1. Discounting one selected item or the whole cart? : A theoretical analysis of two mutually exclusive supermarket discount formatsŽiga Velkavrh, 2026, original scientific article Abstract: The article addresses two real-world decision-making problems faced by customers who are offered two mutually exclusive supermarket discount formats: an unconditional per-selected-item discount and a conditional per-purchase discount applicable only when the total purchase amount reaches a specified spending threshold. The analysis provides a normative benchmark for comparing these formats from the customer's perspective and determines what a customer should do, once they have selected their cart, to minimise total payment. When the threshold is reached, the problem reduces to a monetary comparison between applying a higher discount to a most expensive item in the cart and applying a lower discount to the overall purchase. When the threshold is not reached, the problem becomes more complex, as the analysis requires determining whether applying a higher discount to a most expensive item in the original cart results in a lower or higher total payment than adding an additional item to reach the threshold and applying a lower discount to the new total purchase amount. To automate the required calculations and thereby facilitate discount comparisons, we provide a prototype decision aid in the form of R functions, which could serve as a basis for supermarket decision-support tools.
Keywords: customer behaviour, decision theory, normative benchmark, per-purchase discount, per-selected-item discount
Published in RUP: 14.08.2026; Views: 54; Downloads: 2
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2. Clar numbers of leapfrog fullerenesJack E. Graver, Elizabeth J. Hartung, 2025 Abstract: A fullerene is a 3-regular plane graph with only hexagonal and pentagonal faces. The Fries number of a fullerene G, F(G), is the maximum number of benzene rings over all possible Kekulé structures for G. The Clar number of G, C(G), is the maximum number of independent benzene rings possible over all possible Kekulé structures for G. In this paper, we show that for leapfrog fullerenes, any set of faces attaining the Clar number is a subset of faces attaining the Fries number. This property is false for fullerenes in general (as shown in paper from E. J. Hartung in 2014). We then show that if L(G) is the leapfrog of a fullerene G, then the Clar number of L(G) is equal to the vertex independence number of G.
Keywords: chemical graph theory, fullerenes, leapfrog fullerenes, Clar number, Fries number, Kekulé structure, perfect matching
Published in RUP: 27.07.2026; Views: 172; Downloads: 3
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4. Sustaining accommodation SMEs : drivers and pathways of sustainable transition in the Mediterranean tourist accommodation sectorEmil Juvan, Guido Capanna Piscè, Federica Murmura, Giada Pierli, Alessio Travasi, Massimiliano Rumignani, Gian Andrea Paolo Garancini, Manos Ligerakis, Jana Čakardžić, Dino Mujkić, 2026, scientific monograph Keywords: Triple Bottom Line (TBL), Value–Belief–Norm (VBN) theory, environmentally significant behaviour, accommodation sustainability
Published in RUP: 08.04.2026; Views: 589; Downloads: 10
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6. Random walks and the electronic structure of grapheneNino Bašić, Patrick W. Fowler, Barry T. Pickup, Primož Potočnik, 2026, original scientific article Abstract: Results from the mathematical literature on random walks reveal a closed-form analytical expression for the ▫$\pi$▫-energy and bond number of graphene in the simplest tight-binding model and its Hartree-Fock Hubbard extension. Closed-form expressions follow for all ▫$\pi$▫ spectral moments of graphene. Bond numbers of carbon and boron nitride (BN) zigzag nanotubes are found as finite sums, with graphene and hexagonal boron nitride sheets as asymptotes.
