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The Derivative of Minkowski's ?(x) Function

Journal of Mathematical Analysis and Applications, 2001
The Minkowski function \(?(x): [0,1]\to [0,1]\) is strictly increasing, continuous, and maps the rational numbers onto the dyadic rationals. \textit{R. Salem} has proved in 1943 [Trans. Am. Math. Soc. 53, 427--439 (1943; Zbl 0060.13709)] that if \(x\in[0,1]\) has a continued fraction expansion with unbounded partial quotients and if \(?'(x)\) exists ...
Paradı́s, J., Viader, P., Bibiloni, L.
exaly   +3 more sources

The derivative of the Minkowski function [PDF]

Izvestiya: Mathematics, 2021
Abstract We prove new results on the derivative of the Minkowski question mark function.
Gayfulin, D. R., Kan, I. D.
  +9 more sources

The dual conformal box integral in Minkowski space

Nuclear Physics B, 2021
The dual conformal box integral in Minkowski space is not fully determined by the conformal invariants z and z¯. Depending on the kinematic region its value is on a ‘branch’ of the Bloch-Wigner function which occurs in the Euclidean case.
Luke Corcoran, Matthias Staudacher
doaj   +1 more source

QuantImPy: Minkowski functionals and functions with Python

SoftwareX, 2021
The Minkowski functionals and functions are a family of morphological measures and can be used to describe both the morphology (shape) and topology (connectedness) of a system. This paper presents the QuantImPy Python package which can compute both the Minkowski functionals and functions.
Arnout M. P. Boelens, Hamdi A. Tchelepi
openaire   +2 more sources

Generalized proportional fractional integral functional bounds in Minkowski’s inequalities

Advances in Difference Equations, 2021
In this research paper, we improve some fractional integral inequalities of Minkowski-type. Precisely, we use a proportional fractional integral operator with respect to another strictly increasing continuous function ψ.
Tariq A. Aljaaidi, Deepak B. Pachpatte, Wasfi Shatanawi, Mohammed S. Abdo, Kamaleldin Abodayeh   +4 more
doaj   +1 more source

Field theories on ρ-deformed Minkowski space-time

Journal of High Energy Physics, 2023
We study one-loop perturbative properties of scalar field theories on the ρ-Minkowski space. The corresponding star-product, together with the involution are characterized from a combination of Weyl quantization and defining properties of the convolution
Kilian Hersent, Jean-Christophe Wallet
doaj   +1 more source

Minkowski Weighted Score Functions of Intuitionistic Fuzzy Values

Mathematics, 2020
In multiple attribute decision-making in an intuitionistic fuzzy environment, the decision information is sometimes given by intuitionistic fuzzy soft sets.
Feng Feng, Yujuan Zheng, José Carlos R. Alcantud, Qian Wang   +3 more
doaj   +1 more source

Rigorous reconstruction of gluon propagator in the presence of complex singularities

SciPost Physics Proceedings, 2022
It has been suggested that the Landau-gauge gluon propagator has complex singularities, which invalidates the K\"all\'en-Lehmann spectral representation.
Yui Hayashi, Kei-Ichi Kondo
doaj   +1 more source

Minkowski valuations on convex functions [PDF]

Calculus of Variations and Partial Differential Equations, 2017
A classification of SL$(n)$ contravariant Minkowski valuations on convex functions and a characterization of the projection body operator are established. The associated LYZ measure is characterized. In addition, a new SL$(n)$ covariant Minkowski valuation on convex functions is defined and characterized.
Andrea Colesanti, Monika Ludwig, Fabian Mussnig   +2 more
openaire   +4 more sources

A New Light on Minkowski's ?(x) Function [PDF]

Journal of Number Theory, 1998
The function \(?(x)\) was introduced by H. Minkowski via Farey fractions. Later R. Salem proved, that if \(x=[0;a_1,a_2,\dots]\) is the expansion of \(x\) as a regular continued fraction, then \[ ?(x)= 2^{1-a_1}- 2^{1-a_1-a_2}+ 2^{1-a_1- a_2-a_3} -\dots.
Pelegrí Viader, Jaume Paradís, Lluís Bibiloni   +2 more
openaire   +2 more sources