Related papers: Geometric conditions for multiple sampling and int…
We characterize all pairs of entire functions $(u,\psi)$ for which the induced weighted superposition operator $S_{(u,\psi)}$ transforms one Fock space into another Fock space.Further analytical structures like boundedness and Lipschitz…
We study finite morphisms of varieties and the link between their top multiplicity loci under certain assumptions. More precisely, we focus on how to determine that link in terms of the spaces of arcs of the varieties.
We investigate $\mathcal F$-Borel topological spaces. We focus on finding out how a~complexity of a~space depends on where the~space is embedded. Of a~particular interest is the~problem of determining whether a~complexity of given space $X$…
In this note we study some properties of topological entropy for noncompact non-metrizable spaces.
We study the topology of polynomial functions by deforming them generically. We explain how the non-conservation of the total ``quantity'' of singularity in the neighbourhood of infinity is related to the variation of topology in certain…
This is mainly a survey of recent work on algebraic ways to ``measure'' moduli spaces of connecting trajectories in Morse and Floer theories as well as related applications to symplectic topology. The paper also contains some new results.…
We answer two questions about the topology of end spaces of infinite type surfaces and the action of the mapping class group that have appeared in the literature. First, we give examples of infinite type surfaces with end spaces that are…
The limit of energies of a sequence of harmonic maps as their annular domains approach the boundary of moduli space depends upon the boundary point approached. The infinite energy case is associated with limits of images containing ruled…
We consider the proposition that multiple universes exist by reviewing the various manifestations. In recent years, this idea has been elevated from science fiction and introduced in separate guises as an explanation for coincidence…
We consider a class $\mathcal{F}$ of Markov multi-maps on the unit interval. Any multi-map gives rise to a space of trajectories, which is a closed, shift-invariant subset of $[0,1]^{\mathbb{Z}_+}$. For a multi-map in $\mathcal{F}$, we show…
We apply a notion of geodesics of plurisubharmonic functions to interpolation of compact subsets of $C^n$. Namely, two non-pluripolar, polynomially closed, compact subsets of $C^n$ are interpolated as level sets $L_t=\{z: u_t(z)=-1\}$ for…
Single-photon pulses cannot be generated on demand, due to incompatible requirements of positive frequencies and positive times. Resulting states therefore contain small probabilities for multiphotons. We derive upper and lower bounds for…
In this paper we study a sufficient conditions for continuous and almost continuous extensions of f to space X for an image space Y with different separation axioms.
The coupling space of perceptrons with continuous as well as with binary weights gets partitioned into a disordered multifractal by a set of $p=\gamma N$ random input patterns. The multifractal spectrum $f(\alpha)$ can be calculated…
We describe here some recent progress pertaining to the Serre Intersection Multiplicity Conjecture. In particular, we show that if A is an unramified regular local ring, then just as in the equicharacteristic case, the intersection…
Given a nondecreasing sequence $\Lambda=\{\lambda_n>0\}$ such that $\displaystyle\lim_{n\to\infty} \lambda_n=\infty,$ we consider the sequence $\mathcal N_\Lambda:=\left\{\lambda_ne^{i\theta_n},n\in\,\mathbb N\right\}$, where $\theta_n$ are…
Simultaneity is a well-defined notion in special relativity once a Minkowski metric structure is fixed on the spacetime continuum (manifold) of events. In quantum gravity, however, the metric is not expected to be a fixed, classical…
We derive source integrals for multipole moments that describe the behavior of static and axially symmetric spacetimes close to spatial infinity. We assume that the matter distribution is isolated. We outline also some applications of these…
We study the Fock description of a quantum free field on the three-sphere with a mass that depends explicitly on time, also interpretable as an explicitly time dependent quadratic potential. We show that, under quite mild restrictions on…
We study two-dimensional eigenvalue ensembles close to certain types of singular points in the bulk of the droplet. We prove existence of a microscopic density which quickly approaches the classical equilibrium density, as the distance from…