Related papers: Birkhoff's Theorem for Panstochastic Matrices

In this paper, we consider the Dirichlet problem associated to an elliptic Kirchhoff-type equation depending on two parameters. Under rather general and natural assumptions, we prove that, for certain values of the parameters, the problem…

The classical theorem of Birkhoff states that the $T^N f(x) = (1/N)\sum_{k=0}^{N-1} f(\sigma^k x)$ converges almost everywhere for $x\in X$ and $f\in L^{1}(X)$, where $\sigma$ is a measure preserving transformation of a probability measure…

One of the most fundamental mathematical contributions of Garrett Birkhoff is the HSP theorem, which implies that a finite algebra B satisfies all equations that hold in a finite algebra A of the same signature if and only if B is a…

We show that for almost every map in a transversal one-parameter family of piecewise expanding unimodal maps the Birkhoff sum of suitable observables along the forward orbit of the turning point satisfies the law of iterated logarithm. This…

The discrepancy of the $n \times n$ greater-than matrix is shown to be $\frac{\pi}{2 \ln n}$ up to lower order terms.

Eagleson's Theorem asserts that, given a probability-preserving map, ifrenormalized Birkhoff sums of a function converge in distribution, thenthey also converge with respect to any probability measure which isabsolutely continuous with…

Robin's criterion states that the Riemann Hypothesis (RH) is true if and only if Robin's inequality $\sigma(n):=\sum_{p|n}p<e^{\gamma} n \log \log n$ is satisfied for $n > 5040$, where $\gamma$ denotes the Euler-Mascheroni constant. We show…

We prove that the known sufficient conditions on the real parameters $(p,q)$ for which the matrix power mean inequality $((A^p+B^p)/2)^{1/p}\le((A^q+B^q)/2)^{1/q}$ holds for every pair of matrices $A,B>0$ are indeed best possible. The proof…

Let h \subset g be an inclusion of Lie algebras with quotient h-module n. There is a natural degree filtration on the h-module U(g)/U(g)h whose associated graded h-module is isomorphic to S(n). We give a necessary and sufficient condition…

In this paper, the connections between model theory and the theory of infinite permutation groups are used to study the n-existence and the n-uniqueness for n-amalgamation problems of stable theories. We show that, for any n>1, there exists…

We prove two dichotomy theorems about sequences of operators into $L_1$ given by random matrices. In the second theorem we assume that the entries of each random matrix form a sequence of independent, symmetric random variables. Then the…

We study isomonodromic deformation of Fuchsian linear q-difference systems. Furthermore, we are looking of the behaviour of the Birkhoff connexion matrix when q goes to $1$. We use our results to study the convergence of the Birkhoff…

In a previous paper, we derived necessary and sufficient conditions for the invertibility of square submatrices of the Pascal upper triangular matrix. To do so, we established a connection with the two-point Birkhoff interpolation problem.…

The Subspace Theorem due to Schmidt (1972) is a broad generalisation of Roth's Theorem in Diophantine Approximation (1955) which, in the same way as the latter, suffers a notorious lack of effectivity. This problem is tackled from a…

Due to the distribution of primes among integers, we establish an upper bound for the probability $\mathbb{P}_n$ that the Goldbach conjecture fails. Assuming the conjecture holds true for all even number less than $2N$, we prove this…

The inhomogeneous Khintchine-Groshev Theorem is a classical generalization of Khintchine's Theorem in Diophantine approximation, by approximating points in $\mathbb{R}^m$ by systems of linear forms in $n$ variables. Analogous to the…

In this paper, we establish the super Poincar\'e inequality for the two-parameter Dirichlet process when the partition number of the state space is finite. Furthermore, if the partition number is infinite, the super Poincar'e inequality…

We study the validity of the $L^p$ inequality for the Riesz transform when $p>2$ and of its reverse inequality when $p<2$ on complete Riemannian manifolds under the doubling property and some Poincar\'e inequalities.

The Gasca-Maeztu conjecture for the case $n=4$ was proved for the first time in [J. R. Busch, A note on Lagrange interpolation in $\mathbb{R}^2$, Rev. Un. Mat. Argentina, 36 (1990) 33--38]. Here we bring a short and simple proof of it.

Motivated by the Pierce-Birkhoff conjecture, we launch an extension program for single variable expansivity theory. We study this notion under tuples of polynomials in the ring $\mathbb{R}[x_1,x_2,\ldots,x_n]$. As an application, we develop…