The class \(\mathcal{S}^{\sharp \flat }(\sigma_0, \sigma_1)\) is a very broad class of \(L\) functions that contains the Selberg class, the class of all automorphic \(L\) functions and the Rankin–Selberg \(L\) functions, as well as products of suitable shifts of those functions. In this paper, we consider generalized Euler-Stieltjes constants \(\gamma_n(F)\) attached to functions \(F(s)\) from the class \(\mathcal{S}^{\sharp \flat }(\sigma_0, \sigma_1)\). These are coefficients in Laurent series expansion of function \(F(s)\) at its pole. We derive an integral representation and an upper bound for these constants. The application of the obtained results in the case of product of suitable shifts of the Riemann zeta function is presented.

The hexacyclic system graph Fn is the graph derived from a linear hexagonal chain Ln with n > 1 hexagons by identifying two pairs of ends of Ln. The M¨obious hexacyclic system graph Mn is the graph derived from a linear hexagonal chain Ln with n > 1 hexagons by identifying two pairs of ends of Ln with a twist. In this paper, we compute, in a closed form, the resolvent energy, the Laplacian and the signless Laplacian resolvent energy, as well as the resolvent Estrada index and the resolvent signless Estrada index of Fn and Mn. All five indices are expressed as a rational function in the number n of hexagons, defined in terms of Chebyshev polynomials of the first and the second kind. Those expressions allow for a fast numerical computation of indices and for deducing sharp bounds on their growth.

The paper is concerned with hexacyclic systems (Fn) and their M¨obius counterparts (Mn). Continuing the studies in MATCH Commun. Math. Comput. Chem. 94 (2025) 477, the characteristic polynomial and the eigenvalues of the Sombor matrix of Fn and Mn, and the respective Sombor energies are determined. Upper and lower bounds for the Sombor energy in terms of the number of hexagons are also obtained.

Big Data analytics and Artificial Intelligence (AI) technologies have become the focus of recent research due to the large amount of data. Dimensionality reduction techniques are recognized as an important step in these analyses. The multidimensional nature of Quality of Experience (QoE) is based on a set of Influence Factors (IFs) whose dimensionality is preferable to be higher due to better QoE prediction. As a consequence, dimensionality issues occur in QoE prediction models. This paper gives an overview of the used dimensionality reduction technique in QoE modeling and proposes modification and use of Active Subspaces Method (ASM) for dimensionality reduction. Proposed modified ASM (mASM) uses variance/standard deviation as a measure of function variability. A straightforward benefit of proposed modification is the possibility of its application in cases when discrete or categorical IFs are included. Application of modified ASM is not restricted to QoE modeling only. Obtained results show that QoE function is mostly flat for small variations of input IFs which is an additional motive to propose a modification of the standard version of ASM. This study proposes several metrics that can be used to compare different dimensionality reduction approaches. We prove that the percentage of function variability described by an appropriate linear combination(s) of input IFs is always greater or equal to the percentage that corresponds to the selection of input IF(s) when the reduction degree is the same. Thus, the proposed method and metrics are useful when optimizing the number of IFs for QoE prediction and a better understanding of IFs space in terms of QoE.