Related papers: A local version of Gotzmann's Persistence

Let $R$ be a commutative Noetherian ring, $I$ an ideal, $M$ and $N$ finitely generated $R$-modules. Assume $V(I)\cap Supp(M)\cap Supp(N)$ consists of finitely many maximal ideals and let ${\l}(\e^i(N/I^nN,M))$ denote the length of…

This paper investigates the expressiveness of a fragment of first-order sentences in Gaifman normal form, namely the positive Boolean combinations of basic local sentences. We show that they match exactly the first-order sentences preserved…

If $X \subset \mathbb P^n$ is a reduced subscheme, we say that $X$ admits an unexpected hypersurface of degree $t$ for multiplicity $m$ if the imposition of having multiplicity $m$ at a general point $P$ fails to impose the expected number…

Motivated by certain problems of statistical physics we consider a stationary stochastic process in which deterministic evolution is interrupted at random times by upward jumps of a fixed size. If the evolution consists of linear decay, the…

Let $A = K[x_1, ..., x_n]$ denote the polynomial ring in $n$ variables over a field $K$. We will classify all the Gotzmann ideals of $A$ with at most $n$ generators. In addition, we will study Hilbert functions $H$ for which all homogeneous…

Goodstein's principle is arguably the first purely number-theoretic statement known to be independent of Peano arithmetic. It involves sequences of natural numbers which at first appear to grow very quickly, but eventually decrease to zero.…

Necessary conditions for existence of normal extremals in optimal control of systems subject to nonholonomic constraints are derived as solutions of a constrained second order variational problems. In this work, a geometric interpretation…

We start with some global Maxwellian function $M$, which is a stationary solution (with the constant total density $\rho$) of the Boltzmann equation, and we denote the number of the corresponding space variables by $n$. The notion of…

We address the issue of semiparametric efficiency in the bivariate regression problem with a highly persistent predictor, where the joint distribution of the innovations is regarded an infinite-dimensional nuisance parameter. Using a…

The Gompertz model describes the growth in time of the size of significant quantities associated to a large number of systems, taking into account nonlinearity features by a linear equation satisfied by a nonlinear function of the size.…

We study the Boltzmann equation near a global Maxwellian in the case of bounded domains. We consider the boundary conditions to be either specular reflections or Maxwellian diffusion. Starting from the reference work of Guo in…

We generalize P. M. Neumann's Lemma to the setting of isometric actions on metric spaces and use it to prove several results in continuous logic related to algebraic independence. In particular, we show that algebraic independence satisfies…

We give continued fraction algorithms for a particular class of Fuchsian triangle groups. In particular, we give an explicit form of each such group that is a subgroup of the Hilbert modular group of its trace field and provide an interval…

We prove almost sure convergence of the maximum degree in an evolving graph model combining a growing number of local choices with sublinear preferential attachment. At each step in the growth of the graph, a new vertex is introduced. Then…

We consider a stochastic $N$-particle model for the spatially homogeneous Boltzmann evolution and prove its convergence to the associated Boltzmann equation when $N\to \infty$. For any time $T>0$ we bound the distance between the empirical…

Consider a stochastic process $(S_{[a_i,b_i]})_{[a_i,b_i] \subset \mathbb{N}}$, which is indexed by the collection of all nonempty intervals $[a_i,b_i] \subset \mathbb{N}$ and which is stationary under translations of the intervals. It was…

We study Gibbs partitions that typically form a unique giant component. The remainder is shown to converge in total variation toward a Boltzmann-distributed limit structure. We demon- strate how this setting encompasses arbitrary weighted…

Let $n=\frac{r(r+1)}{2}$ or $n=r(r+1)$. We prove that the property of being extremal is preserved under residuality on the Hilbert scheme of $n$ points in the plane.

We study a hard sphere gas at equilibrium, and prove that in the low density limit, the fluctuations converge to a Gaussian process governed by the fluctuating Boltzmann equation. This result holds for arbitrarily long times. The method of…

For a class of Bellman equations in bounded domains we prove that sub- and supersolutions whose growth at the boundary is suitably controlled must be constant. The ellipticity of the operator is assumed to degenerate at the boundary and a…