Related papers: Kernel Atomicity
In the previous paper, we defined a new category which categorifies the Hecke algebra. This is a generalization of the theory of Soergel bimodules. To prove theorems, the existences of certain homomorphisms between Bott-Samelson bimodules…
Exact sequences are a well known notion in homological algebra. We investigate here the more vague properties of 'homotopical exactness', appearing for instance in the fibre or cofibre sequence of a map. Such notions of exactness can be…
Paragrassmann algebras are given a sesquilinear form for which one subalgebra becomes a Hilbert space known as the Segal-Bargmann space. This Hilbert space as well as the ambient space of the paragrassmann algebra itself are shown to have…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…
We present a phenomenological theory of nuclei that incorporates clustering at the nuclear surface in a general form. The theory explains the recently extracted large symmetry energy by Natowitz et al. at low densities of nuclear matter and…
Atomicity is a ubiquitous assumption in distributed computing, under which actions are indivisible and appear sequential. In classical computing, this assumption has several theoretical and practical guarantees. In quantum computing,…
As an appropriate generalisation of the features of the classical (Schein) theory of representations of inverse semigroups in $\mathscr{I}_{X}$, a theory of representations of inverse semigroups by homomorphisms into complete atomistic…
The open quantum system eigenstate in the vicinity of low-energy decay channel may mimic its features, in particular the characteristic clustering properties of the decay channel. This generic mechanism of clusterization, the so-called…
Two distinct structures of aggregates of atoms connected by anisotropic bonds with a network configuration are discussed from the viewpoint of a point set topology. A specific topological space connects the two types of topological…
The CBH theorem characterises quantum theory within a C*-algebraic framework. Namely, mathematical properties of C*-algebras modelling quantum systems are equivalent to constraints that are information-theoretic in nature: (1)…
In this short note, we give a new sufficient condition for a linear map from a product of copies of a field to endomorphisms of a finite dimensional vector space over the same field to be an algebra homomorphism. We expect that this result…
We describe those reproducing kernel Hilbert spaces of holomorphic functions on domains in ${\Bbb C}^d$ for which an analogue of the Nevanlinna-Pick theorem holds, in other words when the existence of a (possibly matrix-valued) function in…
The notion of atomicity defined by Cohen, Moore and Neisendorfer is studied for the Dickson algebras. Not any ring of invariants respects this property. It depends on the property of the Dickson algebra that given any monomial $d$ there…
In resisting attempts to explain the unity of a whole in terms of a multiplicity of interacting parts, quantum mechanics calls for an explanatory concept that proceeds in the opposite direction: from unity to multiplicity. It concerns the…
Suppose $C$ is an isogeny class of abelian varieties over a finite field $k$. In this paper we give a partial answer to the question of which finite group schemes over $k$ occur as kernels of polarizations of varieties in $C$. We show that…
Asymmetric nuclear matter at sub-saturation densities is shown to present only one type of instabilities. The associated order parameter is dominated by the isoscalar density and so the transition is of liquid-gas type. The instability goes…
Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…
This work introduces topological regularization as a framework for handling ultraviolet divergences in quantum field theory, reinterpreting infinities as topological obstructions at spacetime boundaries. Through geometric compactification…
Strictly proper kernel scores are well-known tool in probabilistic forecasting, while characteristic kernels have been extensively investigated in the machine learning literature. We first show that both notions coincide, so that insights…
Let $E$ be an $1$-Ahlfors regular subset of the Heisenberg group $\mathbb{H}$. We prove that there exists a $-1$-homogeneous kernel $K_1$ such that if $E$ is contained in a $1$-regular curve the corresponding singular integral is bounded in…