Related papers: Gauss' hidden menagerie: from cyclotomy to superch…
In this note we review the theory of Gaussian functions by exploiting a point of view based on symbolic methods of umbral nature. We introduce quasi-Gaussian functions, which are close to Gaussian distribution but have a longer tail. Their…
The relations between the hidden symmetries of the six-dimensional pseudo-Euclidean space with signature (+++ -- ) and the conserved quantum characteristics of elementary particles is established. The hidden symmetries are brought out by…
We present some properties of measures (q-Gaussian) that orthogonalize the set of q-Hermite polynomials. We also present an algorithm for simulating i.i.d. sequences of random variables having q-Gaussian distribution.
Cyclotomic polynomials play an important role in several areas of mathematics and their study has a very long history, which goes back at least to Gauss (1801). In particular, the properties of their coefficients have been intensively…
In this review, we present some fundamental classical and quantum phenomena in view of time fractional formalism. Time fractional formalism is a very useful tool in describing systems with memory and delay. We hope that this study can…
A classical link in 3-space can be represented by a Gauss paragraph encoding a link diagram in a combinatorial way. A Gauss paragraph may code not a classical link diagram, but a diagram with virtual crossings. We present a criterion and a…
The main purpose of this article is to study higher power mean values of generalized quadratic Gauss sums using estimates for character sums, analytic method and algebraic geometric methods. In this article, we prove two conjectures which…
We summarize main properties of vacuum Kerr-Schild spacetimes in higher dimensions.
The nature of gravitational singularities, long mysterious, has now become clear through a combination of mathematical and numerical analysis. As the singularity is approached, the time derivative terms in the field equations dominate, and…
Based on the notion of time translation, we develop a formalism to deal with the logic of quantum properties at different times. In our formalism it is possible to enlarge the usual notion of context to include composed properties involving…
Recently, several complex network approaches to time series analysis have been developed and applied to study a wide range of model systems as well as real-world data, e.g., geophysical or financial time series. Among these techniques,…
The gravitational time advancement is a natural but a consequence of curve space-time geometry. In the present work the expressions of gravitational time advancement have been obtained for geodesic motions. The situation when the distance…
Gaussian splatting has demonstrated excellent performance for view synthesis and scene reconstruction. The representation achieves photorealistic quality by optimizing the position, scale, color, and opacity of thousands to millions of 2D…
Quantum optical Gaussian states are a type of important robust quantum states which are manipulatable by the existing technologies. So far, most of the important quantum information experiments are done with such states, including bright…
We review the properties of the currently known CV population from an accountants point of view. In particular, it is examined to what extent different selection mechanisms (variability, X-ray emission, colours, spectroscopic properties)…
Supersymmetry has been studied for over three decades by physicists, its superset even longer by mathematicians, and superspace has proven to be very useful both conceptually and in facilitating computations. However, the (1) necessary…
Plots of quadratic residues display some features that are analyzed mathematically.
We review the motivation for Gauge-Mediated Supersymmetry Breaking and discuss some recent advances.
A novel kind of self-referential square matrix is introduced. A certain subset of the matrix entries record the frequencies of occurrence of each distinct number appearing within the entire matrix. Such squares are necessarily elusive. Our…
Many theoretical predictions derived from quantum mechanics have been confirmed experimentally during the last 80 years. However, interpretative aspects have long been subject to debate. Among them, the question of the existence of hidden…