Related papers: Cantor type functions in non-integer bases

Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…

By a tensor we mean a multidimensional array (matrix) or hypermatrix over a number field. This article aims to set an account of the studies on the permanent functions of tensors. We formulate the definitions of 1-permanent, 2-permanent,…

Considering quantales as generalised noncommutative spaces, we address as an example a quantale Pen based on the Penrose tilings of the plane. We study in general the representations of involutive quantales on those of binary relations, and…

Analogue of Springer's formula for the Poincar\'e series of the algebra invariants of ternary form is found.

Exact non-perturbative partition functions of coupling constants and external fields exhibit huge hidden symmetry, reflecting the possibility to change integration variables in the functional integral. In many cases this implies also some…

A general solution is found for a large class of time continuous autonomous nonlinear dynamical systems, the so-called quasi-polynomial systems. This solution is expressed in terms of a new type of special functions defined via their Taylor…

We prove that the centralizer algebras of the symplectic and orthogonal group acting on tensor space are cellular algebras over the integers. We do this by providing an axiomatic framework for studying quotient towers for towers of diagram…

There exist uniquely ergodic affine interval exchange transformations of [0,1] with flips having wandering intervals and such that the support of the invariant measure is a Cantor set.

Unlike in complex linear operator theory, polynomials or, more generally, Laurent series in antilinear operators cannot be modelled with complex analysis. There exists a corresponding function space, though, surfacing in spectral mapping…

We study properties of the set of subsums for a convergent series $ k_1 \sin x + \dots + k_m \sin x +\dots + k_1\sin x^n +\dots + k_m \sin x^n + \dots $, where $k_1, k_2, k_3,\dots,k_m$ are fixed positive integers and $0<x<1$. Depends on…

Commutators of a large class of bilinear operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be jointly compact. Under a similar commutation, fractional…

Cantor's famous proof of the non-denumerability of real numbers does apply to any infinite set. The set of exclusively all natural numbers does not exist. This shows that the concept of countability is not well defined. There remains no…

One of the possible representations of three-valued instantaneous noise-based logic is proposed. The third value is an uncertain bit value, which can be useful in artificial intelligence applications. There is a forth value, too, that can…

We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…

It is a significant challenge to design probabilistic programming systems that can accommodate a wide variety of inference strategies within a unified framework. Noting that the versatility of modern automatic differentiation frameworks is…

The goal of the present paper is to introduce and study noncommutative Hardy spaces associated with the regular $\Lambda$-polyball, to develop a functional calculus on noncommutative Hardy spaces for the completely non-coisometric (c.n.c.)…

We prove the existence of a nontrivial uniform algebra that is logmodular and regular on the Cantor set. As a consequence, we obtain that for every compact metrizable space X without isolated points there exists a nontrivial essential…

Random tensors are the natural generalization of random matrices to higher order objects. They provide generating functions for random geometries and, assuming some familiarity with random matrix theory and quantum field theory, we discuss…

Specific definitions of the core and core-EP inverses of complex tensors are introduced. Some characterizations, representations and properties of the core and core-EP inverses are investigated. The results are verified using specific…

Cantor sets in \(\mathbb{R}\) are common examples of sets for which Hausdorff measures can be positive and finite. However, there exist Cantor sets for which no Hausdorff measure is supported and finite. The purpose of this paper is to try…