Related papers: Remark on the Garnier system in two variables
This note is an addendum to [1,2], pointing out the differences between these papers and raising open questions.
Notions of invariance pressure for control systems are introduced based on weights for the control values. The equivalence is shown between inner invariance pressure based on spanning sets of controls and on invariant open covers,…
We begin the study of how to extend few variable means to several variable ones and how to shrink means of several variables to less variables. With the help of one of the techniques we show that it is enough to check an inequality between…
We exhibit a change of variables that maintains the Mahler measure of a given polynomial. This method leads to the construction of highly non-trivial polynomials with given Mahler measure and settles some conjectural numerical formulas due…
Comment on ``Microarrays, Empirical Bayes and the Two-Groups Model'' [arXiv:0808.0572]
Comment on ``Microarrays, Empirical Bayes and the Two-Groups Model'' [arXiv:0808.0572]
We compute the Groebner basis of a system of polynomial equations related to the Jacobian conjecture using a recursive formula for the Catalan numbers.
We prove the existence of recurrent or Poisson stable motions in the Navier-Stokes fluid system under recurrent or Poisson stable forcing, respectively. We use an approach based on nonautonomous dynamical systems ideas.
In this note we establish some appropriate conditions for stochastic equality of two random variables/vectors which are ordered with respect to convex ordering or with respect to supermodular ordering. Multivariate extensions of this result…
A short note on bounds on distance to variety of a point in terms of the Taylor coefficients at the point.
In this paper we adress the question of I. Smirnov and K. Tucker on the dual $F$-signature of the Veronese subrings of polynomial rings in $n$ variables using methods of commutative algebra.
We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.
Let $\{\mathbb{P}_n\}_{n\ge 0}$ and $\{\mathbb{Q}_n\}_{n\ge 0}$ be two monic polynomial systems in several variables satisfying the linear structure relation $$\mathbb{Q}_n = \mathbb{P}_n + M_n \mathbb{P}_{n-1}, \quad n\ge 1,$$ where $M_n$…
We study reduction schemes for functions of "many" variables into system of functions in one variable. Our setting includes infinite-dimensions. Following Cybenko-Kolmogorov, the outline for our results is as follows: We present explicit…
The pair distributions of one-dimensional "hard sphere" fermion and boson systems are exactly evaluated by introducing gap variables.
Here we introduce reflection positive doubles, a general framework for reflection positivity, covering a wide variety of systems in statistical physics and quantum field theory. These systems may be bosonic, fermionic, or parafermionic in…
The 2-dimensional inverse problem for first-order systems is analysed and a method to construct an affine Lagrangian for such systems is developed. The determination of such Lagrangians is based on the theory of the Jacobi multiplier for…
We give an explicit formula for the Bellman function associated with the dual bound related to the unconditional constant of the Haar system.
We verify the Invariance Conjectures of tautological equations in genus two. In particular, a uniform derivation of all known genus two equations is given.
Analogue of Springer's formula for the Poincar\'e series of the algebra invariants of ternary form is found.