Related papers: Characterization of generic transversality
The goal of this note is to provide a geometric setting in which generalized arithmetic means are best predictors in an appropriate metric. This characterization provides a geometric interpretation to the concept of certainty equivalent.…
The main formal structures of Generalized Quantum Theory are summarized. Recent progress has sharpened some of the concepts, in particular the notion of an observable, the action of an observable on states (putting more emphasis on the role…
One of the main problems in any quantum resource theory is the characterization of the conversions between resources by means of the free operations of the theory. In this work, we advance on this characterization within the quantum…
In this paper, we propose a generalization of a congruence due to Carlitz.
Special generic maps are generalizations of Morse functions with exactly two singular points on spheres and canonical projections of unit spheres. They restrict the manifolds of the domains strongly in considerable cases and are important…
The article continues the study of the 'regular' arrangement of a collection of sets near a point in their intersection. Such regular intersection or, in other words, transversality properties are crucial for the validity of qualification…
We explore the algebraic properties of a generalized version of the iterated-sums signature, inspired by previous work of F.~Kir\'aly and H.~Oberhauser. In particular, we show how to recover the character property of the associated linear…
A unified framework for different formulations of quantum theoery is introduced specifying what is meant by a quantum mechanical theory in general.
We explore the notion of sectional number of a group homomorphism, leading to a generalization of the covering number of a group, and present several characterizations when the sectional number is finite, providing estimates for computing…
A foundation for closing the gap between biometrics in the narrower and the broader perspective is presented trough a conceptualization of biometric systems in both perspectives. A clear distinction between verification, identification and…
Generalised contact structures are studied from the point of view of reduced generalised complex structures, naturally incorporating non-coorientable structures as non-trivial fibering. The infinitesimal symmetries are described in detail,…
The paper presents shortly the geometric approach to the problem of a general quantization formalism, both physically meaningful and mathematically consistent.
Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…
This article shows that the approach to generalised curvature and torsion pioneered by Polacek and Siegel [1] is a generalisation of Cartan Geometry -- rendering latter natural from the point of view of O(d,d)-generalised geometry. We…
In this paper, we study spectral properties of generalized weighted Hilbert matrices. In particular, we establish results on the spectral norm, determinant, as well as various relations between the eigenvalues and eigenvectors of such…
In this second of three introductory papers, we extend the notion of generalised Cesaro summation/convergence to the more natural setting of what we call remainder Cesaro summation/convergence. This greatly expands the range of problems…
In this paper we introduce a general framework for defining the depth of a sequence with respect to a class of observers. We show that our general framework captures all depth notions introduced in complexity theory so far. We review most…
This paper proves that the characteristic polynomial is a complete unitary invariant for pairs of projection matrices. Some special cases involving three or more projections are also considered.
This paper introduces a reformulation of the classical convergence theorem for spectral sequences of filtered complexes which provides an algorithm to effectively compute the induced filtration on the total (co)homology, as soon as the…
A definition of summability is put forward in the framework of general Carleman ultraholomorphic classes in sectors, so generalizing $k-$summability theory as developed by J.-P. Ramis. Departing from a strongly regular sequence of positive…