Related papers: On union ultrafilters
We study an order relation on the fibers of a continuous map and its application to the study of the structure of compact spaces of uncountable weight.
Hyperuniform states of matter exhibit unusual suppression of density fluctuations at large scales, contrasting sharply with typical disordered configurations. Various types of hyperuniformity emerge in multicomponent disordered systems,…
We prove that if S is a commutative semigroup with well founded universal semilattice or a solvable inverse semigroup with well founded semilattice of idempotents, then every strongly productive ultrafilter on S is idempotent. Moreover we…
We fully characterise the solvability of Rado equations inside linear combinations $a_{1}\U\oplus\dots\oplus a_{n}\U$ of idempotent ultrafilters $\U\in\beta\Z$ by exploiting known relations between such combinations and strings of integers.…
The paper consists of three parts. In the first of them different kinds stability are discussed. In particular, the stability concept with respect to nef divisor is introduced. A structure of rigid and superrigid vector bundles on smooth…
The issues of robust stability for two types of uncertain fractional-order systems of order $\alpha \in (0,1)$ are dealt with in this paper. For the polytope-type uncertainty case, a less conservative sufficient condition of robust…
We give a new proof of a version of the main theorem of the previous paper in the series about embedding of an algebraic system into ultraproducts.
In the present paper we survey the most recent classification results for proper biharmonic submanifolds in unit Euclidean spheres. We also obtain some new results concerning geometric properties of proper biharmonic constant mean curvature…
The aim of this paper is to construct ultrafilters without immediate predecessors in the Rudin-Frolik order in $\beta \kappa\setminus \kappa$, where $\kappa$ is a regular cardinal. This generalizes the problem posed by Peter Simon more than…
Unstable particles decay sooner or later, so they are not described by asymptotic one-particle states and they should not be included as independent states in unitarity relations such as the optical theorem. The same applies to any…
Upper bounds on projective rigidity of each homogeneously embedded homogeneous variety are determined; and a new, invariant characterization of the Fubini forms is given.
Two results on product of compact filters are shown to be the common principle behind a surprisingly large number of theorems.
We demonstrate that hyperuniformity, the suppression of density fluctuations at large length scales, emerges generically from the interplay between conservation laws and non-equilibrium driving. The underlying mechanism for this emergence…
We present a complete analysis of the linearised dynamics of active solids with orientational order, taking into account a hitherto overlooked consequence of rotation invariance. Our predictions include the possibility of stable active…
The \v{C}ech and Rips constructions of persistent homology are stable with respect to perturbations of the input data. However, neither is robust to outliers, and both can be insensitive to topological structure of high-density regions of…
Unstable holomorphic bundles can be described algebraically by Harder-Narasimhan filtrations. In this note we show how such filtrations correspond to the existence of special metrics defined by Hermitian-Einstein inequalities.
Linear optical circuits of growing complexity are playing an increasing role in emerging photonic quantum technologies. Individual photonic devices are typically described by a unitary matrix containing amplitude and phase information, the…
Non-uniform fast Fourier Transform (NUFFT) and inverse NUFFT (INUFFT) algorithms, based on the Fast Multipole Method (FMM) are developed and tested. Our algorithms are based on a novel factorization of the FFT kernel, and are implemented…
In this letter, by regarding finite-time stability as an inverse problem, we reveal the essence of finite-time stability and fixed-time stability. Some necessary and sufficient conditions are given. As application, we give a new approach…
We review several problems of conventional Grand Unification and some new approaches. In particular, we discuss strongly coupled Grand Unified Theories. Standard Model may emerge as a low energy effective theory of composite particles in…