Axioms, Volume 2, Issue 3

In the first part we recall two famous sources of solutions to the Yang-Baxter equation—R-matrices and Yetter-Drinfel0d (=YD) modules—and an interpretation of the former as a particular case of the latter. We show that this result holds true in the m...

It is indeed a fairly common practice for scientific research journals and scientific research periodicals to publish special issues as well as conference proceedings. Quite frequently, these special issues are devoted exclusively to specific topics...

The Yang-Baxter equation first appeared in a paper by the Nobel laureate, C.N. Yang, and in R.J. Baxter’s work. Later, Vladimir Drinfeld, Vaughan F. R. Jones and Edward Witten were awarded Fields Medals for their work related to the Yang-Baxter equat...

It is known that several discrete integrals, including the Choquet and Sugeno integrals, as well as some of their generalizations, are comonotonically modular functions. Based on a recent description of the class of comonotonically modular functions,...

The main aim of this paper is the development of suitable bases that enable the direct series representation of orthogonal polynomial systems on nonuniform lattices (quadratic lattices of a discrete or a q-discrete variable). We present two bases of...

We study the asymptotics in L2 for complexity penalized least squares regression for the discrete approximation of finite-dimensional signals on continuous domains—e.g., images—by piecewise smooth functions. We introduce a fairly general setting, whi...

Biosurveillance, focused on the early detection of disease outbreaks, relies on classical statistical control charts for detecting disease outbreaks. However, such methods are not always suitable in this context. Assumptions of normality, independenc...

In this paper, we outline a method for constructing nonnegative scaling vectors on the interval. Scaling vectors for the interval have been constructed in [1–3]. The approach here is different in that the we start with an existing scaling vector ϕ th...

The properties of the Gabor and Morlet transforms are examined with respect to the Fourier analysis of discretely sampled data. Forward and inverse transform pairs based on a fixed window with uniform sampling of the frequency axis can satisfy numeri...