The prevalence of counterfeit luxury brands is a multifaceted issue with far-reaching consequences, yet the literature lacks theory and evidence on enforcement activism's role in combating the illicit trade in luxury counterfeits. Using PLS-SEM, this research investigates the mediating roles of deterrence to counterfeiting, consumers' attitudes toward counterfeiting, and moral awareness as mechanisms behind the influence of enforcement activism on counterfeit purchase intentions. The model also examines brand passion's direct and indirect effects on counterfeit purchase intentions through the mediation of consumers' attitudes toward counterfeiting. The findings contribute to brand counterfeiting literature and offer guidelines for enhancing enforcement activism's efficacy.
Erdős first introduced the idea of covering systems in 1950. Since then, much of the work in this area has concentrated on identifying covering systems that meet specific conditions on their moduli. Among the central open problems in this field is the well-known odd covering problem. In this paper, we investigate a variant of that problem, where one odd integer is permitted to appear multiple times as a modulus in the covering system, while all remaining moduli are distinct odd integers greater than 1.
This study investigates whether energy price index stimulates share of electricity produced from renewable energy in the G20 and whether governance quality shapes this relationship. Using annual data for 2000–2021, we test two hypotheses: first, that higher energy prices independently promote share of electricity produced from renewable energy, and second, that governance quality strengthens this price–innovation link. The analysis employs the common correlated effects ARDL (CS-ARDL) estimator to capture both short-run dynamics and long-run relationships while accounting for cross-sectional dependence. The dynamic common correlated effects ARDL (DCCE-ARDL) estimator is used as a robustness check. The results show that energy price index has a statistically significant negative effect on share of electricity produced from renewable energy in both the short and long run, challenging the induced innovation hypothesis. However, the interaction between governance quality and energy price index is positive and statistically significant, supporting the view that strong institutions enhance the responsiveness of renewable supply to price signals. These findings suggest that market signals alone are insufficient. Institutional capacity is essential to translate price pressures into long-term investment and production gains. By adopting a supply-side perspective, the study addresses a critical but underexplored dimension of the energy transition in the world’s most influential economies.
A positive integer is Zeckendorf-Niven (respectively, Lucas-Niven) if it is divisible by the number of summands in its Zeckendorf decomposition (respectively, Lucas decomposition). We show that there exist infinitely many Zeckendorf-Niven numbers and Lucas-Niven numbers in every arithmetic progression. Furthermore, we provide bounds on the maximum number of consecutive Zeckendorf-Niven terms in certain arithmetic progressions.
Symplectic geometry plays an increasingly important role in mathematics, physics and applications, and naturally gives rise to interesting matrix families and properties. One of these is the notion of symplectic eigenvalues, whose existence for positive definite matrices is known as Williamson's theorem or decomposition. This notion of symplectic eigenvalues gives rise to inverse problems. We introduce the inverse symplectic eigenvalue problem for positive definite matrices described by a labeled graph and solve it for several families of labeled graphs and all labeled graphs of order four. To solve these problems we develop various tools such as the Strong Symplectic Spectral Property (SSSP) and its consequences such as the Supergraph Theorem, the Bifurcation Theorem, and the Matrix Liberation Lemma for symplectic eigenvalues, graph couplings to describe collections of labelings of a graph that produce the same symplectic eigenvalues, and coupled graph zero forcing. We establish numerous results for symplectic positive definite matrices, including a sharp lower bound on the number of nonzero entries of such a matrix (or equivalently, the number of edges in its graph). This lower bound is a consequence of a lower bound on the sum of number of nonzero entries in an irreducible positive definite matrix and its inverse.