Keywords: graph theory, random walks, graphene, bond number, tight-binding model, spectral moments, Hubbard model, zigzag nanotubes, hexagonal boron nitride, gamma function
Published in RUP: 10.03.2026; Views: 644; Downloads: 9
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7. Explaining physical activity and self-rated health through motivation and perceived service quality : a structural equation modelVojko Vučković, Klemen Širok, Marta Bon, 2026, original scientific article Keywords: service quality, exercise motivation, physical activity, self-rated health, self-determination theory, SEM, health promotion
Published in RUP: 21.02.2026; Views: 709; Downloads: 7
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8. Clar and Fries structures for fullerenesPatrick W. Fowler, Wendy Myrvold, Rebecca L. Vandenberg, Elizabeth J. Hartung, Jack E. Graver, 2026, original scientific article Abstract: Fries and Clar numbers are qualitative indicators of stability in conjugated π systems. For a given Kekulé structure, call any hexagon that contains three double bonds benzenoid. The Fries number is the maximum number of benzenoid hexagons, whereas the Clar number is the maximum number of independent benzenoid hexagons, in each case taken over all Kekulé structures. A Kekulé structure that realises the Fries (Clar) number is a Fries (Clar) structure. For benzenoids, it is not known whether every Fries structure is also a Clar structure. For fullerenes C_n, it is known that some Clar structures in large examples correspond to no Fries structure. We show that Fries structures that are not Clar occur early: examples where some Fries structure is not Clar start at C_34, and examples where no Fries structure is Clar start at C_48. Hence, it is unsafe to use fullerene Fries structures as routes to Clar number. However, Fries structures often describe the neutral fullerene better than a Clar structure, e.g. in rationalising bond lengths in the experimental isomer of C_60. Conversely, an extension of Clar sextet theory suggests the notion of anionic Clar number for fullerene anions, where both pentagons and hexagons may support sextets.
Keywords: chemical graph theory, fullerenes, benzenoids, Clar, Fries, Kekule, perfect matching
Published in RUP: 22.12.2025; Views: 693; Downloads: 3
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9. Tight upper bounds for the p-anionic Clar number of fullerenesAaron Slobodin, Wendy Myrvold, Gary MacGillivray, Patrick W. Fowler, 2026, original scientific article Abstract: A fullerene is an all-carbon molecule with a polyhedral structure where each atom is bonded to three other atoms and each face is either a pentagon or a hexagon. Fullerenes correspond to 3-regular planar graphs whose faces have sizes 5 or 6. The p-anionic Clar number C_(p)(G) of a fullerene G is equal to p + h, where h is maximized over all choices of p + h independent faces (exactly p pentagons and h hexagons) the deletion of whose vertices leave a graph with a perfect matching. This definition is motivated by the chemical observation that pentagonal rings can accommodate an extra electron, so that the pentagons of a
fullerene with charge −p, compete with the hexagons to host ‘Clar sextets’ of six electrons, and pentagons will preferentially acquire the p excess electrons of the anion.
Tight upper bounds are established for the p-anionic Clar number of fullerenes for p > 0. The upper bounds are derived via graph theoretic arguments and new results on minimal cyclic-k-edge cutsets in IPR fullerenes (fullerenes that have all pentagons pairwise disjoint). These bounds are shown to be tight by infinite families of fullerenes that achieve them.
Keywords: chemical graph theory, anionic Clar number, fullerenes
Published in RUP: 21.12.2025; Views: 836; Downloads: 2
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10. Unveiling Organizational AI Adoption Patterns in Italian Companies through the Lens of the Diffusion of Innovations TheoryGrazia Garlatti Costa, Francesco Venier, Roberto Pugliese, 2025, original scientific article Abstract: This paper investigates the adoption and integration of artificial intelligence (AI) technologies within a sample of 237 Italian enterprises using the Diffusion of Innovations (DOI) theory as the theoretical framework. It examines the characteristics of companies leading in AI adoption, evaluating their alignment with the innovator and early adopter profiles defined by Everett Rogers in 2003 within the DOI framework. The research emphasizes AI’s significant role in enhancing operational efficiency, fostering innovation, securing competitive advantage, and driving long-term growth. It also identifies challenges such as lack of skills, data management issues, and ethical concerns. Our findings contribute empirical evidence to the academic literature on the DOI theory, addressing the underexplored context of AI in Italy. The study provides a nuanced perspective on AI’s impact on employment and sets a foundation for future research, offering managerial insights for strategically deploying AI.
Keywords: artificial intelligence, diffusion of innovations theory, early adopters, implementation challenges, Italian companies
Published in RUP: 18.12.2025; Views: 706; Downloads: 4
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