functions are…

We introduce poly-Bernoulli polynomials in two variables by using a generalization of Stirling numbers of the second kind that we studied in a previous work. We prove the bi-variate poly-Bernoulli polynomial version of some known results on…

Using the algebraic method of Gardner's deformations for completely integrable systems, we construct the recurrence relations for densities of the Hamiltonians for the Boussinesq and the Kaup-Boussinesq equations. By extending the Magri…

In this paper the problem of the gauge in a bound state calculation is discussed. In particular, in order to verify the gauge invariance in the energy levels expansion, some set of gauge invariant contributions are given.

Considered two linear regression models of a given response variable with some predictor set and its subset. It is shown that there is a linear relationship between coefficients of these models. Some corollaries of the proved theorem is…

We are able to derive the equations of motion for forced mechanical systems in a purely variational setting, both in the context of Lagrangian or Hamiltonian mechanics, by duplicating the variables of the system as introduced by Galley…

We prove some special cases of Bergeron's inequality involving two Gaussian polynomials (or $q$-binomials).

We find new bi-Lipschitz invariants for functions of two complex variables.

We give a formula and an estimation for the number of irreducible polynomials in two (or more) variables over a finite field.

Memoir on the Sigma invariants and their applications, version 2

We prove a variation of Gronwall's lemma.

We will pursue a way of building up an algebraic structure that involves, in a mathematical abstract way, the well known Grassmann variables. The problem arises when we tried to understand the grassmannian polynomial expansion on the scope…

Short introduction to the gauge/gravity duality

We give semi-decision procedures for the ground word problem of variable preserving term equation systems and term equation systems. They are natural improvements of two well known trivial semi-decision procedures. We show the correctness…

We analyse a mechanical system in two-dimensional relative motion with friction. Although the system is simple, the peculiar interplay between two kinetic friction forces and gravity leads to the wide range of admissible solutions exceeding…

We discuss some paradoxes arising due to the gauge-dependence of canonical variables in mechanics.

We introduce Poincar\'e type inequalities based on rearrangement invariant spaces in the setting of metric measure spaces and analyze when they imply the doubling condition on the underline measure.

This is the first part of a work devoted to the study of linear Mahler systems in several variables from the perspective of transcendence and algebraic independence. We prove two main results concerning systems that are regular singular at…

In this note, we show that a part of [5, Remark 2.2] is not correct. Some conditions are given under which the same holds.