Related papers: A note on larger orbit size

A short proof to a recent theorem of Giambruno and Mishchenko is given in this note.

Inspired by work of McMullen, we show that any orbit for the action of the diagonal group on the space of lattices, accumulates on a stable lattice. We use this to settle a conjecture of Ramharter about Mordell's constant, get new proofs of…

Here we give a reformulation of a key lemma in the paper [2], "Spaces of Topological Complexity One", which is necessary due to an oversight.

This article is intended to review the recent developments in the Horndeski theory and its generalization, which provide us with a systematic understanding of scalar-tensor theories of gravity as well as a powerful tool to explore…

This note is an addendum to [1,2], pointing out the differences between these papers and raising open questions.

In the context of special relativity, we discuss the specific impulse of a rocket whose exhaust jet consists of massive and/or massless particles. This work generalizes previous results and corrects some errors of a recently published paper…

This is a detailed answer to the criticism of my paper.

In this short note we present some remarks and conjectures on two of Erd\"os's open problems in number theory.

In this investigation we treat a special configuration of two celestial bodies in 1:1 mean motion resonance namely the so-called exchange orbits. There exist -- at least -- theoretically -- two different types: the exchange-a orbits and the…

This is a summary of the `Astronomy Perspective' of the 4th meeting on 'Statistical Challenges in Modern Astronomy' held at Penn State University in June 2006. We comment on trends in the Astronomy community towards Bayesian methods and…

We prove an effective equidistribution result for periodic orbits of semisimple groups on congruence quotients of an ambient semisimple group. This extends previous work of Einsiedler, Margulis and Venkatesh. The main new feature is that we…

We prove a conjecture of Conrad, Diamond, and Taylor on the size of certain deformation rings parametrizing potentially Barsotti-Tate Galois representations. To achieve this, we extend results of Breuil and Mezard (classifying Galois…

This paper extends characterizations of Sobolev spaces by Bourgain, Br\'{e}zis, and Mironescu to the higher order case. As a byproduct, we obtain an integral condition for the Taylor remainder term, which implies that the function is a…

In this short note we improve the best to date bound in Godbersen's conjecture, and show some implications for unbalanced difference bodies.

We show a kind of converse to some results of Hall and Reginatto on exact uncertainty related to the Schroedinger and Wheeler-deWitt equations. Some survey material on statistical geometrodynamics is also sketched.

These lecture notes are intended to introduce the theory of rotating stars in general relativity. The focus is put on the theoretical foundations, with a detailed discussion of the spacetime symmetries, the choice of coordinates and the…

We present numerical results and computer assisted proofs of the existence of periodic orbits for the Kuramoto-Sivashinky equation. These two results are based on writing down the existence of periodic orbits as zeros of functionals. This…

We prove that any two $\mathbb{Z}$-odometers are sub-$L^1$-orbit equivalent, greatly strengthening previous results and giving a definitive picture of quantitative orbit equivalence for these systems.

We establish the existence of time-dependent solitons in a modified gravity framework, which is defined by the low energy limit of theories with a weakly broken galileon symmetry and a mass term. These are regular vacuum configurations of…

We improve constants in the Rademacher-Menchov inequality.