An r-regular graph is an r-graph, if every odd set of vertices is connected to its complement by at least r edges. We prove for r ∈{4,5}, every projective planar r-graph with no Petersen-minor is r-edge colorable.
Dimethoxymethane (DMM, or OME1) has recently raised significant attention as the archetypal species of the oxymethylene ethers (OME) family, identified as a potential sustainable alternative to diesel fuels. However, so far limited attention has been paid to the sensitizing and inhibiting effects of nitrogen oxides (NOx) on its oxidation chemistry, which may play an important role for combustion with exhaust gas recirculation (EGR) systems. In this work, DMM oxidation was systematically studied with and without NO addition through a targeted experimental campaign. Four fuel-oxidizer mixtures were analyzed in a laminar flow reactor, across a range of variable equivalence ratios (0.8 <= <= 2), argon dilution levels (93% and 97%) and NO concentrations (0 and 900 ppm). At the same time, a comprehensive kinetic mechanism was set up, including carbon-nitrogen interactions up to the fuel-NO level. It was found that the dilution level significantly affected the DMM/NO interaction. While the onset temperature of the DMM conversion remained unchanged for a fixed dilution, the addition of NO led to a faster completion of the DMM conversion. The kinetic analysis clarified that the earlier reactivity of DMM at lower dilution triggers C-N interaction both at the fuel level, through the NO-alkoxy reaction inhibiting the low-temperature oxidation, and at a C-0-C-1 level, via the enhanced formation of CH3O, promoting an earlier reactivity (as observed for simpler fuels). Conversely, when the reactivity onset shifted to higher temperatures because of the higher dilution, the interaction was much less emphasized at the fuel level, but mostly controlled by CH3O formation and consumption channels.
This paper presents a conceptual and methodological synthesis of incremental machine learning under uncertainty. It connects the foundations of incremental learning with granular computing through interval, probabilistic, and fuzzy-possibilistic representations as canonical forms of information granules. A unified framework is introduced to organize existing approaches according to data representations, model structures, locally valid functions, information fusion mechanisms, and underlying optimization principles. The resulting classifiers, predictors, or controllers account for input-output, parametric, structural, and representational uncertainty. At their core, granular incremental learners balance multiple regularization criteria—including prediction error, interpretability, coverage-specificity equilibrium, structural compactness, stability, and semantic coherence—that guide how granules and local models are created, adapted, merged, and removed over time. Their outputs are combined through aggregation operators that allow cooperation among localized models without fully interconnected architectures. By systematizing the relationships among granular and structure-adaptive learning methods, this work provides a foundation for extending incremental learning toward interpretable, safe, and autonomous systems operating in complex and multimodal environments.
Artificial intelligence promises to transform marketing, but some relational constants endure across technological ages. The current research proposes a three-layer hierarchical framework that prioritizes three time-invariant foundations of cooperative exchange relationships. Specifically, each foundation comprises a universal principle (interdependence, reciprocity, justice), corresponding psychological construct (trust, gratitude, unfairness), and resulting behaviors that permit, propel, and protect cooperative exchange relationships, regardless of technological contexts. The authors trace the evolution of the three foundations and their manifestations across pre-industrial, industrial, and digital ages to demonstrate their consistency. A projection details how these foundations will shape relationship marketing in the future, guiding marketers to focus on constants to establish effective relationship marketing strategies in an evolving AI age. This hierarchical framework counters the paralysis of uncertainty by offering evidence of stability amid technological disruption. It also reorients relationship marketing from commitment toward cooperation as the practical, dynamic engine of value creation in any technological age.
