Related papers: A Consistent Sandpile Torsor Algorithm for Regular…

In this paper, we prove Morse index theorem of Lagrangian system with any self-adjoint boundary conditions. Based on it, we give some nontrivial estimation on the difference of Morse indices. As an application, we get a new criterion for…

In this paper we extend to a generic class of piecewise smooth dynamical systems a fundamental tool for the analysis of convergence of smooth dynamical systems: contraction theory. We focus on switched systems satisfying Caratheodory…

We prove two results about generically stable types $p$ in arbitrary theories. The first, on existence of strong germs, generalizes results from D. Haskell, E. Hrushovski and D. Macpherson on stably dominated types. The second is an…

A regular parallelism of real projective 3-space PG(3,R) is an equivalence relation on the line space such that every class is equivalent to the set of 1-dimensional complex subspaces of a 2-dimensional complex vector space. We shall assume…

Monodromy in analytic families of smooth complex surfaces yields groups of isotopy classes of orientation preserving diffeomorphisms for each family member X. For all deformation classes of minimal elliptic surfaces with p_g>q=0, we…

A degree-regular triangulation is one in which each vertex has identical degree. Our main result is that any such triangulation of a (possibly non-compact) surface $S$ is geometric, that is, it is combinatorially equivalent to a geodesic…

This work proposes a cooperative strategy for a group of quadrotors interacting over ring digraphs with macro-vertices of size two. Consensus for a group of general double integrators has been initially investigated, and it has been proved…

We show that the product or convex combination of two Markov operators with equivalent stationary measures need not have a stationary measure from the same measure class. More specifically, we exhibit examples of a hitherto undescribed…

Chen and Ye recently proved that the analytic rank of tensors is stable under field extensions, assuming a fixed base field. Using a more careful analysis, we show that this assumption is unnecessary.

The stability of the orbital motion of two long cylindrical magnets interacting exclusively with magnetic forces is described. To carry out analytical studies a model of magnetically interacting symmetric tops [1] is used. The model was…

Let $X$ be a compact smooth manifold, possibly with boundary. Denote by $X_1,\dots,X_r$ the connected components of $X$. Assume that the integral cohomology of $X$ is torsion free and supported in even degrees. We prove that there exists a…

We investigate the iterative behaviour of continuous order preserving subhomogeneous maps that map a polyhedral cone into itself. For these maps we show that every bounded orbit converges to a periodic orbit and, moreover, that there exists…

In this paper we introduce a model describing diffusion of species by a suitable regularization of a "forward-backward" parabolic equation. In particular, we prove existence and uniqueness of solutions, as well as continuous dependence on…

Replacing operators with continuous operator-valued functions, we prove time-dependent versions of well-known results on compressions and diagonals of bounded operators. The setting of smooth functions is also addressed. Our results have no…

A basic result in the elementary theory of continued fractions says that two real numbers share the same tail in their continued fraction expansions iff they belong to the same orbit under the projective action of PGL(2,Z). This result was…

For a connected simply connected semisimple algebraic group $G$ we prove existence of invariant tensors in tensor powers of rational $G$-modules and establish relations between existence of such invariant tensors and stability of diagonal…

Many invertible actions $\tau$ on a set ${\mathcal{S}}$ of combinatorial objects, along with a natural statistic $f$ on ${\mathcal{S}}$, exhibit the following property which we dub \textbf{homomesy}: the average of $f$ over each…

The cycles of a graph give a natural cyclic ordering to their edge-sets, and these orderings are consistent in that two edges are adjacent in one cycle if and only if they are adjacent in every cycle in which they appear together. An…

In this paper, we are interested to study the stability of the ascent of a mutually commuting n-tuple T submitted to a perturbation by an n-tuple S which commutes mutually with T. This study lead us to generalize some well known results for…

We consider the abelian stochastic sandpile model. In this model, a site is deemed unstable when it contains more than one particle. Each unstable site, independently, is toppled at rate $1$, sending two of its particles to neighbouring…