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.

Purpose: This research examines and contributes to the behavioural lit­erature on voluntary tax compliance. It focuses on the use and potential of machine-learning (ML) methods and models to predict individual tax morale across Europe, and it identifies the factors that influence predic­tive accuracy.Design/Methodology/Approach: Using data from the fifth wave (2017– 2020) of the European Values Survey (EVS), a data-driven, systematic approach employing six ML methods is applied to predict individual tax morale across Europe. The importance of formal, informal and socio-de­mographic factors is assessed, and the study tests whether incorporating the Corruption Perception Index (CPI) improves predictive accuracy.Findings: The results indicate that ML methods and models can enhance understanding and prediction of individual tax morale in Europe. Among the deployed models, artificial neural networks (ANNs) achieved the highest accuracy. Accuracy increased across all ML methods when the CPI was included. Attitudes towards bribery, perceptions of immigrants’ im­pact on the national welfare system, and gender emerged as significant formal, informal and socio-demographic factors.Academic contribution to the field: The study offers a novel application of data-driven ML methods to the prediction of individual tax morale. Given the scarcity of empirical ML research in the social sciences, the find­ings provide valuable insights in a European context and may serve as a basis for further global research.Practical Implications: The conclusions are particularly relevant for gov­ernments and tax administrations seeking to improve tax compliance and revenue collection. In the European context, the results confirm the virtu­ous circle linking effective government performance, high tax morale and voluntary tax compliance—insights that are crucial for decision-makers, regulators, European institutions and tax-policy makers.Originality/Value: The findings confirm that, when ML methods are ap­plied, individual tax morale can be viewed as an outcome of interactions between formal and informal institutions. They also show that predictive accuracy is higher in countries with lower corruption, as indicated by a higher CPI.    

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.

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.

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.