Related papers: Sufficiently many projections in archimedean vecto…

A subbundle of a Hermitian vector bundle $(E, h)$ can be metrically and differentiably defined by the orthogonal projection onto this subbundle. A weakly holomorphic subbundle of a Hermitian holomorphic bundle is, by definition, an…

Let $W_\pi$ be the lattice Lie algebra of Witt type associated with an additive inclusion $\pi: \mathbb{Z}^N \hookrightarrow \mathbb{C}^2$ with $N>1$. In this article, the classification of simple $\mathbb{Z}^N$-graded $W_\pi$-modules,…

Let X be an irreducible 2n-dimensional holomorphic symplectic manifold. A reflexive sheaf F is very modular, if its Azumaya algebra End(F) deforms with X to every Kahler deformation of X. We show that if F is a slope-stable reflexive sheaf…

In this paper, a generalized cusp is a properly convex manifold with strictly convex boundary that is diffeomorphic to $M \times [0, \infty)$ where $M$ is a closed Euclidean manifold. These are classified in [2]. The marked moduli space is…

Approximate lattices of Euclidean spaces, also known as Meyer sets, are aperiodic subsets with fascinating properties. In general, approximate lattices are defined as approximate subgroups of locally compact groups that are discrete and…

A perturbed lattice is a point process $\Pi=\{x+Y_x:x\in \mathbb{Z}^d\}$ where the lattice points in $\mathbb{Z}^d$ are perturbed by i.i.d.\ random variables $\{Y_x\}_{x\in \mathbb{Z}^d}$. A random point process $\Pi$ is said to be rigid if…

We extend the strong multiplicity one theorem of Jacquet, Piatetski-Shapiro and Shalika. Let $\pi$ be a unitary, cuspidal, automorphic representation of $GL_n(\A_K)$. Let $S$ be a set of finite places of $K$, such that the sum $\sum_{v\in…

While studying some properties of linear operators in a Euclidean Jordan algebra, Gowda, Sznajder and Tao have introduced generalized lattice operations based on the projection onto the cone of squares. In two recent papers of the authors…

Let $F$ be a locally compact non-Archimedean field, and $\bf G$ a connected quasi-split reductive group over $F$. We are interested in complex irreducible smooth generic representations $\pi$ of ${\bf G}(F)$. When $F$ has positive…

We construct a compact metric space that has any other compact metric space as a tangent, with respect to the Gromov-Hausdorff distance, at all points. Furthermore, we give examples of compact sets in the Euclidean unit cube, that have…

The Schwartz-Zippel Lemma states that if a low-degree multivariate polynomial with coefficients in a field is not zero everywhere in the field, then it has few roots on every finite subcube of the field. This fundamental fact about…

The construction of a multilayer perceptron (MLP) as a piecewise low-order polynomial approximator using a signal processing approach is presented in this work. The constructed MLP contains one input, one intermediate and one output layers.…

An isomorphism of symplectically tame smooth pseudocomplex structures on the complex projective plane which is a homeomorphism and differentiable of full rank at two points is smooth.

It is shown that, given any (n-1)-dimensional lattice L, there is a vector v in Z^n such that the projection of Z^n onto v^perp is arbitrarily close to L. The problem arises in attempting to find the largest cylinder anchored at two points…

Inspired by very ampleness of Zariski Geometries, we introduce and study the notion of a very ample family of plane curves in any strongly minimal set, and the corresponding notion of a very ample strongly minimal set (characterized by the…

In the present work we describe 3-dimensional complex SL_2-varieties where the generic SL_2-orbit is a surface. We apply this result to classify the minimal 3-dimensional projective varieties with Picard-number 1 where a semisimple group…

A discrete set in the Euclidian space is almost periodic, if the measure with the unite masses at points of the set is almost periodic in the weak sense. We prove the following result: if A is a discrete almost periodic set and the set A-A…

We classify static manifolds which admit more than one static decomposition whenever a condition on the curvature is fullfilled. For this, we take a standard static vector field and analyze its associated one parameter family of projections…

Let (X,dX) and (Y,dY) be semimetric spaces with distance sets D(X) and, respectively, D(Y). A mapping F : X \to Y is a weak similarity if it is surjective and there exists a strictly increasing f : D(Y) \to D(X) such that dX = f \circ dY…

The critical loci of a map $f:X\to Y$ between smooth schemes over a field $k$ are the locally closed subschemes $\Sigma^i(f)\subseteq X$ where the differential of $f$ has constant rank. We prove that if $f : X\to \mathbb A^r$ is the general…