Related papers: What is a fundamental domain?
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
Domain shift, caused by variations in imaging modalities and acquisition protocols, limits model generalization in medical image segmentation. While foundation models (FMs) trained on diverse large-scale data hold promise for zero-shot…
The motivation for this paper is to extend the known model theoretic treatment of differential Galois theory to the case of linear difference equations (where the derivative is replaced by an automorphism.) The model theoretic difficulties…
We give a complete description of bounded Reinhardt domains of finite boundary smoothness that have non-compact automorphism group. As part of this program, we show that the classification of domains with non-compact automorphism group and…
Definitions of fractional derivative of order $\alpha$ ($0 < \alpha \leq 1$) using non-singular kernels have been recently proposed. In this note we show that these definitions cannot be useful in modelling problems with a initial value…
We consider the question of which valuation domains (of cardinality aleph_1) have non-standard uniserial modules. We show that a criterion conjectured by Osofsky is independent of ZFC + GCH.
We study generalized means whose domain may contain unbounded sets as well. We investigate usual properties of this type of means and also new attributes that regard for such means only. We examine how a mean defined on bounded sets can be…
A monistic framework is set up where energy is the only fundamental substance. Different states of energy are ordered by a set of scalar qunatum-phase-fields. The dual elements of matter, mass and space, are described as volume- and…
We give an example of a parameter-free definable henselian valuation ring which is neither definable by a parameter-free $\forall\exists$-formula nor by a parameter-free $\exists\forall$-formula in the language of rings. This answers a…
We investigate the notion of a subgroup of a quantum group. We suggest a general definition, which takes into account the work that has been done for quantum homogeneous spaces. We further restrict our attention to reductive subgroups,…
We introduce the notion of the depth of a finite group $G$, defined as the minimal length of an unrefinable chain of subgroups from $G$ to the trivial subgroup. In this paper we investigate the depth of (non-abelian) finite simple groups.…
The majority of traditional classification ru les minimizing the expected probability of error (0-1 loss) are inappropriate if the class probability distributions are ill-defined or impossible to estimate. We argue that in such cases class…
In order to construct a quantum theory of gravity, we may have to abandon certain assumptions we were making. In particular, the concept of spacetime as a continuum substratum is questioned. Causal Sets is an attempt to construct a quantum…
There are various notions of dimension in fractal geometry to characterise (random and non-random) subsets of $\mathbb R^d$. In this expository text, we discuss their analogues for infinite subsets of $\mathbb Z^d$ and, more generally, for…
A historically important but little known debate regarding the necessity and meaning of macroscopic superpositions, in particular those containing different gravitational fields, is discussed from a modern perspective.
We consider the problem of determining the Fourier integral in the Hilbert space of square integrable functions. Fourier integral is the scalar product of two functions belonging to the Hilbert space of square integrable functions and the…
We establish an upper bound on the cardinality of a minimal generating set for the fundamental group of a large family of connected, balanced simplicial complexes and, more generally, simplicial posets.
In this article, we introduce the notion of regular fusible modules. Let $R$ be a ring with an identity and $M$ an $R$-module. An element $0\neq m\in M$ is said to be regular fusible if there exists $r\in R$, a non zero-divisor of $M$, such…
A semigroup $S$ is called an equational domain if any finite union of algebraic sets over $S$ is algebraic. We prove if a completely regular semigroup $S$ is an equational domain then $S$ is completely simple.
The theory of causal fermion systems is an approach to describe fundamental physics. We here introduce the mathematical framework and give an overview of the objectives and current results.